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 | 67.1 | ||
Root | \(0.500000 + 3.23735i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 462.67 |
Dual form | 462.2.i.g.331.1 |
$q$-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 \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | ||||
\(5\) | −2.20942 | − | 3.82682i | −0.988081 | − | 1.71141i | −0.627352 | − | 0.778736i | \(-0.715861\pi\) |
−0.360729 | − | 0.932671i | \(-0.617472\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 2.20942 | − | 1.45550i | 0.835081 | − | 0.550127i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | −2.20942 | + | 3.82682i | −0.698679 | + | 1.21015i | ||||
\(11\) | 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 | \(0.5\pi\) | |||||||||
\(14\) | −2.36521 | − | 1.18566i | −0.632128 | − | 0.316881i | ||||
\(15\) | −4.41883 | −1.14094 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −1.18842 | + | 2.05840i | −0.288233 | + | 0.499235i | −0.973388 | − | 0.229163i | \(-0.926401\pi\) |
0.685155 | + | 0.728398i | \(0.259735\pi\) | |||||||
\(18\) | −0.500000 | + | 0.866025i | −0.117851 | + | 0.204124i | ||||
\(19\) | 1.84421 | + | 3.19426i | 0.423090 | + | 0.732814i | 0.996240 | − | 0.0866367i | \(-0.0276119\pi\) |
−0.573150 | + | 0.819451i | \(0.694279\pi\) | |||||||
\(20\) | 4.41883 | 0.988081 | ||||||||
\(21\) | −0.155792 | − | 2.64116i | −0.0339965 | − | 0.576348i | ||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −2.36521 | − | 4.09666i | −0.493180 | − | 0.854213i | 0.506789 | − | 0.862070i | \(-0.330832\pi\) |
−0.999969 | + | 0.00785730i | \(0.997499\pi\) | |||||||
\(24\) | 0.500000 | − | 0.866025i | 0.102062 | − | 0.176777i | ||||
\(25\) | −7.26304 | + | 12.5800i | −1.45261 | + | 2.51599i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.155792 | + | 2.64116i | 0.0294418 | + | 0.499132i | ||||
\(29\) | −6.52608 | −1.21186 | −0.605932 | − | 0.795517i | \(-0.707199\pi\) | ||||
−0.605932 | + | 0.795517i | \(0.707199\pi\) | |||||||
\(30\) | 2.20942 | + | 3.82682i | 0.403382 | + | 0.698679i | ||||
\(31\) | 1.68842 | − | 2.92442i | 0.303249 | − | 0.525242i | −0.673621 | − | 0.739077i | \(-0.735262\pi\) |
0.976870 | + | 0.213835i | \(0.0685954\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | −0.500000 | − | 0.866025i | −0.0870388 | − | 0.150756i | ||||
\(34\) | 2.37683 | 0.407624 | ||||||||
\(35\) | −10.4515 | − | 5.23924i | −1.76662 | − | 0.885593i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −3.84421 | − | 6.65836i | −0.631984 | − | 1.09463i | −0.987146 | − | 0.159823i | \(-0.948908\pi\) |
0.355162 | − | 0.934805i | \(-0.384426\pi\) | |||||||
\(38\) | 1.84421 | − | 3.19426i | 0.299170 | − | 0.518178i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.20942 | − | 3.82682i | −0.349339 | − | 0.605074i | ||||
\(41\) | 12.1492 | 1.89739 | 0.948697 | − | 0.316187i | \(-0.102403\pi\) | ||||
0.948697 | + | 0.316187i | \(0.102403\pi\) | |||||||
\(42\) | −2.20942 | + | 1.45550i | −0.340920 | + | 0.224588i | ||||
\(43\) | 3.06525 | 0.467446 | 0.233723 | − | 0.972303i | \(-0.424909\pi\) | ||||
0.233723 | + | 0.972303i | \(0.424909\pi\) | |||||||
\(44\) | 0.500000 | + | 0.866025i | 0.0753778 | + | 0.130558i | ||||
\(45\) | −2.20942 | + | 3.82682i | −0.329360 | + | 0.570469i | ||||
\(46\) | −2.36521 | + | 4.09666i | −0.348731 | + | 0.604020i | ||||
\(47\) | 2.05362 | + | 3.55698i | 0.299552 | + | 0.518839i | 0.976033 | − | 0.217620i | \(-0.0698295\pi\) |
−0.676482 | + | 0.736460i | \(0.736496\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 2.76304 | − | 6.43161i | 0.394720 | − | 0.918801i | ||||
\(50\) | 14.5261 | 2.05430 | ||||||||
\(51\) | 1.18842 | + | 2.05840i | 0.166412 | + | 0.288233i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.00000 | + | 6.92820i | −0.549442 | + | 0.951662i | 0.448871 | + | 0.893597i | \(0.351826\pi\) |
−0.998313 | + | 0.0580651i | \(0.981507\pi\) | |||||||
\(54\) | 0.500000 | + | 0.866025i | 0.0680414 | + | 0.117851i | ||||
\(55\) | −4.41883 | −0.595835 | ||||||||
\(56\) | 2.20942 | − | 1.45550i | 0.295246 | − | 0.194499i | ||||
\(57\) | 3.68842 | 0.488543 | ||||||||
\(58\) | 3.26304 | + | 5.65175i | 0.428458 | + | 0.742112i | ||||
\(59\) | 6.26304 | − | 10.8479i | 0.815379 | − | 1.41228i | −0.0936773 | − | 0.995603i | \(-0.529862\pi\) |
0.909056 | − | 0.416674i | \(-0.136804\pi\) | |||||||
\(60\) | 2.20942 | − | 3.82682i | 0.285234 | − | 0.494041i | ||||
\(61\) | −1.89783 | − | 3.28714i | −0.242993 | − | 0.420876i | 0.718573 | − | 0.695452i | \(-0.244796\pi\) |
−0.961565 | + | 0.274576i | \(0.911462\pi\) | |||||||
\(62\) | −3.37683 | −0.428858 | ||||||||
\(63\) | −2.36521 | − | 1.18566i | −0.297988 | − | 0.149379i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.500000 | + | 0.866025i | −0.0615457 | + | 0.106600i | ||||
\(67\) | −5.07462 | + | 8.78951i | −0.619964 | + | 1.07381i | 0.369528 | + | 0.929220i | \(0.379519\pi\) |
−0.989492 | + | 0.144589i | \(0.953814\pi\) | |||||||
\(68\) | −1.18842 | − | 2.05840i | −0.144117 | − | 0.249617i | ||||
\(69\) | −4.73042 | −0.569475 | ||||||||
\(70\) | 0.688417 | + | 11.6708i | 0.0822816 | + | 1.39493i | ||||
\(71\) | 0.934749 | 0.110934 | 0.0554672 | − | 0.998461i | \(-0.482335\pi\) | ||||
0.0554672 | + | 0.998461i | \(0.482335\pi\) | |||||||
\(72\) | −0.500000 | − | 0.866025i | −0.0589256 | − | 0.102062i | ||||
\(73\) | 3.73042 | − | 6.46127i | 0.436612 | − | 0.756234i | −0.560814 | − | 0.827942i | \(-0.689512\pi\) |
0.997426 | + | 0.0717077i | \(0.0228449\pi\) | |||||||
\(74\) | −3.84421 | + | 6.65836i | −0.446880 | + | 0.774019i | ||||
\(75\) | 7.26304 | + | 12.5800i | 0.838664 | + | 1.45261i | ||||
\(76\) | −3.68842 | −0.423090 | ||||||||
\(77\) | −0.155792 | − | 2.64116i | −0.0177541 | − | 0.300988i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.209416 | + | 0.362720i | 0.0235612 | + | 0.0408092i | 0.877566 | − | 0.479457i | \(-0.159166\pi\) |
−0.854004 | + | 0.520266i | \(0.825833\pi\) | |||||||
\(80\) | −2.20942 | + | 3.82682i | −0.247020 | + | 0.427852i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −6.07462 | − | 10.5216i | −0.670830 | − | 1.16191i | ||||
\(83\) | −2.14925 | −0.235911 | −0.117955 | − | 0.993019i | \(-0.537634\pi\) | ||||
−0.117955 | + | 0.993019i | \(0.537634\pi\) | |||||||
\(84\) | 2.36521 | + | 1.18566i | 0.258065 | + | 0.129366i | ||||
\(85\) | 10.5028 | 1.13919 | ||||||||
\(86\) | −1.53263 | − | 2.65458i | −0.165267 | − | 0.286251i | ||||
\(87\) | −3.26304 | + | 5.65175i | −0.349835 | + | 0.605932i | ||||
\(88\) | 0.500000 | − | 0.866025i | 0.0533002 | − | 0.0923186i | ||||
\(89\) | 6.41883 | + | 11.1177i | 0.680395 | + | 1.17848i | 0.974860 | + | 0.222816i | \(0.0715251\pi\) |
−0.294466 | + | 0.955662i | \(0.595142\pi\) | |||||||
\(90\) | 4.41883 | 0.465786 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.73042 | 0.493180 | ||||||||
\(93\) | −1.68842 | − | 2.92442i | −0.175081 | − | 0.303249i | ||||
\(94\) | 2.05362 | − | 3.55698i | 0.211815 | − | 0.366875i | ||||
\(95\) | 8.14925 | − | 14.1149i | 0.836095 | − | 1.44816i | ||||
\(96\) | 0.500000 | + | 0.866025i | 0.0510310 | + | 0.0883883i | ||||
\(97\) | 7.00000 | 0.710742 | 0.355371 | − | 0.934725i | \(-0.384354\pi\) | ||||
0.355371 | + | 0.934725i | \(0.384354\pi\) | |||||||
\(98\) | −6.95146 | + | 0.822941i | −0.702203 | + | 0.0831296i | ||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | −7.26304 | − | 12.5800i | −0.726304 | − | 1.25800i | ||||
\(101\) | 7.68187 | − | 13.3054i | 0.764375 | − | 1.32394i | −0.176201 | − | 0.984354i | \(-0.556381\pi\) |
0.940576 | − | 0.339582i | \(-0.110286\pi\) | |||||||
\(102\) | 1.18842 | − | 2.05840i | 0.117671 | − | 0.203812i | ||||
\(103\) | 1.31158 | + | 2.27173i | 0.129234 | + | 0.223840i | 0.923380 | − | 0.383887i | \(-0.125415\pi\) |
−0.794146 | + | 0.607727i | \(0.792081\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −9.76304 | + | 6.43161i | −0.952775 | + | 0.627661i | ||||
\(106\) | 8.00000 | 0.777029 | ||||||||
\(107\) | −5.45146 | − | 9.44220i | −0.527012 | − | 0.912812i | −0.999504 | − | 0.0314773i | \(-0.989979\pi\) |
0.472492 | − | 0.881335i | \(-0.343355\pi\) | |||||||
\(108\) | 0.500000 | − | 0.866025i | 0.0481125 | − | 0.0833333i | ||||
\(109\) | 5.89783 | − | 10.2153i | 0.564910 | − | 0.978453i | −0.432148 | − | 0.901803i | \(-0.642244\pi\) |
0.997058 | − | 0.0766501i | \(-0.0244224\pi\) | |||||||
\(110\) | 2.20942 | + | 3.82682i | 0.210660 | + | 0.364873i | ||||
\(111\) | −7.68842 | −0.729752 | ||||||||
\(112\) | −2.36521 | − | 1.18566i | −0.223491 | − | 0.112034i | ||||
\(113\) | 5.37683 | 0.505810 | 0.252905 | − | 0.967491i | \(-0.418614\pi\) | ||||
0.252905 | + | 0.967491i | \(0.418614\pi\) | |||||||
\(114\) | −1.84421 | − | 3.19426i | −0.172726 | − | 0.299170i | ||||
\(115\) | −10.4515 | + | 18.1025i | −0.974603 | + | 1.68806i | ||||
\(116\) | 3.26304 | − | 5.65175i | 0.302966 | − | 0.524752i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −12.5261 | −1.15312 | ||||||||
\(119\) | 0.370291 | + | 6.27760i | 0.0339445 | + | 0.575467i | ||||
\(120\) | −4.41883 | −0.403382 | ||||||||
\(121\) | −0.500000 | − | 0.866025i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | −1.89783 | + | 3.28714i | −0.171822 | + | 0.297604i | ||||
\(123\) | 6.07462 | − | 10.5216i | 0.547730 | − | 0.948697i | ||||
\(124\) | 1.68842 | + | 2.92442i | 0.151624 | + | 0.262621i | ||||
\(125\) | 42.0942 | 3.76502 | ||||||||
\(126\) | 0.155792 | + | 2.64116i | 0.0138790 | + | 0.235293i | ||||
\(127\) | 0.730416 | 0.0648139 | 0.0324070 | − | 0.999475i | \(-0.489683\pi\) | ||||
0.0324070 | + | 0.999475i | \(0.489683\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 1.53263 | − | 2.65458i | 0.134940 | − | 0.233723i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.68842 | − | 6.38853i | −0.322258 | − | 0.558168i | 0.658695 | − | 0.752410i | \(-0.271109\pi\) |
−0.980954 | + | 0.194242i | \(0.937775\pi\) | |||||||
\(132\) | 1.00000 | 0.0870388 | ||||||||
\(133\) | 8.72387 | + | 4.37321i | 0.756456 | + | 0.379206i | ||||
\(134\) | 10.1492 | 0.876762 | ||||||||
\(135\) | 2.20942 | + | 3.82682i | 0.190156 | + | 0.329360i | ||||
\(136\) | −1.18842 | + | 2.05840i | −0.101906 | + | 0.176506i | ||||
\(137\) | 4.41883 | − | 7.65364i | 0.377526 | − | 0.653895i | −0.613175 | − | 0.789947i | \(-0.710108\pi\) |
0.990702 | + | 0.136052i | \(0.0434414\pi\) | |||||||
\(138\) | 2.36521 | + | 4.09666i | 0.201340 | + | 0.348731i | ||||
\(139\) | 1.47392 | 0.125016 | 0.0625080 | − | 0.998044i | \(-0.480090\pi\) | ||||
0.0625080 | + | 0.998044i | \(0.480090\pi\) | |||||||
\(140\) | 9.76304 | − | 6.43161i | 0.825128 | − | 0.543570i | ||||
\(141\) | 4.10725 | 0.345893 | ||||||||
\(142\) | −0.467375 | − | 0.809517i | −0.0392212 | − | 0.0679331i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.500000 | + | 0.866025i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | 14.4188 | + | 24.9742i | 1.19742 | + | 2.07399i | ||||
\(146\) | −7.46083 | −0.617463 | ||||||||
\(147\) | −4.18842 | − | 5.60867i | −0.345455 | − | 0.462595i | ||||
\(148\) | 7.68842 | 0.631984 | ||||||||
\(149\) | 4.68187 | + | 8.10924i | 0.383554 | + | 0.664335i | 0.991567 | − | 0.129592i | \(-0.0413667\pi\) |
−0.608013 | + | 0.793927i | \(0.708033\pi\) | |||||||
\(150\) | 7.26304 | − | 12.5800i | 0.593025 | − | 1.02715i | ||||
\(151\) | 6.78404 | − | 11.7503i | 0.552077 | − | 0.956226i | −0.446047 | − | 0.895009i | \(-0.647169\pi\) |
0.998125 | − | 0.0612166i | \(-0.0194980\pi\) | |||||||
\(152\) | 1.84421 | + | 3.19426i | 0.149585 | + | 0.259089i | ||||
\(153\) | 2.37683 | 0.192156 | ||||||||
\(154\) | −2.20942 | + | 1.45550i | −0.178040 | + | 0.117288i | ||||
\(155\) | −14.9217 | −1.19854 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.37029 | − | 16.2298i | 0.747831 | − | 1.29528i | −0.201030 | − | 0.979585i | \(-0.564429\pi\) |
0.948861 | − | 0.315696i | \(-0.102238\pi\) | |||||||
\(158\) | 0.209416 | − | 0.362720i | 0.0166603 | − | 0.0288564i | ||||
\(159\) | 4.00000 | + | 6.92820i | 0.317221 | + | 0.549442i | ||||
\(160\) | 4.41883 | 0.349339 | ||||||||
\(161\) | −11.1884 | − | 5.60867i | −0.881771 | − | 0.442025i | ||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −9.38621 | − | 16.2574i | −0.735185 | − | 1.27338i | −0.954642 | − | 0.297755i | \(-0.903762\pi\) |
0.219458 | − | 0.975622i | \(-0.429571\pi\) | |||||||
\(164\) | −6.07462 | + | 10.5216i | −0.474348 | + | 0.821596i | ||||
\(165\) | −2.20942 | + | 3.82682i | −0.172003 | + | 0.297918i | ||||
\(166\) | 1.07462 | + | 1.86130i | 0.0834070 | + | 0.144465i | ||||
\(167\) | −23.8898 | −1.84865 | −0.924325 | − | 0.381606i | \(-0.875371\pi\) | ||||
−0.924325 | + | 0.381606i | \(0.875371\pi\) | |||||||
\(168\) | −0.155792 | − | 2.64116i | −0.0120196 | − | 0.203770i | ||||
\(169\) | −13.0000 | −1.00000 | ||||||||
\(170\) | −5.25142 | − | 9.09572i | −0.402765 | − | 0.697610i | ||||
\(171\) | 1.84421 | − | 3.19426i | 0.141030 | − | 0.244271i | ||||
\(172\) | −1.53263 | + | 2.65458i | −0.116862 | + | 0.202410i | ||||
\(173\) | −5.68842 | − | 9.85263i | −0.432482 | − | 0.749081i | 0.564604 | − | 0.825362i | \(-0.309029\pi\) |
−0.997086 | + | 0.0762805i | \(0.975696\pi\) | |||||||
\(174\) | 6.52608 | 0.494741 | ||||||||
\(175\) | 2.26304 | + | 38.3657i | 0.171070 | + | 2.90018i | ||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | −6.26304 | − | 10.8479i | −0.470759 | − | 0.815379i | ||||
\(178\) | 6.41883 | − | 11.1177i | 0.481112 | − | 0.833310i | ||||
\(179\) | −12.3050 | + | 21.3130i | −0.919722 | + | 1.59301i | −0.119885 | + | 0.992788i | \(0.538253\pi\) |
−0.799837 | + | 0.600217i | \(0.795081\pi\) | |||||||
\(180\) | −2.20942 | − | 3.82682i | −0.164680 | − | 0.285234i | ||||
\(181\) | 17.4608 | 1.29785 | 0.648927 | − | 0.760851i | \(-0.275218\pi\) | ||||
0.648927 | + | 0.760851i | \(0.275218\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.79567 | −0.280584 | ||||||||
\(184\) | −2.36521 | − | 4.09666i | −0.174365 | − | 0.302010i | ||||
\(185\) | −16.9869 | + | 29.4222i | −1.24890 | + | 2.16316i | ||||
\(186\) | −1.68842 | + | 2.92442i | −0.123801 | + | 0.214429i | ||||
\(187\) | 1.18842 | + | 2.05840i | 0.0869056 | + | 0.150525i | ||||
\(188\) | −4.10725 | −0.299552 | ||||||||
\(189\) | −2.20942 | + | 1.45550i | −0.160711 | + | 0.105872i | ||||
\(190\) | −16.2985 | −1.18242 | ||||||||
\(191\) | 8.41883 | + | 14.5818i | 0.609165 | + | 1.05511i | 0.991378 | + | 0.131031i | \(0.0418288\pi\) |
−0.382213 | + | 0.924074i | \(0.624838\pi\) | |||||||
\(192\) | 0.500000 | − | 0.866025i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | −2.73042 | + | 4.72922i | −0.196540 | + | 0.340417i | −0.947404 | − | 0.320040i | \(-0.896304\pi\) |
0.750865 | + | 0.660456i | \(0.229637\pi\) | |||||||
\(194\) | −3.50000 | − | 6.06218i | −0.251285 | − | 0.435239i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.18842 | + | 5.60867i | 0.299173 | + | 0.400619i | ||||
\(197\) | −9.68842 | −0.690271 | −0.345136 | − | 0.938553i | \(-0.612167\pi\) | ||||
−0.345136 | + | 0.938553i | \(0.612167\pi\) | |||||||
\(198\) | 0.500000 | + | 0.866025i | 0.0355335 | + | 0.0615457i | ||||
\(199\) | −10.1492 | + | 17.5790i | −0.719461 | + | 1.24614i | 0.241752 | + | 0.970338i | \(0.422278\pi\) |
−0.961214 | + | 0.275805i | \(0.911056\pi\) | |||||||
\(200\) | −7.26304 | + | 12.5800i | −0.513575 | + | 0.889537i | ||||
\(201\) | 5.07462 | + | 8.78951i | 0.357936 | + | 0.619964i | ||||
\(202\) | −15.3637 | −1.08099 | ||||||||
\(203\) | −14.4188 | + | 9.49871i | −1.01200 | + | 0.666679i | ||||
\(204\) | −2.37683 | −0.166412 | ||||||||
\(205\) | −26.8427 | − | 46.4930i | −1.87478 | − | 3.24721i | ||||
\(206\) | 1.31158 | − | 2.27173i | 0.0913823 | − | 0.158279i | ||||
\(207\) | −2.36521 | + | 4.09666i | −0.164393 | + | 0.284738i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.68842 | 0.255133 | ||||||||
\(210\) | 10.4515 | + | 5.23924i | 0.721219 | + | 0.361542i | ||||
\(211\) | 22.5130 | 1.54986 | 0.774929 | − | 0.632048i | \(-0.217785\pi\) | ||||
0.774929 | + | 0.632048i | \(0.217785\pi\) | |||||||
\(212\) | −4.00000 | − | 6.92820i | −0.274721 | − | 0.475831i | ||||
\(213\) | 0.467375 | − | 0.809517i | 0.0320240 | − | 0.0554672i | ||||
\(214\) | −5.45146 | + | 9.44220i | −0.372654 | + | 0.645456i | ||||
\(215\) | −6.77241 | − | 11.7302i | −0.461875 | − | 0.799991i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −0.526082 | − | 8.91876i | −0.0357128 | − | 0.605445i | ||||
\(218\) | −11.7957 | −0.798903 | ||||||||
\(219\) | −3.73042 | − | 6.46127i | −0.252078 | − | 0.436612i | ||||
\(220\) | 2.20942 | − | 3.82682i | 0.148959 | − | 0.258004i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 3.84421 | + | 6.65836i | 0.258006 | + | 0.446880i | ||||
\(223\) | −7.46083 | −0.499614 | −0.249807 | − | 0.968296i | \(-0.580367\pi\) | ||||
−0.249807 | + | 0.968296i | \(0.580367\pi\) | |||||||
\(224\) | 0.155792 | + | 2.64116i | 0.0104093 | + | 0.176470i | ||||
\(225\) | 14.5261 | 0.968405 | ||||||||
\(226\) | −2.68842 | − | 4.65647i | −0.178831 | − | 0.309744i | ||||
\(227\) | 1.38621 | − | 2.40098i | 0.0920058 | − | 0.159359i | −0.816349 | − | 0.577559i | \(-0.804005\pi\) |
0.908355 | + | 0.418200i | \(0.137339\pi\) | |||||||
\(228\) | −1.84421 | + | 3.19426i | −0.122136 | + | 0.211545i | ||||
\(229\) | 1.26958 | + | 2.19898i | 0.0838965 | + | 0.145313i | 0.904920 | − | 0.425581i | \(-0.139930\pi\) |
−0.821024 | + | 0.570894i | \(0.806597\pi\) | |||||||
\(230\) | 20.9029 | 1.37830 | ||||||||
\(231\) | −2.36521 | − | 1.18566i | −0.155619 | − | 0.0780108i | ||||
\(232\) | −6.52608 | −0.428458 | ||||||||
\(233\) | 12.0261 | + | 20.8298i | 0.787855 | + | 1.36460i | 0.927279 | + | 0.374372i | \(0.122142\pi\) |
−0.139424 | + | 0.990233i | \(0.544525\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.07462 | − | 15.7177i | 0.591963 | − | 1.02531i | ||||
\(236\) | 6.26304 | + | 10.8479i | 0.407689 | + | 0.706138i | ||||
\(237\) | 0.418833 | 0.0272061 | ||||||||
\(238\) | 5.25142 | − | 3.45948i | 0.340399 | − | 0.224245i | ||||
\(239\) | 7.59133 | 0.491042 | 0.245521 | − | 0.969391i | \(-0.421041\pi\) | ||||
0.245521 | + | 0.969391i | \(0.421041\pi\) | |||||||
\(240\) | 2.20942 | + | 3.82682i | 0.142617 | + | 0.247020i | ||||
\(241\) | −8.14925 | + | 14.1149i | −0.524939 | + | 0.909221i | 0.474639 | + | 0.880181i | \(0.342579\pi\) |
−0.999578 | + | 0.0290409i | \(0.990755\pi\) | |||||||
\(242\) | −0.500000 | + | 0.866025i | −0.0321412 | + | 0.0556702i | ||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 3.79567 | 0.242993 | ||||||||
\(245\) | −30.7173 | + | 3.63644i | −1.96246 | + | 0.232324i | ||||
\(246\) | −12.1492 | −0.774608 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 1.68842 | − | 2.92442i | 0.107215 | − | 0.185701i | ||||
\(249\) | −1.07462 | + | 1.86130i | −0.0681015 | + | 0.117955i | ||||
\(250\) | −21.0471 | − | 36.4546i | −1.33113 | − | 2.30559i | ||||
\(251\) | −8.61008 | −0.543463 | −0.271732 | − | 0.962373i | \(-0.587596\pi\) | ||||
−0.271732 | + | 0.962373i | \(0.587596\pi\) | |||||||
\(252\) | 2.20942 | − | 1.45550i | 0.139180 | − | 0.0916879i | ||||
\(253\) | −4.73042 | −0.297399 | ||||||||
\(254\) | −0.365208 | − | 0.632559i | −0.0229152 | − | 0.0396903i | ||||
\(255\) | 5.25142 | − | 9.09572i | 0.328856 | − | 0.569596i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −0.418833 | − | 0.725439i | −0.0261261 | − | 0.0452517i | 0.852667 | − | 0.522455i | \(-0.174984\pi\) |
−0.878793 | + | 0.477203i | \(0.841650\pi\) | |||||||
\(258\) | −3.06525 | −0.190834 | ||||||||
\(259\) | −18.1847 | − | 9.11585i | −1.12994 | − | 0.566432i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.26304 | + | 5.65175i | 0.201977 | + | 0.349835i | ||||
\(262\) | −3.68842 | + | 6.38853i | −0.227871 | + | 0.394684i | ||||
\(263\) | −5.41883 | + | 9.38569i | −0.334140 | + | 0.578747i | −0.983319 | − | 0.181888i | \(-0.941779\pi\) |
0.649180 | + | 0.760635i | \(0.275112\pi\) | |||||||
\(264\) | −0.500000 | − | 0.866025i | −0.0307729 | − | 0.0533002i | ||||
\(265\) | 35.3507 | 2.17157 | ||||||||
\(266\) | −0.574624 | − | 9.74170i | −0.0352325 | − | 0.597302i | ||||
\(267\) | 12.8377 | 0.785652 | ||||||||
\(268\) | −5.07462 | − | 8.78951i | −0.309982 | − | 0.536905i | ||||
\(269\) | −8.93983 | + | 15.4842i | −0.545071 | + | 0.944091i | 0.453531 | + | 0.891240i | \(0.350164\pi\) |
−0.998602 | + | 0.0528506i | \(0.983169\pi\) | |||||||
\(270\) | 2.20942 | − | 3.82682i | 0.134461 | − | 0.232893i | ||||
\(271\) | 4.41883 | + | 7.65364i | 0.268425 | + | 0.464926i | 0.968455 | − | 0.249187i | \(-0.0801635\pi\) |
−0.700030 | + | 0.714113i | \(0.746830\pi\) | |||||||
\(272\) | 2.37683 | 0.144117 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.83767 | −0.533903 | ||||||||
\(275\) | 7.26304 | + | 12.5800i | 0.437978 | + | 0.758600i | ||||
\(276\) | 2.36521 | − | 4.09666i | 0.142369 | − | 0.246590i | ||||
\(277\) | 8.00000 | − | 13.8564i | 0.480673 | − | 0.832551i | −0.519081 | − | 0.854725i | \(-0.673726\pi\) |
0.999754 | + | 0.0221745i | \(0.00705893\pi\) | |||||||
\(278\) | −0.736959 | − | 1.27645i | −0.0441999 | − | 0.0765564i | ||||
\(279\) | −3.37683 | −0.202166 | ||||||||
\(280\) | −10.4515 | − | 5.23924i | −0.624594 | − | 0.313104i | ||||
\(281\) | −15.9217 | −0.949807 | −0.474903 | − | 0.880038i | \(-0.657517\pi\) | ||||
−0.474903 | + | 0.880038i | \(0.657517\pi\) | |||||||
\(282\) | −2.05362 | − | 3.55698i | −0.122292 | − | 0.211815i | ||||
\(283\) | 9.04200 | − | 15.6612i | 0.537491 | − | 0.930962i | −0.461547 | − | 0.887116i | \(-0.652706\pi\) |
0.999038 | − | 0.0438462i | \(-0.0139611\pi\) | |||||||
\(284\) | −0.467375 | + | 0.809517i | −0.0277336 | + | 0.0480360i | ||||
\(285\) | −8.14925 | − | 14.1149i | −0.482720 | − | 0.836095i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 26.8427 | − | 17.6832i | 1.58448 | − | 1.04381i | ||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 5.67533 | + | 9.82996i | 0.333843 | + | 0.578233i | ||||
\(290\) | 14.4188 | − | 24.9742i | 0.846703 | − | 1.46653i | ||||
\(291\) | 3.50000 | − | 6.06218i | 0.205174 | − | 0.355371i | ||||
\(292\) | 3.73042 | + | 6.46127i | 0.218306 | + | 0.378117i | ||||
\(293\) | 25.1492 | 1.46923 | 0.734617 | − | 0.678482i | \(-0.237362\pi\) | ||||
0.734617 | + | 0.678482i | \(0.237362\pi\) | |||||||
\(294\) | −2.76304 | + | 6.43161i | −0.161144 | + | 0.375099i | ||||
\(295\) | −55.3507 | −3.22264 | ||||||||
\(296\) | −3.84421 | − | 6.65836i | −0.223440 | − | 0.387010i | ||||
\(297\) | −0.500000 | + | 0.866025i | −0.0290129 | + | 0.0502519i | ||||
\(298\) | 4.68187 | − | 8.10924i | 0.271214 | − | 0.469756i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −14.5261 | −0.838664 | ||||||||
\(301\) | 6.77241 | − | 4.46147i | 0.390355 | − | 0.257155i | ||||
\(302\) | −13.5681 | −0.780755 | ||||||||
\(303\) | −7.68187 | − | 13.3054i | −0.441312 | − | 0.764375i | ||||
\(304\) | 1.84421 | − | 3.19426i | 0.105773 | − | 0.183204i | ||||
\(305\) | −8.38621 | + | 14.5253i | −0.480193 | + | 0.831718i | ||||
\(306\) | −1.18842 | − | 2.05840i | −0.0679373 | − | 0.117671i | ||||
\(307\) | −3.86950 | −0.220844 | −0.110422 | − | 0.993885i | \(-0.535220\pi\) | ||||
−0.110422 | + | 0.993885i | \(0.535220\pi\) | |||||||
\(308\) | 2.36521 | + | 1.18566i | 0.134770 | + | 0.0675593i | ||||
\(309\) | 2.62317 | 0.149227 | ||||||||
\(310\) | 7.46083 | + | 12.9225i | 0.423747 | + | 0.733951i | ||||
\(311\) | 6.78404 | − | 11.7503i | 0.384688 | − | 0.666299i | −0.607038 | − | 0.794673i | \(-0.707642\pi\) |
0.991726 | + | 0.128374i | \(0.0409758\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.26304 | − | 2.18765i | −0.0713913 | − | 0.123653i | 0.828120 | − | 0.560551i | \(-0.189411\pi\) |
−0.899511 | + | 0.436898i | \(0.856077\pi\) | |||||||
\(314\) | −18.7406 | −1.05759 | ||||||||
\(315\) | 0.688417 | + | 11.6708i | 0.0387879 | + | 0.657578i | ||||
\(316\) | −0.418833 | −0.0235612 | ||||||||
\(317\) | 10.0051 | + | 17.3293i | 0.561941 | + | 0.973311i | 0.997327 | + | 0.0730670i | \(0.0232787\pi\) |
−0.435386 | + | 0.900244i | \(0.643388\pi\) | |||||||
\(318\) | 4.00000 | − | 6.92820i | 0.224309 | − | 0.388514i | ||||
\(319\) | −3.26304 | + | 5.65175i | −0.182695 | + | 0.316437i | ||||
\(320\) | −2.20942 | − | 3.82682i | −0.123510 | − | 0.213926i | ||||
\(321\) | −10.9029 | −0.608541 | ||||||||
\(322\) | 0.736959 | + | 12.4938i | 0.0410691 | + | 0.696252i | ||||
\(323\) | −8.76675 | −0.487795 | ||||||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −9.38621 | + | 16.2574i | −0.519854 | + | 0.900413i | ||||
\(327\) | −5.89783 | − | 10.2153i | −0.326151 | − | 0.564910i | ||||
\(328\) | 12.1492 | 0.670830 | ||||||||
\(329\) | 9.71450 | + | 4.86980i | 0.535578 | + | 0.268481i | ||||
\(330\) | 4.41883 | 0.243249 | ||||||||
\(331\) | 8.07462 | + | 13.9857i | 0.443821 | + | 0.768721i | 0.997969 | − | 0.0636969i | \(-0.0202891\pi\) |
−0.554148 | + | 0.832418i | \(0.686956\pi\) | |||||||
\(332\) | 1.07462 | − | 1.86130i | 0.0589777 | − | 0.102152i | ||||
\(333\) | −3.84421 | + | 6.65836i | −0.210661 | + | 0.364876i | ||||
\(334\) | 11.9449 | + | 20.6892i | 0.653597 | + | 1.13206i | ||||
\(335\) | 44.8478 | 2.45030 | ||||||||
\(336\) | −2.20942 | + | 1.45550i | −0.120534 | + | 0.0794040i | ||||
\(337\) | 23.1362 | 1.26031 | 0.630154 | − | 0.776471i | \(-0.282992\pi\) | ||||
0.630154 | + | 0.776471i | \(0.282992\pi\) | |||||||
\(338\) | 6.50000 | + | 11.2583i | 0.353553 | + | 0.612372i | ||||
\(339\) | 2.68842 | − | 4.65647i | 0.146015 | − | 0.252905i | ||||
\(340\) | −5.25142 | + | 9.09572i | −0.284798 | + | 0.493285i | ||||
\(341\) | −1.68842 | − | 2.92442i | −0.0914329 | − | 0.158366i | ||||
\(342\) | −3.68842 | −0.199447 | ||||||||
\(343\) | −3.25650 | − | 18.2317i | −0.175834 | − | 0.984420i | ||||
\(344\) | 3.06525 | 0.165267 | ||||||||
\(345\) | 10.4515 | + | 18.1025i | 0.562688 | + | 0.974603i | ||||
\(346\) | −5.68842 | + | 9.85263i | −0.305811 | + | 0.529681i | ||||
\(347\) | −7.82829 | + | 13.5590i | −0.420245 | + | 0.727885i | −0.995963 | − | 0.0897628i | \(-0.971389\pi\) |
0.575718 | + | 0.817648i | \(0.304722\pi\) | |||||||
\(348\) | −3.26304 | − | 5.65175i | −0.174917 | − | 0.302966i | ||||
\(349\) | −20.0102 | −1.07112 | −0.535560 | − | 0.844497i | \(-0.679899\pi\) | ||||
−0.535560 | + | 0.844497i | \(0.679899\pi\) | |||||||
\(350\) | 32.0942 | − | 21.1427i | 1.71551 | − | 1.13013i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.500000 | + | 0.866025i | 0.0266501 | + | 0.0461593i | ||||
\(353\) | −3.73042 | + | 6.46127i | −0.198550 | + | 0.343899i | −0.948058 | − | 0.318096i | \(-0.896957\pi\) |
0.749508 | + | 0.661995i | \(0.230290\pi\) | |||||||
\(354\) | −6.26304 | + | 10.8479i | −0.332877 | + | 0.576560i | ||||
\(355\) | −2.06525 | − | 3.57712i | −0.109612 | − | 0.189854i | ||||
\(356\) | −12.8377 | −0.680395 | ||||||||
\(357\) | 5.62171 | + | 2.81812i | 0.297532 | + | 0.149151i | ||||
\(358\) | 24.6101 | 1.30068 | ||||||||
\(359\) | 5.62317 | + | 9.73961i | 0.296779 | + | 0.514037i | 0.975397 | − | 0.220455i | \(-0.0707541\pi\) |
−0.678618 | + | 0.734492i | \(0.737421\pi\) | |||||||
\(360\) | −2.20942 | + | 3.82682i | −0.116446 | + | 0.201691i | ||||
\(361\) | 2.69779 | − | 4.67271i | 0.141989 | − | 0.245932i | ||||
\(362\) | −8.73042 | − | 15.1215i | −0.458860 | − | 0.794770i | ||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −32.9682 | −1.72563 | ||||||||
\(366\) | 1.89783 | + | 3.28714i | 0.0992013 | + | 0.171822i | ||||
\(367\) | 2.95800 | − | 5.12341i | 0.154406 | − | 0.267440i | −0.778436 | − | 0.627724i | \(-0.783987\pi\) |
0.932843 | + | 0.360284i | \(0.117320\pi\) | |||||||
\(368\) | −2.36521 | + | 4.09666i | −0.123295 | + | 0.213553i | ||||
\(369\) | −6.07462 | − | 10.5216i | −0.316232 | − | 0.547730i | ||||
\(370\) | 33.9738 | 1.76622 | ||||||||
\(371\) | 1.24633 | + | 21.1293i | 0.0647064 | + | 1.09698i | ||||
\(372\) | 3.37683 | 0.175081 | ||||||||
\(373\) | 11.5630 | + | 20.0277i | 0.598709 | + | 1.03700i | 0.993012 | + | 0.118014i | \(0.0376529\pi\) |
−0.394303 | + | 0.918981i | \(0.629014\pi\) | |||||||
\(374\) | 1.18842 | − | 2.05840i | 0.0614516 | − | 0.106437i | ||||
\(375\) | 21.0471 | − | 36.4546i | 1.08687 | − | 1.88251i | ||||
\(376\) | 2.05362 | + | 3.55698i | 0.105908 | + | 0.183437i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 2.36521 | + | 1.18566i | 0.121653 | + | 0.0609838i | ||||
\(379\) | −6.77241 | −0.347876 | −0.173938 | − | 0.984757i | \(-0.555649\pi\) | ||||
−0.173938 | + | 0.984757i | \(0.555649\pi\) | |||||||
\(380\) | 8.14925 | + | 14.1149i | 0.418048 | + | 0.724080i | ||||
\(381\) | 0.365208 | − | 0.632559i | 0.0187102 | − | 0.0324070i | ||||
\(382\) | 8.41883 | − | 14.5818i | 0.430745 | − | 0.746072i | ||||
\(383\) | −12.6819 | − | 21.9656i | −0.648013 | − | 1.12239i | −0.983597 | − | 0.180382i | \(-0.942267\pi\) |
0.335583 | − | 0.942011i | \(-0.391067\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −9.76304 | + | 6.43161i | −0.497571 | + | 0.327785i | ||||
\(386\) | 5.46083 | 0.277949 | ||||||||
\(387\) | −1.53263 | − | 2.65458i | −0.0779077 | − | 0.134940i | ||||
\(388\) | −3.50000 | + | 6.06218i | −0.177686 | + | 0.307760i | ||||
\(389\) | −12.6282 | + | 21.8728i | −0.640278 | + | 1.10899i | 0.345093 | + | 0.938568i | \(0.387847\pi\) |
−0.985371 | + | 0.170425i | \(0.945486\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.2434 | 0.568604 | ||||||||
\(392\) | 2.76304 | − | 6.43161i | 0.139555 | − | 0.324845i | ||||
\(393\) | −7.37683 | −0.372112 | ||||||||
\(394\) | 4.84421 | + | 8.39042i | 0.244048 | + | 0.422703i | ||||
\(395\) | 0.925376 | − | 1.60280i | 0.0465607 | − | 0.0806455i | ||||
\(396\) | 0.500000 | − | 0.866025i | 0.0251259 | − | 0.0435194i | ||||
\(397\) | 6.73696 | + | 11.6688i | 0.338118 | + | 0.585638i | 0.984079 | − | 0.177733i | \(-0.0568763\pi\) |
−0.645961 | + | 0.763371i | \(0.723543\pi\) | |||||||
\(398\) | 20.2985 | 1.01747 | ||||||||
\(399\) | 8.14925 | − | 5.36849i | 0.407973 | − | 0.268761i | ||||
\(400\) | 14.5261 | 0.726304 | ||||||||
\(401\) | −16.9449 | − | 29.3495i | −0.846189 | − | 1.46564i | −0.884585 | − | 0.466379i | \(-0.845558\pi\) |
0.0383962 | − | 0.999263i | \(-0.487775\pi\) | |||||||
\(402\) | 5.07462 | − | 8.78951i | 0.253099 | − | 0.438381i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 7.68187 | + | 13.3054i | 0.382188 | + | 0.661968i | ||||
\(405\) | 4.41883 | 0.219574 | ||||||||
\(406\) | 15.4355 | + | 7.73772i | 0.766053 | + | 0.384017i | ||||
\(407\) | −7.68842 | −0.381101 | ||||||||
\(408\) | 1.18842 | + | 2.05840i | 0.0588354 | + | 0.101906i | ||||
\(409\) | 2.10725 | − | 3.64986i | 0.104197 | − | 0.180474i | −0.809213 | − | 0.587515i | \(-0.800106\pi\) |
0.913410 | + | 0.407041i | \(0.133439\pi\) | |||||||
\(410\) | −26.8427 | + | 46.4930i | −1.32567 | + | 2.29613i | ||||
\(411\) | −4.41883 | − | 7.65364i | −0.217965 | − | 0.377526i | ||||
\(412\) | −2.62317 | −0.129234 | ||||||||
\(413\) | −1.95146 | − | 33.0834i | −0.0960250 | − | 1.62793i | ||||
\(414\) | 4.73042 | 0.232487 | ||||||||
\(415\) | 4.74858 | + | 8.22479i | 0.233099 | + | 0.403739i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.736959 | − | 1.27645i | 0.0360890 | − | 0.0625080i | ||||
\(418\) | −1.84421 | − | 3.19426i | −0.0902032 | − | 0.156236i | ||||
\(419\) | −22.3116 | −1.08999 | −0.544996 | − | 0.838439i | \(-0.683469\pi\) | ||||
−0.544996 | + | 0.838439i | \(0.683469\pi\) | |||||||
\(420\) | −0.688417 | − | 11.6708i | −0.0335913 | − | 0.569479i | ||||
\(421\) | 18.3116 | 0.892452 | 0.446226 | − | 0.894920i | \(-0.352768\pi\) | ||||
0.446226 | + | 0.894920i | \(0.352768\pi\) | |||||||
\(422\) | −11.2565 | − | 19.4968i | −0.547958 | − | 0.949091i | ||||
\(423\) | 2.05362 | − | 3.55698i | 0.0998507 | − | 0.172946i | ||||
\(424\) | −4.00000 | + | 6.92820i | −0.194257 | + | 0.336463i | ||||
\(425\) | −17.2630 | − | 29.9005i | −0.837380 | − | 1.45039i | ||||
\(426\) | −0.934749 | −0.0452888 | ||||||||
\(427\) | −8.97754 | − | 4.50037i | −0.434454 | − | 0.217788i | ||||
\(428\) | 10.9029 | 0.527012 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.77241 | + | 11.7302i | −0.326595 | + | 0.565679i | ||||
\(431\) | 14.4188 | − | 24.9742i | 0.694531 | − | 1.20296i | −0.275808 | − | 0.961213i | \(-0.588945\pi\) |
0.970339 | − | 0.241750i | \(-0.0777213\pi\) | |||||||
\(432\) | 0.500000 | + | 0.866025i | 0.0240563 | + | 0.0416667i | ||||
\(433\) | 7.62317 | 0.366346 | 0.183173 | − | 0.983081i | \(-0.441363\pi\) | ||||
0.183173 | + | 0.983081i | \(0.441363\pi\) | |||||||
\(434\) | −7.46083 | + | 4.91498i | −0.358131 | + | 0.235927i | ||||
\(435\) | 28.8377 | 1.38266 | ||||||||
\(436\) | 5.89783 | + | 10.2153i | 0.282455 | + | 0.489226i | ||||
\(437\) | 8.72387 | − | 15.1102i | 0.417319 | − | 0.722818i | ||||
\(438\) | −3.73042 | + | 6.46127i | −0.178246 | + | 0.308731i | ||||
\(439\) | 16.6870 | + | 28.9027i | 0.796425 | + | 1.37945i | 0.921930 | + | 0.387356i | \(0.126611\pi\) |
−0.125505 | + | 0.992093i | \(0.540055\pi\) | |||||||
\(440\) | −4.41883 | −0.210660 | ||||||||
\(441\) | −6.95146 | + | 0.822941i | −0.331022 | + | 0.0391877i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.42538 | + | 4.20087i | 0.115233 | + | 0.199590i | 0.917873 | − | 0.396874i | \(-0.129905\pi\) |
−0.802640 | + | 0.596464i | \(0.796572\pi\) | |||||||
\(444\) | 3.84421 | − | 6.65836i | 0.182438 | − | 0.315992i | ||||
\(445\) | 28.3637 | − | 49.1275i | 1.34457 | − | 2.32886i | ||||
\(446\) | 3.73042 | + | 6.46127i | 0.176640 | + | 0.305950i | ||||
\(447\) | 9.36375 | 0.442890 | ||||||||
\(448\) | 2.20942 | − | 1.45550i | 0.104385 | − | 0.0687659i | ||||
\(449\) | 14.3450 | 0.676982 | 0.338491 | − | 0.940970i | \(-0.390083\pi\) | ||||
0.338491 | + | 0.940970i | \(0.390083\pi\) | |||||||
\(450\) | −7.26304 | − | 12.5800i | −0.342383 | − | 0.593025i | ||||
\(451\) | 6.07462 | − | 10.5216i | 0.286043 | − | 0.495441i | ||||
\(452\) | −2.68842 | + | 4.65647i | −0.126452 | + | 0.219022i | ||||
\(453\) | −6.78404 | − | 11.7503i | −0.318742 | − | 0.552077i | ||||
\(454\) | −2.77241 | −0.130116 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.68842 | 0.172726 | ||||||||
\(457\) | 12.5913 | + | 21.8088i | 0.588998 | + | 1.02017i | 0.994364 | + | 0.106020i | \(0.0338106\pi\) |
−0.405366 | + | 0.914154i | \(0.632856\pi\) | |||||||
\(458\) | 1.26958 | − | 2.19898i | 0.0593238 | − | 0.102752i | ||||
\(459\) | 1.18842 | − | 2.05840i | 0.0554705 | − | 0.0960778i | ||||
\(460\) | −10.4515 | − | 18.1025i | −0.487302 | − | 0.844031i | ||||
\(461\) | 13.0187 | 0.606344 | 0.303172 | − | 0.952936i | \(-0.401954\pi\) | ||||
0.303172 | + | 0.952936i | \(0.401954\pi\) | |||||||
\(462\) | 0.155792 | + | 2.64116i | 0.00724808 | + | 0.122878i | ||||
\(463\) | −14.2145 | −0.660604 | −0.330302 | − | 0.943875i | \(-0.607151\pi\) | ||||
−0.330302 | + | 0.943875i | \(0.607151\pi\) | |||||||
\(464\) | 3.26304 | + | 5.65175i | 0.151483 | + | 0.262376i | ||||
\(465\) | −7.46083 | + | 12.9225i | −0.345988 | + | 0.599268i | ||||
\(466\) | 12.0261 | − | 20.8298i | 0.557098 | − | 0.964921i | ||||
\(467\) | 1.19779 | + | 2.07463i | 0.0554271 | + | 0.0960026i | 0.892408 | − | 0.451230i | \(-0.149015\pi\) |
−0.836981 | + | 0.547233i | \(0.815681\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.58117 | + | 26.8058i | 0.0730115 | + | 1.23778i | ||||
\(470\) | −18.1492 | −0.837162 | ||||||||
\(471\) | −9.37029 | − | 16.2298i | −0.431760 | − | 0.747831i | ||||
\(472\) | 6.26304 | − | 10.8479i | 0.288280 | − | 0.499315i | ||||
\(473\) | 1.53263 | − | 2.65458i | 0.0704702 | − | 0.122058i | ||||
\(474\) | −0.209416 | − | 0.362720i | −0.00961881 | − | 0.0166603i | ||||
\(475\) | −53.5782 | −2.45834 | ||||||||
\(476\) | −5.62171 | − | 2.81812i | −0.257670 | − | 0.129168i | ||||
\(477\) | 8.00000 | 0.366295 | ||||||||
\(478\) | −3.79567 | − | 6.57429i | −0.173610 | − | 0.300701i | ||||
\(479\) | −5.41883 | + | 9.38569i | −0.247593 | + | 0.428843i | −0.962857 | − | 0.270010i | \(-0.912973\pi\) |
0.715265 | + | 0.698854i | \(0.246306\pi\) | |||||||
\(480\) | 2.20942 | − | 3.82682i | 0.100846 | − | 0.174670i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 16.2985 | 0.742376 | ||||||||
\(483\) | −10.4515 | + | 6.88512i | −0.475558 | + | 0.313284i | ||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −15.4659 | − | 26.7877i | −0.702271 | − | 1.21637i | ||||
\(486\) | 0.500000 | − | 0.866025i | 0.0226805 | − | 0.0392837i | ||||
\(487\) | 17.3217 | − | 30.0021i | 0.784923 | − | 1.35953i | −0.144121 | − | 0.989560i | \(-0.546036\pi\) |
0.929045 | − | 0.369967i | \(-0.120631\pi\) | |||||||
\(488\) | −1.89783 | − | 3.28714i | −0.0859109 | − | 0.148802i | ||||
\(489\) | −18.7724 | −0.848918 | ||||||||
\(490\) | 18.5079 | + | 24.7838i | 0.836102 | + | 1.11962i | ||||
\(491\) | 38.1492 | 1.72165 | 0.860826 | − | 0.508900i | \(-0.169948\pi\) | ||||
0.860826 | + | 0.508900i | \(0.169948\pi\) | |||||||
\(492\) | 6.07462 | + | 10.5216i | 0.273865 | + | 0.474348i | ||||
\(493\) | 7.75571 | − | 13.4333i | 0.349299 | − | 0.605004i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.20942 | + | 3.82682i | 0.0993059 | + | 0.172003i | ||||
\(496\) | −3.37683 | −0.151624 | ||||||||
\(497\) | 2.06525 | − | 1.36053i | 0.0926392 | − | 0.0610280i | ||||
\(498\) | 2.14925 | 0.0963101 | ||||||||
\(499\) | 0.311583 | + | 0.539678i | 0.0139484 | + | 0.0241593i | 0.872915 | − | 0.487872i | \(-0.162227\pi\) |
−0.858967 | + | 0.512031i | \(0.828893\pi\) | |||||||
\(500\) | −21.0471 | + | 36.4546i | −0.941254 | + | 1.63030i | ||||
\(501\) | −11.9449 | + | 20.6892i | −0.533659 | + | 0.924325i | ||||
\(502\) | 4.30504 | + | 7.45655i | 0.192143 | + | 0.332802i | ||||
\(503\) | 31.1362 | 1.38829 | 0.694146 | − | 0.719834i | \(-0.255782\pi\) | ||||
0.694146 | + | 0.719834i | \(0.255782\pi\) | |||||||
\(504\) | −2.36521 | − | 1.18566i | −0.105355 | − | 0.0528135i | ||||
\(505\) | −67.8898 | −3.02106 | ||||||||
\(506\) | 2.36521 | + | 4.09666i | 0.105146 | + | 0.182119i | ||||
\(507\) | −6.50000 | + | 11.2583i | −0.288675 | + | 0.500000i | ||||
\(508\) | −0.365208 | + | 0.632559i | −0.0162035 | + | 0.0280653i | ||||
\(509\) | 21.0522 | + | 36.4634i | 0.933121 | + | 1.61621i | 0.777951 | + | 0.628325i | \(0.216259\pi\) |
0.155170 | + | 0.987888i | \(0.450408\pi\) | |||||||
\(510\) | −10.5028 | −0.465073 | ||||||||
\(511\) | −1.16233 | − | 19.7053i | −0.0514187 | − | 0.871709i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −1.84421 | − | 3.19426i | −0.0814238 | − | 0.141030i | ||||
\(514\) | −0.418833 | + | 0.725439i | −0.0184739 | + | 0.0319978i | ||||
\(515\) | 5.79567 | − | 10.0384i | 0.255388 | − | 0.442344i | ||||
\(516\) | 1.53263 | + | 2.65458i | 0.0674701 | + | 0.116862i | ||||
\(517\) | 4.10725 | 0.180637 | ||||||||
\(518\) | 1.19779 | + | 20.3063i | 0.0526279 | + | 0.892209i | ||||
\(519\) | −11.3768 | −0.499388 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.00000 | − | 15.5885i | 0.394297 | − | 0.682943i | −0.598714 | − | 0.800963i | \(-0.704321\pi\) |
0.993011 | + | 0.118020i | \(0.0376547\pi\) | |||||||
\(522\) | 3.26304 | − | 5.65175i | 0.142819 | − | 0.247371i | ||||
\(523\) | 12.6333 | + | 21.8816i | 0.552417 | + | 0.956814i | 0.998099 | + | 0.0616232i | \(0.0196277\pi\) |
−0.445682 | + | 0.895191i | \(0.647039\pi\) | |||||||
\(524\) | 7.37683 | 0.322258 | ||||||||
\(525\) | 34.3572 | + | 17.2230i | 1.49947 | + | 0.751674i | ||||
\(526\) | 10.8377 | 0.472545 | ||||||||
\(527\) | 4.01309 | + | 6.95087i | 0.174813 | + | 0.302785i | ||||
\(528\) | −0.500000 | + | 0.866025i | −0.0217597 | + | 0.0376889i | ||||
\(529\) | 0.311583 | − | 0.539678i | 0.0135471 | − | 0.0234643i | ||||
\(530\) | −17.6753 | − | 30.6146i | −0.767767 | − | 1.32981i | ||||
\(531\) | −12.5261 | −0.543586 | ||||||||
\(532\) | −8.14925 | + | 5.36849i | −0.353315 | + | 0.232754i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −6.41883 | − | 11.1177i | −0.277770 | − | 0.481112i | ||||
\(535\) | −24.0891 | + | 41.7235i | −1.04146 | + | 1.80386i | ||||
\(536\) | −5.07462 | + | 8.78951i | −0.219190 | + | 0.379649i | ||||
\(537\) | 12.3050 | + | 21.3130i | 0.531002 | + | 0.919722i | ||||
\(538\) | 17.8797 | 0.770847 | ||||||||
\(539\) | −4.18842 | − | 5.60867i | −0.180408 | − | 0.241582i | ||||
\(540\) | −4.41883 | −0.190156 | ||||||||
\(541\) | 2.20942 | + | 3.82682i | 0.0949902 | + | 0.164528i | 0.909605 | − | 0.415475i | \(-0.136385\pi\) |
−0.814614 | + | 0.580003i | \(0.803051\pi\) | |||||||
\(542\) | 4.41883 | − | 7.65364i | 0.189805 | − | 0.328752i | ||||
\(543\) | 8.73042 | − | 15.1215i | 0.374658 | − | 0.648927i | ||||
\(544\) | −1.18842 | − | 2.05840i | −0.0509530 | − | 0.0882531i | ||||
\(545\) | −52.1231 | −2.23271 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.6622 | −1.18275 | −0.591376 | − | 0.806396i | \(-0.701415\pi\) | ||||
−0.591376 | + | 0.806396i | \(0.701415\pi\) | |||||||
\(548\) | 4.41883 | + | 7.65364i | 0.188763 | + | 0.326947i | ||||
\(549\) | −1.89783 | + | 3.28714i | −0.0809975 | + | 0.140292i | ||||
\(550\) | 7.26304 | − | 12.5800i | 0.309697 | − | 0.536411i | ||||
\(551\) | −12.0355 | − | 20.8460i | −0.512728 | − | 0.888070i | ||||
\(552\) | −4.73042 | −0.201340 | ||||||||
\(553\) | 0.990626 | + | 0.496593i | 0.0421257 | + | 0.0211173i | ||||
\(554\) | −16.0000 | −0.679775 | ||||||||
\(555\) | 16.9869 | + | 29.4222i | 0.721054 | + | 1.24890i | ||||
\(556\) | −0.736959 | + | 1.27645i | −0.0312540 | + | 0.0541335i | ||||
\(557\) | 3.99346 | − | 6.91687i | 0.169208 | − | 0.293077i | −0.768934 | − | 0.639329i | \(-0.779212\pi\) |
0.938142 | + | 0.346252i | \(0.112546\pi\) | |||||||
\(558\) | 1.68842 | + | 2.92442i | 0.0714764 | + | 0.123801i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0.688417 | + | 11.6708i | 0.0290909 | + | 0.493183i | ||||
\(561\) | 2.37683 | 0.100350 | ||||||||
\(562\) | 7.96083 | + | 13.7886i | 0.335807 | + | 0.581636i | ||||
\(563\) | 13.6753 | − | 23.6864i | 0.576346 | − | 0.998261i | −0.419547 | − | 0.907733i | \(-0.637811\pi\) |
0.995894 | − | 0.0905280i | \(-0.0288555\pi\) | |||||||
\(564\) | −2.05362 | + | 3.55698i | −0.0864732 | + | 0.149776i | ||||
\(565\) | −11.8797 | − | 20.5762i | −0.499781 | − | 0.865646i | ||||
\(566\) | −18.0840 | −0.760127 | ||||||||
\(567\) | 0.155792 | + | 2.64116i | 0.00654263 | + | 0.110918i | ||||
\(568\) | 0.934749 | 0.0392212 | ||||||||
\(569\) | 14.7239 | + | 25.5025i | 0.617257 | + | 1.06912i | 0.989984 | + | 0.141179i | \(0.0450894\pi\) |
−0.372727 | + | 0.927941i | \(0.621577\pi\) | |||||||
\(570\) | −8.14925 | + | 14.1149i | −0.341334 | + | 0.591209i | ||||
\(571\) | 7.26304 | − | 12.5800i | 0.303949 | − | 0.526455i | −0.673078 | − | 0.739572i | \(-0.735028\pi\) |
0.977027 | + | 0.213117i | \(0.0683615\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.8377 | 0.703404 | ||||||||
\(574\) | −28.7355 | − | 14.4049i | −1.19940 | − | 0.601248i | ||||
\(575\) | 68.7144 | 2.86559 | ||||||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | −6.69779 | + | 11.6009i | −0.278833 | + | 0.482952i | −0.971095 | − | 0.238694i | \(-0.923281\pi\) |
0.692262 | + | 0.721646i | \(0.256614\pi\) | |||||||
\(578\) | 5.67533 | − | 9.82996i | 0.236063 | − | 0.408872i | ||||
\(579\) | 2.73042 | + | 4.72922i | 0.113472 | + | 0.196540i | ||||
\(580\) | −28.8377 | −1.19742 | ||||||||
\(581\) | −4.74858 | + | 3.12823i | −0.197004 | + | 0.129781i | ||||
\(582\) | −7.00000 | −0.290159 | ||||||||
\(583\) | 4.00000 | + | 6.92820i | 0.165663 | + | 0.286937i | ||||
\(584\) | 3.73042 | − | 6.46127i | 0.154366 | − | 0.267369i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.5746 | − | 21.7799i | −0.519453 | − | 0.899719i | ||||
\(587\) | −11.2928 | −0.466105 | −0.233053 | − | 0.972464i | \(-0.574871\pi\) | ||||
−0.233053 | + | 0.972464i | \(0.574871\pi\) | |||||||
\(588\) | 6.95146 | − | 0.822941i | 0.286673 | − | 0.0339375i | ||||
\(589\) | 12.4552 | 0.513206 | ||||||||
\(590\) | 27.6753 | + | 47.9351i | 1.13938 | + | 1.97346i | ||||
\(591\) | −4.84421 | + | 8.39042i | −0.199264 | + | 0.345136i | ||||
\(592\) | −3.84421 | + | 6.65836i | −0.157996 | + | 0.273657i | ||||
\(593\) | 9.78912 | + | 16.9553i | 0.401991 | + | 0.696269i | 0.993966 | − | 0.109687i | \(-0.0349849\pi\) |
−0.591975 | + | 0.805956i | \(0.701652\pi\) | |||||||
\(594\) | 1.00000 | 0.0410305 | ||||||||
\(595\) | 23.2051 | − | 15.2869i | 0.951317 | − | 0.626700i | ||||
\(596\) | −9.36375 | −0.383554 | ||||||||
\(597\) | 10.1492 | + | 17.5790i | 0.415381 | + | 0.719461i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.46591 | + | 9.46724i | −0.223331 | + | 0.386821i | −0.955817 | − | 0.293961i | \(-0.905026\pi\) |
0.732486 | + | 0.680782i | \(0.238360\pi\) | |||||||
\(600\) | 7.26304 | + | 12.5800i | 0.296512 | + | 0.513575i | ||||
\(601\) | −41.2202 | −1.68141 | −0.840703 | − | 0.541497i | \(-0.817858\pi\) | ||||
−0.840703 | + | 0.541497i | \(0.817858\pi\) | |||||||
\(602\) | −7.24995 | − | 3.63435i | −0.295486 | − | 0.148125i | ||||
\(603\) | 10.1492 | 0.413309 | ||||||||
\(604\) | 6.78404 | + | 11.7503i | 0.276039 | + | 0.478113i | ||||
\(605\) | −2.20942 | + | 3.82682i | −0.0898255 | + | 0.155582i | ||||
\(606\) | −7.68187 | + | 13.3054i | −0.312055 | + | 0.540495i | ||||
\(607\) | 15.6702 | + | 27.1417i | 0.636036 | + | 1.10165i | 0.986295 | + | 0.164993i | \(0.0527603\pi\) |
−0.350259 | + | 0.936653i | \(0.613906\pi\) | |||||||
\(608\) | −3.68842 | −0.149585 | ||||||||
\(609\) | 1.01671 | + | 17.2364i | 0.0411991 | + | 0.698455i | ||||
\(610\) | 16.7724 | 0.679095 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −1.18842 | + | 2.05840i | −0.0480389 | + | 0.0832058i | ||||
\(613\) | −8.54425 | + | 14.7991i | −0.345099 | + | 0.597729i | −0.985372 | − | 0.170419i | \(-0.945488\pi\) |
0.640273 | + | 0.768148i | \(0.278821\pi\) | |||||||
\(614\) | 1.93475 | + | 3.35108i | 0.0780801 | + | 0.135239i | ||||
\(615\) | −53.6855 | −2.16481 | ||||||||
\(616\) | −0.155792 | − | 2.64116i | −0.00627702 | − | 0.106415i | ||||
\(617\) | −6.96817 | −0.280528 | −0.140264 | − | 0.990114i | \(-0.544795\pi\) | ||||
−0.140264 | + | 0.990114i | \(0.544795\pi\) | |||||||
\(618\) | −1.31158 | − | 2.27173i | −0.0527596 | − | 0.0913823i | ||||
\(619\) | 0.00937364 | − | 0.0162356i | 0.000376759 | − | 0.000652565i | −0.865837 | − | 0.500326i | \(-0.833213\pi\) |
0.866214 | + | 0.499674i | \(0.166547\pi\) | |||||||
\(620\) | 7.46083 | − | 12.9225i | 0.299634 | − | 0.518982i | ||||
\(621\) | 2.36521 | + | 4.09666i | 0.0949125 | + | 0.164393i | ||||
\(622\) | −13.5681 | −0.544030 | ||||||||
\(623\) | 30.3637 | + | 15.2211i | 1.21650 | + | 0.609821i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −56.6883 | − | 98.1871i | −2.26753 | − | 3.92748i | ||||
\(626\) | −1.26304 | + | 2.18765i | −0.0504813 | + | 0.0874361i | ||||
\(627\) | 1.84421 | − | 3.19426i | 0.0736506 | − | 0.127567i | ||||
\(628\) | 9.37029 | + | 16.2298i | 0.373915 | + | 0.647640i | ||||
\(629\) | 18.2741 | 0.728636 | ||||||||
\(630\) | 9.76304 | − | 6.43161i | 0.388969 | − | 0.256241i | ||||
\(631\) | −5.78550 | −0.230317 | −0.115159 | − | 0.993347i | \(-0.536738\pi\) | ||||
−0.115159 | + | 0.993347i | \(0.536738\pi\) | |||||||
\(632\) | 0.209416 | + | 0.362720i | 0.00833013 | + | 0.0144282i | ||||
\(633\) | 11.2565 | − | 19.4968i | 0.447406 | − | 0.774929i | ||||
\(634\) | 10.0051 | − | 17.3293i | 0.397353 | − | 0.688235i | ||||
\(635\) | −1.61379 | − | 2.79517i | −0.0640414 | − | 0.110923i | ||||
\(636\) | −8.00000 | −0.317221 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 6.52608 | 0.258370 | ||||||||
\(639\) | −0.467375 | − | 0.809517i | −0.0184891 | − | 0.0320240i | ||||
\(640\) | −2.20942 | + | 3.82682i | −0.0873348 | + | 0.151268i | ||||
\(641\) | −7.68842 | + | 13.3167i | −0.303674 | + | 0.525979i | −0.976965 | − | 0.213398i | \(-0.931547\pi\) |
0.673291 | + | 0.739378i | \(0.264880\pi\) | |||||||
\(642\) | 5.45146 | + | 9.44220i | 0.215152 | + | 0.372654i | ||||
\(643\) | −35.8058 | −1.41204 | −0.706022 | − | 0.708190i | \(-0.749512\pi\) | ||||
−0.706022 | + | 0.708190i | \(0.749512\pi\) | |||||||
\(644\) | 10.4515 | − | 6.88512i | 0.411845 | − | 0.271312i | ||||
\(645\) | −13.5448 | −0.533327 | ||||||||
\(646\) | 4.38338 | + | 7.59223i | 0.172462 | + | 0.298712i | ||||
\(647\) | −4.62825 | + | 8.01636i | −0.181955 | + | 0.315156i | −0.942546 | − | 0.334076i | \(-0.891576\pi\) |
0.760591 | + | 0.649231i | \(0.224909\pi\) | |||||||
\(648\) | −0.500000 | + | 0.866025i | −0.0196419 | + | 0.0340207i | ||||
\(649\) | −6.26304 | − | 10.8479i | −0.245846 | − | 0.425818i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.98691 | − | 4.00378i | −0.313032 | − | 0.156920i | ||||
\(652\) | 18.7724 | 0.735185 | ||||||||
\(653\) | −12.4239 | − | 21.5189i | −0.486185 | − | 0.842098i | 0.513689 | − | 0.857977i | \(-0.328279\pi\) |
−0.999874 | + | 0.0158790i | \(0.994945\pi\) | |||||||
\(654\) | −5.89783 | + | 10.2153i | −0.230624 | + | 0.399452i | ||||
\(655\) | −16.2985 | + | 28.2298i | −0.636835 | + | 1.10303i | ||||
\(656\) | −6.07462 | − | 10.5216i | −0.237174 | − | 0.410798i | ||||
\(657\) | −7.46083 | −0.291075 | ||||||||
\(658\) | −0.639875 | − | 10.8479i | −0.0249449 | − | 0.422895i | ||||
\(659\) | −6.60442 | −0.257272 | −0.128636 | − | 0.991692i | \(-0.541060\pi\) | ||||
−0.128636 | + | 0.991692i | \(0.541060\pi\) | |||||||
\(660\) | −2.20942 | − | 3.82682i | −0.0860014 | − | 0.148959i | ||||
\(661\) | 6.61662 | − | 11.4603i | 0.257357 | − | 0.445755i | −0.708176 | − | 0.706036i | \(-0.750482\pi\) |
0.965533 | + | 0.260281i | \(0.0838151\pi\) | |||||||
\(662\) | 8.07462 | − | 13.9857i | 0.313829 | − | 0.543568i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.14925 | −0.0834070 | ||||||||
\(665\) | −2.53917 | − | 43.0469i | −0.0984647 | − | 1.66929i | ||||
\(666\) | 7.68842 | 0.297920 | ||||||||
\(667\) | 15.4355 | + | 26.7351i | 0.597667 | + | 1.03519i | ||||
\(668\) | 11.9449 | − | 20.6892i | 0.462163 | − | 0.800489i | ||||
\(669\) | −3.73042 | + | 6.46127i | −0.144226 | + | 0.249807i | ||||
\(670\) | −22.4239 | − | 38.8394i | −0.866311 | − | 1.50050i | ||||
\(671\) | −3.79567 | −0.146530 | ||||||||
\(672\) | 2.36521 | + | 1.18566i | 0.0912399 | + | 0.0457379i | ||||
\(673\) | 0.130501 | 0.00503045 | 0.00251523 | − | 0.999997i | \(-0.499199\pi\) | ||||
0.00251523 | + | 0.999997i | \(0.499199\pi\) | |||||||
\(674\) | −11.5681 | − | 20.0365i | −0.445586 | − | 0.771777i | ||||
\(675\) | 7.26304 | − | 12.5800i | 0.279555 | − | 0.484203i | ||||
\(676\) | 6.50000 | − | 11.2583i | 0.250000 | − | 0.433013i | ||||
\(677\) | −14.0587 | − | 24.3504i | −0.540320 | − | 0.935862i | −0.998885 | − | 0.0472011i | \(-0.984970\pi\) |
0.458565 | − | 0.888661i | \(-0.348363\pi\) | |||||||
\(678\) | −5.37683 | −0.206496 | ||||||||
\(679\) | 15.4659 | − | 10.1885i | 0.593527 | − | 0.390999i | ||||
\(680\) | 10.5028 | 0.402765 | ||||||||
\(681\) | −1.38621 | − | 2.40098i | −0.0531196 | − | 0.0920058i | ||||
\(682\) | −1.68842 | + | 2.92442i | −0.0646528 | + | 0.111982i | ||||
\(683\) | −7.95146 | + | 13.7723i | −0.304254 | + | 0.526984i | −0.977095 | − | 0.212804i | \(-0.931741\pi\) |
0.672841 | + | 0.739787i | \(0.265074\pi\) | |||||||
\(684\) | 1.84421 | + | 3.19426i | 0.0705151 | + | 0.122136i | ||||
\(685\) | −39.0522 | −1.49211 | ||||||||
\(686\) | −14.1609 | + | 11.9361i | −0.540665 | + | 0.455721i | ||||
\(687\) | 2.53917 | 0.0968753 | ||||||||
\(688\) | −1.53263 | − | 2.65458i | −0.0584308 | − | 0.101205i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 10.4515 | − | 18.1025i | 0.397880 | − | 0.689149i | ||||
\(691\) | 7.99063 | + | 13.8402i | 0.303978 | + | 0.526505i | 0.977033 | − | 0.213087i | \(-0.0683518\pi\) |
−0.673055 | + | 0.739592i | \(0.735018\pi\) | |||||||
\(692\) | 11.3768 | 0.432482 | ||||||||
\(693\) | −2.20942 | + | 1.45550i | −0.0839288 | + | 0.0552899i | ||||
\(694\) | 15.6566 | 0.594316 | ||||||||
\(695\) | −3.25650 | − | 5.64042i | −0.123526 | − | 0.213953i | ||||
\(696\) | −3.26304 | + | 5.65175i | −0.123685 | + | 0.214229i | ||||
\(697\) | −14.4384 | + | 25.0080i | −0.546892 | + | 0.947245i | ||||
\(698\) | 10.0051 | + | 17.3293i | 0.378698 | + | 0.655924i | ||||
\(699\) | 24.0522 | 0.909736 | ||||||||
\(700\) | −34.3572 | − | 17.2230i | −1.29858 | − | 0.650968i | ||||
\(701\) | 13.9869 | 0.528278 | 0.264139 | − | 0.964485i | \(-0.414912\pi\) | ||||
0.264139 | + | 0.964485i | \(0.414912\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.1790 | − | 24.5588i | 0.534773 | − | 0.926254i | ||||
\(704\) | 0.500000 | − | 0.866025i | 0.0188445 | − | 0.0326396i | ||||
\(705\) | −9.07462 | − | 15.7177i | −0.341770 | − | 0.591963i | ||||
\(706\) | 7.46083 | 0.280792 | ||||||||
\(707\) | −2.39354 | − | 40.5781i | −0.0900184 | − | 1.52610i | ||||
\(708\) | 12.5261 | 0.470759 | ||||||||
\(709\) | −3.82096 | − | 6.61809i | −0.143499 | − | 0.248548i | 0.785313 | − | 0.619099i | \(-0.212502\pi\) |
−0.928812 | + | 0.370551i | \(0.879169\pi\) | |||||||
\(710\) | −2.06525 | + | 3.57712i | −0.0775075 | + | 0.134247i | ||||
\(711\) | 0.209416 | − | 0.362720i | 0.00785373 | − | 0.0136031i | ||||
\(712\) | 6.41883 | + | 11.1177i | 0.240556 | + | 0.416655i | ||||
\(713\) | −15.9738 | −0.598225 | ||||||||
\(714\) | −0.370291 | − | 6.27760i | −0.0138578 | − | 0.234933i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12.3050 | − | 21.3130i | −0.459861 | − | 0.796503i | ||||
\(717\) | 3.79567 | − | 6.57429i | 0.141752 | − | 0.245521i | ||||
\(718\) | 5.62317 | − | 9.73961i | 0.209855 | − | 0.363479i | ||||
\(719\) | 9.71879 | + | 16.8334i | 0.362450 | + | 0.627781i | 0.988363 | − | 0.152111i | \(-0.0486071\pi\) |
−0.625914 | + | 0.779892i | \(0.715274\pi\) | |||||||
\(720\) | 4.41883 | 0.164680 | ||||||||
\(721\) | 6.20433 | + | 3.11019i | 0.231061 | + | 0.115829i | ||||
\(722\) | −5.39558 | −0.200803 | ||||||||
\(723\) | 8.14925 | + | 14.1149i | 0.303074 | + | 0.524939i | ||||
\(724\) | −8.73042 | + | 15.1215i | −0.324463 | + | 0.561987i | ||||
\(725\) | 47.3992 | − | 82.0978i | 1.76036 | − | 3.04904i | ||||
\(726\) | 0.500000 | + | 0.866025i | 0.0185567 | + | 0.0321412i | ||||
\(727\) | −44.9217 | −1.66605 | −0.833026 | − | 0.553234i | \(-0.813394\pi\) | ||||
−0.833026 | + | 0.553234i | \(0.813394\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 16.4841 | + | 28.5513i | 0.610103 | + | 1.05673i | ||||
\(731\) | −3.64280 | + | 6.30951i | −0.134734 | + | 0.233366i | ||||
\(732\) | 1.89783 | − | 3.28714i | 0.0701459 | − | 0.121496i | ||||
\(733\) | −12.5210 | − | 21.6870i | −0.462474 | − | 0.801028i | 0.536610 | − | 0.843830i | \(-0.319705\pi\) |
−0.999084 | + | 0.0428026i | \(0.986371\pi\) | |||||||
\(734\) | −5.91600 | −0.218364 | ||||||||
\(735\) | −12.2094 | + | 28.4202i | −0.450351 | + | 1.04830i | ||||
\(736\) | 4.73042 | 0.174365 | ||||||||
\(737\) | 5.07462 | + | 8.78951i | 0.186926 | + | 0.323766i | ||||
\(738\) | −6.07462 | + | 10.5216i | −0.223610 | + | 0.387304i | ||||
\(739\) | 3.31158 | − | 5.73583i | 0.121819 | − | 0.210996i | −0.798666 | − | 0.601774i | \(-0.794461\pi\) |
0.920485 | + | 0.390778i | \(0.127794\pi\) | |||||||
\(740\) | −16.9869 | − | 29.4222i | −0.624451 | − | 1.08158i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 17.6753 | − | 11.6440i | 0.648882 | − | 0.427465i | ||||
\(743\) | −39.3972 | −1.44534 | −0.722671 | − | 0.691192i | \(-0.757086\pi\) | ||||
−0.722671 | + | 0.691192i | \(0.757086\pi\) | |||||||
\(744\) | −1.68842 | − | 2.92442i | −0.0619004 | − | 0.107215i | ||||
\(745\) | 20.6884 | − | 35.8334i | 0.757965 | − | 1.31283i | ||||
\(746\) | 11.5630 | − | 20.0277i | 0.423351 | − | 0.733266i | ||||
\(747\) | 1.07462 | + | 1.86130i | 0.0393184 | + | 0.0681015i | ||||
\(748\) | −2.37683 | −0.0869056 | ||||||||
\(749\) | −25.7877 | − | 12.9272i | −0.942261 | − | 0.472348i | ||||
\(750\) | −42.0942 | −1.53706 | ||||||||
\(751\) | 5.35358 | + | 9.27268i | 0.195355 | + | 0.338365i | 0.947017 | − | 0.321184i | \(-0.104081\pi\) |
−0.751662 | + | 0.659549i | \(0.770747\pi\) | |||||||
\(752\) | 2.05362 | − | 3.55698i | 0.0748880 | − | 0.129710i | ||||
\(753\) | −4.30504 | + | 7.45655i | −0.156884 | + | 0.271732i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −59.9551 | −2.18199 | ||||||||
\(756\) | −0.155792 | − | 2.64116i | −0.00566608 | − | 0.0960581i | ||||
\(757\) | −17.2797 | −0.628043 | −0.314022 | − | 0.949416i | \(-0.601676\pi\) | ||||
−0.314022 | + | 0.949416i | \(0.601676\pi\) | |||||||
\(758\) | 3.38621 | + | 5.86508i | 0.122993 | + | 0.213029i | ||||
\(759\) | −2.36521 | + | 4.09666i | −0.0858516 | + | 0.148699i | ||||
\(760\) | 8.14925 | − | 14.1149i | 0.295604 | − | 0.512002i | ||||
\(761\) | 16.3544 | + | 28.3266i | 0.592846 | + | 1.02684i | 0.993847 | + | 0.110761i | \(0.0353289\pi\) |
−0.401001 | + | 0.916077i | \(0.631338\pi\) | |||||||
\(762\) | −0.730416 | −0.0264602 | ||||||||
\(763\) | −1.83767 | − | 31.1542i | −0.0665280 | − | 1.12786i | ||||
\(764\) | −16.8377 | −0.609165 | ||||||||
\(765\) | −5.25142 | − | 9.09572i | −0.189865 | − | 0.328856i | ||||
\(766\) | −12.6819 | + | 21.9656i | −0.458215 | + | 0.793651i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0.500000 | + | 0.866025i | 0.0180422 | + | 0.0312500i | ||||
\(769\) | 12.2145 | 0.440466 | 0.220233 | − | 0.975447i | \(-0.429318\pi\) | ||||
0.220233 | + | 0.975447i | \(0.429318\pi\) | |||||||
\(770\) | 10.4515 | + | 5.23924i | 0.376644 | + | 0.188809i | ||||
\(771\) | −0.837665 | −0.0301678 | ||||||||
\(772\) | −2.73042 | − | 4.72922i | −0.0982698 | − | 0.170208i | ||||
\(773\) | −0.102167 | + | 0.176958i | −0.00367468 | + | 0.00636474i | −0.867857 | − | 0.496814i | \(-0.834503\pi\) |
0.864182 | + | 0.503179i | \(0.167836\pi\) | |||||||
\(774\) | −1.53263 | + | 2.65458i | −0.0550891 | + | 0.0954171i | ||||
\(775\) | 24.5261 | + | 42.4804i | 0.881003 | + | 1.52594i | ||||
\(776\) | 7.00000 | 0.251285 | ||||||||
\(777\) | −16.9869 | + | 11.1905i | −0.609402 | + | 0.401457i | ||||
\(778\) | 25.2565 | 0.905489 | ||||||||
\(779\) | 22.4057 | + | 38.8079i | 0.802769 | + | 1.39044i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.467375 | − | 0.809517i | 0.0167240 | − | 0.0289668i | ||||
\(782\) | −5.62171 | − | 9.73708i | −0.201032 | − | 0.348197i | ||||
\(783\) | 6.52608 | 0.233223 | ||||||||
\(784\) | −6.95146 | + | 0.822941i | −0.248266 | + | 0.0293908i | ||||
\(785\) | −82.8115 | −2.95567 | ||||||||
\(786\) | 3.68842 | + | 6.38853i | 0.131561 | + | 0.227871i | ||||
\(787\) | −12.7790 | + | 22.1338i | −0.455521 | + | 0.788985i | −0.998718 | − | 0.0506202i | \(-0.983880\pi\) |
0.543197 | + | 0.839605i | \(0.317214\pi\) | |||||||
\(788\) | 4.84421 | − | 8.39042i | 0.172568 | − | 0.298896i | ||||
\(789\) | 5.41883 | + | 9.38569i | 0.192916 | + | 0.334140i | ||||
\(790\) | −1.85075 | −0.0658468 | ||||||||
\(791\) | 11.8797 | − | 7.82598i | 0.422392 | − | 0.278260i | ||||
\(792\) | −1.00000 | −0.0355335 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 6.73696 | − | 11.6688i | 0.239086 | − | 0.414109i | ||||
\(795\) | 17.6753 | − | 30.6146i | 0.626879 | − | 1.08579i | ||||
\(796\) | −10.1492 | − | 17.5790i | −0.359731 | − | 0.623072i | ||||
\(797\) | 30.0477 | 1.06434 | 0.532171 | − | 0.846637i | \(-0.321376\pi\) | ||||
0.532171 | + | 0.846637i | \(0.321376\pi\) | |||||||
\(798\) | −8.72387 | − | 4.37321i | −0.308822 | − | 0.154810i | ||||
\(799\) | −9.76225 | −0.345364 | ||||||||
\(800\) | −7.26304 | − | 12.5800i | −0.256787 | − | 0.444769i | ||||
\(801\) | 6.41883 | − | 11.1177i | 0.226798 | − | 0.392826i | ||||
\(802\) | −16.9449 | + | 29.3495i | −0.598346 | + | 1.03637i | ||||
\(803\) | −3.73042 | − | 6.46127i | −0.131644 | − | 0.228013i | ||||
\(804\) | −10.1492 | −0.357936 | ||||||||
\(805\) | 3.25650 | + | 55.2080i | 0.114776 | + | 1.94582i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.93983 | + | 15.4842i | 0.314697 | + | 0.545071i | ||||
\(808\) | 7.68187 | − | 13.3054i | 0.270247 | − | 0.468082i | ||||
\(809\) | −1.17171 | + | 2.02946i | −0.0411951 | + | 0.0713520i | −0.885888 | − | 0.463900i | \(-0.846450\pi\) |
0.844693 | + | 0.535252i | \(0.179783\pi\) | |||||||
\(810\) | −2.20942 | − | 3.82682i | −0.0776310 | − | 0.134461i | ||||
\(811\) | −11.8695 | −0.416794 | −0.208397 | − | 0.978044i | \(-0.566825\pi\) | ||||
−0.208397 | + | 0.978044i | \(0.566825\pi\) | |||||||
\(812\) | −1.01671 | − | 17.2364i | −0.0356795 | − | 0.604880i | ||||
\(813\) | 8.83767 | 0.309950 | ||||||||
\(814\) | 3.84421 | + | 6.65836i | 0.134739 | + | 0.233376i | ||||
\(815\) | −41.4761 | + | 71.8387i | −1.45284 | + | 2.51640i | ||||
\(816\) | 1.18842 | − | 2.05840i | 0.0416029 | − | 0.0720584i | ||||
\(817\) | 5.65296 | + | 9.79122i | 0.197772 | + | 0.342551i | ||||
\(818\) | −4.21450 | −0.147357 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 53.6855 | 1.87478 | ||||||||
\(821\) | 18.7406 | + | 32.4596i | 0.654051 | + | 1.13285i | 0.982131 | + | 0.188199i | \(0.0602651\pi\) |
−0.328080 | + | 0.944650i | \(0.606402\pi\) | |||||||
\(822\) | −4.41883 | + | 7.65364i | −0.154124 | + | 0.266951i | ||||
\(823\) | −0.646418 | + | 1.11963i | −0.0225327 | + | 0.0390278i | −0.877072 | − | 0.480359i | \(-0.840506\pi\) |
0.854539 | + | 0.519387i | \(0.173840\pi\) | |||||||
\(824\) | 1.31158 | + | 2.27173i | 0.0456912 | + | 0.0791394i | ||||
\(825\) | 14.5261 | 0.505733 | ||||||||
\(826\) | −27.6753 | + | 18.2317i | −0.962948 | + | 0.634362i | ||||
\(827\) | 43.3319 | 1.50680 | 0.753399 | − | 0.657563i | \(-0.228413\pi\) | ||||
0.753399 | + | 0.657563i | \(0.228413\pi\) | |||||||
\(828\) | −2.36521 | − | 4.09666i | −0.0821967 | − | 0.142369i | ||||
\(829\) | −20.0587 | + | 34.7427i | −0.696668 | + | 1.20666i | 0.272948 | + | 0.962029i | \(0.412001\pi\) |
−0.969615 | + | 0.244635i | \(0.921332\pi\) | |||||||
\(830\) | 4.74858 | − | 8.22479i | 0.164826 | − | 0.285487i | ||||
\(831\) | −8.00000 | − | 13.8564i | −0.277517 | − | 0.480673i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.95517 | + | 13.3309i | 0.344926 | + | 0.461887i | ||||
\(834\) | −1.47392 | −0.0510376 | ||||||||
\(835\) | 52.7826 | + | 91.4221i | 1.82662 | + | 3.16379i | ||||
\(836\) | −1.84421 | + | 3.19426i | −0.0637833 | + | 0.110476i | ||||
\(837\) | −1.68842 | + | 2.92442i | −0.0583602 | + | 0.101083i | ||||
\(838\) | 11.1558 | + | 19.3224i | 0.385370 | + | 0.667481i | ||||
\(839\) | 54.6912 | 1.88815 | 0.944074 | − | 0.329733i | \(-0.106959\pi\) | ||||
0.944074 | + | 0.329733i | \(0.106959\pi\) | |||||||
\(840\) | −9.76304 | + | 6.43161i | −0.336857 | + | 0.221912i | ||||
\(841\) | 13.5897 | 0.468612 | ||||||||
\(842\) | −9.15579 | − | 15.8583i | −0.315529 | − | 0.546513i | ||||
\(843\) | −7.96083 | + | 13.7886i | −0.274186 | + | 0.474903i | ||||
\(844\) | −11.2565 | + | 19.4968i | −0.387465 | + | 0.671108i | ||||
\(845\) | 28.7224 | + | 49.7487i | 0.988081 | + | 1.71141i | ||||
\(846\) | −4.10725 | −0.141210 | ||||||||
\(847\) | −2.36521 | − | 1.18566i | −0.0812695 | − | 0.0407398i | ||||
\(848\) | 8.00000 | 0.274721 | ||||||||
\(849\) | −9.04200 | − | 15.6612i | −0.310321 | − | 0.537491i | ||||
\(850\) | −17.2630 | + | 29.9005i | −0.592117 | + | 1.02558i | ||||
\(851\) | −18.1847 | + | 31.4968i | −0.623364 | + | 1.07970i | ||||
\(852\) | 0.467375 | + | 0.809517i | 0.0160120 | + | 0.0277336i | ||||
\(853\) | −20.8275 | −0.713120 | −0.356560 | − | 0.934272i | \(-0.616050\pi\) | ||||
−0.356560 | + | 0.934272i | \(0.616050\pi\) | |||||||
\(854\) | 0.591333 | + | 10.0250i | 0.0202350 | + | 0.343047i | ||||
\(855\) | −16.2985 | −0.557397 | ||||||||
\(856\) | −5.45146 | − | 9.44220i | −0.186327 | − | 0.322728i | ||||
\(857\) | 18.4217 | − | 31.9073i | 0.629272 | − | 1.08993i | −0.358426 | − | 0.933558i | \(-0.616686\pi\) |
0.987698 | − | 0.156373i | \(-0.0499802\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.2891 | − | 33.4097i | −0.658136 | − | 1.13993i | −0.981098 | − | 0.193513i | \(-0.938012\pi\) |
0.322961 | − | 0.946412i | \(-0.395322\pi\) | |||||||
\(860\) | 13.5448 | 0.461875 | ||||||||
\(861\) | −1.89275 | − | 32.0881i | −0.0645048 | − | 1.09356i | ||||
\(862\) | −28.8377 | −0.982215 | ||||||||
\(863\) | 8.62825 | + | 14.9446i | 0.293709 | + | 0.508719i | 0.974684 | − | 0.223588i | \(-0.0717770\pi\) |
−0.680975 | + | 0.732307i | \(0.738444\pi\) | |||||||
\(864\) | 0.500000 | − | 0.866025i | 0.0170103 | − | 0.0294628i | ||||
\(865\) | −25.1362 | + | 43.5371i | −0.854655 | + | 1.48031i | ||||
\(866\) | −3.81158 | − | 6.60186i | −0.129523 | − | 0.224340i | ||||
\(867\) | 11.3507 | 0.385489 | ||||||||
\(868\) | 7.98691 | + | 4.00378i | 0.271094 | + | 0.135897i | ||||
\(869\) | 0.418833 | 0.0142079 | ||||||||
\(870\) | −14.4188 | − | 24.9742i | −0.488844 | − | 0.846703i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 5.89783 | − | 10.2153i | 0.199726 | − | 0.345935i | ||||
\(873\) | −3.50000 | − | 6.06218i | −0.118457 | − | 0.205174i | ||||
\(874\) | −17.4477 | −0.590179 | ||||||||
\(875\) | 93.0035 | − | 61.2680i | 3.14409 | − | 2.07124i | ||||
\(876\) | 7.46083 | 0.252078 | ||||||||
\(877\) | −0.125418 | − | 0.217231i | −0.00423508 | − | 0.00733537i | 0.863900 | − | 0.503663i | \(-0.168015\pi\) |
−0.868135 | + | 0.496328i | \(0.834681\pi\) | |||||||
\(878\) | 16.6870 | − | 28.9027i | 0.563158 | − | 0.975417i | ||||
\(879\) | 12.5746 | − | 21.7799i | 0.424132 | − | 0.734617i | ||||
\(880\) | 2.20942 | + | 3.82682i | 0.0744794 | + | 0.129002i | ||||
\(881\) | 16.2985 | 0.549110 | 0.274555 | − | 0.961571i | \(-0.411469\pi\) | ||||
0.274555 | + | 0.961571i | \(0.411469\pi\) | |||||||
\(882\) | 4.18842 | + | 5.60867i | 0.141031 | + | 0.188854i | ||||
\(883\) | −33.9551 | −1.14268 | −0.571340 | − | 0.820714i | \(-0.693576\pi\) | ||||
−0.571340 | + | 0.820714i | \(0.693576\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −27.6753 | + | 47.9351i | −0.930296 | + | 1.61132i | ||||
\(886\) | 2.42538 | − | 4.20087i | 0.0814821 | − | 0.141131i | ||||
\(887\) | −9.73042 | − | 16.8536i | −0.326715 | − | 0.565888i | 0.655143 | − | 0.755505i | \(-0.272609\pi\) |
−0.981858 | + | 0.189618i | \(0.939275\pi\) | |||||||
\(888\) | −7.68842 | −0.258006 | ||||||||
\(889\) | 1.61379 | − | 1.06312i | 0.0541249 | − | 0.0356559i | ||||
\(890\) | −56.7275 | −1.90151 | ||||||||
\(891\) | 0.500000 | + | 0.866025i | 0.0167506 | + | 0.0290129i | ||||
\(892\) | 3.73042 | − | 6.46127i | 0.124904 | − | 0.216339i | ||||
\(893\) | −7.57462 | + | 13.1196i | −0.253475 | + | 0.439032i | ||||
\(894\) | −4.68187 | − | 8.10924i | −0.156585 | − | 0.271214i | ||||
\(895\) | 108.748 | 3.63504 | ||||||||
\(896\) | −2.36521 | − | 1.18566i | −0.0790161 | − | 0.0396101i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −7.17250 | − | 12.4231i | −0.239349 | − | 0.414565i | ||||
\(899\) | −11.0187 | + | 19.0850i | −0.367496 | + | 0.636521i | ||||
\(900\) | −7.26304 | + | 12.5800i | −0.242101 | + | 0.419332i | ||||
\(901\) | −9.50733 | − | 16.4672i | −0.316735 | − | 0.548602i | ||||
\(902\) | −12.1492 | −0.404526 | ||||||||
\(903\) | −0.477540 | − | 8.09582i | −0.0158915 | − | 0.269412i | ||||
\(904\) | 5.37683 | 0.178831 | ||||||||
\(905\) | −38.5782 | − | 66.8195i | −1.28238 | − | 2.22115i | ||||
\(906\) | −6.78404 | + | 11.7503i | −0.225385 | + | 0.390378i | ||||
\(907\) | −0.386207 | + | 0.668931i | −0.0128238 | + | 0.0222115i | −0.872366 | − | 0.488853i | \(-0.837415\pi\) |
0.859542 | + | 0.511065i | \(0.170749\pi\) | |||||||
\(908\) | 1.38621 | + | 2.40098i | 0.0460029 | + | 0.0796794i | ||||
\(909\) | −15.3637 | −0.509583 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.94491 | −0.296358 | −0.148179 | − | 0.988961i | \(-0.547341\pi\) | ||||
−0.148179 | + | 0.988961i | \(0.547341\pi\) | |||||||
\(912\) | −1.84421 | − | 3.19426i | −0.0610678 | − | 0.105773i | ||||
\(913\) | −1.07462 | + | 1.86130i | −0.0355649 | + | 0.0616002i | ||||
\(914\) | 12.5913 | − | 21.8088i | 0.416484 | − | 0.721372i | ||||
\(915\) | 8.38621 | + | 14.5253i | 0.277239 | + | 0.480193i | ||||
\(916\) | −2.53917 | −0.0838965 | ||||||||
\(917\) | −17.4477 | − | 8.74642i | −0.576175 | − | 0.288832i | ||||
\(918\) | −2.37683 | −0.0784472 | ||||||||
\(919\) | −29.4406 | − | 50.9927i | −0.971157 | − | 1.68209i | −0.692076 | − | 0.721825i | \(-0.743304\pi\) |
−0.279081 | − | 0.960268i | \(-0.590030\pi\) | |||||||
\(920\) | −10.4515 | + | 18.1025i | −0.344574 | + | 0.596820i | ||||
\(921\) | −1.93475 | + | 3.35108i | −0.0637522 | + | 0.110422i | ||||
\(922\) | −6.50937 | − | 11.2746i | −0.214375 | − | 0.371308i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 2.20942 | − | 1.45550i | 0.0726845 | − | 0.0478824i | ||||
\(925\) | 111.683 | 3.67210 | ||||||||
\(926\) | 7.10725 | + | 12.3101i | 0.233559 | + | 0.404536i | ||||
\(927\) | 1.31158 | − | 2.27173i | 0.0430780 | − | 0.0746134i | ||||
\(928\) | 3.26304 | − | 5.65175i | 0.107115 | − | 0.185528i | ||||
\(929\) | 11.2696 | + | 19.5195i | 0.369743 | + | 0.640414i | 0.989525 | − | 0.144360i | \(-0.0461124\pi\) |
−0.619782 | + | 0.784774i | \(0.712779\pi\) | |||||||
\(930\) | 14.9217 | 0.489301 | ||||||||
\(931\) | 25.6399 | − | 3.03535i | 0.840313 | − | 0.0994796i | ||||
\(932\) | −24.0522 | −0.787855 | ||||||||
\(933\) | −6.78404 | − | 11.7503i | −0.222100 | − | 0.384688i | ||||
\(934\) | 1.19779 | − | 2.07463i | 0.0391929 | − | 0.0678841i | ||||
\(935\) | 5.25142 | − | 9.09572i | 0.171740 | − | 0.297462i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.9478 | −0.422987 | −0.211494 | − | 0.977379i | \(-0.567833\pi\) | ||||
−0.211494 | + | 0.977379i | \(0.567833\pi\) | |||||||
\(938\) | 22.4239 | − | 14.7722i | 0.732167 | − | 0.482330i | ||||
\(939\) | −2.52608 | −0.0824356 | ||||||||
\(940\) | 9.07462 | + | 15.7177i | 0.295982 | + | 0.512655i | ||||
\(941\) | −24.4123 | + | 42.2833i | −0.795818 | + | 1.37840i | 0.126501 | + | 0.991967i | \(0.459625\pi\) |
−0.922319 | + | 0.386431i | \(0.873708\pi\) | |||||||
\(942\) | −9.37029 | + | 16.2298i | −0.305301 | + | 0.528796i | ||||
\(943\) | −28.7355 | − | 49.7713i | −0.935757 | − | 1.62078i | ||||
\(944\) | −12.5261 | −0.407689 | ||||||||
\(945\) | 10.4515 | + | 5.23924i | 0.339986 | + | 0.170432i | ||||
\(946\) | −3.06525 | −0.0996599 | ||||||||
\(947\) | 15.5615 | + | 26.9534i | 0.505682 | + | 0.875867i | 0.999978 | + | 0.00657353i | \(0.00209243\pi\) |
−0.494296 | + | 0.869293i | \(0.664574\pi\) | |||||||
\(948\) | −0.209416 | + | 0.362720i | −0.00680153 | + | 0.0117806i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 26.7891 | + | 46.4001i | 0.869154 | + | 1.50542i | ||||
\(951\) | 20.0102 | 0.648874 | ||||||||
\(952\) | 0.370291 | + | 6.27760i | 0.0120012 | + | 0.203458i | ||||
\(953\) | 16.2797 | 0.527353 | 0.263676 | − | 0.964611i | \(-0.415065\pi\) | ||||
0.263676 | + | 0.964611i | \(0.415065\pi\) | |||||||
\(954\) | −4.00000 | − | 6.92820i | −0.129505 | − | 0.224309i | ||||
\(955\) | 37.2014 | − | 64.4347i | 1.20381 | − | 2.08506i | ||||
\(956\) | −3.79567 | + | 6.57429i | −0.122761 | + | 0.212628i | ||||
\(957\) | 3.26304 | + | 5.65175i | 0.105479 | + | 0.182695i | ||||
\(958\) | 10.8377 | 0.350149 | ||||||||
\(959\) | −1.37683 | − | 23.3417i | −0.0444603 | − | 0.753743i | ||||
\(960\) | −4.41883 | −0.142617 | ||||||||
\(961\) | 9.79850 | + | 16.9715i | 0.316081 | + | 0.547468i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.45146 | + | 9.44220i | −0.175671 | + | 0.304271i | ||||
\(964\) | −8.14925 | − | 14.1149i | −0.262470 | − | 0.454611i | ||||
\(965\) | 24.1305 | 0.776788 | ||||||||
\(966\) | 11.1884 | + | 5.60867i | 0.359981 | + | 0.180456i | ||||
\(967\) | 3.91308 | 0.125836 | 0.0629181 | − | 0.998019i | \(-0.479959\pi\) | ||||
0.0629181 | + | 0.998019i | \(0.479959\pi\) | |||||||
\(968\) | −0.500000 | − | 0.866025i | −0.0160706 | − | 0.0278351i | ||||
\(969\) | −4.38338 | + | 7.59223i | −0.140814 | + | 0.243898i | ||||
\(970\) | −15.4659 | + | 26.7877i | −0.496581 | + | 0.860103i | ||||
\(971\) | −19.6566 | − | 34.0462i | −0.630810 | − | 1.09259i | −0.987386 | − | 0.158329i | \(-0.949389\pi\) |
0.356577 | − | 0.934266i | \(-0.383944\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 3.25650 | − | 2.14529i | 0.104399 | − | 0.0687747i | ||||
\(974\) | −34.6435 | −1.11005 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.89783 | + | 3.28714i | −0.0607482 | + | 0.105219i | ||||
\(977\) | 11.6753 | − | 20.2223i | 0.373527 | − | 0.646968i | −0.616578 | − | 0.787293i | \(-0.711482\pi\) |
0.990105 | + | 0.140326i | \(0.0448150\pi\) | |||||||
\(978\) | 9.38621 | + | 16.2574i | 0.300138 | + | 0.519854i | ||||
\(979\) | 12.8377 | 0.410294 | ||||||||
\(980\) | 12.2094 | − | 28.4202i | 0.390015 | − | 0.907850i | ||||
\(981\) | −11.7957 | −0.376607 | ||||||||
\(982\) | −19.0746 | − | 33.0382i | −0.608696 | − | 1.05429i | ||||
\(983\) | 2.25796 | − | 3.91090i | 0.0720177 | − | 0.124738i | −0.827768 | − | 0.561071i | \(-0.810390\pi\) |
0.899785 | + | 0.436333i | \(0.143723\pi\) | |||||||
\(984\) | 6.07462 | − | 10.5216i | 0.193652 | − | 0.335415i | ||||
\(985\) | 21.4057 | + | 37.0758i | 0.682044 | + | 1.18133i | ||||
\(986\) | −15.5114 | −0.493984 | ||||||||
\(987\) | 9.07462 | − | 5.97810i | 0.288848 | − | 0.190285i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.24995 | − | 12.5573i | −0.230535 | − | 0.399299i | ||||
\(990\) | 2.20942 | − | 3.82682i | 0.0702199 | − | 0.121624i | ||||
\(991\) | −29.9637 | + | 51.8986i | −0.951827 | + | 1.64861i | −0.210360 | + | 0.977624i | \(0.567463\pi\) |
−0.741467 | + | 0.670989i | \(0.765870\pi\) | |||||||
\(992\) | 1.68842 | + | 2.92442i | 0.0536073 | + | 0.0928505i | ||||
\(993\) | 16.1492 | 0.512481 | ||||||||
\(994\) | −2.21088 | − | 1.10830i | −0.0701247 | − | 0.0351530i | ||||
\(995\) | 89.6957 | 2.84354 | ||||||||
\(996\) | −1.07462 | − | 1.86130i | −0.0340508 | − | 0.0589777i | ||||
\(997\) | 10.7537 | − | 18.6259i | 0.340572 | − | 0.589888i | −0.643967 | − | 0.765053i | \(-0.722713\pi\) |
0.984539 | + | 0.175165i | \(0.0560459\pi\) | |||||||
\(998\) | 0.311583 | − | 0.539678i | 0.00986299 | − | 0.0170832i | ||||
\(999\) | 3.84421 | + | 6.65836i | 0.121625 | + | 0.210661i |
(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.67.1 | ✓ | 6 | |
3.2 | odd | 2 | 1386.2.k.v.991.3 | 6 | |||
7.2 | even | 3 | inner | 462.2.i.g.331.1 | yes | 6 | |
7.3 | odd | 6 | 3234.2.a.bh.1.1 | 3 | |||
7.4 | even | 3 | 3234.2.a.bf.1.3 | 3 | |||
21.2 | odd | 6 | 1386.2.k.v.793.3 | 6 | |||
21.11 | odd | 6 | 9702.2.a.dv.1.1 | 3 | |||
21.17 | even | 6 | 9702.2.a.dw.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.i.g.67.1 | ✓ | 6 | 1.1 | even | 1 | trivial | |
462.2.i.g.331.1 | yes | 6 | 7.2 | even | 3 | inner | |
1386.2.k.v.793.3 | 6 | 21.2 | odd | 6 | |||
1386.2.k.v.991.3 | 6 | 3.2 | odd | 2 | |||
3234.2.a.bf.1.3 | 3 | 7.4 | even | 3 | |||
3234.2.a.bh.1.1 | 3 | 7.3 | odd | 6 | |||
9702.2.a.dv.1.1 | 3 | 21.11 | odd | 6 | |||
9702.2.a.dw.1.3 | 3 | 21.17 | even | 6 |