Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3330,2,Mod(1999,3330)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3330, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3330.1999");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3330.d (of order \(2\), degree \(1\), 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: | \(26.5901838731\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} + 2x^{8} - 4x^{7} + 51x^{6} - 124x^{5} + 154x^{4} - 46x^{3} + x^{2} + 4x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 370) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1999.10 | ||
Root | \(1.51933 - 1.51933i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3330.1999 |
Dual form | 3330.2.d.p.1999.5 |
$q$-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 \(\left(\mathbb{Z}/3330\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.42149 | + | 1.72608i | 0.635711 | + | 0.771927i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.14336i | 1.56604i | 0.621994 | + | 0.783022i | \(0.286323\pi\) | ||||
−0.621994 | + | 0.783022i | \(0.713677\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.72608 | + | 1.42149i | −0.545835 | + | 0.449515i | ||||
\(11\) | 4.76853 | 1.43777 | 0.718883 | − | 0.695131i | \(-0.244654\pi\) | ||||
0.718883 | + | 0.695131i | \(0.244654\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3.91744i | − | 1.08650i | −0.839570 | − | 0.543251i | \(-0.817193\pi\) | ||
0.839570 | − | 0.543251i | \(-0.182807\pi\) | |||||||
\(14\) | −4.14336 | −1.10736 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.31637i | 0.804337i | 0.915566 | + | 0.402169i | \(0.131743\pi\) | ||||
−0.915566 | + | 0.402169i | \(0.868257\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.85109 | 0.424670 | 0.212335 | − | 0.977197i | \(-0.431893\pi\) | ||||
0.212335 | + | 0.977197i | \(0.431893\pi\) | |||||||
\(20\) | −1.42149 | − | 1.72608i | −0.317855 | − | 0.385964i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.76853i | 1.01665i | ||||||||
\(23\) | 1.54229i | 0.321590i | 0.986988 | + | 0.160795i | \(0.0514058\pi\) | ||||
−0.986988 | + | 0.160795i | \(0.948594\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.958719 | + | 4.90723i | −0.191744 | + | 0.981445i | ||||
\(26\) | 3.91744 | 0.768273 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 4.14336i | − | 0.783022i | ||||||
\(29\) | 8.87323 | 1.64772 | 0.823859 | − | 0.566795i | \(-0.191817\pi\) | ||||
0.823859 | + | 0.566795i | \(0.191817\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.75286 | 1.75166 | 0.875832 | − | 0.482615i | \(-0.160313\pi\) | ||||
0.875832 | + | 0.482615i | \(0.160313\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.31637 | −0.568752 | ||||||||
\(35\) | −7.15179 | + | 5.88976i | −1.20887 | + | 0.995551i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 1.00000i | − | 0.164399i | ||||||
\(38\) | 1.85109i | 0.300287i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.72608 | − | 1.42149i | 0.272918 | − | 0.224758i | ||||
\(41\) | 5.06977 | 0.791764 | 0.395882 | − | 0.918301i | \(-0.370439\pi\) | ||||
0.395882 | + | 0.918301i | \(0.370439\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 9.99446i | − | 1.52414i | −0.647494 | − | 0.762070i | \(-0.724183\pi\) | ||
0.647494 | − | 0.762070i | \(-0.275817\pi\) | |||||||
\(44\) | −4.76853 | −0.718883 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.54229 | −0.227399 | ||||||||
\(47\) | 4.82700i | 0.704090i | 0.935983 | + | 0.352045i | \(0.114514\pi\) | ||||
−0.935983 | + | 0.352045i | \(0.885486\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −10.1675 | −1.45249 | ||||||||
\(50\) | −4.90723 | − | 0.958719i | −0.693986 | − | 0.135583i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.91744i | 0.543251i | ||||||||
\(53\) | 5.13611i | 0.705499i | 0.935718 | + | 0.352750i | \(0.114753\pi\) | ||||
−0.935718 | + | 0.352750i | \(0.885247\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.77843 | + | 8.23088i | 0.914003 | + | 1.10985i | ||||
\(56\) | 4.14336 | 0.553680 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 8.87323i | 1.16511i | ||||||||
\(59\) | −1.05324 | −0.137120 | −0.0685598 | − | 0.997647i | \(-0.521840\pi\) | ||||
−0.0685598 | + | 0.997647i | \(0.521840\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.14422 | −0.530613 | −0.265306 | − | 0.964164i | \(-0.585473\pi\) | ||||
−0.265306 | + | 0.964164i | \(0.585473\pi\) | |||||||
\(62\) | 9.75286i | 1.23861i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 6.76182 | − | 5.56861i | 0.838701 | − | 0.690701i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 1.00811i | − | 0.123160i | −0.998102 | − | 0.0615800i | \(-0.980386\pi\) | ||
0.998102 | − | 0.0615800i | \(-0.0196139\pi\) | |||||||
\(68\) | − | 3.31637i | − | 0.402169i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −5.88976 | − | 7.15179i | −0.703961 | − | 0.854802i | ||||
\(71\) | −6.45248 | −0.765768 | −0.382884 | − | 0.923796i | \(-0.625069\pi\) | ||||
−0.382884 | + | 0.923796i | \(0.625069\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.7714i | 1.26070i | 0.776312 | + | 0.630349i | \(0.217088\pi\) | ||||
−0.776312 | + | 0.630349i | \(0.782912\pi\) | |||||||
\(74\) | 1.00000 | 0.116248 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.85109 | −0.212335 | ||||||||
\(77\) | 19.7578i | 2.25161i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.19856 | 0.134849 | 0.0674243 | − | 0.997724i | \(-0.478522\pi\) | ||||
0.0674243 | + | 0.997724i | \(0.478522\pi\) | |||||||
\(80\) | 1.42149 | + | 1.72608i | 0.158928 | + | 0.192982i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.06977i | 0.559862i | ||||||||
\(83\) | − | 10.6932i | − | 1.17373i | −0.809683 | − | 0.586867i | \(-0.800361\pi\) | ||
0.809683 | − | 0.586867i | \(-0.199639\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.72432 | + | 4.71419i | −0.620890 | + | 0.511326i | ||||
\(86\) | 9.99446 | 1.07773 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 4.76853i | − | 0.508327i | ||||||
\(89\) | 7.29569 | 0.773342 | 0.386671 | − | 0.922218i | \(-0.373625\pi\) | ||||
0.386671 | + | 0.922218i | \(0.373625\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 16.2314 | 1.70151 | ||||||||
\(92\) | − | 1.54229i | − | 0.160795i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.82700 | −0.497867 | ||||||||
\(95\) | 2.63131 | + | 3.19514i | 0.269967 | + | 0.327814i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 14.8988i | − | 1.51274i | −0.654143 | − | 0.756371i | \(-0.726970\pi\) | ||
0.654143 | − | 0.756371i | \(-0.273030\pi\) | |||||||
\(98\) | − | 10.1675i | − | 1.02707i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.958719 | − | 4.90723i | 0.0958719 | − | 0.490723i | ||||
\(101\) | −18.5903 | −1.84980 | −0.924902 | − | 0.380206i | \(-0.875853\pi\) | ||||
−0.924902 | + | 0.380206i | \(0.875853\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 13.3033i | − | 1.31081i | −0.755278 | − | 0.655404i | \(-0.772498\pi\) | ||
0.755278 | − | 0.655404i | \(-0.227502\pi\) | |||||||
\(104\) | −3.91744 | −0.384136 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.13611 | −0.498863 | ||||||||
\(107\) | 12.4763i | 1.20613i | 0.797691 | + | 0.603066i | \(0.206054\pi\) | ||||
−0.797691 | + | 0.603066i | \(0.793946\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.35447 | 0.417083 | 0.208541 | − | 0.978014i | \(-0.433128\pi\) | ||||
0.208541 | + | 0.978014i | \(0.433128\pi\) | |||||||
\(110\) | −8.23088 | + | 6.77843i | −0.784783 | + | 0.646298i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.14336i | 0.391511i | ||||||||
\(113\) | − | 9.54261i | − | 0.897693i | −0.893609 | − | 0.448846i | \(-0.851835\pi\) | ||
0.893609 | − | 0.448846i | \(-0.148165\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.66212 | + | 2.19236i | −0.248244 | + | 0.204438i | ||||
\(116\) | −8.87323 | −0.823859 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 1.05324i | − | 0.0969582i | ||||||
\(119\) | −13.7409 | −1.25963 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.7389 | 1.06717 | ||||||||
\(122\) | − | 4.14422i | − | 0.375200i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −9.75286 | −0.875832 | ||||||||
\(125\) | −9.83309 | + | 5.32076i | −0.879498 | + | 0.475903i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 8.33492i | − | 0.739605i | −0.929110 | − | 0.369802i | \(-0.879425\pi\) | ||
0.929110 | − | 0.369802i | \(-0.120575\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5.56861 | + | 6.76182i | 0.488399 | + | 0.593051i | ||||
\(131\) | −3.68597 | −0.322045 | −0.161022 | − | 0.986951i | \(-0.551479\pi\) | ||||
−0.161022 | + | 0.986951i | \(0.551479\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.66975i | 0.665052i | ||||||||
\(134\) | 1.00811 | 0.0870873 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.31637 | 0.284376 | ||||||||
\(137\) | − | 12.3027i | − | 1.05109i | −0.850765 | − | 0.525546i | \(-0.823861\pi\) | ||
0.850765 | − | 0.525546i | \(-0.176139\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.842442 | 0.0714550 | 0.0357275 | − | 0.999362i | \(-0.488625\pi\) | ||||
0.0357275 | + | 0.999362i | \(0.488625\pi\) | |||||||
\(140\) | 7.15179 | − | 5.88976i | 0.604436 | − | 0.497776i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 6.45248i | − | 0.541480i | ||||||
\(143\) | − | 18.6804i | − | 1.56214i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.6132 | + | 15.3159i | 1.04747 | + | 1.27192i | ||||
\(146\) | −10.7714 | −0.891448 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.00000i | 0.0821995i | ||||||||
\(149\) | −16.7723 | −1.37404 | −0.687019 | − | 0.726640i | \(-0.741081\pi\) | ||||
−0.687019 | + | 0.726640i | \(0.741081\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.59755 | −0.618280 | −0.309140 | − | 0.951017i | \(-0.600041\pi\) | ||||
−0.309140 | + | 0.951017i | \(0.600041\pi\) | |||||||
\(152\) | − | 1.85109i | − | 0.150143i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −19.7578 | −1.59213 | ||||||||
\(155\) | 13.8636 | + | 16.8342i | 1.11355 | + | 1.35216i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 4.45631i | − | 0.355652i | −0.984062 | − | 0.177826i | \(-0.943094\pi\) | ||
0.984062 | − | 0.177826i | \(-0.0569065\pi\) | |||||||
\(158\) | 1.19856i | 0.0953523i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.72608 | + | 1.42149i | −0.136459 | + | 0.112379i | ||||
\(161\) | −6.39028 | −0.503624 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.4599i | 1.52422i | 0.647447 | + | 0.762110i | \(0.275837\pi\) | ||||
−0.647447 | + | 0.762110i | \(0.724163\pi\) | |||||||
\(164\) | −5.06977 | −0.395882 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 10.6932 | 0.829955 | ||||||||
\(167\) | 7.13813i | 0.552365i | 0.961105 | + | 0.276183i | \(0.0890695\pi\) | ||||
−0.961105 | + | 0.276183i | \(0.910931\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.34632 | −0.180486 | ||||||||
\(170\) | −4.71419 | − | 5.72432i | −0.361562 | − | 0.439035i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 9.99446i | 0.762070i | ||||||||
\(173\) | 11.6199i | 0.883448i | 0.897151 | + | 0.441724i | \(0.145633\pi\) | ||||
−0.897151 | + | 0.441724i | \(0.854367\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −20.3324 | − | 3.97232i | −1.53699 | − | 0.300279i | ||||
\(176\) | 4.76853 | 0.359442 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.29569i | 0.546835i | ||||||||
\(179\) | −17.2224 | −1.28726 | −0.643631 | − | 0.765336i | \(-0.722573\pi\) | ||||
−0.643631 | + | 0.765336i | \(0.722573\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.5098 | −1.74747 | −0.873733 | − | 0.486405i | \(-0.838308\pi\) | ||||
−0.873733 | + | 0.486405i | \(0.838308\pi\) | |||||||
\(182\) | 16.2314i | 1.20315i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.54229 | 0.113699 | ||||||||
\(185\) | 1.72608 | − | 1.42149i | 0.126904 | − | 0.104510i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.8142i | 1.15645i | ||||||||
\(188\) | − | 4.82700i | − | 0.352045i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.19514 | + | 2.63131i | −0.231800 | + | 0.190896i | ||||
\(191\) | −1.16660 | −0.0844125 | −0.0422063 | − | 0.999109i | \(-0.513439\pi\) | ||||
−0.0422063 | + | 0.999109i | \(0.513439\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 9.36727i | − | 0.674271i | −0.941456 | − | 0.337135i | \(-0.890542\pi\) | ||
0.941456 | − | 0.337135i | \(-0.109458\pi\) | |||||||
\(194\) | 14.8988 | 1.06967 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 10.1675 | 0.726247 | ||||||||
\(197\) | 3.21836i | 0.229299i | 0.993406 | + | 0.114649i | \(0.0365744\pi\) | ||||
−0.993406 | + | 0.114649i | \(0.963426\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.99104 | 0.212029 | 0.106014 | − | 0.994365i | \(-0.466191\pi\) | ||||
0.106014 | + | 0.994365i | \(0.466191\pi\) | |||||||
\(200\) | 4.90723 | + | 0.958719i | 0.346993 | + | 0.0677917i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 18.5903i | − | 1.30801i | ||||||
\(203\) | 36.7650i | 2.58040i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.20663 | + | 8.75083i | 0.503333 | + | 0.611185i | ||||
\(206\) | 13.3033 | 0.926882 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 3.91744i | − | 0.271625i | ||||||
\(209\) | 8.82700 | 0.610576 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.75340 | 0.327237 | 0.163619 | − | 0.986524i | \(-0.447683\pi\) | ||||
0.163619 | + | 0.986524i | \(0.447683\pi\) | |||||||
\(212\) | − | 5.13611i | − | 0.352750i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −12.4763 | −0.852864 | ||||||||
\(215\) | 17.2513 | − | 14.2070i | 1.17653 | − | 0.968912i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 40.4096i | 2.74318i | ||||||||
\(218\) | 4.35447i | 0.294922i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6.77843 | − | 8.23088i | −0.457002 | − | 0.554926i | ||||
\(221\) | 12.9917 | 0.873914 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 6.95635i | − | 0.465832i | −0.972497 | − | 0.232916i | \(-0.925173\pi\) | ||
0.972497 | − | 0.232916i | \(-0.0748267\pi\) | |||||||
\(224\) | −4.14336 | −0.276840 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.54261 | 0.634765 | ||||||||
\(227\) | − | 22.2980i | − | 1.47997i | −0.672622 | − | 0.739986i | \(-0.734832\pi\) | ||
0.672622 | − | 0.739986i | \(-0.265168\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.9648 | −0.856739 | −0.428370 | − | 0.903604i | \(-0.640912\pi\) | ||||
−0.428370 | + | 0.903604i | \(0.640912\pi\) | |||||||
\(230\) | −2.19236 | − | 2.66212i | −0.144560 | − | 0.175535i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 8.87323i | − | 0.582556i | ||||||
\(233\) | 10.4327i | 0.683468i | 0.939797 | + | 0.341734i | \(0.111014\pi\) | ||||
−0.939797 | + | 0.341734i | \(0.888986\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.33179 | + | 6.86154i | −0.543506 | + | 0.447597i | ||||
\(236\) | 1.05324 | 0.0685598 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − | 13.7409i | − | 0.890691i | ||||||
\(239\) | 1.58711 | 0.102661 | 0.0513307 | − | 0.998682i | \(-0.483654\pi\) | ||||
0.0513307 | + | 0.998682i | \(0.483654\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.2576 | 1.04724 | 0.523622 | − | 0.851951i | \(-0.324581\pi\) | ||||
0.523622 | + | 0.851951i | \(0.324581\pi\) | |||||||
\(242\) | 11.7389i | 0.754604i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.14422 | 0.265306 | ||||||||
\(245\) | −14.4530 | − | 17.5499i | −0.923366 | − | 1.12122i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 7.25154i | − | 0.461405i | ||||||
\(248\) | − | 9.75286i | − | 0.619307i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −5.32076 | − | 9.83309i | −0.336514 | − | 0.621899i | ||||
\(251\) | −14.9486 | −0.943547 | −0.471774 | − | 0.881720i | \(-0.656386\pi\) | ||||
−0.471774 | + | 0.881720i | \(0.656386\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.35447i | 0.462372i | ||||||||
\(254\) | 8.33492 | 0.522979 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 14.9968i | 0.935474i | 0.883868 | + | 0.467737i | \(0.154931\pi\) | ||||
−0.883868 | + | 0.467737i | \(0.845069\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.14336 | 0.257456 | ||||||||
\(260\) | −6.76182 | + | 5.56861i | −0.419350 | + | 0.345350i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 3.68597i | − | 0.227720i | ||||||
\(263\) | − | 22.9610i | − | 1.41583i | −0.706295 | − | 0.707917i | \(-0.749635\pi\) | ||
0.706295 | − | 0.707917i | \(-0.250365\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.86535 | + | 7.30094i | −0.544594 | + | 0.448493i | ||||
\(266\) | −7.66975 | −0.470263 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.00811i | 0.0615800i | ||||||||
\(269\) | 10.0896 | 0.615175 | 0.307588 | − | 0.951520i | \(-0.400478\pi\) | ||||
0.307588 | + | 0.951520i | \(0.400478\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.30678 | 0.200872 | 0.100436 | − | 0.994943i | \(-0.467976\pi\) | ||||
0.100436 | + | 0.994943i | \(0.467976\pi\) | |||||||
\(272\) | 3.31637i | 0.201084i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12.3027 | 0.743234 | ||||||||
\(275\) | −4.57168 | + | 23.4003i | −0.275683 | + | 1.41109i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.9046i | 0.955617i | 0.878464 | + | 0.477809i | \(0.158569\pi\) | ||||
−0.878464 | + | 0.477809i | \(0.841431\pi\) | |||||||
\(278\) | 0.842442i | 0.0505263i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.88976 | + | 7.15179i | 0.351980 | + | 0.427401i | ||||
\(281\) | −11.3609 | −0.677732 | −0.338866 | − | 0.940835i | \(-0.610043\pi\) | ||||
−0.338866 | + | 0.940835i | \(0.610043\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.1530i | 1.19797i | 0.800761 | + | 0.598984i | \(0.204429\pi\) | ||||
−0.800761 | + | 0.598984i | \(0.795571\pi\) | |||||||
\(284\) | 6.45248 | 0.382884 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 18.6804 | 1.10460 | ||||||||
\(287\) | 21.0059i | 1.23994i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.00171 | 0.353042 | ||||||||
\(290\) | −15.3159 | + | 12.6132i | −0.899382 | + | 0.740674i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 10.7714i | − | 0.630349i | ||||||
\(293\) | 21.0517i | 1.22986i | 0.788583 | + | 0.614928i | \(0.210815\pi\) | ||||
−0.788583 | + | 0.614928i | \(0.789185\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.49717 | − | 1.81797i | −0.0871684 | − | 0.105846i | ||||
\(296\) | −1.00000 | −0.0581238 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 16.7723i | − | 0.971591i | ||||||
\(299\) | 6.04184 | 0.349408 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 41.4107 | 2.38687 | ||||||||
\(302\) | − | 7.59755i | − | 0.437190i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.85109 | 0.106167 | ||||||||
\(305\) | −5.89098 | − | 7.15326i | −0.337316 | − | 0.409595i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 17.0946i | − | 0.975638i | −0.872945 | − | 0.487819i | \(-0.837793\pi\) | ||
0.872945 | − | 0.487819i | \(-0.162207\pi\) | |||||||
\(308\) | − | 19.7578i | − | 1.12580i | ||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −16.8342 | + | 13.8636i | −0.956120 | + | 0.787400i | ||||
\(311\) | −20.0503 | −1.13695 | −0.568473 | − | 0.822702i | \(-0.692466\pi\) | ||||
−0.568473 | + | 0.822702i | \(0.692466\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.3400i | 0.754019i | 0.926209 | + | 0.377010i | \(0.123048\pi\) | ||||
−0.926209 | + | 0.377010i | \(0.876952\pi\) | |||||||
\(314\) | 4.45631 | 0.251484 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.19856 | −0.0674243 | ||||||||
\(317\) | 12.8528i | 0.721885i | 0.932588 | + | 0.360943i | \(0.117545\pi\) | ||||
−0.932588 | + | 0.360943i | \(0.882455\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 42.3123 | 2.36903 | ||||||||
\(320\) | −1.42149 | − | 1.72608i | −0.0794638 | − | 0.0964909i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − | 6.39028i | − | 0.356116i | ||||||
\(323\) | 6.13890i | 0.341578i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 19.2238 | + | 3.75572i | 1.06634 | + | 0.208330i | ||||
\(326\) | −19.4599 | −1.07779 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 5.06977i | − | 0.279931i | ||||||
\(329\) | −20.0000 | −1.10264 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.5835 | −1.29627 | −0.648134 | − | 0.761526i | \(-0.724451\pi\) | ||||
−0.648134 | + | 0.761526i | \(0.724451\pi\) | |||||||
\(332\) | 10.6932i | 0.586867i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −7.13813 | −0.390581 | ||||||||
\(335\) | 1.74008 | − | 1.43302i | 0.0950706 | − | 0.0782942i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 26.6074i | − | 1.44940i | −0.689067 | − | 0.724698i | \(-0.741979\pi\) | ||
0.689067 | − | 0.724698i | \(-0.258021\pi\) | |||||||
\(338\) | − | 2.34632i | − | 0.127623i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5.72432 | − | 4.71419i | 0.310445 | − | 0.255663i | ||||
\(341\) | 46.5068 | 2.51848 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 13.1239i | − | 0.708626i | ||||||
\(344\) | −9.99446 | −0.538865 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −11.6199 | −0.624692 | ||||||||
\(347\) | − | 17.2626i | − | 0.926707i | −0.886174 | − | 0.463353i | \(-0.846646\pi\) | ||
0.886174 | − | 0.463353i | \(-0.153354\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.1619 | −0.597484 | −0.298742 | − | 0.954334i | \(-0.596567\pi\) | ||||
−0.298742 | + | 0.954334i | \(0.596567\pi\) | |||||||
\(350\) | 3.97232 | − | 20.3324i | 0.212330 | − | 1.08681i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.76853i | 0.254164i | ||||||||
\(353\) | 12.6563i | 0.673628i | 0.941571 | + | 0.336814i | \(0.109349\pi\) | ||||
−0.941571 | + | 0.336814i | \(0.890651\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.17215 | − | 11.1375i | −0.486807 | − | 0.591117i | ||||
\(356\) | −7.29569 | −0.386671 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 17.2224i | − | 0.910232i | ||||||
\(359\) | −23.2778 | −1.22855 | −0.614277 | − | 0.789091i | \(-0.710552\pi\) | ||||
−0.614277 | + | 0.789091i | \(0.710552\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.5735 | −0.819655 | ||||||||
\(362\) | − | 23.5098i | − | 1.23565i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −16.2314 | −0.850755 | ||||||||
\(365\) | −18.5923 | + | 15.3115i | −0.973167 | + | 0.801439i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.09417i | 0.474712i | 0.971423 | + | 0.237356i | \(0.0762808\pi\) | ||||
−0.971423 | + | 0.237356i | \(0.923719\pi\) | |||||||
\(368\) | 1.54229i | 0.0803976i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.42149 | + | 1.72608i | 0.0738999 | + | 0.0897347i | ||||
\(371\) | −21.2808 | −1.10484 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.75976i | 0.298229i | 0.988820 | + | 0.149114i | \(0.0476423\pi\) | ||||
−0.988820 | + | 0.149114i | \(0.952358\pi\) | |||||||
\(374\) | −15.8142 | −0.817733 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.82700 | 0.248933 | ||||||||
\(377\) | − | 34.7603i | − | 1.79025i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.0902 | −0.929229 | −0.464614 | − | 0.885513i | \(-0.653807\pi\) | ||||
−0.464614 | + | 0.885513i | \(0.653807\pi\) | |||||||
\(380\) | −2.63131 | − | 3.19514i | −0.134984 | − | 0.163907i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 1.16660i | − | 0.0596887i | ||||||
\(383\) | − | 3.54752i | − | 0.181270i | −0.995884 | − | 0.0906350i | \(-0.971110\pi\) | ||
0.995884 | − | 0.0906350i | \(-0.0288896\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −34.1035 | + | 28.0855i | −1.73808 | + | 1.43137i | ||||
\(386\) | 9.36727 | 0.476781 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 14.8988i | 0.756371i | ||||||||
\(389\) | 25.6053 | 1.29824 | 0.649119 | − | 0.760687i | \(-0.275138\pi\) | ||||
0.649119 | + | 0.760687i | \(0.275138\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.11481 | −0.258667 | ||||||||
\(392\) | 10.1675i | 0.513534i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.21836 | −0.162139 | ||||||||
\(395\) | 1.70374 | + | 2.06881i | 0.0857247 | + | 0.104093i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 31.4597i | − | 1.57892i | −0.613803 | − | 0.789459i | \(-0.710361\pi\) | ||
0.613803 | − | 0.789459i | \(-0.289639\pi\) | |||||||
\(398\) | 2.99104i | 0.149927i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.958719 | + | 4.90723i | −0.0479360 | + | 0.245361i | ||||
\(401\) | 22.9940 | 1.14826 | 0.574132 | − | 0.818763i | \(-0.305340\pi\) | ||||
0.574132 | + | 0.818763i | \(0.305340\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 38.2062i | − | 1.90319i | ||||||
\(404\) | 18.5903 | 0.924902 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −36.7650 | −1.82462 | ||||||||
\(407\) | − | 4.76853i | − | 0.236367i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 33.3828 | 1.65067 | 0.825337 | − | 0.564640i | \(-0.190985\pi\) | ||||
0.825337 | + | 0.564640i | \(0.190985\pi\) | |||||||
\(410\) | −8.75083 | + | 7.20663i | −0.432173 | + | 0.355910i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 13.3033i | 0.655404i | ||||||||
\(413\) | − | 4.36394i | − | 0.214735i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.4574 | − | 15.2003i | 0.906037 | − | 0.746155i | ||||
\(416\) | 3.91744 | 0.192068 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 8.82700i | 0.431743i | ||||||||
\(419\) | 8.32565 | 0.406734 | 0.203367 | − | 0.979103i | \(-0.434811\pi\) | ||||
0.203367 | + | 0.979103i | \(0.434811\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.41521 | −0.410132 | −0.205066 | − | 0.978748i | \(-0.565741\pi\) | ||||
−0.205066 | + | 0.978748i | \(0.565741\pi\) | |||||||
\(422\) | 4.75340i | 0.231392i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5.13611 | 0.249432 | ||||||||
\(425\) | −16.2742 | − | 3.17946i | −0.789413 | − | 0.154227i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 17.1710i | − | 0.830963i | ||||||
\(428\) | − | 12.4763i | − | 0.603066i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 14.2070 | + | 17.2513i | 0.685124 | + | 0.831929i | ||||
\(431\) | −3.04769 | −0.146802 | −0.0734011 | − | 0.997303i | \(-0.523385\pi\) | ||||
−0.0734011 | + | 0.997303i | \(0.523385\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 22.9439i | 1.10262i | 0.834302 | + | 0.551308i | \(0.185871\pi\) | ||||
−0.834302 | + | 0.551308i | \(0.814129\pi\) | |||||||
\(434\) | −40.4096 | −1.93972 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.35447 | −0.208541 | ||||||||
\(437\) | 2.85493i | 0.136570i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.3033 | −0.491751 | −0.245875 | − | 0.969301i | \(-0.579075\pi\) | ||||
−0.245875 | + | 0.969301i | \(0.579075\pi\) | |||||||
\(440\) | 8.23088 | − | 6.77843i | 0.392392 | − | 0.323149i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 12.9917i | 0.617950i | ||||||||
\(443\) | 4.84236i | 0.230067i | 0.993362 | + | 0.115034i | \(0.0366976\pi\) | ||||
−0.993362 | + | 0.115034i | \(0.963302\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.3708 | + | 12.5930i | 0.491622 | + | 0.596964i | ||||
\(446\) | 6.95635 | 0.329393 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 4.14336i | − | 0.195756i | ||||||
\(449\) | 25.3149 | 1.19468 | 0.597341 | − | 0.801987i | \(-0.296224\pi\) | ||||
0.597341 | + | 0.801987i | \(0.296224\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24.1753 | 1.13837 | ||||||||
\(452\) | 9.54261i | 0.448846i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 22.2980 | 1.04650 | ||||||||
\(455\) | 23.0728 | + | 28.0167i | 1.08167 | + | 1.31344i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 11.9945i | − | 0.561077i | −0.959843 | − | 0.280539i | \(-0.909487\pi\) | ||
0.959843 | − | 0.280539i | \(-0.0905130\pi\) | |||||||
\(458\) | − | 12.9648i | − | 0.605806i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.66212 | − | 2.19236i | 0.124122 | − | 0.102219i | ||||
\(461\) | 23.6570 | 1.10182 | 0.550909 | − | 0.834565i | \(-0.314281\pi\) | ||||
0.550909 | + | 0.834565i | \(0.314281\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 17.3667i | − | 0.807099i | −0.914958 | − | 0.403550i | \(-0.867776\pi\) | ||
0.914958 | − | 0.403550i | \(-0.132224\pi\) | |||||||
\(464\) | 8.87323 | 0.411929 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −10.4327 | −0.483285 | ||||||||
\(467\) | − | 20.4476i | − | 0.946200i | −0.881009 | − | 0.473100i | \(-0.843135\pi\) | ||
0.881009 | − | 0.473100i | \(-0.156865\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.17696 | 0.192874 | ||||||||
\(470\) | −6.86154 | − | 8.33179i | −0.316499 | − | 0.384317i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.05324i | 0.0484791i | ||||||||
\(473\) | − | 47.6589i | − | 2.19136i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.77468 | + | 9.08373i | −0.0814278 | + | 0.416790i | ||||
\(476\) | 13.7409 | 0.629814 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.58711i | 0.0725925i | ||||||||
\(479\) | −34.1325 | −1.55955 | −0.779777 | − | 0.626057i | \(-0.784668\pi\) | ||||
−0.779777 | + | 0.626057i | \(0.784668\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.91744 | −0.178620 | ||||||||
\(482\) | 16.2576i | 0.740513i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −11.7389 | −0.533586 | ||||||||
\(485\) | 25.7165 | − | 21.1785i | 1.16773 | − | 0.961667i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 6.16917i | − | 0.279552i | −0.990183 | − | 0.139776i | \(-0.955362\pi\) | ||
0.990183 | − | 0.139776i | \(-0.0446382\pi\) | |||||||
\(488\) | 4.14422i | 0.187600i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 17.5499 | − | 14.4530i | 0.792822 | − | 0.652918i | ||||
\(491\) | 11.8290 | 0.533836 | 0.266918 | − | 0.963719i | \(-0.413995\pi\) | ||||
0.266918 | + | 0.963719i | \(0.413995\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 29.4269i | 1.32532i | ||||||||
\(494\) | 7.25154 | 0.326262 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.75286 | 0.437916 | ||||||||
\(497\) | − | 26.7350i | − | 1.19923i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −31.4004 | −1.40568 | −0.702839 | − | 0.711349i | \(-0.748084\pi\) | ||||
−0.702839 | + | 0.711349i | \(0.748084\pi\) | |||||||
\(500\) | 9.83309 | − | 5.32076i | 0.439749 | − | 0.237951i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 14.9486i | − | 0.667189i | ||||||
\(503\) | − | 39.7743i | − | 1.77345i | −0.462299 | − | 0.886724i | \(-0.652975\pi\) | ||
0.462299 | − | 0.886724i | \(-0.347025\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −26.4260 | − | 32.0884i | −1.17594 | − | 1.42791i | ||||
\(506\) | −7.35447 | −0.326946 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8.33492i | 0.369802i | ||||||||
\(509\) | −6.82812 | −0.302651 | −0.151326 | − | 0.988484i | \(-0.548354\pi\) | ||||
−0.151326 | + | 0.988484i | \(0.548354\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −44.6299 | −1.97431 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −14.9968 | −0.661480 | ||||||||
\(515\) | 22.9625 | − | 18.9105i | 1.01185 | − | 0.833295i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 23.0177i | 1.01232i | ||||||||
\(518\) | 4.14336i | 0.182049i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −5.56861 | − | 6.76182i | −0.244200 | − | 0.296525i | ||||
\(521\) | 30.6638 | 1.34341 | 0.671703 | − | 0.740821i | \(-0.265563\pi\) | ||||
0.671703 | + | 0.740821i | \(0.265563\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.1618i | 0.531800i | 0.964001 | + | 0.265900i | \(0.0856690\pi\) | ||||
−0.964001 | + | 0.265900i | \(0.914331\pi\) | |||||||
\(524\) | 3.68597 | 0.161022 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 22.9610 | 1.00115 | ||||||||
\(527\) | 32.3441i | 1.40893i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.6213 | 0.896580 | ||||||||
\(530\) | −7.30094 | − | 8.86535i | −0.317133 | − | 0.385086i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 7.66975i | − | 0.332526i | ||||||
\(533\) | − | 19.8605i | − | 0.860253i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −21.5352 | + | 17.7350i | −0.931046 | + | 0.766751i | ||||
\(536\) | −1.00811 | −0.0435437 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 10.0896i | 0.434995i | ||||||||
\(539\) | −48.4839 | −2.08835 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.5469 | 0.453446 | 0.226723 | − | 0.973959i | \(-0.427199\pi\) | ||||
0.226723 | + | 0.973959i | \(0.427199\pi\) | |||||||
\(542\) | 3.30678i | 0.142038i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.31637 | −0.142188 | ||||||||
\(545\) | 6.18985 | + | 7.51617i | 0.265144 | + | 0.321957i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 4.09517i | − | 0.175097i | −0.996160 | − | 0.0875484i | \(-0.972097\pi\) | ||
0.996160 | − | 0.0875484i | \(-0.0279032\pi\) | |||||||
\(548\) | 12.3027i | 0.525546i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −23.4003 | − | 4.57168i | −0.997790 | − | 0.194937i | ||||
\(551\) | 16.4252 | 0.699736 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.96607i | 0.211179i | ||||||||
\(554\) | −15.9046 | −0.675723 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.842442 | −0.0357275 | ||||||||
\(557\) | − | 2.50711i | − | 0.106230i | −0.998588 | − | 0.0531149i | \(-0.983085\pi\) | ||
0.998588 | − | 0.0531149i | \(-0.0169149\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −39.1527 | −1.65598 | ||||||||
\(560\) | −7.15179 | + | 5.88976i | −0.302218 | + | 0.248888i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 11.3609i | − | 0.479229i | ||||||
\(563\) | − | 9.87532i | − | 0.416195i | −0.978108 | − | 0.208097i | \(-0.933273\pi\) | ||
0.978108 | − | 0.208097i | \(-0.0667271\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 16.4713 | − | 13.5647i | 0.692954 | − | 0.570673i | ||||
\(566\) | −20.1530 | −0.847092 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.45248i | 0.270740i | ||||||||
\(569\) | 12.5198 | 0.524858 | 0.262429 | − | 0.964951i | \(-0.415477\pi\) | ||||
0.262429 | + | 0.964951i | \(0.415477\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.3156 | 0.850179 | 0.425090 | − | 0.905151i | \(-0.360243\pi\) | ||||
0.425090 | + | 0.905151i | \(0.360243\pi\) | |||||||
\(572\) | 18.6804i | 0.781068i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −21.0059 | −0.876769 | ||||||||
\(575\) | −7.56838 | − | 1.47863i | −0.315623 | − | 0.0616629i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 20.0756i | − | 0.835759i | −0.908502 | − | 0.417880i | \(-0.862773\pi\) | ||
0.908502 | − | 0.417880i | \(-0.137227\pi\) | |||||||
\(578\) | 6.00171i | 0.249638i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −12.6132 | − | 15.3159i | −0.523736 | − | 0.635959i | ||||
\(581\) | 44.3059 | 1.83812 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 24.4917i | 1.01434i | ||||||||
\(584\) | 10.7714 | 0.445724 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −21.0517 | −0.869639 | ||||||||
\(587\) | 3.71178i | 0.153201i | 0.997062 | + | 0.0766007i | \(0.0244067\pi\) | ||||
−0.997062 | + | 0.0766007i | \(0.975593\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.0534 | 0.743879 | ||||||||
\(590\) | 1.81797 | − | 1.49717i | 0.0748447 | − | 0.0616373i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 1.00000i | − | 0.0410997i | ||||||
\(593\) | − | 36.2899i | − | 1.49025i | −0.666926 | − | 0.745124i | \(-0.732390\pi\) | ||
0.666926 | − | 0.745124i | \(-0.267610\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −19.5326 | − | 23.7179i | −0.800759 | − | 0.972341i | ||||
\(596\) | 16.7723 | 0.687019 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 6.04184i | 0.247069i | ||||||||
\(599\) | 23.7528 | 0.970515 | 0.485257 | − | 0.874371i | \(-0.338726\pi\) | ||||
0.485257 | + | 0.874371i | \(0.338726\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.9718 | 0.651502 | 0.325751 | − | 0.945456i | \(-0.394383\pi\) | ||||
0.325751 | + | 0.945456i | \(0.394383\pi\) | |||||||
\(602\) | 41.4107i | 1.68777i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 7.59755 | 0.309140 | ||||||||
\(605\) | 16.6867 | + | 20.2623i | 0.678413 | + | 0.823779i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 38.0139i | − | 1.54294i | −0.636267 | − | 0.771469i | \(-0.719522\pi\) | ||
0.636267 | − | 0.771469i | \(-0.280478\pi\) | |||||||
\(608\) | 1.85109i | 0.0750717i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.15326 | − | 5.89098i | 0.289627 | − | 0.238519i | ||||
\(611\) | 18.9095 | 0.764995 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 8.40204i | − | 0.339355i | −0.985500 | − | 0.169678i | \(-0.945727\pi\) | ||
0.985500 | − | 0.169678i | \(-0.0542726\pi\) | |||||||
\(614\) | 17.0946 | 0.689880 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 19.7578 | 0.796063 | ||||||||
\(617\) | − | 6.72707i | − | 0.270822i | −0.990790 | − | 0.135411i | \(-0.956765\pi\) | ||
0.990790 | − | 0.135411i | \(-0.0432354\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24.3689 | −0.979470 | −0.489735 | − | 0.871871i | \(-0.662906\pi\) | ||||
−0.489735 | + | 0.871871i | \(0.662906\pi\) | |||||||
\(620\) | −13.8636 | − | 16.8342i | −0.556776 | − | 0.676079i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 20.0503i | − | 0.803943i | ||||||
\(623\) | 30.2287i | 1.21109i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.1617 | − | 9.40930i | −0.926469 | − | 0.376372i | ||||
\(626\) | −13.3400 | −0.533172 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.45631i | 0.177826i | ||||||||
\(629\) | 3.31637 | 0.132232 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.7737 | 1.38432 | 0.692160 | − | 0.721744i | \(-0.256659\pi\) | ||||
0.692160 | + | 0.721744i | \(0.256659\pi\) | |||||||
\(632\) | − | 1.19856i | − | 0.0476762i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −12.8528 | −0.510450 | ||||||||
\(635\) | 14.3868 | − | 11.8480i | 0.570921 | − | 0.470175i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 39.8304i | 1.57814i | ||||||||
\(638\) | 42.3123i | 1.67516i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.72608 | − | 1.42149i | 0.0682294 | − | 0.0561894i | ||||
\(641\) | 27.8544 | 1.10018 | 0.550091 | − | 0.835105i | \(-0.314593\pi\) | ||||
0.550091 | + | 0.835105i | \(0.314593\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 35.4013i | − | 1.39609i | −0.716054 | − | 0.698045i | \(-0.754053\pi\) | ||
0.716054 | − | 0.698045i | \(-0.245947\pi\) | |||||||
\(644\) | 6.39028 | 0.251812 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.13890 | −0.241532 | ||||||||
\(647\) | 16.1343i | 0.634305i | 0.948375 | + | 0.317152i | \(0.102727\pi\) | ||||
−0.948375 | + | 0.317152i | \(0.897273\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.02239 | −0.197146 | ||||||||
\(650\) | −3.75572 | + | 19.2238i | −0.147312 | + | 0.754018i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 19.4599i | − | 0.762110i | ||||||
\(653\) | − | 11.9146i | − | 0.466256i | −0.972446 | − | 0.233128i | \(-0.925104\pi\) | ||
0.972446 | − | 0.233128i | \(-0.0748961\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.23958 | − | 6.36229i | −0.204727 | − | 0.248595i | ||||
\(656\) | 5.06977 | 0.197941 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 20.0000i | − | 0.779681i | ||||||
\(659\) | −30.5124 | −1.18859 | −0.594297 | − | 0.804246i | \(-0.702569\pi\) | ||||
−0.594297 | + | 0.804246i | \(0.702569\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 42.0973 | 1.63740 | 0.818698 | − | 0.574224i | \(-0.194696\pi\) | ||||
0.818698 | + | 0.574224i | \(0.194696\pi\) | |||||||
\(662\) | − | 23.5835i | − | 0.916600i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10.6932 | −0.414977 | ||||||||
\(665\) | −13.2386 | + | 10.9025i | −0.513372 | + | 0.422781i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13.6851i | 0.529890i | ||||||||
\(668\) | − | 7.13813i | − | 0.276183i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.43302 | + | 1.74008i | 0.0553623 | + | 0.0672251i | ||||
\(671\) | −19.7618 | −0.762897 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 41.1540i | − | 1.58637i | −0.608982 | − | 0.793184i | \(-0.708422\pi\) | ||
0.608982 | − | 0.793184i | \(-0.291578\pi\) | |||||||
\(674\) | 26.6074 | 1.02488 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.34632 | 0.0902431 | ||||||||
\(677\) | − | 10.3914i | − | 0.399373i | −0.979860 | − | 0.199686i | \(-0.936008\pi\) | ||
0.979860 | − | 0.199686i | \(-0.0639923\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 61.7311 | 2.36902 | ||||||||
\(680\) | 4.71419 | + | 5.72432i | 0.180781 | + | 0.219518i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 46.5068i | 1.78084i | ||||||||
\(683\) | − | 5.05345i | − | 0.193365i | −0.995315 | − | 0.0966824i | \(-0.969177\pi\) | ||
0.995315 | − | 0.0966824i | \(-0.0308231\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.2355 | − | 17.4882i | 0.811367 | − | 0.668190i | ||||
\(686\) | 13.1239 | 0.501074 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 9.99446i | − | 0.381035i | ||||||
\(689\) | 20.1204 | 0.766526 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.7857 | 0.524432 | 0.262216 | − | 0.965009i | \(-0.415547\pi\) | ||||
0.262216 | + | 0.965009i | \(0.415547\pi\) | |||||||
\(692\) | − | 11.6199i | − | 0.441724i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 17.2626 | 0.655280 | ||||||||
\(695\) | 1.19753 | + | 1.45412i | 0.0454247 | + | 0.0551581i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.8132i | 0.636846i | ||||||||
\(698\) | − | 11.1619i | − | 0.422485i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 20.3324 | + | 3.97232i | 0.768493 | + | 0.150140i | ||||
\(701\) | 2.20512 | 0.0832862 | 0.0416431 | − | 0.999133i | \(-0.486741\pi\) | ||||
0.0416431 | + | 0.999133i | \(0.486741\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1.85109i | − | 0.0698153i | ||||||
\(704\) | −4.76853 | −0.179721 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −12.6563 | −0.476327 | ||||||||
\(707\) | − | 77.0264i | − | 2.89687i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.7194 | 0.477687 | 0.238843 | − | 0.971058i | \(-0.423232\pi\) | ||||
0.238843 | + | 0.971058i | \(0.423232\pi\) | |||||||
\(710\) | 11.1375 | − | 9.17215i | 0.417983 | − | 0.344225i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 7.29569i | − | 0.273418i | ||||||
\(713\) | 15.0418i | 0.563318i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 32.2439 | − | 26.5541i | 1.20586 | − | 0.993066i | ||||
\(716\) | 17.2224 | 0.643631 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 23.2778i | − | 0.868718i | ||||||
\(719\) | 34.9654 | 1.30399 | 0.651996 | − | 0.758223i | \(-0.273932\pi\) | ||||
0.651996 | + | 0.758223i | \(0.273932\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 55.1202 | 2.05278 | ||||||||
\(722\) | − | 15.5735i | − | 0.579584i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 23.5098 | 0.873733 | ||||||||
\(725\) | −8.50693 | + | 43.5429i | −0.315940 | + | 1.61714i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.90635i | 0.367406i | 0.982982 | + | 0.183703i | \(0.0588085\pi\) | ||||
−0.982982 | + | 0.183703i | \(0.941191\pi\) | |||||||
\(728\) | − | 16.2314i | − | 0.601575i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −15.3115 | − | 18.5923i | −0.566703 | − | 0.688133i | ||||
\(731\) | 33.1453 | 1.22592 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 37.3826i | 1.38076i | 0.723448 | + | 0.690379i | \(0.242556\pi\) | ||||
−0.723448 | + | 0.690379i | \(0.757444\pi\) | |||||||
\(734\) | −9.09417 | −0.335672 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.54229 | −0.0568497 | ||||||||
\(737\) | − | 4.80720i | − | 0.177075i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.4487 | −0.531506 | −0.265753 | − | 0.964041i | \(-0.585620\pi\) | ||||
−0.265753 | + | 0.964041i | \(0.585620\pi\) | |||||||
\(740\) | −1.72608 | + | 1.42149i | −0.0634520 | + | 0.0522551i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 21.2808i | − | 0.781242i | ||||||
\(743\) | − | 45.1826i | − | 1.65759i | −0.559553 | − | 0.828794i | \(-0.689027\pi\) | ||
0.559553 | − | 0.828794i | \(-0.310973\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −23.8416 | − | 28.9503i | −0.873490 | − | 1.06066i | ||||
\(746\) | −5.75976 | −0.210880 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 15.8142i | − | 0.578224i | ||||||
\(749\) | −51.6939 | −1.88886 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 49.3127 | 1.79945 | 0.899723 | − | 0.436461i | \(-0.143768\pi\) | ||||
0.899723 | + | 0.436461i | \(0.143768\pi\) | |||||||
\(752\) | 4.82700i | 0.176022i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 34.7603 | 1.26590 | ||||||||
\(755\) | −10.7999 | − | 13.1140i | −0.393047 | − | 0.477267i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 21.5911i | − | 0.784741i | −0.919807 | − | 0.392370i | \(-0.871655\pi\) | ||
0.919807 | − | 0.392370i | \(-0.128345\pi\) | |||||||
\(758\) | − | 18.0902i | − | 0.657064i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.19514 | − | 2.63131i | 0.115900 | − | 0.0954478i | ||||
\(761\) | −18.4253 | −0.667917 | −0.333959 | − | 0.942588i | \(-0.608385\pi\) | ||||
−0.333959 | + | 0.942588i | \(0.608385\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 18.0422i | 0.653170i | ||||||||
\(764\) | 1.16660 | 0.0422063 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.54752 | 0.128177 | ||||||||
\(767\) | 4.12598i | 0.148981i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.50829 | −0.234695 | −0.117348 | − | 0.993091i | \(-0.537439\pi\) | ||||
−0.117348 | + | 0.993091i | \(0.537439\pi\) | |||||||
\(770\) | −28.0855 | − | 34.1035i | −1.01213 | − | 1.22901i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 9.36727i | 0.337135i | ||||||||
\(773\) | 40.5853i | 1.45975i | 0.683581 | + | 0.729875i | \(0.260422\pi\) | ||||
−0.683581 | + | 0.729875i | \(0.739578\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.35025 | + | 47.8595i | −0.335871 | + | 1.71916i | ||||
\(776\) | −14.8988 | −0.534835 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 25.6053i | 0.917993i | ||||||||
\(779\) | 9.38461 | 0.336239 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −30.7688 | −1.10100 | ||||||||
\(782\) | − | 5.11481i | − | 0.182905i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −10.1675 | −0.363124 | ||||||||
\(785\) | 7.69196 | − | 6.33461i | 0.274538 | − | 0.226092i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 37.5389i | 1.33812i | 0.743210 | + | 0.669059i | \(0.233302\pi\) | ||||
−0.743210 | + | 0.669059i | \(0.766698\pi\) | |||||||
\(788\) | − | 3.21836i | − | 0.114649i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.06881 | + | 1.70374i | −0.0736051 | + | 0.0606165i | ||||
\(791\) | 39.5385 | 1.40583 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.2347i | 0.576512i | ||||||||
\(794\) | 31.4597 | 1.11646 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.99104 | −0.106014 | ||||||||
\(797\) | 28.8746i | 1.02279i | 0.859345 | + | 0.511396i | \(0.170871\pi\) | ||||
−0.859345 | + | 0.511396i | \(0.829129\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16.0081 | −0.566326 | ||||||||
\(800\) | −4.90723 | − | 0.958719i | −0.173497 | − | 0.0338958i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 22.9940i | 0.811945i | ||||||||
\(803\) | 51.3638i | 1.81259i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.08373 | − | 11.0301i | −0.320159 | − | 0.388762i | ||||
\(806\) | 38.2062 | 1.34576 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 18.5903i | 0.654004i | ||||||||
\(809\) | −8.98633 | −0.315943 | −0.157971 | − | 0.987444i | \(-0.550495\pi\) | ||||
−0.157971 | + | 0.987444i | \(0.550495\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −24.4949 | −0.860134 | −0.430067 | − | 0.902797i | \(-0.641510\pi\) | ||||
−0.430067 | + | 0.902797i | \(0.641510\pi\) | |||||||
\(812\) | − | 36.7650i | − | 1.29020i | ||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.76853 | 0.167137 | ||||||||
\(815\) | −33.5895 | + | 27.6622i | −1.17659 | + | 0.968963i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 18.5007i | − | 0.647257i | ||||||
\(818\) | 33.3828i | 1.16720i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.20663 | − | 8.75083i | −0.251667 | − | 0.305592i | ||||
\(821\) | −27.1346 | −0.947005 | −0.473502 | − | 0.880793i | \(-0.657010\pi\) | ||||
−0.473502 | + | 0.880793i | \(0.657010\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 10.7460i | − | 0.374584i | −0.982304 | − | 0.187292i | \(-0.940029\pi\) | ||
0.982304 | − | 0.187292i | \(-0.0599710\pi\) | |||||||
\(824\) | −13.3033 | −0.463441 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.36394 | 0.151841 | ||||||||
\(827\) | 19.1035i | 0.664293i | 0.943228 | + | 0.332147i | \(0.107773\pi\) | ||||
−0.943228 | + | 0.332147i | \(0.892227\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −51.1250 | −1.77565 | −0.887823 | − | 0.460185i | \(-0.847783\pi\) | ||||
−0.887823 | + | 0.460185i | \(0.847783\pi\) | |||||||
\(830\) | 15.2003 | + | 18.4574i | 0.527611 | + | 0.640665i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.91744i | 0.135813i | ||||||||
\(833\) | − | 33.7190i | − | 1.16830i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.3210 | + | 10.1468i | −0.426386 | + | 0.351145i | ||||
\(836\) | −8.82700 | −0.305288 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8.32565i | 0.287605i | ||||||||
\(839\) | −42.1947 | −1.45672 | −0.728361 | − | 0.685193i | \(-0.759718\pi\) | ||||
−0.728361 | + | 0.685193i | \(0.759718\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 49.7342 | 1.71497 | ||||||||
\(842\) | − | 8.41521i | − | 0.290007i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.75340 | −0.163619 | ||||||||
\(845\) | −3.33528 | − | 4.04994i | −0.114737 | − | 0.139322i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 48.6385i | 1.67124i | ||||||||
\(848\) | 5.13611i | 0.176375i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.17946 | − | 16.2742i | 0.109055 | − | 0.558199i | ||||
\(851\) | 1.54229 | 0.0528691 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 42.5489i | 1.45685i | 0.685128 | + | 0.728423i | \(0.259746\pi\) | ||||
−0.685128 | + | 0.728423i | \(0.740254\pi\) | |||||||
\(854\) | 17.1710 | 0.587580 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12.4763 | 0.426432 | ||||||||
\(857\) | 29.7588i | 1.01654i | 0.861197 | + | 0.508271i | \(0.169715\pi\) | ||||
−0.861197 | + | 0.508271i | \(0.830285\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.40182 | −0.286666 | −0.143333 | − | 0.989674i | \(-0.545782\pi\) | ||||
−0.143333 | + | 0.989674i | \(0.545782\pi\) | |||||||
\(860\) | −17.2513 | + | 14.2070i | −0.588263 | + | 0.484456i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 3.04769i | − | 0.103805i | ||||||
\(863\) | 36.3794i | 1.23837i | 0.785245 | + | 0.619185i | \(0.212537\pi\) | ||||
−0.785245 | + | 0.619185i | \(0.787463\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −20.0570 | + | 16.5177i | −0.681957 | + | 0.561617i | ||||
\(866\) | −22.9439 | −0.779667 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 40.4096i | − | 1.37159i | ||||||
\(869\) | 5.71537 | 0.193881 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.94920 | −0.133814 | ||||||||
\(872\) | − | 4.35447i | − | 0.147461i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.85493 | −0.0965694 | ||||||||
\(875\) | −22.0458 | − | 40.7420i | −0.745285 | − | 1.37733i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 41.3380i | − | 1.39588i | −0.716154 | − | 0.697942i | \(-0.754099\pi\) | ||
0.716154 | − | 0.697942i | \(-0.245901\pi\) | |||||||
\(878\) | − | 10.3033i | − | 0.347720i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 6.77843 | + | 8.23088i | 0.228501 | + | 0.277463i | ||||
\(881\) | −21.1354 | −0.712071 | −0.356035 | − | 0.934472i | \(-0.615872\pi\) | ||||
−0.356035 | + | 0.934472i | \(0.615872\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 10.7365i | − | 0.361312i | −0.983546 | − | 0.180656i | \(-0.942178\pi\) | ||
0.983546 | − | 0.180656i | \(-0.0578221\pi\) | |||||||
\(884\) | −12.9917 | −0.436957 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.84236 | −0.162682 | ||||||||
\(887\) | − | 11.1798i | − | 0.375379i | −0.982228 | − | 0.187690i | \(-0.939900\pi\) | ||
0.982228 | − | 0.187690i | \(-0.0600999\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 34.5346 | 1.15825 | ||||||||
\(890\) | −12.5930 | + | 10.3708i | −0.422117 | + | 0.347629i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.95635i | 0.232916i | ||||||||
\(893\) | 8.93522i | 0.299006i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −24.4815 | − | 29.7273i | −0.818327 | − | 0.993674i | ||||
\(896\) | 4.14336 | 0.138420 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 25.3149i | 0.844768i | ||||||||
\(899\) | 86.5393 | 2.88625 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17.0332 | −0.567459 | ||||||||
\(902\) | 24.1753i | 0.804951i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9.54261 | −0.317382 | ||||||||
\(905\) | −33.4189 | − | 40.5798i | −1.11088 | − | 1.34892i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.5343i | 0.681831i | 0.940094 | + | 0.340915i | \(0.110737\pi\) | ||||
−0.940094 | + | 0.340915i | \(0.889263\pi\) | |||||||
\(908\) | 22.2980i | 0.739986i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −28.0167 | + | 23.0728i | −0.928744 | + | 0.764855i | ||||
\(911\) | −17.5197 | −0.580454 | −0.290227 | − | 0.956958i | \(-0.593731\pi\) | ||||
−0.290227 | + | 0.956958i | \(0.593731\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 50.9910i | − | 1.68755i | ||||||
\(914\) | 11.9945 | 0.396741 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 12.9648 | 0.428370 | ||||||||
\(917\) | − | 15.2723i | − | 0.504336i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −43.8760 | −1.44734 | −0.723668 | − | 0.690149i | \(-0.757545\pi\) | ||||
−0.723668 | + | 0.690149i | \(0.757545\pi\) | |||||||
\(920\) | 2.19236 | + | 2.66212i | 0.0722799 | + | 0.0877676i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 23.6570i | 0.779103i | ||||||||
\(923\) | 25.2772i | 0.832009i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.90723 | + | 0.958719i | 0.161349 | + | 0.0315225i | ||||
\(926\) | 17.3667 | 0.570705 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 8.87323i | 0.291278i | ||||||||
\(929\) | −21.9800 | −0.721142 | −0.360571 | − | 0.932732i | \(-0.617418\pi\) | ||||
−0.360571 | + | 0.932732i | \(0.617418\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.8209 | −0.616831 | ||||||||
\(932\) | − | 10.4327i | − | 0.341734i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 20.4476 | 0.669065 | ||||||||
\(935\) | −27.2966 | + | 22.4798i | −0.892695 | + | 0.735167i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.62735i | 0.314512i | 0.987558 | + | 0.157256i | \(0.0502648\pi\) | ||||
−0.987558 | + | 0.157256i | \(0.949735\pi\) | |||||||
\(938\) | 4.17696i | 0.136383i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 8.33179 | − | 6.86154i | 0.271753 | − | 0.223799i | ||||
\(941\) | 28.3548 | 0.924340 | 0.462170 | − | 0.886791i | \(-0.347071\pi\) | ||||
0.462170 | + | 0.886791i | \(0.347071\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.81906i | 0.254624i | ||||||||
\(944\) | −1.05324 | −0.0342799 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 47.6589 | 1.54952 | ||||||||
\(947\) | − | 12.5179i | − | 0.406778i | −0.979098 | − | 0.203389i | \(-0.934804\pi\) | ||
0.979098 | − | 0.203389i | \(-0.0651956\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 42.1963 | 1.36975 | ||||||||
\(950\) | −9.08373 | − | 1.77468i | −0.294715 | − | 0.0575782i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 13.7409i | 0.445346i | ||||||||
\(953\) | 3.39730i | 0.110049i | 0.998485 | + | 0.0550247i | \(0.0175238\pi\) | ||||
−0.998485 | + | 0.0550247i | \(0.982476\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.65832 | − | 2.01366i | −0.0536620 | − | 0.0651603i | ||||
\(956\) | −1.58711 | −0.0513307 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 34.1325i | − | 1.10277i | ||||||
\(959\) | 50.9746 | 1.64606 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 64.1182 | 2.06833 | ||||||||
\(962\) | − | 3.91744i | − | 0.126303i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −16.2576 | −0.523622 | ||||||||
\(965\) | 16.1687 | − | 13.3155i | 0.520488 | − | 0.428641i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 2.54955i | − | 0.0819879i | −0.999159 | − | 0.0409940i | \(-0.986948\pi\) | ||
0.999159 | − | 0.0409940i | \(-0.0130524\pi\) | |||||||
\(968\) | − | 11.7389i | − | 0.377302i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 21.1785 | + | 25.7165i | 0.680001 | + | 0.825708i | ||||
\(971\) | 35.2223 | 1.13034 | 0.565168 | − | 0.824976i | \(-0.308811\pi\) | ||||
0.565168 | + | 0.824976i | \(0.308811\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.49054i | 0.111902i | ||||||||
\(974\) | 6.16917 | 0.197673 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.14422 | −0.132653 | ||||||||
\(977\) | − | 5.79786i | − | 0.185490i | −0.995690 | − | 0.0927450i | \(-0.970436\pi\) | ||
0.995690 | − | 0.0927450i | \(-0.0295641\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 34.7897 | 1.11188 | ||||||||
\(980\) | 14.4530 | + | 17.5499i | 0.461683 | + | 0.560610i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 11.8290i | 0.377479i | ||||||||
\(983\) | 20.6825i | 0.659671i | 0.944038 | + | 0.329835i | \(0.106993\pi\) | ||||
−0.944038 | + | 0.329835i | \(0.893007\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.55515 | + | 4.57487i | −0.177002 | + | 0.145768i | ||||
\(986\) | −29.4269 | −0.937143 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 7.25154i | 0.230702i | ||||||||
\(989\) | 15.4144 | 0.490149 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 49.7158 | 1.57927 | 0.789637 | − | 0.613574i | \(-0.210269\pi\) | ||||
0.789637 | + | 0.613574i | \(0.210269\pi\) | |||||||
\(992\) | 9.75286i | 0.309654i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 26.7350 | 0.847981 | ||||||||
\(995\) | 4.25173 | + | 5.16277i | 0.134789 | + | 0.163671i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 53.1550i | 1.68344i | 0.539918 | + | 0.841718i | \(0.318455\pi\) | ||||
−0.539918 | + | 0.841718i | \(0.681545\pi\) | |||||||
\(998\) | − | 31.4004i | − | 0.993964i | ||||||
\(999\) | 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 | 3330.2.d.p.1999.10 | 10 | ||
3.2 | odd | 2 | 370.2.b.d.149.1 | ✓ | 10 | ||
5.4 | even | 2 | inner | 3330.2.d.p.1999.5 | 10 | ||
15.2 | even | 4 | 1850.2.a.be.1.1 | 5 | |||
15.8 | even | 4 | 1850.2.a.bd.1.5 | 5 | |||
15.14 | odd | 2 | 370.2.b.d.149.10 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.2.b.d.149.1 | ✓ | 10 | 3.2 | odd | 2 | ||
370.2.b.d.149.10 | yes | 10 | 15.14 | odd | 2 | ||
1850.2.a.bd.1.5 | 5 | 15.8 | even | 4 | |||
1850.2.a.be.1.1 | 5 | 15.2 | even | 4 | |||
3330.2.d.p.1999.5 | 10 | 5.4 | even | 2 | inner | ||
3330.2.d.p.1999.10 | 10 | 1.1 | even | 1 | trivial |