Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1568,3,Mod(97,1568)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1568, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1568.97");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1568 = 2^{5} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1568.c (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: | \(42.7249054517\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 36x^{14} + 522x^{12} + 3644x^{10} + 12219x^{8} + 15156x^{6} + 15478x^{4} - 10992x^{2} + 11025 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{28} \) |
Twist minimal: | no (minimal twist has level 224) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 97.14 | ||
Root | \(-0.707107 - 2.60548i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1568.97 |
Dual form | 1568.3.c.h.97.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1568\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(1471\) | \(1473\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.68470i | 1.22823i | 0.789215 | + | 0.614116i | \(0.210487\pi\) | ||||
−0.789215 | + | 0.614116i | \(0.789513\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.04770i | 0.609540i | 0.952426 | + | 0.304770i | \(0.0985795\pi\) | ||||
−0.952426 | + | 0.304770i | \(0.901420\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.57700 | −0.508556 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.35033 | −0.213666 | −0.106833 | − | 0.994277i | \(-0.534071\pi\) | ||||
−0.106833 | + | 0.994277i | \(0.534071\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 25.3073i | − 1.94672i | −0.229292 | − | 0.973358i | \(-0.573641\pi\) | ||||
0.229292 | − | 0.973358i | \(-0.426359\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −11.2298 | −0.748656 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.56426i | 0.209662i | 0.994490 | + | 0.104831i | \(0.0334302\pi\) | ||||
−0.994490 | + | 0.104831i | \(0.966570\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 16.3704i | − 0.861602i | −0.902447 | − | 0.430801i | \(-0.858231\pi\) | ||||
0.902447 | − | 0.430801i | \(-0.141769\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 17.6683 | 0.768185 | 0.384093 | − | 0.923295i | \(-0.374514\pi\) | ||||
0.384093 | + | 0.923295i | \(0.374514\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 15.7115 | 0.628462 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 16.2974i | 0.603608i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 36.1220 | 1.24559 | 0.622793 | − | 0.782387i | \(-0.285998\pi\) | ||||
0.622793 | + | 0.782387i | \(0.285998\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 7.22414i | − 0.233037i | −0.993189 | − | 0.116518i | \(-0.962827\pi\) | ||||
0.993189 | − | 0.116518i | \(-0.0371734\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 8.66025i | − 0.262432i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 36.8043 | 0.994711 | 0.497355 | − | 0.867547i | \(-0.334305\pi\) | ||||
0.497355 | + | 0.867547i | \(0.334305\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 93.2498 | 2.39102 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 53.7118i | − 1.31004i | −0.755610 | − | 0.655022i | \(-0.772659\pi\) | ||||
0.755610 | − | 0.655022i | \(-0.227341\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 51.2382 | 1.19159 | 0.595793 | − | 0.803138i | \(-0.296838\pi\) | ||||
0.595793 | + | 0.803138i | \(0.296838\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 13.9493i | − 0.309985i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 31.3627i | − 0.667292i | −0.942698 | − | 0.333646i | \(-0.891721\pi\) | ||||
0.942698 | − | 0.333646i | \(-0.108279\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −13.1332 | −0.257514 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −70.2274 | −1.32504 | −0.662522 | − | 0.749042i | \(-0.730514\pi\) | ||||
−0.662522 | + | 0.749042i | \(0.730514\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 7.16309i | − 0.130238i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 60.3201 | 1.05825 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 94.0044i | 1.59329i | 0.604444 | + | 0.796647i | \(0.293395\pi\) | ||||
−0.604444 | + | 0.796647i | \(0.706605\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.18942i | 0.0358921i | 0.999839 | + | 0.0179461i | \(0.00571271\pi\) | ||||
−0.999839 | + | 0.0179461i | \(0.994287\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 77.1290 | 1.18660 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −24.9619 | −0.372566 | −0.186283 | − | 0.982496i | \(-0.559644\pi\) | ||||
−0.186283 | + | 0.982496i | \(0.559644\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 65.1022i | 0.943510i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −50.8890 | −0.716746 | −0.358373 | − | 0.933579i | \(-0.616668\pi\) | ||||
−0.358373 | + | 0.933579i | \(0.616668\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 79.5598i | − 1.08986i | −0.838481 | − | 0.544930i | \(-0.816556\pi\) | ||||
0.838481 | − | 0.544930i | \(-0.183444\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 57.8923i | 0.771897i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 115.023 | 1.45599 | 0.727996 | − | 0.685581i | \(-0.240452\pi\) | ||||
0.727996 | + | 0.685581i | \(0.240452\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −101.244 | −1.24993 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 154.132i | 1.85701i | 0.371318 | + | 0.928506i | \(0.378906\pi\) | ||||
−0.371318 | + | 0.928506i | \(0.621094\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.8628 | −0.127797 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 133.099i | 1.52987i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 114.001i | − 1.28091i | −0.767998 | − | 0.640453i | \(-0.778747\pi\) | ||||
0.767998 | − | 0.640453i | \(-0.221253\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 26.6188 | 0.286224 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 49.8921 | 0.525180 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 53.9940i | − 0.556640i | −0.960488 | − | 0.278320i | \(-0.910222\pi\) | ||||
0.960488 | − | 0.278320i | \(-0.0897775\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10.7575 | 0.108661 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 20.8198i | 0.206136i | 0.994674 | + | 0.103068i | \(0.0328660\pi\) | ||||
−0.994674 | + | 0.103068i | \(0.967134\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 122.248i | − 1.18687i | −0.804882 | − | 0.593435i | \(-0.797771\pi\) | ||||
0.804882 | − | 0.593435i | \(-0.202229\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −114.536 | −1.07043 | −0.535216 | − | 0.844715i | \(-0.679770\pi\) | ||||
−0.535216 | + | 0.844715i | \(0.679770\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 165.811 | 1.52121 | 0.760603 | − | 0.649218i | \(-0.224904\pi\) | ||||
0.760603 | + | 0.649218i | \(0.224904\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 135.613i | 1.22174i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −123.071 | −1.08912 | −0.544560 | − | 0.838722i | \(-0.683303\pi\) | ||||
−0.544560 | + | 0.838722i | \(0.683303\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 53.8475i | 0.468239i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 115.832i | 0.990014i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −115.476 | −0.954347 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 197.912 | 1.60904 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 124.076i | 0.992612i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 160.105 | 1.26067 | 0.630334 | − | 0.776324i | \(-0.282918\pi\) | ||||
0.630334 | + | 0.776324i | \(0.282918\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 188.797i | 1.46355i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 61.5770i | 0.470053i | 0.971989 | + | 0.235027i | \(0.0755177\pi\) | ||||
−0.971989 | + | 0.235027i | \(0.924482\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −49.6696 | −0.367923 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 95.1022 | 0.694176 | 0.347088 | − | 0.937832i | \(-0.387170\pi\) | ||||
0.347088 | + | 0.937832i | \(0.387170\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 92.0558i | − 0.662272i | −0.943583 | − | 0.331136i | \(-0.892568\pi\) | ||||
0.943583 | − | 0.331136i | \(-0.107432\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 115.562 | 0.819590 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 59.4805i | 0.415947i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 110.089i | 0.759234i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −177.445 | −1.19091 | −0.595453 | − | 0.803390i | \(-0.703027\pi\) | ||||
−0.595453 | + | 0.803390i | \(0.703027\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 229.788 | 1.52178 | 0.760888 | − | 0.648884i | \(-0.224764\pi\) | ||||
0.760888 | + | 0.648884i | \(0.224764\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 16.3136i | − 0.106625i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 22.0170 | 0.142045 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 49.6372i | − 0.316161i | −0.987426 | − | 0.158080i | \(-0.949470\pi\) | ||||
0.987426 | − | 0.158080i | \(-0.0505305\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 258.767i | − 1.62746i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 66.5227 | 0.408115 | 0.204057 | − | 0.978959i | \(-0.434587\pi\) | ||||
0.204057 | + | 0.978959i | \(0.434587\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 26.3938 | 0.159963 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 164.292i | 0.983786i | 0.870656 | + | 0.491893i | \(0.163695\pi\) | ||||
−0.870656 | + | 0.491893i | \(0.836305\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −471.460 | −2.78970 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 74.9275i | 0.438173i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 38.6819i | 0.223595i | 0.993731 | + | 0.111797i | \(0.0356607\pi\) | ||||
−0.993731 | + | 0.111797i | \(0.964339\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −346.378 | −1.95694 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 102.415 | 0.572152 | 0.286076 | − | 0.958207i | \(-0.407649\pi\) | ||||
0.286076 | + | 0.958207i | \(0.407649\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 44.5843i | 0.246322i | 0.992387 | + | 0.123161i | \(0.0393032\pi\) | ||||
−0.992387 | + | 0.123161i | \(0.960697\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.06735 | −0.0440839 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 112.168i | 0.606315i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 8.37718i | − 0.0447977i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 330.062 | 1.72808 | 0.864038 | − | 0.503427i | \(-0.167928\pi\) | ||||
0.864038 | + | 0.503427i | \(0.167928\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 139.355 | 0.722048 | 0.361024 | − | 0.932556i | \(-0.382427\pi\) | ||||
0.361024 | + | 0.932556i | \(0.382427\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 284.197i | 1.45742i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 174.724 | 0.886925 | 0.443462 | − | 0.896293i | \(-0.353750\pi\) | ||||
0.443462 | + | 0.896293i | \(0.353750\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 227.487i | 1.14315i | 0.820550 | + | 0.571574i | \(0.193667\pi\) | ||||
−0.820550 | + | 0.571574i | \(0.806333\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − 91.9772i | − 0.457598i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 163.697 | 0.798524 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −80.8677 | −0.390665 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 38.4759i | 0.184095i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −251.350 | −1.19123 | −0.595617 | − | 0.803269i | \(-0.703092\pi\) | ||||
−0.595617 | + | 0.803269i | \(0.703092\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 187.510i | − 0.880331i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 156.159i | 0.726319i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 293.154 | 1.33860 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 90.2017 | 0.408153 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 108.297i | − 0.485636i | −0.970072 | − | 0.242818i | \(-0.921928\pi\) | ||||
0.970072 | − | 0.242818i | \(-0.0780718\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −71.9118 | −0.319608 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 282.953i | 1.24649i | 0.782027 | + | 0.623245i | \(0.214186\pi\) | ||||
−0.782027 | + | 0.623245i | \(0.785814\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 176.682i | 0.771539i | 0.922595 | + | 0.385769i | \(0.126064\pi\) | ||||
−0.922595 | + | 0.385769i | \(0.873936\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 355.385 | 1.52526 | 0.762630 | − | 0.646835i | \(-0.223908\pi\) | ||||
0.762630 | + | 0.646835i | \(0.223908\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 95.5841 | 0.406741 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 423.826i | 1.78830i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.5451 | −0.0734104 | −0.0367052 | − | 0.999326i | \(-0.511686\pi\) | ||||
−0.0367052 | + | 0.999326i | \(0.511686\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 121.139i | 0.502650i | 0.967903 | + | 0.251325i | \(0.0808663\pi\) | ||||
−0.967903 | + | 0.251325i | \(0.919134\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 226.377i | − 0.931593i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −414.292 | −1.67729 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −567.930 | −2.28084 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 219.342i | − 0.873874i | −0.899492 | − | 0.436937i | \(-0.856063\pi\) | ||||
0.899492 | − | 0.436937i | \(-0.143937\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −41.5262 | −0.164135 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 40.0261i | − 0.156965i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 482.026i | − 1.87559i | −0.347192 | − | 0.937794i | \(-0.612865\pi\) | ||||
0.347192 | − | 0.937794i | \(-0.387135\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −165.330 | −0.633450 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 89.6879 | 0.341019 | 0.170509 | − | 0.985356i | \(-0.445459\pi\) | ||||
0.170509 | + | 0.985356i | \(0.445459\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 214.032i | − 0.807667i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 420.058 | 1.57325 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 38.0783i | − 0.141555i | −0.997492 | − | 0.0707776i | \(-0.977452\pi\) | ||||
0.997492 | − | 0.0707776i | \(-0.0225481\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 84.9632i | 0.313517i | 0.987637 | + | 0.156759i | \(0.0501045\pi\) | ||||
−0.987637 | + | 0.156759i | \(0.949896\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −36.9273 | −0.134281 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 62.5046 | 0.225648 | 0.112824 | − | 0.993615i | \(-0.464010\pi\) | ||||
0.112824 | + | 0.993615i | \(0.464010\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 33.0649i | 0.118512i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 58.6599 | 0.208754 | 0.104377 | − | 0.994538i | \(-0.466715\pi\) | ||||
0.104377 | + | 0.994538i | \(0.466715\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 239.556i | − 0.846486i | −0.906016 | − | 0.423243i | \(-0.860892\pi\) | ||||
0.906016 | − | 0.423243i | \(-0.139108\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 183.837i | 0.645044i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 276.296 | 0.956042 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 198.952 | 0.683683 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 196.503i | 0.670658i | 0.942101 | + | 0.335329i | \(0.108848\pi\) | ||||
−0.942101 | + | 0.335329i | \(0.891152\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −286.497 | −0.971176 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 38.3043i | − 0.128971i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 447.136i | − 1.49544i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −76.7146 | −0.253183 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.67268 | −0.0218777 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 246.955i | 0.804415i | 0.915549 | + | 0.402208i | \(0.131757\pi\) | ||||
−0.915549 | + | 0.402208i | \(0.868243\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 450.446 | 1.45775 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 340.045i | − 1.09339i | −0.837331 | − | 0.546696i | \(-0.815885\pi\) | ||||
0.837331 | − | 0.546696i | \(-0.184115\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 113.397i | − 0.362292i | −0.983456 | − | 0.181146i | \(-0.942019\pi\) | ||||
0.983456 | − | 0.181146i | \(-0.0579806\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 242.310 | 0.764385 | 0.382192 | − | 0.924083i | \(-0.375169\pi\) | ||||
0.382192 | + | 0.924083i | \(0.375169\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −84.8986 | −0.266140 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − 422.031i | − 1.31474i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 58.3484 | 0.180645 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 397.617i | − 1.22344i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 610.965i | 1.86839i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 69.7089 | 0.210601 | 0.105300 | − | 0.994440i | \(-0.466420\pi\) | ||||
0.105300 | + | 0.994440i | \(0.466420\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −168.453 | −0.505866 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 76.0764i | − 0.227094i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 165.816 | 0.492037 | 0.246019 | − | 0.969265i | \(-0.420878\pi\) | ||||
0.246019 | + | 0.969265i | \(0.420878\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 453.478i | − 1.33769i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.9791i | 0.0497921i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −198.412 | −0.575107 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −566.904 | −1.63373 | −0.816864 | − | 0.576830i | \(-0.804289\pi\) | ||||
−0.816864 | + | 0.576830i | \(0.804289\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 245.773i | − 0.704219i | −0.935959 | − | 0.352110i | \(-0.885464\pi\) | ||||
0.935959 | − | 0.352110i | \(-0.114536\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 412.443 | 1.17505 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 159.160i | − 0.450879i | −0.974257 | − | 0.225439i | \(-0.927618\pi\) | ||||
0.974257 | − | 0.225439i | \(-0.0723817\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 155.094i | − 0.436885i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −205.025 | −0.571101 | −0.285550 | − | 0.958364i | \(-0.592176\pi\) | ||||
−0.285550 | + | 0.958364i | \(0.592176\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 93.0089 | 0.257642 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 425.494i | − 1.17216i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 242.474 | 0.664313 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 1.68715i | − 0.00459715i | −0.999997 | − | 0.00229858i | \(-0.999268\pi\) | ||||
0.999997 | − | 0.00229858i | \(-0.000731660\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 245.839i | 0.666231i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 463.405 | 1.24237 | 0.621186 | − | 0.783663i | \(-0.286651\pi\) | ||||
0.621186 | + | 0.783663i | \(0.286651\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −457.184 | −1.21916 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 914.150i | − 2.42480i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −493.215 | −1.30136 | −0.650680 | − | 0.759352i | \(-0.725516\pi\) | ||||
−0.650680 | + | 0.759352i | \(0.725516\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 589.938i | 1.54839i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 573.038i | 1.49618i | 0.663595 | + | 0.748092i | \(0.269030\pi\) | ||||
−0.663595 | + | 0.748092i | \(0.730970\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −234.518 | −0.605988 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −46.5513 | −0.119669 | −0.0598346 | − | 0.998208i | \(-0.519057\pi\) | ||||
−0.0598346 | + | 0.998208i | \(0.519057\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 62.9742i | 0.161059i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −226.893 | −0.577335 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 350.556i | 0.887485i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 208.704i | − 0.525704i | −0.964836 | − | 0.262852i | \(-0.915337\pi\) | ||||
0.964836 | − | 0.262852i | \(-0.0846631\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −221.190 | −0.551596 | −0.275798 | − | 0.961216i | \(-0.588942\pi\) | ||||
−0.275798 | + | 0.961216i | \(0.588942\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −182.824 | −0.453657 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 308.561i | − 0.761880i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −86.5022 | −0.212536 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 96.4289i | 0.235767i | 0.993027 | + | 0.117884i | \(0.0376110\pi\) | ||||
−0.993027 | + | 0.117884i | \(0.962389\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 350.423i | 0.852610i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −469.748 | −1.13192 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 339.198 | 0.813424 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 239.093i | − 0.570627i | −0.958434 | − | 0.285313i | \(-0.907902\pi\) | ||||
0.958434 | − | 0.285313i | \(-0.0920977\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 508.228 | 1.20719 | 0.603596 | − | 0.797290i | \(-0.293734\pi\) | ||||
0.603596 | + | 0.797290i | \(0.293734\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 143.547i | 0.339355i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 56.0000i | 0.131765i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −219.168 | −0.510880 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −598.349 | −1.38828 | −0.694140 | − | 0.719840i | \(-0.744215\pi\) | ||||
−0.694140 | + | 0.719840i | \(0.744215\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 283.405i | 0.654516i | 0.944935 | + | 0.327258i | \(0.106125\pi\) | ||||
−0.944935 | + | 0.327258i | \(0.893875\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −405.644 | −0.932516 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 289.237i | − 0.661870i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 342.480i | − 0.780137i | −0.920786 | − | 0.390068i | \(-0.872451\pi\) | ||||
0.920786 | − | 0.390068i | \(-0.127549\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 587.817 | 1.32690 | 0.663451 | − | 0.748220i | \(-0.269091\pi\) | ||||
0.663451 | + | 0.748220i | \(0.269091\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 347.439 | 0.780762 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 653.831i | − 1.46271i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −265.522 | −0.591364 | −0.295682 | − | 0.955286i | \(-0.595547\pi\) | ||||
−0.295682 | + | 0.955286i | \(0.595547\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 126.240i | 0.279912i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 846.700i | 1.86909i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −396.591 | −0.867815 | −0.433907 | − | 0.900957i | \(-0.642866\pi\) | ||||
−0.433907 | + | 0.900957i | \(0.642866\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −58.0882 | −0.126554 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 143.388i | 0.311037i | 0.987833 | + | 0.155519i | \(0.0497049\pi\) | ||||
−0.987833 | + | 0.155519i | \(0.950295\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 72.3400 | 0.156242 | 0.0781210 | − | 0.996944i | \(-0.475108\pi\) | ||||
0.0781210 | + | 0.996944i | \(0.475108\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 81.1260i | 0.174465i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 523.869i | 1.12178i | 0.827892 | + | 0.560888i | \(0.189540\pi\) | ||||
−0.827892 | + | 0.560888i | \(0.810460\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 182.898 | 0.388319 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −120.427 | −0.254602 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 257.205i | − 0.541484i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 321.431 | 0.673859 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 849.580i | − 1.77365i | −0.462103 | − | 0.886826i | \(-0.652905\pi\) | ||||
0.462103 | − | 0.886826i | \(-0.347095\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − 931.417i | − 1.93642i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 164.558 | 0.339294 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −405.963 | −0.833600 | −0.416800 | − | 0.908998i | \(-0.636848\pi\) | ||||
−0.416800 | + | 0.908998i | \(0.636848\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 245.116i | 0.501260i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 661.455 | 1.34716 | 0.673580 | − | 0.739115i | \(-0.264756\pi\) | ||||
0.673580 | + | 0.739115i | \(0.264756\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 128.748i | 0.261152i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 32.7855i | 0.0662333i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −239.568 | −0.480096 | −0.240048 | − | 0.970761i | \(-0.577163\pi\) | ||||
−0.240048 | + | 0.970761i | \(0.577163\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −605.367 | −1.20832 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 578.149i | 1.14940i | 0.818364 | + | 0.574701i | \(0.194882\pi\) | ||||
−0.818364 | + | 0.574701i | \(0.805118\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −63.4524 | −0.125648 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 1737.19i | − 3.42640i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 301.289i | − 0.591923i | −0.955200 | − | 0.295962i | \(-0.904360\pi\) | ||||
0.955200 | − | 0.295962i | \(-0.0956401\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 266.796 | 0.520070 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 372.574 | 0.723445 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 73.7127i | 0.142578i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −142.531 | −0.274626 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 132.574i | − 0.254460i | −0.991873 | − | 0.127230i | \(-0.959391\pi\) | ||||
0.991873 | − | 0.127230i | \(-0.0406086\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 111.000i | − 0.212238i | −0.994353 | − | 0.106119i | \(-0.966158\pi\) | ||||
0.994353 | − | 0.106119i | \(-0.0338424\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 25.7487 | 0.0488590 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −216.833 | −0.409891 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 430.258i | − 0.810279i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1359.30 | −2.55028 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 349.071i | − 0.652470i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 377.369i | 0.702736i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 85.7043 | 0.158418 | 0.0792092 | − | 0.996858i | \(-0.474761\pi\) | ||||
0.0792092 | + | 0.996858i | \(0.474761\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −164.280 | −0.302541 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 505.343i | 0.927235i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −674.162 | −1.23247 | −0.616236 | − | 0.787562i | \(-0.711343\pi\) | ||||
−0.616236 | + | 0.787562i | \(0.711343\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 10.0210i | − 0.0182531i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 591.333i | − 1.07320i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −413.307 | −0.744696 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 763.490 | 1.37072 | 0.685359 | − | 0.728205i | \(-0.259645\pi\) | ||||
0.685359 | + | 0.728205i | \(0.259645\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 1296.70i | − 2.31968i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 30.8674 | 0.0550221 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 355.022i | − 0.630590i | −0.948994 | − | 0.315295i | \(-0.897897\pi\) | ||||
0.948994 | − | 0.315295i | \(-0.102103\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 375.082i | − 0.663861i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 527.069 | 0.926308 | 0.463154 | − | 0.886278i | \(-0.346718\pi\) | ||||
0.463154 | + | 0.886278i | \(0.346718\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −515.772 | −0.903278 | −0.451639 | − | 0.892201i | \(-0.649161\pi\) | ||||
−0.451639 | + | 0.892201i | \(0.649161\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1216.18i | 2.12248i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 277.596 | 0.482775 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 210.190i | 0.364280i | 0.983273 | + | 0.182140i | \(0.0583024\pi\) | ||||
−0.983273 | + | 0.182140i | \(0.941698\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 513.482i | 0.886844i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 165.057 | 0.283117 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −353.020 | −0.603452 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 91.8797i | 0.156524i | 0.996933 | + | 0.0782621i | \(0.0249371\pi\) | ||||
−0.996933 | + | 0.0782621i | \(0.975063\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −118.262 | −0.200785 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 643.806i | 1.08935i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 448.871i | 0.756950i | 0.925612 | + | 0.378475i | \(0.123551\pi\) | ||||
−0.925612 | + | 0.378475i | \(0.876449\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −838.219 | −1.40405 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 197.705 | 0.330058 | 0.165029 | − | 0.986289i | \(-0.447228\pi\) | ||||
0.165029 | + | 0.986289i | \(0.447228\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 232.075i | 0.386148i | 0.981184 | + | 0.193074i | \(0.0618458\pi\) | ||||
−0.981184 | + | 0.193074i | \(0.938154\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 114.251 | 0.189471 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 351.936i | − 0.581712i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 819.633i | − 1.35030i | −0.737680 | − | 0.675151i | \(-0.764079\pi\) | ||||
0.737680 | − | 0.675151i | \(-0.235921\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −793.706 | −1.29903 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −811.390 | −1.32364 | −0.661819 | − | 0.749664i | \(-0.730215\pi\) | ||||
−0.661819 | + | 0.749664i | \(0.730215\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 603.175i | 0.980773i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 248.808 | 0.403255 | 0.201627 | − | 0.979462i | \(-0.435377\pi\) | ||||
0.201627 | + | 0.979462i | \(0.435377\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 544.744i | 0.880039i | 0.897988 | + | 0.440020i | \(0.145029\pi\) | ||||
−0.897988 | + | 0.440020i | \(0.854971\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 287.947i | 0.463683i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.6410 | 0.0234256 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −141.772 | −0.226112 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 131.180i | 0.208553i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −407.805 | −0.646284 | −0.323142 | − | 0.946350i | \(-0.604739\pi\) | ||||
−0.323142 | + | 0.946350i | \(0.604739\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 926.150i | − 1.46311i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 487.951i | 0.768427i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 232.919 | 0.364505 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 645.679 | 1.00730 | 0.503650 | − | 0.863908i | \(-0.331990\pi\) | ||||
0.503650 | + | 0.863908i | \(0.331990\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 932.869i | − 1.45081i | −0.688324 | − | 0.725403i | \(-0.741653\pi\) | ||||
0.688324 | − | 0.725403i | \(-0.258347\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −575.397 | −0.892089 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 485.306i | − 0.750086i | −0.927007 | − | 0.375043i | \(-0.877628\pi\) | ||||
0.927007 | − | 0.375043i | \(-0.122372\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − 220.941i | − 0.340433i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −361.174 | −0.553099 | −0.276550 | − | 0.961000i | \(-0.589191\pi\) | ||||
−0.276550 | + | 0.961000i | \(0.589191\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −187.668 | −0.286516 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 364.146i | 0.554255i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −180.761 | −0.274296 | −0.137148 | − | 0.990551i | \(-0.543794\pi\) | ||||
−0.137148 | + | 0.990551i | \(0.543794\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 589.821i | 0.892316i | 0.894954 | + | 0.446158i | \(0.147208\pi\) | ||||
−0.894954 | + | 0.446158i | \(0.852792\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 332.366i | 0.501307i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 638.213 | 0.956841 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 399.041 | 0.596474 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 5.14585i | − 0.00766893i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −416.772 | −0.619276 | −0.309638 | − | 0.950855i | \(-0.600208\pi\) | ||||
−0.309638 | + | 0.950855i | \(0.600208\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 256.057i | 0.379344i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 459.702i | − 0.679028i | −0.940601 | − | 0.339514i | \(-0.889737\pi\) | ||||
0.940601 | − | 0.339514i | \(-0.110263\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1042.60 | −1.53098 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1120.19 | −1.64010 | −0.820048 | − | 0.572295i | \(-0.806053\pi\) | ||||
−0.820048 | + | 0.572295i | \(0.806053\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 289.843i | 0.423128i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −651.021 | −0.947629 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1777.27i | 2.57949i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 427.332i | 0.618425i | 0.950993 | + | 0.309213i | \(0.100066\pi\) | ||||
−0.950993 | + | 0.309213i | \(0.899934\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 280.558 | 0.403681 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 191.443 | 0.274667 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1309.49i | 1.87337i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −99.9460 | −0.142576 | −0.0712882 | − | 0.997456i | \(-0.522711\pi\) | ||||
−0.0712882 | + | 0.997456i | \(0.522711\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 602.502i | − 0.857044i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 352.199i | 0.499573i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 39.1725 | 0.0552504 | 0.0276252 | − | 0.999618i | \(-0.491206\pi\) | ||||
0.0276252 | + | 0.999618i | \(0.491206\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −526.462 | −0.740453 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 127.638i | − 0.179015i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −181.279 | −0.253536 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 64.6484i | − 0.0901651i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 771.897i | 1.07357i | 0.843719 | + | 0.536785i | \(0.180361\pi\) | ||||
−0.843719 | + | 0.536785i | \(0.819639\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −446.359 | −0.617371 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 567.532 | 0.782803 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 963.864i | − 1.32581i | −0.748703 | − | 0.662905i | \(-0.769323\pi\) | ||||
0.748703 | − | 0.662905i | \(-0.230677\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −77.0650 | −0.105713 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 182.626i | 0.249831i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 95.0862i | 0.129722i | 0.997894 | + | 0.0648610i | \(0.0206604\pi\) | ||||
−0.997894 | + | 0.0648610i | \(0.979340\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 58.6687 | 0.0796048 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1148.80 | −1.55454 | −0.777268 | − | 0.629169i | \(-0.783395\pi\) | ||||
−0.777268 | + | 0.629169i | \(0.783395\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 1526.54i | − 2.06011i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 232.652 | 0.313126 | 0.156563 | − | 0.987668i | \(-0.449959\pi\) | ||||
0.156563 | + | 0.987668i | \(0.449959\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 540.799i | − 0.725904i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 705.463i | − 0.944394i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 686.158 | 0.913659 | 0.456829 | − | 0.889554i | \(-0.348985\pi\) | ||||
0.456829 | + | 0.889554i | \(0.348985\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 808.210 | 1.07332 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 700.325i | 0.927582i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 657.058 | 0.867976 | 0.433988 | − | 0.900919i | \(-0.357106\pi\) | ||||
0.433988 | + | 0.900919i | \(0.357106\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 153.012i | − 0.201596i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1228.17i | 1.61389i | 0.590626 | + | 0.806946i | \(0.298881\pi\) | ||||
−0.590626 | + | 0.806946i | \(0.701119\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 49.7190 | 0.0649921 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2379.00 | 3.10169 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 499.279i | 0.649257i | 0.945842 | + | 0.324629i | \(0.105239\pi\) | ||||
−0.945842 | + | 0.324629i | \(0.894761\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1776.12 | 2.30366 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 320.220i | − 0.414256i | −0.978314 | − | 0.207128i | \(-0.933588\pi\) | ||||
0.978314 | − | 0.207128i | \(-0.0664116\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 113.502i | − 0.146455i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −879.286 | −1.12874 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 119.606 | 0.153144 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 588.695i | 0.751845i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 151.279 | 0.192712 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 566.896i | 0.720325i | 0.932890 | + | 0.360162i | \(0.117279\pi\) | ||||
−0.932890 | + | 0.360162i | \(0.882721\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 330.473i | 0.418850i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 55.4083 | 0.0698717 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 788.643 | 0.992003 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 1416.99i | − 1.77791i | −0.457996 | − | 0.888954i | \(-0.651433\pi\) | ||||
0.457996 | − | 0.888954i | \(-0.348567\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 111.785 | 0.139906 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 521.781i | 0.651412i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 186.992i | 0.232867i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 140.307 | 0.173863 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −997.261 | −1.23271 | −0.616354 | − | 0.787469i | \(-0.711391\pi\) | ||||
−0.616354 | + | 0.787469i | \(0.711391\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 1201.56i | − 1.48158i | −0.671735 | − | 0.740792i | \(-0.734450\pi\) | ||||
0.671735 | − | 0.740792i | \(-0.265550\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −313.064 | −0.385072 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 202.741i | 0.248762i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 838.792i | − 1.02667i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −185.790 | −0.226298 | −0.113149 | − | 0.993578i | \(-0.536094\pi\) | ||||
−0.113149 | + | 0.993578i | \(0.536094\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 858.902 | 1.04362 | 0.521812 | − | 0.853061i | \(-0.325256\pi\) | ||||
0.521812 | + | 0.853061i | \(0.325256\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − 136.066i | − 0.164928i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 217.847 | 0.263418 | 0.131709 | − | 0.991288i | \(-0.457954\pi\) | ||||
0.131709 | + | 0.991288i | \(0.457954\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 991.084i | 1.19552i | 0.801676 | + | 0.597759i | \(0.203942\pi\) | ||||
−0.801676 | + | 0.597759i | \(0.796058\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 230.311i | 0.277149i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −500.713 | −0.599656 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 117.735 | 0.140663 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 415.268i | − 0.494956i | −0.968894 | − | 0.247478i | \(-0.920398\pi\) | ||||
0.968894 | − | 0.247478i | \(-0.0796017\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 463.798 | 0.551484 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 216.144i | 0.256398i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 1436.87i | − 1.70043i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 882.690 | 1.03968 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 650.268 | 0.764122 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 1335.36i | − 1.56549i | −0.622343 | − | 0.782745i | \(-0.713819\pi\) | ||||
0.622343 | − | 0.782745i | \(-0.286181\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −228.356 | −0.267084 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 1607.75i | − 1.87602i | −0.346611 | − | 0.938009i | \(-0.612668\pi\) | ||||
0.346611 | − | 0.938009i | \(-0.387332\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 152.282i | − 0.177278i | −0.996064 | − | 0.0886391i | \(-0.971748\pi\) | ||||
0.996064 | − | 0.0886391i | \(-0.0282518\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −960.275 | −1.11272 | −0.556358 | − | 0.830942i | \(-0.687802\pi\) | ||||
−0.556358 | + | 0.830942i | \(0.687802\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −117.891 | −0.136290 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1018.07i | 1.17424i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −270.343 | −0.311096 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 631.719i | 0.725280i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 247.131i | 0.283082i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.9410 | 0.0136158 | 0.00680790 | − | 0.999977i | \(-0.497833\pi\) | ||||
0.00680790 | + | 0.999977i | \(0.497833\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −724.054 | −0.823725 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 625.457i | 0.709940i | 0.934878 | + | 0.354970i | \(0.115509\pi\) | ||||
−0.934878 | + | 0.354970i | \(0.884491\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 78.6167 | 0.0890337 | 0.0445168 | − | 0.999009i | \(-0.485825\pi\) | ||||
0.0445168 | + | 0.999009i | \(0.485825\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 1055.65i | − 1.19283i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 731.689i | − 0.824903i | −0.910980 | − | 0.412451i | \(-0.864673\pi\) | ||||
0.910980 | − | 0.412451i | \(-0.135327\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 237.957 | 0.267067 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −513.422 | −0.574940 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 312.131i | 0.348749i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1647.56 | 1.83675 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 260.950i | − 0.290267i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 250.308i | − 0.277812i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −135.880 | −0.150143 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −287.701 | −0.317201 | −0.158601 | − | 0.987343i | \(-0.550698\pi\) | ||||
−0.158601 | + | 0.987343i | \(0.550698\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 95.2922i | − 0.104832i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −249.315 | −0.273672 | −0.136836 | − | 0.990594i | \(-0.543693\pi\) | ||||
−0.136836 | + | 0.990594i | \(0.543693\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 362.261i | − 0.396781i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 24.5868i | − 0.0268709i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −20.1150 | −0.0218879 | −0.0109440 | − | 0.999940i | \(-0.503484\pi\) | ||||
−0.0109440 | + | 0.999940i | \(0.503484\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −909.956 | −0.988009 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1287.86i | 1.39530i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 578.252 | 0.625137 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 559.528i | 0.603590i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1232.64i | 1.32685i | 0.748244 | + | 0.663424i | \(0.230897\pi\) | ||||
−0.748244 | + | 0.663424i | \(0.769103\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1252.96 | 1.34294 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 25.5311 | 0.0273060 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 283.840i | 0.302924i | 0.988463 | + | 0.151462i | \(0.0483981\pi\) | ||||
−0.988463 | + | 0.151462i | \(0.951602\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 417.835 | 0.444979 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 648.090i | 0.688725i | 0.938837 | + | 0.344362i | \(0.111905\pi\) | ||||
−0.938837 | + | 0.344362i | \(0.888095\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 948.994i | − 1.00636i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1718.20 | 1.81436 | 0.907181 | − | 0.420740i | \(-0.138229\pi\) | ||||
0.907181 | + | 0.420740i | \(0.138229\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2013.44 | −2.12165 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 892.839i | 0.938842i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1085.95 | 1.13950 | 0.569752 | − | 0.821817i | \(-0.307039\pi\) | ||||
0.569752 | + | 0.821817i | \(0.307039\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1005.93i | 1.05333i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 312.826i | − 0.326882i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 908.812 | 0.945694 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 524.232 | 0.544374 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 424.713i | 0.440117i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −969.512 | −1.00260 | −0.501299 | − | 0.865274i | \(-0.667144\pi\) | ||||
−0.501299 | + | 0.865274i | \(0.667144\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 214.996i | 0.221875i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 837.111i | 0.862112i | 0.902325 | + | 0.431056i | \(0.141859\pi\) | ||||
−0.902325 | + | 0.431056i | \(0.858141\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1465.10 | 1.50266 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1360.23 | 1.39225 | 0.696125 | − | 0.717921i | \(-0.254906\pi\) | ||||
0.696125 | + | 0.717921i | \(0.254906\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 267.939i | 0.273686i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −758.919 | −0.773618 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 397.275i | 0.404145i | 0.979371 | + | 0.202073i | \(0.0647677\pi\) | ||||
−0.979371 | + | 0.202073i | \(0.935232\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 532.506i | 0.540616i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 905.290 | 0.915359 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 278.500 | 0.281029 | 0.140514 | − | 0.990079i | \(-0.455124\pi\) | ||||
0.140514 | + | 0.990079i | \(0.455124\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 256.856i | 0.258667i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −693.310 | −0.696794 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 827.397i | − 0.829887i | −0.909847 | − | 0.414943i | \(-0.863801\pi\) | ||||
0.909847 | − | 0.414943i | \(-0.136199\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 599.815i | 0.600415i |
(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 | 1568.3.c.h.97.14 | 16 | ||
4.3 | odd | 2 | inner | 1568.3.c.h.97.4 | 16 | ||
7.4 | even | 3 | 224.3.s.a.33.7 | yes | 16 | ||
7.5 | odd | 6 | 224.3.s.a.129.7 | yes | 16 | ||
7.6 | odd | 2 | inner | 1568.3.c.h.97.3 | 16 | ||
28.11 | odd | 6 | 224.3.s.a.33.2 | ✓ | 16 | ||
28.19 | even | 6 | 224.3.s.a.129.2 | yes | 16 | ||
28.27 | even | 2 | inner | 1568.3.c.h.97.13 | 16 | ||
56.5 | odd | 6 | 448.3.s.g.129.2 | 16 | |||
56.11 | odd | 6 | 448.3.s.g.257.7 | 16 | |||
56.19 | even | 6 | 448.3.s.g.129.7 | 16 | |||
56.53 | even | 6 | 448.3.s.g.257.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.3.s.a.33.2 | ✓ | 16 | 28.11 | odd | 6 | ||
224.3.s.a.33.7 | yes | 16 | 7.4 | even | 3 | ||
224.3.s.a.129.2 | yes | 16 | 28.19 | even | 6 | ||
224.3.s.a.129.7 | yes | 16 | 7.5 | odd | 6 | ||
448.3.s.g.129.2 | 16 | 56.5 | odd | 6 | |||
448.3.s.g.129.7 | 16 | 56.19 | even | 6 | |||
448.3.s.g.257.2 | 16 | 56.53 | even | 6 | |||
448.3.s.g.257.7 | 16 | 56.11 | odd | 6 | |||
1568.3.c.h.97.3 | 16 | 7.6 | odd | 2 | inner | ||
1568.3.c.h.97.4 | 16 | 4.3 | odd | 2 | inner | ||
1568.3.c.h.97.13 | 16 | 28.27 | even | 2 | inner | ||
1568.3.c.h.97.14 | 16 | 1.1 | even | 1 | trivial |