Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [539,2,Mod(214,539)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(539, base_ring=CyclotomicField(30))
chi = DirichletCharacter(H, H._module([20, 12]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("539.214");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 539 = 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 539.q (of order \(15\), degree \(8\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.30393666895\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{15})\) |
Twist minimal: | no (minimal twist has level 77) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{15}]$ |
Embedding invariants
Embedding label | 361.4 | ||
Character | \(\chi\) | \(=\) | 539.361 |
Dual form | 539.2.q.f.324.4 |
$q$-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 \(\left(\mathbb{Z}/539\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(442\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{3}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.37734 | − | 0.505320i | 1.68103 | − | 0.357315i | 0.734174 | − | 0.678961i | \(-0.237570\pi\) |
0.946860 | + | 0.321646i | \(0.104236\pi\) | |||||||
\(3\) | 0.149915 | + | 1.42635i | 0.0865537 | + | 0.823503i | 0.948558 | + | 0.316603i | \(0.102542\pi\) |
−0.862005 | + | 0.506901i | \(0.830791\pi\) | |||||||
\(4\) | 3.56931 | − | 1.58916i | 1.78466 | − | 0.794580i | ||||
\(5\) | −0.842189 | + | 0.935345i | −0.376638 | + | 0.418299i | −0.901425 | − | 0.432934i | \(-0.857478\pi\) |
0.524787 | + | 0.851233i | \(0.324145\pi\) | |||||||
\(6\) | 1.07716 | + | 3.31516i | 0.439750 | + | 1.35341i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 3.74989 | − | 2.72445i | 1.32579 | − | 0.963239i | ||||
\(9\) | 0.922445 | − | 0.196072i | 0.307482 | − | 0.0653572i | ||||
\(10\) | −1.52952 | + | 2.64921i | −0.483677 | + | 0.837754i | ||||
\(11\) | −0.785524 | + | 3.22226i | −0.236844 | + | 0.971548i | ||||
\(12\) | 2.80179 | + | 4.85285i | 0.808808 | + | 1.40090i | ||||
\(13\) | 0.982152 | − | 3.02275i | 0.272400 | − | 0.838361i | −0.717496 | − | 0.696563i | \(-0.754712\pi\) |
0.989896 | − | 0.141798i | \(-0.0452882\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.46039 | − | 1.06103i | −0.377070 | − | 0.273957i | ||||
\(16\) | 2.30932 | − | 2.56476i | 0.577331 | − | 0.641191i | ||||
\(17\) | 5.79472 | + | 1.23171i | 1.40543 | + | 0.298733i | 0.847340 | − | 0.531050i | \(-0.178202\pi\) |
0.558086 | + | 0.829783i | \(0.311536\pi\) | |||||||
\(18\) | 2.09389 | − | 0.932259i | 0.493534 | − | 0.219735i | ||||
\(19\) | −2.61477 | − | 1.16417i | −0.599868 | − | 0.267079i | 0.0842558 | − | 0.996444i | \(-0.473149\pi\) |
−0.684124 | + | 0.729366i | \(0.739815\pi\) | |||||||
\(20\) | −1.51962 | + | 4.67691i | −0.339798 | + | 1.04579i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.239188 | + | 8.05735i | −0.0509950 | + | 1.71783i | ||||
\(23\) | −3.38171 | − | 5.85730i | −0.705136 | − | 1.22133i | −0.966642 | − | 0.256130i | \(-0.917552\pi\) |
0.261506 | − | 0.965202i | \(-0.415781\pi\) | |||||||
\(24\) | 4.44819 | + | 4.94021i | 0.907982 | + | 1.00842i | ||||
\(25\) | 0.357053 | + | 3.39714i | 0.0714107 | + | 0.679427i | ||||
\(26\) | 0.807454 | − | 7.68241i | 0.158355 | − | 1.50665i | ||||
\(27\) | 1.74754 | + | 5.37837i | 0.336314 | + | 1.03507i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.63693 | − | 2.64238i | −0.675361 | − | 0.490678i | 0.196454 | − | 0.980513i | \(-0.437057\pi\) |
−0.871815 | + | 0.489834i | \(0.837057\pi\) | |||||||
\(30\) | −4.00800 | − | 1.78448i | −0.731757 | − | 0.325799i | ||||
\(31\) | −6.50898 | − | 7.22895i | −1.16905 | − | 1.29836i | −0.946229 | − | 0.323498i | \(-0.895141\pi\) |
−0.222818 | − | 0.974860i | \(-0.571525\pi\) | |||||||
\(32\) | −0.441092 | + | 0.763993i | −0.0779748 | + | 0.135056i | ||||
\(33\) | −4.71383 | − | 0.637365i | −0.820572 | − | 0.110951i | ||||
\(34\) | 14.3984 | 2.46931 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.98090 | − | 2.16575i | 0.496817 | − | 0.360959i | ||||
\(37\) | 0.570198 | − | 5.42507i | 0.0937400 | − | 0.891876i | −0.842069 | − | 0.539369i | \(-0.818663\pi\) |
0.935809 | − | 0.352507i | \(-0.114671\pi\) | |||||||
\(38\) | −6.80447 | − | 1.44633i | −1.10383 | − | 0.234626i | ||||
\(39\) | 4.45874 | + | 0.947734i | 0.713970 | + | 0.151759i | ||||
\(40\) | −0.609809 | + | 5.80194i | −0.0964192 | + | 0.917368i | ||||
\(41\) | −0.254423 | + | 0.184849i | −0.0397342 | + | 0.0288686i | −0.607475 | − | 0.794339i | \(-0.707818\pi\) |
0.567741 | + | 0.823207i | \(0.307818\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.132562 | −0.0202155 | −0.0101078 | − | 0.999949i | \(-0.503217\pi\) | ||||
−0.0101078 | + | 0.999949i | \(0.503217\pi\) | |||||||
\(44\) | 2.31691 | + | 12.7496i | 0.349287 | + | 1.92207i | ||||
\(45\) | −0.593478 | + | 1.02793i | −0.0884704 | + | 0.153235i | ||||
\(46\) | −10.9993 | − | 12.2160i | −1.62176 | − | 1.80114i | ||||
\(47\) | −8.56453 | − | 3.81318i | −1.24927 | − | 0.556209i | −0.327829 | − | 0.944737i | \(-0.606317\pi\) |
−0.921437 | + | 0.388528i | \(0.872984\pi\) | |||||||
\(48\) | 4.00445 | + | 2.90940i | 0.577993 | + | 0.419936i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.56548 | + | 7.89572i | 0.362813 | + | 1.11662i | ||||
\(51\) | −0.888126 | + | 8.44995i | −0.124362 | + | 1.18323i | ||||
\(52\) | −1.29803 | − | 12.3499i | −0.180005 | − | 1.71263i | ||||
\(53\) | 2.91201 | + | 3.23411i | 0.399995 | + | 0.444239i | 0.909171 | − | 0.416423i | \(-0.136717\pi\) |
−0.509176 | + | 0.860662i | \(0.670050\pi\) | |||||||
\(54\) | 6.87229 | + | 11.9032i | 0.935200 | + | 1.61981i | ||||
\(55\) | −2.35237 | − | 3.44849i | −0.317193 | − | 0.464994i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.26852 | − | 3.90410i | 0.168019 | − | 0.517110i | ||||
\(58\) | −9.98147 | − | 4.44404i | −1.31063 | − | 0.583531i | ||||
\(59\) | 6.34627 | − | 2.82554i | 0.826213 | − | 0.367854i | 0.0503319 | − | 0.998733i | \(-0.483972\pi\) |
0.775882 | + | 0.630879i | \(0.217305\pi\) | |||||||
\(60\) | −6.89873 | − | 1.46637i | −0.890622 | − | 0.189308i | ||||
\(61\) | 1.64081 | − | 1.82231i | 0.210084 | − | 0.233322i | −0.628889 | − | 0.777495i | \(-0.716490\pi\) |
0.838973 | + | 0.544173i | \(0.183157\pi\) | |||||||
\(62\) | −19.1270 | − | 13.8966i | −2.42913 | − | 1.76487i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.79554 | + | 8.60379i | −0.349443 | + | 1.07547i | ||||
\(65\) | 2.00016 | + | 3.46438i | 0.248089 | + | 0.429703i | ||||
\(66\) | −11.5285 | + | 0.866755i | −1.41905 | + | 0.106690i | ||||
\(67\) | 4.70993 | − | 8.15784i | 0.575410 | − | 0.996639i | −0.420587 | − | 0.907252i | \(-0.638176\pi\) |
0.995997 | − | 0.0893871i | \(-0.0284908\pi\) | |||||||
\(68\) | 22.6406 | − | 4.81240i | 2.74557 | − | 0.583589i | ||||
\(69\) | 7.84759 | − | 5.70161i | 0.944739 | − | 0.686393i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.0360345 | − | 0.110903i | −0.00427651 | − | 0.0131617i | 0.948895 | − | 0.315590i | \(-0.102203\pi\) |
−0.953172 | + | 0.302429i | \(0.902203\pi\) | |||||||
\(72\) | 2.92488 | − | 3.24840i | 0.344700 | − | 0.382828i | ||||
\(73\) | −0.561859 | + | 0.250156i | −0.0657607 | + | 0.0292785i | −0.439353 | − | 0.898314i | \(-0.644792\pi\) |
0.373593 | + | 0.927593i | \(0.378126\pi\) | |||||||
\(74\) | −1.38584 | − | 13.1854i | −0.161101 | − | 1.53277i | ||||
\(75\) | −4.79197 | + | 1.01857i | −0.553330 | + | 0.117614i | ||||
\(76\) | −11.1830 | −1.28277 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 11.0789 | 1.25443 | ||||||||
\(79\) | −8.34290 | + | 1.77334i | −0.938649 | + | 0.199516i | −0.651741 | − | 0.758442i | \(-0.725961\pi\) |
−0.286909 | + | 0.957958i | \(0.592628\pi\) | |||||||
\(80\) | 0.454053 | + | 4.32003i | 0.0507647 | + | 0.482994i | ||||
\(81\) | −4.82488 | + | 2.14818i | −0.536098 | + | 0.238686i | ||||
\(82\) | −0.511443 | + | 0.568015i | −0.0564794 | + | 0.0627267i | ||||
\(83\) | −0.293731 | − | 0.904010i | −0.0322411 | − | 0.0992280i | 0.933641 | − | 0.358210i | \(-0.116613\pi\) |
−0.965882 | + | 0.258982i | \(0.916613\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.03232 | + | 4.38274i | −0.654297 | + | 0.475375i | ||||
\(86\) | −0.315145 | + | 0.0669862i | −0.0339830 | + | 0.00722330i | ||||
\(87\) | 3.22373 | − | 5.58367i | 0.345620 | − | 0.598632i | ||||
\(88\) | 5.83327 | + | 14.2232i | 0.621828 | + | 1.51620i | ||||
\(89\) | 5.02758 | + | 8.70803i | 0.532923 | + | 0.923049i | 0.999261 | + | 0.0384427i | \(0.0122397\pi\) |
−0.466338 | + | 0.884607i | \(0.654427\pi\) | |||||||
\(90\) | −0.891464 | + | 2.74364i | −0.0939686 | + | 0.289206i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −21.3786 | − | 15.5325i | −2.22887 | − | 1.61937i | ||||
\(93\) | 9.33521 | − | 10.3678i | 0.968017 | − | 1.07509i | ||||
\(94\) | −22.2877 | − | 4.73740i | −2.29880 | − | 0.488625i | ||||
\(95\) | 3.29103 | − | 1.46526i | 0.337652 | − | 0.150332i | ||||
\(96\) | −1.15585 | − | 0.514617i | −0.117968 | − | 0.0525228i | ||||
\(97\) | −5.43159 | + | 16.7167i | −0.551495 | + | 1.69733i | 0.153530 | + | 0.988144i | \(0.450936\pi\) |
−0.705025 | + | 0.709182i | \(0.749064\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.0928085 | + | 3.12637i | −0.00932760 | + | 0.314212i | ||||
\(100\) | 6.67303 | + | 11.5580i | 0.667303 | + | 1.15580i | ||||
\(101\) | 8.34817 | + | 9.27158i | 0.830674 | + | 0.922557i | 0.997992 | − | 0.0633460i | \(-0.0201772\pi\) |
−0.167318 | + | 0.985903i | \(0.553510\pi\) | |||||||
\(102\) | 2.15855 | + | 20.5372i | 0.213728 | + | 2.03349i | ||||
\(103\) | 0.859017 | − | 8.17301i | 0.0846415 | − | 0.805310i | −0.867043 | − | 0.498233i | \(-0.833982\pi\) |
0.951685 | − | 0.307077i | \(-0.0993509\pi\) | |||||||
\(104\) | −4.55239 | − | 14.0108i | −0.446398 | − | 1.37387i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.55709 | + | 6.21709i | 0.831138 | + | 0.603857i | ||||
\(107\) | 11.1348 | + | 4.95752i | 1.07644 | + | 0.479261i | 0.866871 | − | 0.498533i | \(-0.166128\pi\) |
0.209568 | + | 0.977794i | \(0.432794\pi\) | |||||||
\(108\) | 14.7846 | + | 16.4200i | 1.42265 | + | 1.58001i | ||||
\(109\) | −0.443044 | + | 0.767375i | −0.0424359 | + | 0.0735012i | −0.886463 | − | 0.462799i | \(-0.846845\pi\) |
0.844027 | + | 0.536300i | \(0.180178\pi\) | |||||||
\(110\) | −7.33496 | − | 7.00953i | −0.699361 | − | 0.668333i | ||||
\(111\) | 7.82353 | 0.742577 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.67700 | + | 2.67149i | −0.345903 | + | 0.251313i | −0.747148 | − | 0.664658i | \(-0.768577\pi\) |
0.401245 | + | 0.915971i | \(0.368577\pi\) | |||||||
\(114\) | 1.04288 | − | 9.92238i | 0.0976750 | − | 0.929316i | ||||
\(115\) | 8.32664 | + | 1.76988i | 0.776463 | + | 0.165042i | ||||
\(116\) | −17.1805 | − | 3.65183i | −1.59517 | − | 0.339064i | ||||
\(117\) | 0.313305 | − | 2.98089i | 0.0289650 | − | 0.275584i | ||||
\(118\) | 13.6594 | − | 9.92416i | 1.25745 | − | 0.913593i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −8.36702 | −0.763801 | ||||||||
\(121\) | −9.76591 | − | 5.06232i | −0.887810 | − | 0.460211i | ||||
\(122\) | 2.97992 | − | 5.16138i | 0.269789 | − | 0.467289i | ||||
\(123\) | −0.301802 | − | 0.335185i | −0.0272125 | − | 0.0302226i | ||||
\(124\) | −34.7205 | − | 15.4586i | −3.11800 | − | 1.38822i | ||||
\(125\) | −8.56947 | − | 6.22608i | −0.766477 | − | 0.556878i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.48072 | − | 7.63488i | −0.220129 | − | 0.677486i | −0.998750 | − | 0.0499916i | \(-0.984081\pi\) |
0.778621 | − | 0.627494i | \(-0.215919\pi\) | |||||||
\(128\) | −2.11387 | + | 20.1121i | −0.186841 | + | 1.77767i | ||||
\(129\) | −0.0198731 | − | 0.189080i | −0.00174973 | − | 0.0166475i | ||||
\(130\) | 6.50568 | + | 7.22529i | 0.570586 | + | 0.633700i | ||||
\(131\) | 0.0507303 | + | 0.0878675i | 0.00443233 | + | 0.00767702i | 0.868233 | − | 0.496157i | \(-0.165256\pi\) |
−0.863801 | + | 0.503834i | \(0.831922\pi\) | |||||||
\(132\) | −17.8380 | + | 5.21608i | −1.55260 | + | 0.454001i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 7.07480 | − | 21.7740i | 0.611170 | − | 1.88099i | ||||
\(135\) | −6.50239 | − | 2.89505i | −0.559636 | − | 0.249166i | ||||
\(136\) | 25.0853 | − | 11.1687i | 2.15105 | − | 0.957707i | ||||
\(137\) | 4.46435 | + | 0.948928i | 0.381416 | + | 0.0810724i | 0.394630 | − | 0.918840i | \(-0.370873\pi\) |
−0.0132140 | + | 0.999913i | \(0.504206\pi\) | |||||||
\(138\) | 15.7753 | − | 17.5202i | 1.34288 | − | 1.49142i | ||||
\(139\) | −3.09475 | − | 2.24847i | −0.262494 | − | 0.190713i | 0.448752 | − | 0.893656i | \(-0.351869\pi\) |
−0.711246 | + | 0.702944i | \(0.751869\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.15497 | − | 12.7877i | 0.349911 | − | 1.07692i | ||||
\(142\) | −0.141708 | − | 0.245445i | −0.0118918 | − | 0.0205973i | ||||
\(143\) | 8.96859 | + | 5.53919i | 0.749991 | + | 0.463210i | ||||
\(144\) | 1.62734 | − | 2.81864i | 0.135612 | − | 0.234887i | ||||
\(145\) | 5.53452 | − | 1.17640i | 0.459617 | − | 0.0976946i | ||||
\(146\) | −1.20932 | + | 0.878624i | −0.100084 | + | 0.0727155i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.58609 | − | 20.2699i | −0.541374 | − | 1.66618i | ||||
\(149\) | −3.26016 | + | 3.62078i | −0.267083 | + | 0.296625i | −0.861736 | − | 0.507357i | \(-0.830623\pi\) |
0.594653 | + | 0.803982i | \(0.297289\pi\) | |||||||
\(150\) | −10.8775 | + | 4.84296i | −0.888141 | + | 0.395426i | ||||
\(151\) | 1.77425 | + | 16.8809i | 0.144387 | + | 1.37375i | 0.791414 | + | 0.611280i | \(0.209345\pi\) |
−0.647028 | + | 0.762467i | \(0.723988\pi\) | |||||||
\(152\) | −12.9768 | + | 2.75830i | −1.05256 | + | 0.223728i | ||||
\(153\) | 5.58681 | 0.451667 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.2434 | 0.983410 | ||||||||
\(156\) | 17.4207 | − | 3.70289i | 1.39478 | − | 0.296469i | ||||
\(157\) | 0.234649 | + | 2.23253i | 0.0187270 | + | 0.178175i | 0.999887 | − | 0.0150205i | \(-0.00478135\pi\) |
−0.981160 | + | 0.193196i | \(0.938115\pi\) | |||||||
\(158\) | −18.9378 | + | 8.43166i | −1.50661 | + | 0.670787i | ||||
\(159\) | −4.17642 | + | 4.63838i | −0.331211 | + | 0.367847i | ||||
\(160\) | −0.343115 | − | 1.05600i | −0.0271256 | − | 0.0834841i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −10.3849 | + | 7.54506i | −0.815913 | + | 0.592796i | ||||
\(163\) | 15.4912 | − | 3.29275i | 1.21336 | − | 0.257908i | 0.443592 | − | 0.896229i | \(-0.353704\pi\) |
0.769770 | + | 0.638321i | \(0.220371\pi\) | |||||||
\(164\) | −0.614361 | + | 1.06410i | −0.0479735 | + | 0.0830926i | ||||
\(165\) | 4.56609 | − | 3.87228i | 0.355470 | − | 0.301456i | ||||
\(166\) | −1.15511 | − | 2.00071i | −0.0896540 | − | 0.155285i | ||||
\(167\) | −6.40950 | + | 19.7264i | −0.495982 | + | 1.52647i | 0.319440 | + | 0.947607i | \(0.396505\pi\) |
−0.815421 | + | 0.578868i | \(0.803495\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.34481 | + | 1.70361i | 0.180370 | + | 0.131047i | ||||
\(170\) | −12.1262 | + | 13.4675i | −0.930037 | + | 1.03291i | ||||
\(171\) | −2.64024 | − | 0.561200i | −0.201904 | − | 0.0429160i | ||||
\(172\) | −0.473155 | + | 0.210662i | −0.0360778 | + | 0.0160628i | ||||
\(173\) | 19.6919 | + | 8.76738i | 1.49714 | + | 0.666571i | 0.981714 | − | 0.190361i | \(-0.0609657\pi\) |
0.515429 | + | 0.856932i | \(0.327632\pi\) | |||||||
\(174\) | 4.84238 | − | 14.9033i | 0.367100 | − | 1.12982i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6.45030 | + | 9.45592i | 0.486210 | + | 0.712767i | ||||
\(177\) | 4.98161 | + | 8.62840i | 0.374441 | + | 0.648550i | ||||
\(178\) | 16.3526 | + | 18.1614i | 1.22568 | + | 1.36126i | ||||
\(179\) | −0.499814 | − | 4.75541i | −0.0373579 | − | 0.355436i | −0.997193 | − | 0.0748721i | \(-0.976145\pi\) |
0.959835 | − | 0.280564i | \(-0.0905215\pi\) | |||||||
\(180\) | −0.484756 | + | 4.61215i | −0.0361316 | + | 0.343769i | ||||
\(181\) | 2.42666 | + | 7.46850i | 0.180372 | + | 0.555129i | 0.999838 | − | 0.0179992i | \(-0.00572963\pi\) |
−0.819466 | + | 0.573128i | \(0.805730\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.84523 | + | 2.06718i | 0.210325 | + | 0.152810i | ||||
\(184\) | −28.6390 | − | 12.7509i | −2.11129 | − | 0.940009i | ||||
\(185\) | 4.59410 | + | 5.10227i | 0.337765 | + | 0.375126i | ||||
\(186\) | 16.9539 | − | 29.3651i | 1.24312 | − | 2.15315i | ||||
\(187\) | −8.52077 | + | 17.7046i | −0.623100 | + | 1.29469i | ||||
\(188\) | −36.6293 | −2.67146 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 7.08347 | − | 5.14644i | 0.513889 | − | 0.373362i | ||||
\(191\) | 0.923016 | − | 8.78191i | 0.0667871 | − | 0.635437i | −0.909012 | − | 0.416769i | \(-0.863162\pi\) |
0.975799 | − | 0.218668i | \(-0.0701711\pi\) | |||||||
\(192\) | −12.6911 | − | 2.69758i | −0.915902 | − | 0.194681i | ||||
\(193\) | −25.0428 | − | 5.32301i | −1.80262 | − | 0.383159i | −0.820535 | − | 0.571597i | \(-0.806324\pi\) |
−0.982085 | + | 0.188438i | \(0.939657\pi\) | |||||||
\(194\) | −4.46546 | + | 42.4861i | −0.320602 | + | 3.05032i | ||||
\(195\) | −4.64156 | + | 3.37229i | −0.332389 | + | 0.241495i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.1977 | −0.797802 | −0.398901 | − | 0.916994i | \(-0.630608\pi\) | ||||
−0.398901 | + | 0.916994i | \(0.630608\pi\) | |||||||
\(198\) | 1.35918 | + | 7.47936i | 0.0965928 | + | 0.531535i | ||||
\(199\) | −6.12514 | + | 10.6091i | −0.434200 | + | 0.752056i | −0.997230 | − | 0.0743802i | \(-0.976302\pi\) |
0.563030 | + | 0.826436i | \(0.309635\pi\) | |||||||
\(200\) | 10.5942 | + | 11.7661i | 0.749126 | + | 0.831989i | ||||
\(201\) | 12.3420 | + | 5.49503i | 0.870540 | + | 0.387589i | ||||
\(202\) | 24.5316 | + | 17.8232i | 1.72603 | + | 1.25404i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 10.2583 | + | 31.5719i | 0.718227 | + | 2.21048i | ||||
\(205\) | 0.0413744 | − | 0.393651i | 0.00288972 | − | 0.0274938i | ||||
\(206\) | −2.08780 | − | 19.8641i | −0.145464 | − | 1.38400i | ||||
\(207\) | −4.26790 | − | 4.73998i | −0.296639 | − | 0.329451i | ||||
\(208\) | −5.48454 | − | 9.49949i | −0.380284 | − | 0.658671i | ||||
\(209\) | 5.80521 | − | 7.51097i | 0.401555 | − | 0.519545i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.40769 | + | 13.5655i | −0.303438 | + | 0.933887i | 0.676817 | + | 0.736151i | \(0.263359\pi\) |
−0.980255 | + | 0.197736i | \(0.936641\pi\) | |||||||
\(212\) | 15.5334 | + | 6.91591i | 1.06684 | + | 0.474986i | ||||
\(213\) | 0.152784 | − | 0.0680239i | 0.0104686 | − | 0.00466092i | ||||
\(214\) | 28.9763 | + | 6.15910i | 1.98078 | + | 0.421027i | ||||
\(215\) | 0.111642 | − | 0.123991i | 0.00761394 | − | 0.00845613i | ||||
\(216\) | 21.2062 | + | 15.4072i | 1.44290 | + | 1.04833i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −0.665497 | + | 2.04819i | −0.0450732 | + | 0.138721i | ||||
\(219\) | −0.441041 | − | 0.763905i | −0.0298028 | − | 0.0516199i | ||||
\(220\) | −13.8765 | − | 8.57044i | −0.935555 | − | 0.577819i | ||||
\(221\) | 9.41444 | − | 16.3063i | 0.633284 | − | 1.09688i | ||||
\(222\) | 18.5992 | − | 3.95338i | 1.24830 | − | 0.265334i | ||||
\(223\) | −2.39793 | + | 1.74220i | −0.160577 | + | 0.116666i | −0.665172 | − | 0.746690i | \(-0.731642\pi\) |
0.504595 | + | 0.863356i | \(0.331642\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.995444 | + | 3.06366i | 0.0663629 | + | 0.204244i | ||||
\(226\) | −7.39152 | + | 8.20911i | −0.491676 | + | 0.546062i | ||||
\(227\) | −7.54228 | + | 3.35804i | −0.500599 | + | 0.222881i | −0.641472 | − | 0.767147i | \(-0.721676\pi\) |
0.140873 | + | 0.990028i | \(0.455009\pi\) | |||||||
\(228\) | −1.67650 | − | 15.9508i | −0.111029 | − | 1.05637i | ||||
\(229\) | 12.8217 | − | 2.72533i | 0.847280 | − | 0.180095i | 0.236240 | − | 0.971695i | \(-0.424085\pi\) |
0.611040 | + | 0.791600i | \(0.290752\pi\) | |||||||
\(230\) | 20.6896 | 1.36423 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −20.8371 | −1.36802 | ||||||||
\(233\) | 12.5474 | − | 2.66702i | 0.822005 | − | 0.174723i | 0.222335 | − | 0.974970i | \(-0.428632\pi\) |
0.599670 | + | 0.800248i | \(0.295299\pi\) | |||||||
\(234\) | −0.761472 | − | 7.24492i | −0.0497790 | − | 0.473615i | ||||
\(235\) | 10.7796 | − | 4.79938i | 0.703183 | − | 0.313077i | ||||
\(236\) | 18.1616 | − | 20.1705i | 1.18222 | − | 1.31299i | ||||
\(237\) | −3.78013 | − | 11.6340i | −0.245546 | − | 0.755712i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.02979 | − | 2.92781i | 0.260665 | − | 0.189384i | −0.449775 | − | 0.893142i | \(-0.648496\pi\) |
0.710440 | + | 0.703758i | \(0.248496\pi\) | |||||||
\(240\) | −6.09380 | + | 1.29528i | −0.393353 | + | 0.0836098i | ||||
\(241\) | −1.31343 | + | 2.27492i | −0.0846053 | + | 0.146541i | −0.905223 | − | 0.424937i | \(-0.860296\pi\) |
0.820618 | + | 0.571478i | \(0.193630\pi\) | |||||||
\(242\) | −25.7750 | − | 7.09996i | −1.65688 | − | 0.456403i | ||||
\(243\) | 4.69535 | + | 8.13258i | 0.301207 | + | 0.521706i | ||||
\(244\) | 2.96063 | − | 9.11189i | 0.189535 | − | 0.583329i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.886861 | − | 0.644342i | −0.0565442 | − | 0.0410818i | ||||
\(247\) | −6.08709 | + | 6.76040i | −0.387312 | + | 0.430154i | ||||
\(248\) | −44.1029 | − | 9.37435i | −2.80053 | − | 0.595272i | ||||
\(249\) | 1.24540 | − | 0.554487i | 0.0789240 | − | 0.0351392i | ||||
\(250\) | −23.5187 | − | 10.4712i | −1.48745 | − | 0.662257i | ||||
\(251\) | 8.10332 | − | 24.9395i | 0.511477 | − | 1.57417i | −0.278124 | − | 0.960545i | \(-0.589713\pi\) |
0.789601 | − | 0.613620i | \(-0.210287\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 21.5302 | − | 6.29571i | 1.35359 | − | 0.395808i | ||||
\(254\) | −9.75558 | − | 16.8972i | −0.612119 | − | 1.06022i | ||||
\(255\) | −7.15565 | − | 7.94716i | −0.448104 | − | 0.497670i | ||||
\(256\) | 3.24640 | + | 30.8875i | 0.202900 | + | 1.93047i | ||||
\(257\) | 3.13081 | − | 29.7877i | 0.195295 | − | 1.85811i | −0.257225 | − | 0.966352i | \(-0.582808\pi\) |
0.452520 | − | 0.891754i | \(-0.350525\pi\) | |||||||
\(258\) | −0.142791 | − | 0.439465i | −0.00888977 | − | 0.0273599i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 12.6446 | + | 9.18688i | 0.784188 | + | 0.569746i | ||||
\(261\) | −3.87296 | − | 1.72435i | −0.239730 | − | 0.106735i | ||||
\(262\) | 0.165005 | + | 0.183256i | 0.0101940 | + | 0.0113216i | ||||
\(263\) | −1.66854 | + | 2.89000i | −0.102887 | + | 0.178205i | −0.912873 | − | 0.408244i | \(-0.866141\pi\) |
0.809986 | + | 0.586449i | \(0.199475\pi\) | |||||||
\(264\) | −19.4128 | + | 10.4526i | −1.19478 | + | 0.643310i | ||||
\(265\) | −5.47747 | −0.336478 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −11.6670 | + | 8.47656i | −0.714008 | + | 0.518757i | ||||
\(268\) | 3.84710 | − | 36.6027i | 0.234999 | − | 2.23587i | ||||
\(269\) | −1.69788 | − | 0.360896i | −0.103522 | − | 0.0220042i | 0.155860 | − | 0.987779i | \(-0.450185\pi\) |
−0.259381 | + | 0.965775i | \(0.583519\pi\) | |||||||
\(270\) | −16.9213 | − | 3.59674i | −1.02980 | − | 0.218890i | ||||
\(271\) | −0.258808 | + | 2.46239i | −0.0157215 | + | 0.149580i | −0.999566 | − | 0.0294426i | \(-0.990627\pi\) |
0.983845 | + | 0.179022i | \(0.0572934\pi\) | |||||||
\(272\) | 16.5409 | − | 12.0177i | 1.00294 | − | 0.728679i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.0928 | 0.670141 | ||||||||
\(275\) | −11.2269 | − | 1.51801i | −0.677009 | − | 0.0915396i | ||||
\(276\) | 18.9497 | − | 32.8219i | 1.14064 | − | 1.97565i | ||||
\(277\) | 3.44984 | + | 3.83144i | 0.207281 | + | 0.230209i | 0.837817 | − | 0.545951i | \(-0.183832\pi\) |
−0.630536 | + | 0.776160i | \(0.717165\pi\) | |||||||
\(278\) | −8.49348 | − | 3.78154i | −0.509405 | − | 0.226802i | ||||
\(279\) | −7.42156 | − | 5.39208i | −0.444317 | − | 0.322815i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.97467 | − | 21.4658i | −0.416074 | − | 1.28054i | −0.911287 | − | 0.411772i | \(-0.864910\pi\) |
0.495213 | − | 0.868772i | \(-0.335090\pi\) | |||||||
\(282\) | 3.41591 | − | 32.5002i | 0.203415 | − | 1.93536i | ||||
\(283\) | −0.887193 | − | 8.44107i | −0.0527381 | − | 0.501770i | −0.988726 | − | 0.149737i | \(-0.952157\pi\) |
0.935988 | − | 0.352033i | \(-0.114509\pi\) | |||||||
\(284\) | −0.304861 | − | 0.338582i | −0.0180902 | − | 0.0200912i | ||||
\(285\) | 2.58335 | + | 4.47449i | 0.153024 | + | 0.265046i | ||||
\(286\) | 24.1205 | + | 8.63654i | 1.42627 | + | 0.510690i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −0.257085 | + | 0.791227i | −0.0151489 | + | 0.0466235i | ||||
\(289\) | 16.5314 | + | 7.36027i | 0.972438 | + | 0.432957i | ||||
\(290\) | 12.5630 | − | 5.59341i | 0.737724 | − | 0.328456i | ||||
\(291\) | −24.6582 | − | 5.24126i | −1.44549 | − | 0.307248i | ||||
\(292\) | −1.60791 | + | 1.78577i | −0.0940960 | + | 0.104504i | ||||
\(293\) | 19.9229 | + | 14.4749i | 1.16391 | + | 0.845630i | 0.990267 | − | 0.139178i | \(-0.0444462\pi\) |
0.173643 | + | 0.984809i | \(0.444446\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.70190 | + | 8.31559i | −0.157311 | + | 0.484152i | ||||
\(296\) | −12.6422 | − | 21.8969i | −0.734811 | − | 1.27273i | ||||
\(297\) | −18.7032 | + | 1.40618i | −1.08527 | + | 0.0815950i | ||||
\(298\) | −5.92087 | + | 10.2552i | −0.342987 | + | 0.594070i | ||||
\(299\) | −21.0265 | + | 4.46933i | −1.21600 | + | 0.258468i | ||||
\(300\) | −15.4854 | + | 11.2508i | −0.894050 | + | 0.649565i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 12.7482 | + | 39.2351i | 0.733579 | + | 2.25772i | ||||
\(303\) | −11.9730 | + | 13.2974i | −0.687831 | + | 0.763914i | ||||
\(304\) | −9.02415 | + | 4.01781i | −0.517571 | + | 0.230437i | ||||
\(305\) | 0.322612 | + | 3.06945i | 0.0184727 | + | 0.175756i | ||||
\(306\) | 13.2818 | − | 2.82313i | 0.759268 | − | 0.161387i | ||||
\(307\) | −4.59391 | −0.262188 | −0.131094 | − | 0.991370i | \(-0.541849\pi\) | ||||
−0.131094 | + | 0.991370i | \(0.541849\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.7863 | 0.670502 | ||||||||
\(310\) | 29.1066 | − | 6.18680i | 1.65315 | − | 0.351387i | ||||
\(311\) | −0.231085 | − | 2.19862i | −0.0131036 | − | 0.124672i | 0.986015 | − | 0.166659i | \(-0.0532980\pi\) |
−0.999118 | + | 0.0419867i | \(0.986631\pi\) | |||||||
\(312\) | 19.3018 | − | 8.59373i | 1.09275 | − | 0.486524i | ||||
\(313\) | 6.49009 | − | 7.20797i | 0.366841 | − | 0.407419i | −0.531259 | − | 0.847210i | \(-0.678281\pi\) |
0.898100 | + | 0.439791i | \(0.144947\pi\) | |||||||
\(314\) | 1.68598 | + | 5.18892i | 0.0951455 | + | 0.292828i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −26.9603 | + | 19.5878i | −1.51664 | + | 1.10190i | ||||
\(317\) | −6.31433 | + | 1.34215i | −0.354648 | + | 0.0753828i | −0.381791 | − | 0.924249i | \(-0.624692\pi\) |
0.0271427 | + | 0.999632i | \(0.491359\pi\) | |||||||
\(318\) | −7.58490 | + | 13.1374i | −0.425340 | + | 0.736711i | ||||
\(319\) | 11.3713 | − | 9.64348i | 0.636673 | − | 0.539931i | ||||
\(320\) | −5.69314 | − | 9.86081i | −0.318256 | − | 0.551236i | ||||
\(321\) | −5.40188 | + | 16.6253i | −0.301504 | + | 0.927933i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −13.7179 | − | 9.96666i | −0.763286 | − | 0.554560i | ||||
\(324\) | −13.8077 | + | 15.3350i | −0.767096 | + | 0.851946i | ||||
\(325\) | 10.6194 | + | 2.25722i | 0.589057 | + | 0.125208i | ||||
\(326\) | 35.1639 | − | 15.6560i | 1.94755 | − | 0.867104i | ||||
\(327\) | −1.16096 | − | 0.516894i | −0.0642014 | − | 0.0285843i | ||||
\(328\) | −0.450445 | + | 1.38633i | −0.0248717 | + | 0.0765471i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 8.89842 | − | 11.5131i | 0.489842 | − | 0.633773i | ||||
\(331\) | −1.81038 | − | 3.13567i | −0.0995075 | − | 0.172352i | 0.811973 | − | 0.583694i | \(-0.198393\pi\) |
−0.911481 | + | 0.411342i | \(0.865060\pi\) | |||||||
\(332\) | −2.48503 | − | 2.75991i | −0.136384 | − | 0.151470i | ||||
\(333\) | −0.537727 | − | 5.11613i | −0.0294672 | − | 0.280362i | ||||
\(334\) | −5.26942 | + | 50.1352i | −0.288330 | + | 2.74328i | ||||
\(335\) | 3.66375 | + | 11.2759i | 0.200172 | + | 0.616066i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.18183 | + | 3.76482i | 0.282272 | + | 0.205083i | 0.719908 | − | 0.694070i | \(-0.244184\pi\) |
−0.437636 | + | 0.899152i | \(0.644184\pi\) | |||||||
\(338\) | 6.43529 | + | 2.86518i | 0.350034 | + | 0.155845i | ||||
\(339\) | −4.36172 | − | 4.84418i | −0.236896 | − | 0.263100i | ||||
\(340\) | −14.5664 | + | 25.2297i | −0.789972 | + | 1.36827i | ||||
\(341\) | 28.4065 | − | 15.2951i | 1.53830 | − | 0.828276i | ||||
\(342\) | −6.56033 | −0.354742 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −0.497093 | + | 0.361159i | −0.0268014 | + | 0.0194724i | ||||
\(345\) | −1.27618 | + | 12.1420i | −0.0687072 | + | 0.653705i | ||||
\(346\) | 51.2446 | + | 10.8924i | 2.75493 | + | 0.585578i | ||||
\(347\) | 17.0785 | + | 3.63014i | 0.916819 | + | 0.194876i | 0.642075 | − | 0.766641i | \(-0.278074\pi\) |
0.274744 | + | 0.961517i | \(0.411407\pi\) | |||||||
\(348\) | 2.63316 | − | 25.0529i | 0.141152 | − | 1.34298i | ||||
\(349\) | −17.4949 | + | 12.7108i | −0.936481 | + | 0.680393i | −0.947571 | − | 0.319545i | \(-0.896470\pi\) |
0.0110900 | + | 0.999939i | \(0.496470\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 17.9738 | 0.959371 | ||||||||
\(352\) | −2.11530 | − | 2.02145i | −0.112746 | − | 0.107743i | ||||
\(353\) | 2.20075 | − | 3.81181i | 0.117134 | − | 0.202882i | −0.801497 | − | 0.597999i | \(-0.795963\pi\) |
0.918631 | + | 0.395117i | \(0.129296\pi\) | |||||||
\(354\) | 16.2031 | + | 17.9954i | 0.861184 | + | 0.956442i | ||||
\(355\) | 0.134080 | + | 0.0596964i | 0.00711624 | + | 0.00316836i | ||||
\(356\) | 31.7835 | + | 23.0920i | 1.68452 | + | 1.22388i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.59123 | − | 11.0527i | −0.189802 | − | 0.584152i | ||||
\(359\) | 1.11655 | − | 10.6232i | 0.0589290 | − | 0.560672i | −0.924729 | − | 0.380626i | \(-0.875709\pi\) |
0.983658 | − | 0.180046i | \(-0.0576247\pi\) | |||||||
\(360\) | 0.575082 | + | 5.47154i | 0.0303095 | + | 0.288375i | ||||
\(361\) | −7.23177 | − | 8.03169i | −0.380619 | − | 0.422721i | ||||
\(362\) | 9.54298 | + | 16.5289i | 0.501568 | + | 0.868741i | ||||
\(363\) | 5.75658 | − | 14.6885i | 0.302142 | − | 0.770947i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.239209 | − | 0.736211i | 0.0125208 | − | 0.0385350i | ||||
\(366\) | 7.80866 | + | 3.47664i | 0.408165 | + | 0.181727i | ||||
\(367\) | −9.33346 | + | 4.15552i | −0.487202 | + | 0.216916i | −0.635611 | − | 0.772010i | \(-0.719252\pi\) |
0.148408 | + | 0.988926i | \(0.452585\pi\) | |||||||
\(368\) | −22.8321 | − | 4.85310i | −1.19020 | − | 0.252986i | ||||
\(369\) | −0.198448 | + | 0.220398i | −0.0103308 | + | 0.0114735i | ||||
\(370\) | 13.5000 | + | 9.80834i | 0.701833 | + | 0.509911i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 16.8442 | − | 51.8411i | 0.873331 | − | 2.68784i | ||||
\(373\) | 13.9425 | + | 24.1492i | 0.721917 | + | 1.25040i | 0.960231 | + | 0.279208i | \(0.0900720\pi\) |
−0.238314 | + | 0.971188i | \(0.576595\pi\) | |||||||
\(374\) | −11.3103 | + | 46.3955i | −0.584843 | + | 2.39905i | ||||
\(375\) | 7.59588 | − | 13.1564i | 0.392249 | − | 0.679396i | ||||
\(376\) | −42.5049 | + | 9.03469i | −2.19202 | + | 0.465928i | ||||
\(377\) | −11.5593 | + | 8.39832i | −0.595334 | + | 0.432535i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.354761 | + | 1.09184i | 0.0182228 | + | 0.0560841i | 0.959754 | − | 0.280841i | \(-0.0906132\pi\) |
−0.941532 | + | 0.336925i | \(0.890613\pi\) | |||||||
\(380\) | 9.41817 | − | 10.4599i | 0.483142 | − | 0.536583i | ||||
\(381\) | 10.5181 | − | 4.68296i | 0.538859 | − | 0.239915i | ||||
\(382\) | −2.24335 | − | 21.3440i | −0.114780 | − | 1.09206i | ||||
\(383\) | −19.5156 | + | 4.14818i | −0.997202 | + | 0.211962i | −0.677473 | − | 0.735547i | \(-0.736925\pi\) |
−0.319729 | + | 0.947509i | \(0.603592\pi\) | |||||||
\(384\) | −29.0038 | −1.48009 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −62.2251 | −3.16717 | ||||||||
\(387\) | −0.122281 | + | 0.0259917i | −0.00621590 | + | 0.00132123i | ||||
\(388\) | 7.17850 | + | 68.2989i | 0.364433 | + | 3.46735i | ||||
\(389\) | 2.37522 | − | 1.05752i | 0.120428 | − | 0.0536182i | −0.345638 | − | 0.938368i | \(-0.612337\pi\) |
0.466066 | + | 0.884750i | \(0.345671\pi\) | |||||||
\(390\) | −9.33049 | + | 10.3626i | −0.472468 | + | 0.524728i | ||||
\(391\) | −12.3816 | − | 38.1067i | −0.626166 | − | 1.92714i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.117725 | + | 0.0855319i | −0.00593842 | + | 0.00431451i | ||||
\(394\) | −26.6207 | + | 5.65841i | −1.34113 | + | 0.285066i | ||||
\(395\) | 5.36761 | − | 9.29697i | 0.270074 | − | 0.467782i | ||||
\(396\) | 4.63705 | + | 11.3065i | 0.233020 | + | 0.568173i | ||||
\(397\) | 4.38618 | + | 7.59709i | 0.220136 | + | 0.381287i | 0.954849 | − | 0.297091i | \(-0.0960165\pi\) |
−0.734713 | + | 0.678378i | \(0.762683\pi\) | |||||||
\(398\) | −9.20059 | + | 28.3165i | −0.461184 | + | 1.41938i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9.53740 | + | 6.92932i | 0.476870 | + | 0.346466i | ||||
\(401\) | 18.9722 | − | 21.0708i | 0.947426 | − | 1.05222i | −0.0511402 | − | 0.998691i | \(-0.516286\pi\) |
0.998566 | − | 0.0535317i | \(-0.0170478\pi\) | |||||||
\(402\) | 32.1180 | + | 6.82688i | 1.60190 | + | 0.340494i | ||||
\(403\) | −28.2441 | + | 12.5751i | −1.40694 | + | 0.626410i | ||||
\(404\) | 44.5313 | + | 19.8266i | 2.21551 | + | 0.986410i | ||||
\(405\) | 2.05418 | − | 6.32210i | 0.102073 | − | 0.314148i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 17.0331 | + | 6.09885i | 0.844298 | + | 0.302309i | ||||
\(408\) | 19.6911 | + | 34.1060i | 0.974856 | + | 1.68850i | ||||
\(409\) | −13.3194 | − | 14.7927i | −0.658601 | − | 0.731451i | 0.317622 | − | 0.948217i | \(-0.397116\pi\) |
−0.976223 | + | 0.216767i | \(0.930449\pi\) | |||||||
\(410\) | −0.100559 | − | 0.956751i | −0.00496624 | − | 0.0472506i | ||||
\(411\) | −0.684227 | + | 6.50999i | −0.0337504 | + | 0.321114i | ||||
\(412\) | −9.92212 | − | 30.5371i | −0.488828 | − | 1.50446i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −12.5414 | − | 9.11189i | −0.616379 | − | 0.447825i | ||||
\(415\) | 1.09294 | + | 0.486607i | 0.0536502 | + | 0.0238866i | ||||
\(416\) | 1.87614 | + | 2.08367i | 0.0919855 | + | 0.102160i | ||||
\(417\) | 2.74315 | − | 4.75128i | 0.134333 | − | 0.232671i | ||||
\(418\) | 10.0055 | − | 20.7896i | 0.489387 | − | 1.01685i | ||||
\(419\) | 30.8957 | 1.50935 | 0.754676 | − | 0.656097i | \(-0.227794\pi\) | ||||
0.754676 | + | 0.656097i | \(0.227794\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.5727 | − | 14.2204i | 0.953913 | − | 0.693058i | 0.00218371 | − | 0.999998i | \(-0.499305\pi\) |
0.951729 | + | 0.306939i | \(0.0993049\pi\) | |||||||
\(422\) | −3.62369 | + | 34.4771i | −0.176398 | + | 1.67832i | ||||
\(423\) | −8.64796 | − | 1.83818i | −0.420478 | − | 0.0893755i | ||||
\(424\) | 19.7309 | + | 4.19393i | 0.958216 | + | 0.203675i | ||||
\(425\) | −2.11525 | + | 20.1252i | −0.102605 | + | 0.976218i | ||||
\(426\) | 0.328846 | − | 0.238921i | 0.0159326 | − | 0.0115757i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 47.6218 | 2.30188 | ||||||||
\(429\) | −6.55629 | + | 13.6227i | −0.316541 | + | 0.657712i | ||||
\(430\) | 0.202756 | − | 0.351184i | 0.00977778 | − | 0.0169356i | ||||
\(431\) | 12.9812 | + | 14.4171i | 0.625281 | + | 0.694445i | 0.969680 | − | 0.244378i | \(-0.0785839\pi\) |
−0.344399 | + | 0.938823i | \(0.611917\pi\) | |||||||
\(432\) | 17.8299 | + | 7.93837i | 0.857840 | + | 0.381935i | ||||
\(433\) | −17.3030 | − | 12.5714i | −0.831530 | − | 0.604142i | 0.0884616 | − | 0.996080i | \(-0.471805\pi\) |
−0.919992 | + | 0.391937i | \(0.871805\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.50767 | + | 7.71780i | 0.120233 | + | 0.370040i | ||||
\(436\) | −0.361881 | + | 3.44307i | −0.0173310 | + | 0.164893i | ||||
\(437\) | 2.02350 | + | 19.2524i | 0.0967974 | + | 0.920965i | ||||
\(438\) | −1.43452 | − | 1.59320i | −0.0685441 | − | 0.0761259i | ||||
\(439\) | −15.8658 | − | 27.4803i | −0.757232 | − | 1.31156i | −0.944257 | − | 0.329209i | \(-0.893218\pi\) |
0.187025 | − | 0.982355i | \(-0.440115\pi\) | |||||||
\(440\) | −18.2163 | − | 6.52252i | −0.868430 | − | 0.310949i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 14.1415 | − | 43.5229i | 0.672640 | − | 2.07017i | ||||
\(443\) | −1.52206 | − | 0.677666i | −0.0723154 | − | 0.0321969i | 0.370260 | − | 0.928928i | \(-0.379269\pi\) |
−0.442576 | + | 0.896731i | \(0.645935\pi\) | |||||||
\(444\) | 27.9246 | − | 12.4328i | 1.32524 | − | 0.590037i | ||||
\(445\) | −12.3792 | − | 2.63128i | −0.586830 | − | 0.124735i | ||||
\(446\) | −4.82032 | + | 5.35351i | −0.228249 | + | 0.253496i | ||||
\(447\) | −5.65324 | − | 4.10732i | −0.267389 | − | 0.194270i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.31070 | + | 16.3447i | −0.250627 | + | 0.771352i | 0.744032 | + | 0.668144i | \(0.232911\pi\) |
−0.994660 | + | 0.103208i | \(0.967089\pi\) | |||||||
\(450\) | 3.91464 | + | 6.78035i | 0.184538 | + | 0.319629i | ||||
\(451\) | −0.395777 | − | 0.965021i | −0.0186364 | − | 0.0454411i | ||||
\(452\) | −8.87892 | + | 15.3787i | −0.417629 | + | 0.723355i | ||||
\(453\) | −23.8121 | + | 5.06141i | −1.11879 | + | 0.237806i | ||||
\(454\) | −16.2337 | + | 11.7945i | −0.761885 | + | 0.553542i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.87973 | − | 18.0959i | −0.275343 | − | 0.847420i | ||||
\(457\) | 6.83894 | − | 7.59541i | 0.319912 | − | 0.355299i | −0.561643 | − | 0.827380i | \(-0.689830\pi\) |
0.881555 | + | 0.472081i | \(0.156497\pi\) | |||||||
\(458\) | 29.1043 | − | 12.9581i | 1.35996 | − | 0.605491i | ||||
\(459\) | 3.50193 | + | 33.3186i | 0.163456 | + | 1.55518i | ||||
\(460\) | 32.5330 | − | 6.91511i | 1.51686 | − | 0.322418i | ||||
\(461\) | 22.1160 | 1.03004 | 0.515022 | − | 0.857177i | \(-0.327784\pi\) | ||||
0.515022 | + | 0.857177i | \(0.327784\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −30.3717 | −1.41149 | −0.705747 | − | 0.708464i | \(-0.749389\pi\) | ||||
−0.705747 | + | 0.708464i | \(0.749389\pi\) | |||||||
\(464\) | −15.1759 | + | 3.22574i | −0.704525 | + | 0.149751i | ||||
\(465\) | 1.83547 | + | 17.4633i | 0.0851177 | + | 0.809841i | ||||
\(466\) | 28.4817 | − | 12.6809i | 1.31939 | − | 0.587429i | ||||
\(467\) | −16.8560 | + | 18.7205i | −0.780002 | + | 0.866280i | −0.993867 | − | 0.110583i | \(-0.964728\pi\) |
0.213865 | + | 0.976863i | \(0.431395\pi\) | |||||||
\(468\) | −3.61884 | − | 11.1376i | −0.167281 | − | 0.514837i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 23.2015 | − | 16.8569i | 1.07021 | − | 0.777551i | ||||
\(471\) | −3.14919 | + | 0.669382i | −0.145107 | + | 0.0308435i | ||||
\(472\) | 16.0997 | − | 27.8856i | 0.741050 | − | 1.28354i | ||||
\(473\) | 0.104131 | − | 0.427149i | 0.00478793 | − | 0.0196403i | ||||
\(474\) | −14.8656 | − | 25.7479i | −0.682798 | − | 1.18264i | ||||
\(475\) | 3.02123 | − | 9.29838i | 0.138623 | − | 0.426639i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.32028 | + | 2.41233i | 0.152025 | + | 0.110453i | ||||
\(478\) | 8.10070 | − | 8.99674i | 0.370517 | − | 0.411501i | ||||
\(479\) | −20.7406 | − | 4.40856i | −0.947663 | − | 0.201432i | −0.291943 | − | 0.956436i | \(-0.594302\pi\) |
−0.655721 | + | 0.755004i | \(0.727635\pi\) | |||||||
\(480\) | 1.45479 | − | 0.647713i | 0.0664016 | − | 0.0295639i | ||||
\(481\) | −15.8386 | − | 7.05181i | −0.722179 | − | 0.321535i | ||||
\(482\) | −1.97290 | + | 6.07197i | −0.0898633 | + | 0.276571i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −42.9024 | − | 2.54942i | −1.95011 | − | 0.115883i | ||||
\(485\) | −11.0615 | − | 19.1591i | −0.502276 | − | 0.869968i | ||||
\(486\) | 15.2720 | + | 16.9613i | 0.692752 | + | 0.769379i | ||||
\(487\) | 1.75814 | + | 16.7276i | 0.0796691 | + | 0.758001i | 0.959309 | + | 0.282360i | \(0.0911172\pi\) |
−0.879639 | + | 0.475641i | \(0.842216\pi\) | |||||||
\(488\) | 1.18807 | − | 11.3038i | 0.0537815 | − | 0.511697i | ||||
\(489\) | 7.01897 | + | 21.6022i | 0.317409 | + | 0.976884i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.91406 | − | 2.84373i | −0.176639 | − | 0.128336i | 0.495953 | − | 0.868350i | \(-0.334819\pi\) |
−0.672592 | + | 0.740014i | \(0.734819\pi\) | |||||||
\(492\) | −1.60989 | − | 0.716768i | −0.0725793 | − | 0.0323144i | ||||
\(493\) | −17.8204 | − | 19.7915i | −0.802589 | − | 0.891365i | ||||
\(494\) | −11.0549 | + | 19.1477i | −0.497385 | + | 0.861496i | ||||
\(495\) | −2.84608 | − | 2.71980i | −0.127922 | − | 0.122246i | ||||
\(496\) | −33.5719 | −1.50742 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 2.68055 | − | 1.94753i | 0.120118 | − | 0.0872709i | ||||
\(499\) | −3.19685 | + | 30.4160i | −0.143111 | + | 1.36161i | 0.653413 | + | 0.757001i | \(0.273336\pi\) |
−0.796524 | + | 0.604607i | \(0.793330\pi\) | |||||||
\(500\) | −40.4814 | − | 8.60458i | −1.81038 | − | 0.384809i | ||||
\(501\) | −29.0976 | − | 6.18489i | −1.29999 | − | 0.276320i | ||||
\(502\) | 6.66197 | − | 63.3844i | 0.297338 | − | 2.82898i | ||||
\(503\) | −22.8472 | + | 16.5994i | −1.01871 | + | 0.740133i | −0.966017 | − | 0.258478i | \(-0.916779\pi\) |
−0.0526880 | + | 0.998611i | \(0.516779\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.7029 | −0.698768 | ||||||||
\(506\) | 48.0032 | − | 25.8467i | 2.13400 | − | 1.14902i | ||||
\(507\) | −2.07842 | + | 3.59992i | −0.0923057 | + | 0.159878i | ||||
\(508\) | −20.9875 | − | 23.3090i | −0.931171 | − | 1.03417i | ||||
\(509\) | 3.83748 | + | 1.70856i | 0.170093 | + | 0.0757305i | 0.490017 | − | 0.871713i | \(-0.336991\pi\) |
−0.319924 | + | 0.947443i | \(0.603657\pi\) | |||||||
\(510\) | −21.0273 | − | 15.2772i | −0.931104 | − | 0.676486i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 10.8274 | + | 33.3234i | 0.478509 | + | 1.47270i | ||||
\(513\) | 1.69193 | − | 16.0976i | 0.0747004 | − | 0.710726i | ||||
\(514\) | −7.60929 | − | 72.3976i | −0.335632 | − | 3.19332i | ||||
\(515\) | 6.92113 | + | 7.68669i | 0.304981 | + | 0.338716i | ||||
\(516\) | −0.371411 | − | 0.643303i | −0.0163505 | − | 0.0283198i | ||||
\(517\) | 19.0147 | − | 24.6018i | 0.836265 | − | 1.08199i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.55323 | + | 29.4018i | −0.419340 | + | 1.29060i | ||||
\(520\) | 16.9389 | + | 7.54169i | 0.742820 | + | 0.330725i | ||||
\(521\) | 18.8619 | − | 8.39787i | 0.826356 | − | 0.367918i | 0.0504195 | − | 0.998728i | \(-0.483944\pi\) |
0.775937 | + | 0.630811i | \(0.217278\pi\) | |||||||
\(522\) | −10.0787 | − | 2.14230i | −0.441133 | − | 0.0937657i | ||||
\(523\) | 15.1451 | − | 16.8204i | 0.662251 | − | 0.735504i | −0.314647 | − | 0.949209i | \(-0.601886\pi\) |
0.976898 | + | 0.213704i | \(0.0685529\pi\) | |||||||
\(524\) | 0.320708 | + | 0.233008i | 0.0140102 | + | 0.0101790i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.50632 | + | 7.71367i | −0.109281 | + | 0.336332i | ||||
\(527\) | −28.8138 | − | 49.9069i | −1.25515 | − | 2.17398i | ||||
\(528\) | −12.5204 | + | 10.6180i | −0.544882 | + | 0.462088i | ||||
\(529\) | −11.3720 | + | 19.6969i | −0.494434 | + | 0.856385i | ||||
\(530\) | −13.0218 | + | 2.76787i | −0.565631 | + | 0.120229i | ||||
\(531\) | 5.30007 | − | 3.85073i | 0.230003 | − | 0.167107i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.308871 | + | 0.950608i | 0.0133787 | + | 0.0411754i | ||||
\(534\) | −23.4530 | + | 26.0472i | −1.01491 | + | 1.12717i | ||||
\(535\) | −14.0146 | + | 6.23969i | −0.605903 | + | 0.269765i | ||||
\(536\) | −4.56394 | − | 43.4230i | −0.197132 | − | 1.87559i | ||||
\(537\) | 6.70795 | − | 1.42582i | 0.289469 | − | 0.0615286i | ||||
\(538\) | −4.21881 | −0.181886 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −27.8098 | −1.19674 | ||||||||
\(541\) | −41.7828 | + | 8.88122i | −1.79638 | + | 0.381833i | −0.980521 | − | 0.196412i | \(-0.937071\pi\) |
−0.815863 | + | 0.578245i | \(0.803738\pi\) | |||||||
\(542\) | 0.629021 | + | 5.98473i | 0.0270188 | + | 0.257066i | ||||
\(543\) | −10.2889 | + | 4.58091i | −0.441539 | + | 0.196586i | ||||
\(544\) | −3.49702 | + | 3.88383i | −0.149934 | + | 0.166518i | ||||
\(545\) | −0.344634 | − | 1.06067i | −0.0147625 | − | 0.0454343i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −35.9873 | + | 26.1463i | −1.53870 | + | 1.11793i | −0.587563 | + | 0.809178i | \(0.699913\pi\) |
−0.951141 | + | 0.308756i | \(0.900087\pi\) | |||||||
\(548\) | 17.4427 | − | 3.70756i | 0.745114 | − | 0.158379i | ||||
\(549\) | 1.15626 | − | 2.00269i | 0.0493478 | − | 0.0854728i | ||||
\(550\) | −27.4573 | + | 2.06435i | −1.17078 | + | 0.0880242i | ||||
\(551\) | 6.43354 | + | 11.1432i | 0.274078 | + | 0.474717i | ||||
\(552\) | 13.8938 | − | 42.7608i | 0.591360 | − | 1.82002i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 10.1376 | + | 7.36536i | 0.430703 | + | 0.312924i | ||||
\(555\) | −6.58889 | + | 7.31770i | −0.279683 | + | 0.310619i | ||||
\(556\) | −14.6193 | − | 3.10743i | −0.619998 | − | 0.131785i | ||||
\(557\) | −22.8305 | + | 10.1648i | −0.967360 | + | 0.430696i | −0.828730 | − | 0.559648i | \(-0.810936\pi\) |
−0.138629 | + | 0.990344i | \(0.544270\pi\) | |||||||
\(558\) | −20.3683 | − | 9.06856i | −0.862259 | − | 0.383903i | ||||
\(559\) | −0.130196 | + | 0.400702i | −0.00550670 | + | 0.0169479i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −26.5303 | − | 9.49941i | −1.12011 | − | 0.401065i | ||||
\(562\) | −27.4283 | − | 47.5072i | −1.15699 | − | 2.00397i | ||||
\(563\) | −6.02890 | − | 6.69578i | −0.254088 | − | 0.282193i | 0.602583 | − | 0.798056i | \(-0.294138\pi\) |
−0.856671 | + | 0.515863i | \(0.827471\pi\) | |||||||
\(564\) | −5.49129 | − | 52.2461i | −0.231225 | − | 2.19996i | ||||
\(565\) | 0.597955 | − | 5.68916i | 0.0251562 | − | 0.239345i | ||||
\(566\) | −6.37460 | − | 19.6190i | −0.267944 | − | 0.824648i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.437275 | − | 0.317699i | −0.0183476 | − | 0.0133303i | ||||
\(569\) | 26.6516 | + | 11.8661i | 1.11729 | + | 0.497452i | 0.880471 | − | 0.474101i | \(-0.157227\pi\) |
0.236824 | + | 0.971553i | \(0.423893\pi\) | |||||||
\(570\) | 8.40254 | + | 9.33197i | 0.351944 | + | 0.390873i | ||||
\(571\) | −0.894970 | + | 1.55013i | −0.0374533 | + | 0.0648711i | −0.884144 | − | 0.467214i | \(-0.845258\pi\) |
0.846691 | + | 0.532085i | \(0.178591\pi\) | |||||||
\(572\) | 40.8144 | + | 5.51858i | 1.70653 | + | 0.230743i | ||||
\(573\) | 12.6645 | 0.529065 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 18.6906 | − | 13.5795i | 0.779452 | − | 0.566305i | ||||
\(576\) | −0.891772 | + | 8.48465i | −0.0371572 | + | 0.353527i | ||||
\(577\) | −21.1133 | − | 4.48777i | −0.878958 | − | 0.186828i | −0.253734 | − | 0.967274i | \(-0.581659\pi\) |
−0.625223 | + | 0.780446i | \(0.714992\pi\) | |||||||
\(578\) | 43.0202 | + | 9.14422i | 1.78940 | + | 0.380349i | ||||
\(579\) | 3.83817 | − | 36.5178i | 0.159509 | − | 1.51763i | ||||
\(580\) | 17.8850 | − | 12.9942i | 0.742633 | − | 0.539554i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −61.2694 | −2.53970 | ||||||||
\(583\) | −12.7086 | + | 6.84276i | −0.526336 | + | 0.283398i | ||||
\(584\) | −1.42537 | + | 2.46881i | −0.0589823 | + | 0.102160i | ||||
\(585\) | 2.52430 | + | 2.80352i | 0.104367 | + | 0.115911i | ||||
\(586\) | 54.6780 | + | 24.3442i | 2.25873 | + | 1.00565i | ||||
\(587\) | 4.46865 | + | 3.24666i | 0.184441 | + | 0.134004i | 0.676174 | − | 0.736742i | \(-0.263637\pi\) |
−0.491734 | + | 0.870746i | \(0.663637\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.60373 | + | 26.4796i | 0.354511 | + | 1.09107i | ||||
\(590\) | −2.22131 | + | 21.1343i | −0.0914497 | + | 0.870086i | ||||
\(591\) | −1.67871 | − | 15.9718i | −0.0690527 | − | 0.656993i | ||||
\(592\) | −12.5972 | − | 13.9907i | −0.517744 | − | 0.575013i | ||||
\(593\) | −20.3933 | − | 35.3223i | −0.837454 | − | 1.45051i | −0.892017 | − | 0.452002i | \(-0.850710\pi\) |
0.0545633 | − | 0.998510i | \(-0.482623\pi\) | |||||||
\(594\) | −43.7534 | + | 12.7941i | −1.79522 | + | 0.524948i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.88254 | + | 18.1046i | −0.240958 | + | 0.741593i | ||||
\(597\) | −16.0505 | − | 7.14613i | −0.656902 | − | 0.292472i | ||||
\(598\) | −47.7288 | + | 21.2502i | −1.95178 | + | 0.868986i | ||||
\(599\) | 25.9355 | + | 5.51276i | 1.05970 | + | 0.225245i | 0.704615 | − | 0.709590i | \(-0.251120\pi\) |
0.355081 | + | 0.934835i | \(0.384453\pi\) | |||||||
\(600\) | −15.1943 | + | 16.8750i | −0.620306 | + | 0.688919i | ||||
\(601\) | −30.5565 | − | 22.2006i | −1.24643 | − | 0.905581i | −0.248417 | − | 0.968653i | \(-0.579910\pi\) |
−0.998009 | + | 0.0630720i | \(0.979910\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.74513 | − | 8.44864i | 0.111790 | − | 0.344055i | ||||
\(604\) | 33.1593 | + | 57.4336i | 1.34923 | + | 2.33694i | ||||
\(605\) | 12.9598 | − | 4.87106i | 0.526889 | − | 0.198037i | ||||
\(606\) | −21.7445 | + | 37.6626i | −0.883310 | + | 1.52994i | ||||
\(607\) | −27.1185 | + | 5.76422i | −1.10071 | + | 0.233962i | −0.722233 | − | 0.691650i | \(-0.756884\pi\) |
−0.378474 | + | 0.925612i | \(0.623551\pi\) | |||||||
\(608\) | 2.04277 | − | 1.48416i | 0.0828452 | − | 0.0601906i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.31801 | + | 7.13411i | 0.0938536 | + | 0.288852i | ||||
\(611\) | −19.9380 | + | 22.1433i | −0.806603 | + | 0.895824i | ||||
\(612\) | 19.9411 | − | 8.87834i | 0.806071 | − | 0.358886i | ||||
\(613\) | −3.78669 | − | 36.0280i | −0.152943 | − | 1.45516i | −0.754486 | − | 0.656316i | \(-0.772114\pi\) |
0.601543 | − | 0.798841i | \(-0.294553\pi\) | |||||||
\(614\) | −10.9213 | + | 2.32139i | −0.440747 | + | 0.0936837i | ||||
\(615\) | 0.567687 | 0.0228914 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 41.1920 | 1.65833 | 0.829163 | − | 0.559007i | \(-0.188817\pi\) | ||||
0.829163 | + | 0.559007i | \(0.188817\pi\) | |||||||
\(618\) | 28.0202 | − | 5.95587i | 1.12714 | − | 0.239580i | ||||
\(619\) | −3.73580 | − | 35.5437i | −0.150154 | − | 1.42862i | −0.767054 | − | 0.641582i | \(-0.778278\pi\) |
0.616900 | − | 0.787042i | \(-0.288388\pi\) | |||||||
\(620\) | 43.7004 | − | 19.4567i | 1.75505 | − | 0.781398i | ||||
\(621\) | 25.5930 | − | 28.4240i | 1.02701 | − | 1.14061i | ||||
\(622\) | −1.66037 | − | 5.11010i | −0.0665749 | − | 0.204897i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 12.7274 | − | 9.24698i | 0.509503 | − | 0.370176i | ||||
\(625\) | −3.66537 | + | 0.779098i | −0.146615 | + | 0.0311639i | ||||
\(626\) | 11.7868 | − | 20.4154i | 0.471096 | − | 0.815963i | ||||
\(627\) | 11.5836 | + | 7.15425i | 0.462603 | + | 0.285713i | ||||
\(628\) | 4.38539 | + | 7.59571i | 0.174996 | + | 0.303102i | ||||
\(629\) | 9.98623 | − | 30.7345i | 0.398177 | − | 1.22546i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.23700 | − | 1.62527i | −0.0890534 | − | 0.0647011i | 0.542368 | − | 0.840141i | \(-0.317528\pi\) |
−0.631421 | + | 0.775440i | \(0.717528\pi\) | |||||||
\(632\) | −26.4535 | + | 29.3796i | −1.05227 | + | 1.16866i | ||||
\(633\) | −20.0099 | − | 4.25324i | −0.795322 | − | 0.169051i | ||||
\(634\) | −14.3331 | + | 6.38151i | −0.569240 | + | 0.253442i | ||||
\(635\) | 9.23048 | + | 4.10968i | 0.366301 | + | 0.163088i | ||||
\(636\) | −7.53581 | + | 23.1928i | −0.298814 | + | 0.919655i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 22.1605 | − | 28.6720i | 0.877344 | − | 1.13514i | ||||
\(639\) | −0.0549848 | − | 0.0952364i | −0.00217516 | − | 0.00376749i | ||||
\(640\) | −17.0315 | − | 18.9154i | −0.673228 | − | 0.747696i | ||||
\(641\) | −4.02293 | − | 38.2756i | −0.158896 | − | 1.51180i | −0.725739 | − | 0.687970i | \(-0.758502\pi\) |
0.566843 | − | 0.823826i | \(-0.308165\pi\) | |||||||
\(642\) | −4.44104 | + | 42.2536i | −0.175274 | + | 1.66762i | ||||
\(643\) | 8.15130 | + | 25.0871i | 0.321456 | + | 0.989339i | 0.973015 | + | 0.230741i | \(0.0741151\pi\) |
−0.651559 | + | 0.758598i | \(0.725885\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.193592 | + | 0.140653i | 0.00762267 | + | 0.00553819i | ||||
\(646\) | −37.6486 | − | 16.7622i | −1.48126 | − | 0.659501i | ||||
\(647\) | 18.2814 | + | 20.3035i | 0.718715 | + | 0.798214i | 0.986237 | − | 0.165338i | \(-0.0528714\pi\) |
−0.267522 | + | 0.963552i | \(0.586205\pi\) | |||||||
\(648\) | −12.2402 | + | 21.2006i | −0.480839 | + | 0.832838i | ||||
\(649\) | 4.11948 | + | 22.6688i | 0.161704 | + | 0.889830i | ||||
\(650\) | 26.3865 | 1.03496 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 50.0601 | − | 36.3708i | 1.96051 | − | 1.42439i | ||||
\(653\) | 0.884484 | − | 8.41530i | 0.0346125 | − | 0.329316i | −0.963490 | − | 0.267744i | \(-0.913722\pi\) |
0.998103 | − | 0.0615722i | \(-0.0196114\pi\) | |||||||
\(654\) | −3.02120 | − | 0.642177i | −0.118138 | − | 0.0251111i | ||||
\(655\) | −0.124911 | − | 0.0265506i | −0.00488068 | − | 0.00103742i | ||||
\(656\) | −0.113451 | + | 1.07941i | −0.00442951 | + | 0.0421439i | ||||
\(657\) | −0.469236 | + | 0.340920i | −0.0183066 | + | 0.0133005i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.29247 | −0.206165 | −0.103083 | − | 0.994673i | \(-0.532871\pi\) | ||||
−0.103083 | + | 0.994673i | \(0.532871\pi\) | |||||||
\(660\) | 10.1441 | − | 21.0776i | 0.394860 | − | 0.820445i | ||||
\(661\) | −9.63501 | + | 16.6883i | −0.374759 | + | 0.649101i | −0.990291 | − | 0.139011i | \(-0.955608\pi\) |
0.615532 | + | 0.788112i | \(0.288941\pi\) | |||||||
\(662\) | −5.88841 | − | 6.53974i | −0.228859 | − | 0.254174i | ||||
\(663\) | 24.6698 | + | 10.9837i | 0.958097 | + | 0.426572i | ||||
\(664\) | −3.56439 | − | 2.58968i | −0.138325 | − | 0.100499i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.86364 | − | 11.8911i | −0.149713 | − | 0.460769i | ||||
\(667\) | −3.17818 | + | 30.2384i | −0.123060 | + | 1.17084i | ||||
\(668\) | 8.47092 | + | 80.5954i | 0.327750 | + | 3.11833i | ||||
\(669\) | −2.84447 | − | 3.15910i | −0.109973 | − | 0.122138i | ||||
\(670\) | 14.4079 | + | 24.9552i | 0.556625 | + | 0.964104i | ||||
\(671\) | 4.58304 | + | 6.71858i | 0.176926 | + | 0.259368i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.86892 | + | 18.0627i | −0.226230 | + | 0.696265i | 0.771934 | + | 0.635702i | \(0.219289\pi\) |
−0.998164 | + | 0.0605625i | \(0.980711\pi\) | |||||||
\(674\) | 14.2214 | + | 6.33178i | 0.547789 | + | 0.243891i | ||||
\(675\) | −17.6471 | + | 7.85699i | −0.679236 | + | 0.302416i | ||||
\(676\) | 11.0767 | + | 2.35442i | 0.426026 | + | 0.0905547i | ||||
\(677\) | −21.6945 | + | 24.0942i | −0.833786 | + | 0.926013i | −0.998175 | − | 0.0603821i | \(-0.980768\pi\) |
0.164389 | + | 0.986396i | \(0.447435\pi\) | |||||||
\(678\) | −12.8172 | − | 9.31222i | −0.492240 | − | 0.357633i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −10.6800 | + | 32.8695i | −0.409558 | + | 1.26049i | ||||
\(681\) | −5.92044 | − | 10.2545i | −0.226872 | − | 0.392954i | ||||
\(682\) | 59.8031 | − | 50.7160i | 2.28998 | − | 1.94202i | ||||
\(683\) | −7.56298 | + | 13.0995i | −0.289389 | + | 0.501237i | −0.973664 | − | 0.227987i | \(-0.926786\pi\) |
0.684275 | + | 0.729224i | \(0.260119\pi\) | |||||||
\(684\) | −10.3157 | + | 2.19266i | −0.394430 | + | 0.0838386i | ||||
\(685\) | −4.64740 | + | 3.37654i | −0.177568 | + | 0.129011i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.80944 | + | 17.8796i | 0.221644 | + | 0.682150i | ||||
\(688\) | −0.306128 | + | 0.339990i | −0.0116710 | + | 0.0129620i | ||||
\(689\) | 12.6359 | − | 5.62588i | 0.481391 | − | 0.214329i | ||||
\(690\) | 3.10169 | + | 29.5106i | 0.118079 | + | 1.12345i | ||||
\(691\) | −30.7244 | + | 6.53067i | −1.16881 | + | 0.248438i | −0.751129 | − | 0.660155i | \(-0.770490\pi\) |
−0.417681 | + | 0.908594i | \(0.637157\pi\) | |||||||
\(692\) | 84.2192 | 3.20153 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 42.4357 | 1.61084 | ||||||||
\(695\) | 4.70946 | − | 1.00103i | 0.178640 | − | 0.0379711i | ||||
\(696\) | −3.12381 | − | 29.7210i | −0.118408 | − | 1.12657i | ||||
\(697\) | −1.70199 | + | 0.757776i | −0.0644675 | + | 0.0287028i | ||||
\(698\) | −35.1684 | + | 39.0584i | −1.33114 | + | 1.47838i | ||||
\(699\) | 5.68515 | + | 17.4971i | 0.215032 | + | 0.661801i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.9966 | − | 9.44259i | 0.490875 | − | 0.356642i | −0.314646 | − | 0.949209i | \(-0.601886\pi\) |
0.805521 | + | 0.592568i | \(0.201886\pi\) | |||||||
\(702\) | 42.7299 | − | 9.08252i | 1.61274 | − | 0.342798i | ||||
\(703\) | −7.80663 | + | 13.5215i | −0.294433 | + | 0.509972i | ||||
\(704\) | −25.5277 | − | 15.7664i | −0.962111 | − | 0.594220i | ||||
\(705\) | 8.46162 | + | 14.6560i | 0.318683 | + | 0.551975i | ||||
\(706\) | 3.30575 | − | 10.1741i | 0.124414 | − | 0.382906i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 31.4928 | + | 22.8809i | 1.18357 | + | 0.859916i | ||||
\(709\) | 26.5630 | − | 29.5012i | 0.997594 | − | 1.10794i | 0.00343775 | − | 0.999994i | \(-0.498906\pi\) |
0.994157 | − | 0.107947i | \(-0.0344276\pi\) | |||||||
\(710\) | 0.348920 | + | 0.0741653i | 0.0130948 | + | 0.00278338i | ||||
\(711\) | −7.34816 | + | 3.27161i | −0.275578 | + | 0.122695i | ||||
\(712\) | 42.5775 | + | 18.9567i | 1.59566 | + | 0.710433i | ||||
\(713\) | −20.3306 | + | 62.5713i | −0.761389 | + | 2.34331i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.7343 | + | 3.72368i | −0.476236 | + | 0.139258i | ||||
\(716\) | −9.34111 | − | 16.1793i | −0.349094 | − | 0.604648i | ||||
\(717\) | 4.78021 | + | 5.30896i | 0.178520 | + | 0.198267i | ||||
\(718\) | −2.71371 | − | 25.8192i | −0.101275 | − | 0.963565i | ||||
\(719\) | −1.03090 | + | 9.80838i | −0.0384462 | + | 0.365791i | 0.958337 | + | 0.285641i | \(0.0922065\pi\) |
−0.996783 | + | 0.0801497i | \(0.974460\pi\) | |||||||
\(720\) | 1.26587 | + | 3.89596i | 0.0471763 | + | 0.145194i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −21.2510 | − | 15.4397i | −0.790879 | − | 0.574607i | ||||
\(723\) | −3.44174 | − | 1.53236i | −0.128000 | − | 0.0569891i | ||||
\(724\) | 20.5302 | + | 22.8011i | 0.762998 | + | 0.847395i | ||||
\(725\) | 7.67796 | − | 13.2986i | 0.285152 | − | 0.493898i | ||||
\(726\) | 6.26296 | − | 37.8285i | 0.232440 | − | 1.40395i | ||||
\(727\) | 31.5764 | 1.17111 | 0.585553 | − | 0.810634i | \(-0.300878\pi\) | ||||
0.585553 | + | 0.810634i | \(0.300878\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.7145 | + | 17.2296i | −0.878313 | + | 0.638132i | ||||
\(730\) | 0.196661 | − | 1.87110i | 0.00727874 | − | 0.0692526i | ||||
\(731\) | −0.768160 | − | 0.163277i | −0.0284114 | − | 0.00603904i | ||||
\(732\) | 13.4406 | + | 2.85688i | 0.496778 | + | 0.105594i | ||||
\(733\) | 4.31625 | − | 41.0664i | 0.159424 | − | 1.51682i | −0.563629 | − | 0.826028i | \(-0.690595\pi\) |
0.723053 | − | 0.690793i | \(-0.242738\pi\) | |||||||
\(734\) | −20.0889 | + | 14.5955i | −0.741496 | + | 0.538729i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.96659 | 0.219931 | ||||||||
\(737\) | 22.5869 | + | 21.5848i | 0.832000 | + | 0.795087i | ||||
\(738\) | −0.360406 | + | 0.624242i | −0.0132667 | + | 0.0229787i | ||||
\(739\) | 23.6936 | + | 26.3144i | 0.871584 | + | 0.967992i | 0.999718 | − | 0.0237652i | \(-0.00756542\pi\) |
−0.128134 | + | 0.991757i | \(0.540899\pi\) | |||||||
\(740\) | 24.5061 | + | 10.9108i | 0.900862 | + | 0.401090i | ||||
\(741\) | −10.5552 | − | 7.66883i | −0.387756 | − | 0.281722i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.24351 | − | 3.82713i | −0.0456200 | − | 0.140404i | 0.925652 | − | 0.378376i | \(-0.123517\pi\) |
−0.971272 | + | 0.237972i | \(0.923517\pi\) | |||||||
\(744\) | 6.75941 | − | 64.3114i | 0.247812 | − | 2.35777i | ||||
\(745\) | −0.641005 | − | 6.09875i | −0.0234846 | − | 0.223441i | ||||
\(746\) | 45.3492 | + | 50.3654i | 1.66035 | + | 1.84401i | ||||
\(747\) | −0.448201 | − | 0.776307i | −0.0163988 | − | 0.0284036i | ||||
\(748\) | −2.27790 | + | 76.7340i | −0.0832882 | + | 2.80567i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 11.4098 | − | 35.1157i | 0.416626 | − | 1.28224i | ||||
\(751\) | 22.3079 | + | 9.93210i | 0.814025 | + | 0.362427i | 0.771150 | − | 0.636653i | \(-0.219682\pi\) |
0.0428749 | + | 0.999080i | \(0.486348\pi\) | |||||||
\(752\) | −29.5582 | + | 13.1601i | −1.07788 | + | 0.479901i | ||||
\(753\) | 36.7872 | + | 7.81936i | 1.34060 | + | 0.284953i | ||||
\(754\) | −23.2365 | + | 25.8068i | −0.846225 | + | 0.939828i | ||||
\(755\) | −17.2837 | − | 12.5573i | −0.629019 | − | 0.457009i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.407046 | + | 1.25276i | −0.0147943 | + | 0.0455323i | −0.958181 | − | 0.286162i | \(-0.907620\pi\) |
0.943387 | + | 0.331695i | \(0.107620\pi\) | |||||||
\(758\) | 1.39512 | + | 2.41641i | 0.0506729 | + | 0.0877680i | ||||
\(759\) | 12.2076 | + | 29.7657i | 0.443107 | + | 1.08043i | ||||
\(760\) | 8.34895 | − | 14.4608i | 0.302848 | − | 0.524548i | ||||
\(761\) | −7.08574 | + | 1.50612i | −0.256858 | + | 0.0545968i | −0.334541 | − | 0.942381i | \(-0.608581\pi\) |
0.0776828 | + | 0.996978i | \(0.475248\pi\) | |||||||
\(762\) | 22.6387 | − | 16.4480i | 0.820115 | − | 0.595848i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −10.6613 | − | 32.8122i | −0.385714 | − | 1.18710i | ||||
\(765\) | −4.70515 | + | 5.22560i | −0.170115 | + | 0.188932i | ||||
\(766\) | −44.2992 | + | 19.7233i | −1.60059 | + | 0.712630i | ||||
\(767\) | −2.30791 | − | 21.9583i | −0.0833338 | − | 0.792868i | ||||
\(768\) | −43.5696 | + | 9.26101i | −1.57218 | + | 0.334178i | ||||
\(769\) | −44.3139 | −1.59800 | −0.798999 | − | 0.601332i | \(-0.794637\pi\) | ||||
−0.798999 | + | 0.601332i | \(0.794637\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 42.9570 | 1.54706 | ||||||||
\(772\) | −97.8447 | + | 20.7975i | −3.52151 | + | 0.748520i | ||||
\(773\) | 1.99189 | + | 18.9516i | 0.0716433 | + | 0.681640i | 0.970121 | + | 0.242621i | \(0.0780072\pi\) |
−0.898478 | + | 0.439019i | \(0.855326\pi\) | |||||||
\(774\) | −0.277570 | + | 0.123582i | −0.00997704 | + | 0.00444207i | ||||
\(775\) | 22.2337 | − | 24.6930i | 0.798657 | − | 0.886999i | ||||
\(776\) | 25.1761 | + | 77.4839i | 0.903768 | + | 2.78151i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5.11232 | − | 3.71432i | 0.183286 | − | 0.133165i | ||||
\(779\) | 0.880453 | − | 0.187146i | 0.0315455 | − | 0.00670520i | ||||
\(780\) | −11.2081 | + | 19.4129i | −0.401313 | + | 0.695095i | ||||
\(781\) | 0.385664 | − | 0.0289957i | 0.0138001 | − | 0.00103755i | ||||
\(782\) | −48.6914 | − | 84.3360i | −1.74120 | − | 3.01585i | ||||
\(783\) | 7.85604 | − | 24.1784i | 0.280752 | − | 0.864066i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.28581 | − | 1.66074i | −0.0815840 | − | 0.0592742i | ||||
\(786\) | −0.236650 | + | 0.262827i | −0.00844104 | + | 0.00937473i | ||||
\(787\) | 30.7725 | + | 6.54091i | 1.09692 | + | 0.233158i | 0.720614 | − | 0.693336i | \(-0.243860\pi\) |
0.376308 | + | 0.926494i | \(0.377193\pi\) | |||||||
\(788\) | −39.9680 | + | 17.7949i | −1.42380 | + | 0.633918i | ||||
\(789\) | −4.37229 | − | 1.94667i | −0.155658 | − | 0.0693033i | ||||
\(790\) | 8.06270 | − | 24.8144i | 0.286858 | − | 0.882858i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 8.16964 | + | 11.9764i | 0.290295 | + | 0.425563i | ||||
\(793\) | −3.89685 | − | 6.74955i | −0.138381 | − | 0.239683i | ||||
\(794\) | 14.2664 | + | 15.8445i | 0.506296 | + | 0.562299i | ||||
\(795\) | −0.821156 | − | 7.81278i | −0.0291234 | − | 0.277091i | ||||
\(796\) | −5.00305 | + | 47.6009i | −0.177329 | + | 1.68717i | ||||
\(797\) | 3.87670 | + | 11.9313i | 0.137320 | + | 0.422627i | 0.995944 | − | 0.0899793i | \(-0.0286801\pi\) |
−0.858624 | + | 0.512606i | \(0.828680\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −44.9324 | − | 32.6453i | −1.58959 | − | 1.15491i | ||||
\(800\) | −2.75288 | − | 1.22566i | −0.0973291 | − | 0.0433337i | ||||
\(801\) | 6.34506 | + | 7.04691i | 0.224192 | + | 0.248990i | ||||
\(802\) | 34.4559 | − | 59.6794i | 1.21668 | − | 2.10735i | ||||
\(803\) | −0.364713 | − | 2.00696i | −0.0128704 | − | 0.0708241i | ||||
\(804\) | 52.7850 | 1.86159 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −60.7915 | + | 44.1676i | −2.14129 | + | 1.55574i | ||||
\(807\) | 0.260225 | − | 2.47587i | 0.00916035 | − | 0.0871549i | ||||
\(808\) | 56.5647 | + | 12.0232i | 1.98994 | + | 0.422975i | ||||
\(809\) | 5.26267 | + | 1.11861i | 0.185026 | + | 0.0393284i | 0.299492 | − | 0.954099i | \(-0.403183\pi\) |
−0.114467 | + | 0.993427i | \(0.536516\pi\) | |||||||
\(810\) | 1.68880 | − | 16.0678i | 0.0593382 | − | 0.564565i | ||||
\(811\) | 11.0835 | − | 8.05262i | 0.389194 | − | 0.282766i | −0.375931 | − | 0.926647i | \(-0.622677\pi\) |
0.765125 | + | 0.643882i | \(0.222677\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.55103 | −0.124540 | ||||||||
\(814\) | 43.5753 | + | 5.89189i | 1.52731 | + | 0.206511i | ||||
\(815\) | −9.96663 | + | 17.2627i | −0.349116 | + | 0.604686i | ||||
\(816\) | 19.6212 | + | 21.7915i | 0.686878 | + | 0.762855i | ||||
\(817\) | 0.346619 | + | 0.154325i | 0.0121266 | + | 0.00539913i | ||||
\(818\) | −39.1398 | − | 28.4367i | −1.36849 | − | 0.994266i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.477897 | − | 1.47082i | −0.0166889 | − | 0.0513631i | ||||
\(821\) | 0.964918 | − | 9.18059i | 0.0336759 | − | 0.320405i | −0.964696 | − | 0.263366i | \(-0.915167\pi\) |
0.998372 | − | 0.0570390i | \(-0.0181659\pi\) | |||||||
\(822\) | 1.66298 | + | 15.8222i | 0.0580032 | + | 0.551863i | ||||
\(823\) | −8.32577 | − | 9.24670i | −0.290218 | − | 0.322320i | 0.580351 | − | 0.814367i | \(-0.302916\pi\) |
−0.870569 | + | 0.492047i | \(0.836249\pi\) | |||||||
\(824\) | −19.0457 | − | 32.9882i | −0.663490 | − | 1.14920i | ||||
\(825\) | 0.482127 | − | 16.2411i | 0.0167855 | − | 0.565442i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.38559 | + | 4.26441i | −0.0481817 | + | 0.148288i | −0.972253 | − | 0.233932i | \(-0.924841\pi\) |
0.924071 | + | 0.382221i | \(0.124841\pi\) | |||||||
\(828\) | −22.7660 | − | 10.1361i | −0.791175 | − | 0.352254i | ||||
\(829\) | 33.6893 | − | 14.9995i | 1.17008 | − | 0.520953i | 0.272650 | − | 0.962113i | \(-0.412100\pi\) |
0.897428 | + | 0.441161i | \(0.145433\pi\) | |||||||
\(830\) | 2.84418 | + | 0.604549i | 0.0987229 | + | 0.0209842i | ||||
\(831\) | −4.94778 | + | 5.49507i | −0.171637 | + | 0.190622i | ||||
\(832\) | 23.2615 | + | 16.9005i | 0.806447 | + | 0.585918i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 4.12050 | − | 12.6816i | 0.142681 | − | 0.439127i | ||||
\(835\) | −13.0530 | − | 22.6084i | −0.451717 | − | 0.782397i | ||||
\(836\) | 8.78449 | − | 36.0344i | 0.303818 | − | 1.24628i | ||||
\(837\) | 27.5053 | − | 47.6405i | 0.950721 | − | 1.64670i | ||||
\(838\) | 73.4496 | − | 15.6122i | 2.53727 | − | 0.539314i | ||||
\(839\) | 7.41389 | − | 5.38651i | 0.255956 | − | 0.185963i | −0.452406 | − | 0.891812i | \(-0.649434\pi\) |
0.708362 | + | 0.705849i | \(0.249434\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.71643 | − | 8.36030i | −0.0936699 | − | 0.288286i | ||||
\(842\) | 39.3451 | − | 43.6971i | 1.35592 | − | 1.50590i | ||||
\(843\) | 29.5722 | − | 13.1664i | 1.01852 | − | 0.453474i | ||||
\(844\) | 5.82530 | + | 55.4240i | 0.200515 | + | 1.90777i | ||||
\(845\) | −3.56824 | + | 0.758452i | −0.122751 | + | 0.0260915i | ||||
\(846\) | −21.4880 | −0.738774 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 15.0195 | 0.515771 | ||||||||
\(849\) | 11.9069 | − | 2.53089i | 0.408644 | − | 0.0868600i | ||||
\(850\) | 5.14101 | + | 48.9134i | 0.176335 | + | 1.67772i | ||||
\(851\) | −33.7045 | + | 15.0062i | −1.15538 | + | 0.514407i | ||||
\(852\) | 0.437233 | − | 0.485597i | 0.0149794 | − | 0.0166363i | ||||
\(853\) | −2.01494 | − | 6.20135i | −0.0689903 | − | 0.212330i | 0.910617 | − | 0.413251i | \(-0.135607\pi\) |
−0.979608 | + | 0.200921i | \(0.935607\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.74849 | − | 1.99690i | 0.0939965 | − | 0.0682924i | ||||
\(856\) | 55.2606 | − | 11.7460i | 1.88877 | − | 0.401470i | ||||
\(857\) | 24.0368 | − | 41.6330i | 0.821082 | − | 1.42216i | −0.0837952 | − | 0.996483i | \(-0.526704\pi\) |
0.904877 | − | 0.425673i | \(-0.139962\pi\) | |||||||
\(858\) | −8.70270 | + | 35.6989i | −0.297105 | + | 1.21874i | ||||
\(859\) | −0.158149 | − | 0.273922i | −0.00539598 | − | 0.00934610i | 0.863315 | − | 0.504666i | \(-0.168384\pi\) |
−0.868711 | + | 0.495320i | \(0.835051\pi\) | |||||||
\(860\) | 0.201444 | − | 0.619981i | 0.00686918 | − | 0.0211412i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 38.1459 | + | 27.7146i | 1.29925 | + | 0.943963i | ||||
\(863\) | 2.42689 | − | 2.69533i | 0.0826123 | − | 0.0917502i | −0.700421 | − | 0.713730i | \(-0.747005\pi\) |
0.783034 | + | 0.621979i | \(0.213671\pi\) | |||||||
\(864\) | −4.87986 | − | 1.03725i | −0.166016 | − | 0.0352878i | ||||
\(865\) | −24.7848 | + | 11.0349i | −0.842708 | + | 0.375198i | ||||
\(866\) | −47.4878 | − | 21.1429i | −1.61370 | − | 0.718465i | ||||
\(867\) | −8.02000 | + | 24.6830i | −0.272374 | + | 0.838280i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.839391 | − | 28.2760i | 0.0284744 | − | 0.959197i | ||||
\(870\) | 9.86154 | + | 17.0807i | 0.334337 | + | 0.579089i | ||||
\(871\) | −20.0333 | − | 22.2492i | −0.678802 | − | 0.753885i | ||||
\(872\) | 0.429311 | + | 4.08462i | 0.0145383 | + | 0.138323i | ||||
\(873\) | −1.73267 | + | 16.4852i | −0.0586419 | + | 0.557941i | ||||
\(874\) | 14.5392 | + | 44.7469i | 0.491794 | + | 1.51359i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.78818 | − | 2.02573i | −0.0942039 | − | 0.0684432i | ||||
\(877\) | 24.3986 | + | 10.8630i | 0.823883 | + | 0.366816i | 0.774979 | − | 0.631987i | \(-0.217761\pi\) |
0.0489039 | + | 0.998803i | \(0.484427\pi\) | |||||||
\(878\) | −51.6047 | − | 57.3128i | −1.74157 | − | 1.93421i | ||||
\(879\) | −17.6595 | + | 30.5871i | −0.595639 | + | 1.03168i | ||||
\(880\) | −14.2769 | − | 1.93041i | −0.481275 | − | 0.0650740i | ||||
\(881\) | −2.91937 | −0.0983560 | −0.0491780 | − | 0.998790i | \(-0.515660\pi\) | ||||
−0.0491780 | + | 0.998790i | \(0.515660\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36.5331 | − | 26.5429i | 1.22944 | − | 0.893238i | 0.232589 | − | 0.972575i | \(-0.425280\pi\) |
0.996848 | + | 0.0793369i | \(0.0252803\pi\) | |||||||
\(884\) | 7.68977 | − | 73.1633i | 0.258635 | − | 2.46075i | ||||
\(885\) | −12.2660 | − | 2.60722i | −0.412317 | − | 0.0876406i | ||||
\(886\) | −3.96090 | − | 0.841915i | −0.133069 | − | 0.0282847i | ||||
\(887\) | −2.51128 | + | 23.8932i | −0.0843206 | + | 0.802257i | 0.867878 | + | 0.496777i | \(0.165483\pi\) |
−0.952199 | + | 0.305479i | \(0.901183\pi\) | |||||||
\(888\) | 29.3373 | − | 21.3148i | 0.984497 | − | 0.715279i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −30.7592 | −1.03105 | ||||||||
\(891\) | −3.13192 | − | 17.2345i | −0.104923 | − | 0.577377i | ||||
\(892\) | −5.79032 | + | 10.0291i | −0.193874 | + | 0.335800i | ||||
\(893\) | 17.9551 | + | 19.9411i | 0.600844 | + | 0.667304i | ||||
\(894\) | −15.5152 | − | 6.90781i | −0.518906 | − | 0.231032i | ||||
\(895\) | 4.86889 | + | 3.53746i | 0.162749 | + | 0.118244i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.52702 | − | 29.3212i | −0.318098 | − | 0.979005i | ||||
\(898\) | −4.36607 | + | 41.5404i | −0.145698 | + | 1.38622i | ||||
\(899\) | 4.57103 | + | 43.4904i | 0.152452 | + | 1.45049i | ||||
\(900\) | 8.42170 | + | 9.35325i | 0.280723 | + | 0.311775i | ||||
\(901\) | 12.8908 | + | 22.3275i | 0.429455 | + | 0.743837i | ||||
\(902\) | −1.42854 | − | 2.09419i | −0.0475652 | − | 0.0697289i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.50996 | + | 20.0356i | −0.216518 | + | 0.666374i | ||||
\(905\) | −9.02933 | − | 4.02012i | −0.300145 | − | 0.133633i | ||||
\(906\) | −54.0517 | + | 24.0654i | −1.79575 | + | 0.799519i | ||||
\(907\) | 15.6767 | + | 3.33219i | 0.520537 | + | 0.110644i | 0.460685 | − | 0.887564i | \(-0.347604\pi\) |
0.0598522 | + | 0.998207i | \(0.480937\pi\) | |||||||
\(908\) | −21.5843 | + | 23.9718i | −0.716300 | + | 0.795532i | ||||
\(909\) | 9.51862 | + | 6.91568i | 0.315713 | + | 0.229379i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.06922 | + | 15.6014i | −0.167951 | + | 0.516899i | −0.999242 | − | 0.0389385i | \(-0.987602\pi\) |
0.831291 | + | 0.555838i | \(0.187602\pi\) | |||||||
\(912\) | −7.08366 | − | 12.2693i | −0.234564 | − | 0.406276i | ||||
\(913\) | 3.14369 | − | 0.236355i | 0.104041 | − | 0.00782220i | ||||
\(914\) | 12.4204 | − | 21.5127i | 0.410830 | − | 0.711578i | ||||
\(915\) | −4.32974 | + | 0.920316i | −0.143137 | + | 0.0304247i | ||||
\(916\) | 41.4336 | − | 30.1032i | 1.36900 | − | 0.994639i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 25.1618 | + | 77.4401i | 0.830464 | + | 2.55590i | ||||
\(919\) | 21.6264 | − | 24.0185i | 0.713389 | − | 0.792298i | −0.272058 | − | 0.962281i | \(-0.587704\pi\) |
0.985447 | + | 0.169982i | \(0.0543711\pi\) | |||||||
\(920\) | 36.0459 | − | 16.0487i | 1.18840 | − | 0.529109i | ||||
\(921\) | −0.688697 | − | 6.55252i | −0.0226933 | − | 0.215913i | ||||
\(922\) | 52.5772 | − | 11.1756i | 1.73154 | − | 0.368050i | ||||
\(923\) | −0.370623 | −0.0121992 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18.6333 | 0.612659 | ||||||||
\(926\) | −72.2040 | + | 15.3474i | −2.37277 | + | 0.504348i | ||||
\(927\) | −0.810099 | − | 7.70757i | −0.0266071 | − | 0.253150i | ||||
\(928\) | 3.62298 | − | 1.61306i | 0.118930 | − | 0.0529512i | ||||
\(929\) | 5.48373 | − | 6.09030i | 0.179915 | − | 0.199816i | −0.646441 | − | 0.762964i | \(-0.723743\pi\) |
0.826356 | + | 0.563148i | \(0.190410\pi\) | |||||||
\(930\) | 13.1881 | + | 40.5887i | 0.432454 | + | 1.33096i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 40.5471 | − | 29.4592i | 1.32817 | − | 0.964969i | ||||
\(933\) | 3.10136 | − | 0.659215i | 0.101534 | − | 0.0215817i | ||||
\(934\) | −30.6126 | + | 53.0226i | −1.00168 | + | 1.73495i | ||||
\(935\) | −9.38378 | − | 22.8804i | −0.306883 | − | 0.748271i | ||||
\(936\) | −6.94645 | − | 12.0316i | −0.227052 | − | 0.393265i | ||||
\(937\) | −10.5490 | + | 32.4666i | −0.344622 | + | 1.06064i | 0.617164 | + | 0.786835i | \(0.288282\pi\) |
−0.961786 | + | 0.273803i | \(0.911718\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11.2541 | + | 8.17655i | 0.367262 | + | 0.266831i | ||||
\(940\) | 30.8487 | − | 34.2610i | 1.00618 | − | 1.11747i | ||||
\(941\) | 0.957969 | + | 0.203623i | 0.0312289 | + | 0.00663791i | 0.223500 | − | 0.974704i | \(-0.428252\pi\) |
−0.192271 | + | 0.981342i | \(0.561585\pi\) | |||||||
\(942\) | −7.14846 | + | 3.18270i | −0.232909 | + | 0.103698i | ||||
\(943\) | 1.94310 | + | 0.865126i | 0.0632762 | + | 0.0281724i | ||||
\(944\) | 7.40874 | − | 22.8017i | 0.241134 | − | 0.742134i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.0317072 | − | 1.06810i | 0.00103089 | − | 0.0347269i | ||||
\(947\) | −0.467800 | − | 0.810253i | −0.0152014 | − | 0.0263297i | 0.858325 | − | 0.513107i | \(-0.171506\pi\) |
−0.873526 | + | 0.486777i | \(0.838172\pi\) | |||||||
\(948\) | −31.9808 | − | 35.5183i | −1.03869 | − | 1.15358i | ||||
\(949\) | 0.204328 | + | 1.94405i | 0.00663277 | + | 0.0631066i | ||||
\(950\) | 2.48384 | − | 23.6321i | 0.0805863 | − | 0.766727i | ||||
\(951\) | −2.86099 | − | 8.80523i | −0.0927740 | − | 0.285529i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −13.5365 | − | 9.83486i | −0.438491 | − | 0.318582i | 0.346544 | − | 0.938034i | \(-0.387355\pi\) |
−0.785035 | + | 0.619451i | \(0.787355\pi\) | |||||||
\(954\) | 9.11244 | + | 4.05712i | 0.295026 | + | 0.131354i | ||||
\(955\) | 7.43677 | + | 8.25937i | 0.240648 | + | 0.267267i | ||||
\(956\) | 9.73081 | − | 16.8543i | 0.314717 | − | 0.545106i | ||||
\(957\) | 15.4597 | + | 14.7738i | 0.499741 | + | 0.477569i | ||||
\(958\) | −51.5353 | −1.66503 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 13.2115 | − | 9.59870i | 0.426399 | − | 0.309797i | ||||
\(961\) | −6.65057 | + | 63.2760i | −0.214535 | + | 2.04116i | ||||
\(962\) | −41.2172 | − | 8.76099i | −1.32890 | − | 0.282466i | ||||
\(963\) | 11.2432 | + | 2.38982i | 0.362308 | + | 0.0770110i | ||||
\(964\) | −1.07282 | + | 10.2072i | −0.0345531 | + | 0.328751i | ||||
\(965\) | 26.0696 | − | 18.9407i | 0.839210 | − | 0.609722i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36.4439 | 1.17196 | 0.585978 | − | 0.810327i | \(-0.300710\pi\) | ||||
0.585978 | + | 0.810327i | \(0.300710\pi\) | |||||||
\(968\) | −50.4131 | + | 7.62361i | −1.62034 | + | 0.245032i | ||||
\(969\) | 12.1594 | − | 21.0607i | 0.390617 | − | 0.676568i | ||||
\(970\) | −35.9784 | − | 39.9580i | −1.15520 | − | 1.28297i | ||||
\(971\) | 30.3678 | + | 13.5206i | 0.974550 | + | 0.433898i | 0.831321 | − | 0.555792i | \(-0.187585\pi\) |
0.143229 | + | 0.989690i | \(0.454252\pi\) | |||||||
\(972\) | 29.6832 | + | 21.5661i | 0.952088 | + | 0.691732i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 12.6325 | + | 38.8788i | 0.404771 | + | 1.24576i | ||||
\(975\) | −1.62757 | + | 15.4853i | −0.0521241 | + | 0.495928i | ||||
\(976\) | −0.884619 | − | 8.41658i | −0.0283159 | − | 0.269408i | ||||
\(977\) | 15.1000 | + | 16.7703i | 0.483092 | + | 0.536528i | 0.934582 | − | 0.355748i | \(-0.115774\pi\) |
−0.451490 | + | 0.892276i | \(0.649107\pi\) | |||||||
\(978\) | 27.6025 | + | 47.8089i | 0.882631 | + | 1.52876i | ||||
\(979\) | −32.0088 | + | 9.35981i | −1.02301 | + | 0.299141i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.258223 | + | 0.794729i | −0.00824443 | + | 0.0253737i | ||||
\(982\) | −10.7420 | − | 4.78267i | −0.342793 | − | 0.152621i | ||||
\(983\) | 13.7989 | − | 6.14366i | 0.440116 | − | 0.195952i | −0.174702 | − | 0.984621i | \(-0.555896\pi\) |
0.614818 | + | 0.788669i | \(0.289229\pi\) | |||||||
\(984\) | −2.04492 | − | 0.434660i | −0.0651896 | − | 0.0138565i | ||||
\(985\) | 9.43056 | − | 10.4737i | 0.300483 | − | 0.333720i | ||||
\(986\) | −52.3661 | − | 38.0462i | −1.66768 | − | 1.21164i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −10.9834 | + | 33.8033i | −0.349428 | + | 1.07543i | ||||
\(989\) | 0.448287 | + | 0.776456i | 0.0142547 | + | 0.0246899i | ||||
\(990\) | −8.14047 | − | 5.02773i | −0.258721 | − | 0.159792i | ||||
\(991\) | 27.5767 | − | 47.7643i | 0.876003 | − | 1.51728i | 0.0203128 | − | 0.999794i | \(-0.493534\pi\) |
0.855690 | − | 0.517488i | \(-0.173133\pi\) | |||||||
\(992\) | 8.39393 | − | 1.78418i | 0.266507 | − | 0.0566479i | ||||
\(993\) | 4.20116 | − | 3.05232i | 0.133320 | − | 0.0968624i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.76461 | − | 14.6639i | −0.151048 | − | 0.464878i | ||||
\(996\) | 3.56405 | − | 3.95828i | 0.112931 | − | 0.125423i | ||||
\(997\) | −45.4076 | + | 20.2168i | −1.43807 | + | 0.640271i | −0.969930 | − | 0.243382i | \(-0.921743\pi\) |
−0.468142 | + | 0.883653i | \(0.655076\pi\) | |||||||
\(998\) | 7.76980 | + | 73.9247i | 0.245949 | + | 2.34005i | ||||
\(999\) | 30.1745 | − | 6.41378i | 0.954678 | − | 0.202923i |
(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 | 539.2.q.f.361.4 | 32 | ||
7.2 | even | 3 | inner | 539.2.q.f.471.1 | 32 | ||
7.3 | odd | 6 | 77.2.f.b.64.1 | ✓ | 16 | ||
7.4 | even | 3 | 539.2.f.e.295.1 | 16 | |||
7.5 | odd | 6 | 539.2.q.g.471.1 | 32 | |||
7.6 | odd | 2 | 539.2.q.g.361.4 | 32 | |||
11.5 | even | 5 | inner | 539.2.q.f.214.1 | 32 | ||
21.17 | even | 6 | 693.2.m.i.64.4 | 16 | |||
77.3 | odd | 30 | 847.2.f.w.323.4 | 16 | |||
77.4 | even | 15 | 5929.2.a.bt.1.1 | 8 | |||
77.5 | odd | 30 | 539.2.q.g.324.4 | 32 | |||
77.10 | even | 6 | 847.2.f.x.372.4 | 16 | |||
77.16 | even | 15 | inner | 539.2.q.f.324.4 | 32 | ||
77.17 | even | 30 | 847.2.f.x.148.4 | 16 | |||
77.18 | odd | 30 | 5929.2.a.bs.1.8 | 8 | |||
77.24 | even | 30 | 847.2.f.v.729.1 | 16 | |||
77.27 | odd | 10 | 539.2.q.g.214.1 | 32 | |||
77.31 | odd | 30 | 847.2.f.w.729.4 | 16 | |||
77.38 | odd | 30 | 77.2.f.b.71.1 | yes | 16 | ||
77.52 | even | 30 | 847.2.f.v.323.1 | 16 | |||
77.59 | odd | 30 | 847.2.a.p.1.1 | 8 | |||
77.60 | even | 15 | 539.2.f.e.148.1 | 16 | |||
77.73 | even | 30 | 847.2.a.o.1.8 | 8 | |||
231.38 | even | 30 | 693.2.m.i.379.4 | 16 | |||
231.59 | even | 30 | 7623.2.a.ct.1.8 | 8 | |||
231.227 | odd | 30 | 7623.2.a.cw.1.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.2.f.b.64.1 | ✓ | 16 | 7.3 | odd | 6 | ||
77.2.f.b.71.1 | yes | 16 | 77.38 | odd | 30 | ||
539.2.f.e.148.1 | 16 | 77.60 | even | 15 | |||
539.2.f.e.295.1 | 16 | 7.4 | even | 3 | |||
539.2.q.f.214.1 | 32 | 11.5 | even | 5 | inner | ||
539.2.q.f.324.4 | 32 | 77.16 | even | 15 | inner | ||
539.2.q.f.361.4 | 32 | 1.1 | even | 1 | trivial | ||
539.2.q.f.471.1 | 32 | 7.2 | even | 3 | inner | ||
539.2.q.g.214.1 | 32 | 77.27 | odd | 10 | |||
539.2.q.g.324.4 | 32 | 77.5 | odd | 30 | |||
539.2.q.g.361.4 | 32 | 7.6 | odd | 2 | |||
539.2.q.g.471.1 | 32 | 7.5 | odd | 6 | |||
693.2.m.i.64.4 | 16 | 21.17 | even | 6 | |||
693.2.m.i.379.4 | 16 | 231.38 | even | 30 | |||
847.2.a.o.1.8 | 8 | 77.73 | even | 30 | |||
847.2.a.p.1.1 | 8 | 77.59 | odd | 30 | |||
847.2.f.v.323.1 | 16 | 77.52 | even | 30 | |||
847.2.f.v.729.1 | 16 | 77.24 | even | 30 | |||
847.2.f.w.323.4 | 16 | 77.3 | odd | 30 | |||
847.2.f.w.729.4 | 16 | 77.31 | odd | 30 | |||
847.2.f.x.148.4 | 16 | 77.17 | even | 30 | |||
847.2.f.x.372.4 | 16 | 77.10 | even | 6 | |||
5929.2.a.bs.1.8 | 8 | 77.18 | odd | 30 | |||
5929.2.a.bt.1.1 | 8 | 77.4 | even | 15 | |||
7623.2.a.ct.1.8 | 8 | 231.59 | even | 30 | |||
7623.2.a.cw.1.1 | 8 | 231.227 | odd | 30 |