Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4864,2,Mod(1,4864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4864, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4864.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4864 = 2^{8} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4864.a (trivial) |
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: | yes |
Analytic conductor: | \(38.8392355432\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.316.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2432) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.470683\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4864.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | 0 | ||||||||
\(3\) | 2.24914 | 1.29854 | 0.649271 | − | 0.760557i | \(-0.275074\pi\) | ||||
0.649271 | + | 0.760557i | \(0.275074\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.47068 | −0.657710 | −0.328855 | − | 0.944380i | \(-0.606663\pi\) | ||||
−0.328855 | + | 0.944380i | \(0.606663\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.47068 | −0.555866 | −0.277933 | − | 0.960600i | \(-0.589649\pi\) | ||||
−0.277933 | + | 0.960600i | \(0.589649\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.05863 | 0.686211 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.77846 | 1.44076 | 0.720380 | − | 0.693580i | \(-0.243968\pi\) | ||||
0.720380 | + | 0.693580i | \(0.243968\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.49828 | −1.24760 | −0.623799 | − | 0.781585i | \(-0.714412\pi\) | ||||
−0.623799 | + | 0.781585i | \(0.714412\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.30777 | −0.854063 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.71982 | 0.417119 | 0.208559 | − | 0.978010i | \(-0.433123\pi\) | ||||
0.208559 | + | 0.978010i | \(0.433123\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.30777 | −0.721815 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.00000 | −0.834058 | −0.417029 | − | 0.908893i | \(-0.636929\pi\) | ||||
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.83709 | −0.567418 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.11727 | −0.407468 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.80605 | −1.44955 | −0.724774 | − | 0.688987i | \(-0.758056\pi\) | ||||
−0.724774 | + | 0.688987i | \(0.758056\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.13187 | 0.742107 | 0.371053 | − | 0.928612i | \(-0.378997\pi\) | ||||
0.371053 | + | 0.928612i | \(0.378997\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 10.7474 | 1.87089 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.16291 | 0.365598 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.30777 | −0.543795 | −0.271897 | − | 0.962326i | \(-0.587651\pi\) | ||||
−0.271897 | + | 0.962326i | \(0.587651\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −10.1173 | −1.62006 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.80605 | −1.53145 | −0.765724 | − | 0.643169i | \(-0.777619\pi\) | ||||
−0.765724 | + | 0.643169i | \(0.777619\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.83709 | −0.280154 | −0.140077 | − | 0.990141i | \(-0.544735\pi\) | ||||
−0.140077 | + | 0.990141i | \(0.544735\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.02760 | −0.451328 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.14486 | 0.750456 | 0.375228 | − | 0.926933i | \(-0.377564\pi\) | ||||
0.375228 | + | 0.926933i | \(0.377564\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.83709 | −0.691013 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.86813 | 0.541646 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.8647 | 1.76710 | 0.883550 | − | 0.468336i | \(-0.155146\pi\) | ||||
0.883550 | + | 0.468336i | \(0.155146\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.02760 | −0.947601 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.24914 | 0.297906 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.05863 | −1.17933 | −0.589667 | − | 0.807647i | \(-0.700741\pi\) | ||||
−0.589667 | + | 0.807647i | \(0.700741\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.91033 | −1.14085 | −0.570426 | − | 0.821349i | \(-0.693222\pi\) | ||||
−0.570426 | + | 0.821349i | \(0.693222\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.02760 | −0.381441 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.61555 | 0.820558 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.92332 | −0.723649 | −0.361824 | − | 0.932246i | \(-0.617846\pi\) | ||||
−0.361824 | + | 0.932246i | \(0.617846\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −8.99656 | −1.08306 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.05520 | 0.718619 | 0.359310 | − | 0.933218i | \(-0.383012\pi\) | ||||
0.359310 | + | 0.933218i | \(0.383012\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.335371 | −0.0392522 | −0.0196261 | − | 0.999807i | \(-0.506248\pi\) | ||||
−0.0196261 | + | 0.999807i | \(0.506248\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.38101 | −0.736816 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.02760 | −0.800869 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.366407 | 0.0412240 | 0.0206120 | − | 0.999788i | \(-0.493439\pi\) | ||||
0.0206120 | + | 0.999788i | \(0.493439\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.9379 | −1.21533 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 18.0552 | 1.98182 | 0.990908 | − | 0.134544i | \(-0.0429571\pi\) | ||||
0.990908 | + | 0.134544i | \(0.0429571\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.52932 | −0.274343 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −17.5569 | −1.88230 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.36641 | 0.250839 | 0.125419 | − | 0.992104i | \(-0.459972\pi\) | ||||
0.125419 | + | 0.992104i | \(0.459972\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.61555 | 0.693498 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.29317 | 0.963656 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.47068 | −0.150889 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.05863 | −0.716696 | −0.358348 | − | 0.933588i | \(-0.616660\pi\) | ||||
−0.358348 | + | 0.933588i | \(0.616660\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 9.83709 | 0.988665 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.94137 | 0.690692 | 0.345346 | − | 0.938475i | \(-0.387762\pi\) | ||||
0.345346 | + | 0.938475i | \(0.387762\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.824101 | −0.0812010 | −0.0406005 | − | 0.999175i | \(-0.512927\pi\) | ||||
−0.0406005 | + | 0.999175i | \(0.512927\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.86469 | 0.474745 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.4396 | −1.10591 | −0.552956 | − | 0.833210i | \(-0.686500\pi\) | ||||
−0.552956 | + | 0.833210i | \(0.686500\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.13187 | 0.395762 | 0.197881 | − | 0.980226i | \(-0.436594\pi\) | ||||
0.197881 | + | 0.980226i | \(0.436594\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.43965 | −0.706140 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.92332 | −0.745363 | −0.372682 | − | 0.927959i | \(-0.621562\pi\) | ||||
−0.372682 | + | 0.927959i | \(0.621562\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.88273 | 0.548568 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −9.26031 | −0.856116 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.52932 | −0.231862 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.8337 | 1.07579 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −22.0552 | −1.98865 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.5259 | 1.03091 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.19051 | −0.105640 | −0.0528202 | − | 0.998604i | \(-0.516821\pi\) | ||||
−0.0528202 | + | 0.998604i | \(0.516821\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.13187 | −0.363791 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.39744 | −0.209466 | −0.104733 | − | 0.994500i | \(-0.533399\pi\) | ||||
−0.104733 | + | 0.994500i | \(0.533399\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.47068 | −0.127524 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.11383 | 0.267996 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.39400 | −0.802584 | −0.401292 | − | 0.915950i | \(-0.631439\pi\) | ||||
−0.401292 | + | 0.915950i | \(0.631439\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.2181 | 1.03633 | 0.518163 | − | 0.855282i | \(-0.326616\pi\) | ||||
0.518163 | + | 0.855282i | \(0.326616\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.5715 | 0.974498 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −21.4948 | −1.79749 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.4802 | 0.953382 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −10.8793 | −0.897309 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.8190 | −1.37787 | −0.688935 | − | 0.724823i | \(-0.741921\pi\) | ||||
−0.688935 | + | 0.724823i | \(0.741921\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.17590 | 0.583966 | 0.291983 | − | 0.956423i | \(-0.405685\pi\) | ||||
0.291983 | + | 0.956423i | \(0.405685\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.54049 | 0.286231 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.07668 | −0.488091 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.6742 | −1.25094 | −0.625468 | − | 0.780250i | \(-0.715092\pi\) | ||||
−0.625468 | + | 0.780250i | \(0.715092\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 28.9345 | 2.29465 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.88273 | 0.463624 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.32238 | −0.730185 | −0.365093 | − | 0.930971i | \(-0.618963\pi\) | ||||
−0.365093 | + | 0.930971i | \(0.618963\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −15.8061 | −1.23050 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −20.3043 | −1.57120 | −0.785598 | − | 0.618737i | \(-0.787645\pi\) | ||||
−0.785598 | + | 0.618737i | \(0.787645\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.23453 | 0.556503 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.05863 | 0.157428 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.560352 | 0.0426028 | 0.0213014 | − | 0.999773i | \(-0.493219\pi\) | ||||
0.0213014 | + | 0.999773i | \(0.493219\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.17246 | 0.315408 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −20.3741 | −1.53141 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.36641 | −0.326361 | −0.163180 | − | 0.986596i | \(-0.552175\pi\) | ||||
−0.163180 | + | 0.986596i | \(0.552175\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.05863 | −0.376005 | −0.188003 | − | 0.982169i | \(-0.560201\pi\) | ||||
−0.188003 | + | 0.982169i | \(0.560201\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −20.0406 | −1.48144 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.86469 | 0.357659 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.21811 | 0.600967 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.11383 | 0.226498 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.46725 | 0.178524 | 0.0892618 | − | 0.996008i | \(-0.471549\pi\) | ||||
0.0892618 | + | 0.996008i | \(0.471549\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.2491 | 0.881712 | 0.440856 | − | 0.897578i | \(-0.354675\pi\) | ||||
0.440856 | + | 0.897578i | \(0.354675\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 14.8793 | 1.06553 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.23109 | 0.0877119 | 0.0438559 | − | 0.999038i | \(-0.486036\pi\) | ||||
0.0438559 | + | 0.999038i | \(0.486036\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −27.0276 | −1.91594 | −0.957968 | − | 0.286876i | \(-0.907383\pi\) | ||||
−0.957968 | + | 0.286876i | \(0.907383\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.3224 | −0.939688 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 11.4802 | 0.805755 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.4216 | 1.00725 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.23453 | −0.572340 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.77846 | 0.330533 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.325819 | −0.0224303 | −0.0112152 | − | 0.999937i | \(-0.503570\pi\) | ||||
−0.0112152 | + | 0.999937i | \(0.503570\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 13.6190 | 0.933157 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.70178 | 0.184260 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.07668 | −0.412512 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.754297 | −0.0509707 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.73625 | −0.520397 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −23.4182 | −1.56820 | −0.784098 | − | 0.620637i | \(-0.786874\pi\) | ||||
−0.784098 | + | 0.620637i | \(0.786874\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.84053 | −0.389369 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 23.8466 | 1.58276 | 0.791379 | − | 0.611326i | \(-0.209364\pi\) | ||||
0.791379 | + | 0.611326i | \(0.209364\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.9690 | 0.923095 | 0.461548 | − | 0.887115i | \(-0.347294\pi\) | ||||
0.461548 | + | 0.887115i | \(0.347294\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −15.8061 | −1.03996 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.8337 | −0.840761 | −0.420380 | − | 0.907348i | \(-0.638103\pi\) | ||||
−0.420380 | + | 0.907348i | \(0.638103\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.56647 | −0.493582 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.824101 | 0.0535311 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −24.2587 | −1.56916 | −0.784582 | − | 0.620025i | \(-0.787123\pi\) | ||||
−0.784582 | + | 0.620025i | \(0.787123\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −26.0698 | −1.67930 | −0.839652 | − | 0.543125i | \(-0.817241\pi\) | ||||
−0.839652 | + | 0.543125i | \(0.817241\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −18.2491 | −1.17068 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7.11383 | 0.454486 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.49828 | −0.286219 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 40.6087 | 2.57347 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.3319 | −1.47270 | −0.736349 | − | 0.676602i | \(-0.763452\pi\) | ||||
−0.736349 | + | 0.676602i | \(0.763452\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −19.1138 | −1.20168 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.68879 | −0.356246 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.82410 | 0.176163 | 0.0880813 | − | 0.996113i | \(-0.471926\pi\) | ||||
0.0880813 | + | 0.996113i | \(0.471926\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.86469 | 0.302277 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −16.0698 | −0.994696 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.08967 | −0.437168 | −0.218584 | − | 0.975818i | \(-0.570144\pi\) | ||||
−0.218584 | + | 0.975818i | \(0.570144\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −18.9199 | −1.16224 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.32238 | 0.325724 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 20.8647 | 1.27214 | 0.636071 | − | 0.771630i | \(-0.280558\pi\) | ||||
0.636071 | + | 0.771630i | \(0.280558\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.0620710 | −0.00377055 | −0.00188527 | − | 0.999998i | \(-0.500600\pi\) | ||||
−0.00188527 | + | 0.999998i | \(0.500600\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 14.8793 | 0.900536 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −13.5569 | −0.817513 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.82248 | −0.470007 | −0.235004 | − | 0.971994i | \(-0.575510\pi\) | ||||
−0.235004 | + | 0.971994i | \(0.575510\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.50601 | 0.509242 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.6448 | 1.23156 | 0.615782 | − | 0.787917i | \(-0.288840\pi\) | ||||
0.615782 | + | 0.787917i | \(0.288840\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.3871 | −1.27133 | −0.635666 | − | 0.771964i | \(-0.719275\pi\) | ||||
−0.635666 | + | 0.771964i | \(0.719275\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.30777 | −0.195936 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14.4216 | 0.851280 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.0422 | −0.826012 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −15.8759 | −0.930659 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.6087 | 1.43765 | 0.718827 | − | 0.695189i | \(-0.244679\pi\) | ||||
0.718827 | + | 0.695189i | \(0.244679\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.3224 | 0.775659 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −10.1173 | −0.587063 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 17.9931 | 1.04057 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.70178 | 0.155728 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 15.6121 | 0.896892 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.1043 | 0.750349 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.4216 | 0.594792 | 0.297396 | − | 0.954754i | \(-0.403882\pi\) | ||||
0.297396 | + | 0.954754i | \(0.403882\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.85352 | −0.105443 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.91377 | −0.448749 | −0.224374 | − | 0.974503i | \(-0.572034\pi\) | ||||
−0.224374 | + | 0.974503i | \(0.572034\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.7846 | −1.00524 | −0.502622 | − | 0.864506i | \(-0.667631\pi\) | ||||
−0.502622 | + | 0.864506i | \(0.667631\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.45264 | 0.250878 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 30.0552 | 1.68807 | 0.844034 | − | 0.536290i | \(-0.180175\pi\) | ||||
0.844034 | + | 0.536290i | \(0.180175\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −37.3009 | −2.08845 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −25.7294 | −1.43607 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.71982 | 0.0956936 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.7620 | 0.707910 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9.29317 | 0.513913 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.56647 | −0.417153 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.8095 | 1.03386 | 0.516932 | − | 0.856027i | \(-0.327074\pi\) | ||||
0.516932 | + | 0.856027i | \(0.327074\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.80949 | −0.373158 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.71133 | 0.475951 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 30.2017 | 1.64519 | 0.822595 | − | 0.568628i | \(-0.192525\pi\) | ||||
0.822595 | + | 0.568628i | \(0.192525\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −17.8207 | −0.967886 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 19.7440 | 1.06920 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.4086 | 0.939977 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 13.2311 | 0.712338 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.36802 | −0.502902 | −0.251451 | − | 0.967870i | \(-0.580908\pi\) | ||||
−0.251451 | + | 0.967870i | \(0.580908\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.3173 | 1.14109 | 0.570545 | − | 0.821266i | \(-0.306732\pi\) | ||||
0.570545 | + | 0.821266i | \(0.306732\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.52406 | 0.508357 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.4362 | 0.981260 | 0.490630 | − | 0.871368i | \(-0.336767\pi\) | ||||
0.490630 | + | 0.871368i | \(0.336767\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.90528 | −0.472643 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.68879 | −0.301083 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −37.1932 | −1.96298 | −0.981491 | − | 0.191510i | \(-0.938661\pi\) | ||||
−0.981491 | + | 0.191510i | \(0.938661\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 26.6155 | 1.39695 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.493225 | 0.0258166 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.6121 | −0.606147 | −0.303074 | − | 0.952967i | \(-0.598013\pi\) | ||||
−0.303074 | + | 0.952967i | \(0.598013\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −20.1871 | −1.05090 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −18.9199 | −0.982271 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.6087 | 1.27419 | 0.637094 | − | 0.770786i | \(-0.280136\pi\) | ||||
0.637094 | + | 0.770786i | \(0.280136\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 25.9233 | 1.33867 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 35.1138 | 1.80845 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.05863 | 0.0543783 | 0.0271892 | − | 0.999630i | \(-0.491344\pi\) | ||||
0.0271892 | + | 0.999630i | \(0.491344\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.67762 | −0.137179 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.4837 | −0.944472 | −0.472236 | − | 0.881472i | \(-0.656553\pi\) | ||||
−0.472236 | + | 0.881472i | \(0.656553\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.3354 | 0.526739 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.78189 | −0.192245 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.46725 | 0.125094 | 0.0625472 | − | 0.998042i | \(-0.480078\pi\) | ||||
0.0625472 | + | 0.998042i | \(0.480078\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.87930 | −0.347901 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.39218 | −0.272000 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.538868 | −0.0271134 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.91721 | 0.347165 | 0.173582 | − | 0.984819i | \(-0.444466\pi\) | ||||
0.173582 | + | 0.984819i | \(0.444466\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.30777 | −0.165596 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 20.8578 | 1.04159 | 0.520795 | − | 0.853682i | \(-0.325636\pi\) | ||||
0.520795 | + | 0.853682i | \(0.325636\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −18.5863 | −0.925851 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 16.0862 | 0.799331 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −15.8061 | −0.783477 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −24.9820 | −1.23528 | −0.617639 | − | 0.786462i | \(-0.711911\pi\) | ||||
−0.617639 | + | 0.786462i | \(0.711911\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −21.1284 | −1.04219 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13.3224 | 0.655552 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −26.5535 | −1.30346 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 27.4802 | 1.34571 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 31.6742 | 1.54738 | 0.773692 | − | 0.633561i | \(-0.218408\pi\) | ||||
0.773692 | + | 0.633561i | \(0.218408\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 38.5941 | 1.88096 | 0.940480 | − | 0.339850i | \(-0.110376\pi\) | ||||
0.940480 | + | 0.339850i | \(0.110376\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10.5914 | 0.514971 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.87930 | −0.236681 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.1043 | 0.634160 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −48.3449 | −2.33411 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −37.4948 | −1.80606 | −0.903032 | − | 0.429574i | \(-0.858664\pi\) | ||||
−0.903032 | + | 0.429574i | \(0.858664\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.4182 | 0.644836 | 0.322418 | − | 0.946597i | \(-0.395504\pi\) | ||||
0.322418 | + | 0.946597i | \(0.395504\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 25.8207 | 1.23801 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.00000 | −0.191346 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 36.3043 | 1.73271 | 0.866356 | − | 0.499427i | \(-0.166456\pi\) | ||||
0.866356 | + | 0.499427i | \(0.166456\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.95779 | −0.474181 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 27.9215 | 1.32659 | 0.663295 | − | 0.748358i | \(-0.269157\pi\) | ||||
0.663295 | + | 0.748358i | \(0.269157\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.48024 | −0.164979 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −37.8284 | −1.78922 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.2086 | −0.576157 | −0.288079 | − | 0.957607i | \(-0.593016\pi\) | ||||
−0.288079 | + | 0.957607i | \(0.593016\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −46.8578 | −2.20645 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 16.1396 | 0.758305 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.72938 | −0.456120 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.42666 | −0.207070 | −0.103535 | − | 0.994626i | \(-0.533015\pi\) | ||||
−0.103535 | + | 0.994626i | \(0.533015\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.64133 | −0.169963 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.96553 | 0.324417 | 0.162208 | − | 0.986757i | \(-0.448138\pi\) | ||||
0.162208 | + | 0.986757i | \(0.448138\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 30.7501 | 1.42908 | 0.714539 | − | 0.699595i | \(-0.246636\pi\) | ||||
0.714539 | + | 0.699595i | \(0.246636\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −13.6673 | −0.633806 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.16635 | −0.239070 | −0.119535 | − | 0.992830i | \(-0.538140\pi\) | ||||
−0.119535 | + | 0.992830i | \(0.538140\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.71133 | 0.402252 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −35.2534 | −1.62439 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.77846 | −0.403634 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.83709 | −0.130175 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 26.4837 | 1.21260 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 23.3776 | 1.06815 | 0.534074 | − | 0.845437i | \(-0.320660\pi\) | ||||
0.534074 | + | 0.845437i | \(0.320660\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.8793 | 0.678437 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 13.2311 | 0.602036 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.3810 | 0.471378 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 41.9018 | 1.89875 | 0.949377 | − | 0.314140i | \(-0.101716\pi\) | ||||
0.949377 | + | 0.314140i | \(0.101716\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −20.9673 | −0.948176 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.90528 | 0.221372 | 0.110686 | − | 0.993855i | \(-0.464695\pi\) | ||||
0.110686 | + | 0.993855i | \(0.464695\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13.4250 | −0.604633 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −14.4672 | −0.650254 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.90528 | −0.399456 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.77502 | 0.258525 | 0.129263 | − | 0.991610i | \(-0.458739\pi\) | ||||
0.129263 | + | 0.991610i | \(0.458739\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −45.6673 | −2.04026 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 31.3776 | 1.39906 | 0.699529 | − | 0.714605i | \(-0.253393\pi\) | ||||
0.699529 | + | 0.714605i | \(0.253393\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.2086 | −0.454275 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 16.2715 | 0.722642 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.2603 | −0.765050 | −0.382525 | − | 0.923945i | \(-0.624945\pi\) | ||||
−0.382525 | + | 0.923945i | \(0.624945\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.493225 | 0.0218190 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.11727 | −0.0934796 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.21199 | 0.0534067 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 24.5845 | 1.08123 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.26031 | 0.0553215 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.8939 | −0.827757 | −0.413878 | − | 0.910332i | \(-0.635826\pi\) | ||||
−0.413878 | + | 0.910332i | \(0.635826\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 40.2017 | 1.75790 | 0.878948 | − | 0.476917i | \(-0.158246\pi\) | ||||
0.878948 | + | 0.476917i | \(0.158246\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 9.38445 | 0.409571 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.10610 | 0.309546 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −18.6484 | −0.809272 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 44.1104 | 1.91063 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16.8241 | 0.727369 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.82066 | −0.423793 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −23.1138 | −0.995583 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.4052 | 0.963274 | 0.481637 | − | 0.876371i | \(-0.340042\pi\) | ||||
0.481637 | + | 0.876371i | \(0.340042\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11.3776 | −0.488259 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.07668 | −0.260296 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 37.9931 | 1.62447 | 0.812234 | − | 0.583331i | \(-0.198251\pi\) | ||||
0.812234 | + | 0.583331i | \(0.198251\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −18.3431 | −0.782865 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.80605 | −0.332549 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.538868 | −0.0229150 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 10.9414 | 0.464435 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −16.1775 | −0.685463 | −0.342732 | − | 0.939433i | \(-0.611352\pi\) | ||||
−0.342732 | + | 0.939433i | \(0.611352\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.26375 | 0.349519 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 18.4837 | 0.780381 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.59750 | 0.404486 | 0.202243 | − | 0.979335i | \(-0.435177\pi\) | ||||
0.202243 | + | 0.979335i | \(0.435177\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.6527 | 0.490233 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 16.0862 | 0.675558 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 23.9018 | 1.00202 | 0.501009 | − | 0.865442i | \(-0.332963\pi\) | ||||
0.501009 | + | 0.865442i | \(0.332963\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.1725 | 1.51377 | 0.756885 | − | 0.653548i | \(-0.226720\pi\) | ||||
0.756885 | + | 0.653548i | \(0.226720\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.54918 | 0.231820 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 11.3484 | 0.473259 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.5699 | −0.523292 | −0.261646 | − | 0.965164i | \(-0.584265\pi\) | ||||
−0.261646 | + | 0.965164i | \(0.584265\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 27.5500 | 1.14494 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −26.5535 | −1.10162 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 61.4734 | 2.54597 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 13.6190 | 0.563076 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.107714 | 0.00444585 | 0.00222292 | − | 0.999998i | \(-0.499292\pi\) | ||||
0.00222292 | + | 0.999998i | \(0.499292\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.13187 | 0.170251 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.76891 | 0.113898 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 25.7846 | 1.05885 | 0.529423 | − | 0.848358i | \(-0.322409\pi\) | ||||
0.529423 | + | 0.848358i | \(0.322409\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.71982 | 0.152498 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −60.7889 | −2.48792 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −23.6336 | −0.965642 | −0.482821 | − | 0.875719i | \(-0.660388\pi\) | ||||
−0.482821 | + | 0.875719i | \(0.660388\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 35.3415 | 1.44161 | 0.720805 | − | 0.693138i | \(-0.243772\pi\) | ||||
0.720805 | + | 0.693138i | \(0.243772\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12.1939 | −0.496576 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −17.4036 | −0.707555 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.8432 | 1.17071 | 0.585355 | − | 0.810777i | \(-0.300955\pi\) | ||||
0.585355 | + | 0.810777i | \(0.300955\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 25.8207 | 1.04631 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −23.1430 | −0.936267 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −27.7604 | −1.12123 | −0.560616 | − | 0.828076i | \(-0.689436\pi\) | ||||
−0.560616 | + | 0.828076i | \(0.689436\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 32.4362 | 1.30795 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 32.5370 | 1.30989 | 0.654946 | − | 0.755676i | \(-0.272691\pi\) | ||||
0.654946 | + | 0.755676i | \(0.272691\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.20855 | 0.249543 | 0.124771 | − | 0.992186i | \(-0.460180\pi\) | ||||
0.124771 | + | 0.992186i | \(0.460180\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.46907 | 0.339852 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.48024 | −0.139433 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.76547 | −0.110619 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10.7474 | 0.429211 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.68879 | −0.226827 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.67256 | −0.106393 | −0.0531965 | − | 0.998584i | \(-0.516941\pi\) | ||||
−0.0531965 | + | 0.998584i | \(0.516941\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.732814 | −0.0291267 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.75086 | 0.0694807 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 21.7586 | 0.862107 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.4654 | 0.493125 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24.6639 | −0.974164 | −0.487082 | − | 0.873356i | \(-0.661939\pi\) | ||||
−0.487082 | + | 0.873356i | \(0.661939\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25.5405 | −1.00722 | −0.503609 | − | 0.863932i | \(-0.667995\pi\) | ||||
−0.503609 | + | 0.863932i | \(0.667995\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.07668 | 0.239269 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.7535 | 0.855220 | 0.427610 | − | 0.903963i | \(-0.359356\pi\) | ||||
0.427610 | + | 0.903963i | \(0.359356\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −43.2863 | −1.69914 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −13.6673 | −0.535664 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.37940 | −0.367044 | −0.183522 | − | 0.983016i | \(-0.558750\pi\) | ||||
−0.183522 | + | 0.983016i | \(0.558750\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.52588 | 0.137767 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.690407 | −0.0269353 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −39.8138 | −1.55092 | −0.775462 | − | 0.631394i | \(-0.782483\pi\) | ||||
−0.775462 | + | 0.631394i | \(0.782483\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.1138 | −0.743442 | −0.371721 | − | 0.928345i | \(-0.621232\pi\) | ||||
−0.371721 | + | 0.928345i | \(0.621232\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −17.3999 | −0.675757 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.16291 | 0.0838740 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 31.2242 | 1.20901 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −52.6707 | −2.03637 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −42.5776 | −1.64369 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21.1138 | −0.813878 | −0.406939 | − | 0.913455i | \(-0.633404\pi\) | ||||
−0.406939 | + | 0.913455i | \(0.633404\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.00688 | 0.231205 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −36.3855 | −1.39841 | −0.699204 | − | 0.714922i | \(-0.746462\pi\) | ||||
−0.699204 | + | 0.714922i | \(0.746462\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.3810 | 0.398387 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 53.6344 | 2.05528 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.6087 | −0.482457 | −0.241229 | − | 0.970468i | \(-0.577550\pi\) | ||||
−0.241229 | + | 0.970468i | \(0.577550\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.8156 | 0.527867 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 31.4182 | 1.19868 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −57.8690 | −2.20463 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.8405 | −0.640644 | −0.320322 | − | 0.947309i | \(-0.603791\pi\) | ||||
−0.320322 | + | 0.947309i | \(0.603791\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −14.4672 | −0.549565 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −17.9690 | −0.681602 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16.8647 | −0.638796 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −28.8647 | −1.09176 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33.9311 | 1.28156 | 0.640779 | − | 0.767725i | \(-0.278611\pi\) | ||||
0.640779 | + | 0.767725i | \(0.278611\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.30777 | −0.124755 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −17.0180 | −0.640937 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10.2086 | −0.383932 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −30.8984 | −1.16041 | −0.580207 | − | 0.814469i | \(-0.697028\pi\) | ||||
−0.580207 | + | 0.814469i | \(0.697028\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.754297 | 0.0282884 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −16.5275 | −0.618960 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 31.6121 | 1.18223 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −54.5612 | −2.03763 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −26.8122 | −0.999925 | −0.499963 | − | 0.866047i | \(-0.666653\pi\) | ||||
−0.499963 | + | 0.866047i | \(0.666653\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.21199 | 0.0451369 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −58.6347 | −2.18065 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 22.1465 | 0.822500 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −30.1897 | −1.11968 | −0.559838 | − | 0.828602i | \(-0.689137\pi\) | ||||
−0.559838 | + | 0.828602i | \(0.689137\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8.23109 | −0.304855 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.15947 | −0.116857 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −37.8207 | −1.39694 | −0.698469 | − | 0.715640i | \(-0.746135\pi\) | ||||
−0.698469 | + | 0.715640i | \(0.746135\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 16.0000 | 0.590169 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −28.3043 | −1.04260 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 39.3803 | 1.44863 | 0.724313 | − | 0.689471i | \(-0.242157\pi\) | ||||
0.724313 | + | 0.689471i | \(0.242157\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.1173 | −0.371667 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13.9854 | −0.513074 | −0.256537 | − | 0.966534i | \(-0.582582\pi\) | ||||
−0.256537 | + | 0.966534i | \(0.582582\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 24.7355 | 0.906238 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 37.1690 | 1.35994 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 16.8241 | 0.614739 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.0777 | −0.915100 | −0.457550 | − | 0.889184i | \(-0.651273\pi\) | ||||
−0.457550 | + | 0.889184i | \(0.651273\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −52.4768 | −1.91236 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10.5535 | −0.384080 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.6137 | −0.894601 | −0.447301 | − | 0.894384i | \(-0.647615\pi\) | ||||
−0.447301 | + | 0.894384i | \(0.647615\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −42.9897 | −1.56043 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −37.8010 | −1.37029 | −0.685143 | − | 0.728409i | \(-0.740260\pi\) | ||||
−0.685143 | + | 0.728409i | \(0.740260\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.07668 | −0.219991 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.20693 | −0.188257 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 40.7483 | 1.47134 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.98357 | 0.360017 | 0.180008 | − | 0.983665i | \(-0.442388\pi\) | ||||
0.180008 | + | 0.983665i | \(0.442388\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.35180 | 0.228754 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.5896 | −0.452815 | −0.226408 | − | 0.974033i | \(-0.572698\pi\) | ||||
−0.226408 | + | 0.974033i | \(0.572698\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11.7225 | −0.421085 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 10.9414 | 0.392519 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.80605 | −0.351338 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 28.9345 | 1.03536 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 16.5275 | 0.590645 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 23.0518 | 0.822753 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −29.2603 | −1.04302 | −0.521509 | − | 0.853246i | \(-0.674631\pi\) | ||||
−0.521509 | + | 0.853246i | \(0.674631\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −15.9457 | −0.567681 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.6527 | 0.414322 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 40.0812 | 1.42332 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −42.5535 | −1.50922 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −46.8578 | −1.65979 | −0.829894 | − | 0.557920i | \(-0.811599\pi\) | ||||
−0.829894 | + | 0.557920i | \(0.811599\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.84826 | 0.313029 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.87156 | 0.172128 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.60256 | −0.0565530 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.65164 | −0.304930 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 46.9276 | 1.65193 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −22.6681 | −0.796967 | −0.398483 | − | 0.917176i | \(-0.630463\pi\) | ||||
−0.398483 | + | 0.917176i | \(0.630463\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.7620 | 1.15043 | 0.575215 | − | 0.818002i | \(-0.304918\pi\) | ||||
0.575215 | + | 0.818002i | \(0.304918\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.139606 | −0.00489621 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13.7103 | 0.480250 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.83709 | −0.0642717 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 13.6190 | 0.475886 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.20006 | −0.111683 | −0.0558414 | − | 0.998440i | \(-0.517784\pi\) | ||||
−0.0558414 | + | 0.998440i | \(0.517784\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.4741 | 0.853114 | 0.426557 | − | 0.904461i | \(-0.359726\pi\) | ||||
0.426557 | + | 0.904461i | \(0.359726\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −30.4914 | −1.06157 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24.5681 | −0.854316 | −0.427158 | − | 0.904177i | \(-0.640485\pi\) | ||||
−0.427158 | + | 0.904177i | \(0.640485\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.2380 | 0.390311 | 0.195155 | − | 0.980772i | \(-0.437479\pi\) | ||||
0.195155 | + | 0.980772i | \(0.437479\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17.5939 | −0.610324 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.31894 | −0.288234 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 29.8613 | 1.03339 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.74828 | −0.302385 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.94480 | −0.0671421 | −0.0335711 | − | 0.999436i | \(-0.510688\pi\) | ||||
−0.0335711 | + | 0.999436i | \(0.510688\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 31.9345 | 1.10119 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 46.4330 | 1.59924 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10.6397 | −0.366017 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17.4036 | −0.597993 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −48.1027 | −1.65088 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13.2311 | 0.453556 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.8207 | 1.02104 | 0.510520 | − | 0.859866i | \(-0.329453\pi\) | ||||
0.510520 | + | 0.859866i | \(0.329453\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.02760 | −0.103542 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.49828 | −0.221977 | −0.110989 | − | 0.993822i | \(-0.535402\pi\) | ||||
−0.110989 | + | 0.993822i | \(0.535402\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.0422 | −0.717951 | −0.358975 | − | 0.933347i | \(-0.616874\pi\) | ||||
−0.358975 | + | 0.933347i | \(0.616874\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 32.4362 | 1.10542 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.80605 | −0.265721 | −0.132861 | − | 0.991135i | \(-0.542416\pi\) | ||||
−0.132861 | + | 0.991135i | \(0.542416\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.824101 | −0.0280203 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −31.5829 | −1.07261 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.75086 | 0.0593938 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 26.6448 | 0.902823 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −14.5311 | −0.491804 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −16.9509 | −0.573046 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.32582 | 0.146073 | 0.0730363 | − | 0.997329i | \(-0.476731\pi\) | ||||
0.0730363 | + | 0.997329i | \(0.476731\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 55.3484 | 1.86685 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.65775 | −0.190615 | −0.0953073 | − | 0.995448i | \(-0.530383\pi\) | ||||
−0.0953073 | + | 0.995448i | \(0.530383\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.6578 | −0.661536 | −0.330768 | − | 0.943712i | \(-0.607308\pi\) | ||||
−0.330768 | + | 0.943712i | \(0.607308\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 29.9639 | 1.00723 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 40.7811 | 1.36930 | 0.684648 | − | 0.728874i | \(-0.259956\pi\) | ||||
0.684648 | + | 0.728874i | \(0.259956\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.75086 | 0.0587219 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −52.2664 | −1.75099 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.14486 | 0.172166 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.42160 | 0.214650 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 40.4691 | 1.35122 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −32.2536 | −1.07572 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22.1250 | 0.737091 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.07668 | 0.202219 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.43965 | 0.247302 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 37.1475 | 1.23346 | 0.616732 | − | 0.787173i | \(-0.288456\pi\) | ||||
0.616732 | + | 0.787173i | \(0.288456\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 14.2897 | 0.473960 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.4070 | −0.676114 | −0.338057 | − | 0.941126i | \(-0.609770\pi\) | ||||
−0.338057 | + | 0.941126i | \(0.609770\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 86.2760 | 2.85532 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 29.4734 | 0.974359 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.52588 | 0.116435 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 52.9536 | 1.74678 | 0.873389 | − | 0.487023i | \(-0.161917\pi\) | ||||
0.873389 | + | 0.487023i | \(0.161917\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 23.4396 | 0.772363 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −27.2380 | −0.896549 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.38445 | 0.308559 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.69652 | −0.0557210 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 56.8984 | 1.86678 | 0.933388 | − | 0.358869i | \(-0.116837\pi\) | ||||
0.933388 | + | 0.358869i | \(0.116837\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.83709 | −0.158529 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −17.7992 | −0.582719 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −12.0862 | −0.395262 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40.9148 | 1.33663 | 0.668315 | − | 0.743879i | \(-0.267016\pi\) | ||||
0.668315 | + | 0.743879i | \(0.267016\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −40.0000 | −1.30535 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.59644 | −0.0846416 | −0.0423208 | − | 0.999104i | \(-0.513475\pi\) | ||||
−0.0423208 | + | 0.999104i | \(0.513475\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 39.2242 | 1.27732 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.57946 | −0.148970 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25.7586 | −0.837042 | −0.418521 | − | 0.908207i | \(-0.637451\pi\) | ||||
−0.418521 | + | 0.908207i | \(0.637451\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.50859 | 0.0489711 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 67.5984 | 2.19203 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.25602 | 0.0730795 | 0.0365398 | − | 0.999332i | \(-0.488366\pi\) | ||||
0.0365398 | + | 0.999332i | \(0.488366\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.62854 | −0.117417 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −83.8950 | −2.71194 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 13.8156 | 0.446129 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.9276 | −0.449278 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −23.5500 | −0.758889 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −18.0146 | −0.579911 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −45.0449 | −1.44855 | −0.724273 | − | 0.689513i | \(-0.757824\pi\) | ||||
−0.724273 | + | 0.689513i | \(0.757824\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.86813 | 0.124262 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −17.5760 | −0.564041 | −0.282021 | − | 0.959408i | \(-0.591005\pi\) | ||||
−0.282021 | + | 0.959408i | \(0.591005\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −17.9690 | −0.576059 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 28.7036 | 0.919251 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −15.9042 | −0.508821 | −0.254410 | − | 0.967096i | \(-0.581881\pi\) | ||||
−0.254410 | + | 0.967096i | \(0.581881\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.3078 | 0.361398 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.50601 | 0.271576 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −41.7294 | −1.33096 | −0.665480 | − | 0.746416i | \(-0.731773\pi\) | ||||
−0.665480 | + | 0.746416i | \(0.731773\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.81055 | −0.0576889 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −17.0180 | −0.541690 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.34836 | 0.233664 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.193945 | 0.00616087 | 0.00308044 | − | 0.999995i | \(-0.499019\pi\) | ||||
0.00308044 | + | 0.999995i | \(0.499019\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 42.3052 | 1.34251 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 39.7490 | 1.26013 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −40.6949 | −1.28882 | −0.644410 | − | 0.764680i | \(-0.722897\pi\) | ||||
−0.644410 | + | 0.764680i | \(0.722897\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.00344 | 0.221579 |
(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 | 4864.2.a.ba.1.3 | 3 | ||
4.3 | odd | 2 | 4864.2.a.bg.1.1 | 3 | |||
8.3 | odd | 2 | 4864.2.a.bb.1.3 | 3 | |||
8.5 | even | 2 | 4864.2.a.bh.1.1 | 3 | |||
16.3 | odd | 4 | 2432.2.c.e.1217.2 | ✓ | 6 | ||
16.5 | even | 4 | 2432.2.c.h.1217.2 | yes | 6 | ||
16.11 | odd | 4 | 2432.2.c.e.1217.5 | yes | 6 | ||
16.13 | even | 4 | 2432.2.c.h.1217.5 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2432.2.c.e.1217.2 | ✓ | 6 | 16.3 | odd | 4 | ||
2432.2.c.e.1217.5 | yes | 6 | 16.11 | odd | 4 | ||
2432.2.c.h.1217.2 | yes | 6 | 16.5 | even | 4 | ||
2432.2.c.h.1217.5 | yes | 6 | 16.13 | even | 4 | ||
4864.2.a.ba.1.3 | 3 | 1.1 | even | 1 | trivial | ||
4864.2.a.bb.1.3 | 3 | 8.3 | odd | 2 | |||
4864.2.a.bg.1.1 | 3 | 4.3 | odd | 2 | |||
4864.2.a.bh.1.1 | 3 | 8.5 | even | 2 |