Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [156,2,Mod(155,156)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(156, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("156.155");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 156 = 2^{2} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 156.h (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: | \(1.24566627153\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 43x^{12} + 517x^{8} + 1804x^{4} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 155.8 | ||
Root | \(-1.12073 - 1.12073i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 156.155 |
Dual form | 156.2.h.b.155.6 |
$q$-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 \(\left(\mathbb{Z}/156\mathbb{Z}\right)^\times\).
\(n\) | \(53\) | \(79\) | \(145\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.599676 | + | 1.28078i | −0.424035 | + | 0.905646i | ||||
\(3\) | 1.62493 | − | 0.599676i | 0.938152 | − | 0.346223i | ||||
\(4\) | −1.28078 | − | 1.53610i | −0.640388 | − | 0.768051i | ||||
\(5\) | 2.13578 | 0.955149 | 0.477575 | − | 0.878591i | \(-0.341516\pi\) | ||||
0.477575 | + | 0.878591i | \(0.341516\pi\) | |||||||
\(6\) | −0.206379 | + | 2.44078i | −0.0842539 | + | 0.996444i | ||||
\(7\) | −1.52162 | −0.575120 | −0.287560 | − | 0.957763i | \(-0.592844\pi\) | ||||
−0.287560 | + | 0.957763i | \(0.592844\pi\) | |||||||
\(8\) | 2.73546 | − | 0.719224i | 0.967130 | − | 0.254284i | ||||
\(9\) | 2.28078 | − | 1.94886i | 0.760259 | − | 0.649620i | ||||
\(10\) | −1.28078 | + | 2.73546i | −0.405017 | + | 0.865027i | ||||
\(11\) | 2.00000i | 0.603023i | 0.953463 | + | 0.301511i | \(0.0974911\pi\) | ||||
−0.953463 | + | 0.301511i | \(0.902509\pi\) | |||||||
\(12\) | −3.00233 | − | 1.72800i | −0.866699 | − | 0.498832i | ||||
\(13\) | 1.56155 | − | 3.24985i | 0.433097 | − | 0.901347i | ||||
\(14\) | 0.912482 | − | 1.94886i | 0.243871 | − | 0.520855i | ||||
\(15\) | 3.47049 | − | 1.28078i | 0.896076 | − | 0.330695i | ||||
\(16\) | −0.719224 | + | 3.93481i | −0.179806 | + | 0.983702i | ||||
\(17\) | 6.94097i | 1.68343i | 0.539920 | + | 0.841716i | \(0.318455\pi\) | ||||
−0.539920 | + | 0.841716i | \(0.681545\pi\) | |||||||
\(18\) | 1.12833 | + | 4.08985i | 0.265949 | + | 0.963987i | ||||
\(19\) | −5.41935 | −1.24328 | −0.621642 | − | 0.783302i | \(-0.713534\pi\) | ||||
−0.621642 | + | 0.783302i | \(0.713534\pi\) | |||||||
\(20\) | −2.73546 | − | 3.28078i | −0.611666 | − | 0.733604i | ||||
\(21\) | −2.47253 | + | 0.912482i | −0.539550 | + | 0.199120i | ||||
\(22\) | −2.56155 | − | 1.19935i | −0.546125 | − | 0.255703i | ||||
\(23\) | −5.07482 | −1.05817 | −0.529086 | − | 0.848568i | \(-0.677465\pi\) | ||||
−0.529086 | + | 0.848568i | \(0.677465\pi\) | |||||||
\(24\) | 4.01361 | − | 2.80907i | 0.819276 | − | 0.573400i | ||||
\(25\) | −0.438447 | −0.0876894 | ||||||||
\(26\) | 3.22591 | + | 3.94886i | 0.632653 | + | 0.774435i | ||||
\(27\) | 2.53741 | − | 4.53448i | 0.488325 | − | 0.872662i | ||||
\(28\) | 1.94886 | + | 2.33737i | 0.368300 | + | 0.441722i | ||||
\(29\) | − | 3.04325i | − | 0.565117i | −0.959250 | − | 0.282559i | \(-0.908817\pi\) | ||
0.959250 | − | 0.282559i | \(-0.0911832\pi\) | |||||||
\(30\) | −0.440780 | + | 5.21297i | −0.0804751 | + | 0.951753i | ||||
\(31\) | 5.41935 | 0.973343 | 0.486672 | − | 0.873585i | \(-0.338211\pi\) | ||||
0.486672 | + | 0.873585i | \(0.338211\pi\) | |||||||
\(32\) | −4.60831 | − | 3.28078i | −0.814642 | − | 0.579965i | ||||
\(33\) | 1.19935 | + | 3.24985i | 0.208781 | + | 0.565727i | ||||
\(34\) | −8.88983 | − | 4.16234i | −1.52459 | − | 0.713835i | ||||
\(35\) | −3.24985 | −0.549326 | ||||||||
\(36\) | −5.91482 | − | 1.00745i | −0.985803 | − | 0.167909i | ||||
\(37\) | − | 1.82496i | − | 0.300022i | −0.988684 | − | 0.150011i | \(-0.952069\pi\) | ||
0.988684 | − | 0.150011i | \(-0.0479310\pi\) | |||||||
\(38\) | 3.24985 | − | 6.94097i | 0.527196 | − | 1.12597i | ||||
\(39\) | 0.588549 | − | 6.21720i | 0.0942432 | − | 0.995549i | ||||
\(40\) | 5.84233 | − | 1.53610i | 0.923753 | − | 0.242879i | ||||
\(41\) | −5.73384 | −0.895475 | −0.447737 | − | 0.894165i | \(-0.647770\pi\) | ||||
−0.447737 | + | 0.894165i | \(0.647770\pi\) | |||||||
\(42\) | 0.314031 | − | 3.71395i | 0.0484561 | − | 0.573075i | ||||
\(43\) | − | 3.07221i | − | 0.468507i | −0.972176 | − | 0.234253i | \(-0.924735\pi\) | ||
0.972176 | − | 0.234253i | \(-0.0752646\pi\) | |||||||
\(44\) | 3.07221 | − | 2.56155i | 0.463152 | − | 0.386169i | ||||
\(45\) | 4.87123 | − | 4.16234i | 0.726161 | − | 0.620485i | ||||
\(46\) | 3.04325 | − | 6.49971i | 0.448703 | − | 0.958330i | ||||
\(47\) | − | 5.68466i | − | 0.829193i | −0.910005 | − | 0.414596i | \(-0.863923\pi\) | ||
0.910005 | − | 0.414596i | \(-0.136077\pi\) | |||||||
\(48\) | 1.19093 | + | 6.82508i | 0.171895 | + | 0.985115i | ||||
\(49\) | −4.68466 | −0.669237 | ||||||||
\(50\) | 0.262926 | − | 0.561553i | 0.0371834 | − | 0.0794156i | ||||
\(51\) | 4.16234 | + | 11.2786i | 0.582844 | + | 1.57932i | ||||
\(52\) | −6.99211 | + | 1.76363i | −0.969631 | + | 0.244572i | ||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | 4.28604 | + | 5.96908i | 0.583256 | + | 0.812289i | ||||
\(55\) | 4.27156i | 0.575977i | ||||||||
\(56\) | −4.16234 | + | 1.09439i | −0.556216 | + | 0.146244i | ||||
\(57\) | −8.80604 | + | 3.24985i | −1.16639 | + | 0.430454i | ||||
\(58\) | 3.89772 | + | 1.82496i | 0.511796 | + | 0.239630i | ||||
\(59\) | 11.1231i | 1.44811i | 0.689745 | + | 0.724053i | \(0.257723\pi\) | ||||
−0.689745 | + | 0.724053i | \(0.742277\pi\) | |||||||
\(60\) | −6.41232 | − | 3.69063i | −0.827827 | − | 0.476459i | ||||
\(61\) | −5.12311 | −0.655946 | −0.327973 | − | 0.944687i | \(-0.606366\pi\) | ||||
−0.327973 | + | 0.944687i | \(0.606366\pi\) | |||||||
\(62\) | −3.24985 | + | 6.94097i | −0.412732 | + | 0.881504i | ||||
\(63\) | −3.47049 | + | 2.96543i | −0.437240 | + | 0.373610i | ||||
\(64\) | 6.96543 | − | 3.93481i | 0.870679 | − | 0.491851i | ||||
\(65\) | 3.33513 | − | 6.94097i | 0.413672 | − | 0.860922i | ||||
\(66\) | −4.88156 | − | 0.412758i | −0.600879 | − | 0.0508070i | ||||
\(67\) | 8.46260 | 1.03387 | 0.516935 | − | 0.856024i | \(-0.327073\pi\) | ||||
0.516935 | + | 0.856024i | \(0.327073\pi\) | |||||||
\(68\) | 10.6620 | − | 8.88983i | 1.29296 | − | 1.07805i | ||||
\(69\) | −8.24621 | + | 3.04325i | −0.992727 | + | 0.366364i | ||||
\(70\) | 1.94886 | − | 4.16234i | 0.232933 | − | 0.497494i | ||||
\(71\) | − | 2.31534i | − | 0.274780i | −0.990517 | − | 0.137390i | \(-0.956129\pi\) | ||
0.990517 | − | 0.137390i | \(-0.0438714\pi\) | |||||||
\(72\) | 4.83730 | − | 6.97141i | 0.570081 | − | 0.821589i | ||||
\(73\) | 10.1496i | 1.18793i | 0.804493 | + | 0.593963i | \(0.202437\pi\) | ||||
−0.804493 | + | 0.593963i | \(0.797563\pi\) | |||||||
\(74\) | 2.33737 | + | 1.09439i | 0.271714 | + | 0.127220i | ||||
\(75\) | −0.712445 | + | 0.262926i | −0.0822660 | + | 0.0303601i | ||||
\(76\) | 6.94097 | + | 8.32467i | 0.796184 | + | 0.954906i | ||||
\(77\) | − | 3.04325i | − | 0.346810i | ||||||
\(78\) | 7.60991 | + | 4.48211i | 0.861652 | + | 0.507499i | ||||
\(79\) | 9.06897i | 1.02034i | 0.860074 | + | 0.510169i | \(0.170417\pi\) | ||||
−0.860074 | + | 0.510169i | \(0.829583\pi\) | |||||||
\(80\) | −1.53610 | + | 8.40388i | −0.171742 | + | 0.939583i | ||||
\(81\) | 1.40388 | − | 8.88983i | 0.155987 | − | 0.987759i | ||||
\(82\) | 3.43845 | − | 7.34376i | 0.379713 | − | 0.810983i | ||||
\(83\) | 6.00000i | 0.658586i | 0.944228 | + | 0.329293i | \(0.106810\pi\) | ||||
−0.944228 | + | 0.329293i | \(0.893190\pi\) | |||||||
\(84\) | 4.56842 | + | 2.62937i | 0.498456 | + | 0.286888i | ||||
\(85\) | 14.8244i | 1.60793i | ||||||||
\(86\) | 3.93481 | + | 1.84233i | 0.424301 | + | 0.198663i | ||||
\(87\) | −1.82496 | − | 4.94506i | −0.195657 | − | 0.530166i | ||||
\(88\) | 1.43845 | + | 5.47091i | 0.153339 | + | 0.583201i | ||||
\(89\) | 11.3524 | 1.20335 | 0.601676 | − | 0.798740i | \(-0.294500\pi\) | ||||
0.601676 | + | 0.798740i | \(0.294500\pi\) | |||||||
\(90\) | 2.40986 | + | 8.73502i | 0.254021 | + | 0.920752i | ||||
\(91\) | −2.37610 | + | 4.94506i | −0.249083 | + | 0.518383i | ||||
\(92\) | 6.49971 | + | 7.79544i | 0.677641 | + | 0.812731i | ||||
\(93\) | 8.80604 | − | 3.24985i | 0.913144 | − | 0.336994i | ||||
\(94\) | 7.28078 | + | 3.40896i | 0.750955 | + | 0.351607i | ||||
\(95\) | −11.5745 | −1.18752 | ||||||||
\(96\) | −9.45557 | − | 2.56753i | −0.965055 | − | 0.262047i | ||||
\(97\) | − | 16.6493i | − | 1.69049i | −0.534383 | − | 0.845243i | \(-0.679456\pi\) | ||
0.534383 | − | 0.845243i | \(-0.320544\pi\) | |||||||
\(98\) | 2.80928 | − | 6.00000i | 0.283780 | − | 0.606092i | ||||
\(99\) | 3.89772 | + | 4.56155i | 0.391736 | + | 0.458453i | ||||
\(100\) | 0.561553 | + | 0.673500i | 0.0561553 | + | 0.0673500i | ||||
\(101\) | 6.08650i | 0.605629i | 0.953049 | + | 0.302815i | \(0.0979263\pi\) | ||||
−0.953049 | + | 0.302815i | \(0.902074\pi\) | |||||||
\(102\) | −16.9414 | − | 1.43247i | −1.67745 | − | 0.141836i | ||||
\(103\) | − | 19.4849i | − | 1.91991i | −0.280157 | − | 0.959954i | \(-0.590387\pi\) | ||
0.280157 | − | 0.959954i | \(-0.409613\pi\) | |||||||
\(104\) | 1.93419 | − | 10.0129i | 0.189663 | − | 0.981849i | ||||
\(105\) | −5.28078 | + | 1.94886i | −0.515351 | + | 0.190189i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.1496 | 0.981203 | 0.490601 | − | 0.871384i | \(-0.336777\pi\) | ||||
0.490601 | + | 0.871384i | \(0.336777\pi\) | |||||||
\(108\) | −10.2153 | + | 1.90994i | −0.982967 | + | 0.183784i | ||||
\(109\) | 8.32467i | 0.797359i | 0.917090 | + | 0.398680i | \(0.130531\pi\) | ||||
−0.917090 | + | 0.398680i | \(0.869469\pi\) | |||||||
\(110\) | −5.47091 | − | 2.56155i | −0.521631 | − | 0.244234i | ||||
\(111\) | −1.09439 | − | 2.96543i | −0.103875 | − | 0.281467i | ||||
\(112\) | 1.09439 | − | 5.98730i | 0.103410 | − | 0.565747i | ||||
\(113\) | 10.8387i | 1.01962i | 0.860287 | + | 0.509809i | \(0.170284\pi\) | ||||
−0.860287 | + | 0.509809i | \(0.829716\pi\) | |||||||
\(114\) | 1.11844 | − | 13.2274i | 0.104751 | − | 1.23886i | ||||
\(115\) | −10.8387 | −1.01071 | ||||||||
\(116\) | −4.67474 | + | 3.89772i | −0.434039 | + | 0.361894i | ||||
\(117\) | −2.77196 | − | 10.4554i | −0.256268 | − | 0.966606i | ||||
\(118\) | −14.2462 | − | 6.67026i | −1.31147 | − | 0.614048i | ||||
\(119\) | − | 10.5616i | − | 0.968176i | ||||||
\(120\) | 8.57219 | − | 5.99956i | 0.782531 | − | 0.547683i | ||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | 3.07221 | − | 6.56155i | 0.278144 | − | 0.594055i | ||||
\(123\) | −9.31707 | + | 3.43845i | −0.840092 | + | 0.310034i | ||||
\(124\) | −6.94097 | − | 8.32467i | −0.623318 | − | 0.747578i | ||||
\(125\) | −11.6153 | −1.03891 | ||||||||
\(126\) | −1.71689 | − | 6.22322i | −0.152953 | − | 0.554408i | ||||
\(127\) | − | 6.67026i | − | 0.591890i | −0.955205 | − | 0.295945i | \(-0.904365\pi\) | ||
0.955205 | − | 0.295945i | \(-0.0956346\pi\) | |||||||
\(128\) | 0.862603 | + | 11.2808i | 0.0762440 | + | 0.997089i | ||||
\(129\) | −1.84233 | − | 4.99211i | −0.162208 | − | 0.439531i | ||||
\(130\) | 6.88983 | + | 8.43390i | 0.604278 | + | 0.739702i | ||||
\(131\) | −1.82496 | −0.159448 | −0.0797240 | − | 0.996817i | \(-0.525404\pi\) | ||||
−0.0797240 | + | 0.996817i | \(0.525404\pi\) | |||||||
\(132\) | 3.45601 | − | 6.00467i | 0.300807 | − | 0.522639i | ||||
\(133\) | 8.24621 | 0.715037 | ||||||||
\(134\) | −5.07482 | + | 10.8387i | −0.438398 | + | 0.936320i | ||||
\(135\) | 5.41935 | − | 9.68466i | 0.466423 | − | 0.833523i | ||||
\(136\) | 4.99211 | + | 18.9867i | 0.428070 | + | 1.62810i | ||||
\(137\) | −8.95369 | −0.764965 | −0.382483 | − | 0.923963i | \(-0.624931\pi\) | ||||
−0.382483 | + | 0.923963i | \(0.624931\pi\) | |||||||
\(138\) | 1.04734 | − | 12.3865i | 0.0891552 | − | 1.05441i | ||||
\(139\) | 6.81791i | 0.578288i | 0.957286 | + | 0.289144i | \(0.0933706\pi\) | ||||
−0.957286 | + | 0.289144i | \(0.906629\pi\) | |||||||
\(140\) | 4.16234 | + | 4.99211i | 0.351782 | + | 0.421910i | ||||
\(141\) | −3.40896 | − | 9.23716i | −0.287086 | − | 0.777909i | ||||
\(142\) | 2.96543 | + | 1.38846i | 0.248854 | + | 0.116517i | ||||
\(143\) | 6.49971 | + | 3.12311i | 0.543533 | + | 0.261167i | ||||
\(144\) | 6.02801 | + | 10.3761i | 0.502334 | + | 0.864674i | ||||
\(145\) | − | 6.49971i | − | 0.539771i | ||||||
\(146\) | −12.9994 | − | 6.08650i | −1.07584 | − | 0.503722i | ||||
\(147\) | −7.61223 | + | 2.80928i | −0.627846 | + | 0.231705i | ||||
\(148\) | −2.80333 | + | 2.33737i | −0.230433 | + | 0.192131i | ||||
\(149\) | 0.410574 | 0.0336355 | 0.0168177 | − | 0.999859i | \(-0.494646\pi\) | ||||
0.0168177 | + | 0.999859i | \(0.494646\pi\) | |||||||
\(150\) | 0.0904863 | − | 1.07015i | 0.00738818 | − | 0.0873776i | ||||
\(151\) | 17.1125 | 1.39260 | 0.696298 | − | 0.717753i | \(-0.254829\pi\) | ||||
0.696298 | + | 0.717753i | \(0.254829\pi\) | |||||||
\(152\) | −14.8244 | + | 3.89772i | −1.20242 | + | 0.316147i | ||||
\(153\) | 13.5270 | + | 15.8308i | 1.09359 | + | 1.27984i | ||||
\(154\) | 3.89772 | + | 1.82496i | 0.314087 | + | 0.147060i | ||||
\(155\) | 11.5745 | 0.929688 | ||||||||
\(156\) | −10.3041 | + | 7.05878i | −0.824985 | + | 0.565154i | ||||
\(157\) | 6.24621 | 0.498502 | 0.249251 | − | 0.968439i | \(-0.419816\pi\) | ||||
0.249251 | + | 0.968439i | \(0.419816\pi\) | |||||||
\(158\) | −11.6153 | − | 5.43845i | −0.924065 | − | 0.432660i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −9.84233 | − | 7.00701i | −0.778104 | − | 0.553953i | ||||
\(161\) | 7.72197 | 0.608576 | ||||||||
\(162\) | 10.5440 | + | 7.12908i | 0.828416 | + | 0.560114i | ||||
\(163\) | 13.2148 | 1.03506 | 0.517531 | − | 0.855664i | \(-0.326851\pi\) | ||||
0.517531 | + | 0.855664i | \(0.326851\pi\) | |||||||
\(164\) | 7.34376 | + | 8.80776i | 0.573452 | + | 0.687771i | ||||
\(165\) | 2.56155 | + | 6.94097i | 0.199417 | + | 0.540354i | ||||
\(166\) | −7.68466 | − | 3.59806i | −0.596445 | − | 0.279263i | ||||
\(167\) | − | 17.3693i | − | 1.34408i | −0.740516 | − | 0.672039i | \(-0.765419\pi\) | ||
0.740516 | − | 0.672039i | \(-0.234581\pi\) | |||||||
\(168\) | −6.10721 | + | 4.27436i | −0.471182 | + | 0.329774i | ||||
\(169\) | −8.12311 | − | 10.1496i | −0.624854 | − | 0.780741i | ||||
\(170\) | −18.9867 | − | 8.88983i | −1.45621 | − | 0.681819i | ||||
\(171\) | −12.3603 | + | 10.5616i | −0.945217 | + | 0.807662i | ||||
\(172\) | −4.71922 | + | 3.93481i | −0.359837 | + | 0.300026i | ||||
\(173\) | − | 7.79544i | − | 0.592677i | −0.955083 | − | 0.296338i | \(-0.904234\pi\) | ||
0.955083 | − | 0.296338i | \(-0.0957656\pi\) | |||||||
\(174\) | 7.42790 | + | 0.628063i | 0.563108 | + | 0.0476133i | ||||
\(175\) | 0.667152 | 0.0504320 | ||||||||
\(176\) | −7.86962 | − | 1.43845i | −0.593195 | − | 0.108427i | ||||
\(177\) | 6.67026 | + | 18.0742i | 0.501368 | + | 1.35854i | ||||
\(178\) | −6.80776 | + | 14.5399i | −0.510263 | + | 1.08981i | ||||
\(179\) | 1.82496 | 0.136404 | 0.0682021 | − | 0.997672i | \(-0.478274\pi\) | ||||
0.0682021 | + | 0.997672i | \(0.478274\pi\) | |||||||
\(180\) | −12.6327 | − | 2.15169i | −0.941589 | − | 0.160378i | ||||
\(181\) | 19.3693 | 1.43971 | 0.719855 | − | 0.694124i | \(-0.244208\pi\) | ||||
0.719855 | + | 0.694124i | \(0.244208\pi\) | |||||||
\(182\) | −4.90862 | − | 6.00868i | −0.363851 | − | 0.445393i | ||||
\(183\) | −8.32467 | + | 3.07221i | −0.615378 | + | 0.227104i | ||||
\(184\) | −13.8819 | + | 3.64993i | −1.02339 | + | 0.269076i | ||||
\(185\) | − | 3.89772i | − | 0.286566i | ||||||
\(186\) | −1.11844 | + | 13.2274i | −0.0820080 | + | 0.969882i | ||||
\(187\) | −13.8819 | −1.01515 | ||||||||
\(188\) | −8.73222 | + | 7.28078i | −0.636863 | + | 0.531005i | ||||
\(189\) | −3.86098 | + | 6.89978i | −0.280845 | + | 0.501885i | ||||
\(190\) | 6.94097 | − | 14.8244i | 0.503551 | − | 1.07547i | ||||
\(191\) | 11.5745 | 0.837503 | 0.418752 | − | 0.908101i | \(-0.362468\pi\) | ||||
0.418752 | + | 0.908101i | \(0.362468\pi\) | |||||||
\(192\) | 8.95871 | − | 10.5708i | 0.646539 | − | 0.762881i | ||||
\(193\) | − | 19.4991i | − | 1.40358i | −0.712385 | − | 0.701789i | \(-0.752385\pi\) | ||
0.712385 | − | 0.701789i | \(-0.247615\pi\) | |||||||
\(194\) | 21.3241 | + | 9.98422i | 1.53098 | + | 0.716825i | ||||
\(195\) | 1.25701 | − | 13.2786i | 0.0900163 | − | 0.950898i | ||||
\(196\) | 6.00000 | + | 7.19612i | 0.428571 | + | 0.514008i | ||||
\(197\) | −8.28019 | −0.589939 | −0.294970 | − | 0.955507i | \(-0.595310\pi\) | ||||
−0.294970 | + | 0.955507i | \(0.595310\pi\) | |||||||
\(198\) | −8.17970 | + | 2.25665i | −0.581306 | + | 0.160373i | ||||
\(199\) | − | 5.61856i | − | 0.398289i | −0.979970 | − | 0.199145i | \(-0.936184\pi\) | ||
0.979970 | − | 0.199145i | \(-0.0638163\pi\) | |||||||
\(200\) | −1.19935 | + | 0.315342i | −0.0848071 | + | 0.0222980i | ||||
\(201\) | 13.7511 | − | 5.07482i | 0.969928 | − | 0.357950i | ||||
\(202\) | −7.79544 | − | 3.64993i | −0.548486 | − | 0.256808i | ||||
\(203\) | 4.63068i | 0.325010i | ||||||||
\(204\) | 11.9940 | − | 20.8391i | 0.839750 | − | 1.45903i | ||||
\(205\) | −12.2462 | −0.855312 | ||||||||
\(206\) | 24.9559 | + | 11.6847i | 1.73876 | + | 0.814109i | ||||
\(207\) | −11.5745 | + | 9.89012i | −0.804485 | + | 0.687411i | ||||
\(208\) | 11.6644 | + | 8.48178i | 0.808784 | + | 0.588106i | ||||
\(209\) | − | 10.8387i | − | 0.749728i | ||||||
\(210\) | 0.670702 | − | 7.93218i | 0.0462828 | − | 0.547372i | ||||
\(211\) | − | 1.19935i | − | 0.0825669i | −0.999147 | − | 0.0412834i | \(-0.986855\pi\) | ||
0.999147 | − | 0.0412834i | \(-0.0131447\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.38846 | − | 3.76226i | −0.0951354 | − | 0.257786i | ||||
\(214\) | −6.08650 | + | 12.9994i | −0.416064 | + | 0.888622i | ||||
\(215\) | − | 6.56155i | − | 0.447494i | ||||||
\(216\) | 3.67966 | − | 14.2288i | 0.250369 | − | 0.968150i | ||||
\(217\) | −8.24621 | −0.559789 | ||||||||
\(218\) | −10.6620 | − | 4.99211i | −0.722125 | − | 0.338108i | ||||
\(219\) | 6.08650 | + | 16.4924i | 0.411287 | + | 1.11445i | ||||
\(220\) | 6.56155 | − | 5.47091i | 0.442380 | − | 0.368849i | ||||
\(221\) | 22.5571 | + | 10.8387i | 1.51736 | + | 0.729089i | ||||
\(222\) | 4.45434 | + | 0.376635i | 0.298956 | + | 0.0252781i | ||||
\(223\) | −29.2855 | −1.96110 | −0.980551 | − | 0.196263i | \(-0.937120\pi\) | ||||
−0.980551 | + | 0.196263i | \(0.937120\pi\) | |||||||
\(224\) | 7.01212 | + | 4.99211i | 0.468517 | + | 0.333549i | ||||
\(225\) | −1.00000 | + | 0.854473i | −0.0666667 | + | 0.0569648i | ||||
\(226\) | −13.8819 | − | 6.49971i | −0.923413 | − | 0.432354i | ||||
\(227\) | − | 7.75379i | − | 0.514637i | −0.966327 | − | 0.257319i | \(-0.917161\pi\) | ||
0.966327 | − | 0.257319i | \(-0.0828390\pi\) | |||||||
\(228\) | 16.2707 | + | 9.36465i | 1.07755 | + | 0.620189i | ||||
\(229\) | 27.8238i | 1.83865i | 0.393501 | + | 0.919324i | \(0.371264\pi\) | ||||
−0.393501 | + | 0.919324i | \(0.628736\pi\) | |||||||
\(230\) | 6.49971 | − | 13.8819i | 0.428578 | − | 0.915348i | ||||
\(231\) | −1.82496 | − | 4.94506i | −0.120074 | − | 0.325361i | ||||
\(232\) | −2.18878 | − | 8.32467i | −0.143700 | − | 0.546542i | ||||
\(233\) | − | 11.6932i | − | 0.766045i | −0.923739 | − | 0.383022i | \(-0.874883\pi\) | ||
0.923739 | − | 0.383022i | \(-0.125117\pi\) | |||||||
\(234\) | 15.0534 | + | 2.71962i | 0.984069 | + | 0.177787i | ||||
\(235\) | − | 12.1412i | − | 0.792003i | ||||||
\(236\) | 17.0862 | − | 14.2462i | 1.11222 | − | 0.927349i | ||||
\(237\) | 5.43845 | + | 14.7364i | 0.353265 | + | 0.957233i | ||||
\(238\) | 13.5270 | + | 6.33351i | 0.876824 | + | 0.410541i | ||||
\(239\) | 19.9309i | 1.28922i | 0.764511 | + | 0.644610i | \(0.222980\pi\) | ||||
−0.764511 | + | 0.644610i | \(0.777020\pi\) | |||||||
\(240\) | 2.54355 | + | 14.5769i | 0.164186 | + | 0.940932i | ||||
\(241\) | 3.64993i | 0.235113i | 0.993066 | + | 0.117556i | \(0.0375061\pi\) | ||||
−0.993066 | + | 0.117556i | \(0.962494\pi\) | |||||||
\(242\) | −4.19773 | + | 8.96543i | −0.269841 | + | 0.576320i | ||||
\(243\) | −3.04982 | − | 15.2872i | −0.195646 | − | 0.980675i | ||||
\(244\) | 6.56155 | + | 7.86962i | 0.420060 | + | 0.503801i | ||||
\(245\) | −10.0054 | −0.639221 | ||||||||
\(246\) | 1.18334 | − | 13.9950i | 0.0754473 | − | 0.892291i | ||||
\(247\) | −8.46260 | + | 17.6121i | −0.538462 | + | 1.12063i | ||||
\(248\) | 14.8244 | − | 3.89772i | 0.941349 | − | 0.247506i | ||||
\(249\) | 3.59806 | + | 9.74956i | 0.228018 | + | 0.617853i | ||||
\(250\) | 6.96543 | − | 14.8766i | 0.440533 | − | 0.940881i | ||||
\(251\) | 18.0742 | 1.14084 | 0.570418 | − | 0.821355i | \(-0.306781\pi\) | ||||
0.570418 | + | 0.821355i | \(0.306781\pi\) | |||||||
\(252\) | 9.00013 | + | 1.53296i | 0.566955 | + | 0.0965676i | ||||
\(253\) | − | 10.1496i | − | 0.638102i | ||||||
\(254\) | 8.54312 | + | 4.00000i | 0.536043 | + | 0.250982i | ||||
\(255\) | 8.88983 | + | 24.0885i | 0.556703 | + | 1.50848i | ||||
\(256\) | −14.9654 | − | 5.66001i | −0.935340 | − | 0.353751i | ||||
\(257\) | − | 2.18878i | − | 0.136532i | −0.997667 | − | 0.0682661i | \(-0.978253\pi\) | ||
0.997667 | − | 0.0682661i | \(-0.0217467\pi\) | |||||||
\(258\) | 7.49858 | + | 0.634039i | 0.466841 | + | 0.0394735i | ||||
\(259\) | 2.77691i | 0.172549i | ||||||||
\(260\) | −14.9336 | + | 3.76673i | −0.926143 | + | 0.233602i | ||||
\(261\) | −5.93087 | − | 6.94097i | −0.367112 | − | 0.429635i | ||||
\(262\) | 1.09439 | − | 2.33737i | 0.0676115 | − | 0.144403i | ||||
\(263\) | −3.64993 | −0.225064 | −0.112532 | − | 0.993648i | \(-0.535896\pi\) | ||||
−0.112532 | + | 0.993648i | \(0.535896\pi\) | |||||||
\(264\) | 5.61815 | + | 8.02723i | 0.345773 | + | 0.494042i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −4.94506 | + | 10.5616i | −0.303201 | + | 0.647570i | ||||
\(267\) | 18.4468 | − | 6.80776i | 1.12893 | − | 0.416628i | ||||
\(268\) | −10.8387 | − | 12.9994i | −0.662079 | − | 0.794066i | ||||
\(269\) | − | 18.6341i | − | 1.13614i | −0.822979 | − | 0.568072i | \(-0.807690\pi\) | ||
0.822979 | − | 0.568072i | \(-0.192310\pi\) | |||||||
\(270\) | 9.15403 | + | 12.7486i | 0.557096 | + | 0.775857i | ||||
\(271\) | 7.60812 | 0.462161 | 0.231080 | − | 0.972935i | \(-0.425774\pi\) | ||||
0.231080 | + | 0.972935i | \(0.425774\pi\) | |||||||
\(272\) | −27.3114 | − | 4.99211i | −1.65600 | − | 0.302691i | ||||
\(273\) | −0.895550 | + | 9.46025i | −0.0542012 | + | 0.572560i | ||||
\(274\) | 5.36932 | − | 11.4677i | 0.324372 | − | 0.692788i | ||||
\(275\) | − | 0.876894i | − | 0.0528787i | ||||||
\(276\) | 15.2363 | + | 8.76931i | 0.917117 | + | 0.527850i | ||||
\(277\) | −3.75379 | −0.225543 | −0.112772 | − | 0.993621i | \(-0.535973\pi\) | ||||
−0.112772 | + | 0.993621i | \(0.535973\pi\) | |||||||
\(278\) | −8.73222 | − | 4.08854i | −0.523724 | − | 0.245214i | ||||
\(279\) | 12.3603 | − | 10.5616i | 0.739993 | − | 0.632304i | ||||
\(280\) | −8.88983 | + | 2.33737i | −0.531269 | + | 0.139685i | ||||
\(281\) | −17.2015 | −1.02616 | −0.513078 | − | 0.858342i | \(-0.671495\pi\) | ||||
−0.513078 | + | 0.858342i | \(0.671495\pi\) | |||||||
\(282\) | 13.8750 | + | 1.17319i | 0.826244 | + | 0.0698627i | ||||
\(283\) | 16.5604i | 0.984412i | 0.870479 | + | 0.492206i | \(0.163809\pi\) | ||||
−0.870479 | + | 0.492206i | \(0.836191\pi\) | |||||||
\(284\) | −3.55660 | + | 2.96543i | −0.211046 | + | 0.175966i | ||||
\(285\) | −18.8078 | + | 6.94097i | −1.11408 | + | 0.411148i | ||||
\(286\) | −7.89772 | + | 6.45182i | −0.467002 | + | 0.381504i | ||||
\(287\) | 8.72475 | 0.515006 | ||||||||
\(288\) | −16.9043 | + | 1.49823i | −0.996095 | + | 0.0882843i | ||||
\(289\) | −31.1771 | −1.83395 | ||||||||
\(290\) | 8.32467 | + | 3.89772i | 0.488842 | + | 0.228882i | ||||
\(291\) | −9.98422 | − | 27.0540i | −0.585285 | − | 1.58593i | ||||
\(292\) | 15.5909 | − | 12.9994i | 0.912388 | − | 0.760733i | ||||
\(293\) | 2.66163 | 0.155494 | 0.0777471 | − | 0.996973i | \(-0.475227\pi\) | ||||
0.0777471 | + | 0.996973i | \(0.475227\pi\) | |||||||
\(294\) | 0.966815 | − | 11.4342i | 0.0563858 | − | 0.666857i | ||||
\(295\) | 23.7565i | 1.38316i | ||||||||
\(296\) | −1.31256 | − | 4.99211i | −0.0762909 | − | 0.290161i | ||||
\(297\) | 9.06897 | + | 5.07482i | 0.526235 | + | 0.294471i | ||||
\(298\) | −0.246211 | + | 0.525853i | −0.0142626 | + | 0.0304618i | ||||
\(299\) | −7.92460 | + | 16.4924i | −0.458291 | + | 0.953781i | ||||
\(300\) | 1.31636 | + | 0.757638i | 0.0760003 | + | 0.0437423i | ||||
\(301\) | 4.67474i | 0.269448i | ||||||||
\(302\) | −10.2620 | + | 21.9173i | −0.590510 | + | 1.26120i | ||||
\(303\) | 3.64993 | + | 9.89012i | 0.209683 | + | 0.568172i | ||||
\(304\) | 3.89772 | − | 21.3241i | 0.223550 | − | 1.22302i | ||||
\(305\) | −10.9418 | −0.626527 | ||||||||
\(306\) | −28.3875 | + | 7.83169i | −1.62281 | + | 0.447708i | ||||
\(307\) | 2.37610 | 0.135611 | 0.0678055 | − | 0.997699i | \(-0.478400\pi\) | ||||
0.0678055 | + | 0.997699i | \(0.478400\pi\) | |||||||
\(308\) | −4.67474 | + | 3.89772i | −0.266368 | + | 0.222093i | ||||
\(309\) | −11.6847 | − | 31.6616i | −0.664717 | − | 1.80117i | ||||
\(310\) | −6.94097 | + | 14.8244i | −0.394221 | + | 0.841968i | ||||
\(311\) | −24.5739 | −1.39346 | −0.696730 | − | 0.717333i | \(-0.745363\pi\) | ||||
−0.696730 | + | 0.717333i | \(0.745363\pi\) | |||||||
\(312\) | −2.86161 | − | 17.4302i | −0.162007 | − | 0.986790i | ||||
\(313\) | 7.43845 | 0.420446 | 0.210223 | − | 0.977653i | \(-0.432581\pi\) | ||||
0.210223 | + | 0.977653i | \(0.432581\pi\) | |||||||
\(314\) | −3.74571 | + | 8.00000i | −0.211382 | + | 0.451466i | ||||
\(315\) | −7.41219 | + | 6.33351i | −0.417630 | + | 0.356853i | ||||
\(316\) | 13.9309 | − | 11.6153i | 0.783673 | − | 0.653413i | ||||
\(317\) | −0.410574 | −0.0230601 | −0.0115301 | − | 0.999934i | \(-0.503670\pi\) | ||||
−0.0115301 | + | 0.999934i | \(0.503670\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.08650 | 0.340778 | ||||||||
\(320\) | 14.8766 | − | 8.40388i | 0.831629 | − | 0.469791i | ||||
\(321\) | 16.4924 | − | 6.08650i | 0.920517 | − | 0.339715i | ||||
\(322\) | −4.63068 | + | 9.89012i | −0.258058 | + | 0.551155i | ||||
\(323\) | − | 37.6155i | − | 2.09298i | ||||||
\(324\) | −15.4538 | + | 9.22938i | −0.858542 | + | 0.512743i | ||||
\(325\) | −0.684658 | + | 1.42489i | −0.0379780 | + | 0.0790386i | ||||
\(326\) | −7.92460 | + | 16.9252i | −0.438903 | + | 0.937400i | ||||
\(327\) | 4.99211 | + | 13.5270i | 0.276064 | + | 0.748044i | ||||
\(328\) | −15.6847 | + | 4.12391i | −0.866040 | + | 0.227705i | ||||
\(329\) | 8.64992i | 0.476885i | ||||||||
\(330\) | −10.4259 | − | 0.881560i | −0.573929 | − | 0.0485283i | ||||
\(331\) | −5.41935 | −0.297874 | −0.148937 | − | 0.988847i | \(-0.547585\pi\) | ||||
−0.148937 | + | 0.988847i | \(0.547585\pi\) | |||||||
\(332\) | 9.21662 | − | 7.68466i | 0.505828 | − | 0.421750i | ||||
\(333\) | −3.55660 | − | 4.16234i | −0.194901 | − | 0.228095i | ||||
\(334\) | 22.2462 | + | 10.4160i | 1.21726 | + | 0.569936i | ||||
\(335\) | 18.0742 | 0.987501 | ||||||||
\(336\) | −1.81214 | − | 10.3852i | −0.0988605 | − | 0.566560i | ||||
\(337\) | −9.68466 | −0.527557 | −0.263778 | − | 0.964583i | \(-0.584969\pi\) | ||||
−0.263778 | + | 0.964583i | \(0.584969\pi\) | |||||||
\(338\) | 17.8707 | − | 4.31738i | 0.972035 | − | 0.234835i | ||||
\(339\) | 6.49971 | + | 17.6121i | 0.353016 | + | 0.956557i | ||||
\(340\) | 22.7718 | − | 18.9867i | 1.23497 | − | 1.02970i | ||||
\(341\) | 10.8387i | 0.586948i | ||||||||
\(342\) | −6.11480 | − | 22.1643i | −0.330650 | − | 1.19851i | ||||
\(343\) | 17.7797 | 0.960012 | ||||||||
\(344\) | −2.20960 | − | 8.40388i | −0.119134 | − | 0.453107i | ||||
\(345\) | −17.6121 | + | 6.49971i | −0.948203 | + | 0.349933i | ||||
\(346\) | 9.98422 | + | 4.67474i | 0.536755 | + | 0.251316i | ||||
\(347\) | −19.8992 | −1.06825 | −0.534123 | − | 0.845407i | \(-0.679358\pi\) | ||||
−0.534123 | + | 0.845407i | \(0.679358\pi\) | |||||||
\(348\) | −5.25875 | + | 9.13685i | −0.281898 | + | 0.489786i | ||||
\(349\) | − | 1.82496i | − | 0.0976881i | −0.998806 | − | 0.0488441i | \(-0.984446\pi\) | ||
0.998806 | − | 0.0488441i | \(-0.0155537\pi\) | |||||||
\(350\) | −0.400075 | + | 0.854473i | −0.0213849 | + | 0.0456735i | ||||
\(351\) | −10.7741 | − | 15.3270i | −0.575080 | − | 0.818097i | ||||
\(352\) | 6.56155 | − | 9.21662i | 0.349732 | − | 0.491247i | ||||
\(353\) | 26.5658 | 1.41395 | 0.706977 | − | 0.707237i | \(-0.250058\pi\) | ||||
0.706977 | + | 0.707237i | \(0.250058\pi\) | |||||||
\(354\) | −27.1491 | − | 2.29558i | −1.44296 | − | 0.122009i | ||||
\(355\) | − | 4.94506i | − | 0.262456i | ||||||
\(356\) | −14.5399 | − | 17.4384i | −0.770612 | − | 0.924236i | ||||
\(357\) | −6.33351 | − | 17.1618i | −0.335205 | − | 0.908296i | ||||
\(358\) | −1.09439 | + | 2.33737i | −0.0578402 | + | 0.123534i | ||||
\(359\) | − | 11.1231i | − | 0.587055i | −0.955951 | − | 0.293528i | \(-0.905171\pi\) | ||
0.955951 | − | 0.293528i | \(-0.0948292\pi\) | |||||||
\(360\) | 10.3314 | − | 14.8894i | 0.544512 | − | 0.784740i | ||||
\(361\) | 10.3693 | 0.545754 | ||||||||
\(362\) | −11.6153 | + | 24.8078i | −0.610488 | + | 1.30387i | ||||
\(363\) | 11.3745 | − | 4.19773i | 0.597006 | − | 0.220324i | ||||
\(364\) | 10.6394 | − | 2.68358i | 0.557654 | − | 0.140658i | ||||
\(365\) | 21.6774i | 1.13465i | ||||||||
\(366\) | 1.05730 | − | 12.5044i | 0.0552661 | − | 0.653614i | ||||
\(367\) | − | 21.8836i | − | 1.14232i | −0.820840 | − | 0.571158i | \(-0.806494\pi\) | ||
0.820840 | − | 0.571158i | \(-0.193506\pi\) | |||||||
\(368\) | 3.64993 | − | 19.9684i | 0.190266 | − | 1.04093i | ||||
\(369\) | −13.0776 | + | 11.1745i | −0.680793 | + | 0.581719i | ||||
\(370\) | 4.99211 | + | 2.33737i | 0.259527 | + | 0.121514i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −16.2707 | − | 9.36465i | −0.843596 | − | 0.485535i | ||||
\(373\) | −0.876894 | −0.0454039 | −0.0227019 | − | 0.999742i | \(-0.507227\pi\) | ||||
−0.0227019 | + | 0.999742i | \(0.507227\pi\) | |||||||
\(374\) | 8.32467 | − | 17.7797i | 0.430459 | − | 0.919365i | ||||
\(375\) | −18.8741 | + | 6.96543i | −0.974652 | + | 0.359694i | ||||
\(376\) | −4.08854 | − | 15.5501i | −0.210850 | − | 0.801937i | ||||
\(377\) | −9.89012 | − | 4.75219i | −0.509367 | − | 0.244750i | ||||
\(378\) | −6.52174 | − | 9.08270i | −0.335442 | − | 0.467163i | ||||
\(379\) | 8.46260 | 0.434694 | 0.217347 | − | 0.976094i | \(-0.430260\pi\) | ||||
0.217347 | + | 0.976094i | \(0.430260\pi\) | |||||||
\(380\) | 14.8244 | + | 17.7797i | 0.760475 | + | 0.912078i | ||||
\(381\) | −4.00000 | − | 10.8387i | −0.204926 | − | 0.555283i | ||||
\(382\) | −6.94097 | + | 14.8244i | −0.355131 | + | 0.758481i | ||||
\(383\) | 19.4384i | 0.993258i | 0.867963 | + | 0.496629i | \(0.165429\pi\) | ||||
−0.867963 | + | 0.496629i | \(0.834571\pi\) | |||||||
\(384\) | 8.16648 | + | 17.8132i | 0.416744 | + | 0.909024i | ||||
\(385\) | − | 6.49971i | − | 0.331256i | ||||||
\(386\) | 24.9740 | + | 11.6932i | 1.27114 | + | 0.595166i | ||||
\(387\) | −5.98730 | − | 7.00701i | −0.304352 | − | 0.356187i | ||||
\(388\) | −25.5751 | + | 21.3241i | −1.29838 | + | 1.08257i | ||||
\(389\) | 32.5161i | 1.64863i | 0.566131 | + | 0.824315i | \(0.308440\pi\) | ||||
−0.566131 | + | 0.824315i | \(0.691560\pi\) | |||||||
\(390\) | 16.2531 | + | 9.57280i | 0.823007 | + | 0.484737i | ||||
\(391\) | − | 35.2242i | − | 1.78136i | ||||||
\(392\) | −12.8147 | + | 3.36932i | −0.647239 | + | 0.170176i | ||||
\(393\) | −2.96543 | + | 1.09439i | −0.149586 | + | 0.0552046i | ||||
\(394\) | 4.96543 | − | 10.6051i | 0.250155 | − | 0.534276i | ||||
\(395\) | 19.3693i | 0.974576i | ||||||||
\(396\) | 2.01490 | − | 11.8296i | 0.101253 | − | 0.594461i | ||||
\(397\) | 3.64993i | 0.183185i | 0.995797 | + | 0.0915924i | \(0.0291957\pi\) | ||||
−0.995797 | + | 0.0915924i | \(0.970804\pi\) | |||||||
\(398\) | 7.19612 | + | 3.36932i | 0.360709 | + | 0.168889i | ||||
\(399\) | 13.3995 | − | 4.94506i | 0.670814 | − | 0.247563i | ||||
\(400\) | 0.315342 | − | 1.72521i | 0.0157671 | − | 0.0862603i | ||||
\(401\) | −15.8545 | −0.791737 | −0.395868 | − | 0.918307i | \(-0.629556\pi\) | ||||
−0.395868 | + | 0.918307i | \(0.629556\pi\) | |||||||
\(402\) | −1.74650 | + | 20.6553i | −0.0871076 | + | 1.03019i | ||||
\(403\) | 8.46260 | − | 17.6121i | 0.421552 | − | 0.877321i | ||||
\(404\) | 9.34949 | − | 7.79544i | 0.465154 | − | 0.387838i | ||||
\(405\) | 2.99838 | − | 18.9867i | 0.148991 | − | 0.943458i | ||||
\(406\) | −5.93087 | − | 2.77691i | −0.294344 | − | 0.137816i | ||||
\(407\) | 3.64993 | 0.180920 | ||||||||
\(408\) | 19.4977 | + | 27.8584i | 0.965280 | + | 1.37920i | ||||
\(409\) | − | 2.84978i | − | 0.140912i | −0.997515 | − | 0.0704562i | \(-0.977554\pi\) | ||
0.997515 | − | 0.0704562i | \(-0.0224455\pi\) | |||||||
\(410\) | 7.34376 | − | 15.6847i | 0.362683 | − | 0.774610i | ||||
\(411\) | −14.5491 | + | 5.36932i | −0.717654 | + | 0.264849i | ||||
\(412\) | −29.9309 | + | 24.9559i | −1.47459 | + | 1.22949i | ||||
\(413\) | − | 16.9252i | − | 0.832834i | ||||||
\(414\) | −5.72606 | − | 20.7553i | −0.281420 | − | 1.02006i | ||||
\(415\) | 12.8147i | 0.629048i | ||||||||
\(416\) | −17.8582 | + | 9.85323i | −0.875568 | + | 0.483094i | ||||
\(417\) | 4.08854 | + | 11.0786i | 0.200217 | + | 0.542522i | ||||
\(418\) | 13.8819 | + | 6.49971i | 0.678988 | + | 0.317911i | ||||
\(419\) | −35.1237 | −1.71590 | −0.857951 | − | 0.513731i | \(-0.828263\pi\) | ||||
−0.857951 | + | 0.513731i | \(0.828263\pi\) | |||||||
\(420\) | 9.75714 | + | 5.61576i | 0.476100 | + | 0.274021i | ||||
\(421\) | 8.32467i | 0.405720i | 0.979208 | + | 0.202860i | \(0.0650236\pi\) | ||||
−0.979208 | + | 0.202860i | \(0.934976\pi\) | |||||||
\(422\) | 1.53610 | + | 0.719224i | 0.0747763 | + | 0.0350113i | ||||
\(423\) | −11.0786 | − | 12.9654i | −0.538660 | − | 0.630401i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 3.04325i | − | 0.147619i | ||||||
\(426\) | 5.65124 | + | 0.477838i | 0.273803 | + | 0.0231513i | ||||
\(427\) | 7.79544 | 0.377248 | ||||||||
\(428\) | −12.9994 | − | 15.5909i | −0.628351 | − | 0.753614i | ||||
\(429\) | 12.4344 | + | 1.17710i | 0.600339 | + | 0.0568308i | ||||
\(430\) | 8.40388 | + | 3.93481i | 0.405271 | + | 0.189753i | ||||
\(431\) | 9.19224i | 0.442774i | 0.975186 | + | 0.221387i | \(0.0710585\pi\) | ||||
−0.975186 | + | 0.221387i | \(0.928942\pi\) | |||||||
\(432\) | 16.0174 | + | 13.2455i | 0.770636 | + | 0.637276i | ||||
\(433\) | 36.1771 | 1.73856 | 0.869280 | − | 0.494320i | \(-0.164583\pi\) | ||||
0.869280 | + | 0.494320i | \(0.164583\pi\) | |||||||
\(434\) | 4.94506 | − | 10.5616i | 0.237370 | − | 0.506971i | ||||
\(435\) | −3.89772 | − | 10.5616i | −0.186881 | − | 0.506388i | ||||
\(436\) | 12.7876 | − | 10.6620i | 0.612413 | − | 0.510619i | ||||
\(437\) | 27.5022 | 1.31561 | ||||||||
\(438\) | −24.7730 | − | 2.09467i | −1.18370 | − | 0.100087i | ||||
\(439\) | 25.6294i | 1.22322i | 0.791159 | + | 0.611611i | \(0.209478\pi\) | ||||
−0.791159 | + | 0.611611i | \(0.790522\pi\) | |||||||
\(440\) | 3.07221 | + | 11.6847i | 0.146462 | + | 0.557044i | ||||
\(441\) | −10.6847 | + | 9.12975i | −0.508793 | + | 0.434750i | ||||
\(442\) | −27.4089 | + | 22.3910i | −1.30371 | + | 1.06503i | ||||
\(443\) | −1.82496 | −0.0867067 | −0.0433533 | − | 0.999060i | \(-0.513804\pi\) | ||||
−0.0433533 | + | 0.999060i | \(0.513804\pi\) | |||||||
\(444\) | −3.15355 | + | 5.47915i | −0.149661 | + | 0.260029i | ||||
\(445\) | 24.2462 | 1.14938 | ||||||||
\(446\) | 17.5618 | − | 37.5082i | 0.831577 | − | 1.77606i | ||||
\(447\) | 0.667152 | − | 0.246211i | 0.0315552 | − | 0.0116454i | ||||
\(448\) | −10.5988 | + | 5.98730i | −0.500745 | + | 0.282873i | ||||
\(449\) | 14.2770 | 0.673771 | 0.336886 | − | 0.941546i | \(-0.390626\pi\) | ||||
0.336886 | + | 0.941546i | \(0.390626\pi\) | |||||||
\(450\) | −0.494712 | − | 1.79318i | −0.0233209 | − | 0.0845315i | ||||
\(451\) | − | 11.4677i | − | 0.539992i | ||||||
\(452\) | 16.6493 | − | 13.8819i | 0.783119 | − | 0.652952i | ||||
\(453\) | 27.8066 | − | 10.2620i | 1.30647 | − | 0.482149i | ||||
\(454\) | 9.93087 | + | 4.64976i | 0.466079 | + | 0.218224i | ||||
\(455\) | −5.07482 | + | 10.5616i | −0.237911 | + | 0.495133i | ||||
\(456\) | −21.7512 | + | 15.2233i | −1.01859 | + | 0.712899i | ||||
\(457\) | 6.49971i | 0.304044i | 0.988377 | + | 0.152022i | \(0.0485784\pi\) | ||||
−0.988377 | + | 0.152022i | \(0.951422\pi\) | |||||||
\(458\) | −35.6361 | − | 16.6853i | −1.66516 | − | 0.779652i | ||||
\(459\) | 31.4737 | + | 17.6121i | 1.46907 | + | 0.822062i | ||||
\(460\) | 13.8819 | + | 16.6493i | 0.647249 | + | 0.776280i | ||||
\(461\) | 25.0711 | 1.16768 | 0.583839 | − | 0.811869i | \(-0.301550\pi\) | ||||
0.583839 | + | 0.811869i | \(0.301550\pi\) | |||||||
\(462\) | 7.42790 | + | 0.628063i | 0.345577 | + | 0.0292201i | ||||
\(463\) | −27.0967 | −1.25929 | −0.629646 | − | 0.776882i | \(-0.716800\pi\) | ||||
−0.629646 | + | 0.776882i | \(0.716800\pi\) | |||||||
\(464\) | 11.9746 | + | 2.18878i | 0.555907 | + | 0.101611i | ||||
\(465\) | 18.8078 | − | 6.94097i | 0.872189 | − | 0.321880i | ||||
\(466\) | 14.9763 | + | 7.01212i | 0.693765 | + | 0.324830i | ||||
\(467\) | 10.7744 | 0.498579 | 0.249289 | − | 0.968429i | \(-0.419803\pi\) | ||||
0.249289 | + | 0.968429i | \(0.419803\pi\) | |||||||
\(468\) | −12.5104 | + | 17.6491i | −0.578292 | + | 0.815830i | ||||
\(469\) | −12.8769 | −0.594600 | ||||||||
\(470\) | 15.5501 | + | 7.28078i | 0.717274 | + | 0.335837i | ||||
\(471\) | 10.1496 | − | 3.74571i | 0.467671 | − | 0.172593i | ||||
\(472\) | 8.00000 | + | 30.4268i | 0.368230 | + | 1.40051i | ||||
\(473\) | 6.14441 | 0.282520 | ||||||||
\(474\) | −22.1354 | − | 1.87165i | −1.01671 | − | 0.0859675i | ||||
\(475\) | 2.37610 | 0.109023 | ||||||||
\(476\) | −16.2236 | + | 13.5270i | −0.743609 | + | 0.620008i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −25.5270 | − | 11.9521i | −1.16758 | − | 0.546675i | ||||
\(479\) | 7.43845i | 0.339871i | 0.985455 | + | 0.169936i | \(0.0543560\pi\) | ||||
−0.985455 | + | 0.169936i | \(0.945644\pi\) | |||||||
\(480\) | −20.1950 | − | 5.48367i | −0.921772 | − | 0.250294i | ||||
\(481\) | −5.93087 | − | 2.84978i | −0.270424 | − | 0.129939i | ||||
\(482\) | −4.67474 | − | 2.18878i | −0.212929 | − | 0.0996960i | ||||
\(483\) | 12.5476 | − | 4.63068i | 0.570937 | − | 0.210703i | ||||
\(484\) | −8.96543 | − | 10.7527i | −0.407520 | − | 0.488760i | ||||
\(485\) | − | 35.5593i | − | 1.61467i | ||||||
\(486\) | 21.4084 | + | 5.26124i | 0.971104 | + | 0.238655i | ||||
\(487\) | −5.41935 | −0.245574 | −0.122787 | − | 0.992433i | \(-0.539183\pi\) | ||||
−0.122787 | + | 0.992433i | \(0.539183\pi\) | |||||||
\(488\) | −14.0140 | + | 3.68466i | −0.634385 | + | 0.166797i | ||||
\(489\) | 21.4731 | − | 7.92460i | 0.971046 | − | 0.358363i | ||||
\(490\) | 6.00000 | − | 12.8147i | 0.271052 | − | 0.578908i | ||||
\(491\) | −22.7490 | −1.02665 | −0.513324 | − | 0.858195i | \(-0.671586\pi\) | ||||
−0.513324 | + | 0.858195i | \(0.671586\pi\) | |||||||
\(492\) | 17.2149 | + | 9.90809i | 0.776107 | + | 0.446691i | ||||
\(493\) | 21.1231 | 0.951337 | ||||||||
\(494\) | −17.4823 | − | 21.4002i | −0.786567 | − | 0.962843i | ||||
\(495\) | 8.32467 | + | 9.74247i | 0.374166 | + | 0.437891i | ||||
\(496\) | −3.89772 | + | 21.3241i | −0.175013 | + | 0.957480i | ||||
\(497\) | 3.52308i | 0.158032i | ||||||||
\(498\) | −14.6447 | − | 1.23827i | −0.656244 | − | 0.0554884i | ||||
\(499\) | 5.41935 | 0.242603 | 0.121302 | − | 0.992616i | \(-0.461293\pi\) | ||||
0.121302 | + | 0.992616i | \(0.461293\pi\) | |||||||
\(500\) | 14.8766 | + | 17.8423i | 0.665303 | + | 0.797933i | ||||
\(501\) | −10.4160 | − | 28.2239i | −0.465351 | − | 1.26095i | ||||
\(502\) | −10.8387 | + | 23.1491i | −0.483755 | + | 1.03319i | ||||
\(503\) | 22.3489 | 0.996488 | 0.498244 | − | 0.867037i | \(-0.333978\pi\) | ||||
0.498244 | + | 0.867037i | \(0.333978\pi\) | |||||||
\(504\) | −7.36055 | + | 10.6079i | −0.327865 | + | 0.472512i | ||||
\(505\) | 12.9994i | 0.578466i | ||||||||
\(506\) | 12.9994 | + | 6.08650i | 0.577895 | + | 0.270578i | ||||
\(507\) | −19.2860 | − | 11.6212i | −0.856519 | − | 0.516115i | ||||
\(508\) | −10.2462 | + | 8.54312i | −0.454602 | + | 0.379040i | ||||
\(509\) | −32.9407 | −1.46007 | −0.730036 | − | 0.683408i | \(-0.760497\pi\) | ||||
−0.730036 | + | 0.683408i | \(0.760497\pi\) | |||||||
\(510\) | −36.1831 | − | 3.05944i | −1.60221 | − | 0.135474i | ||||
\(511\) | − | 15.4439i | − | 0.683200i | ||||||
\(512\) | 16.2236 | − | 15.7732i | 0.716990 | − | 0.697083i | ||||
\(513\) | −13.7511 | + | 24.5739i | −0.607126 | + | 1.08497i | ||||
\(514\) | 2.80333 | + | 1.31256i | 0.123650 | + | 0.0578944i | ||||
\(515\) | − | 41.6155i | − | 1.83380i | ||||||
\(516\) | −5.30878 | + | 9.22378i | −0.233706 | + | 0.406054i | ||||
\(517\) | 11.3693 | 0.500022 | ||||||||
\(518\) | −3.55660 | − | 1.66525i | −0.156268 | − | 0.0731668i | ||||
\(519\) | −4.67474 | − | 12.6670i | −0.205198 | − | 0.556021i | ||||
\(520\) | 4.13100 | − | 21.3854i | 0.181156 | − | 0.937813i | ||||
\(521\) | 14.7364i | 0.645614i | 0.946465 | + | 0.322807i | \(0.104626\pi\) | ||||
−0.946465 | + | 0.322807i | \(0.895374\pi\) | |||||||
\(522\) | 12.4464 | − | 3.43378i | 0.544766 | − | 0.150293i | ||||
\(523\) | 19.4849i | 0.852017i | 0.904719 | + | 0.426008i | \(0.140081\pi\) | ||||
−0.904719 | + | 0.426008i | \(0.859919\pi\) | |||||||
\(524\) | 2.33737 | + | 2.80333i | 0.102109 | + | 0.122464i | ||||
\(525\) | 1.08407 | − | 0.400075i | 0.0473128 | − | 0.0174607i | ||||
\(526\) | 2.18878 | − | 4.67474i | 0.0954352 | − | 0.203829i | ||||
\(527\) | 37.6155i | 1.63856i | ||||||||
\(528\) | −13.6502 | + | 2.38185i | −0.594047 | + | 0.103657i | ||||
\(529\) | 2.75379 | 0.119730 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 21.6774 | + | 25.3693i | 0.940718 | + | 1.10093i | ||||
\(532\) | −10.5616 | − | 12.6670i | −0.457901 | − | 0.549185i | ||||
\(533\) | −8.95369 | + | 18.6341i | −0.387827 | + | 0.807134i | ||||
\(534\) | −2.34290 | + | 27.7087i | −0.101387 | + | 1.19907i | ||||
\(535\) | 21.6774 | 0.937195 | ||||||||
\(536\) | 23.1491 | − | 6.08650i | 0.999887 | − | 0.262897i | ||||
\(537\) | 2.96543 | − | 1.09439i | 0.127968 | − | 0.0472263i | ||||
\(538\) | 23.8662 | + | 11.1745i | 1.02894 | + | 0.481765i | ||||
\(539\) | − | 9.36932i | − | 0.403565i | ||||||
\(540\) | −21.8176 | + | 4.07921i | −0.938880 | + | 0.175541i | ||||
\(541\) | − | 21.3241i | − | 0.916794i | −0.888747 | − | 0.458397i | \(-0.848424\pi\) | ||
0.888747 | − | 0.458397i | \(-0.151576\pi\) | |||||||
\(542\) | −4.56241 | + | 9.74430i | −0.195972 | + | 0.418554i | ||||
\(543\) | 31.4737 | − | 11.6153i | 1.35067 | − | 0.498461i | ||||
\(544\) | 22.7718 | − | 31.9861i | 0.976332 | − | 1.37139i | ||||
\(545\) | 17.7797i | 0.761597i | ||||||||
\(546\) | −11.5794 | − | 6.82009i | −0.495554 | − | 0.291873i | ||||
\(547\) | 24.6606i | 1.05441i | 0.849738 | + | 0.527205i | \(0.176760\pi\) | ||||
−0.849738 | + | 0.527205i | \(0.823240\pi\) | |||||||
\(548\) | 11.4677 | + | 13.7538i | 0.489875 | + | 0.587533i | ||||
\(549\) | −11.6847 | + | 9.98422i | −0.498689 | + | 0.426116i | ||||
\(550\) | 1.12311 | + | 0.525853i | 0.0478894 | + | 0.0224224i | ||||
\(551\) | 16.4924i | 0.702601i | ||||||||
\(552\) | −20.3684 | + | 14.2555i | −0.866935 | + | 0.606756i | ||||
\(553\) | − | 13.7996i | − | 0.586817i | ||||||
\(554\) | 2.25106 | − | 4.80776i | 0.0956383 | − | 0.204262i | ||||
\(555\) | −2.33737 | − | 6.33351i | −0.0992159 | − | 0.268843i | ||||
\(556\) | 10.4730 | − | 8.73222i | 0.444155 | − | 0.370329i | ||||
\(557\) | −18.4009 | −0.779670 | −0.389835 | − | 0.920885i | \(-0.627468\pi\) | ||||
−0.389835 | + | 0.920885i | \(0.627468\pi\) | |||||||
\(558\) | 6.11480 | + | 22.1643i | 0.258860 | + | 0.938290i | ||||
\(559\) | −9.98422 | − | 4.79741i | −0.422288 | − | 0.202909i | ||||
\(560\) | 2.33737 | − | 12.7876i | 0.0987720 | − | 0.540373i | ||||
\(561\) | −22.5571 | + | 8.32467i | −0.952363 | + | 0.351468i | ||||
\(562\) | 10.3153 | − | 22.0313i | 0.435126 | − | 0.929334i | ||||
\(563\) | 11.1745 | 0.470947 | 0.235474 | − | 0.971881i | \(-0.424336\pi\) | ||||
0.235474 | + | 0.971881i | \(0.424336\pi\) | |||||||
\(564\) | −9.82311 | + | 17.0672i | −0.413628 | + | 0.718660i | ||||
\(565\) | 23.1491i | 0.973888i | ||||||||
\(566\) | −21.2101 | − | 9.93087i | −0.891529 | − | 0.417426i | ||||
\(567\) | −2.13618 | + | 13.5270i | −0.0897112 | + | 0.568080i | ||||
\(568\) | −1.66525 | − | 6.33351i | −0.0698723 | − | 0.265748i | ||||
\(569\) | − | 2.18878i | − | 0.0917583i | −0.998947 | − | 0.0458791i | \(-0.985391\pi\) | ||
0.998947 | − | 0.0458791i | \(-0.0146089\pi\) | |||||||
\(570\) | 2.38874 | − | 28.2509i | 0.100053 | − | 1.18330i | ||||
\(571\) | − | 22.0313i | − | 0.921981i | −0.887405 | − | 0.460990i | \(-0.847494\pi\) | ||
0.887405 | − | 0.460990i | \(-0.152506\pi\) | |||||||
\(572\) | −3.52726 | − | 13.9842i | −0.147482 | − | 0.584710i | ||||
\(573\) | 18.8078 | − | 6.94097i | 0.785706 | − | 0.289963i | ||||
\(574\) | −5.23203 | + | 11.1745i | −0.218381 | + | 0.466413i | ||||
\(575\) | 2.22504 | 0.0927906 | ||||||||
\(576\) | 8.21820 | − | 22.5491i | 0.342425 | − | 0.939545i | ||||
\(577\) | − | 23.1491i | − | 0.963708i | −0.876252 | − | 0.481854i | \(-0.839964\pi\) | ||
0.876252 | − | 0.481854i | \(-0.160036\pi\) | |||||||
\(578\) | 18.6962 | − | 39.9309i | 0.777658 | − | 1.66091i | ||||
\(579\) | −11.6932 | − | 31.6847i | −0.485951 | − | 1.31677i | ||||
\(580\) | −9.98422 | + | 8.32467i | −0.414572 | + | 0.345663i | ||||
\(581\) | − | 9.12975i | − | 0.378766i | ||||||
\(582\) | 40.6374 | + | 3.43608i | 1.68447 | + | 0.142430i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 7.29986 | + | 27.7639i | 0.302070 | + | 1.14888i | ||||
\(585\) | −5.92030 | − | 22.3305i | −0.244774 | − | 0.923253i | ||||
\(586\) | −1.59612 | + | 3.40896i | −0.0659350 | + | 0.140823i | ||||
\(587\) | − | 15.6155i | − | 0.644522i | −0.946651 | − | 0.322261i | \(-0.895557\pi\) | ||
0.946651 | − | 0.322261i | \(-0.104443\pi\) | |||||||
\(588\) | 14.0649 | + | 8.09511i | 0.580027 | + | 0.333837i | ||||
\(589\) | −29.3693 | −1.21014 | ||||||||
\(590\) | −30.4268 | − | 14.2462i | −1.25265 | − | 0.586507i | ||||
\(591\) | −13.4547 | + | 4.96543i | −0.553453 | + | 0.204251i | ||||
\(592\) | 7.18089 | + | 1.31256i | 0.295133 | + | 0.0539458i | ||||
\(593\) | −31.3632 | −1.28793 | −0.643966 | − | 0.765054i | \(-0.722712\pi\) | ||||
−0.643966 | + | 0.765054i | \(0.722712\pi\) | |||||||
\(594\) | −11.9382 | + | 8.57207i | −0.489828 | + | 0.351716i | ||||
\(595\) | − | 22.5571i | − | 0.924753i | ||||||
\(596\) | −0.525853 | − | 0.630683i | −0.0215398 | − | 0.0258338i | ||||
\(597\) | −3.36932 | − | 9.12975i | −0.137897 | − | 0.373656i | ||||
\(598\) | −16.3709 | − | 20.0398i | −0.669456 | − | 0.819487i | ||||
\(599\) | −33.2987 | −1.36055 | −0.680274 | − | 0.732958i | \(-0.738139\pi\) | ||||
−0.680274 | + | 0.732958i | \(0.738139\pi\) | |||||||
\(600\) | −1.75976 | + | 1.23163i | −0.0718418 | + | 0.0502811i | ||||
\(601\) | 2.80776 | 0.114531 | 0.0572655 | − | 0.998359i | \(-0.481762\pi\) | ||||
0.0572655 | + | 0.998359i | \(0.481762\pi\) | |||||||
\(602\) | −5.98730 | − | 2.80333i | −0.244024 | − | 0.114255i | ||||
\(603\) | 19.3013 | − | 16.4924i | 0.786009 | − | 0.671623i | ||||
\(604\) | −21.9173 | − | 26.2866i | −0.891802 | − | 1.06959i | ||||
\(605\) | 14.9505 | 0.607822 | ||||||||
\(606\) | −14.8558 | − | 1.25613i | −0.603476 | − | 0.0510266i | ||||
\(607\) | 13.3405i | 0.541475i | 0.962653 | + | 0.270738i | \(0.0872676\pi\) | ||||
−0.962653 | + | 0.270738i | \(0.912732\pi\) | |||||||
\(608\) | 24.9740 | + | 17.7797i | 1.01283 | + | 0.721061i | ||||
\(609\) | 2.77691 | + | 7.52452i | 0.112526 | + | 0.304909i | ||||
\(610\) | 6.56155 | − | 14.0140i | 0.265670 | − | 0.567411i | ||||
\(611\) | −18.4743 | − | 8.87689i | −0.747391 | − | 0.359121i | ||||
\(612\) | 6.99269 | − | 41.0546i | 0.282663 | − | 1.65953i | ||||
\(613\) | 6.49971i | 0.262521i | 0.991348 | + | 0.131260i | \(0.0419024\pi\) | ||||
−0.991348 | + | 0.131260i | \(0.958098\pi\) | |||||||
\(614\) | −1.42489 | + | 3.04325i | −0.0575039 | + | 0.122816i | ||||
\(615\) | −19.8992 | + | 7.34376i | −0.802413 | + | 0.296129i | ||||
\(616\) | −2.18878 | − | 8.32467i | −0.0881883 | − | 0.335411i | ||||
\(617\) | 18.5485 | 0.746735 | 0.373368 | − | 0.927684i | \(-0.378203\pi\) | ||||
0.373368 | + | 0.927684i | \(0.378203\pi\) | |||||||
\(618\) | 47.5585 | + | 4.02128i | 1.91308 | + | 0.161760i | ||||
\(619\) | −4.08504 | −0.164192 | −0.0820959 | − | 0.996624i | \(-0.526161\pi\) | ||||
−0.0820959 | + | 0.996624i | \(0.526161\pi\) | |||||||
\(620\) | −14.8244 | − | 17.7797i | −0.595362 | − | 0.714048i | ||||
\(621\) | −12.8769 | + | 23.0117i | −0.516732 | + | 0.923427i | ||||
\(622\) | 14.7364 | − | 31.4737i | 0.590876 | − | 1.26198i | ||||
\(623\) | −17.2741 | −0.692072 | ||||||||
\(624\) | 24.0402 | + | 6.78738i | 0.962378 | + | 0.271713i | ||||
\(625\) | −22.6155 | −0.904621 | ||||||||
\(626\) | −4.46066 | + | 9.52699i | −0.178284 | + | 0.380775i | ||||
\(627\) | −6.49971 | − | 17.6121i | −0.259573 | − | 0.703359i | ||||
\(628\) | −8.00000 | − | 9.59482i | −0.319235 | − | 0.382875i | ||||
\(629\) | 12.6670 | 0.505067 | ||||||||
\(630\) | −3.66690 | − | 13.2914i | −0.146093 | − | 0.529543i | ||||
\(631\) | −30.9945 | −1.23387 | −0.616935 | − | 0.787014i | \(-0.711626\pi\) | ||||
−0.616935 | + | 0.787014i | \(0.711626\pi\) | |||||||
\(632\) | 6.52262 | + | 24.8078i | 0.259456 | + | 0.986800i | ||||
\(633\) | −0.719224 | − | 1.94886i | −0.0285866 | − | 0.0774603i | ||||
\(634\) | 0.246211 | − | 0.525853i | 0.00977830 | − | 0.0208843i | ||||
\(635\) | − | 14.2462i | − | 0.565344i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.31534 | + | 15.2245i | −0.289844 | + | 0.603215i | ||||
\(638\) | −3.64993 | + | 7.79544i | −0.144502 | + | 0.308625i | ||||
\(639\) | −4.51228 | − | 5.28078i | −0.178503 | − | 0.208904i | ||||
\(640\) | 1.84233 | + | 24.0932i | 0.0728245 | + | 0.952369i | ||||
\(641\) | − | 1.33430i | − | 0.0527018i | −0.999653 | − | 0.0263509i | \(-0.991611\pi\) | ||
0.999653 | − | 0.0263509i | \(-0.00838873\pi\) | |||||||
\(642\) | −2.09467 | + | 24.7730i | −0.0826701 | + | 0.977714i | ||||
\(643\) | 1.04179 | 0.0410843 | 0.0205422 | − | 0.999789i | \(-0.493461\pi\) | ||||
0.0205422 | + | 0.999789i | \(0.493461\pi\) | |||||||
\(644\) | −9.89012 | − | 11.8617i | −0.389725 | − | 0.467418i | ||||
\(645\) | −3.93481 | − | 10.6620i | −0.154933 | − | 0.419818i | ||||
\(646\) | 48.1771 | + | 22.5571i | 1.89550 | + | 0.887499i | ||||
\(647\) | 33.2987 | 1.30911 | 0.654553 | − | 0.756016i | \(-0.272857\pi\) | ||||
0.654553 | + | 0.756016i | \(0.272857\pi\) | |||||||
\(648\) | −2.55352 | − | 25.3274i | −0.100312 | − | 0.994956i | ||||
\(649\) | −22.2462 | −0.873240 | ||||||||
\(650\) | −1.41439 | − | 1.73137i | −0.0554770 | − | 0.0679098i | ||||
\(651\) | −13.3995 | + | 4.94506i | −0.525168 | + | 0.193812i | ||||
\(652\) | −16.9252 | − | 20.2993i | −0.662842 | − | 0.794981i | ||||
\(653\) | 26.4296i | 1.03427i | 0.855904 | + | 0.517135i | \(0.173001\pi\) | ||||
−0.855904 | + | 0.517135i | \(0.826999\pi\) | |||||||
\(654\) | −20.3187 | − | 1.71804i | −0.794524 | − | 0.0671806i | ||||
\(655\) | −3.89772 | −0.152297 | ||||||||
\(656\) | 4.12391 | − | 22.5616i | 0.161012 | − | 0.880881i | ||||
\(657\) | 19.7802 | + | 23.1491i | 0.771700 | + | 0.903131i | ||||
\(658\) | −11.0786 | − | 5.18715i | −0.431889 | − | 0.202216i | ||||
\(659\) | −23.7738 | −0.926096 | −0.463048 | − | 0.886333i | \(-0.653244\pi\) | ||||
−0.463048 | + | 0.886333i | \(0.653244\pi\) | |||||||
\(660\) | 7.38127 | − | 12.8246i | 0.287315 | − | 0.499198i | ||||
\(661\) | 29.6488i | 1.15320i | 0.817025 | + | 0.576602i | \(0.195622\pi\) | ||||
−0.817025 | + | 0.576602i | \(0.804378\pi\) | |||||||
\(662\) | 3.24985 | − | 6.94097i | 0.126309 | − | 0.269769i | ||||
\(663\) | 43.1534 | + | 4.08510i | 1.67594 | + | 0.158652i | ||||
\(664\) | 4.31534 | + | 16.4127i | 0.167468 | + | 0.636938i | ||||
\(665\) | 17.6121 | 0.682967 | ||||||||
\(666\) | 7.46383 | − | 2.05916i | 0.289218 | − | 0.0797907i | ||||
\(667\) | 15.4439i | 0.597992i | ||||||||
\(668\) | −26.6811 | + | 22.2462i | −1.03232 | + | 0.860732i | ||||
\(669\) | −47.5868 | + | 17.5618i | −1.83981 | + | 0.678980i | ||||
\(670\) | −10.8387 | + | 23.1491i | −0.418735 | + | 0.894326i | ||||
\(671\) | − | 10.2462i | − | 0.395551i | ||||||
\(672\) | 14.3878 | + | 3.90682i | 0.555023 | + | 0.150709i | ||||
\(673\) | −11.6847 | −0.450410 | −0.225205 | − | 0.974311i | \(-0.572305\pi\) | ||||
−0.225205 | + | 0.974311i | \(0.572305\pi\) | |||||||
\(674\) | 5.80766 | − | 12.4039i | 0.223703 | − | 0.477780i | ||||
\(675\) | −1.11252 | + | 1.98813i | −0.0428209 | + | 0.0765232i | ||||
\(676\) | −5.18701 | + | 25.4773i | −0.199500 | + | 0.979898i | ||||
\(677\) | − | 29.4728i | − | 1.13273i | −0.824154 | − | 0.566366i | \(-0.808349\pi\) | ||
0.824154 | − | 0.566366i | \(-0.191651\pi\) | |||||||
\(678\) | −26.4549 | − | 2.23688i | −1.01599 | − | 0.0859068i | ||||
\(679\) | 25.3341i | 0.972232i | ||||||||
\(680\) | 10.6620 | + | 40.5514i | 0.408871 | + | 1.55508i | ||||
\(681\) | −4.64976 | − | 12.5993i | −0.178179 | − | 0.482808i | ||||
\(682\) | −13.8819 | − | 6.49971i | −0.531567 | − | 0.248887i | ||||
\(683\) | 38.9848i | 1.49171i | 0.666106 | + | 0.745857i | \(0.267960\pi\) | ||||
−0.666106 | + | 0.745857i | \(0.732040\pi\) | |||||||
\(684\) | 32.0544 | + | 5.45973i | 1.22563 | + | 0.208758i | ||||
\(685\) | −19.1231 | −0.730656 | ||||||||
\(686\) | −10.6620 | + | 22.7718i | −0.407079 | + | 0.869430i | ||||
\(687\) | 16.6853 | + | 45.2116i | 0.636583 | + | 1.72493i | ||||
\(688\) | 12.0885 | + | 2.20960i | 0.460871 | + | 0.0842403i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 2.23688 | − | 26.4549i | 0.0851565 | − | 1.00712i | ||||
\(691\) | 31.4743 | 1.19734 | 0.598669 | − | 0.800996i | \(-0.295696\pi\) | ||||
0.598669 | + | 0.800996i | \(0.295696\pi\) | |||||||
\(692\) | −11.9746 | + | 9.98422i | −0.455206 | + | 0.379543i | ||||
\(693\) | −5.93087 | − | 6.94097i | −0.225295 | − | 0.263666i | ||||
\(694\) | 11.9331 | − | 25.4864i | 0.452974 | − | 0.967452i | ||||
\(695\) | 14.5616i | 0.552351i | ||||||||
\(696\) | −8.54871 | − | 12.2144i | −0.324038 | − | 0.462987i | ||||
\(697\) | − | 39.7984i | − | 1.50747i | ||||||
\(698\) | 2.33737 | + | 1.09439i | 0.0884708 | + | 0.0414232i | ||||
\(699\) | −7.01212 | − | 19.0005i | −0.265223 | − | 0.718667i | ||||
\(700\) | −0.854473 | − | 1.02481i | −0.0322960 | − | 0.0387343i | ||||
\(701\) | − | 26.4296i | − | 0.998231i | −0.866535 | − | 0.499116i | \(-0.833658\pi\) | ||
0.866535 | − | 0.499116i | \(-0.166342\pi\) | |||||||
\(702\) | 26.0915 | − | 4.60796i | 0.984760 | − | 0.173916i | ||||
\(703\) | 9.89012i | 0.373013i | ||||||||
\(704\) | 7.86962 | + | 13.9309i | 0.296597 | + | 0.525039i | ||||
\(705\) | −7.28078 | − | 19.7285i | −0.274210 | − | 0.743019i | ||||
\(706\) | −15.9309 | + | 34.0248i | −0.599566 | + | 1.28054i | ||||
\(707\) | − | 9.26137i | − | 0.348310i | ||||||
\(708\) | 19.2208 | − | 33.3953i | 0.722361 | − | 1.25507i | ||||
\(709\) | − | 23.9492i | − | 0.899431i | −0.893172 | − | 0.449716i | \(-0.851525\pi\) | ||
0.893172 | − | 0.449716i | \(-0.148475\pi\) | |||||||
\(710\) | 6.33351 | + | 2.96543i | 0.237693 | + | 0.111291i | ||||
\(711\) | 17.6742 | + | 20.6843i | 0.662833 | + | 0.775722i | ||||
\(712\) | 31.0540 | − | 8.16491i | 1.16380 | − | 0.305993i | ||||
\(713\) | −27.5022 | −1.02997 | ||||||||
\(714\) | 25.7784 | + | 2.17968i | 0.964733 | + | 0.0815726i | ||||
\(715\) | 13.8819 | + | 6.67026i | 0.519155 | + | 0.249454i | ||||
\(716\) | −2.33737 | − | 2.80333i | −0.0873517 | − | 0.104765i | ||||
\(717\) | 11.9521 | + | 32.3862i | 0.446358 | + | 1.20949i | ||||
\(718\) | 14.2462 | + | 6.67026i | 0.531664 | + | 0.248932i | ||||
\(719\) | −31.0737 | −1.15885 | −0.579426 | − | 0.815025i | \(-0.696723\pi\) | ||||
−0.579426 | + | 0.815025i | \(0.696723\pi\) | |||||||
\(720\) | 12.8745 | + | 22.1610i | 0.479804 | + | 0.825893i | ||||
\(721\) | 29.6488i | 1.10418i | ||||||||
\(722\) | −6.21823 | + | 13.2808i | −0.231419 | + | 0.494259i | ||||
\(723\) | 2.18878 | + | 5.93087i | 0.0814015 | + | 0.220571i | ||||
\(724\) | −24.8078 | − | 29.7533i | −0.921973 | − | 1.10577i | ||||
\(725\) | 1.33430i | 0.0495548i | ||||||||
\(726\) | −1.44465 | + | 17.0855i | −0.0536161 | + | 0.634101i | ||||
\(727\) | − | 5.32326i | − | 0.197429i | −0.995116 | − | 0.0987145i | \(-0.968527\pi\) | ||
0.995116 | − | 0.0987145i | \(-0.0314730\pi\) | |||||||
\(728\) | −2.94311 | + | 15.2359i | −0.109079 | + | 0.564681i | ||||
\(729\) | −14.1231 | − | 23.0117i | −0.523078 | − | 0.852285i | ||||
\(730\) | −27.7639 | − | 12.9994i | −1.02759 | − | 0.481130i | ||||
\(731\) | 21.3241 | 0.788700 | ||||||||
\(732\) | 15.3813 | + | 8.85275i | 0.568508 | + | 0.327207i | ||||
\(733\) | − | 5.47489i | − | 0.202220i | −0.994875 | − | 0.101110i | \(-0.967761\pi\) | ||
0.994875 | − | 0.101110i | \(-0.0322394\pi\) | |||||||
\(734\) | 28.0281 | + | 13.1231i | 1.03453 | + | 0.484383i | ||||
\(735\) | −16.2580 | + | 6.00000i | −0.599687 | + | 0.221313i | ||||
\(736\) | 23.3863 | + | 16.6493i | 0.862032 | + | 0.613703i | ||||
\(737\) | 16.9252i | 0.623447i | ||||||||
\(738\) | −6.46965 | − | 23.4505i | −0.238151 | − | 0.863226i | ||||
\(739\) | −23.6788 | −0.871040 | −0.435520 | − | 0.900179i | \(-0.643436\pi\) | ||||
−0.435520 | + | 0.900179i | \(0.643436\pi\) | |||||||
\(740\) | −5.98730 | + | 4.99211i | −0.220098 | + | 0.183514i | ||||
\(741\) | −3.18955 | + | 33.6932i | −0.117171 | + | 1.23775i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 12.5616i | − | 0.460839i | −0.973091 | − | 0.230419i | \(-0.925990\pi\) | ||
0.973091 | − | 0.230419i | \(-0.0740098\pi\) | |||||||
\(744\) | 21.7512 | − | 15.2233i | 0.797437 | − | 0.558115i | ||||
\(745\) | 0.876894 | 0.0321269 | ||||||||
\(746\) | 0.525853 | − | 1.12311i | 0.0192528 | − | 0.0411198i | ||||
\(747\) | 11.6932 | + | 13.6847i | 0.427831 | + | 0.500695i | ||||
\(748\) | 17.7797 | + | 21.3241i | 0.650089 | + | 0.779686i | ||||
\(749\) | −15.4439 | −0.564309 | ||||||||
\(750\) | 2.39716 | − | 28.3504i | 0.0875319 | − | 1.03521i | ||||
\(751\) | 38.6746i | 1.41126i | 0.708583 | + | 0.705628i | \(0.249335\pi\) | ||||
−0.708583 | + | 0.705628i | \(0.750665\pi\) | |||||||
\(752\) | 22.3680 | + | 4.08854i | 0.815679 | + | 0.149094i | ||||
\(753\) | 29.3693 | − | 10.8387i | 1.07028 | − | 0.394984i | ||||
\(754\) | 12.0174 | − | 9.81725i | 0.437647 | − | 0.357523i | ||||
\(755\) | 36.5485 | 1.33014 | ||||||||
\(756\) | 15.5438 | − | 2.90621i | 0.565324 | − | 0.105698i | ||||
\(757\) | −4.49242 | −0.163280 | −0.0816399 | − | 0.996662i | \(-0.526016\pi\) | ||||
−0.0816399 | + | 0.996662i | \(0.526016\pi\) | |||||||
\(758\) | −5.07482 | + | 10.8387i | −0.184326 | + | 0.393679i | ||||
\(759\) | −6.08650 | − | 16.4924i | −0.220926 | − | 0.598637i | ||||
\(760\) | −31.6616 | + | 8.32467i | −1.14849 | + | 0.301968i | ||||
\(761\) | 23.3459 | 0.846289 | 0.423145 | − | 0.906062i | \(-0.360926\pi\) | ||||
0.423145 | + | 0.906062i | \(0.360926\pi\) | |||||||
\(762\) | 16.2806 | + | 1.37660i | 0.589786 | + | 0.0498691i | ||||
\(763\) | − | 12.6670i | − | 0.458577i | ||||||
\(764\) | −14.8244 | − | 17.7797i | −0.536327 | − | 0.643246i | ||||
\(765\) | 28.8907 | + | 33.8111i | 1.04454 | + | 1.22244i | ||||
\(766\) | −24.8963 | − | 11.6568i | −0.899540 | − | 0.421177i | ||||
\(767\) | 36.1485 | + | 17.3693i | 1.30525 | + | 0.627170i | ||||
\(768\) | −27.7119 | − | 0.222692i | −0.999968 | − | 0.00803572i | ||||
\(769\) | − | 28.8486i | − | 1.04031i | −0.854073 | − | 0.520154i | \(-0.825875\pi\) | ||
0.854073 | − | 0.520154i | \(-0.174125\pi\) | |||||||
\(770\) | 8.32467 | + | 3.89772i | 0.300000 | + | 0.140464i | ||||
\(771\) | −1.31256 | − | 3.55660i | −0.0472706 | − | 0.128088i | ||||
\(772\) | −29.9527 | + | 24.9740i | −1.07802 | + | 0.898835i | ||||
\(773\) | −2.13578 | −0.0768186 | −0.0384093 | − | 0.999262i | \(-0.512229\pi\) | ||||
−0.0384093 | + | 0.999262i | \(0.512229\pi\) | |||||||
\(774\) | 12.5649 | − | 3.46645i | 0.451635 | − | 0.124599i | ||||
\(775\) | −2.37610 | −0.0853519 | ||||||||
\(776\) | −11.9746 | − | 45.5435i | −0.429863 | − | 1.63492i | ||||
\(777\) | 1.66525 | + | 4.51228i | 0.0597404 | + | 0.161877i | ||||
\(778\) | −41.6458 | − | 19.4991i | −1.49308 | − | 0.699078i | ||||
\(779\) | 31.0737 | 1.11333 | ||||||||
\(780\) | −22.0072 | + | 15.0760i | −0.787984 | + | 0.539807i | ||||
\(781\) | 4.63068 | 0.165699 | ||||||||
\(782\) | 45.1143 | + | 21.1231i | 1.61328 | + | 0.755361i | ||||
\(783\) | −13.7996 | − | 7.72197i | −0.493156 | − | 0.275961i | ||||
\(784\) | 3.36932 | − | 18.4332i | 0.120333 | − | 0.658330i | ||||
\(785\) | 13.3405 | 0.476144 | ||||||||
\(786\) | 0.376635 | − | 4.45434i | 0.0134341 | − | 0.158881i | ||||
\(787\) | −39.2697 | −1.39981 | −0.699907 | − | 0.714234i | \(-0.746775\pi\) | ||||
−0.699907 | + | 0.714234i | \(0.746775\pi\) | |||||||
\(788\) | 10.6051 | + | 12.7192i | 0.377790 | + | 0.453104i | ||||
\(789\) | −5.93087 | + | 2.18878i | −0.211145 | + | 0.0779225i | ||||
\(790\) | −24.8078 | − | 11.6153i | −0.882621 | − | 0.413255i | ||||
\(791\) | − | 16.4924i | − | 0.586403i | ||||||
\(792\) | 13.9428 | + | 9.67459i | 0.495437 | + | 0.343772i | ||||
\(793\) | −8.00000 | + | 16.6493i | −0.284088 | + | 0.591236i | ||||
\(794\) | −4.67474 | − | 2.18878i | −0.165900 | − | 0.0776768i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.63068 | + | 7.19612i | −0.305906 | + | 0.255060i | ||||
\(797\) | 15.2162i | 0.538987i | 0.963002 | + | 0.269494i | \(0.0868563\pi\) | ||||
−0.963002 | + | 0.269494i | \(0.913144\pi\) | |||||||
\(798\) | −1.70185 | + | 20.1272i | −0.0602447 | + | 0.712495i | ||||
\(799\) | 39.4571 | 1.39589 | ||||||||
\(800\) | 2.02050 | + | 1.43845i | 0.0714355 | + | 0.0508568i | ||||
\(801\) | 25.8923 | − | 22.1242i | 0.914859 | − | 0.781722i | ||||
\(802\) | 9.50758 | − | 20.3061i | 0.335724 | − | 0.717033i | ||||
\(803\) | −20.2993 | −0.716346 | ||||||||
\(804\) | −25.4075 | − | 14.6234i | −0.896055 | − | 0.515727i | ||||
\(805\) | 16.4924 | 0.581282 | ||||||||
\(806\) | 17.4823 | + | 21.4002i | 0.615789 | + | 0.753792i | ||||
\(807\) | −11.1745 | − | 30.2791i | −0.393359 | − | 1.06588i | ||||
\(808\) | 4.37755 | + | 16.6493i | 0.154002 | + | 0.585722i | ||||
\(809\) | − | 11.3185i | − | 0.397938i | −0.980006 | − | 0.198969i | \(-0.936241\pi\) | ||
0.980006 | − | 0.198969i | \(-0.0637593\pi\) | |||||||
\(810\) | 22.5197 | + | 15.2261i | 0.791261 | + | 0.534992i | ||||
\(811\) | −24.0535 | −0.844632 | −0.422316 | − | 0.906449i | \(-0.638783\pi\) | ||||
−0.422316 | + | 0.906449i | \(0.638783\pi\) | |||||||
\(812\) | 7.11321 | − | 5.93087i | 0.249625 | − | 0.208133i | ||||
\(813\) | 12.3626 | − | 4.56241i | 0.433577 | − | 0.160011i | ||||
\(814\) | −2.18878 | + | 4.67474i | −0.0767166 | + | 0.163850i | ||||
\(815\) | 28.2239 | 0.988639 | ||||||||
\(816\) | −47.3727 | + | 8.26618i | −1.65838 | + | 0.289374i | ||||
\(817\) | 16.6493i | 0.582487i | ||||||||
\(818\) | 3.64993 | + | 1.70895i | 0.127617 | + | 0.0597519i | ||||
\(819\) | 4.21788 | + | 15.9093i | 0.147385 | + | 0.555914i | ||||
\(820\) | 15.6847 | + | 18.8114i | 0.547732 | + | 0.656924i | ||||
\(821\) | 9.85775 | 0.344038 | 0.172019 | − | 0.985094i | \(-0.444971\pi\) | ||||
0.172019 | + | 0.985094i | \(0.444971\pi\) | |||||||
\(822\) | 1.84785 | − | 21.8540i | 0.0644513 | − | 0.762245i | ||||
\(823\) | − | 9.59482i | − | 0.334454i | −0.985918 | − | 0.167227i | \(-0.946519\pi\) | ||
0.985918 | − | 0.167227i | \(-0.0534814\pi\) | |||||||
\(824\) | −14.0140 | − | 53.3002i | −0.488202 | − | 1.85680i | ||||
\(825\) | −0.525853 | − | 1.42489i | −0.0183078 | − | 0.0496083i | ||||
\(826\) | 21.6774 | + | 10.1496i | 0.754253 | + | 0.353151i | ||||
\(827\) | − | 13.5076i | − | 0.469704i | −0.972031 | − | 0.234852i | \(-0.924539\pi\) | ||
0.972031 | − | 0.234852i | \(-0.0754606\pi\) | |||||||
\(828\) | 30.0166 | + | 5.11264i | 1.04315 | + | 0.177676i | ||||
\(829\) | 24.0000 | 0.833554 | 0.416777 | − | 0.909009i | \(-0.363160\pi\) | ||||
0.416777 | + | 0.909009i | \(0.363160\pi\) | |||||||
\(830\) | −16.4127 | − | 7.68466i | −0.569694 | − | 0.266738i | ||||
\(831\) | −6.09963 | + | 2.25106i | −0.211594 | + | 0.0780884i | ||||
\(832\) | −1.91066 | − | 28.7811i | −0.0662402 | − | 0.997804i | ||||
\(833\) | − | 32.5161i | − | 1.12662i | ||||||
\(834\) | −16.6410 | − | 1.40707i | −0.576231 | − | 0.0487230i | ||||
\(835\) | − | 37.0970i | − | 1.28380i | ||||||
\(836\) | −16.6493 | + | 13.8819i | −0.575830 | + | 0.480117i | ||||
\(837\) | 13.7511 | − | 24.5739i | 0.475308 | − | 0.849400i | ||||
\(838\) | 21.0628 | − | 44.9856i | 0.727603 | − | 1.55400i | ||||
\(839\) | − | 19.1231i | − | 0.660203i | −0.943945 | − | 0.330101i | \(-0.892917\pi\) | ||
0.943945 | − | 0.330101i | \(-0.107083\pi\) | |||||||
\(840\) | −13.0437 | + | 9.12908i | −0.450049 | + | 0.314983i | ||||
\(841\) | 19.7386 | 0.680643 | ||||||||
\(842\) | −10.6620 | − | 4.99211i | −0.367438 | − | 0.172039i | ||||
\(843\) | −27.9512 | + | 10.3153i | −0.962691 | + | 0.355279i | ||||
\(844\) | −1.84233 | + | 1.53610i | −0.0634156 | + | 0.0528748i | ||||
\(845\) | −17.3492 | − | 21.6774i | −0.596829 | − | 0.745725i | ||||
\(846\) | 23.2494 | − | 6.41416i | 0.799331 | − | 0.220523i | ||||
\(847\) | −10.6514 | −0.365985 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.93087 | + | 26.9094i | 0.340827 | + | 0.923529i | ||||
\(850\) | 3.89772 | + | 1.82496i | 0.133691 | + | 0.0625958i | ||||
\(851\) | 9.26137i | 0.317476i | ||||||||
\(852\) | −4.00092 | + | 6.95143i | −0.137069 | + | 0.238152i | ||||
\(853\) | − | 21.3241i | − | 0.730123i | −0.930983 | − | 0.365061i | \(-0.881048\pi\) | ||
0.930983 | − | 0.365061i | \(-0.118952\pi\) | |||||||
\(854\) | −4.67474 | + | 9.98422i | −0.159966 | + | 0.341653i | ||||
\(855\) | −26.3989 | + | 22.5571i | −0.902824 | + | 0.771438i | ||||
\(856\) | 27.7639 | − | 7.29986i | 0.948950 | − | 0.249504i | ||||
\(857\) | − | 49.4413i | − | 1.68888i | −0.535649 | − | 0.844441i | \(-0.679933\pi\) | ||
0.535649 | − | 0.844441i | \(-0.320067\pi\) | |||||||
\(858\) | −8.96422 | + | 15.2198i | −0.306033 | + | 0.519596i | ||||
\(859\) | − | 9.06897i | − | 0.309429i | −0.987959 | − | 0.154715i | \(-0.950554\pi\) | ||
0.987959 | − | 0.154715i | \(-0.0494458\pi\) | |||||||
\(860\) | −10.0792 | + | 8.40388i | −0.343699 | + | 0.286570i | ||||
\(861\) | 14.1771 | − | 5.23203i | 0.483154 | − | 0.178307i | ||||
\(862\) | −11.7732 | − | 5.51237i | −0.400997 | − | 0.187752i | ||||
\(863\) | 0.561553i | 0.0191155i | 0.999954 | + | 0.00955774i | \(0.00304237\pi\) | ||||
−0.999954 | + | 0.00955774i | \(0.996958\pi\) | |||||||
\(864\) | −26.5698 | + | 12.5716i | −0.903923 | + | 0.427696i | ||||
\(865\) | − | 16.6493i | − | 0.566095i | ||||||
\(866\) | −21.6945 | + | 46.3348i | −0.737211 | + | 1.57452i | ||||
\(867\) | −50.6605 | + | 18.6962i | −1.72052 | + | 0.634955i | ||||
\(868\) | 10.5616 | + | 12.6670i | 0.358482 | + | 0.429947i | ||||
\(869\) | −18.1379 | −0.615287 | ||||||||
\(870\) | 15.8644 | + | 1.34140i | 0.537852 | + | 0.0454778i | ||||
\(871\) | 13.2148 | − | 27.5022i | 0.447766 | − | 0.931877i | ||||
\(872\) | 5.98730 | + | 22.7718i | 0.202756 | + | 0.771150i | ||||
\(873\) | −32.4473 | − | 37.9734i | −1.09817 | − | 1.28521i | ||||
\(874\) | −16.4924 | + | 35.2242i | −0.557865 | + | 1.19148i | ||||
\(875\) | 17.6742 | 0.597496 | ||||||||
\(876\) | 17.5386 | − | 30.4726i | 0.592575 | − | 1.02957i | ||||
\(877\) | 14.8244i | 0.500584i | 0.968170 | + | 0.250292i | \(0.0805266\pi\) | ||||
−0.968170 | + | 0.250292i | \(0.919473\pi\) | |||||||
\(878\) | −32.8255 | − | 15.3693i | −1.10781 | − | 0.518689i | ||||
\(879\) | 4.32496 | − | 1.59612i | 0.145877 | − | 0.0538357i | ||||
\(880\) | −16.8078 | − | 3.07221i | −0.566590 | − | 0.103564i | ||||
\(881\) | 43.8346i | 1.47683i | 0.674349 | + | 0.738413i | \(0.264424\pi\) | ||||
−0.674349 | + | 0.738413i | \(0.735576\pi\) | |||||||
\(882\) | −5.28583 | − | 19.1596i | −0.177983 | − | 0.645136i | ||||
\(883\) | 47.6606i | 1.60391i | 0.597386 | + | 0.801954i | \(0.296206\pi\) | ||||
−0.597386 | + | 0.801954i | \(0.703794\pi\) | |||||||
\(884\) | −12.2413 | − | 48.5320i | −0.411720 | − | 1.63231i | ||||
\(885\) | 14.2462 | + | 38.6026i | 0.478881 | + | 1.29761i | ||||
\(886\) | 1.09439 | − | 2.33737i | 0.0367667 | − | 0.0785255i | ||||
\(887\) | 34.7236 | 1.16590 | 0.582952 | − | 0.812507i | \(-0.301898\pi\) | ||||
0.582952 | + | 0.812507i | \(0.301898\pi\) | |||||||
\(888\) | −5.12646 | − | 7.32471i | −0.172033 | − | 0.245801i | ||||
\(889\) | 10.1496i | 0.340408i | ||||||||
\(890\) | −14.5399 | + | 31.0540i | −0.487378 | + | 1.04093i | ||||
\(891\) | 17.7797 | + | 2.80776i | 0.595641 | + | 0.0940636i | ||||
\(892\) | 37.5082 | + | 44.9856i | 1.25587 | + | 1.50623i | ||||
\(893\) | 30.8071i | 1.03092i | ||||||||
\(894\) | −0.0847338 | + | 1.00212i | −0.00283392 | + | 0.0335159i | ||||
\(895\) | 3.89772 | 0.130286 | ||||||||
\(896\) | −1.31256 | − | 17.1651i | −0.0438495 | − | 0.573446i | ||||
\(897\) | −2.98678 | + | 31.5512i | −0.0997256 | + | 1.05346i | ||||
\(898\) | −8.56155 | + | 18.2856i | −0.285703 | + | 0.610198i | ||||
\(899\) | − | 16.4924i | − | 0.550053i | ||||||
\(900\) | 2.59333 | + | 0.441714i | 0.0864445 | + | 0.0147238i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 14.6875 | + | 6.87689i | 0.489041 | + | 0.228976i | ||||
\(903\) | 2.80333 | + | 7.59612i | 0.0932891 | + | 0.252783i | ||||
\(904\) | 7.79544 | + | 29.6488i | 0.259273 | + | 0.986103i | ||||
\(905\) | 41.3686 | 1.37514 | ||||||||
\(906\) | −3.53166 | + | 41.7679i | −0.117332 | + | 1.38764i | ||||
\(907\) | − | 31.3308i | − | 1.04032i | −0.854068 | − | 0.520161i | \(-0.825872\pi\) | ||
0.854068 | − | 0.520161i | \(-0.174128\pi\) | |||||||
\(908\) | −11.9106 | + | 9.93087i | −0.395268 | + | 0.329567i | ||||
\(909\) | 11.8617 | + | 13.8819i | 0.393429 | + | 0.460435i | ||||
\(910\) | −10.4837 | − | 12.8332i | −0.347533 | − | 0.425417i | ||||
\(911\) | −8.72475 | −0.289064 | −0.144532 | − | 0.989500i | \(-0.546168\pi\) | ||||
−0.144532 | + | 0.989500i | \(0.546168\pi\) | |||||||
\(912\) | −6.45404 | − | 36.9875i | −0.213715 | − | 1.22478i | ||||
\(913\) | −12.0000 | −0.397142 | ||||||||
\(914\) | −8.32467 | − | 3.89772i | −0.275356 | − | 0.128925i | ||||
\(915\) | −17.7797 | + | 6.56155i | −0.587778 | + | 0.216918i | ||||
\(916\) | 42.7402 | − | 35.6361i | 1.41218 | − | 1.17745i | ||||
\(917\) | 2.77691 | 0.0917017 | ||||||||
\(918\) | −41.4312 | + | 29.7493i | −1.36743 | + | 0.981872i | ||||
\(919\) | − | 47.2824i | − | 1.55970i | −0.625964 | − | 0.779852i | \(-0.715294\pi\) | ||
0.625964 | − | 0.779852i | \(-0.284706\pi\) | |||||||
\(920\) | −29.6488 | + | 7.79544i | −0.977491 | + | 0.257008i | ||||
\(921\) | 3.86098 | − | 1.42489i | 0.127224 | − | 0.0469517i | ||||
\(922\) | −15.0346 | + | 32.1105i | −0.495137 | + | 1.05750i | ||||
\(923\) | −7.52452 | − | 3.61553i | −0.247673 | − | 0.119007i | ||||
\(924\) | −5.25875 | + | 9.13685i | −0.173000 | + | 0.300580i | ||||
\(925\) | 0.800151i | 0.0263088i | ||||||||
\(926\) | 16.2493 | − | 34.7049i | 0.533984 | − | 1.14047i | ||||
\(927\) | −37.9734 | − | 44.4408i | −1.24721 | − | 1.45963i | ||||
\(928\) | −9.98422 | + | 14.0242i | −0.327748 | + | 0.460368i | ||||
\(929\) | −9.77484 | −0.320702 | −0.160351 | − | 0.987060i | \(-0.551263\pi\) | ||||
−0.160351 | + | 0.987060i | \(0.551263\pi\) | |||||||
\(930\) | −2.38874 | + | 28.2509i | −0.0783299 | + | 0.926383i | ||||
\(931\) | 25.3878 | 0.832051 | ||||||||
\(932\) | −17.9619 | + | 14.9763i | −0.588362 | + | 0.490566i | ||||
\(933\) | −39.9309 | + | 14.7364i | −1.30728 | + | 0.482449i | ||||
\(934\) | −6.46114 | + | 13.7996i | −0.211415 | + | 0.451536i | ||||
\(935\) | −29.6488 | −0.969618 | ||||||||
\(936\) | −15.1024 | − | 26.6067i | −0.493637 | − | 0.869668i | ||||
\(937\) | 55.8617 | 1.82492 | 0.912462 | − | 0.409162i | \(-0.134179\pi\) | ||||
0.912462 | + | 0.409162i | \(0.134179\pi\) | |||||||
\(938\) | 7.72197 | − | 16.4924i | 0.252131 | − | 0.538497i | ||||
\(939\) | 12.0869 | − | 4.46066i | 0.394442 | − | 0.145568i | ||||
\(940\) | −18.6501 | + | 15.5501i | −0.608299 | + | 0.507189i | ||||
\(941\) | −49.4182 | −1.61099 | −0.805494 | − | 0.592604i | \(-0.798100\pi\) | ||||
−0.805494 | + | 0.592604i | \(0.798100\pi\) | |||||||
\(942\) | −1.28909 | + | 15.2456i | −0.0420007 | + | 0.496729i | ||||
\(943\) | 29.0982 | 0.947567 | ||||||||
\(944\) | −43.7673 | − | 8.00000i | −1.42450 | − | 0.260378i | ||||
\(945\) | −8.24621 | + | 14.7364i | −0.268249 | + | 0.479376i | ||||
\(946\) | −3.68466 | + | 7.86962i | −0.119799 | + | 0.255863i | ||||
\(947\) | 2.00000i | 0.0649913i | 0.999472 | + | 0.0324956i | \(0.0103455\pi\) | ||||
−0.999472 | + | 0.0324956i | \(0.989654\pi\) | |||||||
\(948\) | 15.6712 | − | 27.2281i | 0.508977 | − | 0.884326i | ||||
\(949\) | 32.9848 | + | 15.8492i | 1.07073 | + | 0.514487i | ||||
\(950\) | −1.42489 | + | 3.04325i | −0.0462295 | + | 0.0987360i | ||||
\(951\) | −0.667152 | + | 0.246211i | −0.0216339 | + | 0.00798395i | ||||
\(952\) | −7.59612 | − | 28.8907i | −0.246192 | − | 0.936352i | ||||
\(953\) | 29.9527i | 0.970262i | 0.874442 | + | 0.485131i | \(0.161228\pi\) | ||||
−0.874442 | + | 0.485131i | \(0.838772\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24.7206 | 0.799941 | ||||||||
\(956\) | 30.6159 | − | 25.5270i | 0.990188 | − | 0.825602i | ||||
\(957\) | 9.89012 | − | 3.64993i | 0.319702 | − | 0.117985i | ||||
\(958\) | −9.52699 | − | 4.46066i | −0.307803 | − | 0.144117i | ||||
\(959\) | 13.6242 | 0.439947 | ||||||||
\(960\) | 19.1338 | − | 22.5769i | 0.617542 | − | 0.728665i | ||||
\(961\) | −1.63068 | −0.0526027 | ||||||||
\(962\) | 7.20653 | − | 5.88717i | 0.232348 | − | 0.189810i | ||||
\(963\) | 23.1491 | − | 19.7802i | 0.745968 | − | 0.637409i | ||||
\(964\) | 5.60667 | − | 4.67474i | 0.180579 | − | 0.150563i | ||||
\(965\) | − | 41.6458i | − | 1.34063i | ||||||
\(966\) | −1.59365 | + | 18.8476i | −0.0512749 | + | 0.606413i | ||||
\(967\) | −38.7899 | −1.24740 | −0.623700 | − | 0.781664i | \(-0.714371\pi\) | ||||
−0.623700 | + | 0.781664i | \(0.714371\pi\) | |||||||
\(968\) | 19.1482 | − | 5.03457i | 0.615446 | − | 0.161817i | ||||
\(969\) | −22.5571 | − | 61.1225i | −0.724640 | − | 1.96354i | ||||
\(970\) | 45.5435 | + | 21.3241i | 1.46232 | + | 0.684675i | ||||
\(971\) | −6.09963 | −0.195747 | −0.0978733 | − | 0.995199i | \(-0.531204\pi\) | ||||
−0.0978733 | + | 0.995199i | \(0.531204\pi\) | |||||||
\(972\) | −19.5766 | + | 24.2643i | −0.627919 | + | 0.778279i | ||||
\(973\) | − | 10.3743i | − | 0.332585i | ||||||
\(974\) | 3.24985 | − | 6.94097i | 0.104132 | − | 0.222403i | ||||
\(975\) | −0.258047 | + | 2.72592i | −0.00826413 | + | 0.0872991i | ||||
\(976\) | 3.68466 | − | 20.1584i | 0.117943 | − | 0.645256i | ||||
\(977\) | −28.9645 | −0.926656 | −0.463328 | − | 0.886187i | \(-0.653345\pi\) | ||||
−0.463328 | + | 0.886187i | \(0.653345\pi\) | |||||||
\(978\) | −2.72726 | + | 32.2544i | −0.0872080 | + | 1.03138i | ||||
\(979\) | 22.7048i | 0.725648i | ||||||||
\(980\) | 12.8147 | + | 15.3693i | 0.409350 | + | 0.490955i | ||||
\(981\) | 16.2236 | + | 18.9867i | 0.517981 | + | 0.606199i | ||||
\(982\) | 13.6420 | − | 29.1364i | 0.435335 | − | 0.929779i | ||||
\(983\) | − | 35.9309i | − | 1.14602i | −0.819550 | − | 0.573008i | \(-0.805776\pi\) | ||
0.819550 | − | 0.573008i | \(-0.194224\pi\) | |||||||
\(984\) | −23.0134 | + | 16.1068i | −0.733641 | + | 0.513465i | ||||
\(985\) | −17.6847 | −0.563480 | ||||||||
\(986\) | −12.6670 | + | 27.0540i | −0.403400 | + | 0.861574i | ||||
\(987\) | 5.18715 | + | 14.0555i | 0.165109 | + | 0.447391i | ||||
\(988\) | 37.8927 | − | 9.55773i | 1.20553 | − | 0.304072i | ||||
\(989\) | 15.5909i | 0.495761i | ||||||||
\(990\) | −17.4700 | + | 4.81972i | −0.555234 | + | 0.153181i | ||||
\(991\) | 47.8083i | 1.51868i | 0.650694 | + | 0.759340i | \(0.274478\pi\) | ||||
−0.650694 | + | 0.759340i | \(0.725522\pi\) | |||||||
\(992\) | −24.9740 | − | 17.7797i | −0.792926 | − | 0.564505i | ||||
\(993\) | −8.80604 | + | 3.24985i | −0.279451 | + | 0.103131i | ||||
\(994\) | −4.51228 | − | 2.11271i | −0.143121 | − | 0.0670110i | ||||
\(995\) | − | 12.0000i | − | 0.380426i | ||||||
\(996\) | 10.3680 | − | 18.0140i | 0.328523 | − | 0.570795i | ||||
\(997\) | 10.0000 | 0.316703 | 0.158352 | − | 0.987383i | \(-0.449382\pi\) | ||||
0.158352 | + | 0.987383i | \(0.449382\pi\) | |||||||
\(998\) | −3.24985 | + | 6.94097i | −0.102872 | + | 0.219713i | ||||
\(999\) | −8.27528 | − | 4.63068i | −0.261818 | − | 0.146508i |
(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 | 156.2.h.b.155.8 | yes | 16 | |
3.2 | odd | 2 | inner | 156.2.h.b.155.9 | yes | 16 | |
4.3 | odd | 2 | inner | 156.2.h.b.155.5 | ✓ | 16 | |
12.11 | even | 2 | inner | 156.2.h.b.155.12 | yes | 16 | |
13.12 | even | 2 | inner | 156.2.h.b.155.10 | yes | 16 | |
39.38 | odd | 2 | inner | 156.2.h.b.155.7 | yes | 16 | |
52.51 | odd | 2 | inner | 156.2.h.b.155.11 | yes | 16 | |
156.155 | even | 2 | inner | 156.2.h.b.155.6 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
156.2.h.b.155.5 | ✓ | 16 | 4.3 | odd | 2 | inner | |
156.2.h.b.155.6 | yes | 16 | 156.155 | even | 2 | inner | |
156.2.h.b.155.7 | yes | 16 | 39.38 | odd | 2 | inner | |
156.2.h.b.155.8 | yes | 16 | 1.1 | even | 1 | trivial | |
156.2.h.b.155.9 | yes | 16 | 3.2 | odd | 2 | inner | |
156.2.h.b.155.10 | yes | 16 | 13.12 | even | 2 | inner | |
156.2.h.b.155.11 | yes | 16 | 52.51 | odd | 2 | inner | |
156.2.h.b.155.12 | yes | 16 | 12.11 | even | 2 | inner |