Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1134,2,Mod(647,1134)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1134, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1134.647");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1134 = 2 \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1134.k (of order \(6\), degree \(2\), 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: | \(9.05503558921\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 52 x^{14} - 224 x^{13} + 796 x^{12} - 2228 x^{11} + 5254 x^{10} - 10232 x^{9} + \cdots + 225 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 971.5 | ||
Root | \(0.500000 - 1.42873i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1134.971 |
Dual form | 1134.2.k.d.647.5 |
$q$-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 \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | −0.894533 | + | 1.54938i | −0.400048 | + | 0.692903i | −0.993731 | − | 0.111796i | \(-0.964340\pi\) |
0.593684 | + | 0.804699i | \(0.297673\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.54252 | − | 0.731847i | 0.960982 | − | 0.276612i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.54938 | + | 0.894533i | −0.489956 | + | 0.282876i | ||||
\(11\) | 4.52838 | − | 2.61446i | 1.36536 | − | 0.788290i | 0.375027 | − | 0.927014i | \(-0.377633\pi\) |
0.990331 | + | 0.138724i | \(0.0443001\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.03863i | − | 1.39746i | −0.715383 | − | 0.698732i | \(-0.753748\pi\) | ||
0.715383 | − | 0.698732i | \(-0.246252\pi\) | |||||||
\(14\) | 2.56781 | + | 0.637461i | 0.686276 | + | 0.170369i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 1.13182 | + | 1.96037i | 0.274506 | + | 0.475458i | 0.970010 | − | 0.243063i | \(-0.0781523\pi\) |
−0.695504 | + | 0.718522i | \(0.744819\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.45534 | − | 1.99494i | −0.792709 | − | 0.457671i | 0.0482065 | − | 0.998837i | \(-0.484649\pi\) |
−0.840915 | + | 0.541167i | \(0.817983\pi\) | |||||||
\(20\) | −1.78907 | −0.400048 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.22892 | 1.11481 | ||||||||
\(23\) | 6.84102 | + | 3.94966i | 1.42645 | + | 0.823561i | 0.996839 | − | 0.0794524i | \(-0.0253172\pi\) |
0.429612 | + | 0.903014i | \(0.358650\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.899620 | + | 1.55819i | 0.179924 | + | 0.311637i | ||||
\(26\) | 2.51931 | − | 4.36358i | 0.494078 | − | 0.855769i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.90506 | + | 1.83596i | 0.360022 | + | 0.346964i | ||||
\(29\) | 3.38604i | 0.628772i | 0.949295 | + | 0.314386i | \(0.101799\pi\) | ||||
−0.949295 | + | 0.314386i | \(0.898201\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.73522 | − | 3.88858i | 1.20968 | − | 0.698410i | 0.246992 | − | 0.969017i | \(-0.420558\pi\) |
0.962690 | + | 0.270607i | \(0.0872245\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.26364i | 0.388210i | ||||||||
\(35\) | −1.14046 | + | 4.59398i | −0.192773 | + | 0.776525i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.74728 | + | 6.49047i | −0.616049 | + | 1.06703i | 0.374151 | + | 0.927368i | \(0.377934\pi\) |
−0.990200 | + | 0.139660i | \(0.955399\pi\) | |||||||
\(38\) | −1.99494 | − | 3.45534i | −0.323622 | − | 0.560530i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.54938 | − | 0.894533i | −0.244978 | − | 0.141438i | ||||
\(41\) | −9.03171 | −1.41052 | −0.705258 | − | 0.708951i | \(-0.749169\pi\) | ||||
−0.705258 | + | 0.708951i | \(0.749169\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.81060 | −1.34360 | −0.671802 | − | 0.740731i | \(-0.734479\pi\) | ||||
−0.671802 | + | 0.740731i | \(0.734479\pi\) | |||||||
\(44\) | 4.52838 | + | 2.61446i | 0.682679 | + | 0.394145i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.94966 | + | 6.84102i | 0.582346 | + | 1.00865i | ||||
\(47\) | 2.07085 | − | 3.58682i | 0.302064 | − | 0.523191i | −0.674539 | − | 0.738239i | \(-0.735658\pi\) |
0.976603 | + | 0.215048i | \(0.0689909\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.92880 | − | 3.72147i | 0.846972 | − | 0.531638i | ||||
\(50\) | 1.79924i | 0.254451i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.36358 | − | 2.51931i | 0.605120 | − | 0.349366i | ||||
\(53\) | −1.93277 | + | 1.11588i | −0.265486 | + | 0.153278i | −0.626834 | − | 0.779152i | \(-0.715650\pi\) |
0.361349 | + | 0.932431i | \(0.382316\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.35489i | 1.26141i | ||||||||
\(56\) | 0.731847 | + | 2.54252i | 0.0977971 | + | 0.339758i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.69302 | + | 2.93240i | −0.222304 | + | 0.385042i | ||||
\(59\) | 5.43025 | + | 9.40546i | 0.706958 | + | 1.22449i | 0.965980 | + | 0.258616i | \(0.0832663\pi\) |
−0.259023 | + | 0.965871i | \(0.583400\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.65589 | + | 2.11073i | 0.468089 | + | 0.270251i | 0.715440 | − | 0.698675i | \(-0.246226\pi\) |
−0.247350 | + | 0.968926i | \(0.579560\pi\) | |||||||
\(62\) | 7.77717 | 0.987701 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 7.80674 | + | 4.50722i | 0.968307 | + | 0.559052i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.705066 | − | 1.22121i | −0.0861376 | − | 0.149195i | 0.819738 | − | 0.572739i | \(-0.194119\pi\) |
−0.905875 | + | 0.423544i | \(0.860786\pi\) | |||||||
\(68\) | −1.13182 | + | 1.96037i | −0.137253 | + | 0.237729i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.28466 | + | 3.40827i | −0.392592 | + | 0.407367i | ||||
\(71\) | 2.11331i | 0.250804i | 0.992106 | + | 0.125402i | \(0.0400221\pi\) | ||||
−0.992106 | + | 0.125402i | \(0.959978\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.06851 | + | 2.34896i | −0.476184 | + | 0.274925i | −0.718825 | − | 0.695191i | \(-0.755320\pi\) |
0.242641 | + | 0.970116i | \(0.421986\pi\) | |||||||
\(74\) | −6.49047 | + | 3.74728i | −0.754502 | + | 0.435612i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 3.98988i | − | 0.457671i | ||||||
\(77\) | 9.60011 | − | 9.96140i | 1.09403 | − | 1.13521i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.53115 | − | 6.11613i | 0.397285 | − | 0.688119i | −0.596105 | − | 0.802907i | \(-0.703286\pi\) |
0.993390 | + | 0.114788i | \(0.0366190\pi\) | |||||||
\(80\) | −0.894533 | − | 1.54938i | −0.100012 | − | 0.173226i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −7.82169 | − | 4.51585i | −0.863761 | − | 0.498693i | ||||
\(83\) | 3.52907 | 0.387365 | 0.193683 | − | 0.981064i | \(-0.437957\pi\) | ||||
0.193683 | + | 0.981064i | \(0.437957\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.04979 | −0.439262 | ||||||||
\(86\) | −7.63021 | − | 4.40530i | −0.822786 | − | 0.475036i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.61446 | + | 4.52838i | 0.278703 | + | 0.482727i | ||||
\(89\) | −2.97335 | + | 5.15000i | −0.315175 | + | 0.545899i | −0.979475 | − | 0.201567i | \(-0.935396\pi\) |
0.664300 | + | 0.747466i | \(0.268730\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.68750 | − | 12.8108i | −0.386555 | − | 1.34294i | ||||
\(92\) | 7.89932i | 0.823561i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.58682 | − | 2.07085i | 0.369952 | − | 0.213592i | ||||
\(95\) | 6.18183 | − | 3.56908i | 0.634242 | − | 0.366180i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 19.3006i | − | 1.95968i | −0.199777 | − | 0.979841i | \(-0.564022\pi\) | ||
0.199777 | − | 0.979841i | \(-0.435978\pi\) | |||||||
\(98\) | 6.99523 | − | 0.258485i | 0.706625 | − | 0.0261109i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.899620 | + | 1.55819i | −0.0899620 | + | 0.155819i | ||||
\(101\) | −0.511479 | − | 0.885907i | −0.0508940 | − | 0.0881510i | 0.839456 | − | 0.543428i | \(-0.182874\pi\) |
−0.890350 | + | 0.455277i | \(0.849540\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.66075 | − | 5.00029i | −0.853369 | − | 0.492693i | 0.00841718 | − | 0.999965i | \(-0.497321\pi\) |
−0.861786 | + | 0.507272i | \(0.830654\pi\) | |||||||
\(104\) | 5.03863 | 0.494078 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.23177 | −0.216768 | ||||||||
\(107\) | 0.265236 | + | 0.153134i | 0.0256414 | + | 0.0148040i | 0.512766 | − | 0.858528i | \(-0.328621\pi\) |
−0.487125 | + | 0.873333i | \(0.661954\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.55347 | − | 2.69068i | −0.148795 | − | 0.257721i | 0.781987 | − | 0.623294i | \(-0.214206\pi\) |
−0.930782 | + | 0.365574i | \(0.880873\pi\) | |||||||
\(110\) | −4.67745 | + | 8.10158i | −0.445977 | + | 0.772455i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.637461 | + | 2.56781i | −0.0602344 | + | 0.242635i | ||||
\(113\) | 2.49935i | 0.235119i | 0.993066 | + | 0.117560i | \(0.0375071\pi\) | ||||
−0.993066 | + | 0.117560i | \(0.962493\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.2390 | + | 7.06621i | −1.14130 | + | 0.658927i | ||||
\(116\) | −2.93240 | + | 1.69302i | −0.272266 | + | 0.157193i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.8605i | 0.999789i | ||||||||
\(119\) | 4.31235 | + | 4.15595i | 0.395313 | + | 0.380975i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.17082 | − | 14.1523i | 0.742802 | − | 1.28657i | ||||
\(122\) | 2.11073 | + | 3.65589i | 0.191097 | + | 0.330989i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.73522 | + | 3.88858i | 0.604841 | + | 0.349205i | ||||
\(125\) | −12.1643 | −1.08801 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.26929 | 0.467574 | 0.233787 | − | 0.972288i | \(-0.424888\pi\) | ||||
0.233787 | + | 0.972288i | \(0.424888\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.50722 | + | 7.80674i | 0.395310 | + | 0.684696i | ||||
\(131\) | 4.16632 | − | 7.21628i | 0.364013 | − | 0.630489i | −0.624604 | − | 0.780941i | \(-0.714740\pi\) |
0.988617 | + | 0.150452i | \(0.0480730\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.2453 | − | 2.54339i | −0.888376 | − | 0.220540i | ||||
\(134\) | − | 1.41013i | − | 0.121817i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.96037 | + | 1.13182i | −0.168100 | + | 0.0970526i | ||||
\(137\) | 11.8291 | − | 6.82952i | 1.01063 | − | 0.583485i | 0.0992512 | − | 0.995062i | \(-0.468355\pi\) |
0.911375 | + | 0.411577i | \(0.135022\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.36383i | 0.539773i | 0.962892 | + | 0.269887i | \(0.0869863\pi\) | ||||
−0.962892 | + | 0.269887i | \(0.913014\pi\) | |||||||
\(140\) | −4.54874 | + | 1.30932i | −0.384438 | + | 0.110658i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.05666 | + | 1.83018i | −0.0886727 | + | 0.153586i | ||||
\(143\) | −13.1733 | − | 22.8168i | −1.10161 | − | 1.90804i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.24625 | − | 3.02892i | −0.435677 | − | 0.251539i | ||||
\(146\) | −4.69792 | −0.388802 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.49455 | −0.616049 | ||||||||
\(149\) | −14.9759 | − | 8.64636i | −1.22688 | − | 0.708337i | −0.260501 | − | 0.965474i | \(-0.583888\pi\) |
−0.966375 | + | 0.257137i | \(0.917221\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.12261 | + | 14.0688i | 0.661009 | + | 1.14490i | 0.980351 | + | 0.197261i | \(0.0632047\pi\) |
−0.319342 | + | 0.947639i | \(0.603462\pi\) | |||||||
\(152\) | 1.99494 | − | 3.45534i | 0.161811 | − | 0.280265i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 13.2946 | − | 3.82677i | 1.07131 | − | 0.308370i | ||||
\(155\) | 13.9139i | 1.11759i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.0877 | + | 9.86561i | −1.36375 | + | 0.787361i | −0.990121 | − | 0.140217i | \(-0.955220\pi\) |
−0.373629 | + | 0.927578i | \(0.621887\pi\) | |||||||
\(158\) | 6.11613 | − | 3.53115i | 0.486573 | − | 0.280923i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 1.78907i | − | 0.141438i | ||||||
\(161\) | 20.2840 | + | 5.03551i | 1.59860 | + | 0.396854i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.61394 | − | 11.4557i | 0.518043 | − | 0.897277i | −0.481737 | − | 0.876316i | \(-0.659994\pi\) |
0.999780 | − | 0.0209616i | \(-0.00667277\pi\) | |||||||
\(164\) | −4.51585 | − | 7.82169i | −0.352629 | − | 0.610771i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.05626 | + | 1.76453i | 0.237212 | + | 0.136954i | ||||
\(167\) | −13.8250 | −1.06981 | −0.534905 | − | 0.844912i | \(-0.679653\pi\) | ||||
−0.534905 | + | 0.844912i | \(0.679653\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.3878 | −0.952906 | ||||||||
\(170\) | −3.50723 | − | 2.02490i | −0.268992 | − | 0.155303i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.40530 | − | 7.63021i | −0.335901 | − | 0.581798i | ||||
\(173\) | 4.99869 | − | 8.65798i | 0.380043 | − | 0.658254i | −0.611025 | − | 0.791611i | \(-0.709242\pi\) |
0.991068 | + | 0.133357i | \(0.0425758\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.42765 | + | 3.30334i | 0.259106 | + | 0.249709i | ||||
\(176\) | 5.22892i | 0.394145i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.15000 | + | 2.97335i | −0.386009 | + | 0.222862i | ||||
\(179\) | −13.0876 | + | 7.55610i | −0.978209 | + | 0.564769i | −0.901729 | − | 0.432302i | \(-0.857702\pi\) |
−0.0764804 | + | 0.997071i | \(0.524368\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 16.6235i | − | 1.23562i | −0.786329 | − | 0.617808i | \(-0.788021\pi\) | ||
0.786329 | − | 0.617808i | \(-0.211979\pi\) | |||||||
\(182\) | 3.21193 | − | 12.9382i | 0.238084 | − | 0.959046i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.94966 | + | 6.84102i | −0.291173 | + | 0.504326i | ||||
\(185\) | −6.70413 | − | 11.6119i | −0.492897 | − | 0.853723i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.2506 | + | 5.91819i | 0.749598 | + | 0.432781i | ||||
\(188\) | 4.14170 | 0.302064 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 7.13816 | 0.517857 | ||||||||
\(191\) | −17.3858 | − | 10.0377i | −1.25799 | − | 0.726302i | −0.285308 | − | 0.958436i | \(-0.592096\pi\) |
−0.972684 | + | 0.232134i | \(0.925429\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.34219 | + | 4.05680i | 0.168595 | + | 0.292015i | 0.937926 | − | 0.346835i | \(-0.112744\pi\) |
−0.769331 | + | 0.638850i | \(0.779410\pi\) | |||||||
\(194\) | 9.65032 | − | 16.7148i | 0.692852 | − | 1.20006i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.18729 | + | 3.27376i | 0.441949 | + | 0.233840i | ||||
\(197\) | 12.0673i | 0.859760i | 0.902886 | + | 0.429880i | \(0.141444\pi\) | ||||
−0.902886 | + | 0.429880i | \(0.858556\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.9506 | + | 11.5185i | −1.41426 | + | 0.816524i | −0.995786 | − | 0.0917037i | \(-0.970769\pi\) |
−0.418475 | + | 0.908228i | \(0.637435\pi\) | |||||||
\(200\) | −1.55819 | + | 0.899620i | −0.110180 | + | 0.0636127i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 1.02296i | − | 0.0719750i | ||||||
\(203\) | 2.47806 | + | 8.60907i | 0.173926 | + | 0.604238i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.07917 | − | 13.9935i | 0.564273 | − | 0.977350i | ||||
\(206\) | −5.00029 | − | 8.66075i | −0.348386 | − | 0.603423i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.36358 | + | 2.51931i | 0.302560 | + | 0.174683i | ||||
\(209\) | −20.8628 | −1.44311 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.4011 | −1.54215 | −0.771076 | − | 0.636743i | \(-0.780281\pi\) | ||||
−0.771076 | + | 0.636743i | \(0.780281\pi\) | |||||||
\(212\) | −1.93277 | − | 1.11588i | −0.132743 | − | 0.0766392i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.153134 | + | 0.265236i | 0.0104680 | + | 0.0181312i | ||||
\(215\) | 7.88138 | − | 13.6509i | 0.537506 | − | 0.930987i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.2786 | − | 14.8159i | 0.969294 | − | 1.00577i | ||||
\(218\) | − | 3.10693i | − | 0.210428i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −8.10158 | + | 4.67745i | −0.546208 | + | 0.315353i | ||||
\(221\) | 9.87755 | − | 5.70281i | 0.664436 | − | 0.383612i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 9.99069i | − | 0.669026i | −0.942391 | − | 0.334513i | \(-0.891428\pi\) | ||
0.942391 | − | 0.334513i | \(-0.108572\pi\) | |||||||
\(224\) | −1.83596 | + | 1.90506i | −0.122670 | + | 0.127287i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.24968 | + | 2.16450i | −0.0831272 | + | 0.143981i | ||||
\(227\) | −1.59918 | − | 2.76985i | −0.106141 | − | 0.183842i | 0.808063 | − | 0.589096i | \(-0.200516\pi\) |
−0.914204 | + | 0.405255i | \(0.867183\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.6832 | + | 8.47736i | 0.970294 | + | 0.560200i | 0.899326 | − | 0.437279i | \(-0.144058\pi\) |
0.0709683 | + | 0.997479i | \(0.477391\pi\) | |||||||
\(230\) | −14.1324 | −0.931864 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.38604 | −0.222304 | ||||||||
\(233\) | 7.24714 | + | 4.18414i | 0.474776 | + | 0.274112i | 0.718237 | − | 0.695799i | \(-0.244949\pi\) |
−0.243461 | + | 0.969911i | \(0.578283\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.70489 | + | 6.41705i | 0.241680 | + | 0.418602i | ||||
\(236\) | −5.43025 | + | 9.40546i | −0.353479 | + | 0.612243i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.65663 | + | 5.75533i | 0.107384 | + | 0.373063i | ||||
\(239\) | 13.6753i | 0.884581i | 0.896872 | + | 0.442290i | \(0.145834\pi\) | ||||
−0.896872 | + | 0.442290i | \(0.854166\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.5782 | − | 13.0355i | 1.45439 | − | 0.839692i | 0.455664 | − | 0.890152i | \(-0.349402\pi\) |
0.998726 | + | 0.0504597i | \(0.0160687\pi\) | |||||||
\(242\) | 14.1523 | − | 8.17082i | 0.909742 | − | 0.525240i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.22146i | 0.270251i | ||||||||
\(245\) | 0.462447 | + | 12.5149i | 0.0295446 | + | 0.799549i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.0518 | + | 17.4102i | −0.639578 | + | 1.10778i | ||||
\(248\) | 3.88858 | + | 6.73522i | 0.246925 | + | 0.427687i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −10.5346 | − | 6.08215i | −0.666266 | − | 0.384669i | ||||
\(251\) | −15.2554 | −0.962913 | −0.481456 | − | 0.876470i | \(-0.659892\pi\) | ||||
−0.481456 | + | 0.876470i | \(0.659892\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 41.3050 | 2.59682 | ||||||||
\(254\) | 4.56334 | + | 2.63465i | 0.286330 | + | 0.165312i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −11.5586 | + | 20.0200i | −0.721004 | + | 1.24882i | 0.239593 | + | 0.970873i | \(0.422986\pi\) |
−0.960598 | + | 0.277943i | \(0.910347\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.77749 | + | 19.2446i | −0.296859 | + | 1.19580i | ||||
\(260\) | 9.01444i | 0.559052i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 7.21628 | − | 4.16632i | 0.445823 | − | 0.257396i | ||||
\(263\) | −13.8951 | + | 8.02232i | −0.856806 | + | 0.494677i | −0.862942 | − | 0.505304i | \(-0.831380\pi\) |
0.00613517 | + | 0.999981i | \(0.498047\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 3.99278i | − | 0.245274i | ||||||
\(266\) | −7.60095 | − | 7.32527i | −0.466044 | − | 0.449141i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.705066 | − | 1.22121i | 0.0430688 | − | 0.0745973i | ||||
\(269\) | −2.80639 | − | 4.86081i | −0.171109 | − | 0.296369i | 0.767699 | − | 0.640811i | \(-0.221402\pi\) |
−0.938808 | + | 0.344442i | \(0.888068\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.94080 | − | 2.85257i | −0.300132 | − | 0.173281i | 0.342370 | − | 0.939565i | \(-0.388770\pi\) |
−0.642502 | + | 0.766284i | \(0.722104\pi\) | |||||||
\(272\) | −2.26364 | −0.137253 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 13.6590 | 0.825173 | ||||||||
\(275\) | 8.14764 | + | 4.70404i | 0.491321 | + | 0.283664i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.40114 | + | 5.89094i | 0.204355 | + | 0.353953i | 0.949927 | − | 0.312472i | \(-0.101157\pi\) |
−0.745572 | + | 0.666425i | \(0.767824\pi\) | |||||||
\(278\) | −3.18192 | + | 5.51124i | −0.190839 | + | 0.330542i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4.59398 | − | 1.14046i | −0.274543 | − | 0.0681556i | ||||
\(281\) | − | 29.5436i | − | 1.76243i | −0.472720 | − | 0.881213i | \(-0.656728\pi\) | ||
0.472720 | − | 0.881213i | \(-0.343272\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.27866 | + | 4.77969i | −0.492115 | + | 0.284123i | −0.725452 | − | 0.688273i | \(-0.758369\pi\) |
0.233336 | + | 0.972396i | \(0.425036\pi\) | |||||||
\(284\) | −1.83018 | + | 1.05666i | −0.108601 | + | 0.0627011i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 26.3466i | − | 1.55791i | ||||||
\(287\) | −22.9633 | + | 6.60983i | −1.35548 | + | 0.390166i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.93798 | − | 10.2849i | 0.349293 | − | 0.604993i | ||||
\(290\) | −3.02892 | − | 5.24625i | −0.177865 | − | 0.308070i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.06851 | − | 2.34896i | −0.238092 | − | 0.137462i | ||||
\(293\) | −24.9693 | −1.45872 | −0.729360 | − | 0.684130i | \(-0.760182\pi\) | ||||
−0.729360 | + | 0.684130i | \(0.760182\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −19.4301 | −1.13127 | ||||||||
\(296\) | −6.49047 | − | 3.74728i | −0.377251 | − | 0.217806i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −8.64636 | − | 14.9759i | −0.500870 | − | 0.867532i | ||||
\(299\) | 19.9009 | − | 34.4693i | 1.15090 | − | 1.99341i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −22.4011 | + | 6.44801i | −1.29118 | + | 0.371657i | ||||
\(302\) | 16.2452i | 0.934808i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.45534 | − | 1.99494i | 0.198177 | − | 0.114418i | ||||
\(305\) | −6.54064 | + | 3.77624i | −0.374516 | + | 0.216227i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 29.7991i | 1.70072i | 0.526199 | + | 0.850362i | \(0.323617\pi\) | ||||
−0.526199 | + | 0.850362i | \(0.676383\pi\) | |||||||
\(308\) | 13.4269 | + | 3.33324i | 0.765067 | + | 0.189929i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6.95694 | + | 12.0498i | −0.395127 | + | 0.684381i | ||||
\(311\) | −6.16702 | − | 10.6816i | −0.349700 | − | 0.605697i | 0.636496 | − | 0.771280i | \(-0.280383\pi\) |
−0.986196 | + | 0.165582i | \(0.947050\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.5823 | + | 11.8832i | 1.16338 | + | 0.671678i | 0.952112 | − | 0.305750i | \(-0.0989073\pi\) |
0.211268 | + | 0.977428i | \(0.432241\pi\) | |||||||
\(314\) | −19.7312 | −1.11350 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.06230 | 0.397285 | ||||||||
\(317\) | −13.5850 | − | 7.84330i | −0.763009 | − | 0.440524i | 0.0673660 | − | 0.997728i | \(-0.478540\pi\) |
−0.830375 | + | 0.557205i | \(0.811874\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.85267 | + | 15.3333i | 0.495654 | + | 0.858498i | ||||
\(320\) | 0.894533 | − | 1.54938i | 0.0500059 | − | 0.0866128i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 15.0487 | + | 14.5029i | 0.838629 | + | 0.808213i | ||||
\(323\) | − | 9.03163i | − | 0.502534i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.85113 | − | 4.53285i | 0.435502 | − | 0.251437i | ||||
\(326\) | 11.4557 | − | 6.61394i | 0.634471 | − | 0.366312i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 9.03171i | − | 0.498693i | ||||||
\(329\) | 2.64017 | − | 10.6351i | 0.145557 | − | 0.586331i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.228762 | − | 0.396228i | 0.0125739 | − | 0.0217787i | −0.859670 | − | 0.510850i | \(-0.829331\pi\) |
0.872244 | + | 0.489071i | \(0.162664\pi\) | |||||||
\(332\) | 1.76453 | + | 3.05626i | 0.0968413 | + | 0.167734i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −11.9728 | − | 6.91250i | −0.655123 | − | 0.378235i | ||||
\(335\) | 2.52282 | 0.137836 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.8429 | 1.35328 | 0.676640 | − | 0.736314i | \(-0.263435\pi\) | ||||
0.676640 | + | 0.736314i | \(0.263435\pi\) | |||||||
\(338\) | −10.7281 | − | 6.19389i | −0.583533 | − | 0.336903i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.02490 | − | 3.50723i | −0.109815 | − | 0.190206i | ||||
\(341\) | 20.3331 | − | 35.2180i | 1.10110 | − | 1.90716i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.3505 | − | 13.8009i | 0.666867 | − | 0.745177i | ||||
\(344\) | − | 8.81060i | − | 0.475036i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.65798 | − | 4.99869i | 0.465456 | − | 0.268731i | ||||
\(347\) | 18.9446 | − | 10.9377i | 1.01700 | − | 0.587165i | 0.103766 | − | 0.994602i | \(-0.466911\pi\) |
0.913233 | + | 0.407437i | \(0.133577\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.272742i | 0.0145995i | 0.999973 | + | 0.00729976i | \(0.00232361\pi\) | ||||
−0.999973 | + | 0.00729976i | \(0.997676\pi\) | |||||||
\(350\) | 1.31677 | + | 4.57460i | 0.0703842 | + | 0.244523i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.61446 | + | 4.52838i | −0.139351 | + | 0.241363i | ||||
\(353\) | 7.59242 | + | 13.1504i | 0.404103 | + | 0.699928i | 0.994217 | − | 0.107393i | \(-0.0342502\pi\) |
−0.590113 | + | 0.807321i | \(0.700917\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.27432 | − | 1.89043i | −0.173783 | − | 0.100334i | ||||
\(356\) | −5.94671 | −0.315175 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −15.1122 | −0.798705 | ||||||||
\(359\) | −19.3894 | − | 11.1944i | −1.02333 | − | 0.590820i | −0.108264 | − | 0.994122i | \(-0.534529\pi\) |
−0.915067 | + | 0.403302i | \(0.867862\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.54043 | − | 2.66810i | −0.0810751 | − | 0.140426i | ||||
\(362\) | 8.31176 | − | 14.3964i | 0.436856 | − | 0.756657i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 9.25073 | − | 9.59888i | 0.484870 | − | 0.503118i | ||||
\(365\) | − | 8.40489i | − | 0.439932i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.17856 | + | 0.680440i | −0.0615202 | + | 0.0355187i | −0.530445 | − | 0.847720i | \(-0.677975\pi\) |
0.468924 | + | 0.883238i | \(0.344642\pi\) | |||||||
\(368\) | −6.84102 | + | 3.94966i | −0.356613 | + | 0.205890i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 13.4083i | − | 0.697062i | ||||||
\(371\) | −4.09744 | + | 4.25164i | −0.212728 | + | 0.220734i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.8820 | − | 22.3123i | 0.667006 | − | 1.15529i | −0.311731 | − | 0.950170i | \(-0.600909\pi\) |
0.978737 | − | 0.205118i | \(-0.0657578\pi\) | |||||||
\(374\) | 5.91819 | + | 10.2506i | 0.306022 | + | 0.530046i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.58682 | + | 2.07085i | 0.184976 | + | 0.106796i | ||||
\(377\) | 17.0610 | 0.878686 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.5945 | 0.544201 | 0.272101 | − | 0.962269i | \(-0.412282\pi\) | ||||
0.272101 | + | 0.962269i | \(0.412282\pi\) | |||||||
\(380\) | 6.18183 | + | 3.56908i | 0.317121 | + | 0.183090i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −10.0377 | − | 17.3858i | −0.513573 | − | 0.889534i | ||||
\(383\) | −5.60081 | + | 9.70088i | −0.286188 | + | 0.495692i | −0.972897 | − | 0.231241i | \(-0.925721\pi\) |
0.686709 | + | 0.726933i | \(0.259055\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.84635 | + | 23.7850i | 0.348922 | + | 1.21220i | ||||
\(386\) | 4.68438i | 0.238429i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 16.7148 | − | 9.65032i | 0.848568 | − | 0.489921i | ||||
\(389\) | −17.1324 | + | 9.89141i | −0.868648 | + | 0.501514i | −0.866899 | − | 0.498484i | \(-0.833890\pi\) |
−0.00174936 | + | 0.999998i | \(0.500557\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17.8812i | 0.904290i | ||||||||
\(392\) | 3.72147 | + | 5.92880i | 0.187962 | + | 0.299450i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6.03365 | + | 10.4506i | −0.303971 | + | 0.526493i | ||||
\(395\) | 6.31746 | + | 10.9422i | 0.317866 | + | 0.550560i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −28.1940 | − | 16.2778i | −1.41502 | − | 0.816959i | −0.419160 | − | 0.907912i | \(-0.637675\pi\) |
−0.995855 | + | 0.0909529i | \(0.971009\pi\) | |||||||
\(398\) | −23.0370 | −1.15474 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.79924 | −0.0899620 | ||||||||
\(401\) | 25.6068 | + | 14.7841i | 1.27874 | + | 0.738282i | 0.976617 | − | 0.214987i | \(-0.0689708\pi\) |
0.302125 | + | 0.953268i | \(0.402304\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −19.5931 | − | 33.9363i | −0.976003 | − | 1.69049i | ||||
\(404\) | 0.511479 | − | 0.885907i | 0.0254470 | − | 0.0440755i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.15847 | + | 8.69470i | −0.107123 | + | 0.431511i | ||||
\(407\) | 39.1884i | 1.94250i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.70610 | + | 2.71707i | −0.232702 | + | 0.134350i | −0.611818 | − | 0.790999i | \(-0.709561\pi\) |
0.379116 | + | 0.925349i | \(0.376228\pi\) | |||||||
\(410\) | 13.9935 | − | 8.07917i | 0.691091 | − | 0.399002i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 10.0006i | − | 0.492693i | ||||||
\(413\) | 20.6899 | + | 19.9395i | 1.01808 | + | 0.981156i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.15687 | + | 5.46785i | −0.154965 | + | 0.268406i | ||||
\(416\) | 2.51931 | + | 4.36358i | 0.123520 | + | 0.213942i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −18.0677 | − | 10.4314i | −0.883720 | − | 0.510216i | ||||
\(419\) | −4.37591 | −0.213777 | −0.106888 | − | 0.994271i | \(-0.534089\pi\) | ||||
−0.106888 | + | 0.994271i | \(0.534089\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.34954 | −0.358195 | −0.179097 | − | 0.983831i | \(-0.557318\pi\) | ||||
−0.179097 | + | 0.983831i | \(0.557318\pi\) | |||||||
\(422\) | −19.3999 | − | 11.2005i | −0.944372 | − | 0.545233i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.11588 | − | 1.93277i | −0.0541921 | − | 0.0938634i | ||||
\(425\) | −2.03641 | + | 3.52717i | −0.0987804 | + | 0.171093i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.8399 | + | 2.69102i | 0.524580 | + | 0.130228i | ||||
\(428\) | 0.306268i | 0.0148040i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 13.6509 | − | 7.88138i | 0.658307 | − | 0.380074i | ||||
\(431\) | 26.3948 | − | 15.2390i | 1.27139 | − | 0.734038i | 0.296142 | − | 0.955144i | \(-0.404300\pi\) |
0.975250 | + | 0.221106i | \(0.0709666\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 27.8980i | 1.34069i | 0.742048 | + | 0.670347i | \(0.233855\pi\) | ||||
−0.742048 | + | 0.670347i | \(0.766145\pi\) | |||||||
\(434\) | 19.7736 | − | 5.69169i | 0.949163 | − | 0.273210i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.55347 | − | 2.69068i | 0.0743975 | − | 0.128860i | ||||
\(437\) | −15.7587 | − | 27.2948i | −0.753840 | − | 1.30569i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.92025 | + | 4.57276i | 0.378013 | + | 0.218246i | 0.676953 | − | 0.736026i | \(-0.263300\pi\) |
−0.298941 | + | 0.954272i | \(0.596633\pi\) | |||||||
\(440\) | −9.35489 | −0.445977 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 11.4056 | 0.542510 | ||||||||
\(443\) | −18.9603 | − | 10.9467i | −0.900831 | − | 0.520095i | −0.0233611 | − | 0.999727i | \(-0.507437\pi\) |
−0.877470 | + | 0.479632i | \(0.840770\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.31953 | − | 9.21369i | −0.252170 | − | 0.436771i | ||||
\(446\) | 4.99534 | − | 8.65219i | 0.236536 | − | 0.409693i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.54252 | + | 0.731847i | −0.120123 | + | 0.0345765i | ||||
\(449\) | 20.8625i | 0.984564i | 0.870436 | + | 0.492282i | \(0.163837\pi\) | ||||
−0.870436 | + | 0.492282i | \(0.836163\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −40.8990 | + | 23.6131i | −1.92586 | + | 1.11190i | ||||
\(452\) | −2.16450 | + | 1.24968i | −0.101810 | + | 0.0587798i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 3.19835i | − | 0.150106i | ||||||
\(455\) | 23.1474 | + | 5.74636i | 1.08517 | + | 0.269394i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.96173 | + | 6.86192i | −0.185322 | + | 0.320987i | −0.943685 | − | 0.330845i | \(-0.892666\pi\) |
0.758363 | + | 0.651832i | \(0.225999\pi\) | |||||||
\(458\) | 8.47736 | + | 14.6832i | 0.396121 | + | 0.686102i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −12.2390 | − | 7.06621i | −0.570648 | − | 0.329464i | ||||
\(461\) | 9.06227 | 0.422072 | 0.211036 | − | 0.977478i | \(-0.432316\pi\) | ||||
0.211036 | + | 0.977478i | \(0.432316\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.499886 | −0.0232317 | −0.0116158 | − | 0.999933i | \(-0.503698\pi\) | ||||
−0.0116158 | + | 0.999933i | \(0.503698\pi\) | |||||||
\(464\) | −2.93240 | − | 1.69302i | −0.136133 | − | 0.0785964i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.18414 | + | 7.24714i | 0.193826 | + | 0.335717i | ||||
\(467\) | 0.804921 | − | 1.39416i | 0.0372473 | − | 0.0645142i | −0.846801 | − | 0.531910i | \(-0.821474\pi\) |
0.884048 | + | 0.467396i | \(0.154808\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.68638 | − | 2.58895i | −0.124046 | − | 0.119547i | ||||
\(470\) | 7.40977i | 0.341787i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −9.40546 | + | 5.43025i | −0.432921 | + | 0.249947i | ||||
\(473\) | −39.8978 | + | 23.0350i | −1.83450 | + | 1.05915i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 7.17875i | − | 0.329384i | ||||||
\(476\) | −1.44298 | + | 5.81258i | −0.0661389 | + | 0.266419i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6.83764 | + | 11.8431i | −0.312747 | + | 0.541693i | ||||
\(479\) | 3.26795 | + | 5.66026i | 0.149317 | + | 0.258624i | 0.930975 | − | 0.365083i | \(-0.118959\pi\) |
−0.781658 | + | 0.623707i | \(0.785626\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 32.7031 | + | 18.8811i | 1.49113 | + | 0.860906i | ||||
\(482\) | 26.0711 | 1.18750 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 16.3416 | 0.742802 | ||||||||
\(485\) | 29.9040 | + | 17.2651i | 1.35787 | + | 0.783966i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.57311 | + | 2.72470i | 0.0712844 | + | 0.123468i | 0.899464 | − | 0.436994i | \(-0.143957\pi\) |
−0.828180 | + | 0.560462i | \(0.810624\pi\) | |||||||
\(488\) | −2.11073 | + | 3.65589i | −0.0955483 | + | 0.165495i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −5.85697 | + | 11.0695i | −0.264591 | + | 0.500068i | ||||
\(491\) | 25.6076i | 1.15566i | 0.816158 | + | 0.577828i | \(0.196100\pi\) | ||||
−0.816158 | + | 0.577828i | \(0.803900\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.63787 | + | 3.83238i | −0.298955 | + | 0.172602i | ||||
\(494\) | −17.4102 | + | 10.0518i | −0.783320 | + | 0.452250i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.77717i | 0.349205i | ||||||||
\(497\) | 1.54662 | + | 5.37314i | 0.0693755 | + | 0.241018i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.35305 | − | 9.27176i | 0.239635 | − | 0.415061i | −0.720974 | − | 0.692962i | \(-0.756305\pi\) |
0.960610 | + | 0.277901i | \(0.0896387\pi\) | |||||||
\(500\) | −6.08215 | − | 10.5346i | −0.272002 | − | 0.471121i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −13.2116 | − | 7.62770i | −0.589661 | − | 0.340441i | ||||
\(503\) | 22.4205 | 0.999681 | 0.499840 | − | 0.866118i | \(-0.333392\pi\) | ||||
0.499840 | + | 0.866118i | \(0.333392\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.83014 | 0.0814401 | ||||||||
\(506\) | 35.7711 | + | 20.6525i | 1.59022 | + | 0.918115i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.63465 | + | 4.56334i | 0.116894 | + | 0.202466i | ||||
\(509\) | 19.5614 | − | 33.8814i | 0.867045 | − | 1.50177i | 0.00204257 | − | 0.999998i | \(-0.499350\pi\) |
0.865002 | − | 0.501768i | \(-0.167317\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.62520 | + | 8.94980i | −0.381556 | + | 0.395916i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −20.0200 | + | 11.5586i | −0.883046 | + | 0.509827i | ||||
\(515\) | 15.4947 | − | 8.94585i | 0.682776 | − | 0.394201i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 21.6566i | − | 0.952457i | ||||||
\(518\) | −13.7597 | + | 14.2776i | −0.604567 | + | 0.627320i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.50722 | + | 7.80674i | −0.197655 | + | 0.342348i | ||||
\(521\) | −0.205750 | − | 0.356370i | −0.00901408 | − | 0.0156128i | 0.861483 | − | 0.507786i | \(-0.169536\pi\) |
−0.870497 | + | 0.492173i | \(0.836203\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.69723 | + | 1.55725i | 0.117942 | + | 0.0680936i | 0.557810 | − | 0.829969i | \(-0.311642\pi\) |
−0.439869 | + | 0.898062i | \(0.644975\pi\) | |||||||
\(524\) | 8.33264 | 0.364013 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −16.0446 | −0.699579 | ||||||||
\(527\) | 15.2461 | + | 8.80233i | 0.664130 | + | 0.383436i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.6997 | + | 34.1208i | 0.856507 | + | 1.48351i | ||||
\(530\) | 1.99639 | − | 3.45785i | 0.0867176 | − | 0.150199i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.91998 | − | 10.1443i | −0.126597 | − | 0.439813i | ||||
\(533\) | 45.5074i | 1.97115i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.474525 | + | 0.273967i | −0.0205155 | + | 0.0118446i | ||||
\(536\) | 1.22121 | − | 0.705066i | 0.0527483 | − | 0.0304542i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 5.61279i | − | 0.241984i | ||||||
\(539\) | 17.1182 | − | 32.3528i | 0.737334 | − | 1.39354i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.540066 | + | 0.935422i | −0.0232193 | + | 0.0402170i | −0.877402 | − | 0.479757i | \(-0.840725\pi\) |
0.854182 | + | 0.519974i | \(0.174058\pi\) | |||||||
\(542\) | −2.85257 | − | 4.94080i | −0.122528 | − | 0.212225i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.96037 | − | 1.13182i | −0.0840500 | − | 0.0485263i | ||||
\(545\) | 5.55851 | 0.238100 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.9053 | 0.680060 | 0.340030 | − | 0.940415i | \(-0.389563\pi\) | ||||
0.340030 | + | 0.940415i | \(0.389563\pi\) | |||||||
\(548\) | 11.8291 | + | 6.82952i | 0.505313 | + | 0.291743i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4.70404 | + | 8.14764i | 0.200581 | + | 0.347417i | ||||
\(551\) | 6.75494 | − | 11.6999i | 0.287770 | − | 0.498433i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.50194 | − | 18.1346i | 0.191442 | − | 0.771163i | ||||
\(554\) | 6.80228i | 0.289001i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.51124 | + | 3.18192i | −0.233729 | + | 0.134943i | ||||
\(557\) | 24.2503 | − | 14.0009i | 1.02752 | − | 0.593238i | 0.111245 | − | 0.993793i | \(-0.464516\pi\) |
0.916273 | + | 0.400555i | \(0.131183\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 44.3934i | 1.87764i | ||||||||
\(560\) | −3.40827 | − | 3.28466i | −0.144026 | − | 0.138802i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 14.7718 | − | 25.5855i | 0.623111 | − | 1.07926i | ||||
\(563\) | −1.23558 | − | 2.14008i | −0.0520734 | − | 0.0901938i | 0.838814 | − | 0.544419i | \(-0.183250\pi\) |
−0.890887 | + | 0.454225i | \(0.849916\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.87244 | − | 2.23575i | −0.162915 | − | 0.0940589i | ||||
\(566\) | −9.55937 | −0.401810 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.11331 | −0.0886727 | ||||||||
\(569\) | −13.1647 | − | 7.60064i | −0.551892 | − | 0.318635i | 0.197993 | − | 0.980204i | \(-0.436558\pi\) |
−0.749885 | + | 0.661568i | \(0.769891\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.754880 | + | 1.30749i | 0.0315907 | + | 0.0547168i | 0.881389 | − | 0.472392i | \(-0.156609\pi\) |
−0.849798 | + | 0.527109i | \(0.823276\pi\) | |||||||
\(572\) | 13.1733 | − | 22.8168i | 0.550803 | − | 0.954019i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −23.1917 | − | 5.75737i | −0.968003 | − | 0.240308i | ||||
\(575\) | 14.2128i | 0.592714i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.5521 | + | 8.40169i | −0.605814 | + | 0.349767i | −0.771325 | − | 0.636441i | \(-0.780406\pi\) |
0.165511 | + | 0.986208i | \(0.447073\pi\) | |||||||
\(578\) | 10.2849 | − | 5.93798i | 0.427795 | − | 0.246987i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 6.05785i | − | 0.251539i | ||||||
\(581\) | 8.97271 | − | 2.58273i | 0.372251 | − | 0.107150i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.83487 | + | 10.1063i | −0.241655 | + | 0.418560i | ||||
\(584\) | −2.34896 | − | 4.06851i | −0.0972006 | − | 0.168356i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −21.6240 | − | 12.4846i | −0.893280 | − | 0.515735i | ||||
\(587\) | −44.4505 | −1.83467 | −0.917334 | − | 0.398118i | \(-0.869663\pi\) | ||||
−0.917334 | + | 0.398118i | \(0.869663\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −31.0300 | −1.27857 | ||||||||
\(590\) | −16.8270 | − | 9.71507i | −0.692757 | − | 0.399963i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.74728 | − | 6.49047i | −0.154012 | − | 0.266757i | ||||
\(593\) | −14.2575 | + | 24.6947i | −0.585485 | + | 1.01409i | 0.409330 | + | 0.912386i | \(0.365762\pi\) |
−0.994815 | + | 0.101703i | \(0.967571\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.2967 | + | 2.96383i | −0.422123 | + | 0.121505i | ||||
\(596\) | − | 17.2927i | − | 0.708337i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 34.4693 | − | 19.9009i | 1.40956 | − | 0.813807i | ||||
\(599\) | 18.0679 | − | 10.4315i | 0.738235 | − | 0.426220i | −0.0831923 | − | 0.996534i | \(-0.526512\pi\) |
0.821427 | + | 0.570313i | \(0.193178\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 35.7447i | − | 1.45806i | −0.684483 | − | 0.729029i | \(-0.739972\pi\) | ||
0.684483 | − | 0.729029i | \(-0.260028\pi\) | |||||||
\(602\) | −22.6239 | − | 5.61642i | −0.922083 | − | 0.228908i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8.12261 | + | 14.0688i | −0.330504 | + | 0.572450i | ||||
\(605\) | 14.6181 | + | 25.3194i | 0.594312 | + | 1.02938i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.76417 | + | 2.75060i | 0.193372 | + | 0.111643i | 0.593560 | − | 0.804790i | \(-0.297722\pi\) |
−0.400188 | + | 0.916433i | \(0.631055\pi\) | |||||||
\(608\) | 3.98988 | 0.161811 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −7.55248 | −0.305791 | ||||||||
\(611\) | −18.0726 | − | 10.4342i | −0.731140 | − | 0.422124i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.13512 | − | 12.3584i | −0.288185 | − | 0.499150i | 0.685192 | − | 0.728363i | \(-0.259718\pi\) |
−0.973376 | + | 0.229212i | \(0.926385\pi\) | |||||||
\(614\) | −14.8995 | + | 25.8068i | −0.601296 | + | 1.04148i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 9.96140 | + | 9.60011i | 0.401356 | + | 0.386799i | ||||
\(617\) | 7.84352i | 0.315768i | 0.987458 | + | 0.157884i | \(0.0504672\pi\) | ||||
−0.987458 | + | 0.157884i | \(0.949533\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.3512 | + | 8.86301i | −0.617016 | + | 0.356235i | −0.775706 | − | 0.631094i | \(-0.782606\pi\) |
0.158690 | + | 0.987328i | \(0.449273\pi\) | |||||||
\(620\) | −12.0498 | + | 6.95694i | −0.483930 | + | 0.279397i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 12.3340i | − | 0.494550i | ||||||
\(623\) | −3.79080 | + | 15.2700i | −0.151875 | + | 0.611780i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.38327 | − | 11.0561i | 0.255331 | − | 0.442246i | ||||
\(626\) | 11.8832 | + | 20.5823i | 0.474948 | + | 0.822634i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −17.0877 | − | 9.86561i | −0.681875 | − | 0.393681i | ||||
\(629\) | −16.9649 | −0.676436 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.3165 | −0.530121 | −0.265060 | − | 0.964232i | \(-0.585392\pi\) | ||||
−0.265060 | + | 0.964232i | \(0.585392\pi\) | |||||||
\(632\) | 6.11613 | + | 3.53115i | 0.243287 | + | 0.140462i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −7.84330 | − | 13.5850i | −0.311497 | − | 0.539529i | ||||
\(635\) | −4.71356 | + | 8.16412i | −0.187052 | + | 0.323983i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −18.7511 | − | 29.8730i | −0.742945 | − | 1.18361i | ||||
\(638\) | 17.7053i | 0.700961i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.54938 | − | 0.894533i | 0.0612445 | − | 0.0353595i | ||||
\(641\) | −4.68708 | + | 2.70609i | −0.185128 | + | 0.106884i | −0.589700 | − | 0.807622i | \(-0.700754\pi\) |
0.404572 | + | 0.914506i | \(0.367421\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.48634i | 0.0586156i | 0.999570 | + | 0.0293078i | \(0.00933030\pi\) | ||||
−0.999570 | + | 0.0293078i | \(0.990670\pi\) | |||||||
\(644\) | 5.78109 | + | 20.0842i | 0.227807 | + | 0.791427i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.51582 | − | 7.82162i | 0.177672 | − | 0.307738i | ||||
\(647\) | −3.15886 | − | 5.47131i | −0.124188 | − | 0.215099i | 0.797227 | − | 0.603679i | \(-0.206299\pi\) |
−0.921415 | + | 0.388580i | \(0.872966\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 49.1804 | + | 28.3943i | 1.93050 | + | 1.11458i | ||||
\(650\) | 9.06570 | 0.355586 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13.2279 | 0.518043 | ||||||||
\(653\) | −32.9692 | − | 19.0348i | −1.29019 | − | 0.744889i | −0.311498 | − | 0.950247i | \(-0.600831\pi\) |
−0.978687 | + | 0.205358i | \(0.934164\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.45382 | + | 12.9104i | 0.291245 | + | 0.504451i | ||||
\(656\) | 4.51585 | − | 7.82169i | 0.176314 | − | 0.305386i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 7.60400 | − | 7.89017i | 0.296435 | − | 0.307591i | ||||
\(659\) | 36.9345i | 1.43877i | 0.694614 | + | 0.719383i | \(0.255575\pi\) | ||||
−0.694614 | + | 0.719383i | \(0.744425\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.8641 | − | 14.9327i | 1.00600 | − | 0.580813i | 0.0959808 | − | 0.995383i | \(-0.469401\pi\) |
0.910018 | + | 0.414570i | \(0.136068\pi\) | |||||||
\(662\) | 0.396228 | − | 0.228762i | 0.0153998 | − | 0.00889110i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.52907i | 0.136954i | ||||||||
\(665\) | 13.1054 | − | 13.5986i | 0.508206 | − | 0.527331i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.3737 | + | 23.1639i | −0.517832 | + | 0.896911i | ||||
\(668\) | −6.91250 | − | 11.9728i | −0.267453 | − | 0.463242i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.18483 | + | 1.26141i | 0.0844073 | + | 0.0487326i | ||||
\(671\) | 22.0737 | 0.852146 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −49.0590 | −1.89109 | −0.945543 | − | 0.325498i | \(-0.894468\pi\) | ||||
−0.945543 | + | 0.325498i | \(0.894468\pi\) | |||||||
\(674\) | 21.5146 | + | 12.4215i | 0.828711 | + | 0.478457i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.19389 | − | 10.7281i | −0.238227 | − | 0.412620i | ||||
\(677\) | 4.27797 | − | 7.40965i | 0.164416 | − | 0.284776i | −0.772032 | − | 0.635584i | \(-0.780760\pi\) |
0.936448 | + | 0.350808i | \(0.114093\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14.1251 | − | 49.0722i | −0.542072 | − | 1.88322i | ||||
\(680\) | − | 4.04979i | − | 0.155303i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 35.2180 | − | 20.3331i | 1.34857 | − | 0.778595i | ||||
\(683\) | 6.33101 | − | 3.65521i | 0.242249 | − | 0.139863i | −0.373961 | − | 0.927445i | \(-0.622001\pi\) |
0.616210 | + | 0.787582i | \(0.288667\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 24.4369i | 0.933687i | ||||||||
\(686\) | 17.5963 | − | 5.77664i | 0.671831 | − | 0.220553i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.40530 | − | 7.63021i | 0.167951 | − | 0.290899i | ||||
\(689\) | 5.62252 | + | 9.73849i | 0.214201 | + | 0.371007i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 43.9240 | + | 25.3596i | 1.67095 | + | 0.964723i | 0.967108 | + | 0.254366i | \(0.0818668\pi\) |
0.703842 | + | 0.710357i | \(0.251466\pi\) | |||||||
\(692\) | 9.99738 | 0.380043 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 21.8753 | 0.830377 | ||||||||
\(695\) | −9.85998 | − | 5.69266i | −0.374010 | − | 0.215935i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.2222 | − | 17.7054i | −0.387195 | − | 0.670642i | ||||
\(698\) | −0.136371 | + | 0.236201i | −0.00516171 | + | 0.00894035i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.14695 | + | 4.62010i | −0.0433505 | + | 0.174623i | ||||
\(701\) | 21.6542i | 0.817866i | 0.912564 | + | 0.408933i | \(0.134099\pi\) | ||||
−0.912564 | + | 0.408933i | \(0.865901\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25.8962 | − | 14.9512i | 0.976694 | − | 0.563895i | ||||
\(704\) | −4.52838 | + | 2.61446i | −0.170670 | + | 0.0985362i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 15.1848i | 0.571489i | ||||||||
\(707\) | −1.94879 | − | 1.87811i | −0.0732919 | − | 0.0706336i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.31807 | − | 16.1394i | 0.349947 | − | 0.606127i | −0.636292 | − | 0.771448i | \(-0.719533\pi\) |
0.986240 | + | 0.165321i | \(0.0528661\pi\) | |||||||
\(710\) | −1.89043 | − | 3.27432i | −0.0709466 | − | 0.122883i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −5.15000 | − | 2.97335i | −0.193004 | − | 0.111431i | ||||
\(713\) | 61.4344 | 2.30074 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 47.1358 | 1.76278 | ||||||||
\(716\) | −13.0876 | − | 7.55610i | −0.489105 | − | 0.282385i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −11.1944 | − | 19.3894i | −0.417773 | − | 0.723604i | ||||
\(719\) | −18.1893 | + | 31.5048i | −0.678347 | + | 1.17493i | 0.297132 | + | 0.954836i | \(0.403970\pi\) |
−0.975479 | + | 0.220095i | \(0.929363\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −25.6796 | − | 6.37498i | −0.956357 | − | 0.237417i | ||||
\(722\) | − | 3.08085i | − | 0.114658i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 14.3964 | − | 8.31176i | 0.535037 | − | 0.308904i | ||||
\(725\) | −5.27608 | + | 3.04615i | −0.195949 | + | 0.113131i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 49.7512i | 1.84517i | 0.385793 | + | 0.922585i | \(0.373928\pi\) | ||||
−0.385793 | + | 0.922585i | \(0.626072\pi\) | |||||||
\(728\) | 12.8108 | − | 3.68750i | 0.474800 | − | 0.136668i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4.20244 | − | 7.27884i | 0.155539 | − | 0.269402i | ||||
\(731\) | −9.97199 | − | 17.2720i | −0.368828 | − | 0.638828i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.91333 | + | 5.72347i | 0.366157 | + | 0.211401i | 0.671778 | − | 0.740752i | \(-0.265531\pi\) |
−0.305621 | + | 0.952153i | \(0.598864\pi\) | |||||||
\(734\) | −1.36088 | −0.0502310 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.89932 | −0.291173 | ||||||||
\(737\) | −6.38562 | − | 3.68674i | −0.235217 | − | 0.135803i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.4946 | − | 21.6413i | −0.459622 | − | 0.796089i | 0.539319 | − | 0.842102i | \(-0.318682\pi\) |
−0.998941 | + | 0.0460128i | \(0.985348\pi\) | |||||||
\(740\) | 6.70413 | − | 11.6119i | 0.246449 | − | 0.426862i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.67431 | + | 1.63331i | −0.208310 | + | 0.0599607i | ||||
\(743\) | 18.0985i | 0.663971i | 0.943285 | + | 0.331985i | \(0.107718\pi\) | ||||
−0.943285 | + | 0.331985i | \(0.892282\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 26.7929 | − | 15.4689i | 0.981617 | − | 0.566737i | ||||
\(746\) | 22.3123 | − | 12.8820i | 0.816912 | − | 0.471644i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 11.8364i | 0.432781i | ||||||||
\(749\) | 0.786439 | + | 0.195234i | 0.0287358 | + | 0.00713371i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.22436 | + | 2.12066i | −0.0446776 | + | 0.0773839i | −0.887499 | − | 0.460809i | \(-0.847559\pi\) |
0.842822 | + | 0.538193i | \(0.180893\pi\) | |||||||
\(752\) | 2.07085 | + | 3.58682i | 0.0755161 | + | 0.130798i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 14.7753 | + | 8.53049i | 0.538083 | + | 0.310662i | ||||
\(755\) | −29.0638 | −1.05774 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −54.5475 | −1.98256 | −0.991282 | − | 0.131758i | \(-0.957938\pi\) | ||||
−0.991282 | + | 0.131758i | \(0.957938\pi\) | |||||||
\(758\) | 9.17508 | + | 5.29724i | 0.333254 | + | 0.192404i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.56908 | + | 6.18183i | 0.129464 | + | 0.224239i | ||||
\(761\) | −0.524034 | + | 0.907654i | −0.0189962 | + | 0.0329024i | −0.875367 | − | 0.483459i | \(-0.839380\pi\) |
0.856371 | + | 0.516361i | \(0.172714\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.91888 | − | 5.70421i | −0.214278 | − | 0.206506i | ||||
\(764\) | − | 20.0754i | − | 0.726302i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9.70088 | + | 5.60081i | −0.350507 | + | 0.202365i | ||||
\(767\) | 47.3906 | − | 27.3610i | 1.71118 | − | 0.987948i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 39.7610i | 1.43382i | 0.697166 | + | 0.716910i | \(0.254444\pi\) | ||||
−0.697166 | + | 0.716910i | \(0.745556\pi\) | |||||||
\(770\) | −5.96338 | + | 24.0216i | −0.214905 | + | 0.865678i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2.34219 | + | 4.05680i | −0.0842974 | + | 0.146007i | ||||
\(773\) | 16.9933 | + | 29.4333i | 0.611207 | + | 1.05864i | 0.991037 | + | 0.133585i | \(0.0426490\pi\) |
−0.379830 | + | 0.925056i | \(0.624018\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 12.1183 | + | 6.99649i | 0.435302 | + | 0.251321i | ||||
\(776\) | 19.3006 | 0.692852 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −19.7828 | −0.709248 | ||||||||
\(779\) | 31.2076 | + | 18.0177i | 1.11813 | + | 0.645552i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.52518 | + | 9.56989i | 0.197706 | + | 0.342438i | ||||
\(782\) | −8.94059 | + | 15.4856i | −0.319715 | + | 0.553763i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.258485 | + | 6.99523i | 0.00923160 | + | 0.249829i | ||||
\(785\) | − | 35.3005i | − | 1.25993i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18.0687 | + | 10.4320i | −0.644080 | + | 0.371860i | −0.786184 | − | 0.617992i | \(-0.787946\pi\) |
0.142104 | + | 0.989852i | \(0.454613\pi\) | |||||||
\(788\) | −10.4506 | + | 6.03365i | −0.372287 | + | 0.214940i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 12.6349i | 0.449531i | ||||||||
\(791\) | 1.82914 | + | 6.35465i | 0.0650368 | + | 0.225945i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.6352 | − | 18.4207i | 0.377667 | − | 0.654138i | ||||
\(794\) | −16.2778 | − | 28.1940i | −0.577678 | − | 1.00057i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −19.9506 | − | 11.5185i | −0.707131 | − | 0.408262i | ||||
\(797\) | −12.9251 | −0.457832 | −0.228916 | − | 0.973446i | \(-0.573518\pi\) | ||||
−0.228916 | + | 0.973446i | \(0.573518\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.37529 | 0.331674 | ||||||||
\(800\) | −1.55819 | − | 0.899620i | −0.0550902 | − | 0.0318064i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 14.7841 | + | 25.6068i | 0.522044 | + | 0.904207i | ||||
\(803\) | −12.2825 | + | 21.2739i | −0.433441 | + | 0.750741i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −25.9466 | + | 26.9231i | −0.914497 | + | 0.948913i | ||||
\(806\) | − | 39.1863i | − | 1.38028i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0.885907 | − | 0.511479i | 0.0311661 | − | 0.0179938i | ||||
\(809\) | 16.3360 | − | 9.43161i | 0.574344 | − | 0.331598i | −0.184538 | − | 0.982825i | \(-0.559079\pi\) |
0.758883 | + | 0.651227i | \(0.225746\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.08486i | 0.108324i | 0.998532 | + | 0.0541620i | \(0.0172487\pi\) | ||||
−0.998532 | + | 0.0541620i | \(0.982751\pi\) | |||||||
\(812\) | −6.21664 | + | 6.45060i | −0.218161 | + | 0.226372i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −19.5942 | + | 33.9382i | −0.686777 | + | 1.18953i | ||||
\(815\) | 11.8328 | + | 20.4950i | 0.414484 | + | 0.717907i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 30.4436 | + | 17.5766i | 1.06509 | + | 0.614928i | ||||
\(818\) | −5.43413 | −0.190000 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 16.1583 | 0.564273 | ||||||||
\(821\) | −10.3331 | − | 5.96584i | −0.360629 | − | 0.208209i | 0.308728 | − | 0.951150i | \(-0.400097\pi\) |
−0.669357 | + | 0.742941i | \(0.733430\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.32060 | + | 16.1437i | 0.324896 | + | 0.562736i | 0.981491 | − | 0.191507i | \(-0.0613375\pi\) |
−0.656596 | + | 0.754243i | \(0.728004\pi\) | |||||||
\(824\) | 5.00029 | − | 8.66075i | 0.174193 | − | 0.301711i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7.94821 | + | 27.6130i | 0.276554 | + | 0.960779i | ||||
\(827\) | − | 40.8001i | − | 1.41876i | −0.704826 | − | 0.709380i | \(-0.748975\pi\) | ||
0.704826 | − | 0.709380i | \(-0.251025\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.2452 | − | 11.6886i | 0.703144 | − | 0.405961i | −0.105373 | − | 0.994433i | \(-0.533604\pi\) |
0.808517 | + | 0.588472i | \(0.200270\pi\) | |||||||
\(830\) | −5.46785 | + | 3.15687i | −0.189792 | + | 0.109576i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.03863i | 0.174683i | ||||||||
\(833\) | 14.0058 | + | 7.41059i | 0.485271 | + | 0.256762i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.3669 | − | 21.4201i | 0.427975 | − | 0.741275i | ||||
\(836\) | −10.4314 | − | 18.0677i | −0.360777 | − | 0.624884i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −3.78965 | − | 2.18795i | −0.130911 | − | 0.0755816i | ||||
\(839\) | −17.3583 | −0.599274 | −0.299637 | − | 0.954053i | \(-0.596866\pi\) | ||||
−0.299637 | + | 0.954053i | \(0.596866\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.5347 | 0.604646 | ||||||||
\(842\) | −6.36489 | − | 3.67477i | −0.219349 | − | 0.126641i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −11.2005 | − | 19.3999i | −0.385538 | − | 0.667772i | ||||
\(845\) | 11.0813 | − | 19.1933i | 0.381208 | − | 0.660271i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.4172 | − | 41.9622i | 0.357938 | − | 1.44184i | ||||
\(848\) | − | 2.23177i | − | 0.0766392i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3.52717 | + | 2.03641i | −0.120981 | + | 0.0698483i | ||||
\(851\) | −51.2704 | + | 29.6010i | −1.75753 | + | 1.01471i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 5.34663i | − | 0.183065i | −0.995802 | − | 0.0915326i | \(-0.970823\pi\) | ||
0.995802 | − | 0.0915326i | \(-0.0291766\pi\) | |||||||
\(854\) | 8.04213 | + | 7.75045i | 0.275196 | + | 0.265215i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.153134 | + | 0.265236i | −0.00523402 | + | 0.00906559i | ||||
\(857\) | −7.28154 | − | 12.6120i | −0.248733 | − | 0.430818i | 0.714442 | − | 0.699695i | \(-0.246681\pi\) |
−0.963174 | + | 0.268877i | \(0.913347\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.29046 | + | 5.36385i | 0.316987 | + | 0.183012i | 0.650049 | − | 0.759893i | \(-0.274749\pi\) |
−0.333062 | + | 0.942905i | \(0.608082\pi\) | |||||||
\(860\) | 15.7628 | 0.537506 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 30.4781 | 1.03809 | ||||||||
\(863\) | 25.0062 | + | 14.4374i | 0.851222 | + | 0.491453i | 0.861063 | − | 0.508498i | \(-0.169799\pi\) |
−0.00984090 | + | 0.999952i | \(0.503133\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.94299 | + | 15.4897i | 0.304071 | + | 0.526666i | ||||
\(866\) | −13.9490 | + | 24.1604i | −0.474007 | + | 0.821004i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 19.9703 | + | 4.95764i | 0.677835 | + | 0.168273i | ||||
\(869\) | − | 36.9282i | − | 1.25270i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.15323 | + | 3.55257i | −0.208494 | + | 0.120374i | ||||
\(872\) | 2.69068 | − | 1.55347i | 0.0911180 | − | 0.0526070i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 31.5174i | − | 1.06609i | ||||||
\(875\) | −30.9279 | + | 8.90240i | −1.04556 | + | 0.300956i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.9519 | + | 20.7013i | −0.403588 | + | 0.699035i | −0.994156 | − | 0.107953i | \(-0.965570\pi\) |
0.590568 | + | 0.806988i | \(0.298904\pi\) | |||||||
\(878\) | 4.57276 | + | 7.92025i | 0.154323 | + | 0.267295i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −8.10158 | − | 4.67745i | −0.273104 | − | 0.157677i | ||||
\(881\) | −23.6586 | −0.797078 | −0.398539 | − | 0.917151i | \(-0.630483\pi\) | ||||
−0.398539 | + | 0.917151i | \(0.630483\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 43.8523 | 1.47575 | 0.737873 | − | 0.674940i | \(-0.235830\pi\) | ||||
0.737873 | + | 0.674940i | \(0.235830\pi\) | |||||||
\(884\) | 9.87755 | + | 5.70281i | 0.332218 | + | 0.191806i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10.9467 | − | 18.9603i | −0.367763 | − | 0.636983i | ||||
\(887\) | −14.7804 | + | 25.6005i | −0.496279 | + | 0.859580i | −0.999991 | − | 0.00429142i | \(-0.998634\pi\) |
0.503712 | + | 0.863872i | \(0.331967\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.3973 | − | 3.85631i | 0.449330 | − | 0.129337i | ||||
\(890\) | − | 10.6391i | − | 0.356622i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.65219 | − | 4.99534i | 0.289697 | − | 0.167256i | ||||
\(893\) | −14.3110 | + | 8.26244i | −0.478898 | + | 0.276492i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 27.0367i | − | 0.903739i | ||||||
\(896\) | −2.56781 | − | 0.637461i | −0.0857845 | − | 0.0212961i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −10.4313 | + | 18.0675i | −0.348096 | + | 0.602920i | ||||
\(899\) | 13.1669 | + | 22.8057i | 0.439140 | + | 0.760614i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.37508 | − | 2.52595i | −0.145755 | − | 0.0841517i | ||||
\(902\) | −47.2261 | −1.57246 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.49935 | −0.0831272 | ||||||||
\(905\) | 25.7561 | + | 14.8703i | 0.856162 | + | 0.494305i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.37858 | − | 9.31597i | −0.178593 | − | 0.309332i | 0.762806 | − | 0.646627i | \(-0.223821\pi\) |
−0.941399 | + | 0.337296i | \(0.890488\pi\) | |||||||
\(908\) | 1.59918 | − | 2.76985i | 0.0530705 | − | 0.0919208i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 17.1730 | + | 16.5502i | 0.569280 | + | 0.548633i | ||||
\(911\) | − | 53.5414i | − | 1.77391i | −0.461860 | − | 0.886953i | \(-0.652818\pi\) | ||
0.461860 | − | 0.886953i | \(-0.347182\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.9809 | − | 9.22661i | 0.528892 | − | 0.305356i | ||||
\(914\) | −6.86192 | + | 3.96173i | −0.226972 | + | 0.131042i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 16.9547i | 0.560200i | ||||||||
\(917\) | 5.31174 | − | 21.3966i | 0.175409 | − | 0.706579i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.817192 | + | 1.41542i | −0.0269567 | + | 0.0466903i | −0.879189 | − | 0.476473i | \(-0.841915\pi\) |
0.852232 | + | 0.523163i | \(0.175248\pi\) | |||||||
\(920\) | −7.06621 | − | 12.2390i | −0.232966 | − | 0.403509i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 7.84815 | + | 4.53113i | 0.258465 | + | 0.149225i | ||||
\(923\) | 10.6482 | 0.350490 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.4845 | −0.443367 | ||||||||
\(926\) | −0.432914 | − | 0.249943i | −0.0142264 | − | 0.00821364i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.69302 | − | 2.93240i | −0.0555761 | − | 0.0962606i | ||||
\(929\) | 16.0349 | − | 27.7733i | 0.526088 | − | 0.911211i | −0.473450 | − | 0.880821i | \(-0.656992\pi\) |
0.999538 | − | 0.0303906i | \(-0.00967512\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −27.9101 | + | 1.03132i | −0.914717 | + | 0.0338003i | ||||
\(932\) | 8.36828i | 0.274112i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.39416 | − | 0.804921i | 0.0456184 | − | 0.0263378i | ||||
\(935\) | −18.3390 | + | 10.5880i | −0.599750 | + | 0.346266i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 11.9407i | − | 0.390086i | −0.980795 | − | 0.195043i | \(-0.937515\pi\) | ||
0.980795 | − | 0.195043i | \(-0.0624847\pi\) | |||||||
\(938\) | −1.03200 | − | 3.58529i | −0.0336960 | − | 0.117064i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.70489 | + | 6.41705i | −0.120840 | + | 0.209301i | ||||
\(941\) | −23.8800 | − | 41.3614i | −0.778467 | − | 1.34834i | −0.932825 | − | 0.360329i | \(-0.882665\pi\) |
0.154359 | − | 0.988015i | \(-0.450669\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −61.7860 | − | 35.6722i | −2.01203 | − | 1.16165i | ||||
\(944\) | −10.8605 | −0.353479 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −46.0700 | −1.49786 | ||||||||
\(947\) | 28.8204 | + | 16.6395i | 0.936537 | + | 0.540710i | 0.888873 | − | 0.458154i | \(-0.151489\pi\) |
0.0476636 | + | 0.998863i | \(0.484822\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.8355 | + | 20.4997i | 0.384197 | + | 0.665449i | ||||
\(950\) | 3.58937 | − | 6.21698i | 0.116455 | − | 0.201705i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −4.15595 | + | 4.31235i | −0.134695 | + | 0.139764i | ||||
\(953\) | 3.57700i | 0.115870i | 0.998320 | + | 0.0579352i | \(0.0184517\pi\) | ||||
−0.998320 | + | 0.0579352i | \(0.981548\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 31.1043 | − | 17.9581i | 1.00651 | − | 0.581110i | ||||
\(956\) | −11.8431 | + | 6.83764i | −0.383035 | + | 0.221145i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 6.53591i | 0.211166i | ||||||||
\(959\) | 25.0775 | − | 26.0213i | 0.809794 | − | 0.840270i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.7422 | − | 25.5342i | 0.475554 | − | 0.823683i | ||||
\(962\) | 18.8811 | + | 32.7031i | 0.608752 | + | 1.05439i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 22.5782 | + | 13.0355i | 0.727195 | + | 0.419846i | ||||
\(965\) | −8.38068 | −0.269784 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.1745 | −0.648768 | −0.324384 | − | 0.945925i | \(-0.605157\pi\) | ||||
−0.324384 | + | 0.945925i | \(0.605157\pi\) | |||||||
\(968\) | 14.1523 | + | 8.17082i | 0.454871 | + | 0.262620i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 17.2651 | + | 29.9040i | 0.554348 | + | 0.960159i | ||||
\(971\) | −3.86876 | + | 6.70088i | −0.124154 | + | 0.215042i | −0.921402 | − | 0.388611i | \(-0.872955\pi\) |
0.797248 | + | 0.603652i | \(0.206288\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.65735 | + | 16.1802i | 0.149308 | + | 0.518712i | ||||
\(974\) | 3.14622i | 0.100811i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.65589 | + | 2.11073i | −0.117022 | + | 0.0675629i | ||||
\(977\) | −21.0883 | + | 12.1753i | −0.674674 | + | 0.389523i | −0.797845 | − | 0.602862i | \(-0.794027\pi\) |
0.123172 | + | 0.992385i | \(0.460693\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 31.0949i | 0.993796i | ||||||||
\(980\) | −10.6070 | + | 6.65795i | −0.338829 | + | 0.212681i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −12.8038 | + | 22.1769i | −0.408586 | + | 0.707692i | ||||
\(983\) | 7.12004 | + | 12.3323i | 0.227094 | + | 0.393339i | 0.956946 | − | 0.290267i | \(-0.0937442\pi\) |
−0.729852 | + | 0.683606i | \(0.760411\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18.6968 | − | 10.7946i | −0.595730 | − | 0.343945i | ||||
\(986\) | −7.66476 | −0.244096 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −20.1035 | −0.639578 | ||||||||
\(989\) | −60.2735 | − | 34.7989i | −1.91658 | − | 1.10654i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.4719 | − | 31.9943i | −0.586779 | − | 1.01633i | −0.994651 | − | 0.103292i | \(-0.967062\pi\) |
0.407872 | − | 0.913039i | \(-0.366271\pi\) | |||||||
\(992\) | −3.88858 | + | 6.73522i | −0.123463 | + | 0.213844i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.34716 | + | 5.42659i | −0.0427292 | + | 0.172121i | ||||
\(995\) | − | 41.2147i | − | 1.30659i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.2946 | + | 9.98502i | −0.547724 | + | 0.316229i | −0.748204 | − | 0.663469i | \(-0.769083\pi\) |
0.200480 | + | 0.979698i | \(0.435750\pi\) | |||||||
\(998\) | 9.27176 | − | 5.35305i | 0.293492 | − | 0.169448i | ||||
\(999\) | 0 | 0 |
(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 | 1134.2.k.d.971.5 | yes | 16 | |
3.2 | odd | 2 | 1134.2.k.c.971.4 | yes | 16 | ||
7.3 | odd | 6 | 1134.2.k.c.647.4 | ✓ | 16 | ||
9.2 | odd | 6 | 1134.2.l.h.215.8 | 16 | |||
9.4 | even | 3 | 1134.2.t.g.593.4 | 16 | |||
9.5 | odd | 6 | 1134.2.t.h.593.5 | 16 | |||
9.7 | even | 3 | 1134.2.l.g.215.1 | 16 | |||
21.17 | even | 6 | inner | 1134.2.k.d.647.5 | yes | 16 | |
63.31 | odd | 6 | 1134.2.l.h.269.4 | 16 | |||
63.38 | even | 6 | 1134.2.t.g.1025.4 | 16 | |||
63.52 | odd | 6 | 1134.2.t.h.1025.5 | 16 | |||
63.59 | even | 6 | 1134.2.l.g.269.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1134.2.k.c.647.4 | ✓ | 16 | 7.3 | odd | 6 | ||
1134.2.k.c.971.4 | yes | 16 | 3.2 | odd | 2 | ||
1134.2.k.d.647.5 | yes | 16 | 21.17 | even | 6 | inner | |
1134.2.k.d.971.5 | yes | 16 | 1.1 | even | 1 | trivial | |
1134.2.l.g.215.1 | 16 | 9.7 | even | 3 | |||
1134.2.l.g.269.5 | 16 | 63.59 | even | 6 | |||
1134.2.l.h.215.8 | 16 | 9.2 | odd | 6 | |||
1134.2.l.h.269.4 | 16 | 63.31 | odd | 6 | |||
1134.2.t.g.593.4 | 16 | 9.4 | even | 3 | |||
1134.2.t.g.1025.4 | 16 | 63.38 | even | 6 | |||
1134.2.t.h.593.5 | 16 | 9.5 | odd | 6 | |||
1134.2.t.h.1025.5 | 16 | 63.52 | odd | 6 |