Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1386,2,Mod(793,1386)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1386, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1386.793");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1386.k (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: | \(11.0672657201\) |
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: | no (minimal twist has level 462) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 991.3 | ||
Root | \(0.500000 + 3.23735i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1386.991 |
Dual form | 1386.2.k.v.793.3 |
$q$-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 \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(1135\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | 0 | ||||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 2.20942 | + | 3.82682i | 0.988081 | + | 1.71141i | 0.627352 | + | 0.778736i | \(0.284139\pi\) |
0.360729 | + | 0.932671i | \(0.382528\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.20942 | − | 1.45550i | 0.835081 | − | 0.550127i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.20942 | + | 3.82682i | −0.698679 | + | 1.21015i | ||||
\(11\) | −0.500000 | + | 0.866025i | −0.150756 | + | 0.261116i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | 2.36521 | + | 1.18566i | 0.632128 | + | 0.316881i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 1.18842 | − | 2.05840i | 0.288233 | − | 0.499235i | −0.685155 | − | 0.728398i | \(-0.740265\pi\) |
0.973388 | + | 0.229163i | \(0.0735988\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 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 | 0 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | 2.36521 | + | 4.09666i | 0.493180 | + | 0.854213i | 0.999969 | − | 0.00785730i | \(-0.00250108\pi\) |
−0.506789 | + | 0.862070i | \(0.669168\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −7.26304 | + | 12.5800i | −1.45261 | + | 2.51599i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.155792 | + | 2.64116i | 0.0294418 | + | 0.499132i | ||||
\(29\) | 6.52608 | 1.21186 | 0.605932 | − | 0.795517i | \(-0.292801\pi\) | ||||
0.605932 | + | 0.795517i | \(0.292801\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 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 | 0 | ||||||||
\(34\) | 2.37683 | 0.407624 | ||||||||
\(35\) | 10.4515 | + | 5.23924i | 1.76662 | + | 0.885593i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −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 | \(-0.897597\pi\) | ||||
−0.948697 | + | 0.316187i | \(0.897597\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 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 | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.36521 | + | 4.09666i | −0.348731 | + | 0.604020i | ||||
\(47\) | −2.05362 | − | 3.55698i | −0.299552 | − | 0.518839i | 0.676482 | − | 0.736460i | \(-0.263504\pi\) |
−0.976033 | + | 0.217620i | \(0.930171\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.76304 | − | 6.43161i | 0.394720 | − | 0.918801i | ||||
\(50\) | −14.5261 | −2.05430 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.00000 | − | 6.92820i | 0.549442 | − | 0.951662i | −0.448871 | − | 0.893597i | \(-0.648174\pi\) |
0.998313 | − | 0.0580651i | \(-0.0184931\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.41883 | −0.595835 | ||||||||
\(56\) | −2.20942 | + | 1.45550i | −0.295246 | + | 0.194499i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.26304 | + | 5.65175i | 0.428458 | + | 0.742112i | ||||
\(59\) | −6.26304 | + | 10.8479i | −0.815379 | + | 1.41228i | 0.0936773 | + | 0.995603i | \(0.470138\pi\) |
−0.909056 | + | 0.416674i | \(0.863196\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −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 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −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 | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.688417 | + | 11.6708i | 0.0822816 | + | 1.39493i | ||||
\(71\) | −0.934749 | −0.110934 | −0.0554672 | − | 0.998461i | \(-0.517665\pi\) | ||||
−0.0554672 | + | 0.998461i | \(0.517665\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 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 | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −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 | 0 | ||||||||
\(82\) | −6.07462 | − | 10.5216i | −0.670830 | − | 1.16191i | ||||
\(83\) | 2.14925 | 0.235911 | 0.117955 | − | 0.993019i | \(-0.462366\pi\) | ||||
0.117955 | + | 0.993019i | \(0.462366\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.5028 | 1.13919 | ||||||||
\(86\) | 1.53263 | + | 2.65458i | 0.165267 | + | 0.286251i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.500000 | − | 0.866025i | 0.0533002 | − | 0.0923186i | ||||
\(89\) | −6.41883 | − | 11.1177i | −0.680395 | − | 1.17848i | −0.974860 | − | 0.222816i | \(-0.928475\pi\) |
0.294466 | − | 0.955662i | \(-0.404858\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.73042 | −0.493180 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.05362 | − | 3.55698i | 0.211815 | − | 0.366875i | ||||
\(95\) | −8.14925 | + | 14.1149i | −0.836095 | + | 1.44816i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 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 | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −7.26304 | − | 12.5800i | −0.726304 | − | 1.25800i | ||||
\(101\) | −7.68187 | + | 13.3054i | −0.764375 | + | 1.32394i | 0.176201 | + | 0.984354i | \(0.443619\pi\) |
−0.940576 | + | 0.339582i | \(0.889714\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 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 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.00000 | 0.777029 | ||||||||
\(107\) | 5.45146 | + | 9.44220i | 0.527012 | + | 0.912812i | 0.999504 | + | 0.0314773i | \(0.0100212\pi\) |
−0.472492 | + | 0.881335i | \(0.656645\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 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 | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.36521 | − | 1.18566i | −0.223491 | − | 0.112034i | ||||
\(113\) | −5.37683 | −0.505810 | −0.252905 | − | 0.967491i | \(-0.581386\pi\) | ||||
−0.252905 | + | 0.967491i | \(0.581386\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −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 | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.500000 | − | 0.866025i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | 1.89783 | − | 3.28714i | 0.171822 | − | 0.297604i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.68842 | + | 2.92442i | 0.151624 | + | 0.262621i | ||||
\(125\) | −42.0942 | −3.76502 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 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 | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.68842 | + | 6.38853i | 0.322258 | + | 0.558168i | 0.980954 | − | 0.194242i | \(-0.0622246\pi\) |
−0.658695 | + | 0.752410i | \(0.728891\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.72387 | + | 4.37321i | 0.756456 | + | 0.379206i | ||||
\(134\) | −10.1492 | −0.876762 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.18842 | + | 2.05840i | −0.101906 | + | 0.176506i | ||||
\(137\) | −4.41883 | + | 7.65364i | −0.377526 | + | 0.653895i | −0.990702 | − | 0.136052i | \(-0.956559\pi\) |
0.613175 | + | 0.789947i | \(0.289892\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 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 | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.467375 | − | 0.809517i | −0.0392212 | − | 0.0679331i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 14.4188 | + | 24.9742i | 1.19742 | + | 2.07399i | ||||
\(146\) | 7.46083 | 0.617463 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.68842 | 0.631984 | ||||||||
\(149\) | −4.68187 | − | 8.10924i | −0.383554 | − | 0.664335i | 0.608013 | − | 0.793927i | \(-0.291967\pi\) |
−0.991567 | + | 0.129592i | \(0.958633\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 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 | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −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 | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.41883 | 0.349339 | ||||||||
\(161\) | 11.1884 | + | 5.60867i | 0.881771 | + | 0.442025i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −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 | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.07462 | + | 1.86130i | 0.0834070 | + | 0.144465i | ||||
\(167\) | 23.8898 | 1.84865 | 0.924325 | − | 0.381606i | \(-0.124629\pi\) | ||||
0.924325 | + | 0.381606i | \(0.124629\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13.0000 | −1.00000 | ||||||||
\(170\) | 5.25142 | + | 9.09572i | 0.402765 | + | 0.697610i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.53263 | + | 2.65458i | −0.116862 | + | 0.202410i | ||||
\(173\) | 5.68842 | + | 9.85263i | 0.432482 | + | 0.749081i | 0.997086 | − | 0.0762805i | \(-0.0243045\pi\) |
−0.564604 | + | 0.825362i | \(0.690971\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.26304 | + | 38.3657i | 0.171070 | + | 2.90018i | ||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.41883 | − | 11.1177i | 0.481112 | − | 0.833310i | ||||
\(179\) | 12.3050 | − | 21.3130i | 0.919722 | − | 1.59301i | 0.119885 | − | 0.992788i | \(-0.461747\pi\) |
0.799837 | − | 0.600217i | \(-0.204919\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.4608 | 1.29785 | 0.648927 | − | 0.760851i | \(-0.275218\pi\) | ||||
0.648927 | + | 0.760851i | \(0.275218\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.36521 | − | 4.09666i | −0.174365 | − | 0.302010i | ||||
\(185\) | 16.9869 | − | 29.4222i | 1.24890 | − | 2.16316i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.18842 | + | 2.05840i | 0.0869056 | + | 0.150525i | ||||
\(188\) | 4.10725 | 0.299552 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −16.2985 | −1.18242 | ||||||||
\(191\) | −8.41883 | − | 14.5818i | −0.609165 | − | 1.05511i | −0.991378 | − | 0.131031i | \(-0.958171\pi\) |
0.382213 | − | 0.924074i | \(-0.375162\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −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 | \(-0.387833\pi\) | ||||
0.345136 | + | 0.938553i | \(0.387833\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −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 | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −15.3637 | −1.08099 | ||||||||
\(203\) | 14.4188 | − | 9.49871i | 1.01200 | − | 0.666679i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −26.8427 | − | 46.4930i | −1.87478 | − | 3.24721i | ||||
\(206\) | −1.31158 | + | 2.27173i | −0.0913823 | + | 0.158279i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.68842 | −0.255133 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 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 | 0 | ||||||||
\(214\) | −5.45146 | + | 9.44220i | −0.372654 | + | 0.645456i | ||||
\(215\) | 6.77241 | + | 11.7302i | 0.461875 | + | 0.799991i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.526082 | − | 8.91876i | −0.0357128 | − | 0.605445i | ||||
\(218\) | 11.7957 | 0.798903 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.20942 | − | 3.82682i | 0.148959 | − | 0.258004i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −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 | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.68842 | − | 4.65647i | −0.178831 | − | 0.309744i | ||||
\(227\) | −1.38621 | + | 2.40098i | −0.0920058 | + | 0.159359i | −0.908355 | − | 0.418200i | \(-0.862661\pi\) |
0.816349 | + | 0.577559i | \(0.195995\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 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 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.52608 | −0.428458 | ||||||||
\(233\) | −12.0261 | − | 20.8298i | −0.787855 | − | 1.36460i | −0.927279 | − | 0.374372i | \(-0.877858\pi\) |
0.139424 | − | 0.990233i | \(-0.455475\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.07462 | − | 15.7177i | 0.591963 | − | 1.02531i | ||||
\(236\) | −6.26304 | − | 10.8479i | −0.407689 | − | 0.706138i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5.25142 | − | 3.45948i | 0.340399 | − | 0.224245i | ||||
\(239\) | −7.59133 | −0.491042 | −0.245521 | − | 0.969391i | \(-0.578959\pi\) | ||||
−0.245521 | + | 0.969391i | \(0.578959\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −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 | 0 | ||||||||
\(244\) | 3.79567 | 0.242993 | ||||||||
\(245\) | 30.7173 | − | 3.63644i | 1.96246 | − | 0.232324i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −1.68842 | + | 2.92442i | −0.107215 | + | 0.185701i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −21.0471 | − | 36.4546i | −1.33113 | − | 2.30559i | ||||
\(251\) | 8.61008 | 0.543463 | 0.271732 | − | 0.962373i | \(-0.412404\pi\) | ||||
0.271732 | + | 0.962373i | \(0.412404\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.73042 | −0.297399 | ||||||||
\(254\) | 0.365208 | + | 0.632559i | 0.0229152 | + | 0.0396903i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 0.418833 | + | 0.725439i | 0.0261261 | + | 0.0452517i | 0.878793 | − | 0.477203i | \(-0.158350\pi\) |
−0.852667 | + | 0.522455i | \(0.825016\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −18.1847 | − | 9.11585i | −1.12994 | − | 0.566432i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.68842 | + | 6.38853i | −0.227871 | + | 0.394684i | ||||
\(263\) | 5.41883 | − | 9.38569i | 0.334140 | − | 0.578747i | −0.649180 | − | 0.760635i | \(-0.724888\pi\) |
0.983319 | + | 0.181888i | \(0.0582210\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 35.3507 | 2.17157 | ||||||||
\(266\) | 0.574624 | + | 9.74170i | 0.0352325 | + | 0.597302i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.07462 | − | 8.78951i | −0.309982 | − | 0.536905i | ||||
\(269\) | 8.93983 | − | 15.4842i | 0.545071 | − | 0.944091i | −0.453531 | − | 0.891240i | \(-0.649836\pi\) |
0.998602 | − | 0.0528506i | \(-0.0168307\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 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 | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 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 | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −10.4515 | − | 5.23924i | −0.624594 | − | 0.313104i | ||||
\(281\) | 15.9217 | 0.949807 | 0.474903 | − | 0.880038i | \(-0.342483\pi\) | ||||
0.474903 | + | 0.880038i | \(0.342483\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 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 | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −26.8427 | + | 17.6832i | −1.58448 | + | 1.04381i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.67533 | + | 9.82996i | 0.333843 | + | 0.578233i | ||||
\(290\) | −14.4188 | + | 24.9742i | −0.846703 | + | 1.46653i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.73042 | + | 6.46127i | 0.218306 | + | 0.378117i | ||||
\(293\) | −25.1492 | −1.46923 | −0.734617 | − | 0.678482i | \(-0.762638\pi\) | ||||
−0.734617 | + | 0.678482i | \(0.762638\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −55.3507 | −3.22264 | ||||||||
\(296\) | 3.84421 | + | 6.65836i | 0.223440 | + | 0.387010i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.68187 | − | 8.10924i | 0.271214 | − | 0.469756i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.77241 | − | 4.46147i | 0.390355 | − | 0.257155i | ||||
\(302\) | 13.5681 | 0.780755 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.84421 | − | 3.19426i | 0.105773 | − | 0.183204i | ||||
\(305\) | 8.38621 | − | 14.5253i | 0.480193 | − | 0.831718i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −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 | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 7.46083 | + | 12.9225i | 0.423747 | + | 0.733951i | ||||
\(311\) | −6.78404 | + | 11.7503i | −0.384688 | + | 0.666299i | −0.991726 | − | 0.128374i | \(-0.959024\pi\) |
0.607038 | + | 0.794673i | \(0.292358\pi\) | |||||||
\(312\) | 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 | 0 | ||||||||
\(316\) | −0.418833 | −0.0235612 | ||||||||
\(317\) | −10.0051 | − | 17.3293i | −0.561941 | − | 0.973311i | −0.997327 | − | 0.0730670i | \(-0.976721\pi\) |
0.435386 | − | 0.900244i | \(-0.356612\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.26304 | + | 5.65175i | −0.182695 | + | 0.316437i | ||||
\(320\) | 2.20942 | + | 3.82682i | 0.123510 | + | 0.213926i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.736959 | + | 12.4938i | 0.0410691 | + | 0.696252i | ||||
\(323\) | 8.76675 | 0.487795 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 9.38621 | − | 16.2574i | 0.519854 | − | 0.900413i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 12.1492 | 0.670830 | ||||||||
\(329\) | −9.71450 | − | 4.86980i | −0.535578 | − | 0.268481i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 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 | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 11.9449 | + | 20.6892i | 0.653597 | + | 1.13206i | ||||
\(335\) | −44.8478 | −2.45030 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 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 | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −5.25142 | + | 9.09572i | −0.284798 | + | 0.493285i | ||||
\(341\) | 1.68842 | + | 2.92442i | 0.0914329 | + | 0.158366i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.25650 | − | 18.2317i | −0.175834 | − | 0.984420i | ||||
\(344\) | −3.06525 | −0.165267 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.68842 | + | 9.85263i | −0.305811 | + | 0.529681i | ||||
\(347\) | 7.82829 | − | 13.5590i | 0.420245 | − | 0.727885i | −0.575718 | − | 0.817648i | \(-0.695278\pi\) |
0.995963 | + | 0.0897628i | \(0.0286109\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −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 | −0.749508 | − | 0.661995i | \(-0.769710\pi\) |
0.948058 | + | 0.318096i | \(0.103043\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.06525 | − | 3.57712i | −0.109612 | − | 0.189854i | ||||
\(356\) | 12.8377 | 0.680395 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 24.6101 | 1.30068 | ||||||||
\(359\) | −5.62317 | − | 9.73961i | −0.296779 | − | 0.514037i | 0.678618 | − | 0.734492i | \(-0.262579\pi\) |
−0.975397 | + | 0.220455i | \(0.929246\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.69779 | − | 4.67271i | 0.141989 | − | 0.245932i | ||||
\(362\) | 8.73042 | + | 15.1215i | 0.458860 | + | 0.794770i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 32.9682 | 1.72563 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 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 | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 33.9738 | 1.76622 | ||||||||
\(371\) | −1.24633 | − | 21.1293i | −0.0647064 | − | 1.09698i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 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 | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.05362 | + | 3.55698i | 0.105908 | + | 0.183437i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −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 | 0 | ||||||||
\(382\) | 8.41883 | − | 14.5818i | 0.430745 | − | 0.746072i | ||||
\(383\) | 12.6819 | + | 21.9656i | 0.648013 | + | 1.12239i | 0.983597 | + | 0.180382i | \(0.0577333\pi\) |
−0.335583 | + | 0.942011i | \(0.608933\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.76304 | + | 6.43161i | −0.497571 | + | 0.327785i | ||||
\(386\) | −5.46083 | −0.277949 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.50000 | + | 6.06218i | −0.177686 | + | 0.307760i | ||||
\(389\) | 12.6282 | − | 21.8728i | 0.640278 | − | 1.10899i | −0.345093 | − | 0.938568i | \(-0.612153\pi\) |
0.985371 | − | 0.170425i | \(-0.0545140\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.2434 | 0.568604 | ||||||||
\(392\) | −2.76304 | + | 6.43161i | −0.139555 | + | 0.324845i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4.84421 | + | 8.39042i | 0.244048 | + | 0.422703i | ||||
\(395\) | −0.925376 | + | 1.60280i | −0.0465607 | + | 0.0806455i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 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 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 14.5261 | 0.726304 | ||||||||
\(401\) | 16.9449 | + | 29.3495i | 0.846189 | + | 1.46564i | 0.884585 | + | 0.466379i | \(0.154442\pi\) |
−0.0383962 | + | 0.999263i | \(0.512225\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −7.68187 | − | 13.3054i | −0.382188 | − | 0.661968i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 15.4355 | + | 7.73772i | 0.766053 | + | 0.384017i | ||||
\(407\) | 7.68842 | 0.381101 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 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 | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.62317 | −0.129234 | ||||||||
\(413\) | 1.95146 | + | 33.0834i | 0.0960250 | + | 1.62793i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.74858 | + | 8.22479i | 0.233099 | + | 0.403739i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.84421 | − | 3.19426i | −0.0902032 | − | 0.156236i | ||||
\(419\) | 22.3116 | 1.08999 | 0.544996 | − | 0.838439i | \(-0.316531\pi\) | ||||
0.544996 | + | 0.838439i | \(0.316531\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 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 | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.00000 | + | 6.92820i | −0.194257 | + | 0.336463i | ||||
\(425\) | 17.2630 | + | 29.9005i | 0.837380 | + | 1.45039i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −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 | \(0.411055\pi\) |
−0.970339 | + | 0.241750i | \(0.922279\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 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 | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.89783 | + | 10.2153i | 0.282455 | + | 0.489226i | ||||
\(437\) | −8.72387 | + | 15.1102i | −0.417319 | + | 0.722818i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 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 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.42538 | − | 4.20087i | −0.115233 | − | 0.199590i | 0.802640 | − | 0.596464i | \(-0.203428\pi\) |
−0.917873 | + | 0.396874i | \(0.870095\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 28.3637 | − | 49.1275i | 1.34457 | − | 2.32886i | ||||
\(446\) | −3.73042 | − | 6.46127i | −0.176640 | − | 0.305950i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.20942 | − | 1.45550i | 0.104385 | − | 0.0687659i | ||||
\(449\) | −14.3450 | −0.676982 | −0.338491 | − | 0.940970i | \(-0.609917\pi\) | ||||
−0.338491 | + | 0.940970i | \(0.609917\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.07462 | − | 10.5216i | 0.286043 | − | 0.495441i | ||||
\(452\) | 2.68842 | − | 4.65647i | 0.126452 | − | 0.219022i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.77241 | −0.130116 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 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 | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −10.4515 | − | 18.1025i | −0.487302 | − | 0.844031i | ||||
\(461\) | −13.0187 | −0.606344 | −0.303172 | − | 0.952936i | \(-0.598046\pi\) | ||||
−0.303172 | + | 0.952936i | \(0.598046\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −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 | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12.0261 | − | 20.8298i | 0.557098 | − | 0.964921i | ||||
\(467\) | −1.19779 | − | 2.07463i | −0.0554271 | − | 0.0960026i | 0.836981 | − | 0.547233i | \(-0.184319\pi\) |
−0.892408 | + | 0.451230i | \(0.850985\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.58117 | + | 26.8058i | 0.0730115 | + | 1.23778i | ||||
\(470\) | 18.1492 | 0.837162 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.26304 | − | 10.8479i | 0.288280 | − | 0.499315i | ||||
\(473\) | −1.53263 | + | 2.65458i | −0.0704702 | + | 0.122058i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −53.5782 | −2.45834 | ||||||||
\(476\) | 5.62171 | + | 2.81812i | 0.257670 | + | 0.129168i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.79567 | − | 6.57429i | −0.173610 | − | 0.300701i | ||||
\(479\) | 5.41883 | − | 9.38569i | 0.247593 | − | 0.428843i | −0.715265 | − | 0.698854i | \(-0.753694\pi\) |
0.962857 | + | 0.270010i | \(0.0870272\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −16.2985 | −0.742376 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 15.4659 | + | 26.7877i | 0.702271 | + | 1.21637i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 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 | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 18.5079 | + | 24.7838i | 0.836102 | + | 1.11962i | ||||
\(491\) | −38.1492 | −1.72165 | −0.860826 | − | 0.508900i | \(-0.830052\pi\) | ||||
−0.860826 | + | 0.508900i | \(0.830052\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.75571 | − | 13.4333i | 0.349299 | − | 0.605004i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.37683 | −0.151624 | ||||||||
\(497\) | −2.06525 | + | 1.36053i | −0.0926392 | + | 0.0610280i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 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 | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4.30504 | + | 7.45655i | 0.192143 | + | 0.332802i | ||||
\(503\) | −31.1362 | −1.38829 | −0.694146 | − | 0.719834i | \(-0.744218\pi\) | ||||
−0.694146 | + | 0.719834i | \(0.744218\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −67.8898 | −3.02106 | ||||||||
\(506\) | −2.36521 | − | 4.09666i | −0.105146 | − | 0.182119i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.365208 | + | 0.632559i | −0.0162035 | + | 0.0280653i | ||||
\(509\) | −21.0522 | − | 36.4634i | −0.933121 | − | 1.61621i | −0.777951 | − | 0.628325i | \(-0.783741\pi\) |
−0.155170 | − | 0.987888i | \(-0.549592\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.16233 | − | 19.7053i | −0.0514187 | − | 0.871709i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −0.418833 | + | 0.725439i | −0.0184739 | + | 0.0319978i | ||||
\(515\) | −5.79567 | + | 10.0384i | −0.255388 | + | 0.442344i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.10725 | 0.180637 | ||||||||
\(518\) | −1.19779 | − | 20.3063i | −0.0526279 | − | 0.892209i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.00000 | + | 15.5885i | −0.394297 | + | 0.682943i | −0.993011 | − | 0.118020i | \(-0.962345\pi\) |
0.598714 | + | 0.800963i | \(0.295679\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 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 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10.8377 | 0.472545 | ||||||||
\(527\) | −4.01309 | − | 6.95087i | −0.174813 | − | 0.302785i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.311583 | − | 0.539678i | 0.0135471 | − | 0.0234643i | ||||
\(530\) | 17.6753 | + | 30.6146i | 0.767767 | + | 1.32981i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −8.14925 | + | 5.36849i | −0.353315 | + | 0.232754i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −24.0891 | + | 41.7235i | −1.04146 | + | 1.80386i | ||||
\(536\) | 5.07462 | − | 8.78951i | 0.219190 | − | 0.379649i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 17.8797 | 0.770847 | ||||||||
\(539\) | 4.18842 | + | 5.60867i | 0.180408 | + | 0.241582i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 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 | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −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 | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 7.26304 | − | 12.5800i | 0.309697 | − | 0.536411i | ||||
\(551\) | 12.0355 | + | 20.8460i | 0.512728 | + | 0.888070i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.990626 | + | 0.496593i | 0.0421257 | + | 0.0211173i | ||||
\(554\) | 16.0000 | 0.679775 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.736959 | + | 1.27645i | −0.0312540 | + | 0.0541335i | ||||
\(557\) | −3.99346 | + | 6.91687i | −0.169208 | + | 0.293077i | −0.938142 | − | 0.346252i | \(-0.887454\pi\) |
0.768934 | + | 0.639329i | \(0.220788\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −0.688417 | − | 11.6708i | −0.0290909 | − | 0.493183i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7.96083 | + | 13.7886i | 0.335807 | + | 0.581636i | ||||
\(563\) | −13.6753 | + | 23.6864i | −0.576346 | + | 0.998261i | 0.419547 | + | 0.907733i | \(0.362189\pi\) |
−0.995894 | + | 0.0905280i | \(0.971145\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.8797 | − | 20.5762i | −0.499781 | − | 0.865646i | ||||
\(566\) | 18.0840 | 0.760127 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0.934749 | 0.0392212 | ||||||||
\(569\) | −14.7239 | − | 25.5025i | −0.617257 | − | 1.06912i | −0.989984 | − | 0.141179i | \(-0.954911\pi\) |
0.372727 | − | 0.927941i | \(-0.378423\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 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 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −28.7355 | − | 14.4049i | −1.19940 | − | 0.601248i | ||||
\(575\) | −68.7144 | −2.86559 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −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 | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −28.8377 | −1.19742 | ||||||||
\(581\) | 4.74858 | − | 3.12823i | 0.197004 | − | 0.129781i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 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 | \(-0.425129\pi\) | ||||
0.233053 | + | 0.972464i | \(0.425129\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.4552 | 0.513206 | ||||||||
\(590\) | −27.6753 | − | 47.9351i | −1.13938 | − | 1.97346i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.84421 | + | 6.65836i | −0.157996 | + | 0.273657i | ||||
\(593\) | −9.78912 | − | 16.9553i | −0.401991 | − | 0.696269i | 0.591975 | − | 0.805956i | \(-0.298348\pi\) |
−0.993966 | + | 0.109687i | \(0.965015\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 23.2051 | − | 15.2869i | 0.951317 | − | 0.626700i | ||||
\(596\) | 9.36375 | 0.383554 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.46591 | − | 9.46724i | 0.223331 | − | 0.386821i | −0.732486 | − | 0.680782i | \(-0.761640\pi\) |
0.955817 | + | 0.293961i | \(0.0949735\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −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 | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 6.78404 | + | 11.7503i | 0.276039 | + | 0.478113i | ||||
\(605\) | 2.20942 | − | 3.82682i | 0.0898255 | − | 0.155582i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 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 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 16.7724 | 0.679095 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −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 | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.155792 | − | 2.64116i | −0.00627702 | − | 0.106415i | ||||
\(617\) | 6.96817 | 0.280528 | 0.140264 | − | 0.990114i | \(-0.455205\pi\) | ||||
0.140264 | + | 0.990114i | \(0.455205\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 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 | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −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 | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.37029 | + | 16.2298i | 0.373915 | + | 0.647640i | ||||
\(629\) | −18.2741 | −0.728636 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −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 | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 10.0051 | − | 17.3293i | 0.397353 | − | 0.688235i | ||||
\(635\) | 1.61379 | + | 2.79517i | 0.0640414 | + | 0.110923i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −6.52608 | −0.258370 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.20942 | + | 3.82682i | −0.0873348 | + | 0.151268i | ||||
\(641\) | 7.68842 | − | 13.3167i | 0.303674 | − | 0.525979i | −0.673291 | − | 0.739378i | \(-0.735120\pi\) |
0.976965 | + | 0.213398i | \(0.0684532\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −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 | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.38338 | + | 7.59223i | 0.172462 | + | 0.298712i | ||||
\(647\) | 4.62825 | − | 8.01636i | 0.181955 | − | 0.315156i | −0.760591 | − | 0.649231i | \(-0.775091\pi\) |
0.942546 | + | 0.334076i | \(0.108424\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.26304 | − | 10.8479i | −0.245846 | − | 0.425818i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 18.7724 | 0.735185 | ||||||||
\(653\) | 12.4239 | + | 21.5189i | 0.486185 | + | 0.842098i | 0.999874 | − | 0.0158790i | \(-0.00505464\pi\) |
−0.513689 | + | 0.857977i | \(0.671721\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16.2985 | + | 28.2298i | −0.636835 | + | 1.10303i | ||||
\(656\) | 6.07462 | + | 10.5216i | 0.237174 | + | 0.410798i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.639875 | − | 10.8479i | −0.0249449 | − | 0.422895i | ||||
\(659\) | 6.60442 | 0.257272 | 0.128636 | − | 0.991692i | \(-0.458940\pi\) | ||||
0.128636 | + | 0.991692i | \(0.458940\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 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 | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15.4355 | + | 26.7351i | 0.597667 | + | 1.03519i | ||||
\(668\) | −11.9449 | + | 20.6892i | −0.462163 | + | 0.800489i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −22.4239 | − | 38.8394i | −0.866311 | − | 1.50050i | ||||
\(671\) | 3.79567 | 0.146530 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 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 | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.50000 | − | 11.2583i | 0.250000 | − | 0.433013i | ||||
\(677\) | 14.0587 | + | 24.3504i | 0.540320 | + | 0.935862i | 0.998885 | + | 0.0472011i | \(0.0150301\pi\) |
−0.458565 | + | 0.888661i | \(0.651637\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.4659 | − | 10.1885i | 0.593527 | − | 0.390999i | ||||
\(680\) | −10.5028 | −0.402765 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.68842 | + | 2.92442i | −0.0646528 | + | 0.111982i | ||||
\(683\) | 7.95146 | − | 13.7723i | 0.304254 | − | 0.526984i | −0.672841 | − | 0.739787i | \(-0.734926\pi\) |
0.977095 | + | 0.212804i | \(0.0682595\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −39.0522 | −1.49211 | ||||||||
\(686\) | 14.1609 | − | 11.9361i | 0.540665 | − | 0.455721i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.53263 | − | 2.65458i | −0.0584308 | − | 0.101205i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 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 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 15.6566 | 0.594316 | ||||||||
\(695\) | 3.25650 | + | 5.64042i | 0.123526 | + | 0.213953i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.4384 | + | 25.0080i | −0.546892 | + | 0.947245i | ||||
\(698\) | −10.0051 | − | 17.3293i | −0.378698 | − | 0.655924i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −34.3572 | − | 17.2230i | −1.29858 | − | 0.650968i | ||||
\(701\) | −13.9869 | −0.528278 | −0.264139 | − | 0.964485i | \(-0.585088\pi\) | ||||
−0.264139 | + | 0.964485i | \(0.585088\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.1790 | − | 24.5588i | 0.534773 | − | 0.926254i | ||||
\(704\) | −0.500000 | + | 0.866025i | −0.0188445 | + | 0.0326396i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.46083 | 0.280792 | ||||||||
\(707\) | 2.39354 | + | 40.5781i | 0.0900184 | + | 1.52610i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −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 | 0 | ||||||||
\(712\) | 6.41883 | + | 11.1177i | 0.240556 | + | 0.416655i | ||||
\(713\) | 15.9738 | 0.598225 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 12.3050 | + | 21.3130i | 0.459861 | + | 0.796503i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5.62317 | − | 9.73961i | 0.209855 | − | 0.363479i | ||||
\(719\) | −9.71879 | − | 16.8334i | −0.362450 | − | 0.627781i | 0.625914 | − | 0.779892i | \(-0.284726\pi\) |
−0.988363 | + | 0.152111i | \(0.951393\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.20433 | + | 3.11019i | 0.231061 | + | 0.115829i | ||||
\(722\) | 5.39558 | 0.200803 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −8.73042 | + | 15.1215i | −0.324463 | + | 0.561987i | ||||
\(725\) | −47.3992 | + | 82.0978i | −1.76036 | + | 3.04904i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −44.9217 | −1.66605 | −0.833026 | − | 0.553234i | \(-0.813394\pi\) | ||||
−0.833026 | + | 0.553234i | \(0.813394\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 16.4841 | + | 28.5513i | 0.610103 | + | 1.05673i | ||||
\(731\) | 3.64280 | − | 6.30951i | 0.134734 | − | 0.233366i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −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 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.73042 | 0.174365 | ||||||||
\(737\) | −5.07462 | − | 8.78951i | −0.186926 | − | 0.323766i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 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 | \(-0.242914\pi\) | ||||
0.722671 | + | 0.691192i | \(0.242914\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20.6884 | − | 35.8334i | 0.757965 | − | 1.31283i | ||||
\(746\) | −11.5630 | + | 20.0277i | −0.423351 | + | 0.733266i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.37683 | −0.0869056 | ||||||||
\(749\) | 25.7877 | + | 12.9272i | 0.942261 | + | 0.472348i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 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 | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 59.9551 | 2.18199 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −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 | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 8.14925 | − | 14.1149i | 0.295604 | − | 0.512002i | ||||
\(761\) | −16.3544 | − | 28.3266i | −0.592846 | − | 1.02684i | −0.993847 | − | 0.110761i | \(-0.964671\pi\) |
0.401001 | − | 0.916077i | \(-0.368662\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.83767 | − | 31.1542i | −0.0665280 | − | 1.12786i | ||||
\(764\) | 16.8377 | 0.609165 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −12.6819 | + | 21.9656i | −0.458215 | + | 0.793651i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 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 | 0 | ||||||||
\(772\) | −2.73042 | − | 4.72922i | −0.0982698 | − | 0.170208i | ||||
\(773\) | 0.102167 | − | 0.176958i | 0.00367468 | − | 0.00636474i | −0.864182 | − | 0.503179i | \(-0.832164\pi\) |
0.867857 | + | 0.496814i | \(0.165497\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 24.5261 | + | 42.4804i | 0.881003 | + | 1.52594i | ||||
\(776\) | −7.00000 | −0.251285 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 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 | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.95146 | + | 0.822941i | −0.248266 | + | 0.0293908i | ||||
\(785\) | 82.8115 | 2.95567 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −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 | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.85075 | −0.0658468 | ||||||||
\(791\) | −11.8797 | + | 7.82598i | −0.422392 | + | 0.278260i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −6.73696 | + | 11.6688i | −0.239086 | + | 0.414109i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.1492 | − | 17.5790i | −0.359731 | − | 0.623072i | ||||
\(797\) | −30.0477 | −1.06434 | −0.532171 | − | 0.846637i | \(-0.678624\pi\) | ||||
−0.532171 | + | 0.846637i | \(0.678624\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.76225 | −0.345364 | ||||||||
\(800\) | 7.26304 | + | 12.5800i | 0.256787 | + | 0.444769i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −16.9449 | + | 29.3495i | −0.598346 | + | 1.03637i | ||||
\(803\) | 3.73042 | + | 6.46127i | 0.131644 | + | 0.228013i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.25650 | + | 55.2080i | 0.114776 | + | 1.94582i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 7.68187 | − | 13.3054i | 0.270247 | − | 0.468082i | ||||
\(809\) | 1.17171 | − | 2.02946i | 0.0411951 | − | 0.0713520i | −0.844693 | − | 0.535252i | \(-0.820217\pi\) |
0.885888 | + | 0.463900i | \(0.153550\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −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 | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3.84421 | + | 6.65836i | 0.134739 | + | 0.233376i | ||||
\(815\) | 41.4761 | − | 71.8387i | 1.45284 | − | 2.51640i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 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 | \(-0.939735\pi\) |
0.328080 | − | 0.944650i | \(-0.393598\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −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 | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −27.6753 | + | 18.2317i | −0.962948 | + | 0.634362i | ||||
\(827\) | −43.3319 | −1.50680 | −0.753399 | − | 0.657563i | \(-0.771587\pi\) | ||||
−0.753399 | + | 0.657563i | \(0.771587\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −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 | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9.95517 | − | 13.3309i | −0.344926 | − | 0.461887i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 52.7826 | + | 91.4221i | 1.82662 | + | 3.16379i | ||||
\(836\) | 1.84421 | − | 3.19426i | 0.0637833 | − | 0.110476i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 11.1558 | + | 19.3224i | 0.385370 | + | 0.667481i | ||||
\(839\) | −54.6912 | −1.88815 | −0.944074 | − | 0.329733i | \(-0.893041\pi\) | ||||
−0.944074 | + | 0.329733i | \(0.893041\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.5897 | 0.468612 | ||||||||
\(842\) | 9.15579 | + | 15.8583i | 0.315529 | + | 0.546513i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −11.2565 | + | 19.4968i | −0.387465 | + | 0.671108i | ||||
\(845\) | −28.7224 | − | 49.7487i | −0.988081 | − | 1.71141i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.36521 | − | 1.18566i | −0.0812695 | − | 0.0407398i | ||||
\(848\) | −8.00000 | −0.274721 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −17.2630 | + | 29.9005i | −0.592117 | + | 1.02558i | ||||
\(851\) | 18.1847 | − | 31.4968i | 0.623364 | − | 1.07970i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −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 | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.45146 | − | 9.44220i | −0.186327 | − | 0.322728i | ||||
\(857\) | −18.4217 | + | 31.9073i | −0.629272 | + | 1.08993i | 0.358426 | + | 0.933558i | \(0.383314\pi\) |
−0.987698 | + | 0.156373i | \(0.950020\pi\) | |||||||
\(858\) | 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 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −28.8377 | −0.982215 | ||||||||
\(863\) | −8.62825 | − | 14.9446i | −0.293709 | − | 0.508719i | 0.680975 | − | 0.732307i | \(-0.261556\pi\) |
−0.974684 | + | 0.223588i | \(0.928223\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −25.1362 | + | 43.5371i | −0.854655 | + | 1.48031i | ||||
\(866\) | 3.81158 | + | 6.60186i | 0.129523 | + | 0.224340i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 7.98691 | + | 4.00378i | 0.271094 | + | 0.135897i | ||||
\(869\) | −0.418833 | −0.0142079 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −5.89783 | + | 10.2153i | −0.199726 | + | 0.345935i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −17.4477 | −0.590179 | ||||||||
\(875\) | −93.0035 | + | 61.2680i | −3.14409 | + | 2.07124i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −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 | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.20942 | + | 3.82682i | 0.0744794 | + | 0.129002i | ||||
\(881\) | −16.2985 | −0.549110 | −0.274555 | − | 0.961571i | \(-0.588531\pi\) | ||||
−0.274555 | + | 0.961571i | \(0.588531\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33.9551 | −1.14268 | −0.571340 | − | 0.820714i | \(-0.693576\pi\) | ||||
−0.571340 | + | 0.820714i | \(0.693576\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.42538 | − | 4.20087i | 0.0814821 | − | 0.141131i | ||||
\(887\) | 9.73042 | + | 16.8536i | 0.326715 | + | 0.565888i | 0.981858 | − | 0.189618i | \(-0.0607248\pi\) |
−0.655143 | + | 0.755505i | \(0.727391\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.61379 | − | 1.06312i | 0.0541249 | − | 0.0356559i | ||||
\(890\) | 56.7275 | 1.90151 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.73042 | − | 6.46127i | 0.124904 | − | 0.216339i | ||||
\(893\) | 7.57462 | − | 13.1196i | 0.253475 | − | 0.439032i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 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 | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.50733 | − | 16.4672i | −0.316735 | − | 0.548602i | ||||
\(902\) | 12.1492 | 0.404526 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.37683 | 0.178831 | ||||||||
\(905\) | 38.5782 | + | 66.8195i | 1.28238 | + | 2.22115i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −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 | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.94491 | 0.296358 | 0.148179 | − | 0.988961i | \(-0.452659\pi\) | ||||
0.148179 | + | 0.988961i | \(0.452659\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.07462 | + | 1.86130i | −0.0355649 | + | 0.0616002i | ||||
\(914\) | −12.5913 | + | 21.8088i | −0.416484 | + | 0.721372i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.53917 | −0.0838965 | ||||||||
\(917\) | 17.4477 | + | 8.74642i | 0.576175 | + | 0.288832i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −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 | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −6.50937 | − | 11.2746i | −0.214375 | − | 0.371308i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 111.683 | 3.67210 | ||||||||
\(926\) | −7.10725 | − | 12.3101i | −0.233559 | − | 0.404536i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.26304 | − | 5.65175i | 0.107115 | − | 0.185528i | ||||
\(929\) | −11.2696 | − | 19.5195i | −0.369743 | − | 0.640414i | 0.619782 | − | 0.784774i | \(-0.287221\pi\) |
−0.989525 | + | 0.144360i | \(0.953888\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 25.6399 | − | 3.03535i | 0.840313 | − | 0.0994796i | ||||
\(932\) | 24.0522 | 0.787855 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 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 | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 9.07462 | + | 15.7177i | 0.295982 | + | 0.512655i | ||||
\(941\) | 24.4123 | − | 42.2833i | 0.795818 | − | 1.37840i | −0.126501 | − | 0.991967i | \(-0.540375\pi\) |
0.922319 | − | 0.386431i | \(-0.126292\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −28.7355 | − | 49.7713i | −0.935757 | − | 1.62078i | ||||
\(944\) | 12.5261 | 0.407689 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.06525 | −0.0996599 | ||||||||
\(947\) | −15.5615 | − | 26.9534i | −0.505682 | − | 0.875867i | −0.999978 | − | 0.00657353i | \(-0.997908\pi\) |
0.494296 | − | 0.869293i | \(-0.335426\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −26.7891 | − | 46.4001i | −0.869154 | − | 1.50542i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.370291 | + | 6.27760i | 0.0120012 | + | 0.203458i | ||||
\(953\) | −16.2797 | −0.527353 | −0.263676 | − | 0.964611i | \(-0.584935\pi\) | ||||
−0.263676 | + | 0.964611i | \(0.584935\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 37.2014 | − | 64.4347i | 1.20381 | − | 2.08506i | ||||
\(956\) | 3.79567 | − | 6.57429i | 0.122761 | − | 0.212628i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 10.8377 | 0.350149 | ||||||||
\(959\) | 1.37683 | + | 23.3417i | 0.0444603 | + | 0.753743i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.79850 | + | 16.9715i | 0.316081 | + | 0.547468i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −8.14925 | − | 14.1149i | −0.262470 | − | 0.454611i | ||||
\(965\) | −24.1305 | −0.776788 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 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 | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −15.4659 | + | 26.7877i | −0.496581 | + | 0.860103i | ||||
\(971\) | 19.6566 | + | 34.0462i | 0.630810 | + | 1.09259i | 0.987386 | + | 0.158329i | \(0.0506105\pi\) |
−0.356577 | + | 0.934266i | \(0.616056\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 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 | −0.990105 | − | 0.140326i | \(-0.955185\pi\) |
0.616578 | + | 0.787293i | \(0.288518\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.8377 | 0.410294 | ||||||||
\(980\) | −12.2094 | + | 28.4202i | −0.390015 | + | 0.907850i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −19.0746 | − | 33.0382i | −0.608696 | − | 1.05429i | ||||
\(983\) | −2.25796 | + | 3.91090i | −0.0720177 | + | 0.124738i | −0.899785 | − | 0.436333i | \(-0.856277\pi\) |
0.827768 | + | 0.561071i | \(0.189610\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 21.4057 | + | 37.0758i | 0.682044 | + | 1.18133i | ||||
\(986\) | 15.5114 | 0.493984 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.24995 | + | 12.5573i | 0.230535 | + | 0.399299i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −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 | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.21088 | − | 1.10830i | −0.0701247 | − | 0.0351530i | ||||
\(995\) | −89.6957 | −2.84354 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 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 | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1386.2.k.v.991.3 | 6 | ||
3.2 | odd | 2 | 462.2.i.g.67.1 | ✓ | 6 | ||
7.2 | even | 3 | inner | 1386.2.k.v.793.3 | 6 | ||
7.3 | odd | 6 | 9702.2.a.dw.1.3 | 3 | |||
7.4 | even | 3 | 9702.2.a.dv.1.1 | 3 | |||
21.2 | odd | 6 | 462.2.i.g.331.1 | yes | 6 | ||
21.11 | odd | 6 | 3234.2.a.bf.1.3 | 3 | |||
21.17 | even | 6 | 3234.2.a.bh.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.i.g.67.1 | ✓ | 6 | 3.2 | odd | 2 | ||
462.2.i.g.331.1 | yes | 6 | 21.2 | odd | 6 | ||
1386.2.k.v.793.3 | 6 | 7.2 | even | 3 | inner | ||
1386.2.k.v.991.3 | 6 | 1.1 | even | 1 | trivial | ||
3234.2.a.bf.1.3 | 3 | 21.11 | odd | 6 | |||
3234.2.a.bh.1.1 | 3 | 21.17 | even | 6 | |||
9702.2.a.dv.1.1 | 3 | 7.4 | even | 3 | |||
9702.2.a.dw.1.3 | 3 | 7.3 | odd | 6 |