Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [462,2,Mod(67,462)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(462, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("462.67");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 462.i (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: | \(3.68908857338\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.21870000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 24x^{4} - 43x^{3} + 138x^{2} - 117x + 73 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 331.3 | ||
Root | \(0.500000 - 0.679547i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 462.331 |
Dual form | 462.2.i.g.67.3 |
$q$-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 \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 1.40280 | − | 2.42972i | 0.627352 | − | 1.08661i | −0.360729 | − | 0.932671i | \(-0.617472\pi\) |
0.988081 | − | 0.153935i | \(-0.0491945\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −1.40280 | − | 2.24325i | −0.530209 | − | 0.847867i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 1.40280 | + | 2.42972i | 0.443605 | + | 0.768346i | ||||
\(11\) | 0.500000 | + | 0.866025i | 0.150756 | + | 0.261116i | ||||
\(12\) | 0.500000 | − | 0.866025i | 0.144338 | − | 0.250000i | ||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | 2.64411 | − | 0.0932392i | 0.706668 | − | 0.0249192i | ||||
\(15\) | 2.80560 | 0.724404 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −3.98261 | − | 6.89809i | −0.965926 | − | 1.67303i | −0.707108 | − | 0.707106i | \(-0.750000\pi\) |
−0.258818 | − | 0.965926i | \(-0.583333\pi\) | |||||||
\(18\) | −0.500000 | − | 0.866025i | −0.117851 | − | 0.204124i | ||||
\(19\) | 3.24131 | − | 5.61411i | 0.743607 | − | 1.28796i | −0.207236 | − | 0.978291i | \(-0.566447\pi\) |
0.950843 | − | 0.309674i | \(-0.100220\pi\) | |||||||
\(20\) | −2.80560 | −0.627352 | ||||||||
\(21\) | 1.24131 | − | 2.33648i | 0.270875 | − | 0.509863i | ||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | 2.64411 | − | 4.57973i | 0.551335 | − | 0.954940i | −0.446844 | − | 0.894612i | \(-0.647452\pi\) |
0.998179 | − | 0.0603277i | \(-0.0192146\pi\) | |||||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | −1.43570 | − | 2.48671i | −0.287141 | − | 0.497342i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.24131 | + | 2.33648i | −0.234585 | + | 0.441554i | ||||
\(29\) | 5.12859 | 0.952356 | 0.476178 | − | 0.879349i | \(-0.342022\pi\) | ||||
0.476178 | + | 0.879349i | \(0.342022\pi\) | |||||||
\(30\) | −1.40280 | + | 2.42972i | −0.256115 | + | 0.443605i | ||||
\(31\) | 4.48261 | + | 7.76411i | 0.805101 | + | 1.39448i | 0.916223 | + | 0.400669i | \(0.131222\pi\) |
−0.111122 | + | 0.993807i | \(0.535444\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | −0.500000 | + | 0.866025i | −0.0870388 | + | 0.150756i | ||||
\(34\) | 7.96523 | 1.36602 | ||||||||
\(35\) | −7.41832 | + | 0.261592i | −1.25392 | + | 0.0442171i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −5.24131 | + | 9.07821i | −0.861665 | + | 1.49245i | 0.00865499 | + | 0.999963i | \(0.497245\pi\) |
−0.870320 | + | 0.492486i | \(0.836088\pi\) | |||||||
\(38\) | 3.24131 | + | 5.61411i | 0.525809 | + | 0.910728i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.40280 | − | 2.42972i | 0.221802 | − | 0.384173i | ||||
\(41\) | −5.09382 | −0.795521 | −0.397760 | − | 0.917489i | \(-0.630212\pi\) | ||||
−0.397760 | + | 0.917489i | \(0.630212\pi\) | |||||||
\(42\) | 1.40280 | + | 2.24325i | 0.216457 | + | 0.346140i | ||||
\(43\) | 11.4478 | 1.74578 | 0.872890 | − | 0.487918i | \(-0.162243\pi\) | ||||
0.872890 | + | 0.487918i | \(0.162243\pi\) | |||||||
\(44\) | 0.500000 | − | 0.866025i | 0.0753778 | − | 0.130558i | ||||
\(45\) | 1.40280 | + | 2.42972i | 0.209117 | + | 0.362202i | ||||
\(46\) | 2.64411 | + | 4.57973i | 0.389852 | + | 0.675244i | ||||
\(47\) | −0.161495 | + | 0.279717i | −0.0235565 | + | 0.0408010i | −0.877563 | − | 0.479461i | \(-0.840832\pi\) |
0.854007 | + | 0.520262i | \(0.174166\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −3.06430 | + | 6.29365i | −0.437757 | + | 0.899094i | ||||
\(50\) | 2.87141 | 0.406078 | ||||||||
\(51\) | 3.98261 | − | 6.89809i | 0.557677 | − | 0.965926i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.00000 | − | 6.92820i | −0.549442 | − | 0.951662i | −0.998313 | − | 0.0580651i | \(-0.981507\pi\) |
0.448871 | − | 0.893597i | \(-0.351826\pi\) | |||||||
\(54\) | 0.500000 | − | 0.866025i | 0.0680414 | − | 0.117851i | ||||
\(55\) | 2.80560 | 0.378307 | ||||||||
\(56\) | −1.40280 | − | 2.24325i | −0.187457 | − | 0.299766i | ||||
\(57\) | 6.48261 | 0.858643 | ||||||||
\(58\) | −2.56430 | + | 4.44149i | −0.336709 | + | 0.583196i | ||||
\(59\) | 0.435704 | + | 0.754661i | 0.0567238 | + | 0.0982485i | 0.892993 | − | 0.450071i | \(-0.148601\pi\) |
−0.836269 | + | 0.548319i | \(0.815268\pi\) | |||||||
\(60\) | −1.40280 | − | 2.42972i | −0.181101 | − | 0.313676i | ||||
\(61\) | −1.07981 | + | 1.87029i | −0.138256 | + | 0.239466i | −0.926836 | − | 0.375465i | \(-0.877483\pi\) |
0.788581 | + | 0.614931i | \(0.210816\pi\) | |||||||
\(62\) | −8.96523 | −1.13858 | ||||||||
\(63\) | 2.64411 | − | 0.0932392i | 0.333126 | − | 0.0117470i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.500000 | − | 0.866025i | −0.0615457 | − | 0.106600i | ||||
\(67\) | 3.54691 | + | 6.14343i | 0.433324 | + | 0.750539i | 0.997157 | − | 0.0753496i | \(-0.0240073\pi\) |
−0.563833 | + | 0.825889i | \(0.690674\pi\) | |||||||
\(68\) | −3.98261 | + | 6.89809i | −0.482963 | + | 0.836516i | ||||
\(69\) | 5.28822 | 0.636626 | ||||||||
\(70\) | 3.48261 | − | 6.55525i | 0.416252 | − | 0.783502i | ||||
\(71\) | −7.44784 | −0.883896 | −0.441948 | − | 0.897041i | \(-0.645712\pi\) | ||||
−0.441948 | + | 0.897041i | \(0.645712\pi\) | |||||||
\(72\) | −0.500000 | + | 0.866025i | −0.0589256 | + | 0.102062i | ||||
\(73\) | −6.28822 | − | 10.8915i | −0.735980 | − | 1.27475i | −0.954292 | − | 0.298876i | \(-0.903388\pi\) |
0.218312 | − | 0.975879i | \(-0.429945\pi\) | |||||||
\(74\) | −5.24131 | − | 9.07821i | −0.609289 | − | 1.05532i | ||||
\(75\) | 1.43570 | − | 2.48671i | 0.165781 | − | 0.287141i | ||||
\(76\) | −6.48261 | −0.743607 | ||||||||
\(77\) | 1.24131 | − | 2.33648i | 0.141460 | − | 0.266267i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.40280 | + | 5.89382i | −0.382845 | + | 0.663107i | −0.991468 | − | 0.130353i | \(-0.958389\pi\) |
0.608623 | + | 0.793460i | \(0.291722\pi\) | |||||||
\(80\) | 1.40280 | + | 2.42972i | 0.156838 | + | 0.271651i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 2.54691 | − | 4.41138i | 0.281259 | − | 0.487155i | ||||
\(83\) | 15.0938 | 1.65676 | 0.828381 | − | 0.560165i | \(-0.189262\pi\) | ||||
0.828381 | + | 0.560165i | \(0.189262\pi\) | |||||||
\(84\) | −2.64411 | + | 0.0932392i | −0.288496 | + | 0.0101732i | ||||
\(85\) | −22.3473 | −2.42390 | ||||||||
\(86\) | −5.72392 | + | 9.91412i | −0.617226 | + | 1.06907i | ||||
\(87\) | 2.56430 | + | 4.44149i | 0.274921 | + | 0.476178i | ||||
\(88\) | 0.500000 | + | 0.866025i | 0.0533002 | + | 0.0923186i | ||||
\(89\) | −0.805603 | + | 1.39535i | −0.0853937 | + | 0.147906i | −0.905559 | − | 0.424221i | \(-0.860548\pi\) |
0.820165 | + | 0.572127i | \(0.193881\pi\) | |||||||
\(90\) | −2.80560 | −0.295737 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −5.28822 | −0.551335 | ||||||||
\(93\) | −4.48261 | + | 7.76411i | −0.464825 | + | 0.805101i | ||||
\(94\) | −0.161495 | − | 0.279717i | −0.0166569 | − | 0.0288507i | ||||
\(95\) | −9.09382 | − | 15.7510i | −0.933006 | − | 1.61601i | ||||
\(96\) | 0.500000 | − | 0.866025i | 0.0510310 | − | 0.0883883i | ||||
\(97\) | 7.00000 | 0.710742 | 0.355371 | − | 0.934725i | \(-0.384354\pi\) | ||||
0.355371 | + | 0.934725i | \(0.384354\pi\) | |||||||
\(98\) | −3.91832 | − | 5.80059i | −0.395810 | − | 0.585948i | ||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | −1.43570 | + | 2.48671i | −0.143570 | + | 0.248671i | ||||
\(101\) | −5.36990 | − | 9.30094i | −0.534325 | − | 0.925478i | −0.999196 | − | 0.0400994i | \(-0.987233\pi\) |
0.464871 | − | 0.885379i | \(-0.346101\pi\) | |||||||
\(102\) | 3.98261 | + | 6.89809i | 0.394337 | + | 0.683012i | ||||
\(103\) | −1.48261 | + | 2.56796i | −0.146086 | + | 0.253029i | −0.929778 | − | 0.368122i | \(-0.880001\pi\) |
0.783691 | + | 0.621150i | \(0.213334\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.93570 | − | 6.29365i | −0.384085 | − | 0.614198i | ||||
\(106\) | 8.00000 | 0.777029 | ||||||||
\(107\) | −2.41832 | + | 4.18865i | −0.233787 | + | 0.404932i | −0.958920 | − | 0.283678i | \(-0.908445\pi\) |
0.725132 | + | 0.688610i | \(0.241779\pi\) | |||||||
\(108\) | 0.500000 | + | 0.866025i | 0.0481125 | + | 0.0833333i | ||||
\(109\) | 5.07981 | + | 8.79849i | 0.486558 | + | 0.842743i | 0.999881 | − | 0.0154529i | \(-0.00491901\pi\) |
−0.513323 | + | 0.858196i | \(0.671586\pi\) | |||||||
\(110\) | −1.40280 | + | 2.42972i | −0.133752 | + | 0.231665i | ||||
\(111\) | −10.4826 | −0.994966 | ||||||||
\(112\) | 2.64411 | − | 0.0932392i | 0.249845 | − | 0.00881027i | ||||
\(113\) | 10.9652 | 1.03152 | 0.515761 | − | 0.856733i | \(-0.327509\pi\) | ||||
0.515761 | + | 0.856733i | \(0.327509\pi\) | |||||||
\(114\) | −3.24131 | + | 5.61411i | −0.303576 | + | 0.525809i | ||||
\(115\) | −7.41832 | − | 12.8489i | −0.691762 | − | 1.19817i | ||||
\(116\) | −2.56430 | − | 4.44149i | −0.238089 | − | 0.412382i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.871407 | −0.0802195 | ||||||||
\(119\) | −9.88729 | + | 18.6106i | −0.906366 | + | 1.70603i | ||||
\(120\) | 2.80560 | 0.256115 | ||||||||
\(121\) | −0.500000 | + | 0.866025i | −0.0454545 | + | 0.0787296i | ||||
\(122\) | −1.07981 | − | 1.87029i | −0.0977615 | − | 0.169328i | ||||
\(123\) | −2.54691 | − | 4.41138i | −0.229647 | − | 0.397760i | ||||
\(124\) | 4.48261 | − | 7.76411i | 0.402551 | − | 0.697238i | ||||
\(125\) | 5.97199 | 0.534151 | ||||||||
\(126\) | −1.24131 | + | 2.33648i | −0.110584 | + | 0.208151i | ||||
\(127\) | −9.28822 | −0.824196 | −0.412098 | − | 0.911140i | \(-0.635204\pi\) | ||||
−0.412098 | + | 0.911140i | \(0.635204\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 5.72392 | + | 9.91412i | 0.503963 | + | 0.872890i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.48261 | + | 11.2282i | −0.566389 | + | 0.981014i | 0.430530 | + | 0.902576i | \(0.358326\pi\) |
−0.996919 | + | 0.0784377i | \(0.975007\pi\) | |||||||
\(132\) | 1.00000 | 0.0870388 | ||||||||
\(133\) | −17.1407 | + | 0.604433i | −1.48629 | + | 0.0524110i | ||||
\(134\) | −7.09382 | −0.612813 | ||||||||
\(135\) | −1.40280 | + | 2.42972i | −0.120734 | + | 0.209117i | ||||
\(136\) | −3.98261 | − | 6.89809i | −0.341506 | − | 0.591506i | ||||
\(137\) | −2.80560 | − | 4.85945i | −0.239699 | − | 0.415171i | 0.720929 | − | 0.693009i | \(-0.243715\pi\) |
−0.960628 | + | 0.277838i | \(0.910382\pi\) | |||||||
\(138\) | −2.64411 | + | 4.57973i | −0.225081 | + | 0.389852i | ||||
\(139\) | 13.1286 | 1.11355 | 0.556776 | − | 0.830662i | \(-0.312038\pi\) | ||||
0.556776 | + | 0.830662i | \(0.312038\pi\) | |||||||
\(140\) | 3.93570 | + | 6.29365i | 0.332628 | + | 0.531911i | ||||
\(141\) | −0.322990 | −0.0272007 | ||||||||
\(142\) | 3.72392 | − | 6.45002i | 0.312504 | − | 0.541273i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | 7.19440 | − | 12.4611i | 0.597462 | − | 1.03483i | ||||
\(146\) | 12.5764 | 1.04083 | ||||||||
\(147\) | −6.98261 | + | 0.493069i | −0.575916 | + | 0.0406676i | ||||
\(148\) | 10.4826 | 0.861665 | ||||||||
\(149\) | −8.36990 | + | 14.4971i | −0.685689 | + | 1.18765i | 0.287531 | + | 0.957771i | \(0.407166\pi\) |
−0.973220 | + | 0.229877i | \(0.926168\pi\) | |||||||
\(150\) | 1.43570 | + | 2.48671i | 0.117225 | + | 0.203039i | ||||
\(151\) | −5.44971 | − | 9.43918i | −0.443491 | − | 0.768149i | 0.554455 | − | 0.832214i | \(-0.312927\pi\) |
−0.997946 | + | 0.0640648i | \(0.979594\pi\) | |||||||
\(152\) | 3.24131 | − | 5.61411i | 0.262905 | − | 0.455364i | ||||
\(153\) | 7.96523 | 0.643950 | ||||||||
\(154\) | 1.40280 | + | 2.24325i | 0.113041 | + | 0.180766i | ||||
\(155\) | 25.1529 | 2.02033 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.887286 | − | 1.53682i | −0.0708132 | − | 0.122652i | 0.828445 | − | 0.560071i | \(-0.189226\pi\) |
−0.899258 | + | 0.437419i | \(0.855893\pi\) | |||||||
\(158\) | −3.40280 | − | 5.89382i | −0.270712 | − | 0.468888i | ||||
\(159\) | 4.00000 | − | 6.92820i | 0.317221 | − | 0.549442i | ||||
\(160\) | −2.80560 | −0.221802 | ||||||||
\(161\) | −13.9826 | + | 0.493069i | −1.10198 | + | 0.0388593i | ||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 2.02952 | − | 3.51524i | 0.158964 | − | 0.275335i | −0.775531 | − | 0.631309i | \(-0.782518\pi\) |
0.934496 | + | 0.355975i | \(0.115851\pi\) | |||||||
\(164\) | 2.54691 | + | 4.41138i | 0.198880 | + | 0.344471i | ||||
\(165\) | 1.40280 | + | 2.42972i | 0.109208 | + | 0.189154i | ||||
\(166\) | −7.54691 | + | 13.0716i | −0.585754 | + | 1.01456i | ||||
\(167\) | 13.8684 | 1.07317 | 0.536584 | − | 0.843847i | \(-0.319714\pi\) | ||||
0.536584 | + | 0.843847i | \(0.319714\pi\) | |||||||
\(168\) | 1.24131 | − | 2.33648i | 0.0957689 | − | 0.180264i | ||||
\(169\) | −13.0000 | −1.00000 | ||||||||
\(170\) | 11.1736 | − | 19.3533i | 0.856978 | − | 1.48433i | ||||
\(171\) | 3.24131 | + | 5.61411i | 0.247869 | + | 0.429322i | ||||
\(172\) | −5.72392 | − | 9.91412i | −0.436445 | − | 0.755945i | ||||
\(173\) | −8.48261 | + | 14.6923i | −0.644921 | + | 1.11704i | 0.339399 | + | 0.940643i | \(0.389776\pi\) |
−0.984320 | + | 0.176394i | \(0.943557\pi\) | |||||||
\(174\) | −5.12859 | −0.388798 | ||||||||
\(175\) | −3.56430 | + | 6.70900i | −0.269435 | + | 0.507153i | ||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | −0.435704 | + | 0.754661i | −0.0327495 | + | 0.0567238i | ||||
\(178\) | −0.805603 | − | 1.39535i | −0.0603825 | − | 0.104586i | ||||
\(179\) | 6.33513 | + | 10.9728i | 0.473509 | + | 0.820142i | 0.999540 | − | 0.0303231i | \(-0.00965363\pi\) |
−0.526031 | + | 0.850466i | \(0.676320\pi\) | |||||||
\(180\) | 1.40280 | − | 2.42972i | 0.104559 | − | 0.181101i | ||||
\(181\) | −2.57643 | −0.191505 | −0.0957523 | − | 0.995405i | \(-0.530526\pi\) | ||||
−0.0957523 | + | 0.995405i | \(0.530526\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.15962 | −0.159644 | ||||||||
\(184\) | 2.64411 | − | 4.57973i | 0.194926 | − | 0.337622i | ||||
\(185\) | 14.7050 | + | 25.4698i | 1.08113 | + | 1.87258i | ||||
\(186\) | −4.48261 | − | 7.76411i | −0.328681 | − | 0.569292i | ||||
\(187\) | 3.98261 | − | 6.89809i | 0.291238 | − | 0.504438i | ||||
\(188\) | 0.322990 | 0.0235565 | ||||||||
\(189\) | 1.40280 | + | 2.24325i | 0.102039 | + | 0.163172i | ||||
\(190\) | 18.1876 | 1.31947 | ||||||||
\(191\) | 1.19440 | − | 2.06876i | 0.0864235 | − | 0.149690i | −0.819573 | − | 0.572974i | \(-0.805790\pi\) |
0.905997 | + | 0.423284i | \(0.139123\pi\) | |||||||
\(192\) | 0.500000 | + | 0.866025i | 0.0360844 | + | 0.0625000i | ||||
\(193\) | 7.28822 | + | 12.6236i | 0.524617 | + | 0.908664i | 0.999589 | + | 0.0286628i | \(0.00912489\pi\) |
−0.474972 | + | 0.880001i | \(0.657542\pi\) | |||||||
\(194\) | −3.50000 | + | 6.06218i | −0.251285 | + | 0.435239i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.98261 | − | 0.493069i | 0.498758 | − | 0.0352192i | ||||
\(197\) | −12.4826 | −0.889349 | −0.444675 | − | 0.895692i | \(-0.646681\pi\) | ||||
−0.444675 | + | 0.895692i | \(0.646681\pi\) | |||||||
\(198\) | 0.500000 | − | 0.866025i | 0.0355335 | − | 0.0615457i | ||||
\(199\) | 7.09382 | + | 12.2869i | 0.502867 | + | 0.870992i | 0.999995 | + | 0.00331424i | \(0.00105496\pi\) |
−0.497127 | + | 0.867678i | \(0.665612\pi\) | |||||||
\(200\) | −1.43570 | − | 2.48671i | −0.101520 | − | 0.175837i | ||||
\(201\) | −3.54691 | + | 6.14343i | −0.250180 | + | 0.433324i | ||||
\(202\) | 10.7398 | 0.755650 | ||||||||
\(203\) | −7.19440 | − | 11.5047i | −0.504948 | − | 0.807471i | ||||
\(204\) | −7.96523 | −0.557677 | ||||||||
\(205\) | −7.14562 | + | 12.3766i | −0.499071 | + | 0.864417i | ||||
\(206\) | −1.48261 | − | 2.56796i | −0.103299 | − | 0.178918i | ||||
\(207\) | 2.64411 | + | 4.57973i | 0.183778 | + | 0.318313i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.48261 | 0.448412 | ||||||||
\(210\) | 7.41832 | − | 0.261592i | 0.511912 | − | 0.0180516i | ||||
\(211\) | −20.8336 | −1.43425 | −0.717123 | − | 0.696947i | \(-0.754541\pi\) | ||||
−0.717123 | + | 0.696947i | \(0.754541\pi\) | |||||||
\(212\) | −4.00000 | + | 6.92820i | −0.274721 | + | 0.475831i | ||||
\(213\) | −3.72392 | − | 6.45002i | −0.255159 | − | 0.441948i | ||||
\(214\) | −2.41832 | − | 4.18865i | −0.165313 | − | 0.286330i | ||||
\(215\) | 16.0590 | − | 27.8151i | 1.09522 | − | 1.89697i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 11.1286 | − | 20.9471i | 0.755458 | − | 1.42198i | ||||
\(218\) | −10.1596 | −0.688096 | ||||||||
\(219\) | 6.28822 | − | 10.8915i | 0.424918 | − | 0.735980i | ||||
\(220\) | −1.40280 | − | 2.42972i | −0.0945769 | − | 0.163812i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 5.24131 | − | 9.07821i | 0.351773 | − | 0.609289i | ||||
\(223\) | 12.5764 | 0.842180 | 0.421090 | − | 0.907019i | \(-0.361648\pi\) | ||||
0.421090 | + | 0.907019i | \(0.361648\pi\) | |||||||
\(224\) | −1.24131 | + | 2.33648i | −0.0829383 | + | 0.156113i | ||||
\(225\) | 2.87141 | 0.191427 | ||||||||
\(226\) | −5.48261 | + | 9.49616i | −0.364698 | + | 0.631675i | ||||
\(227\) | −10.0295 | − | 17.3716i | −0.665683 | − | 1.15300i | −0.979100 | − | 0.203381i | \(-0.934807\pi\) |
0.313417 | − | 0.949616i | \(-0.398526\pi\) | |||||||
\(228\) | −3.24131 | − | 5.61411i | −0.214661 | − | 0.371803i | ||||
\(229\) | 11.2882 | − | 19.5518i | 0.745946 | − | 1.29202i | −0.203805 | − | 0.979011i | \(-0.565331\pi\) |
0.949751 | − | 0.313005i | \(-0.101336\pi\) | |||||||
\(230\) | 14.8366 | 0.978299 | ||||||||
\(231\) | 2.64411 | − | 0.0932392i | 0.173970 | − | 0.00613469i | ||||
\(232\) | 5.12859 | 0.336709 | ||||||||
\(233\) | 0.371407 | − | 0.643296i | 0.0243317 | − | 0.0421437i | −0.853603 | − | 0.520924i | \(-0.825588\pi\) |
0.877935 | + | 0.478780i | \(0.158921\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.453091 | + | 0.784776i | 0.0295564 | + | 0.0511931i | ||||
\(236\) | 0.435704 | − | 0.754661i | 0.0283619 | − | 0.0491242i | ||||
\(237\) | −6.80560 | −0.442071 | ||||||||
\(238\) | −11.1736 | − | 17.8680i | −0.724279 | − | 1.15821i | ||||
\(239\) | 4.31925 | 0.279389 | 0.139694 | − | 0.990195i | \(-0.455388\pi\) | ||||
0.139694 | + | 0.990195i | \(0.455388\pi\) | |||||||
\(240\) | −1.40280 | + | 2.42972i | −0.0905504 | + | 0.156838i | ||||
\(241\) | 9.09382 | + | 15.7510i | 0.585784 | + | 1.01461i | 0.994777 | + | 0.102071i | \(0.0325468\pi\) |
−0.408993 | + | 0.912538i | \(0.634120\pi\) | |||||||
\(242\) | −0.500000 | − | 0.866025i | −0.0321412 | − | 0.0556702i | ||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 2.15962 | 0.138256 | ||||||||
\(245\) | 10.9932 | + | 16.2741i | 0.702332 | + | 1.03972i | ||||
\(246\) | 5.09382 | 0.324770 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 4.48261 | + | 7.76411i | 0.284646 | + | 0.493022i | ||||
\(249\) | 7.54691 | + | 13.0716i | 0.478266 | + | 0.828381i | ||||
\(250\) | −2.98599 | + | 5.17189i | −0.188851 | + | 0.327099i | ||||
\(251\) | 28.6703 | 1.80965 | 0.904825 | − | 0.425784i | \(-0.140001\pi\) | ||||
0.904825 | + | 0.425784i | \(0.140001\pi\) | |||||||
\(252\) | −1.40280 | − | 2.24325i | −0.0883682 | − | 0.141311i | ||||
\(253\) | 5.28822 | 0.332467 | ||||||||
\(254\) | 4.64411 | − | 8.04383i | 0.291397 | − | 0.504715i | ||||
\(255\) | −11.1736 | − | 19.3533i | −0.699720 | − | 1.21195i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 6.80560 | − | 11.7876i | 0.424522 | − | 0.735293i | −0.571854 | − | 0.820356i | \(-0.693776\pi\) |
0.996376 | + | 0.0850621i | \(0.0271089\pi\) | |||||||
\(258\) | −11.4478 | −0.712711 | ||||||||
\(259\) | 27.7172 | − | 0.977390i | 1.72226 | − | 0.0607321i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.56430 | + | 4.44149i | −0.158726 | + | 0.274921i | ||||
\(262\) | −6.48261 | − | 11.2282i | −0.400497 | − | 0.693681i | ||||
\(263\) | 1.80560 | + | 3.12740i | 0.111338 | + | 0.192843i | 0.916310 | − | 0.400470i | \(-0.131153\pi\) |
−0.804972 | + | 0.593313i | \(0.797820\pi\) | |||||||
\(264\) | −0.500000 | + | 0.866025i | −0.0307729 | + | 0.0533002i | ||||
\(265\) | −22.4448 | −1.37877 | ||||||||
\(266\) | 8.04691 | − | 15.1465i | 0.493388 | − | 0.928693i | ||||
\(267\) | −1.61121 | −0.0986042 | ||||||||
\(268\) | 3.54691 | − | 6.14343i | 0.216662 | − | 0.375270i | ||||
\(269\) | 4.69102 | + | 8.12508i | 0.286016 | + | 0.495395i | 0.972855 | − | 0.231415i | \(-0.0743355\pi\) |
−0.686839 | + | 0.726810i | \(0.741002\pi\) | |||||||
\(270\) | −1.40280 | − | 2.42972i | −0.0853718 | − | 0.147868i | ||||
\(271\) | −2.80560 | + | 4.85945i | −0.170428 | + | 0.295190i | −0.938570 | − | 0.345090i | \(-0.887848\pi\) |
0.768141 | + | 0.640280i | \(0.221182\pi\) | |||||||
\(272\) | 7.96523 | 0.482963 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.61121 | 0.338985 | ||||||||
\(275\) | 1.43570 | − | 2.48671i | 0.0865762 | − | 0.149954i | ||||
\(276\) | −2.64411 | − | 4.57973i | −0.159157 | − | 0.275667i | ||||
\(277\) | 8.00000 | + | 13.8564i | 0.480673 | + | 0.832551i | 0.999754 | − | 0.0221745i | \(-0.00705893\pi\) |
−0.519081 | + | 0.854725i | \(0.673726\pi\) | |||||||
\(278\) | −6.56430 | + | 11.3697i | −0.393700 | + | 0.681909i | ||||
\(279\) | −8.96523 | −0.536734 | ||||||||
\(280\) | −7.41832 | + | 0.261592i | −0.443329 | + | 0.0156331i | ||||
\(281\) | 24.1529 | 1.44084 | 0.720420 | − | 0.693539i | \(-0.243949\pi\) | ||||
0.720420 | + | 0.693539i | \(0.243949\pi\) | |||||||
\(282\) | 0.161495 | − | 0.279717i | 0.00961688 | − | 0.0166569i | ||||
\(283\) | −3.77083 | − | 6.53127i | −0.224152 | − | 0.388244i | 0.731912 | − | 0.681399i | \(-0.238628\pi\) |
−0.956065 | + | 0.293155i | \(0.905295\pi\) | |||||||
\(284\) | 3.72392 | + | 6.45002i | 0.220974 | + | 0.382738i | ||||
\(285\) | 9.09382 | − | 15.7510i | 0.538671 | − | 0.933006i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.14562 | + | 11.4267i | 0.421792 | + | 0.674496i | ||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −23.2224 | + | 40.2224i | −1.36602 | + | 2.36602i | ||||
\(290\) | 7.19440 | + | 12.4611i | 0.422470 | + | 0.731739i | ||||
\(291\) | 3.50000 | + | 6.06218i | 0.205174 | + | 0.355371i | ||||
\(292\) | −6.28822 | + | 10.8915i | −0.367990 | + | 0.637377i | ||||
\(293\) | 7.90618 | 0.461884 | 0.230942 | − | 0.972968i | \(-0.425819\pi\) | ||||
0.230942 | + | 0.972968i | \(0.425819\pi\) | |||||||
\(294\) | 3.06430 | − | 6.29365i | 0.178713 | − | 0.367053i | ||||
\(295\) | 2.44482 | 0.142343 | ||||||||
\(296\) | −5.24131 | + | 9.07821i | −0.304645 | + | 0.527660i | ||||
\(297\) | −0.500000 | − | 0.866025i | −0.0290129 | − | 0.0502519i | ||||
\(298\) | −8.36990 | − | 14.4971i | −0.484855 | − | 0.839794i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −2.87141 | −0.165781 | ||||||||
\(301\) | −16.0590 | − | 25.6803i | −0.925628 | − | 1.48019i | ||||
\(302\) | 10.8994 | 0.627191 | ||||||||
\(303\) | 5.36990 | − | 9.30094i | 0.308493 | − | 0.534325i | ||||
\(304\) | 3.24131 | + | 5.61411i | 0.185902 | + | 0.321991i | ||||
\(305\) | 3.02952 | + | 5.24729i | 0.173470 | + | 0.300459i | ||||
\(306\) | −3.98261 | + | 6.89809i | −0.227671 | + | 0.394337i | ||||
\(307\) | 12.8957 | 0.735995 | 0.367998 | − | 0.929827i | \(-0.380043\pi\) | ||||
0.367998 | + | 0.929827i | \(0.380043\pi\) | |||||||
\(308\) | −2.64411 | + | 0.0932392i | −0.150662 | + | 0.00531279i | ||||
\(309\) | −2.96523 | −0.168686 | ||||||||
\(310\) | −12.5764 | + | 21.7830i | −0.714293 | + | 1.23719i | ||||
\(311\) | −5.44971 | − | 9.43918i | −0.309025 | − | 0.535247i | 0.669125 | − | 0.743150i | \(-0.266669\pi\) |
−0.978149 | + | 0.207904i | \(0.933336\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.56430 | − | 7.90559i | 0.257989 | − | 0.446851i | −0.707714 | − | 0.706499i | \(-0.750273\pi\) |
0.965703 | + | 0.259649i | \(0.0836067\pi\) | |||||||
\(314\) | 1.77457 | 0.100145 | ||||||||
\(315\) | 3.48261 | − | 6.55525i | 0.196223 | − | 0.369346i | ||||
\(316\) | 6.80560 | 0.382845 | ||||||||
\(317\) | 4.75682 | − | 8.23906i | 0.267170 | − | 0.462752i | −0.700960 | − | 0.713201i | \(-0.747245\pi\) |
0.968130 | + | 0.250449i | \(0.0805782\pi\) | |||||||
\(318\) | 4.00000 | + | 6.92820i | 0.224309 | + | 0.388514i | ||||
\(319\) | 2.56430 | + | 4.44149i | 0.143573 | + | 0.248676i | ||||
\(320\) | 1.40280 | − | 2.42972i | 0.0784190 | − | 0.135826i | ||||
\(321\) | −4.83663 | −0.269955 | ||||||||
\(322\) | 6.56430 | − | 12.3558i | 0.365814 | − | 0.688564i | ||||
\(323\) | −51.6355 | −2.87307 | ||||||||
\(324\) | −0.500000 | + | 0.866025i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.02952 | + | 3.51524i | 0.112405 | + | 0.194691i | ||||
\(327\) | −5.07981 | + | 8.79849i | −0.280914 | + | 0.486558i | ||||
\(328\) | −5.09382 | −0.281259 | ||||||||
\(329\) | 0.854020 | − | 0.0301153i | 0.0470837 | − | 0.00166031i | ||||
\(330\) | −2.80560 | −0.154443 | ||||||||
\(331\) | −0.546909 | + | 0.947275i | −0.0300609 | + | 0.0520669i | −0.880664 | − | 0.473741i | \(-0.842903\pi\) |
0.850604 | + | 0.525807i | \(0.176237\pi\) | |||||||
\(332\) | −7.54691 | − | 13.0716i | −0.414190 | − | 0.717399i | ||||
\(333\) | −5.24131 | − | 9.07821i | −0.287222 | − | 0.497483i | ||||
\(334\) | −6.93420 | + | 12.0104i | −0.379422 | + | 0.657179i | ||||
\(335\) | 19.9024 | 1.08739 | ||||||||
\(336\) | 1.40280 | + | 2.24325i | 0.0765291 | + | 0.122379i | ||||
\(337\) | −25.7988 | −1.40535 | −0.702676 | − | 0.711510i | \(-0.748012\pi\) | ||||
−0.702676 | + | 0.711510i | \(0.748012\pi\) | |||||||
\(338\) | 6.50000 | − | 11.2583i | 0.353553 | − | 0.612372i | ||||
\(339\) | 5.48261 | + | 9.49616i | 0.297775 | + | 0.515761i | ||||
\(340\) | 11.1736 | + | 19.3533i | 0.605975 | + | 1.04958i | ||||
\(341\) | −4.48261 | + | 7.76411i | −0.242747 | + | 0.420450i | ||||
\(342\) | −6.48261 | −0.350540 | ||||||||
\(343\) | 18.4168 | − | 1.95478i | 0.994414 | − | 0.105548i | ||||
\(344\) | 11.4478 | 0.617226 | ||||||||
\(345\) | 7.41832 | − | 12.8489i | 0.399389 | − | 0.691762i | ||||
\(346\) | −8.48261 | − | 14.6923i | −0.456028 | − | 0.789864i | ||||
\(347\) | −10.3835 | − | 17.9848i | −0.557418 | − | 0.965476i | −0.997711 | − | 0.0676219i | \(-0.978459\pi\) |
0.440293 | − | 0.897854i | \(-0.354874\pi\) | |||||||
\(348\) | 2.56430 | − | 4.44149i | 0.137461 | − | 0.238089i | ||||
\(349\) | −9.51364 | −0.509254 | −0.254627 | − | 0.967039i | \(-0.581953\pi\) | ||||
−0.254627 | + | 0.967039i | \(0.581953\pi\) | |||||||
\(350\) | −4.02801 | − | 6.44127i | −0.215306 | − | 0.344300i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.500000 | − | 0.866025i | 0.0266501 | − | 0.0461593i | ||||
\(353\) | 6.28822 | + | 10.8915i | 0.334688 | + | 0.579697i | 0.983425 | − | 0.181316i | \(-0.0580358\pi\) |
−0.648737 | + | 0.761013i | \(0.724702\pi\) | |||||||
\(354\) | −0.435704 | − | 0.754661i | −0.0231574 | − | 0.0401098i | ||||
\(355\) | −10.4478 | + | 18.0962i | −0.554514 | + | 0.960446i | ||||
\(356\) | 1.61121 | 0.0853937 | ||||||||
\(357\) | −21.0609 | + | 0.742671i | −1.11466 | + | 0.0393063i | ||||
\(358\) | −12.6703 | −0.669644 | ||||||||
\(359\) | 0.0347742 | − | 0.0602306i | 0.00183531 | − | 0.00317885i | −0.865106 | − | 0.501589i | \(-0.832749\pi\) |
0.866942 | + | 0.498410i | \(0.166082\pi\) | |||||||
\(360\) | 1.40280 | + | 2.42972i | 0.0739341 | + | 0.128058i | ||||
\(361\) | −11.5121 | − | 19.9396i | −0.605902 | − | 1.04945i | ||||
\(362\) | 1.28822 | − | 2.23126i | 0.0677071 | − | 0.117272i | ||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −35.2845 | −1.84687 | ||||||||
\(366\) | 1.07981 | − | 1.87029i | 0.0564427 | − | 0.0977615i | ||||
\(367\) | 15.7708 | + | 27.3159i | 0.823231 | + | 1.42588i | 0.903264 | + | 0.429085i | \(0.141164\pi\) |
−0.0800336 | + | 0.996792i | \(0.525503\pi\) | |||||||
\(368\) | 2.64411 | + | 4.57973i | 0.137834 | + | 0.238735i | ||||
\(369\) | 2.54691 | − | 4.41138i | 0.132587 | − | 0.229647i | ||||
\(370\) | −29.4100 | −1.52896 | ||||||||
\(371\) | −9.93045 | + | 18.6919i | −0.515563 | + | 0.970434i | ||||
\(372\) | 8.96523 | 0.464825 | ||||||||
\(373\) | −7.65624 | + | 13.2610i | −0.396425 | + | 0.686629i | −0.993282 | − | 0.115719i | \(-0.963083\pi\) |
0.596857 | + | 0.802348i | \(0.296416\pi\) | |||||||
\(374\) | 3.98261 | + | 6.89809i | 0.205936 | + | 0.356692i | ||||
\(375\) | 2.98599 | + | 5.17189i | 0.154196 | + | 0.267075i | ||||
\(376\) | −0.161495 | + | 0.279717i | −0.00832847 | + | 0.0144253i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −2.64411 | + | 0.0932392i | −0.135998 | + | 0.00479570i | ||||
\(379\) | 16.0590 | 0.824898 | 0.412449 | − | 0.910981i | \(-0.364674\pi\) | ||||
0.412449 | + | 0.910981i | \(0.364674\pi\) | |||||||
\(380\) | −9.09382 | + | 15.7510i | −0.466503 | + | 0.808007i | ||||
\(381\) | −4.64411 | − | 8.04383i | −0.237925 | − | 0.412098i | ||||
\(382\) | 1.19440 | + | 2.06876i | 0.0611107 | + | 0.105847i | ||||
\(383\) | 0.369899 | − | 0.640684i | 0.0189010 | − | 0.0327374i | −0.856420 | − | 0.516279i | \(-0.827317\pi\) |
0.875321 | + | 0.483542i | \(0.160650\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −3.93570 | − | 6.29365i | −0.200582 | − | 0.320754i | ||||
\(386\) | −14.5764 | −0.741921 | ||||||||
\(387\) | −5.72392 | + | 9.91412i | −0.290963 | + | 0.503963i | ||||
\(388\) | −3.50000 | − | 6.06218i | −0.177686 | − | 0.307760i | ||||
\(389\) | −1.79160 | − | 3.10313i | −0.0908375 | − | 0.157335i | 0.817026 | − | 0.576600i | \(-0.195621\pi\) |
−0.907864 | + | 0.419265i | \(0.862288\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −42.1218 | −2.13019 | ||||||||
\(392\) | −3.06430 | + | 6.29365i | −0.154770 | + | 0.317878i | ||||
\(393\) | −12.9652 | −0.654009 | ||||||||
\(394\) | 6.24131 | − | 10.8103i | 0.314432 | − | 0.544613i | ||||
\(395\) | 9.54691 | + | 16.5357i | 0.480357 | + | 0.832003i | ||||
\(396\) | 0.500000 | + | 0.866025i | 0.0251259 | + | 0.0435194i | ||||
\(397\) | 12.5643 | − | 21.7620i | 0.630584 | − | 1.09220i | −0.356849 | − | 0.934162i | \(-0.616149\pi\) |
0.987433 | − | 0.158041i | \(-0.0505179\pi\) | |||||||
\(398\) | −14.1876 | −0.711162 | ||||||||
\(399\) | −9.09382 | − | 14.5421i | −0.455260 | − | 0.728015i | ||||
\(400\) | 2.87141 | 0.143570 | ||||||||
\(401\) | 1.93420 | − | 3.35013i | 0.0965891 | − | 0.167297i | −0.813682 | − | 0.581311i | \(-0.802540\pi\) |
0.910271 | + | 0.414014i | \(0.135873\pi\) | |||||||
\(402\) | −3.54691 | − | 6.14343i | −0.176904 | − | 0.306406i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −5.36990 | + | 9.30094i | −0.267162 | + | 0.462739i | ||||
\(405\) | −2.80560 | −0.139412 | ||||||||
\(406\) | 13.5606 | − | 0.478186i | 0.672999 | − | 0.0237320i | ||||
\(407\) | −10.4826 | −0.519604 | ||||||||
\(408\) | 3.98261 | − | 6.89809i | 0.197169 | − | 0.341506i | ||||
\(409\) | −2.32299 | − | 4.02354i | −0.114864 | − | 0.198951i | 0.802861 | − | 0.596166i | \(-0.203310\pi\) |
−0.917726 | + | 0.397215i | \(0.869977\pi\) | |||||||
\(410\) | −7.14562 | − | 12.3766i | −0.352897 | − | 0.611235i | ||||
\(411\) | 2.80560 | − | 4.85945i | 0.138390 | − | 0.239699i | ||||
\(412\) | 2.96523 | 0.146086 | ||||||||
\(413\) | 1.08168 | − | 2.03603i | 0.0532262 | − | 0.100186i | ||||
\(414\) | −5.28822 | −0.259902 | ||||||||
\(415\) | 21.1736 | − | 36.6738i | 1.03937 | − | 1.80025i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.56430 | + | 11.3697i | 0.321455 | + | 0.556776i | ||||
\(418\) | −3.24131 | + | 5.61411i | −0.158537 | + | 0.274595i | ||||
\(419\) | −19.5174 | −0.953487 | −0.476743 | − | 0.879043i | \(-0.658183\pi\) | ||||
−0.476743 | + | 0.879043i | \(0.658183\pi\) | |||||||
\(420\) | −3.48261 | + | 6.55525i | −0.169934 | + | 0.319863i | ||||
\(421\) | 15.5174 | 0.756271 | 0.378136 | − | 0.925750i | \(-0.376565\pi\) | ||||
0.378136 | + | 0.925750i | \(0.376565\pi\) | |||||||
\(422\) | 10.4168 | − | 18.0424i | 0.507082 | − | 0.878292i | ||||
\(423\) | −0.161495 | − | 0.279717i | −0.00785215 | − | 0.0136003i | ||||
\(424\) | −4.00000 | − | 6.92820i | −0.194257 | − | 0.336463i | ||||
\(425\) | −11.4357 | + | 19.8072i | −0.554713 | + | 0.960791i | ||||
\(426\) | 7.44784 | 0.360849 | ||||||||
\(427\) | 5.71028 | − | 0.201361i | 0.276340 | − | 0.00974456i | ||||
\(428\) | 4.83663 | 0.233787 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 16.0590 | + | 27.8151i | 0.774436 | + | 1.34136i | ||||
\(431\) | 7.19440 | + | 12.4611i | 0.346542 | + | 0.600228i | 0.985633 | − | 0.168903i | \(-0.0540225\pi\) |
−0.639091 | + | 0.769131i | \(0.720689\pi\) | |||||||
\(432\) | 0.500000 | − | 0.866025i | 0.0240563 | − | 0.0416667i | ||||
\(433\) | 2.03477 | 0.0977850 | 0.0488925 | − | 0.998804i | \(-0.484431\pi\) | ||||
0.0488925 | + | 0.998804i | \(0.484431\pi\) | |||||||
\(434\) | 12.5764 | + | 20.1112i | 0.603688 | + | 0.965368i | ||||
\(435\) | 14.3888 | 0.689890 | ||||||||
\(436\) | 5.07981 | − | 8.79849i | 0.243279 | − | 0.421371i | ||||
\(437\) | −17.1407 | − | 29.6886i | −0.819952 | − | 1.42020i | ||||
\(438\) | 6.28822 | + | 10.8915i | 0.300463 | + | 0.520416i | ||||
\(439\) | −1.61308 | + | 2.79393i | −0.0769880 | + | 0.133347i | −0.901949 | − | 0.431842i | \(-0.857864\pi\) |
0.824961 | + | 0.565190i | \(0.191197\pi\) | |||||||
\(440\) | 2.80560 | 0.133752 | ||||||||
\(441\) | −3.91832 | − | 5.80059i | −0.186587 | − | 0.276218i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.0469 | − | 19.1338i | 0.524854 | − | 0.909075i | −0.474727 | − | 0.880133i | \(-0.657453\pi\) |
0.999581 | − | 0.0289413i | \(-0.00921360\pi\) | |||||||
\(444\) | 5.24131 | + | 9.07821i | 0.248741 | + | 0.430833i | ||||
\(445\) | 2.26020 | + | 3.91478i | 0.107144 | + | 0.185579i | ||||
\(446\) | −6.28822 | + | 10.8915i | −0.297756 | + | 0.515728i | ||||
\(447\) | −16.7398 | −0.791765 | ||||||||
\(448\) | −1.40280 | − | 2.24325i | −0.0662761 | − | 0.105983i | ||||
\(449\) | 22.2497 | 1.05003 | 0.525014 | − | 0.851094i | \(-0.324060\pi\) | ||||
0.525014 | + | 0.851094i | \(0.324060\pi\) | |||||||
\(450\) | −1.43570 | + | 2.48671i | −0.0676797 | + | 0.117225i | ||||
\(451\) | −2.54691 | − | 4.41138i | −0.119929 | − | 0.207724i | ||||
\(452\) | −5.48261 | − | 9.49616i | −0.257880 | − | 0.446662i | ||||
\(453\) | 5.44971 | − | 9.43918i | 0.256050 | − | 0.443491i | ||||
\(454\) | 20.0590 | 0.941418 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.48261 | 0.303576 | ||||||||
\(457\) | 9.31925 | − | 16.1414i | 0.435936 | − | 0.755063i | −0.561436 | − | 0.827520i | \(-0.689751\pi\) |
0.997372 | + | 0.0724572i | \(0.0230841\pi\) | |||||||
\(458\) | 11.2882 | + | 19.5518i | 0.527464 | + | 0.913594i | ||||
\(459\) | 3.98261 | + | 6.89809i | 0.185892 | + | 0.321975i | ||||
\(460\) | −7.41832 | + | 12.8489i | −0.345881 | + | 0.599083i | ||||
\(461\) | −20.9895 | −0.977578 | −0.488789 | − | 0.872402i | \(-0.662561\pi\) | ||||
−0.488789 | + | 0.872402i | \(0.662561\pi\) | |||||||
\(462\) | −1.24131 | + | 2.33648i | −0.0577508 | + | 0.108703i | ||||
\(463\) | −5.35402 | −0.248822 | −0.124411 | − | 0.992231i | \(-0.539704\pi\) | ||||
−0.124411 | + | 0.992231i | \(0.539704\pi\) | |||||||
\(464\) | −2.56430 | + | 4.44149i | −0.119044 | + | 0.206191i | ||||
\(465\) | 12.5764 | + | 21.7830i | 0.583218 | + | 1.01016i | ||||
\(466\) | 0.371407 | + | 0.643296i | 0.0172051 | + | 0.0298001i | ||||
\(467\) | −13.0121 | + | 22.5377i | −0.602130 | + | 1.04292i | 0.390368 | + | 0.920659i | \(0.372348\pi\) |
−0.992498 | + | 0.122261i | \(0.960986\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.80560 | − | 16.5746i | 0.406605 | − | 0.765344i | ||||
\(470\) | −0.906181 | −0.0417990 | ||||||||
\(471\) | 0.887286 | − | 1.53682i | 0.0408840 | − | 0.0708132i | ||||
\(472\) | 0.435704 | + | 0.754661i | 0.0200549 | + | 0.0347361i | ||||
\(473\) | 5.72392 | + | 9.91412i | 0.263186 | + | 0.455852i | ||||
\(474\) | 3.40280 | − | 5.89382i | 0.156296 | − | 0.270712i | ||||
\(475\) | −18.6142 | −0.854079 | ||||||||
\(476\) | 21.0609 | − | 0.742671i | 0.965326 | − | 0.0340403i | ||||
\(477\) | 8.00000 | 0.366295 | ||||||||
\(478\) | −2.15962 | + | 3.74058i | −0.0987789 | + | 0.171090i | ||||
\(479\) | 1.80560 | + | 3.12740i | 0.0825001 | + | 0.142894i | 0.904323 | − | 0.426848i | \(-0.140376\pi\) |
−0.821823 | + | 0.569743i | \(0.807043\pi\) | |||||||
\(480\) | −1.40280 | − | 2.42972i | −0.0640288 | − | 0.110901i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −18.1876 | −0.828424 | ||||||||
\(483\) | −7.41832 | − | 11.8628i | −0.337545 | − | 0.539774i | ||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 9.81961 | − | 17.0081i | 0.445886 | − | 0.772296i | ||||
\(486\) | 0.500000 | + | 0.866025i | 0.0226805 | + | 0.0392837i | ||||
\(487\) | 4.03103 | + | 6.98195i | 0.182663 | + | 0.316382i | 0.942787 | − | 0.333397i | \(-0.108195\pi\) |
−0.760123 | + | 0.649779i | \(0.774861\pi\) | |||||||
\(488\) | −1.07981 | + | 1.87029i | −0.0488808 | + | 0.0846640i | ||||
\(489\) | 4.05904 | 0.183556 | ||||||||
\(490\) | −19.5904 | + | 1.38336i | −0.885006 | + | 0.0624936i | ||||
\(491\) | 20.9062 | 0.943483 | 0.471741 | − | 0.881737i | \(-0.343626\pi\) | ||||
0.471741 | + | 0.881737i | \(0.343626\pi\) | |||||||
\(492\) | −2.54691 | + | 4.41138i | −0.114824 | + | 0.198880i | ||||
\(493\) | −20.4252 | − | 35.3775i | −0.919905 | − | 1.59332i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.40280 | + | 2.42972i | −0.0630512 | + | 0.109208i | ||||
\(496\) | −8.96523 | −0.402551 | ||||||||
\(497\) | 10.4478 | + | 16.7073i | 0.468650 | + | 0.749426i | ||||
\(498\) | −15.0938 | −0.676370 | ||||||||
\(499\) | −2.48261 | + | 4.30001i | −0.111137 | + | 0.192495i | −0.916229 | − | 0.400655i | \(-0.868783\pi\) |
0.805092 | + | 0.593150i | \(0.202116\pi\) | |||||||
\(500\) | −2.98599 | − | 5.17189i | −0.133538 | − | 0.231294i | ||||
\(501\) | 6.93420 | + | 12.0104i | 0.309797 | + | 0.536584i | ||||
\(502\) | −14.3351 | + | 24.8292i | −0.639808 | + | 1.10818i | ||||
\(503\) | −17.7988 | −0.793611 | −0.396806 | − | 0.917903i | \(-0.629881\pi\) | ||||
−0.396806 | + | 0.917903i | \(0.629881\pi\) | |||||||
\(504\) | 2.64411 | − | 0.0932392i | 0.117778 | − | 0.00415320i | ||||
\(505\) | −30.1316 | −1.34084 | ||||||||
\(506\) | −2.64411 | + | 4.57973i | −0.117545 | + | 0.203594i | ||||
\(507\) | −6.50000 | − | 11.2583i | −0.288675 | − | 0.500000i | ||||
\(508\) | 4.64411 | + | 8.04383i | 0.206049 | + | 0.356887i | ||||
\(509\) | −2.25719 | + | 3.90956i | −0.100048 | + | 0.173288i | −0.911704 | − | 0.410847i | \(-0.865233\pi\) |
0.811656 | + | 0.584135i | \(0.198566\pi\) | |||||||
\(510\) | 22.3473 | 0.989553 | ||||||||
\(511\) | −15.6112 | + | 29.3846i | −0.690599 | + | 1.29990i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −3.24131 | + | 5.61411i | −0.143107 | + | 0.247869i | ||||
\(514\) | 6.80560 | + | 11.7876i | 0.300182 | + | 0.519931i | ||||
\(515\) | 4.15962 | + | 7.20468i | 0.183295 | + | 0.317476i | ||||
\(516\) | 5.72392 | − | 9.91412i | 0.251982 | − | 0.436445i | ||||
\(517\) | −0.322990 | −0.0142051 | ||||||||
\(518\) | −13.0121 | + | 24.4925i | −0.571720 | + | 1.07614i | ||||
\(519\) | −16.9652 | −0.744691 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.00000 | + | 15.5885i | 0.394297 | + | 0.682943i | 0.993011 | − | 0.118020i | \(-0.0376547\pi\) |
−0.598714 | + | 0.800963i | \(0.704321\pi\) | |||||||
\(522\) | −2.56430 | − | 4.44149i | −0.112236 | − | 0.194399i | ||||
\(523\) | −3.45158 | + | 5.97832i | −0.150927 | + | 0.261414i | −0.931569 | − | 0.363566i | \(-0.881559\pi\) |
0.780641 | + | 0.624979i | \(0.214893\pi\) | |||||||
\(524\) | 12.9652 | 0.566389 | ||||||||
\(525\) | −7.59231 | + | 0.267728i | −0.331356 | + | 0.0116846i | ||||
\(526\) | −3.61121 | −0.157456 | ||||||||
\(527\) | 35.7050 | − | 61.8429i | 1.55534 | − | 2.69392i | ||||
\(528\) | −0.500000 | − | 0.866025i | −0.0217597 | − | 0.0376889i | ||||
\(529\) | −2.48261 | − | 4.30001i | −0.107940 | − | 0.186957i | ||||
\(530\) | 11.2224 | − | 19.4378i | 0.487470 | − | 0.844323i | ||||
\(531\) | −0.871407 | −0.0378159 | ||||||||
\(532\) | 9.09382 | + | 14.5421i | 0.394267 | + | 0.630480i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0.805603 | − | 1.39535i | 0.0348618 | − | 0.0603825i | ||||
\(535\) | 6.78484 | + | 11.7517i | 0.293334 | + | 0.508069i | ||||
\(536\) | 3.54691 | + | 6.14343i | 0.153203 | + | 0.265356i | ||||
\(537\) | −6.33513 | + | 10.9728i | −0.273381 | + | 0.473509i | ||||
\(538\) | −9.38203 | −0.404488 | ||||||||
\(539\) | −6.98261 | + | 0.493069i | −0.300762 | + | 0.0212380i | ||||
\(540\) | 2.80560 | 0.120734 | ||||||||
\(541\) | −1.40280 | + | 2.42972i | −0.0603111 | + | 0.104462i | −0.894604 | − | 0.446859i | \(-0.852543\pi\) |
0.834293 | + | 0.551321i | \(0.185876\pi\) | |||||||
\(542\) | −2.80560 | − | 4.85945i | −0.120511 | − | 0.208731i | ||||
\(543\) | −1.28822 | − | 2.23126i | −0.0552826 | − | 0.0957523i | ||||
\(544\) | −3.98261 | + | 6.89809i | −0.170753 | + | 0.295753i | ||||
\(545\) | 28.5039 | 1.22097 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.9274 | 1.40788 | 0.703938 | − | 0.710262i | \(-0.251423\pi\) | ||||
0.703938 | + | 0.710262i | \(0.251423\pi\) | |||||||
\(548\) | −2.80560 | + | 4.85945i | −0.119849 | + | 0.207585i | ||||
\(549\) | −1.07981 | − | 1.87029i | −0.0460852 | − | 0.0798220i | ||||
\(550\) | 1.43570 | + | 2.48671i | 0.0612186 | + | 0.106034i | ||||
\(551\) | 16.6233 | − | 28.7925i | 0.708178 | − | 1.22660i | ||||
\(552\) | 5.28822 | 0.225081 | ||||||||
\(553\) | 17.9947 | − | 0.634549i | 0.765215 | − | 0.0269838i | ||||
\(554\) | −16.0000 | −0.679775 | ||||||||
\(555\) | −14.7050 | + | 25.4698i | −0.624194 | + | 1.08113i | ||||
\(556\) | −6.56430 | − | 11.3697i | −0.278388 | − | 0.482182i | ||||
\(557\) | −11.8525 | − | 20.5292i | −0.502207 | − | 0.869848i | −0.999997 | − | 0.00255037i | \(-0.999188\pi\) |
0.497790 | − | 0.867298i | \(-0.334145\pi\) | |||||||
\(558\) | 4.48261 | − | 7.76411i | 0.189764 | − | 0.328681i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 3.48261 | − | 6.55525i | 0.147167 | − | 0.277010i | ||||
\(561\) | 7.96523 | 0.336292 | ||||||||
\(562\) | −12.0764 | + | 20.9170i | −0.509414 | + | 0.882330i | ||||
\(563\) | −15.2224 | − | 26.3660i | −0.641548 | − | 1.11119i | −0.985087 | − | 0.172056i | \(-0.944959\pi\) |
0.343539 | − | 0.939138i | \(-0.388374\pi\) | |||||||
\(564\) | 0.161495 | + | 0.279717i | 0.00680016 | + | 0.0117782i | ||||
\(565\) | 15.3820 | − | 26.6425i | 0.647127 | − | 1.12086i | ||||
\(566\) | 7.54166 | 0.317000 | ||||||||
\(567\) | −1.24131 | + | 2.33648i | −0.0521300 | + | 0.0981231i | ||||
\(568\) | −7.44784 | −0.312504 | ||||||||
\(569\) | −11.1407 | + | 19.2963i | −0.467044 | + | 0.808943i | −0.999291 | − | 0.0376455i | \(-0.988014\pi\) |
0.532248 | + | 0.846589i | \(0.321348\pi\) | |||||||
\(570\) | 9.09382 | + | 15.7510i | 0.380898 | + | 0.659735i | ||||
\(571\) | 1.43570 | + | 2.48671i | 0.0600823 | + | 0.104066i | 0.894502 | − | 0.447064i | \(-0.147530\pi\) |
−0.834420 | + | 0.551130i | \(0.814197\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.38879 | 0.0997933 | ||||||||
\(574\) | −13.4686 | + | 0.474943i | −0.562169 | + | 0.0198238i | ||||
\(575\) | −15.1846 | −0.633242 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 7.51214 | + | 13.0114i | 0.312734 | + | 0.541672i | 0.978953 | − | 0.204084i | \(-0.0654217\pi\) |
−0.666219 | + | 0.745756i | \(0.732088\pi\) | |||||||
\(578\) | −23.2224 | − | 40.2224i | −0.965925 | − | 1.67303i | ||||
\(579\) | −7.28822 | + | 12.6236i | −0.302888 | + | 0.524617i | ||||
\(580\) | −14.3888 | −0.597462 | ||||||||
\(581\) | −21.1736 | − | 33.8591i | −0.878430 | − | 1.40471i | ||||
\(582\) | −7.00000 | −0.290159 | ||||||||
\(583\) | 4.00000 | − | 6.92820i | 0.165663 | − | 0.286937i | ||||
\(584\) | −6.28822 | − | 10.8915i | −0.260208 | − | 0.450694i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.95309 | + | 6.84695i | −0.163301 | + | 0.282845i | ||||
\(587\) | −42.5069 | −1.75445 | −0.877223 | − | 0.480082i | \(-0.840607\pi\) | ||||
−0.877223 | + | 0.480082i | \(0.840607\pi\) | |||||||
\(588\) | 3.91832 | + | 5.80059i | 0.161589 | + | 0.239212i | ||||
\(589\) | 58.1181 | 2.39471 | ||||||||
\(590\) | −1.22241 | + | 2.11728i | −0.0503259 | + | 0.0871670i | ||||
\(591\) | −6.24131 | − | 10.8103i | −0.256733 | − | 0.444675i | ||||
\(592\) | −5.24131 | − | 9.07821i | −0.215416 | − | 0.373112i | ||||
\(593\) | −7.69289 | + | 13.3245i | −0.315909 | + | 0.547171i | −0.979630 | − | 0.200809i | \(-0.935643\pi\) |
0.663721 | + | 0.747980i | \(0.268976\pi\) | |||||||
\(594\) | 1.00000 | 0.0410305 | ||||||||
\(595\) | 31.3488 | + | 50.1304i | 1.28517 | + | 2.05515i | ||||
\(596\) | 16.7398 | 0.685689 | ||||||||
\(597\) | −7.09382 | + | 12.2869i | −0.290331 | + | 0.502867i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19.8196 | + | 34.3286i | 0.809807 | + | 1.40263i | 0.912997 | + | 0.407966i | \(0.133762\pi\) |
−0.103190 | + | 0.994662i | \(0.532905\pi\) | |||||||
\(600\) | 1.43570 | − | 2.48671i | 0.0586124 | − | 0.101520i | ||||
\(601\) | 33.3405 | 1.35999 | 0.679994 | − | 0.733218i | \(-0.261983\pi\) | ||||
0.679994 | + | 0.733218i | \(0.261983\pi\) | |||||||
\(602\) | 30.2693 | − | 1.06739i | 1.23369 | − | 0.0435034i | ||||
\(603\) | −7.09382 | −0.288883 | ||||||||
\(604\) | −5.44971 | + | 9.43918i | −0.221746 | + | 0.384075i | ||||
\(605\) | 1.40280 | + | 2.42972i | 0.0570320 | + | 0.0987823i | ||||
\(606\) | 5.36990 | + | 9.30094i | 0.218137 | + | 0.377825i | ||||
\(607\) | −7.97923 | + | 13.8204i | −0.323867 | + | 0.560954i | −0.981282 | − | 0.192574i | \(-0.938316\pi\) |
0.657415 | + | 0.753528i | \(0.271650\pi\) | |||||||
\(608\) | −6.48261 | −0.262905 | ||||||||
\(609\) | 6.36616 | − | 11.9829i | 0.257970 | − | 0.485571i | ||||
\(610\) | −6.05904 | −0.245324 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −3.98261 | − | 6.89809i | −0.160988 | − | 0.278839i | ||||
\(613\) | −23.3333 | − | 40.4144i | −0.942421 | − | 1.63232i | −0.760834 | − | 0.648947i | \(-0.775210\pi\) |
−0.181587 | − | 0.983375i | \(-0.558123\pi\) | |||||||
\(614\) | −6.44784 | + | 11.1680i | −0.260214 | + | 0.450703i | ||||
\(615\) | −14.2912 | −0.576278 | ||||||||
\(616\) | 1.24131 | − | 2.33648i | 0.0500137 | − | 0.0941396i | ||||
\(617\) | −9.28447 | −0.373779 | −0.186889 | − | 0.982381i | \(-0.559841\pi\) | ||||
−0.186889 | + | 0.982381i | \(0.559841\pi\) | |||||||
\(618\) | 1.48261 | − | 2.56796i | 0.0596394 | − | 0.103299i | ||||
\(619\) | −16.9947 | − | 29.4358i | −0.683077 | − | 1.18312i | −0.974037 | − | 0.226388i | \(-0.927308\pi\) |
0.290961 | − | 0.956735i | \(-0.406025\pi\) | |||||||
\(620\) | −12.5764 | − | 21.7830i | −0.505082 | − | 0.874827i | ||||
\(621\) | −2.64411 | + | 4.57973i | −0.106104 | + | 0.183778i | ||||
\(622\) | 10.8994 | 0.437027 | ||||||||
\(623\) | 4.26020 | − | 0.150227i | 0.170681 | − | 0.00601874i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.5560 | − | 26.9438i | 0.622241 | − | 1.07775i | ||||
\(626\) | 4.56430 | + | 7.90559i | 0.182426 | + | 0.315971i | ||||
\(627\) | 3.24131 | + | 5.61411i | 0.129445 | + | 0.224206i | ||||
\(628\) | −0.887286 | + | 1.53682i | −0.0354066 | + | 0.0613260i | ||||
\(629\) | 83.4964 | 3.32922 | ||||||||
\(630\) | 3.93570 | + | 6.29365i | 0.156802 | + | 0.250745i | ||||
\(631\) | −14.6460 | −0.583047 | −0.291524 | − | 0.956564i | \(-0.594162\pi\) | ||||
−0.291524 | + | 0.956564i | \(0.594162\pi\) | |||||||
\(632\) | −3.40280 | + | 5.89382i | −0.135356 | + | 0.234444i | ||||
\(633\) | −10.4168 | − | 18.0424i | −0.414031 | − | 0.717123i | ||||
\(634\) | 4.75682 | + | 8.23906i | 0.188918 | + | 0.327215i | ||||
\(635\) | −13.0295 | + | 22.5678i | −0.517061 | + | 0.895576i | ||||
\(636\) | −8.00000 | −0.317221 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5.12859 | −0.203043 | ||||||||
\(639\) | 3.72392 | − | 6.45002i | 0.147316 | − | 0.255159i | ||||
\(640\) | 1.40280 | + | 2.42972i | 0.0554506 | + | 0.0960432i | ||||
\(641\) | −10.4826 | − | 18.1564i | −0.414038 | − | 0.717135i | 0.581289 | − | 0.813697i | \(-0.302549\pi\) |
−0.995327 | + | 0.0965620i | \(0.969215\pi\) | |||||||
\(642\) | 2.41832 | − | 4.18865i | 0.0954433 | − | 0.165313i | ||||
\(643\) | −23.6733 | −0.933582 | −0.466791 | − | 0.884368i | \(-0.654590\pi\) | ||||
−0.466791 | + | 0.884368i | \(0.654590\pi\) | |||||||
\(644\) | 7.41832 | + | 11.8628i | 0.292323 | + | 0.467458i | ||||
\(645\) | 32.1181 | 1.26465 | ||||||||
\(646\) | 25.8177 | − | 44.7176i | 1.01579 | − | 1.75939i | ||||
\(647\) | 6.20840 | + | 10.7533i | 0.244078 | + | 0.422755i | 0.961872 | − | 0.273500i | \(-0.0881815\pi\) |
−0.717794 | + | 0.696255i | \(0.754848\pi\) | |||||||
\(648\) | −0.500000 | − | 0.866025i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | −0.435704 | + | 0.754661i | −0.0171029 | + | 0.0296230i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 23.7050 | − | 0.835910i | 0.929073 | − | 0.0327619i | ||||
\(652\) | −4.05904 | −0.158964 | ||||||||
\(653\) | 0.0487812 | − | 0.0844916i | 0.00190896 | − | 0.00330641i | −0.865069 | − | 0.501652i | \(-0.832726\pi\) |
0.866978 | + | 0.498346i | \(0.166059\pi\) | |||||||
\(654\) | −5.07981 | − | 8.79849i | −0.198636 | − | 0.344048i | ||||
\(655\) | 18.1876 | + | 31.5019i | 0.710650 | + | 1.23088i | ||||
\(656\) | 2.54691 | − | 4.41138i | 0.0994401 | − | 0.172235i | ||||
\(657\) | 12.5764 | 0.490653 | ||||||||
\(658\) | −0.400929 | + | 0.754661i | −0.0156299 | + | 0.0294197i | ||||
\(659\) | −35.0243 | −1.36435 | −0.682176 | − | 0.731188i | \(-0.738966\pi\) | ||||
−0.682176 | + | 0.731188i | \(0.738966\pi\) | |||||||
\(660\) | 1.40280 | − | 2.42972i | 0.0546040 | − | 0.0945769i | ||||
\(661\) | −14.8177 | − | 25.6651i | −0.576343 | − | 0.998256i | −0.995894 | − | 0.0905240i | \(-0.971146\pi\) |
0.419551 | − | 0.907732i | \(-0.362188\pi\) | |||||||
\(662\) | −0.546909 | − | 0.947275i | −0.0212562 | − | 0.0368169i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 15.0938 | 0.585754 | ||||||||
\(665\) | −22.5764 | + | 42.4951i | −0.875476 | + | 1.64789i | ||||
\(666\) | 10.4826 | 0.406193 | ||||||||
\(667\) | 13.5606 | − | 23.4876i | 0.525067 | − | 0.909442i | ||||
\(668\) | −6.93420 | − | 12.0104i | −0.268292 | − | 0.464696i | ||||
\(669\) | 6.28822 | + | 10.8915i | 0.243116 | + | 0.421090i | ||||
\(670\) | −9.95122 | + | 17.2360i | −0.384449 | + | 0.665885i | ||||
\(671\) | −2.15962 | −0.0833713 | ||||||||
\(672\) | −2.64411 | + | 0.0932392i | −0.101999 | + | 0.00359678i | ||||
\(673\) | 16.8957 | 0.651281 | 0.325640 | − | 0.945494i | \(-0.394420\pi\) | ||||
0.325640 | + | 0.945494i | \(0.394420\pi\) | |||||||
\(674\) | 12.8994 | − | 22.3425i | 0.496867 | − | 0.860599i | ||||
\(675\) | 1.43570 | + | 2.48671i | 0.0552603 | + | 0.0957136i | ||||
\(676\) | 6.50000 | + | 11.2583i | 0.250000 | + | 0.433013i | ||||
\(677\) | −6.59533 | + | 11.4234i | −0.253479 | + | 0.439038i | −0.964481 | − | 0.264151i | \(-0.914908\pi\) |
0.711002 | + | 0.703190i | \(0.248242\pi\) | |||||||
\(678\) | −10.9652 | −0.421117 | ||||||||
\(679\) | −9.81961 | − | 15.7027i | −0.376842 | − | 0.602615i | ||||
\(680\) | −22.3473 | −0.856978 | ||||||||
\(681\) | 10.0295 | − | 17.3716i | 0.384332 | − | 0.665683i | ||||
\(682\) | −4.48261 | − | 7.76411i | −0.171648 | − | 0.297303i | ||||
\(683\) | −4.91832 | − | 8.51877i | −0.188194 | − | 0.325962i | 0.756454 | − | 0.654047i | \(-0.226930\pi\) |
−0.944648 | + | 0.328085i | \(0.893597\pi\) | |||||||
\(684\) | 3.24131 | − | 5.61411i | 0.123934 | − | 0.214661i | ||||
\(685\) | −15.7428 | −0.601502 | ||||||||
\(686\) | −7.51552 | + | 16.9268i | −0.286944 | + | 0.646269i | ||||
\(687\) | 22.5764 | 0.861345 | ||||||||
\(688\) | −5.72392 | + | 9.91412i | −0.218222 | + | 0.377972i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 7.41832 | + | 12.8489i | 0.282410 | + | 0.489149i | ||||
\(691\) | 24.9947 | − | 43.2922i | 0.950845 | − | 1.64691i | 0.207243 | − | 0.978290i | \(-0.433551\pi\) |
0.743602 | − | 0.668622i | \(-0.233116\pi\) | |||||||
\(692\) | 16.9652 | 0.644921 | ||||||||
\(693\) | 1.40280 | + | 2.24325i | 0.0532880 | + | 0.0852138i | ||||
\(694\) | 20.7671 | 0.788308 | ||||||||
\(695\) | 18.4168 | − | 31.8988i | 0.698589 | − | 1.20999i | ||||
\(696\) | 2.56430 | + | 4.44149i | 0.0971994 | + | 0.168354i | ||||
\(697\) | 20.2867 | + | 35.1376i | 0.768414 | + | 1.33093i | ||||
\(698\) | 4.75682 | − | 8.23906i | 0.180048 | − | 0.311853i | ||||
\(699\) | 0.742815 | 0.0280958 | ||||||||
\(700\) | 7.59231 | − | 0.267728i | 0.286962 | − | 0.0101192i | ||||
\(701\) | −17.7050 | −0.668710 | −0.334355 | − | 0.942447i | \(-0.608518\pi\) | ||||
−0.334355 | + | 0.942447i | \(0.608518\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 33.9774 | + | 58.8505i | 1.28148 | + | 2.21959i | ||||
\(704\) | 0.500000 | + | 0.866025i | 0.0188445 | + | 0.0326396i | ||||
\(705\) | −0.453091 | + | 0.784776i | −0.0170644 | + | 0.0295564i | ||||
\(706\) | −12.5764 | −0.473320 | ||||||||
\(707\) | −13.3314 | + | 25.0934i | −0.501378 | + | 0.943733i | ||||
\(708\) | 0.871407 | 0.0327495 | ||||||||
\(709\) | 15.9774 | − | 27.6736i | 0.600042 | − | 1.03930i | −0.392772 | − | 0.919636i | \(-0.628484\pi\) |
0.992814 | − | 0.119668i | \(-0.0381830\pi\) | |||||||
\(710\) | −10.4478 | − | 18.0962i | −0.392100 | − | 0.679138i | ||||
\(711\) | −3.40280 | − | 5.89382i | −0.127615 | − | 0.221036i | ||||
\(712\) | −0.805603 | + | 1.39535i | −0.0301912 | + | 0.0522928i | ||||
\(713\) | 47.4100 | 1.77552 | ||||||||
\(714\) | 9.88729 | − | 18.6106i | 0.370022 | − | 0.696485i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 6.33513 | − | 10.9728i | 0.236755 | − | 0.410071i | ||||
\(717\) | 2.15962 | + | 3.74058i | 0.0806526 | + | 0.139694i | ||||
\(718\) | 0.0347742 | + | 0.0602306i | 0.00129776 | + | 0.00224779i | ||||
\(719\) | −10.8975 | + | 18.8751i | −0.406410 | + | 0.703923i | −0.994484 | − | 0.104884i | \(-0.966553\pi\) |
0.588074 | + | 0.808807i | \(0.299886\pi\) | |||||||
\(720\) | −2.80560 | −0.104559 | ||||||||
\(721\) | 7.84038 | − | 0.276475i | 0.291991 | − | 0.0102965i | ||||
\(722\) | 23.0243 | 0.856875 | ||||||||
\(723\) | −9.09382 | + | 15.7510i | −0.338203 | + | 0.585784i | ||||
\(724\) | 1.28822 | + | 2.23126i | 0.0478762 | + | 0.0829239i | ||||
\(725\) | −7.36314 | − | 12.7533i | −0.273460 | − | 0.473647i | ||||
\(726\) | 0.500000 | − | 0.866025i | 0.0185567 | − | 0.0321412i | ||||
\(727\) | −4.84714 | −0.179770 | −0.0898852 | − | 0.995952i | \(-0.528650\pi\) | ||||
−0.0898852 | + | 0.995952i | \(0.528650\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 17.6422 | − | 30.5572i | 0.652968 | − | 1.13097i | ||||
\(731\) | −45.5923 | − | 78.9682i | −1.68629 | − | 2.92074i | ||||
\(732\) | 1.07981 | + | 1.87029i | 0.0399110 | + | 0.0691278i | ||||
\(733\) | −6.11459 | + | 10.5908i | −0.225847 | + | 0.391179i | −0.956573 | − | 0.291492i | \(-0.905848\pi\) |
0.730726 | + | 0.682671i | \(0.239182\pi\) | |||||||
\(734\) | −31.5417 | −1.16422 | ||||||||
\(735\) | −8.59720 | + | 17.6575i | −0.317112 | + | 0.651307i | ||||
\(736\) | −5.28822 | −0.194926 | ||||||||
\(737\) | −3.54691 | + | 6.14343i | −0.130652 | + | 0.226296i | ||||
\(738\) | 2.54691 | + | 4.41138i | 0.0937530 | + | 0.162385i | ||||
\(739\) | 0.517387 | + | 0.896141i | 0.0190324 | + | 0.0329651i | 0.875385 | − | 0.483427i | \(-0.160608\pi\) |
−0.856352 | + | 0.516392i | \(0.827275\pi\) | |||||||
\(740\) | 14.7050 | − | 25.4698i | 0.540567 | − | 0.936290i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −11.2224 | − | 17.9460i | −0.411988 | − | 0.658817i | ||||
\(743\) | −23.9925 | −0.880200 | −0.440100 | − | 0.897949i | \(-0.645057\pi\) | ||||
−0.440100 | + | 0.897949i | \(0.645057\pi\) | |||||||
\(744\) | −4.48261 | + | 7.76411i | −0.164341 | + | 0.284646i | ||||
\(745\) | 23.4826 | + | 40.6731i | 0.860336 | + | 1.49015i | ||||
\(746\) | −7.65624 | − | 13.2610i | −0.280315 | − | 0.485520i | ||||
\(747\) | −7.54691 | + | 13.0716i | −0.276127 | + | 0.478266i | ||||
\(748\) | −7.96523 | −0.291238 | ||||||||
\(749\) | 12.7886 | − | 0.450964i | 0.467285 | − | 0.0164779i | ||||
\(750\) | −5.97199 | −0.218066 | ||||||||
\(751\) | −10.2534 | + | 17.7595i | −0.374153 | + | 0.648053i | −0.990200 | − | 0.139657i | \(-0.955400\pi\) |
0.616047 | + | 0.787710i | \(0.288733\pi\) | |||||||
\(752\) | −0.161495 | − | 0.279717i | −0.00588912 | − | 0.0102002i | ||||
\(753\) | 14.3351 | + | 24.8292i | 0.522401 | + | 0.904825i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −30.5794 | −1.11290 | ||||||||
\(756\) | 1.24131 | − | 2.33648i | 0.0451459 | − | 0.0849771i | ||||
\(757\) | −16.8019 | −0.610674 | −0.305337 | − | 0.952244i | \(-0.598769\pi\) | ||||
−0.305337 | + | 0.952244i | \(0.598769\pi\) | |||||||
\(758\) | −8.02952 | + | 13.9075i | −0.291645 | + | 0.505145i | ||||
\(759\) | 2.64411 | + | 4.57973i | 0.0959750 | + | 0.166234i | ||||
\(760\) | −9.09382 | − | 15.7510i | −0.329867 | − | 0.571347i | ||||
\(761\) | 7.25495 | − | 12.5659i | 0.262992 | − | 0.455515i | −0.704044 | − | 0.710157i | \(-0.748624\pi\) |
0.967036 | + | 0.254642i | \(0.0819575\pi\) | |||||||
\(762\) | 9.28822 | 0.336477 | ||||||||
\(763\) | 12.6112 | − | 23.7378i | 0.456556 | − | 0.859366i | ||||
\(764\) | −2.38879 | −0.0864235 | ||||||||
\(765\) | 11.1736 | − | 19.3533i | 0.403983 | − | 0.699720i | ||||
\(766\) | 0.369899 | + | 0.640684i | 0.0133650 | + | 0.0231489i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0.500000 | − | 0.866025i | 0.0180422 | − | 0.0312500i | ||||
\(769\) | 3.35402 | 0.120949 | 0.0604745 | − | 0.998170i | \(-0.480739\pi\) | ||||
0.0604745 | + | 0.998170i | \(0.480739\pi\) | |||||||
\(770\) | 7.41832 | − | 0.261592i | 0.267338 | − | 0.00942712i | ||||
\(771\) | 13.6112 | 0.490196 | ||||||||
\(772\) | 7.28822 | − | 12.6236i | 0.262309 | − | 0.454332i | ||||
\(773\) | −0.920188 | − | 1.59381i | −0.0330969 | − | 0.0573255i | 0.849003 | − | 0.528389i | \(-0.177204\pi\) |
−0.882099 | + | 0.471063i | \(0.843870\pi\) | |||||||
\(774\) | −5.72392 | − | 9.91412i | −0.205742 | − | 0.356356i | ||||
\(775\) | 12.8714 | − | 22.2939i | 0.462355 | − | 0.800822i | ||||
\(776\) | 7.00000 | 0.251285 | ||||||||
\(777\) | 14.7050 | + | 23.5151i | 0.527540 | + | 0.843598i | ||||
\(778\) | 3.58319 | 0.128464 | ||||||||
\(779\) | −16.5106 | + | 28.5972i | −0.591555 | + | 1.02460i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.72392 | − | 6.45002i | −0.133252 | − | 0.230800i | ||||
\(782\) | 21.0609 | − | 36.4786i | 0.753137 | − | 1.30447i | ||||
\(783\) | −5.12859 | −0.183281 | ||||||||
\(784\) | −3.91832 | − | 5.80059i | −0.139940 | − | 0.207164i | ||||
\(785\) | −4.97875 | −0.177699 | ||||||||
\(786\) | 6.48261 | − | 11.2282i | 0.231227 | − | 0.400497i | ||||
\(787\) | −5.79347 | − | 10.0346i | −0.206515 | − | 0.357694i | 0.744099 | − | 0.668069i | \(-0.232879\pi\) |
−0.950614 | + | 0.310375i | \(0.899545\pi\) | |||||||
\(788\) | 6.24131 | + | 10.8103i | 0.222337 | + | 0.385100i | ||||
\(789\) | −1.80560 | + | 3.12740i | −0.0642812 | + | 0.111338i | ||||
\(790\) | −19.0938 | −0.679328 | ||||||||
\(791\) | −15.3820 | − | 24.5977i | −0.546922 | − | 0.874593i | ||||
\(792\) | −1.00000 | −0.0355335 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 12.5643 | + | 21.7620i | 0.445890 | + | 0.772304i | ||||
\(795\) | −11.2224 | − | 19.4378i | −0.398018 | − | 0.689387i | ||||
\(796\) | 7.09382 | − | 12.2869i | 0.251434 | − | 0.435496i | ||||
\(797\) | −48.4653 | −1.71673 | −0.858365 | − | 0.513039i | \(-0.828520\pi\) | ||||
−0.858365 | + | 0.513039i | \(0.828520\pi\) | |||||||
\(798\) | 17.1407 | − | 0.604433i | 0.606775 | − | 0.0213967i | ||||
\(799\) | 2.57269 | 0.0910151 | ||||||||
\(800\) | −1.43570 | + | 2.48671i | −0.0507598 | + | 0.0879185i | ||||
\(801\) | −0.805603 | − | 1.39535i | −0.0284646 | − | 0.0493021i | ||||
\(802\) | 1.93420 | + | 3.35013i | 0.0682988 | + | 0.118297i | ||||
\(803\) | 6.28822 | − | 10.8915i | 0.221906 | − | 0.384353i | ||||
\(804\) | 7.09382 | 0.250180 | ||||||||
\(805\) | −18.4168 | + | 34.6656i | −0.649107 | + | 1.22180i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.69102 | + | 8.12508i | −0.165132 | + | 0.286016i | ||||
\(808\) | −5.36990 | − | 9.30094i | −0.188912 | − | 0.327206i | ||||
\(809\) | 1.38354 | + | 2.39637i | 0.0486428 | + | 0.0842517i | 0.889322 | − | 0.457282i | \(-0.151177\pi\) |
−0.840679 | + | 0.541534i | \(0.817844\pi\) | |||||||
\(810\) | 1.40280 | − | 2.42972i | 0.0492894 | − | 0.0853718i | ||||
\(811\) | 4.89568 | 0.171910 | 0.0859552 | − | 0.996299i | \(-0.472606\pi\) | ||||
0.0859552 | + | 0.996299i | \(0.472606\pi\) | |||||||
\(812\) | −6.36616 | + | 11.9829i | −0.223408 | + | 0.420517i | ||||
\(813\) | −5.61121 | −0.196794 | ||||||||
\(814\) | 5.24131 | − | 9.07821i | 0.183708 | − | 0.318191i | ||||
\(815\) | −5.69403 | − | 9.86235i | −0.199453 | − | 0.345463i | ||||
\(816\) | 3.98261 | + | 6.89809i | 0.139419 | + | 0.241481i | ||||
\(817\) | 37.1060 | − | 64.2694i | 1.29817 | − | 2.24850i | ||||
\(818\) | 4.64598 | 0.162443 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 14.2912 | 0.499071 | ||||||||
\(821\) | −1.77457 | + | 3.07365i | −0.0619330 | + | 0.107271i | −0.895329 | − | 0.445405i | \(-0.853060\pi\) |
0.833396 | + | 0.552676i | \(0.186393\pi\) | |||||||
\(822\) | 2.80560 | + | 4.85945i | 0.0978566 | + | 0.169493i | ||||
\(823\) | −16.2534 | − | 28.1518i | −0.566559 | − | 0.981310i | −0.996903 | − | 0.0786443i | \(-0.974941\pi\) |
0.430343 | − | 0.902665i | \(-0.358392\pi\) | |||||||
\(824\) | −1.48261 | + | 2.56796i | −0.0516493 | + | 0.0894592i | ||||
\(825\) | 2.87141 | 0.0999696 | ||||||||
\(826\) | 1.22241 | + | 1.95478i | 0.0425331 | + | 0.0680155i | ||||
\(827\) | 19.5447 | 0.679635 | 0.339817 | − | 0.940491i | \(-0.389635\pi\) | ||||
0.339817 | + | 0.940491i | \(0.389635\pi\) | |||||||
\(828\) | 2.64411 | − | 4.57973i | 0.0918891 | − | 0.159157i | ||||
\(829\) | −12.5953 | − | 21.8157i | −0.437454 | − | 0.757692i | 0.560039 | − | 0.828467i | \(-0.310786\pi\) |
−0.997492 | + | 0.0707744i | \(0.977453\pi\) | |||||||
\(830\) | 21.1736 | + | 36.6738i | 0.734947 | + | 1.27297i | ||||
\(831\) | −8.00000 | + | 13.8564i | −0.277517 | + | 0.480673i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 55.6181 | − | 3.92740i | 1.92705 | − | 0.136076i | ||||
\(834\) | −13.1286 | −0.454606 | ||||||||
\(835\) | 19.4546 | − | 33.6964i | 0.673254 | − | 1.16611i | ||||
\(836\) | −3.24131 | − | 5.61411i | −0.112103 | − | 0.194168i | ||||
\(837\) | −4.48261 | − | 7.76411i | −0.154942 | − | 0.268367i | ||||
\(838\) | 9.75869 | − | 16.9026i | 0.337108 | − | 0.583889i | ||||
\(839\) | −50.4033 | −1.74011 | −0.870057 | − | 0.492950i | \(-0.835918\pi\) | ||||
−0.870057 | + | 0.492950i | \(0.835918\pi\) | |||||||
\(840\) | −3.93570 | − | 6.29365i | −0.135795 | − | 0.217152i | ||||
\(841\) | −2.69754 | −0.0930185 | ||||||||
\(842\) | −7.75869 | + | 13.4385i | −0.267382 | + | 0.463120i | ||||
\(843\) | 12.0764 | + | 20.9170i | 0.415934 | + | 0.720420i | ||||
\(844\) | 10.4168 | + | 18.0424i | 0.358561 | + | 0.621046i | ||||
\(845\) | −18.2364 | + | 31.5864i | −0.627352 | + | 1.08661i | ||||
\(846\) | 0.322990 | 0.0111046 | ||||||||
\(847\) | 2.64411 | − | 0.0932392i | 0.0908526 | − | 0.00320374i | ||||
\(848\) | 8.00000 | 0.274721 | ||||||||
\(849\) | 3.77083 | − | 6.53127i | 0.129415 | − | 0.224152i | ||||
\(850\) | −11.4357 | − | 19.8072i | −0.392241 | − | 0.679382i | ||||
\(851\) | 27.7172 | + | 48.0075i | 0.950132 | + | 1.64568i | ||||
\(852\) | −3.72392 | + | 6.45002i | −0.127579 | + | 0.220974i | ||||
\(853\) | −16.8752 | −0.577794 | −0.288897 | − | 0.957360i | \(-0.593289\pi\) | ||||
−0.288897 | + | 0.957360i | \(0.593289\pi\) | |||||||
\(854\) | −2.68075 | + | 5.04592i | −0.0917335 | + | 0.172668i | ||||
\(855\) | 18.1876 | 0.622004 | ||||||||
\(856\) | −2.41832 | + | 4.18865i | −0.0826564 | + | 0.143165i | ||||
\(857\) | −21.6529 | − | 37.5039i | −0.739648 | − | 1.28111i | −0.952654 | − | 0.304057i | \(-0.901659\pi\) |
0.213006 | − | 0.977051i | \(-0.431675\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.80711 | + | 3.13001i | −0.0616578 | + | 0.106794i | −0.895207 | − | 0.445651i | \(-0.852972\pi\) |
0.833549 | + | 0.552446i | \(0.186305\pi\) | |||||||
\(860\) | −32.1181 | −1.09522 | ||||||||
\(861\) | −6.32299 | + | 11.9016i | −0.215487 | + | 0.405606i | ||||
\(862\) | −14.3888 | −0.490084 | ||||||||
\(863\) | −2.20840 | + | 3.82507i | −0.0751750 | + | 0.130207i | −0.901162 | − | 0.433482i | \(-0.857285\pi\) |
0.825987 | + | 0.563689i | \(0.190618\pi\) | |||||||
\(864\) | 0.500000 | + | 0.866025i | 0.0170103 | + | 0.0294628i | ||||
\(865\) | 23.7988 | + | 41.2208i | 0.809185 | + | 1.40155i | ||||
\(866\) | −1.01739 | + | 1.76217i | −0.0345722 | + | 0.0598808i | ||||
\(867\) | −46.4448 | −1.57735 | ||||||||
\(868\) | −23.7050 | + | 0.835910i | −0.804601 | + | 0.0283726i | ||||
\(869\) | −6.80560 | −0.230864 | ||||||||
\(870\) | −7.19440 | + | 12.4611i | −0.243913 | + | 0.422470i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 5.07981 | + | 8.79849i | 0.172024 | + | 0.297955i | ||||
\(873\) | −3.50000 | + | 6.06218i | −0.118457 | + | 0.205174i | ||||
\(874\) | 34.2815 | 1.15959 | ||||||||
\(875\) | −8.37751 | − | 13.3966i | −0.283212 | − | 0.452889i | ||||
\(876\) | −12.5764 | −0.424918 | ||||||||
\(877\) | −22.1389 | + | 38.3456i | −0.747576 | + | 1.29484i | 0.201405 | + | 0.979508i | \(0.435449\pi\) |
−0.948982 | + | 0.315332i | \(0.897884\pi\) | |||||||
\(878\) | −1.61308 | − | 2.79393i | −0.0544387 | − | 0.0942907i | ||||
\(879\) | 3.95309 | + | 6.84695i | 0.133334 | + | 0.230942i | ||||
\(880\) | −1.40280 | + | 2.42972i | −0.0472884 | + | 0.0819060i | ||||
\(881\) | −18.1876 | −0.612757 | −0.306379 | − | 0.951910i | \(-0.599117\pi\) | ||||
−0.306379 | + | 0.951910i | \(0.599117\pi\) | |||||||
\(882\) | 6.98261 | − | 0.493069i | 0.235117 | − | 0.0166025i | ||||
\(883\) | −4.57945 | −0.154111 | −0.0770553 | − | 0.997027i | \(-0.524552\pi\) | ||||
−0.0770553 | + | 0.997027i | \(0.524552\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.22241 | + | 2.11728i | 0.0410909 | + | 0.0711715i | ||||
\(886\) | 11.0469 | + | 19.1338i | 0.371128 | + | 0.642813i | ||||
\(887\) | 0.288216 | − | 0.499204i | 0.00967734 | − | 0.0167616i | −0.861146 | − | 0.508357i | \(-0.830253\pi\) |
0.870824 | + | 0.491596i | \(0.163586\pi\) | |||||||
\(888\) | −10.4826 | −0.351773 | ||||||||
\(889\) | 13.0295 | + | 20.8357i | 0.436996 | + | 0.698808i | ||||
\(890\) | −4.52040 | −0.151524 | ||||||||
\(891\) | 0.500000 | − | 0.866025i | 0.0167506 | − | 0.0290129i | ||||
\(892\) | −6.28822 | − | 10.8915i | −0.210545 | − | 0.364675i | ||||
\(893\) | 1.04691 | + | 1.81330i | 0.0350335 | + | 0.0606798i | ||||
\(894\) | 8.36990 | − | 14.4971i | 0.279931 | − | 0.484855i | ||||
\(895\) | 35.5477 | 1.18823 | ||||||||
\(896\) | 2.64411 | − | 0.0932392i | 0.0883334 | − | 0.00311490i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −11.1248 | + | 19.2688i | −0.371241 | + | 0.643008i | ||||
\(899\) | 22.9895 | + | 39.8190i | 0.766743 | + | 1.32804i | ||||
\(900\) | −1.43570 | − | 2.48671i | −0.0478568 | − | 0.0828904i | ||||
\(901\) | −31.8609 | + | 55.1847i | −1.06144 | + | 1.83847i | ||||
\(902\) | 5.09382 | 0.169606 | ||||||||
\(903\) | 14.2103 | − | 26.7477i | 0.472888 | − | 0.890108i | ||||
\(904\) | 10.9652 | 0.364698 | ||||||||
\(905\) | −3.61422 | + | 6.26002i | −0.120141 | + | 0.208090i | ||||
\(906\) | 5.44971 | + | 9.43918i | 0.181055 | + | 0.313596i | ||||
\(907\) | 11.0295 | + | 19.1037i | 0.366229 | + | 0.634328i | 0.988973 | − | 0.148098i | \(-0.0473153\pi\) |
−0.622743 | + | 0.782426i | \(0.713982\pi\) | |||||||
\(908\) | −10.0295 | + | 17.3716i | −0.332841 | + | 0.576498i | ||||
\(909\) | 10.7398 | 0.356217 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.93420 | 0.329135 | 0.164567 | − | 0.986366i | \(-0.447377\pi\) | ||||
0.164567 | + | 0.986366i | \(0.447377\pi\) | |||||||
\(912\) | −3.24131 | + | 5.61411i | −0.107330 | + | 0.185902i | ||||
\(913\) | 7.54691 | + | 13.0716i | 0.249766 | + | 0.432608i | ||||
\(914\) | 9.31925 | + | 16.1414i | 0.308253 | + | 0.533910i | ||||
\(915\) | −3.02952 | + | 5.24729i | −0.100153 | + | 0.173470i | ||||
\(916\) | −22.5764 | −0.745946 | ||||||||
\(917\) | 34.2815 | − | 1.20887i | 1.13207 | − | 0.0399203i | ||||
\(918\) | −7.96523 | −0.262892 | ||||||||
\(919\) | −22.3174 | + | 38.6548i | −0.736182 | + | 1.27511i | 0.218020 | + | 0.975944i | \(0.430040\pi\) |
−0.954203 | + | 0.299161i | \(0.903293\pi\) | |||||||
\(920\) | −7.41832 | − | 12.8489i | −0.244575 | − | 0.423616i | ||||
\(921\) | 6.44784 | + | 11.1680i | 0.212464 | + | 0.367998i | ||||
\(922\) | 10.4947 | − | 18.1774i | 0.345626 | − | 0.598642i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −1.40280 | − | 2.24325i | −0.0461488 | − | 0.0737973i | ||||
\(925\) | 30.0999 | 0.989677 | ||||||||
\(926\) | 2.67701 | − | 4.63672i | 0.0879720 | − | 0.152372i | ||||
\(927\) | −1.48261 | − | 2.56796i | −0.0486954 | − | 0.0843429i | ||||
\(928\) | −2.56430 | − | 4.44149i | −0.0841772 | − | 0.145799i | ||||
\(929\) | 21.2882 | − | 36.8723i | 0.698444 | − | 1.20974i | −0.270562 | − | 0.962702i | \(-0.587210\pi\) |
0.969006 | − | 0.247037i | \(-0.0794571\pi\) | |||||||
\(930\) | −25.1529 | −0.824795 | ||||||||
\(931\) | 25.4009 | + | 37.6030i | 0.832482 | + | 1.23239i | ||||
\(932\) | −0.742815 | −0.0243317 | ||||||||
\(933\) | 5.44971 | − | 9.43918i | 0.178416 | − | 0.309025i | ||||
\(934\) | −13.0121 | − | 22.5377i | −0.425770 | − | 0.737455i | ||||
\(935\) | −11.1736 | − | 19.3533i | −0.365417 | − | 0.632920i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −36.2572 | −1.18447 | −0.592235 | − | 0.805765i | \(-0.701754\pi\) | ||||
−0.592235 | + | 0.805765i | \(0.701754\pi\) | |||||||
\(938\) | 9.95122 | + | 15.9132i | 0.324919 | + | 0.519584i | ||||
\(939\) | 9.12859 | 0.297900 | ||||||||
\(940\) | 0.453091 | − | 0.784776i | 0.0147782 | − | 0.0255966i | ||||
\(941\) | −1.34189 | − | 2.32421i | −0.0437442 | − | 0.0757672i | 0.843324 | − | 0.537405i | \(-0.180595\pi\) |
−0.887069 | + | 0.461638i | \(0.847262\pi\) | |||||||
\(942\) | 0.887286 | + | 1.53682i | 0.0289093 | + | 0.0500725i | ||||
\(943\) | −13.4686 | + | 23.3283i | −0.438598 | + | 0.759674i | ||||
\(944\) | −0.871407 | −0.0283619 | ||||||||
\(945\) | 7.41832 | − | 0.261592i | 0.241318 | − | 0.00850959i | ||||
\(946\) | −11.4478 | −0.372201 | ||||||||
\(947\) | −24.7519 | + | 42.8716i | −0.804330 | + | 1.39314i | 0.112413 | + | 0.993662i | \(0.464142\pi\) |
−0.916743 | + | 0.399478i | \(0.869191\pi\) | |||||||
\(948\) | 3.40280 | + | 5.89382i | 0.110518 | + | 0.191423i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 9.30711 | − | 16.1204i | 0.301963 | − | 0.523014i | ||||
\(951\) | 9.51364 | 0.308501 | ||||||||
\(952\) | −9.88729 | + | 18.6106i | −0.320449 | + | 0.603174i | ||||
\(953\) | 15.8019 | 0.511872 | 0.255936 | − | 0.966694i | \(-0.417616\pi\) | ||||
0.255936 | + | 0.966694i | \(0.417616\pi\) | |||||||
\(954\) | −4.00000 | + | 6.92820i | −0.129505 | + | 0.224309i | ||||
\(955\) | −3.35100 | − | 5.80411i | −0.108436 | − | 0.187817i | ||||
\(956\) | −2.15962 | − | 3.74058i | −0.0698472 | − | 0.120979i | ||||
\(957\) | −2.56430 | + | 4.44149i | −0.0828919 | + | 0.143573i | ||||
\(958\) | −3.61121 | −0.116673 | ||||||||
\(959\) | −6.96523 | + | 13.1105i | −0.224919 | + | 0.423360i | ||||
\(960\) | 2.80560 | 0.0905504 | ||||||||
\(961\) | −24.6876 | + | 42.7602i | −0.796375 | + | 1.37936i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.41832 | − | 4.18865i | −0.0779292 | − | 0.134977i | ||||
\(964\) | 9.09382 | − | 15.7510i | 0.292892 | − | 0.507304i | ||||
\(965\) | 40.8957 | 1.31648 | ||||||||
\(966\) | 13.9826 | − | 0.493069i | 0.449883 | − | 0.0158642i | ||||
\(967\) | −12.6497 | −0.406788 | −0.203394 | − | 0.979097i | \(-0.565197\pi\) | ||||
−0.203394 | + | 0.979097i | \(0.565197\pi\) | |||||||
\(968\) | −0.500000 | + | 0.866025i | −0.0160706 | + | 0.0278351i | ||||
\(969\) | −25.8177 | − | 44.7176i | −0.829385 | − | 1.43654i | ||||
\(970\) | 9.81961 | + | 17.0081i | 0.315289 | + | 0.546096i | ||||
\(971\) | −24.7671 | + | 42.8978i | −0.794814 | + | 1.37666i | 0.128144 | + | 0.991756i | \(0.459098\pi\) |
−0.922957 | + | 0.384902i | \(0.874235\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −18.4168 | − | 29.4507i | −0.590416 | − | 0.944144i | ||||
\(974\) | −8.06206 | −0.258325 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.07981 | − | 1.87029i | −0.0345639 | − | 0.0598665i | ||||
\(977\) | −17.2224 | − | 29.8301i | −0.550994 | − | 0.954349i | −0.998203 | − | 0.0599199i | \(-0.980915\pi\) |
0.447209 | − | 0.894429i | \(-0.352418\pi\) | |||||||
\(978\) | −2.02952 | + | 3.51524i | −0.0648970 | + | 0.112405i | ||||
\(979\) | −1.61121 | −0.0514944 | ||||||||
\(980\) | 8.59720 | − | 17.6575i | 0.274627 | − | 0.564048i | ||||
\(981\) | −10.1596 | −0.324372 | ||||||||
\(982\) | −10.4531 | + | 18.1053i | −0.333572 | + | 0.577763i | ||||
\(983\) | 1.67888 | + | 2.90791i | 0.0535480 | + | 0.0927479i | 0.891557 | − | 0.452909i | \(-0.149614\pi\) |
−0.838009 | + | 0.545657i | \(0.816280\pi\) | |||||||
\(984\) | −2.54691 | − | 4.41138i | −0.0811925 | − | 0.140630i | ||||
\(985\) | −17.5106 | + | 30.3293i | −0.557935 | + | 0.966372i | ||||
\(986\) | 40.8504 | 1.30094 | ||||||||
\(987\) | 0.453091 | + | 0.724546i | 0.0144220 | + | 0.0230625i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 30.2693 | − | 52.4280i | 0.962508 | − | 1.66711i | ||||
\(990\) | −1.40280 | − | 2.42972i | −0.0445840 | − | 0.0772217i | ||||
\(991\) | 22.9237 | + | 39.7050i | 0.728195 | + | 1.26127i | 0.957645 | + | 0.287950i | \(0.0929738\pi\) |
−0.229450 | + | 0.973320i | \(0.573693\pi\) | |||||||
\(992\) | 4.48261 | − | 7.76411i | 0.142323 | − | 0.246511i | ||||
\(993\) | −1.09382 | −0.0347113 | ||||||||
\(994\) | −19.6929 | + | 0.694430i | −0.624621 | + | 0.0220260i | ||||
\(995\) | 39.8049 | 1.26190 | ||||||||
\(996\) | 7.54691 | − | 13.0716i | 0.239133 | − | 0.414190i | ||||
\(997\) | 21.9305 | + | 37.9847i | 0.694544 | + | 1.20299i | 0.970334 | + | 0.241768i | \(0.0777273\pi\) |
−0.275790 | + | 0.961218i | \(0.588939\pi\) | |||||||
\(998\) | −2.48261 | − | 4.30001i | −0.0785857 | − | 0.136114i | ||||
\(999\) | 5.24131 | − | 9.07821i | 0.165828 | − | 0.287222i |
(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 | 462.2.i.g.331.3 | yes | 6 | |
3.2 | odd | 2 | 1386.2.k.v.793.1 | 6 | |||
7.2 | even | 3 | 3234.2.a.bf.1.1 | 3 | |||
7.4 | even | 3 | inner | 462.2.i.g.67.3 | ✓ | 6 | |
7.5 | odd | 6 | 3234.2.a.bh.1.3 | 3 | |||
21.2 | odd | 6 | 9702.2.a.dv.1.3 | 3 | |||
21.5 | even | 6 | 9702.2.a.dw.1.1 | 3 | |||
21.11 | odd | 6 | 1386.2.k.v.991.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.i.g.67.3 | ✓ | 6 | 7.4 | even | 3 | inner | |
462.2.i.g.331.3 | yes | 6 | 1.1 | even | 1 | trivial | |
1386.2.k.v.793.1 | 6 | 3.2 | odd | 2 | |||
1386.2.k.v.991.1 | 6 | 21.11 | odd | 6 | |||
3234.2.a.bf.1.1 | 3 | 7.2 | even | 3 | |||
3234.2.a.bh.1.3 | 3 | 7.5 | odd | 6 | |||
9702.2.a.dv.1.3 | 3 | 21.2 | odd | 6 | |||
9702.2.a.dw.1.1 | 3 | 21.5 | even | 6 |