Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [189,2,Mod(109,189)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(189, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("189.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 189 = 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 189.e (of order \(3\), 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: | \(1.50917259820\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.309123.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 109.2 | ||
Root | \(0.500000 - 1.41036i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 189.109 |
Dual form | 189.2.e.f.163.2 |
$q$-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 \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(136\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.380438 | + | 0.658939i | 0.269011 | + | 0.465940i | 0.968607 | − | 0.248599i | \(-0.0799700\pi\) |
−0.699596 | + | 0.714539i | \(0.746637\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.710533 | − | 1.23068i | 0.355267 | − | 0.615340i | ||||
\(5\) | 1.59097 | + | 2.75564i | 0.711504 | + | 1.23236i | 0.964292 | + | 0.264840i | \(0.0853191\pi\) |
−0.252788 | + | 0.967522i | \(0.581348\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.56238 | + | 0.658939i | −0.968489 | + | 0.249055i | ||||
\(8\) | 2.60301 | 0.920303 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.21053 | + | 2.09671i | −0.382804 | + | 0.663036i | ||||
\(11\) | 1.11956 | − | 1.93914i | 0.337561 | − | 0.584672i | −0.646413 | − | 0.762988i | \(-0.723732\pi\) |
0.983973 | + | 0.178316i | \(0.0570649\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.70370 | 1.02722 | 0.513610 | − | 0.858024i | \(-0.328308\pi\) | ||||
0.513610 | + | 0.858024i | \(0.328308\pi\) | |||||||
\(14\) | −1.40903 | − | 1.43777i | −0.376579 | − | 0.384259i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.430782 | − | 0.746136i | −0.107695 | − | 0.186534i | ||||
\(17\) | −2.80150 | + | 4.85235i | −0.679465 | + | 1.17687i | 0.295678 | + | 0.955288i | \(0.404455\pi\) |
−0.975142 | + | 0.221580i | \(0.928879\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.21053 | − | 3.82876i | −0.507131 | − | 0.878377i | −0.999966 | − | 0.00825398i | \(-0.997373\pi\) |
0.492835 | − | 0.870123i | \(-0.335961\pi\) | |||||||
\(20\) | 4.52175 | 1.01109 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.70370 | 0.363229 | ||||||||
\(23\) | −0.471410 | − | 0.816506i | −0.0982958 | − | 0.170253i | 0.812684 | − | 0.582705i | \(-0.198006\pi\) |
−0.910979 | + | 0.412452i | \(0.864672\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.56238 | + | 4.43818i | −0.512476 | + | 0.887635i | ||||
\(26\) | 1.40903 | + | 2.44051i | 0.276333 | + | 0.478623i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.00972 | + | 3.62167i | −0.190818 | + | 0.684431i | ||||
\(29\) | −10.1248 | −1.88012 | −0.940061 | − | 0.341007i | \(-0.889232\pi\) | ||||
−0.940061 | + | 0.341007i | \(0.889232\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.85185 | − | 4.93955i | 0.512207 | − | 0.887169i | −0.487693 | − | 0.873015i | \(-0.662161\pi\) |
0.999900 | − | 0.0141534i | \(-0.00450531\pi\) | |||||||
\(32\) | 2.93078 | − | 5.07626i | 0.518094 | − | 0.897365i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.26320 | −0.731133 | ||||||||
\(35\) | −5.89248 | − | 6.01266i | −0.996010 | − | 1.01632i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.56238 | − | 2.70612i | −0.256854 | − | 0.444884i | 0.708543 | − | 0.705667i | \(-0.249353\pi\) |
−0.965397 | + | 0.260783i | \(0.916019\pi\) | |||||||
\(38\) | 1.68194 | − | 2.91321i | 0.272847 | − | 0.472585i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.14132 | + | 7.17297i | 0.654799 | + | 1.13415i | ||||
\(41\) | −3.98633 | −0.622560 | −0.311280 | − | 0.950318i | \(-0.600758\pi\) | ||||
−0.311280 | + | 0.950318i | \(0.600758\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.28263 | −0.500596 | −0.250298 | − | 0.968169i | \(-0.580529\pi\) | ||||
−0.250298 | + | 0.968169i | \(0.580529\pi\) | |||||||
\(44\) | −1.59097 | − | 2.75564i | −0.239848 | − | 0.415429i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.358685 | − | 0.621261i | 0.0528852 | − | 0.0915999i | ||||
\(47\) | −0.112725 | − | 0.195246i | −0.0164426 | − | 0.0284795i | 0.857687 | − | 0.514172i | \(-0.171901\pi\) |
−0.874130 | + | 0.485693i | \(0.838567\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.13160 | − | 3.37690i | 0.875943 | − | 0.482415i | ||||
\(50\) | −3.89931 | −0.551446 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.63160 | − | 4.55806i | 0.364937 | − | 0.632090i | ||||
\(53\) | 5.33009 | − | 9.23200i | 0.732145 | − | 1.26811i | −0.223820 | − | 0.974631i | \(-0.571853\pi\) |
0.955965 | − | 0.293482i | \(-0.0948139\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.12476 | 0.960703 | ||||||||
\(56\) | −6.66991 | + | 1.71522i | −0.891304 | + | 0.229206i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.85185 | − | 6.67160i | −0.505772 | − | 0.876024i | ||||
\(59\) | −1.02859 | + | 1.78157i | −0.133911 | + | 0.231941i | −0.925181 | − | 0.379526i | \(-0.876087\pi\) |
0.791270 | + | 0.611467i | \(0.209420\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.92107 | + | 5.05944i | 0.374004 | + | 0.647794i | 0.990177 | − | 0.139816i | \(-0.0446512\pi\) |
−0.616173 | + | 0.787611i | \(0.711318\pi\) | |||||||
\(62\) | 4.33981 | 0.551156 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.73680 | 0.342100 | ||||||||
\(65\) | 5.89248 | + | 10.2061i | 0.730872 | + | 1.26591i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.71053 | + | 6.42683i | −0.453314 | + | 0.785163i | −0.998590 | − | 0.0530942i | \(-0.983092\pi\) |
0.545276 | + | 0.838257i | \(0.316425\pi\) | |||||||
\(68\) | 3.98113 | + | 6.89551i | 0.482782 | + | 0.836204i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.72025 | − | 6.17023i | 0.205609 | − | 0.737483i | ||||
\(71\) | −7.26320 | −0.861983 | −0.430992 | − | 0.902356i | \(-0.641836\pi\) | ||||
−0.430992 | + | 0.902356i | \(0.641836\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.77975 | + | 6.54672i | −0.442386 | + | 0.766236i | −0.997866 | − | 0.0652944i | \(-0.979201\pi\) |
0.555480 | + | 0.831530i | \(0.312535\pi\) | |||||||
\(74\) | 1.18878 | − | 2.05903i | 0.138193 | − | 0.239357i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.28263 | −0.720667 | ||||||||
\(77\) | −1.59097 | + | 5.70653i | −0.181308 | + | 0.650320i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.41423 | + | 5.91362i | 0.384131 | + | 0.665334i | 0.991648 | − | 0.128972i | \(-0.0411678\pi\) |
−0.607517 | + | 0.794306i | \(0.707834\pi\) | |||||||
\(80\) | 1.37072 | − | 2.37416i | 0.153252 | − | 0.265439i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.51655 | − | 2.62674i | −0.167475 | − | 0.290075i | ||||
\(83\) | 8.11109 | 0.890308 | 0.445154 | − | 0.895454i | \(-0.353149\pi\) | ||||
0.445154 | + | 0.895454i | \(0.353149\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −17.8285 | −1.93377 | ||||||||
\(86\) | −1.24884 | − | 2.16305i | −0.134666 | − | 0.233248i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.91423 | − | 5.04759i | 0.310658 | − | 0.538075i | ||||
\(89\) | 4.86389 | + | 8.42450i | 0.515571 | + | 0.892995i | 0.999837 | + | 0.0180741i | \(0.00575348\pi\) |
−0.484266 | + | 0.874921i | \(0.660913\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.49028 | + | 2.44051i | −0.994852 | + | 0.255835i | ||||
\(92\) | −1.33981 | −0.139685 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.0857699 | − | 0.148558i | 0.00884649 | − | 0.0153226i | ||||
\(95\) | 7.03379 | − | 12.1829i | 0.721652 | − | 1.24994i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.842133 | 0.0855057 | 0.0427528 | − | 0.999086i | \(-0.486387\pi\) | ||||
0.0427528 | + | 0.999086i | \(0.486387\pi\) | |||||||
\(98\) | 4.55787 | + | 2.75564i | 0.460414 | + | 0.278362i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.64132 | + | 6.30694i | 0.364132 | + | 0.630694i | ||||
\(101\) | −3.87360 | + | 6.70928i | −0.385438 | + | 0.667598i | −0.991830 | − | 0.127568i | \(-0.959283\pi\) |
0.606392 | + | 0.795166i | \(0.292616\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.21737 | + | 2.10855i | 0.119951 | + | 0.207761i | 0.919748 | − | 0.392509i | \(-0.128393\pi\) |
−0.799797 | + | 0.600271i | \(0.795060\pi\) | |||||||
\(104\) | 9.64076 | 0.945354 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.11109 | 0.787819 | ||||||||
\(107\) | 5.73229 | + | 9.92861i | 0.554161 | + | 0.959835i | 0.997968 | + | 0.0637128i | \(0.0202942\pi\) |
−0.443807 | + | 0.896122i | \(0.646372\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.12476 | − | 15.8046i | 0.873994 | − | 1.51380i | 0.0161631 | − | 0.999869i | \(-0.494855\pi\) |
0.857831 | − | 0.513932i | \(-0.171812\pi\) | |||||||
\(110\) | 2.71053 | + | 4.69478i | 0.258439 | + | 0.447630i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.59549 | + | 1.62803i | 0.150759 | + | 0.153834i | ||||
\(113\) | 5.24953 | 0.493834 | 0.246917 | − | 0.969037i | \(-0.420583\pi\) | ||||
0.246917 | + | 0.969037i | \(0.420583\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.50000 | − | 2.59808i | 0.139876 | − | 0.242272i | ||||
\(116\) | −7.19398 | + | 12.4603i | −0.667944 | + | 1.15691i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.56526 | −0.144094 | ||||||||
\(119\) | 3.98113 | − | 14.2796i | 0.364949 | − | 1.30901i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.99316 | + | 5.18431i | 0.272106 | + | 0.471301i | ||||
\(122\) | −2.22257 | + | 3.84961i | −0.201222 | + | 0.348527i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.05267 | − | 7.01942i | −0.363940 | − | 0.630363i | ||||
\(125\) | −0.396990 | −0.0355079 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.1053 | 1.78406 | 0.892030 | − | 0.451976i | \(-0.149281\pi\) | ||||
0.892030 | + | 0.451976i | \(0.149281\pi\) | |||||||
\(128\) | −4.82038 | − | 8.34914i | −0.426065 | − | 0.737967i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.48345 | + | 7.76556i | −0.393224 | + | 0.681085i | ||||
\(131\) | −2.04063 | − | 3.53447i | −0.178291 | − | 0.308808i | 0.763005 | − | 0.646393i | \(-0.223723\pi\) |
−0.941295 | + | 0.337585i | \(0.890390\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.18715 | + | 8.35413i | 0.709916 | + | 0.724395i | ||||
\(134\) | −5.64652 | −0.487785 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.29235 | + | 12.6307i | −0.625313 | + | 1.08307i | ||||
\(137\) | −0.942820 | + | 1.63301i | −0.0805506 | + | 0.139518i | −0.903487 | − | 0.428616i | \(-0.859001\pi\) |
0.822936 | + | 0.568134i | \(0.192335\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.7954 | −1.08529 | −0.542644 | − | 0.839963i | \(-0.682577\pi\) | ||||
−0.542644 | + | 0.839963i | \(0.682577\pi\) | |||||||
\(140\) | −11.5865 | + | 2.97956i | −0.979234 | + | 0.251819i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.76320 | − | 4.78600i | −0.231883 | − | 0.401632i | ||||
\(143\) | 4.14652 | − | 7.18198i | 0.346749 | − | 0.600587i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −16.1082 | − | 27.9002i | −1.33771 | − | 2.31699i | ||||
\(146\) | −5.75185 | −0.476026 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.44050 | −0.365007 | ||||||||
\(149\) | 4.02859 | + | 6.97772i | 0.330035 | + | 0.571637i | 0.982518 | − | 0.186166i | \(-0.0596061\pi\) |
−0.652483 | + | 0.757803i | \(0.726273\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.14132 | − | 5.44092i | 0.255637 | − | 0.442776i | −0.709432 | − | 0.704774i | \(-0.751048\pi\) |
0.965068 | + | 0.261999i | \(0.0843816\pi\) | |||||||
\(152\) | −5.75404 | − | 9.96629i | −0.466714 | − | 0.808373i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.36552 | + | 1.12263i | −0.351784 | + | 0.0904642i | ||||
\(155\) | 18.1488 | 1.45775 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.351848 | + | 0.609419i | −0.0280806 | + | 0.0486370i | −0.879724 | − | 0.475484i | \(-0.842273\pi\) |
0.851644 | + | 0.524121i | \(0.175606\pi\) | |||||||
\(158\) | −2.59781 | + | 4.49954i | −0.206671 | + | 0.357964i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 18.6512 | 1.47450 | ||||||||
\(161\) | 1.74596 | + | 1.78157i | 0.137601 | + | 0.140407i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.61793 | + | 16.6587i | 0.753334 | + | 1.30481i | 0.946198 | + | 0.323588i | \(0.104889\pi\) |
−0.192864 | + | 0.981225i | \(0.561778\pi\) | |||||||
\(164\) | −2.83242 | + | 4.90589i | −0.221175 | + | 0.383086i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.08577 | + | 5.34471i | 0.239502 | + | 0.414830i | ||||
\(167\) | −23.3880 | −1.80981 | −0.904907 | − | 0.425608i | \(-0.860060\pi\) | ||||
−0.904907 | + | 0.425608i | \(0.860060\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.717370 | 0.0551823 | ||||||||
\(170\) | −6.78263 | − | 11.7479i | −0.520204 | − | 0.901020i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.33242 | + | 4.03987i | −0.177845 | + | 0.308037i | ||||
\(173\) | −4.11956 | − | 7.13529i | −0.313204 | − | 0.542486i | 0.665850 | − | 0.746086i | \(-0.268069\pi\) |
−0.979054 | + | 0.203600i | \(0.934736\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.64132 | − | 13.0608i | 0.275258 | − | 0.987300i | ||||
\(176\) | −1.92915 | −0.145415 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.70082 | + | 6.41001i | −0.277388 | + | 0.480450i | ||||
\(179\) | 4.95486 | − | 8.58207i | 0.370344 | − | 0.641454i | −0.619275 | − | 0.785174i | \(-0.712573\pi\) |
0.989618 | + | 0.143721i | \(0.0459066\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.38796 | −0.697802 | −0.348901 | − | 0.937160i | \(-0.613445\pi\) | ||||
−0.348901 | + | 0.937160i | \(0.613445\pi\) | |||||||
\(182\) | −5.21861 | − | 5.32505i | −0.386829 | − | 0.394719i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.22708 | − | 2.12537i | −0.0904619 | − | 0.156685i | ||||
\(185\) | 4.97141 | − | 8.61073i | 0.365505 | − | 0.633074i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.27292 | + | 10.8650i | 0.458721 | + | 0.794528i | ||||
\(188\) | −0.320380 | −0.0233661 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 10.7037 | 0.776528 | ||||||||
\(191\) | −12.3691 | − | 21.4239i | −0.894996 | − | 1.55018i | −0.833810 | − | 0.552052i | \(-0.813845\pi\) |
−0.0611861 | − | 0.998126i | \(-0.519488\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.414230 | − | 0.717468i | 0.0298169 | − | 0.0516444i | −0.850732 | − | 0.525600i | \(-0.823841\pi\) |
0.880549 | + | 0.473955i | \(0.157174\pi\) | |||||||
\(194\) | 0.320380 | + | 0.554914i | 0.0230019 | + | 0.0398405i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.200818 | − | 9.94544i | 0.0143442 | − | 0.710389i | ||||
\(197\) | −5.86156 | −0.417619 | −0.208810 | − | 0.977956i | \(-0.566959\pi\) | ||||
−0.208810 | + | 0.977956i | \(0.566959\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.62476 | − | 8.01033i | 0.327841 | − | 0.567837i | −0.654242 | − | 0.756285i | \(-0.727012\pi\) |
0.982083 | + | 0.188448i | \(0.0603457\pi\) | |||||||
\(200\) | −6.66991 | + | 11.5526i | −0.471634 | + | 0.816893i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −5.89467 | −0.414747 | ||||||||
\(203\) | 25.9435 | − | 6.67160i | 1.82088 | − | 0.468254i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.34213 | − | 10.9849i | −0.442954 | − | 0.767218i | ||||
\(206\) | −0.926268 | + | 1.60434i | −0.0645362 | + | 0.111780i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.59549 | − | 2.76346i | −0.110627 | − | 0.191612i | ||||
\(209\) | −9.89931 | −0.684750 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.5595 | −0.864632 | −0.432316 | − | 0.901722i | \(-0.642303\pi\) | ||||
−0.432316 | + | 0.901722i | \(0.642303\pi\) | |||||||
\(212\) | −7.57442 | − | 13.1193i | −0.520213 | − | 0.901036i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.36156 | + | 7.55445i | −0.298150 | + | 0.516412i | ||||
\(215\) | −5.22257 | − | 9.04576i | −0.356176 | − | 0.616916i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.05267 | + | 14.5362i | −0.275113 | + | 0.986781i | ||||
\(218\) | 13.8856 | 0.940454 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 5.06238 | − | 8.76830i | 0.341306 | − | 0.591159i | ||||
\(221\) | −10.3759 | + | 17.9716i | −0.697960 | + | 1.20890i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.3880 | −1.43224 | −0.716122 | − | 0.697975i | \(-0.754085\pi\) | ||||
−0.716122 | + | 0.697975i | \(0.754085\pi\) | |||||||
\(224\) | −4.16484 | + | 14.9385i | −0.278275 | + | 0.998122i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.99712 | + | 3.45912i | 0.132847 | + | 0.230097i | ||||
\(227\) | −6.31122 | + | 10.9314i | −0.418890 | + | 0.725539i | −0.995828 | − | 0.0912487i | \(-0.970914\pi\) |
0.576938 | + | 0.816788i | \(0.304248\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.4601 | + | 25.0456i | 0.955548 | + | 1.65506i | 0.733110 | + | 0.680110i | \(0.238068\pi\) |
0.222438 | + | 0.974947i | \(0.428599\pi\) | |||||||
\(230\) | 2.28263 | 0.150512 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −26.3549 | −1.73028 | ||||||||
\(233\) | 10.7255 | + | 18.5770i | 0.702648 | + | 1.21702i | 0.967534 | + | 0.252742i | \(0.0813323\pi\) |
−0.264886 | + | 0.964280i | \(0.585334\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.358685 | − | 0.621261i | 0.0233980 | − | 0.0405266i | ||||
\(236\) | 1.46169 | + | 2.53173i | 0.0951482 | + | 0.164802i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 10.9239 | − | 2.80919i | 0.708094 | − | 0.182093i | ||||
\(239\) | 7.73680 | 0.500452 | 0.250226 | − | 0.968187i | \(-0.419495\pi\) | ||||
0.250226 | + | 0.968187i | \(0.419495\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.04583 | + | 5.27553i | −0.196199 | + | 0.339827i | −0.947293 | − | 0.320369i | \(-0.896193\pi\) |
0.751094 | + | 0.660195i | \(0.229527\pi\) | |||||||
\(242\) | −2.27743 | + | 3.94462i | −0.146399 | + | 0.253570i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 8.30206 | 0.531485 | ||||||||
\(245\) | 19.0607 | + | 11.5239i | 1.21775 | + | 0.736238i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.18715 | − | 14.1806i | −0.520936 | − | 0.902287i | ||||
\(248\) | 7.42339 | − | 12.8577i | 0.471386 | − | 0.816464i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.151030 | − | 0.261592i | −0.00955199 | − | 0.0165445i | ||||
\(251\) | 1.40164 | 0.0884705 | 0.0442352 | − | 0.999021i | \(-0.485915\pi\) | ||||
0.0442352 | + | 0.999021i | \(0.485915\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.11109 | −0.132723 | ||||||||
\(254\) | 7.64884 | + | 13.2482i | 0.479931 | + | 0.831265i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 6.40451 | − | 11.0929i | 0.400282 | − | 0.693309i | ||||
\(257\) | −8.97825 | − | 15.5508i | −0.560048 | − | 0.970031i | −0.997492 | − | 0.0707853i | \(-0.977449\pi\) |
0.437444 | − | 0.899246i | \(-0.355884\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.78659 | + | 5.90461i | 0.359561 | + | 0.366895i | ||||
\(260\) | 16.7472 | 1.03862 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.55267 | − | 2.68930i | 0.0959241 | − | 0.166145i | ||||
\(263\) | −3.58809 | + | 6.21476i | −0.221251 | + | 0.383218i | −0.955188 | − | 0.295999i | \(-0.904347\pi\) |
0.733937 | + | 0.679218i | \(0.237681\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 33.9201 | 2.08370 | ||||||||
\(266\) | −2.39015 | + | 8.57306i | −0.146550 | + | 0.525648i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.27292 | + | 9.13296i | 0.322095 | + | 0.557884i | ||||
\(269\) | 1.69850 | − | 2.94188i | 0.103559 | − | 0.179370i | −0.809590 | − | 0.586996i | \(-0.800310\pi\) |
0.913149 | + | 0.407627i | \(0.133644\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.11793 | + | 8.86451i | 0.310892 | + | 0.538481i | 0.978556 | − | 0.205982i | \(-0.0660389\pi\) |
−0.667664 | + | 0.744463i | \(0.732706\pi\) | |||||||
\(272\) | 4.82735 | 0.292701 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.43474 | −0.0866758 | ||||||||
\(275\) | 5.73749 | + | 9.93762i | 0.345984 | + | 0.599261i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.77975 | − | 3.08262i | 0.106935 | − | 0.185217i | −0.807592 | − | 0.589741i | \(-0.799230\pi\) |
0.914527 | + | 0.404525i | \(0.132563\pi\) | |||||||
\(278\) | −4.86784 | − | 8.43135i | −0.291954 | − | 0.505679i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −15.3382 | − | 15.6510i | −0.916631 | − | 0.935327i | ||||
\(281\) | −6.98633 | −0.416769 | −0.208385 | − | 0.978047i | \(-0.566821\pi\) | ||||
−0.208385 | + | 0.978047i | \(0.566821\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.1082 | − | 26.1682i | 0.898090 | − | 1.55554i | 0.0681568 | − | 0.997675i | \(-0.478288\pi\) |
0.829933 | − | 0.557863i | \(-0.188378\pi\) | |||||||
\(284\) | −5.16075 | + | 8.93867i | −0.306234 | + | 0.530413i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.30998 | 0.373117 | ||||||||
\(287\) | 10.2145 | − | 2.62674i | 0.602942 | − | 0.155052i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.19686 | − | 12.4653i | −0.423345 | − | 0.733255i | ||||
\(290\) | 12.2564 | − | 21.2286i | 0.719718 | − | 1.24659i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.37128 | + | 9.30333i | 0.314330 | + | 0.544436i | ||||
\(293\) | 15.2359 | 0.890088 | 0.445044 | − | 0.895509i | \(-0.353188\pi\) | ||||
0.445044 | + | 0.895509i | \(0.353188\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.54583 | −0.381113 | ||||||||
\(296\) | −4.06690 | − | 7.04407i | −0.236383 | − | 0.409428i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.06526 | + | 5.30919i | −0.177566 | + | 0.307553i | ||||
\(299\) | −1.74596 | − | 3.02409i | −0.100971 | − | 0.174888i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.41135 | − | 2.16305i | 0.484822 | − | 0.124676i | ||||
\(302\) | 4.78031 | 0.275076 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.90451 | + | 3.29872i | −0.109231 | + | 0.189194i | ||||
\(305\) | −9.29467 | + | 16.0988i | −0.532211 | + | 0.921817i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.03310 | −0.0589623 | −0.0294812 | − | 0.999565i | \(-0.509386\pi\) | ||||
−0.0294812 | + | 0.999565i | \(0.509386\pi\) | |||||||
\(308\) | 5.89248 | + | 6.01266i | 0.335755 | + | 0.342603i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6.90451 | + | 11.9590i | 0.392150 | + | 0.679224i | ||||
\(311\) | −4.66019 | + | 8.07169i | −0.264255 | + | 0.457703i | −0.967368 | − | 0.253375i | \(-0.918459\pi\) |
0.703113 | + | 0.711078i | \(0.251793\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.04583 | − | 5.27553i | −0.172160 | − | 0.298191i | 0.767014 | − | 0.641630i | \(-0.221741\pi\) |
−0.939175 | + | 0.343439i | \(0.888408\pi\) | |||||||
\(314\) | −0.535426 | −0.0302159 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.70370 | 0.545876 | ||||||||
\(317\) | 11.6505 | + | 20.1792i | 0.654356 | + | 1.13338i | 0.982055 | + | 0.188595i | \(0.0603935\pi\) |
−0.327699 | + | 0.944782i | \(0.606273\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11.3353 | + | 19.6333i | −0.634655 | + | 1.09925i | ||||
\(320\) | 4.35417 | + | 7.54165i | 0.243406 | + | 0.421591i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.509715 | + | 1.82826i | −0.0284053 | + | 0.101885i | ||||
\(323\) | 24.7713 | 1.37831 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.49028 | + | 16.4377i | −0.526426 | + | 0.911797i | ||||
\(326\) | −7.31806 | + | 12.6752i | −0.405310 | + | 0.702017i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −10.3764 | −0.572944 | ||||||||
\(329\) | 0.417500 | + | 0.426015i | 0.0230175 | + | 0.0234870i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.33818 | − | 12.7101i | −0.403343 | − | 0.698610i | 0.590784 | − | 0.806829i | \(-0.298818\pi\) |
−0.994127 | + | 0.108220i | \(0.965485\pi\) | |||||||
\(332\) | 5.76320 | − | 9.98215i | 0.316297 | − | 0.547842i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8.89768 | − | 15.4112i | −0.486859 | − | 0.843265i | ||||
\(335\) | −23.6134 | −1.29014 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.6238 | 1.39582 | 0.697909 | − | 0.716186i | \(-0.254114\pi\) | ||||
0.697909 | + | 0.716186i | \(0.254114\pi\) | |||||||
\(338\) | 0.272915 | + | 0.472703i | 0.0148446 | + | 0.0257116i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −12.6677 | + | 21.9411i | −0.687003 | + | 1.18992i | ||||
\(341\) | −6.38564 | − | 11.0603i | −0.345802 | − | 0.598946i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.4863 | + | 12.6933i | −0.728193 | + | 0.685372i | ||||
\(344\) | −8.54472 | −0.460700 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.13448 | − | 5.42908i | 0.168511 | − | 0.291869i | ||||
\(347\) | −5.64652 | + | 9.78005i | −0.303121 | + | 0.525021i | −0.976841 | − | 0.213966i | \(-0.931362\pi\) |
0.673720 | + | 0.738986i | \(0.264695\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.2963 | −0.604677 | −0.302339 | − | 0.953201i | \(-0.597767\pi\) | ||||
−0.302339 | + | 0.953201i | \(0.597767\pi\) | |||||||
\(350\) | 9.99153 | − | 2.56941i | 0.534070 | − | 0.137341i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6.56238 | − | 11.3664i | −0.349776 | − | 0.605830i | ||||
\(353\) | 9.25116 | − | 16.0235i | 0.492390 | − | 0.852844i | −0.507572 | − | 0.861609i | \(-0.669457\pi\) |
0.999962 | + | 0.00876550i | \(0.00279018\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.5555 | − | 20.0148i | −0.613305 | − | 1.06227i | ||||
\(356\) | 13.8238 | 0.732661 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.54007 | 0.398505 | ||||||||
\(359\) | −9.94802 | − | 17.2305i | −0.525037 | − | 0.909390i | −0.999575 | − | 0.0291551i | \(-0.990718\pi\) |
0.474538 | − | 0.880235i | \(-0.342615\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.272915 | + | 0.472703i | −0.0143639 | + | 0.0248791i | ||||
\(362\) | −3.57154 | − | 6.18609i | −0.187716 | − | 0.325134i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.73968 | + | 13.4136i | −0.196012 | + | 0.703062i | ||||
\(365\) | −24.0539 | −1.25904 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.87524 | + | 4.98006i | −0.150086 | + | 0.259957i | −0.931259 | − | 0.364358i | \(-0.881288\pi\) |
0.781173 | + | 0.624315i | \(0.214622\pi\) | |||||||
\(368\) | −0.406150 | + | 0.703472i | −0.0211720 | + | 0.0366710i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 7.56526 | 0.393299 | ||||||||
\(371\) | −7.57442 | + | 27.1681i | −0.393244 | + | 1.41050i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.00000 | − | 1.73205i | −0.0517780 | − | 0.0896822i | 0.838975 | − | 0.544170i | \(-0.183156\pi\) |
−0.890753 | + | 0.454488i | \(0.849822\pi\) | |||||||
\(374\) | −4.77292 | + | 8.26693i | −0.246802 | + | 0.427473i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.293425 | − | 0.508226i | −0.0151322 | − | 0.0262098i | ||||
\(377\) | −37.4991 | −1.93130 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.95322 | 0.459896 | 0.229948 | − | 0.973203i | \(-0.426144\pi\) | ||||
0.229948 | + | 0.973203i | \(0.426144\pi\) | |||||||
\(380\) | −9.99549 | − | 17.3127i | −0.512758 | − | 0.888122i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 9.41135 | − | 16.3009i | 0.481527 | − | 0.834029i | ||||
\(383\) | −10.0825 | − | 17.4634i | −0.515192 | − | 0.892338i | −0.999845 | − | 0.0176316i | \(-0.994387\pi\) |
0.484653 | − | 0.874707i | \(-0.338946\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −18.2564 | + | 4.69478i | −0.930430 | + | 0.239268i | ||||
\(386\) | 0.630356 | 0.0320843 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.598364 | − | 1.03640i | 0.0303773 | − | 0.0526151i | ||||
\(389\) | 16.7999 | − | 29.0982i | 0.851787 | − | 1.47534i | −0.0278066 | − | 0.999613i | \(-0.508852\pi\) |
0.879594 | − | 0.475725i | \(-0.157814\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.28263 | 0.267154 | ||||||||
\(392\) | 15.9606 | − | 8.79012i | 0.806133 | − | 0.443968i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.22996 | − | 3.86241i | −0.112344 | − | 0.194585i | ||||
\(395\) | −10.8639 | + | 18.8168i | −0.546621 | + | 0.946776i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.06922 | + | 3.58399i | 0.103851 | + | 0.179875i | 0.913268 | − | 0.407359i | \(-0.133550\pi\) |
−0.809417 | + | 0.587234i | \(0.800217\pi\) | |||||||
\(398\) | 7.03775 | 0.352771 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.41531 | 0.220765 | ||||||||
\(401\) | −7.73461 | − | 13.3967i | −0.386248 | − | 0.669001i | 0.605693 | − | 0.795698i | \(-0.292896\pi\) |
−0.991941 | + | 0.126697i | \(0.959562\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.5624 | − | 18.2946i | 0.526150 | − | 0.911318i | ||||
\(404\) | 5.50465 | + | 9.53433i | 0.273866 | + | 0.474350i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 14.2661 | + | 14.5570i | 0.708014 | + | 0.722454i | ||||
\(407\) | −6.99673 | −0.346815 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.6969 | + | 23.7237i | −0.677266 | + | 1.17306i | 0.298535 | + | 0.954399i | \(0.403502\pi\) |
−0.975801 | + | 0.218661i | \(0.929831\pi\) | |||||||
\(410\) | 4.82558 | − | 8.35815i | 0.238318 | − | 0.412780i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.45993 | 0.170458 | ||||||||
\(413\) | 1.46169 | − | 5.24284i | 0.0719253 | − | 0.257983i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.9045 | + | 22.3513i | 0.633458 | + | 1.09718i | ||||
\(416\) | 10.8547 | − | 18.8009i | 0.532197 | − | 0.921792i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.76608 | − | 6.52304i | −0.184205 | − | 0.319052i | ||||
\(419\) | −21.0000 | −1.02592 | −0.512959 | − | 0.858413i | \(-0.671451\pi\) | ||||
−0.512959 | + | 0.858413i | \(0.671451\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.9590 | 0.972741 | 0.486371 | − | 0.873753i | \(-0.338321\pi\) | ||||
0.486371 | + | 0.873753i | \(0.338321\pi\) | |||||||
\(422\) | −4.77812 | − | 8.27594i | −0.232595 | − | 0.402867i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 13.8743 | − | 24.0310i | 0.673795 | − | 1.16705i | ||||
\(425\) | −14.3571 | − | 24.8671i | −0.696419 | − | 1.20623i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.8187 | − | 11.0394i | −0.523556 | − | 0.534234i | ||||
\(428\) | 16.2919 | 0.787500 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.97373 | − | 6.88271i | 0.191630 | − | 0.331914i | ||||
\(431\) | −10.0647 | + | 17.4326i | −0.484800 | + | 0.839698i | −0.999847 | − | 0.0174637i | \(-0.994441\pi\) |
0.515048 | + | 0.857162i | \(0.327774\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.8558 | 0.569754 | 0.284877 | − | 0.958564i | \(-0.408047\pi\) | ||||
0.284877 | + | 0.958564i | \(0.408047\pi\) | |||||||
\(434\) | −11.1202 | + | 2.85967i | −0.533789 | + | 0.137268i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −12.9669 | − | 22.4593i | −0.621002 | − | 1.07561i | ||||
\(437\) | −2.08414 | + | 3.60983i | −0.0996977 | + | 0.172681i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.07893 | + | 1.86877i | 0.0514947 | + | 0.0891914i | 0.890624 | − | 0.454741i | \(-0.150268\pi\) |
−0.839129 | + | 0.543932i | \(0.816935\pi\) | |||||||
\(440\) | 18.5458 | 0.884138 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −15.7896 | −0.751035 | ||||||||
\(443\) | −0.981125 | − | 1.69936i | −0.0466147 | − | 0.0807390i | 0.841777 | − | 0.539826i | \(-0.181510\pi\) |
−0.888391 | + | 0.459087i | \(0.848177\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −15.4766 | + | 26.8063i | −0.733662 | + | 1.27074i | ||||
\(446\) | −8.13680 | − | 14.0934i | −0.385289 | − | 0.667340i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −7.01273 | + | 1.80338i | −0.331320 | + | 0.0852018i | ||||
\(449\) | −2.15211 | −0.101564 | −0.0507822 | − | 0.998710i | \(-0.516171\pi\) | ||||
−0.0507822 | + | 0.998710i | \(0.516171\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.46294 | + | 7.73004i | −0.210152 | + | 0.363993i | ||||
\(452\) | 3.72996 | − | 6.46049i | 0.175443 | − | 0.303876i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −9.60412 | −0.450744 | ||||||||
\(455\) | −21.8239 | − | 22.2691i | −1.02312 | − | 1.04399i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.55267 | + | 11.3496i | 0.306521 | + | 0.530910i | 0.977599 | − | 0.210477i | \(-0.0675018\pi\) |
−0.671078 | + | 0.741387i | \(0.734168\pi\) | |||||||
\(458\) | −11.0023 | + | 19.0566i | −0.514105 | + | 0.890456i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.13160 | − | 3.69204i | −0.0993864 | − | 0.172142i | ||||
\(461\) | 5.48727 | 0.255568 | 0.127784 | − | 0.991802i | \(-0.459214\pi\) | ||||
0.127784 | + | 0.991802i | \(0.459214\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.4991 | −0.952672 | −0.476336 | − | 0.879263i | \(-0.658035\pi\) | ||||
−0.476336 | + | 0.879263i | \(0.658035\pi\) | |||||||
\(464\) | 4.36156 | + | 7.55445i | 0.202481 | + | 0.350707i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.16075 | + | 14.1348i | −0.378039 | + | 0.654783i | ||||
\(467\) | 19.6758 | + | 34.0795i | 0.910487 | + | 1.57701i | 0.813377 | + | 0.581736i | \(0.197626\pi\) |
0.0971099 | + | 0.995274i | \(0.469040\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.27292 | − | 18.9130i | 0.243481 | − | 0.873322i | ||||
\(470\) | 0.545830 | 0.0251773 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.67743 | + | 4.63744i | −0.123239 | + | 0.213456i | ||||
\(473\) | −3.67511 | + | 6.36547i | −0.168982 | + | 0.292685i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 22.6569 | 1.03957 | ||||||||
\(476\) | −14.7449 | − | 15.0456i | −0.675830 | − | 0.689615i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.94338 | + | 5.09808i | 0.134627 | + | 0.233181i | ||||
\(479\) | −8.37360 | + | 14.5035i | −0.382600 | + | 0.662682i | −0.991433 | − | 0.130616i | \(-0.958304\pi\) |
0.608833 | + | 0.793298i | \(0.291638\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.78659 | − | 10.0227i | −0.263846 | − | 0.456994i | ||||
\(482\) | −4.63500 | −0.211119 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.50697 | 0.386680 | ||||||||
\(485\) | 1.33981 | + | 2.32062i | 0.0608376 | + | 0.105374i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.00288 | + | 3.46909i | −0.0907591 | + | 0.157199i | −0.907831 | − | 0.419337i | \(-0.862263\pi\) |
0.817072 | + | 0.576536i | \(0.195596\pi\) | |||||||
\(488\) | 7.60357 | + | 13.1698i | 0.344197 | + | 0.596167i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.342133 | + | 16.9440i | −0.0154560 | + | 0.765452i | ||||
\(491\) | 24.6512 | 1.11249 | 0.556246 | − | 0.831018i | \(-0.312241\pi\) | ||||
0.556246 | + | 0.831018i | \(0.312241\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 28.3646 | − | 49.1289i | 1.27748 | − | 2.21265i | ||||
\(494\) | 6.22941 | − | 10.7897i | 0.280274 | − | 0.485449i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.91410 | −0.220649 | ||||||||
\(497\) | 18.6111 | − | 4.78600i | 0.834821 | − | 0.214682i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.2798 | + | 21.2692i | 0.549717 | + | 0.952138i | 0.998294 | + | 0.0583936i | \(0.0185978\pi\) |
−0.448576 | + | 0.893744i | \(0.648069\pi\) | |||||||
\(500\) | −0.282075 | + | 0.488568i | −0.0126148 | + | 0.0218494i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0.533236 | + | 0.923592i | 0.0237995 | + | 0.0412219i | ||||
\(503\) | −12.3743 | −0.551742 | −0.275871 | − | 0.961195i | \(-0.588966\pi\) | ||||
−0.275871 | + | 0.961195i | \(0.588966\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −24.6512 | −1.09696 | ||||||||
\(506\) | −0.803140 | − | 1.39108i | −0.0357039 | − | 0.0618410i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 14.2855 | − | 24.7432i | 0.633817 | − | 1.09780i | ||||
\(509\) | 5.59781 | + | 9.69569i | 0.248118 | + | 0.429754i | 0.963004 | − | 0.269488i | \(-0.0868544\pi\) |
−0.714885 | + | 0.699242i | \(0.753521\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.37128 | − | 19.2658i | 0.237611 | − | 0.852270i | ||||
\(512\) | −9.53543 | −0.421410 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.83134 | − | 11.8322i | 0.301317 | − | 0.521897i | ||||
\(515\) | −3.87360 | + | 6.70928i | −0.170691 | + | 0.295646i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.504811 | −0.0222016 | ||||||||
\(518\) | −1.68934 | + | 6.05935i | −0.0742251 | + | 0.266232i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 15.3382 | + | 26.5665i | 0.672623 | + | 1.16502i | ||||
\(521\) | 15.8096 | − | 27.3830i | 0.692631 | − | 1.19967i | −0.278342 | − | 0.960482i | \(-0.589785\pi\) |
0.970973 | − | 0.239189i | \(-0.0768817\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.1179 | + | 24.4530i | 0.617334 | + | 1.06925i | 0.989970 | + | 0.141276i | \(0.0451205\pi\) |
−0.372636 | + | 0.927977i | \(0.621546\pi\) | |||||||
\(524\) | −5.79974 | −0.253363 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.46019 | −0.238076 | ||||||||
\(527\) | 15.9789 | + | 27.6763i | 0.696053 | + | 1.20560i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.0555 | − | 19.1488i | 0.480676 | − | 0.832555i | ||||
\(530\) | 12.9045 | + | 22.3513i | 0.560536 | + | 0.970877i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 16.0985 | − | 4.13987i | 0.697958 | − | 0.179486i | ||||
\(533\) | −14.7641 | −0.639506 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18.2398 | + | 31.5923i | −0.788576 | + | 1.36585i | ||||
\(536\) | −9.65856 | + | 16.7291i | −0.417186 | + | 0.722587i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.58469 | 0.111434 | ||||||||
\(539\) | 0.316422 | − | 15.6707i | 0.0136293 | − | 0.674983i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.4045 | − | 37.0737i | −0.920252 | − | 1.59392i | −0.799025 | − | 0.601298i | \(-0.794650\pi\) |
−0.121227 | − | 0.992625i | \(-0.538683\pi\) | |||||||
\(542\) | −3.89411 | + | 6.74480i | −0.167266 | + | 0.289714i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 16.4212 | + | 28.4424i | 0.704053 | + | 1.21946i | ||||
\(545\) | 58.0690 | 2.48740 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.5516 | 0.579424 | 0.289712 | − | 0.957114i | \(-0.406440\pi\) | ||||
0.289712 | + | 0.957114i | \(0.406440\pi\) | |||||||
\(548\) | 1.33981 | + | 2.32062i | 0.0572339 | + | 0.0991319i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4.36552 | + | 7.56130i | −0.186146 | + | 0.322415i | ||||
\(551\) | 22.3811 | + | 38.7652i | 0.953468 | + | 1.65146i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.6453 | − | 12.9032i | −0.537732 | − | 0.548699i | ||||
\(554\) | 2.70834 | 0.115066 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9.09153 | + | 15.7470i | −0.385567 | + | 0.667821i | ||||
\(557\) | 16.3925 | − | 28.3926i | 0.694572 | − | 1.20303i | −0.275753 | − | 0.961228i | \(-0.588927\pi\) |
0.970325 | − | 0.241805i | \(-0.0777394\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.1579 | −0.514223 | ||||||||
\(560\) | −1.94789 | + | 6.98673i | −0.0823133 | + | 0.295243i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.65787 | − | 4.60356i | −0.112115 | − | 0.194189i | ||||
\(563\) | −8.57730 | + | 14.8563i | −0.361490 | + | 0.626119i | −0.988206 | − | 0.153128i | \(-0.951065\pi\) |
0.626716 | + | 0.779248i | \(0.284399\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.35185 | + | 14.4658i | 0.351365 | + | 0.608582i | ||||
\(566\) | 22.9910 | 0.966383 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −18.9062 | −0.793286 | ||||||||
\(569\) | 6.44966 | + | 11.1711i | 0.270384 | + | 0.468318i | 0.968960 | − | 0.247217i | \(-0.0795161\pi\) |
−0.698576 | + | 0.715535i | \(0.746183\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.141315 | − | 0.244765i | 0.00591385 | − | 0.0102431i | −0.863053 | − | 0.505113i | \(-0.831451\pi\) |
0.868967 | + | 0.494870i | \(0.164784\pi\) | |||||||
\(572\) | −5.89248 | − | 10.2061i | −0.246377 | − | 0.426737i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 5.61685 | + | 5.73141i | 0.234443 | + | 0.239224i | ||||
\(575\) | 4.83173 | 0.201497 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.08289 | − | 1.87562i | 0.0450814 | − | 0.0780832i | −0.842604 | − | 0.538533i | \(-0.818979\pi\) |
0.887686 | + | 0.460450i | \(0.152312\pi\) | |||||||
\(578\) | 5.47592 | − | 9.48458i | 0.227768 | − | 0.394506i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −45.7817 | −1.90098 | ||||||||
\(581\) | −20.7837 | + | 5.34471i | −0.862254 | + | 0.221736i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.9347 | − | 20.6716i | −0.494286 | − | 0.856129i | ||||
\(584\) | −9.83873 | + | 17.0412i | −0.407130 | + | 0.705169i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.79630 | + | 10.0395i | 0.239443 | + | 0.414728i | ||||
\(587\) | 16.7759 | 0.692417 | 0.346208 | − | 0.938158i | \(-0.387469\pi\) | ||||
0.346208 | + | 0.938158i | \(0.387469\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −25.2164 | −1.03902 | ||||||||
\(590\) | −2.49028 | − | 4.31330i | −0.102523 | − | 0.177576i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.34609 | + | 2.33150i | −0.0553240 | + | 0.0958240i | ||||
\(593\) | −12.5933 | − | 21.8122i | −0.517145 | − | 0.895721i | −0.999802 | − | 0.0199114i | \(-0.993662\pi\) |
0.482657 | − | 0.875809i | \(-0.339672\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 45.6833 | − | 11.7479i | 1.87283 | − | 0.481615i | ||||
\(596\) | 11.4498 | 0.469002 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.32846 | − | 2.30096i | 0.0543248 | − | 0.0940933i | ||||
\(599\) | 14.3662 | − | 24.8830i | 0.586987 | − | 1.01669i | −0.407637 | − | 0.913144i | \(-0.633647\pi\) |
0.994624 | − | 0.103548i | \(-0.0330195\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −36.7954 | −1.50091 | −0.750457 | − | 0.660919i | \(-0.770167\pi\) | ||||
−0.750457 | + | 0.660919i | \(0.770167\pi\) | |||||||
\(602\) | 4.62532 | + | 4.71966i | 0.188514 | + | 0.192359i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.46402 | − | 7.73191i | −0.181638 | − | 0.314607i | ||||
\(605\) | −9.52408 | + | 16.4962i | −0.387209 | + | 0.670665i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.9503 | − | 32.8230i | −0.769171 | − | 1.33224i | −0.938013 | − | 0.346600i | \(-0.887336\pi\) |
0.168842 | − | 0.985643i | \(-0.445997\pi\) | |||||||
\(608\) | −25.9144 | −1.05097 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −14.1442 | −0.572682 | ||||||||
\(611\) | −0.417500 | − | 0.723131i | −0.0168902 | − | 0.0292547i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.0196 | + | 32.9428i | −0.768193 | + | 1.33055i | 0.170349 | + | 0.985384i | \(0.445511\pi\) |
−0.938542 | + | 0.345165i | \(0.887823\pi\) | |||||||
\(614\) | −0.393032 | − | 0.680752i | −0.0158615 | − | 0.0274729i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.14132 | + | 14.8542i | −0.166858 | + | 0.598491i | ||||
\(617\) | −26.5264 | −1.06791 | −0.533956 | − | 0.845512i | \(-0.679295\pi\) | ||||
−0.533956 | + | 0.845512i | \(0.679295\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.35185 | + | 11.0017i | −0.255302 | + | 0.442197i | −0.964978 | − | 0.262332i | \(-0.915508\pi\) |
0.709675 | + | 0.704529i | \(0.248842\pi\) | |||||||
\(620\) | 12.8954 | − | 22.3354i | 0.517890 | − | 0.897012i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −7.09166 | −0.284350 | ||||||||
\(623\) | −18.0144 | − | 18.3818i | −0.721730 | − | 0.736450i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.1803 | + | 21.0969i | 0.487212 | + | 0.843877i | ||||
\(626\) | 2.31750 | − | 4.01403i | 0.0926260 | − | 0.160433i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.500000 | + | 0.866025i | 0.0199522 | + | 0.0345582i | ||||
\(629\) | 17.5081 | 0.698093 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.6764 | 0.823113 | 0.411556 | − | 0.911384i | \(-0.364985\pi\) | ||||
0.411556 | + | 0.911384i | \(0.364985\pi\) | |||||||
\(632\) | 8.88727 | + | 15.3932i | 0.353517 | + | 0.612309i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8.86458 | + | 15.3539i | −0.352057 | + | 0.609781i | ||||
\(635\) | 31.9870 | + | 55.4031i | 1.26937 | + | 2.19861i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 22.7096 | − | 12.5070i | 0.899787 | − | 0.495547i | ||||
\(638\) | −17.2495 | −0.682915 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 15.3382 | − | 26.5665i | 0.606295 | − | 1.05013i | ||||
\(641\) | 13.9870 | − | 24.2262i | 0.552454 | − | 0.956878i | −0.445643 | − | 0.895211i | \(-0.647025\pi\) |
0.998097 | − | 0.0616674i | \(-0.0196418\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27.9806 | 1.10345 | 0.551723 | − | 0.834027i | \(-0.313971\pi\) | ||||
0.551723 | + | 0.834027i | \(0.313971\pi\) | |||||||
\(644\) | 3.43310 | − | 0.882853i | 0.135283 | − | 0.0347893i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.42395 | + | 16.3228i | 0.370780 | + | 0.642210i | ||||
\(647\) | −2.30834 | + | 3.99816i | −0.0907503 | + | 0.157184i | −0.907827 | − | 0.419345i | \(-0.862260\pi\) |
0.817077 | + | 0.576529i | \(0.195593\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.30314 | + | 3.98916i | 0.0904061 | + | 0.156588i | ||||
\(650\) | −14.4419 | −0.566457 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 27.3354 | 1.07054 | ||||||||
\(653\) | −5.79016 | − | 10.0288i | −0.226586 | − | 0.392459i | 0.730208 | − | 0.683225i | \(-0.239423\pi\) |
−0.956794 | + | 0.290766i | \(0.906090\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.49316 | − | 11.2465i | 0.253709 | − | 0.439437i | ||||
\(656\) | 1.71724 | + | 2.97434i | 0.0670468 | + | 0.116129i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.121885 | + | 0.437179i | −0.00475156 | + | 0.0170430i | ||||
\(659\) | 4.73680 | 0.184520 | 0.0922598 | − | 0.995735i | \(-0.470591\pi\) | ||||
0.0922598 | + | 0.995735i | \(0.470591\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.91135 | − | 11.9708i | 0.268820 | − | 0.465611i | −0.699737 | − | 0.714400i | \(-0.746700\pi\) |
0.968557 | + | 0.248790i | \(0.0800329\pi\) | |||||||
\(662\) | 5.58345 | − | 9.67081i | 0.217007 | − | 0.375867i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 21.1132 | 0.819353 | ||||||||
\(665\) | −9.99549 | + | 35.8520i | −0.387608 | + | 1.39028i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.77292 | + | 8.26693i | 0.184808 | + | 0.320097i | ||||
\(668\) | −16.6179 | + | 28.7831i | −0.642967 | + | 1.11365i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −8.98345 | − | 15.5598i | −0.347061 | − | 0.601127i | ||||
\(671\) | 13.0813 | 0.504996 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.02735 | 0.232337 | 0.116169 | − | 0.993230i | \(-0.462939\pi\) | ||||
0.116169 | + | 0.993230i | \(0.462939\pi\) | |||||||
\(674\) | 9.74828 | + | 16.8845i | 0.375490 | + | 0.650367i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.509715 | − | 0.882853i | 0.0196044 | − | 0.0339559i | ||||
\(677\) | 11.4428 | + | 19.8195i | 0.439783 | + | 0.761727i | 0.997672 | − | 0.0681884i | \(-0.0217219\pi\) |
−0.557889 | + | 0.829915i | \(0.688389\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.15787 | + | 0.554914i | −0.0828113 | + | 0.0212956i | ||||
\(680\) | −46.4077 | −1.77965 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4.85868 | − | 8.41549i | 0.186049 | − | 0.322246i | ||||
\(683\) | −5.14940 | + | 8.91901i | −0.197036 | + | 0.341277i | −0.947566 | − | 0.319560i | \(-0.896465\pi\) |
0.750530 | + | 0.660836i | \(0.229798\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.00000 | −0.229248 | ||||||||
\(686\) | −13.4948 | − | 4.05766i | −0.515234 | − | 0.154922i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.41410 | + | 2.44929i | 0.0539120 | + | 0.0933782i | ||||
\(689\) | 19.7411 | − | 34.1925i | 0.752074 | − | 1.30263i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.5361 | − | 25.1773i | −0.552980 | − | 0.957789i | −0.998058 | − | 0.0622973i | \(-0.980157\pi\) |
0.445078 | − | 0.895492i | \(-0.353176\pi\) | |||||||
\(692\) | −11.7083 | −0.445084 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.59261 | −0.326171 | ||||||||
\(695\) | −20.3571 | − | 35.2594i | −0.772187 | − | 1.33747i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.1677 | − | 19.3430i | 0.423007 | − | 0.732670i | ||||
\(698\) | −4.29755 | − | 7.44357i | −0.162665 | − | 0.281743i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −13.4863 | − | 13.7614i | −0.509735 | − | 0.520132i | ||||
\(701\) | −27.4153 | −1.03546 | −0.517731 | − | 0.855543i | \(-0.673223\pi\) | ||||
−0.517731 | + | 0.855543i | \(0.673223\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.90739 | + | 11.9640i | −0.260517 | + | 0.451229i | ||||
\(704\) | 3.06402 | − | 5.30703i | 0.115479 | − | 0.200016i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 14.0780 | 0.529832 | ||||||||
\(707\) | 5.50465 | − | 19.7442i | 0.207024 | − | 0.742557i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.4834 | + | 32.0143i | 0.694160 | + | 1.20232i | 0.970463 | + | 0.241250i | \(0.0775575\pi\) |
−0.276302 | + | 0.961071i | \(0.589109\pi\) | |||||||
\(710\) | 8.79235 | − | 15.2288i | 0.329971 | − | 0.571526i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 12.6607 | + | 21.9291i | 0.474481 | + | 0.821826i | ||||
\(713\) | −5.37756 | −0.201391 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 26.3880 | 0.986854 | ||||||||
\(716\) | −7.04118 | − | 12.1957i | −0.263141 | − | 0.455774i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 7.56922 | − | 13.1103i | 0.282481 | − | 0.489271i | ||||
\(719\) | −20.2599 | − | 35.0912i | −0.755568 | − | 1.30868i | −0.945092 | − | 0.326806i | \(-0.894028\pi\) |
0.189524 | − | 0.981876i | \(-0.439306\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.50877 | − | 4.60073i | −0.167915 | − | 0.171340i | ||||
\(722\) | −0.415309 | −0.0154562 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −6.67046 | + | 11.5536i | −0.247906 | + | 0.429385i | ||||
\(725\) | 25.9435 | − | 44.9355i | 0.963518 | − | 1.66886i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.2416 | −0.565280 | −0.282640 | − | 0.959226i | \(-0.591210\pi\) | ||||
−0.282640 | + | 0.959226i | \(0.591210\pi\) | |||||||
\(728\) | −24.7033 | + | 6.35267i | −0.915565 | + | 0.235446i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −9.15103 | − | 15.8500i | −0.338695 | − | 0.586637i | ||||
\(731\) | 9.19630 | − | 15.9285i | 0.340138 | − | 0.589136i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.2895 | − | 28.2142i | −0.601665 | − | 1.04211i | −0.992569 | − | 0.121683i | \(-0.961171\pi\) |
0.390904 | − | 0.920432i | \(-0.372163\pi\) | |||||||
\(734\) | −4.37540 | −0.161499 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.52640 | −0.203706 | ||||||||
\(737\) | 8.30834 | + | 14.3905i | 0.306042 | + | 0.530080i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.50684 | + | 6.07402i | −0.129001 | + | 0.223436i | −0.923290 | − | 0.384104i | \(-0.874510\pi\) |
0.794289 | + | 0.607540i | \(0.207844\pi\) | |||||||
\(740\) | −7.06470 | − | 12.2364i | −0.259704 | − | 0.449820i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −20.7837 | + | 5.34471i | −0.762994 | + | 0.196210i | ||||
\(743\) | −35.0118 | −1.28446 | −0.642229 | − | 0.766513i | \(-0.721990\pi\) | ||||
−0.642229 | + | 0.766513i | \(0.721990\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.8187 | + | 22.2027i | −0.469642 | + | 0.813445i | ||||
\(746\) | 0.760877 | − | 1.31788i | 0.0278577 | − | 0.0482509i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 17.8285 | 0.651873 | ||||||||
\(749\) | −21.2307 | − | 21.6637i | −0.775751 | − | 0.791573i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.13844 | + | 3.70388i | 0.0780327 | + | 0.135157i | 0.902401 | − | 0.430897i | \(-0.141803\pi\) |
−0.824368 | + | 0.566054i | \(0.808469\pi\) | |||||||
\(752\) | −0.0971198 | + | 0.168217i | −0.00354160 | + | 0.00613422i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −14.2661 | − | 24.7096i | −0.519540 | − | 0.899870i | ||||
\(755\) | 19.9910 | 0.727546 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34.9611 | −1.27068 | −0.635342 | − | 0.772231i | \(-0.719141\pi\) | ||||
−0.635342 | + | 0.772231i | \(0.719141\pi\) | |||||||
\(758\) | 3.40615 | + | 5.89962i | 0.123717 | + | 0.214284i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 18.3090 | − | 31.7122i | 0.664138 | − | 1.15032i | ||||
\(761\) | 2.29179 | + | 3.96950i | 0.0830773 | + | 0.143894i | 0.904570 | − | 0.426324i | \(-0.140192\pi\) |
−0.821493 | + | 0.570219i | \(0.806858\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.9669 | + | 46.5100i | −0.469433 | + | 1.68377i | ||||
\(764\) | −35.1546 | −1.27185 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.67154 | − | 13.2875i | 0.277184 | − | 0.480097i | ||||
\(767\) | −3.80959 | + | 6.59840i | −0.137556 | + | 0.238254i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.9590 | 0.611556 | 0.305778 | − | 0.952103i | \(-0.401083\pi\) | ||||
0.305778 | + | 0.952103i | \(0.401083\pi\) | |||||||
\(770\) | −10.0390 | − | 10.2437i | −0.361780 | − | 0.369159i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.588649 | − | 1.01957i | −0.0211859 | − | 0.0366951i | ||||
\(773\) | 20.1420 | − | 34.8870i | 0.724458 | − | 1.25480i | −0.234739 | − | 0.972058i | \(-0.575424\pi\) |
0.959197 | − | 0.282739i | \(-0.0912430\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14.6150 | + | 25.3140i | 0.524988 | + | 0.909306i | ||||
\(776\) | 2.19208 | 0.0786911 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 25.5653 | 0.916559 | ||||||||
\(779\) | 8.81191 | + | 15.2627i | 0.315719 | + | 0.546842i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.13160 | + | 14.0843i | −0.290972 | + | 0.503977i | ||||
\(782\) | 2.00972 | + | 3.48093i | 0.0718673 | + | 0.124478i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5.16101 | − | 3.12030i | −0.184322 | − | 0.111439i | ||||
\(785\) | −2.23912 | −0.0799177 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23.6053 | + | 40.8856i | −0.841439 | + | 1.45742i | 0.0472387 | + | 0.998884i | \(0.484958\pi\) |
−0.888678 | + | 0.458532i | \(0.848375\pi\) | |||||||
\(788\) | −4.16484 | + | 7.21371i | −0.148366 | + | 0.256978i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −16.5322 | −0.588188 | ||||||||
\(791\) | −13.4513 | + | 3.45912i | −0.478273 | + | 0.122992i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.8187 | + | 18.7386i | 0.384185 | + | 0.665428i | ||||
\(794\) | −1.57442 | + | 2.72698i | −0.0558741 | + | 0.0967767i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.57210 | − | 11.3832i | −0.232942 | − | 0.403467i | ||||
\(797\) | 4.02735 | 0.142656 | 0.0713280 | − | 0.997453i | \(-0.477276\pi\) | ||||
0.0713280 | + | 0.997453i | \(0.477276\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.26320 | 0.0446888 | ||||||||
\(800\) | 15.0196 | + | 26.0146i | 0.531022 | + | 0.919757i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 5.88508 | − | 10.1933i | 0.207810 | − | 0.359937i | ||||
\(803\) | 8.46333 | + | 14.6589i | 0.298664 | + | 0.517302i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.13160 | + | 7.64567i | −0.0751290 | + | 0.269474i | ||||
\(806\) | 16.0733 | 0.566159 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −10.0830 | + | 17.4643i | −0.354720 | + | 0.614392i | ||||
\(809\) | 5.94119 | − | 10.2904i | 0.208881 | − | 0.361792i | −0.742481 | − | 0.669867i | \(-0.766351\pi\) |
0.951362 | + | 0.308074i | \(0.0996845\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.1111 | −0.741311 | −0.370655 | − | 0.928770i | \(-0.620867\pi\) | ||||
−0.370655 | + | 0.928770i | \(0.620867\pi\) | |||||||
\(812\) | 10.2231 | − | 36.6685i | 0.358761 | − | 1.28681i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.66182 | − | 4.61042i | −0.0932969 | − | 0.161595i | ||||
\(815\) | −30.6037 | + | 53.0072i | −1.07200 | + | 1.85676i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.25636 | + | 12.5684i | 0.253868 | + | 0.439712i | ||||
\(818\) | −20.8432 | −0.728767 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −18.0252 | −0.629467 | ||||||||
\(821\) | −18.6460 | − | 32.2958i | −0.650749 | − | 1.12713i | −0.982942 | − | 0.183918i | \(-0.941122\pi\) |
0.332193 | − | 0.943211i | \(-0.392211\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.7261 | − | 18.5782i | 0.373890 | − | 0.647596i | −0.616270 | − | 0.787535i | \(-0.711357\pi\) |
0.990160 | + | 0.139939i | \(0.0446905\pi\) | |||||||
\(824\) | 3.16883 | + | 5.48857i | 0.110391 | + | 0.191203i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.01079 | − | 1.03141i | 0.139553 | − | 0.0358874i | ||||
\(827\) | 28.6375 | 0.995823 | 0.497912 | − | 0.867228i | \(-0.334100\pi\) | ||||
0.497912 | + | 0.867228i | \(0.334100\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19.8646 | − | 34.4065i | 0.689925 | − | 1.19499i | −0.281936 | − | 0.959433i | \(-0.590977\pi\) |
0.971862 | − | 0.235552i | \(-0.0756899\pi\) | |||||||
\(830\) | −9.81875 | + | 17.0066i | −0.340814 | + | 0.590306i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 10.1363 | 0.351412 | ||||||||
\(833\) | −0.791790 | + | 39.2131i | −0.0274339 | + | 1.35865i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −37.2096 | − | 64.4489i | −1.28769 | − | 2.23035i | ||||
\(836\) | −7.03379 | + | 12.1829i | −0.243269 | + | 0.421354i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −7.98921 | − | 13.8377i | −0.275983 | − | 0.478016i | ||||
\(839\) | 34.3606 | 1.18626 | 0.593130 | − | 0.805107i | \(-0.297892\pi\) | ||||
0.593130 | + | 0.805107i | \(0.297892\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 73.5108 | 2.53486 | ||||||||
\(842\) | 7.59316 | + | 13.1517i | 0.261678 | + | 0.453239i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −8.92395 | + | 15.4567i | −0.307175 | + | 0.532042i | ||||
\(845\) | 1.14132 | + | 1.97682i | 0.0392624 | + | 0.0680045i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11.0858 | − | 11.3119i | −0.380912 | − | 0.388681i | ||||
\(848\) | −9.18443 | −0.315395 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 10.9239 | − | 18.9208i | 0.374688 | − | 0.648979i | ||||
\(851\) | −1.47304 | + | 2.55139i | −0.0504953 | + | 0.0874605i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.51462 | −0.0518596 | −0.0259298 | − | 0.999664i | \(-0.508255\pi\) | ||||
−0.0259298 | + | 0.999664i | \(0.508255\pi\) | |||||||
\(854\) | 3.15842 | − | 11.3287i | 0.108079 | − | 0.387660i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 14.9212 | + | 25.8443i | 0.509996 | + | 0.883339i | ||||
\(857\) | −2.25473 | + | 3.90530i | −0.0770201 | + | 0.133403i | −0.901963 | − | 0.431813i | \(-0.857874\pi\) |
0.824943 | + | 0.565216i | \(0.191207\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.30314 | − | 10.9174i | −0.215060 | − | 0.372495i | 0.738231 | − | 0.674548i | \(-0.235661\pi\) |
−0.953291 | + | 0.302053i | \(0.902328\pi\) | |||||||
\(860\) | −14.8432 | −0.506150 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −15.3160 | −0.521665 | ||||||||
\(863\) | −5.33009 | − | 9.23200i | −0.181439 | − | 0.314261i | 0.760932 | − | 0.648832i | \(-0.224742\pi\) |
−0.942371 | + | 0.334571i | \(0.891409\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.1082 | − | 22.7041i | 0.445693 | − | 0.771962i | ||||
\(866\) | 4.51040 | + | 7.81225i | 0.153270 | + | 0.265471i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 15.0098 | + | 15.3160i | 0.509467 | + | 0.519858i | ||||
\(869\) | 15.2898 | 0.518670 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.7427 | + | 23.8030i | −0.465653 | + | 0.806535i | ||||
\(872\) | 23.7518 | − | 41.1394i | 0.804339 | − | 1.39316i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3.17154 | −0.107279 | ||||||||
\(875\) | 1.01724 | − | 0.261592i | 0.0343890 | − | 0.00884343i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.1190 | + | 27.9189i | 0.544300 | + | 0.942756i | 0.998651 | + | 0.0519325i | \(0.0165381\pi\) |
−0.454350 | + | 0.890823i | \(0.650129\pi\) | |||||||
\(878\) | −0.820935 | + | 1.42190i | −0.0277052 | + | 0.0479869i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.06922 | − | 5.31604i | −0.103463 | − | 0.179204i | ||||
\(881\) | 55.6375 | 1.87447 | 0.937237 | − | 0.348692i | \(-0.113374\pi\) | ||||
0.937237 | + | 0.348692i | \(0.113374\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −42.4854 | −1.42975 | −0.714873 | − | 0.699254i | \(-0.753516\pi\) | ||||
−0.714873 | + | 0.699254i | \(0.753516\pi\) | |||||||
\(884\) | 14.7449 | + | 25.5389i | 0.495924 | + | 0.858966i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.746515 | − | 1.29300i | 0.0250797 | − | 0.0434393i | ||||
\(887\) | −4.47825 | − | 7.75655i | −0.150365 | − | 0.260439i | 0.780997 | − | 0.624535i | \(-0.214711\pi\) |
−0.931362 | + | 0.364096i | \(0.881378\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −51.5175 | + | 13.2482i | −1.72784 | + | 0.444330i | ||||
\(890\) | −23.5516 | −0.789451 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −15.1969 | + | 26.3217i | −0.508829 | + | 0.881317i | ||||
\(893\) | −0.498365 | + | 0.863194i | −0.0166772 | + | 0.0288857i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 31.5322 | 1.05400 | ||||||||
\(896\) | 17.8532 | + | 18.2174i | 0.596434 | + | 0.608599i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.818745 | − | 1.41811i | −0.0273219 | − | 0.0473229i | ||||
\(899\) | −28.8743 | + | 50.0117i | −0.963011 | + | 1.66798i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 29.8646 | + | 51.7270i | 0.994933 | + | 1.72327i | ||||
\(902\) | −6.79149 | −0.226132 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 13.6646 | 0.454477 | ||||||||
\(905\) | −14.9360 | − | 25.8699i | −0.496489 | − | 0.859944i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.39372 | + | 9.34220i | −0.179096 | + | 0.310203i | −0.941571 | − | 0.336815i | \(-0.890650\pi\) |
0.762475 | + | 0.647017i | \(0.223984\pi\) | |||||||
\(908\) | 8.96866 | + | 15.5342i | 0.297636 | + | 0.515520i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 6.37128 | − | 22.8526i | 0.211206 | − | 0.757558i | ||||
\(911\) | 47.4854 | 1.57326 | 0.786630 | − | 0.617424i | \(-0.211824\pi\) | ||||
0.786630 | + | 0.617424i | \(0.211824\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.08087 | − | 15.7285i | 0.300533 | − | 0.520538i | ||||
\(914\) | −4.98577 | + | 8.63561i | −0.164915 | + | 0.285641i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 41.0974 | 1.35790 | ||||||||
\(917\) | 7.55787 | + | 7.71202i | 0.249583 | + | 0.254673i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.1375 | − | 48.7356i | −0.928170 | − | 1.60764i | −0.786382 | − | 0.617741i | \(-0.788048\pi\) |
−0.141788 | − | 0.989897i | \(-0.545285\pi\) | |||||||
\(920\) | 3.90451 | − | 6.76282i | 0.128728 | − | 0.222964i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2.08757 | + | 3.61578i | 0.0687504 | + | 0.119079i | ||||
\(923\) | −26.9007 | −0.885447 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 16.0137 | 0.526526 | ||||||||
\(926\) | −7.79863 | − | 13.5076i | −0.256279 | − | 0.443888i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −29.6735 | + | 51.3960i | −0.974079 | + | 1.68716i | ||||
\(929\) | 0.380438 | + | 0.658939i | 0.0124818 | + | 0.0216191i | 0.872199 | − | 0.489152i | \(-0.162693\pi\) |
−0.859717 | + | 0.510771i | \(0.829360\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −26.4834 | − | 16.0116i | −0.867960 | − | 0.524760i | ||||
\(932\) | 30.4832 | 0.998509 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −14.9709 | + | 25.9303i | −0.489861 | + | 0.848465i | ||||
\(935\) | −19.9601 | + | 34.5718i | −0.652764 | + | 1.13062i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −30.3218 | −0.990569 | −0.495284 | − | 0.868731i | \(-0.664936\pi\) | ||||
−0.495284 | + | 0.868731i | \(0.664936\pi\) | |||||||
\(938\) | 14.4685 | − | 3.72071i | 0.472414 | − | 0.121485i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.509715 | − | 0.882853i | −0.0166251 | − | 0.0287955i | ||||
\(941\) | 27.5406 | − | 47.7018i | 0.897799 | − | 1.55503i | 0.0674968 | − | 0.997719i | \(-0.478499\pi\) |
0.830302 | − | 0.557314i | \(-0.188168\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.87919 | + | 3.25486i | 0.0611950 | + | 0.105993i | ||||
\(944\) | 1.77239 | 0.0576864 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.59261 | −0.181831 | ||||||||
\(947\) | 15.3103 | + | 26.5182i | 0.497517 | + | 0.861725i | 0.999996 | − | 0.00286470i | \(-0.000911863\pi\) |
−0.502479 | + | 0.864590i | \(0.667579\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.9991 | + | 24.2471i | −0.454429 | + | 0.787093i | ||||
\(950\) | 8.61956 | + | 14.9295i | 0.279656 | + | 0.484378i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 10.3629 | − | 37.1699i | 0.335864 | − | 1.20468i | ||||
\(953\) | −7.83422 | −0.253775 | −0.126888 | − | 0.991917i | \(-0.540499\pi\) | ||||
−0.126888 | + | 0.991917i | \(0.540499\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 39.3577 | − | 68.1696i | 1.27359 | − | 2.20592i | ||||
\(956\) | 5.49725 | − | 9.52152i | 0.177794 | − | 0.307948i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −12.7426 | −0.411693 | ||||||||
\(959\) | 1.33981 | − | 4.80566i | 0.0432647 | − | 0.155183i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.766078 | − | 1.32689i | −0.0247122 | − | 0.0428028i | ||||
\(962\) | 4.40288 | − | 7.62601i | 0.141955 | − | 0.245872i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.32833 | + | 7.49688i | 0.139406 | + | 0.241458i | ||||
\(965\) | 2.63611 | 0.0848595 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.29630 | −0.170318 | −0.0851588 | − | 0.996367i | \(-0.527140\pi\) | ||||
−0.0851588 | + | 0.996367i | \(0.527140\pi\) | |||||||
\(968\) | 7.79123 | + | 13.4948i | 0.250420 | + | 0.433740i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.01943 | + | 1.76571i | −0.0327319 | + | 0.0566934i | ||||
\(971\) | 26.1202 | + | 45.2416i | 0.838239 | + | 1.45187i | 0.891366 | + | 0.453284i | \(0.149748\pi\) |
−0.0531273 | + | 0.998588i | \(0.516919\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 32.7866 | − | 8.43135i | 1.05109 | − | 0.270297i | ||||
\(974\) | −3.04789 | −0.0976606 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.51668 | − | 4.35903i | 0.0805571 | − | 0.139529i | ||||
\(977\) | −2.97304 | + | 5.14946i | −0.0951161 | + | 0.164746i | −0.909657 | − | 0.415360i | \(-0.863656\pi\) |
0.814541 | + | 0.580106i | \(0.196989\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21.7817 | 0.696146 | ||||||||
\(980\) | 27.7256 | − | 15.2695i | 0.885661 | − | 0.487767i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 9.37825 | + | 16.2436i | 0.299272 | + | 0.518354i | ||||
\(983\) | −9.28207 | + | 16.0770i | −0.296052 | + | 0.512777i | −0.975229 | − | 0.221197i | \(-0.929004\pi\) |
0.679177 | + | 0.733975i | \(0.262337\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.32558 | − | 16.1524i | −0.297138 | − | 0.514658i | ||||
\(986\) | 43.1639 | 1.37462 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −23.2690 | −0.740284 | ||||||||
\(989\) | 1.54746 | + | 2.68029i | 0.0492065 | + | 0.0852282i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.31875 | + | 16.1405i | −0.296020 | + | 0.512721i | −0.975222 | − | 0.221230i | \(-0.928993\pi\) |
0.679202 | + | 0.733951i | \(0.262326\pi\) | |||||||
\(992\) | −16.7163 | − | 28.9535i | −0.530743 | − | 0.919273i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 10.2341 | + | 10.4428i | 0.324604 | + | 0.331225i | ||||
\(995\) | 29.4315 | 0.933040 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15.2798 | − | 26.4653i | 0.483915 | − | 0.838165i | −0.515915 | − | 0.856640i | \(-0.672548\pi\) |
0.999829 | + | 0.0184753i | \(0.00588120\pi\) | |||||||
\(998\) | −9.34338 | + | 16.1832i | −0.295759 | + | 0.512270i | ||||
\(999\) | 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 | 189.2.e.f.109.2 | yes | 6 | |
3.2 | odd | 2 | 189.2.e.e.109.2 | ✓ | 6 | ||
7.2 | even | 3 | inner | 189.2.e.f.163.2 | yes | 6 | |
7.3 | odd | 6 | 1323.2.a.y.1.2 | 3 | |||
7.4 | even | 3 | 1323.2.a.x.1.2 | 3 | |||
9.2 | odd | 6 | 567.2.g.h.109.2 | 6 | |||
9.4 | even | 3 | 567.2.h.h.298.2 | 6 | |||
9.5 | odd | 6 | 567.2.h.i.298.2 | 6 | |||
9.7 | even | 3 | 567.2.g.i.109.2 | 6 | |||
21.2 | odd | 6 | 189.2.e.e.163.2 | yes | 6 | ||
21.11 | odd | 6 | 1323.2.a.ba.1.2 | 3 | |||
21.17 | even | 6 | 1323.2.a.z.1.2 | 3 | |||
63.2 | odd | 6 | 567.2.h.i.352.2 | 6 | |||
63.16 | even | 3 | 567.2.h.h.352.2 | 6 | |||
63.23 | odd | 6 | 567.2.g.h.541.2 | 6 | |||
63.58 | even | 3 | 567.2.g.i.541.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
189.2.e.e.109.2 | ✓ | 6 | 3.2 | odd | 2 | ||
189.2.e.e.163.2 | yes | 6 | 21.2 | odd | 6 | ||
189.2.e.f.109.2 | yes | 6 | 1.1 | even | 1 | trivial | |
189.2.e.f.163.2 | yes | 6 | 7.2 | even | 3 | inner | |
567.2.g.h.109.2 | 6 | 9.2 | odd | 6 | |||
567.2.g.h.541.2 | 6 | 63.23 | odd | 6 | |||
567.2.g.i.109.2 | 6 | 9.7 | even | 3 | |||
567.2.g.i.541.2 | 6 | 63.58 | even | 3 | |||
567.2.h.h.298.2 | 6 | 9.4 | even | 3 | |||
567.2.h.h.352.2 | 6 | 63.16 | even | 3 | |||
567.2.h.i.298.2 | 6 | 9.5 | odd | 6 | |||
567.2.h.i.352.2 | 6 | 63.2 | odd | 6 | |||
1323.2.a.x.1.2 | 3 | 7.4 | even | 3 | |||
1323.2.a.y.1.2 | 3 | 7.3 | odd | 6 | |||
1323.2.a.z.1.2 | 3 | 21.17 | even | 6 | |||
1323.2.a.ba.1.2 | 3 | 21.11 | odd | 6 |