Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1440,2,Mod(1439,1440)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1440, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1440.1439");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1440.o (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: | \(11.4984578911\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | 12.0.426337261060096.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4x^{9} - 3x^{8} + 4x^{7} + 8x^{6} + 8x^{5} - 12x^{4} - 32x^{3} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1439.6 | ||
Root | \(-1.35818 - 0.394157i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1440.1439 |
Dual form | 1440.2.o.b.1439.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(991\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.256912 | + | 2.22126i | −0.114894 | + | 0.993378i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.50466 | 1.32464 | 0.662319 | − | 0.749222i | \(-0.269572\pi\) | ||||
0.662319 | + | 0.749222i | \(0.269572\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.92804 | 0.581325 | 0.290663 | − | 0.956826i | \(-0.406124\pi\) | ||||
0.290663 | + | 0.956826i | \(0.406124\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.50466i | − | 1.52672i | −0.645974 | − | 0.763360i | \(-0.723548\pi\) | ||
0.645974 | − | 0.763360i | \(-0.276452\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.44252 | 1.07747 | 0.538735 | − | 0.842475i | \(-0.318903\pi\) | ||||
0.538735 | + | 0.842475i | \(0.318903\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 7.00933i | − | 1.60805i | −0.594595 | − | 0.804025i | \(-0.702688\pi\) | ||
0.594595 | − | 0.804025i | \(-0.297312\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.10027i | 0.229422i | 0.993399 | + | 0.114711i | \(0.0365942\pi\) | ||||
−0.993399 | + | 0.114711i | \(0.963406\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.86799 | − | 1.14134i | −0.973599 | − | 0.228267i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 5.47017i | − | 1.01578i | −0.861421 | − | 0.507892i | \(-0.830425\pi\) | ||
0.861421 | − | 0.507892i | \(-0.169575\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.28267i | 1.48761i | 0.668396 | + | 0.743806i | \(0.266981\pi\) | ||||
−0.668396 | + | 0.743806i | \(0.733019\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.900390 | + | 7.78477i | −0.152194 | + | 1.31587i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 0.778008i | − | 0.127904i | −0.997953 | − | 0.0639519i | \(-0.979630\pi\) | ||
0.997953 | − | 0.0639519i | \(-0.0203704\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 2.44186i | − | 0.381355i | −0.981653 | − | 0.190677i | \(-0.938932\pi\) | ||
0.981653 | − | 0.190677i | \(-0.0610684\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.55602 | 1.45728 | 0.728639 | − | 0.684898i | \(-0.240153\pi\) | ||||
0.728639 | + | 0.684898i | \(0.240153\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.7135i | 1.70858i | 0.519793 | + | 0.854292i | \(0.326009\pi\) | ||||
−0.519793 | + | 0.854292i | \(0.673991\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.28267 | 0.754667 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.5268 | 1.58333 | 0.791663 | − | 0.610959i | \(-0.209216\pi\) | ||||
0.791663 | + | 0.610959i | \(0.209216\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.495336 | + | 4.28267i | −0.0667910 | + | 0.577475i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.78543 | −1.27395 | −0.636977 | − | 0.770883i | \(-0.719815\pi\) | ||||
−0.636977 | + | 0.770883i | \(0.719815\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.45331 | −0.442151 | −0.221076 | − | 0.975257i | \(-0.570957\pi\) | ||||
−0.221076 | + | 0.975257i | \(0.570957\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 12.2273 | + | 1.41421i | 1.51661 | + | 0.175412i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.45331 | −0.666228 | −0.333114 | − | 0.942887i | \(-0.608099\pi\) | ||||
−0.333114 | + | 0.942887i | \(0.608099\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.25583 | 0.505075 | 0.252537 | − | 0.967587i | \(-0.418735\pi\) | ||||
0.252537 | + | 0.967587i | \(0.418735\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 7.27334i | − | 0.851280i | −0.904892 | − | 0.425640i | \(-0.860049\pi\) | ||
0.904892 | − | 0.425640i | \(-0.139951\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.75712 | 0.770046 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.82936i | 0.318328i | 0.987252 | + | 0.159164i | \(0.0508798\pi\) | ||||
−0.987252 | + | 0.159164i | \(0.949120\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.25583i | 0.467138i | 0.972340 | + | 0.233569i | \(0.0750405\pi\) | ||||
−0.972340 | + | 0.233569i | \(0.924959\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.14134 | + | 9.86799i | −0.123795 | + | 1.07033i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.386566i | 0.0409759i | 0.999790 | + | 0.0204880i | \(0.00652198\pi\) | ||||
−0.999790 | + | 0.0204880i | \(0.993478\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 19.2920i | − | 2.02235i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 15.5695 | + | 1.80078i | 1.59740 | + | 0.184756i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 9.29200i | − | 0.943460i | −0.881743 | − | 0.471730i | \(-0.843630\pi\) | ||
0.881743 | − | 0.471730i | \(-0.156370\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.27095i | 0.723486i | 0.932278 | + | 0.361743i | \(0.117818\pi\) | ||||
−0.932278 | + | 0.361743i | \(0.882182\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.9580 | 1.67092 | 0.835460 | − | 0.549552i | \(-0.185202\pi\) | ||||
0.835460 | + | 0.549552i | \(0.185202\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.91269i | 0.958296i | 0.877734 | + | 0.479148i | \(0.159054\pi\) | ||||
−0.877734 | + | 0.479148i | \(0.840946\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.28267 | 0.793336 | 0.396668 | − | 0.917962i | \(-0.370166\pi\) | ||||
0.396668 | + | 0.917962i | \(0.370166\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −17.8115 | −1.67557 | −0.837784 | − | 0.546002i | \(-0.816149\pi\) | ||||
−0.837784 | + | 0.546002i | \(0.816149\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.44398 | − | 0.282672i | −0.227903 | − | 0.0263593i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 15.5695 | 1.42726 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.28267 | −0.662061 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.78585 | − | 10.5199i | 0.338617 | − | 0.940924i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.957977 | 0.0850067 | 0.0425034 | − | 0.999096i | \(-0.486467\pi\) | ||||
0.0425034 | + | 0.999096i | \(0.486467\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.38441 | −0.732549 | −0.366275 | − | 0.930507i | \(-0.619367\pi\) | ||||
−0.366275 | + | 0.930507i | \(0.619367\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 24.5653i | − | 2.13009i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.1270 | 0.950646 | 0.475323 | − | 0.879811i | \(-0.342331\pi\) | ||||
0.475323 | + | 0.879811i | \(0.342331\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.17064i | 0.0992924i | 0.998767 | + | 0.0496462i | \(0.0158094\pi\) | ||||
−0.998767 | + | 0.0496462i | \(0.984191\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 10.6132i | − | 0.887520i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.1507 | + | 1.40535i | 1.00906 | + | 0.116708i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.5268i | 0.944311i | 0.881515 | + | 0.472155i | \(0.156524\pi\) | ||||
−0.881515 | + | 0.472155i | \(0.843476\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.8294i | 0.881281i | 0.897684 | + | 0.440640i | \(0.145249\pi\) | ||||
−0.897684 | + | 0.440640i | \(0.854751\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −18.3980 | − | 2.12792i | −1.47776 | − | 0.170918i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.3340i | 0.824745i | 0.911015 | + | 0.412372i | \(0.135300\pi\) | ||||
−0.911015 | + | 0.412372i | \(0.864700\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.85607i | 0.303901i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.99067 | 0.704204 | 0.352102 | − | 0.935962i | \(-0.385467\pi\) | ||||
0.352102 | + | 0.935962i | \(0.385467\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 13.0683i | − | 1.01125i | −0.862753 | − | 0.505626i | \(-0.831262\pi\) | ||
0.862753 | − | 0.505626i | \(-0.168738\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −17.3013 | −1.33087 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −19.6123 | −1.49110 | −0.745548 | − | 0.666452i | \(-0.767812\pi\) | ||||
−0.745548 | + | 0.666452i | \(0.767812\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −17.0607 | − | 4.00000i | −1.28967 | − | 0.302372i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.58489 | −0.566921 | −0.283461 | − | 0.958984i | \(-0.591483\pi\) | ||||
−0.283461 | + | 0.958984i | \(0.591483\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.82936 | −0.210305 | −0.105152 | − | 0.994456i | \(-0.533533\pi\) | ||||
−0.105152 | + | 0.994456i | \(0.533533\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.72816 | + | 0.199879i | 0.127057 | + | 0.0146954i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.56534 | 0.626360 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.1698 | −1.09765 | −0.548823 | − | 0.835938i | \(-0.684924\pi\) | ||||
−0.548823 | + | 0.835938i | \(0.684924\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.565344i | 0.0406944i | 0.999793 | + | 0.0203472i | \(0.00647716\pi\) | ||||
−0.999793 | + | 0.0203472i | \(0.993523\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.37122 | −0.596424 | −0.298212 | − | 0.954500i | \(-0.596390\pi\) | ||||
−0.298212 | + | 0.954500i | \(0.596390\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.7546i | 1.40037i | 0.713962 | + | 0.700185i | \(0.246899\pi\) | ||||
−0.713962 | + | 0.700185i | \(0.753101\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 19.1711i | − | 1.34555i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.42401 | + | 0.627343i | 0.378829 | + | 0.0438155i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 13.5142i | − | 0.934800i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 14.8294i | − | 1.02090i | −0.859909 | − | 0.510448i | \(-0.829480\pi\) | ||
0.859909 | − | 0.510448i | \(-0.170520\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.45505 | + | 21.2264i | −0.167433 | + | 1.44763i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 29.0280i | 1.97055i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 24.4546i | − | 1.64499i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.5047 | 1.30613 | 0.653064 | − | 0.757302i | \(-0.273483\pi\) | ||||
0.653064 | + | 0.757302i | \(0.273483\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 6.45637i | − | 0.428524i | −0.976776 | − | 0.214262i | \(-0.931265\pi\) | ||
0.976776 | − | 0.214262i | \(-0.0687347\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.8480 | −1.64200 | −0.821002 | − | 0.570926i | \(-0.806584\pi\) | ||||
−0.821002 | + | 0.570926i | \(0.806584\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.04408 | −0.526985 | −0.263493 | − | 0.964661i | \(-0.584874\pi\) | ||||
−0.263493 | + | 0.964661i | \(0.584874\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −26.0187 | − | 3.00933i | −1.69727 | − | 0.196307i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.5709 | 1.26593 | 0.632967 | − | 0.774179i | \(-0.281837\pi\) | ||||
0.632967 | + | 0.774179i | \(0.281837\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 25.1307 | 1.61881 | 0.809405 | − | 0.587251i | \(-0.199790\pi\) | ||||
0.809405 | + | 0.587251i | \(0.199790\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.35718 | + | 11.7342i | −0.0867071 | + | 0.749670i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −38.5840 | −2.45504 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 26.7560 | 1.68882 | 0.844412 | − | 0.535695i | \(-0.179950\pi\) | ||||
0.844412 | + | 0.535695i | \(0.179950\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.12136i | 0.133369i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.69835 | −0.542588 | −0.271294 | − | 0.962496i | \(-0.587452\pi\) | ||||
−0.271294 | + | 0.962496i | \(0.587452\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 2.72666i | − | 0.169426i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 18.0708i | − | 1.11430i | −0.830413 | − | 0.557148i | \(-0.811896\pi\) | ||
0.830413 | − | 0.557148i | \(-0.188104\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.96137 | + | 25.6040i | −0.181915 | + | 1.57284i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.95413i | 0.606914i | 0.952845 | + | 0.303457i | \(0.0981409\pi\) | ||||
−0.952845 | + | 0.303457i | \(0.901859\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 27.1893i | 1.65163i | 0.563939 | + | 0.825816i | \(0.309285\pi\) | ||||
−0.563939 | + | 0.825816i | \(0.690715\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −9.38567 | − | 2.20054i | −0.565977 | − | 0.132697i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.40196i | 0.564909i | 0.959281 | + | 0.282455i | \(0.0911486\pi\) | ||||
−0.959281 | + | 0.282455i | \(0.908851\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.52612i | 0.568281i | 0.958783 | + | 0.284140i | \(0.0917082\pi\) | ||||
−0.958783 | + | 0.284140i | \(0.908292\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.5840 | −0.866929 | −0.433464 | − | 0.901171i | \(-0.642709\pi\) | ||||
−0.433464 | + | 0.901171i | \(0.642709\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 8.55790i | − | 0.505157i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.73599 | 0.160940 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −21.8855 | −1.27856 | −0.639281 | − | 0.768973i | \(-0.720768\pi\) | ||||
−0.639281 | + | 0.768973i | \(0.720768\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.51399 | − | 21.7360i | 0.146370 | − | 1.26552i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.05661 | 0.350263 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 33.4906 | 1.93037 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.887197 | − | 7.67071i | 0.0508008 | − | 0.439223i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.1307 | −1.43428 | −0.717142 | − | 0.696927i | \(-0.754550\pi\) | ||||
−0.717142 | + | 0.696927i | \(0.754550\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −22.8819 | −1.29752 | −0.648758 | − | 0.760995i | \(-0.724711\pi\) | ||||
−0.648758 | + | 0.760995i | \(0.724711\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 32.5653i | − | 1.84070i | −0.391093 | − | 0.920351i | \(-0.627903\pi\) | ||
0.391093 | − | 0.920351i | \(-0.372097\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.91484 | 0.107548 | 0.0537742 | − | 0.998553i | \(-0.482875\pi\) | ||||
0.0537742 | + | 0.998553i | \(0.482875\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 10.5467i | − | 0.590501i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 31.1391i | − | 1.73262i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.28267 | + | 26.7967i | −0.348500 | + | 1.48641i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 41.0518i | 2.26326i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 6.44398i | − | 0.354193i | −0.984193 | − | 0.177097i | \(-0.943329\pi\) | ||
0.984193 | − | 0.177097i | \(-0.0566705\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.40102 | − | 12.1132i | 0.0765459 | − | 0.661816i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.93206i | 0.486560i | 0.969956 | + | 0.243280i | \(0.0782235\pi\) | ||||
−0.969956 | + | 0.243280i | \(0.921777\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.9693i | 0.864786i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.01866 | −0.324977 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 23.2817i | 1.24983i | 0.780694 | + | 0.624913i | \(0.214866\pi\) | ||||
−0.780694 | + | 0.624913i | \(0.785134\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.1120 | 0.915986 | 0.457993 | − | 0.888956i | \(-0.348568\pi\) | ||||
0.457993 | + | 0.888956i | \(0.348568\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.7286 | −0.783923 | −0.391962 | − | 0.919982i | \(-0.628203\pi\) | ||||
−0.391962 | + | 0.919982i | \(0.628203\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.09337 | + | 9.45331i | −0.0580303 | + | 0.501730i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −20.2251 | −1.06744 | −0.533721 | − | 0.845661i | \(-0.679207\pi\) | ||||
−0.533721 | + | 0.845661i | \(0.679207\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −30.1307 | −1.58583 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16.1560 | + | 1.86861i | 0.845643 | + | 0.0978074i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.0700 | 0.630049 | 0.315025 | − | 0.949083i | \(-0.397987\pi\) | ||||
0.315025 | + | 0.949083i | \(0.397987\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 40.3975 | 2.09733 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.8153i | 0.663552i | 0.943358 | + | 0.331776i | \(0.107648\pi\) | ||||
−0.943358 | + | 0.331776i | \(0.892352\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −30.1114 | −1.55082 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.7360i | 0.911036i | 0.890226 | + | 0.455518i | \(0.150546\pi\) | ||||
−0.890226 | + | 0.455518i | \(0.849454\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 25.0825i | − | 1.28165i | −0.767685 | − | 0.640827i | \(-0.778592\pi\) | ||
0.767685 | − | 0.640827i | \(-0.221408\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.73599 | + | 15.0093i | −0.0884740 | + | 0.764946i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 23.4684i | − | 1.18989i | −0.803765 | − | 0.594947i | \(-0.797173\pi\) | ||
0.803765 | − | 0.594947i | \(-0.202827\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.88797i | 0.247195i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.28474 | − | 0.726896i | −0.316220 | − | 0.0365741i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 2.69396i | − | 0.135206i | −0.997712 | − | 0.0676031i | \(-0.978465\pi\) | ||
0.997712 | − | 0.0676031i | \(-0.0215351\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 32.3252i | − | 1.61424i | −0.590386 | − | 0.807121i | \(-0.701025\pi\) | ||
0.590386 | − | 0.807121i | \(-0.298975\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 45.5933 | 2.27117 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 1.50003i | − | 0.0743536i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.6426 | 1.02071 | 0.510356 | − | 0.859963i | \(-0.329514\pi\) | ||||
0.510356 | + | 0.859963i | \(0.329514\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −34.2946 | −1.68753 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.45331 | − | 1.09337i | −0.464045 | − | 0.0536716i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −23.1544 | −1.13117 | −0.565584 | − | 0.824691i | \(-0.691349\pi\) | ||||
−0.565584 | + | 0.824691i | \(0.691349\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.3200 | −1.38023 | −0.690116 | − | 0.723699i | \(-0.742440\pi\) | ||||
−0.690116 | + | 0.723699i | \(0.742440\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −21.6262 | − | 5.07041i | −1.04902 | − | 0.245951i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.1027 | −0.585691 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −26.6287 | −1.28266 | −0.641331 | − | 0.767265i | \(-0.721617\pi\) | ||||
−0.641331 | + | 0.767265i | \(0.721617\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 23.3693i | − | 1.12306i | −0.827458 | − | 0.561528i | \(-0.810214\pi\) | ||
0.827458 | − | 0.561528i | \(-0.189786\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.71215 | 0.368922 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 28.3200i | − | 1.35164i | −0.737067 | − | 0.675820i | \(-0.763790\pi\) | ||
0.737067 | − | 0.675820i | \(-0.236210\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 23.2817i | − | 1.10615i | −0.833133 | − | 0.553073i | \(-0.813455\pi\) | ||
0.833133 | − | 0.553073i | \(-0.186545\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.858664 | − | 0.0993134i | −0.0407046 | − | 0.00470791i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 29.3251i | − | 1.38394i | −0.721927 | − | 0.691969i | \(-0.756744\pi\) | ||
0.721927 | − | 0.691969i | \(-0.243256\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 4.70800i | − | 0.221691i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 42.8526 | + | 4.95634i | 2.00896 | + | 0.232357i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 18.9507i | − | 0.886477i | −0.896404 | − | 0.443239i | \(-0.853829\pi\) | ||
0.896404 | − | 0.443239i | \(-0.146171\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.3539i | 0.482229i | 0.970497 | + | 0.241114i | \(0.0775129\pi\) | ||||
−0.970497 | + | 0.241114i | \(0.922487\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.07934 | −0.143109 | −0.0715545 | − | 0.997437i | \(-0.522796\pi\) | ||||
−0.0715545 | + | 0.997437i | \(0.522796\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 40.9065i | − | 1.89293i | −0.322809 | − | 0.946464i | \(-0.604627\pi\) | ||
0.322809 | − | 0.946464i | \(-0.395373\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −19.1120 | −0.882512 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 18.4244 | 0.847153 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.00000 | + | 34.1214i | −0.367065 | + | 1.56560i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16.3691 | −0.747921 | −0.373961 | − | 0.927445i | \(-0.622001\pi\) | ||||
−0.373961 | + | 0.927445i | \(0.622001\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.28267 | −0.195273 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 20.6400 | + | 2.38723i | 0.937212 | + | 0.108398i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.957977 | −0.0434101 | −0.0217050 | − | 0.999764i | \(-0.506909\pi\) | ||||
−0.0217050 | + | 0.999764i | \(0.506909\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.8395 | −0.489178 | −0.244589 | − | 0.969627i | \(-0.578653\pi\) | ||||
−0.244589 | + | 0.969627i | \(0.578653\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 24.3013i | − | 1.09448i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 14.9153 | 0.669041 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 31.5747i | 1.41348i | 0.707475 | + | 0.706738i | \(0.249834\pi\) | ||||
−0.707475 | + | 0.706738i | \(0.750166\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15.8241i | 0.705560i | 0.935706 | + | 0.352780i | \(0.114764\pi\) | ||||
−0.935706 | + | 0.352780i | \(0.885236\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.1507 | − | 1.86799i | −0.718695 | − | 0.0831246i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 10.1258i | − | 0.448816i | −0.974495 | − | 0.224408i | \(-0.927955\pi\) | ||
0.974495 | − | 0.224408i | \(-0.0720449\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 25.4906i | − | 1.12764i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.35671 | + | 37.6681i | −0.191979 | + | 1.65985i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22.5840i | 0.993243i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.3528i | 1.46121i | 0.682799 | + | 0.730607i | \(0.260763\pi\) | ||||
−0.682799 | + | 0.730607i | \(0.739237\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.9160 | 1.13323 | 0.566613 | − | 0.823984i | \(-0.308254\pi\) | ||||
0.566613 | + | 0.823984i | \(0.308254\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 36.7959i | 1.60286i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.7894 | 0.947366 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −13.4416 | −0.582221 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −22.0187 | − | 2.54669i | −0.951950 | − | 0.110103i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.1852 | 0.438707 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.39470 | 0.145950 | 0.0729749 | − | 0.997334i | \(-0.476751\pi\) | ||||
0.0729749 | + | 0.997334i | \(0.476751\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.12792 | + | 18.3980i | −0.0911499 | + | 0.788082i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.57467 | 0.323870 | 0.161935 | − | 0.986801i | \(-0.448227\pi\) | ||||
0.161935 | + | 0.986801i | \(0.448227\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −38.3422 | −1.63343 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.91595i | 0.421669i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.38596 | 0.0587252 | 0.0293626 | − | 0.999569i | \(-0.490652\pi\) | ||||
0.0293626 | + | 0.999569i | \(0.490652\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 52.6027i | − | 2.22486i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 31.7934i | 1.33993i | 0.742393 | + | 0.669965i | \(0.233691\pi\) | ||||
−0.742393 | + | 0.669965i | \(0.766309\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.57599 | − | 39.5640i | 0.192513 | − | 1.66447i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.3005i | 0.473742i | 0.971541 | + | 0.236871i | \(0.0761219\pi\) | ||||
−0.971541 | + | 0.236871i | \(0.923878\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.5933i | 0.568863i | 0.958696 | + | 0.284432i | \(0.0918049\pi\) | ||||
−0.958696 | + | 0.284432i | \(0.908195\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.25578 | − | 5.35610i | 0.0523695 | − | 0.223365i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 43.0466i | 1.79206i | 0.443998 | + | 0.896028i | \(0.353560\pi\) | ||||
−0.443998 | + | 0.896028i | \(0.646440\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.9153i | 0.618790i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 22.2241 | 0.920427 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.80210i | 0.239478i | 0.992805 | + | 0.119739i | \(0.0382058\pi\) | ||||
−0.992805 | + | 0.119739i | \(0.961794\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 58.0560 | 2.39215 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.9015 | 0.652995 | 0.326498 | − | 0.945198i | \(-0.394131\pi\) | ||||
0.326498 | + | 0.945198i | \(0.394131\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.00000 | + | 34.5840i | −0.163984 | + | 1.41781i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 39.2510 | 1.60375 | 0.801876 | − | 0.597490i | \(-0.203835\pi\) | ||||
0.801876 | + | 0.597490i | \(0.203835\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.73599 | −0.315557 | −0.157779 | − | 0.987474i | \(-0.550433\pi\) | ||||
−0.157779 | + | 0.987474i | \(0.550433\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.87100 | − | 16.1767i | 0.0760672 | − | 0.657677i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.60737 | 0.308774 | 0.154387 | − | 0.988010i | \(-0.450660\pi\) | ||||
0.154387 | + | 0.988010i | \(0.450660\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 64.4787 | 2.60853 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 0.418069i | − | 0.0168856i | −0.999964 | − | 0.00844282i | \(-0.997313\pi\) | ||
0.999964 | − | 0.00844282i | \(-0.00268747\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 44.3214 | 1.78431 | 0.892156 | − | 0.451727i | \(-0.149192\pi\) | ||||
0.892156 | + | 0.451727i | \(0.149192\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 4.07727i | − | 0.163879i | −0.996637 | − | 0.0819396i | \(-0.973889\pi\) | ||
0.996637 | − | 0.0819396i | \(-0.0261115\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.35478i | 0.0542783i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.3947 | + | 11.1120i | 0.895788 | + | 0.444481i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 3.45632i | − | 0.137812i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.71733i | 0.307222i | 0.988131 | + | 0.153611i | \(0.0490903\pi\) | ||||
−0.988131 | + | 0.153611i | \(0.950910\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.246116 | + | 2.12792i | −0.00976680 | + | 0.0844438i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 29.0793i | − | 1.15217i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.18866i | 0.244438i | 0.992503 | + | 0.122219i | \(0.0390010\pi\) | ||||
−0.992503 | + | 0.122219i | \(0.960999\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −26.1214 | −1.03013 | −0.515063 | − | 0.857152i | \(-0.672231\pi\) | ||||
−0.515063 | + | 0.857152i | \(0.672231\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 3.20180i | − | 0.125876i | −0.998017 | − | 0.0629379i | \(-0.979953\pi\) | ||
0.998017 | − | 0.0629379i | \(-0.0200470\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −18.8667 | −0.740582 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.4568 | 0.761403 | 0.380702 | − | 0.924698i | \(-0.375683\pi\) | ||||
0.380702 | + | 0.924698i | \(0.375683\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.15405 | − | 18.6240i | 0.0841659 | − | 0.727698i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.32780 | 0.0906781 | 0.0453390 | − | 0.998972i | \(-0.485563\pi\) | ||||
0.0453390 | + | 0.998972i | \(0.485563\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −38.0373 | −1.47948 | −0.739740 | − | 0.672893i | \(-0.765052\pi\) | ||||
−0.739740 | + | 0.672893i | \(0.765052\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 54.5660 | + | 6.31113i | 2.11598 | + | 0.244735i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.01866 | 0.233043 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.65812 | −0.257034 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 34.6867i | − | 1.33707i | −0.743679 | − | 0.668537i | \(-0.766921\pi\) | ||
0.743679 | − | 0.668537i | \(-0.233079\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 45.1672 | 1.73591 | 0.867957 | − | 0.496639i | \(-0.165433\pi\) | ||||
0.867957 | + | 0.496639i | \(0.165433\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 32.5653i | − | 1.24974i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 44.7986i | 1.71417i | 0.515175 | + | 0.857085i | \(0.327727\pi\) | ||||
−0.515175 | + | 0.857085i | \(0.672273\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.85866 | + | 24.7160i | −0.109224 | + | 0.944350i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 63.4511i | − | 2.41729i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 6.80392i | − | 0.258833i | −0.991590 | − | 0.129417i | \(-0.958690\pi\) | ||
0.991590 | − | 0.129417i | \(-0.0413105\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.60030 | − | 0.300751i | −0.0986349 | − | 0.0114082i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 10.8480i | − | 0.410898i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 29.5250i | − | 1.11514i | −0.830129 | − | 0.557572i | \(-0.811733\pi\) | ||
0.830129 | − | 0.557572i | \(-0.188267\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.45331 | −0.205676 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 25.4822i | 0.958358i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −27.1893 | −1.02112 | −0.510558 | − | 0.859843i | \(-0.670561\pi\) | ||||
−0.510558 | + | 0.859843i | \(0.670561\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.11317 | −0.341291 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 23.5747 | + | 2.72666i | 0.881643 | + | 0.101971i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16.1145 | −0.600971 | −0.300486 | − | 0.953786i | \(-0.597149\pi\) | ||||
−0.300486 | + | 0.953786i | \(0.597149\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 59.4320 | 2.21336 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.24330 | + | 26.6287i | −0.231870 | + | 0.988966i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.1820 | 1.15648 | 0.578239 | − | 0.815867i | \(-0.303740\pi\) | ||||
0.578239 | + | 0.815867i | \(0.303740\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 42.4528 | 1.57017 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 4.41129i | − | 0.162935i | −0.996676 | − | 0.0814674i | \(-0.974039\pi\) | ||
0.996676 | − | 0.0814674i | \(-0.0259606\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10.5142 | −0.387295 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.5560i | 0.645808i | 0.946432 | + | 0.322904i | \(0.104659\pi\) | ||||
−0.946432 | + | 0.322904i | \(0.895341\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.65817i | 0.354324i | 0.984182 | + | 0.177162i | \(0.0566917\pi\) | ||||
−0.984182 | + | 0.177162i | \(0.943308\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −25.6040 | − | 2.96137i | −0.938057 | − | 0.108496i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 34.7406i | 1.26940i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.6053i | 0.459974i | 0.973194 | + | 0.229987i | \(0.0738683\pi\) | ||||
−0.973194 | + | 0.229987i | \(0.926132\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −24.0548 | − | 2.78219i | −0.875445 | − | 0.101254i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 36.0887i | − | 1.31166i | −0.754906 | − | 0.655832i | \(-0.772318\pi\) | ||
0.754906 | − | 0.655832i | \(-0.227682\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 16.8385i | − | 0.610396i | −0.952289 | − | 0.305198i | \(-0.901277\pi\) | ||
0.952289 | − | 0.305198i | \(-0.0987226\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 29.0280 | 1.05088 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 53.8655i | 1.94497i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −54.3200 | −1.95883 | −0.979414 | − | 0.201860i | \(-0.935301\pi\) | ||||
−0.979414 | + | 0.201860i | \(0.935301\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.17068 | 0.221944 | 0.110972 | − | 0.993824i | \(-0.464604\pi\) | ||||
0.110972 | + | 0.993824i | \(0.464604\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.45331 | − | 40.3200i | 0.339573 | − | 1.44834i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −17.1158 | −0.613237 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.20541 | 0.293612 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −22.9546 | − | 2.65493i | −0.819283 | − | 0.0947586i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.12136 | −0.0756183 | −0.0378092 | − | 0.999285i | \(-0.512038\pi\) | ||||
−0.0378092 | + | 0.999285i | \(0.512038\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −62.4234 | −2.21952 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 19.0093i | 0.675041i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7.92522 | −0.280726 | −0.140363 | − | 0.990100i | \(-0.544827\pi\) | ||||
−0.140363 | + | 0.990100i | \(0.544827\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 52.0373i | 1.84095i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 14.0233i | − | 0.494871i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.56534 | − | 0.990671i | −0.301889 | − | 0.0349166i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29.2158i | 1.02717i | 0.858037 | + | 0.513587i | \(0.171684\pi\) | ||||
−0.858037 | + | 0.513587i | \(0.828316\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.3013i | 0.361729i | 0.983508 | + | 0.180864i | \(0.0578895\pi\) | ||||
−0.983508 | + | 0.180864i | \(0.942111\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.30981 | + | 19.9706i | −0.0809091 | + | 0.699540i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 66.9813i | − | 2.34338i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 11.1270i | − | 0.388336i | −0.980968 | − | 0.194168i | \(-0.937799\pi\) | ||
0.980968 | − | 0.194168i | \(-0.0622006\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 35.6447 | 1.24250 | 0.621248 | − | 0.783614i | \(-0.286626\pi\) | ||||
0.621248 | + | 0.783614i | \(0.286626\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 9.11317i | − | 0.316896i | −0.987367 | − | 0.158448i | \(-0.949351\pi\) | ||
0.987367 | − | 0.158448i | \(-0.0506490\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.2640 | 0.356484 | 0.178242 | − | 0.983987i | \(-0.442959\pi\) | ||||
0.178242 | + | 0.983987i | \(0.442959\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 23.4684 | 0.813131 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 29.0280 | + | 3.35739i | 1.00455 | + | 0.116187i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −31.5388 | −1.08884 | −0.544421 | − | 0.838812i | \(-0.683251\pi\) | ||||
−0.544421 | + | 0.838812i | \(0.683251\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.922733 | −0.0318184 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.44492 | − | 38.4308i | 0.152910 | − | 1.32206i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −25.5233 | −0.876992 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.856018 | 0.0293439 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 15.3620i | − | 0.525985i | −0.964798 | − | 0.262993i | \(-0.915291\pi\) | ||
0.964798 | − | 0.262993i | \(-0.0847095\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16.4105 | −0.560572 | −0.280286 | − | 0.959917i | \(-0.590429\pi\) | ||||
−0.280286 | + | 0.959917i | \(0.590429\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.8294i | 0.505971i | 0.967470 | + | 0.252986i | \(0.0814125\pi\) | ||||
−0.967470 | + | 0.252986i | \(0.918587\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 24.3820i | 0.829972i | 0.909828 | + | 0.414986i | \(0.136213\pi\) | ||||
−0.909828 | + | 0.414986i | \(0.863787\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.03863 | − | 43.5640i | 0.171319 | − | 1.48122i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.45511i | 0.185052i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 30.0187i | 1.01714i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 13.2681 | − | 36.8686i | 0.448545 | − | 1.24638i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.6846i | 0.664703i | 0.943156 | + | 0.332351i | \(0.107842\pi\) | ||||
−0.943156 | + | 0.332351i | \(0.892158\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 15.7280i | − | 0.529889i | −0.964264 | − | 0.264945i | \(-0.914646\pi\) | ||
0.964264 | − | 0.264945i | \(-0.0853536\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.99067 | −0.302560 | −0.151280 | − | 0.988491i | \(-0.548340\pi\) | ||||
−0.151280 | + | 0.988491i | \(0.548340\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 8.66717i | − | 0.291015i | −0.989357 | − | 0.145508i | \(-0.953518\pi\) | ||
0.989357 | − | 0.145508i | \(-0.0464815\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.35739 | 0.112603 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 82.1035 | 2.74749 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.94865 | − | 16.8480i | 0.0651361 | − | 0.563167i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 45.3076 | 1.51109 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 51.2080 | 1.70598 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.726896 | − | 6.28474i | 0.0241628 | − | 0.208912i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 39.5747 | 1.31406 | 0.657028 | − | 0.753866i | \(-0.271813\pi\) | ||||
0.657028 | + | 0.753866i | \(0.271813\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.60156 | −0.119325 | −0.0596625 | − | 0.998219i | \(-0.519002\pi\) | ||||
−0.0596625 | + | 0.998219i | \(0.519002\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.20541i | 0.271559i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −29.3845 | −0.970363 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 15.7173i | − | 0.518467i | −0.965815 | − | 0.259233i | \(-0.916530\pi\) | ||
0.965815 | − | 0.259233i | \(-0.0834699\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 23.4269i | − | 0.771107i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.887968 | + | 3.78734i | −0.0291962 | + | 0.124527i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 44.6929i | 1.46633i | 0.680053 | + | 0.733163i | \(0.261957\pi\) | ||||
−0.680053 | + | 0.733163i | \(0.738043\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 37.0280i | − | 1.21354i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.20054 | + | 19.0259i | −0.0719653 | + | 0.622212i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 17.9813i | − | 0.587425i | −0.955894 | − | 0.293712i | \(-0.905109\pi\) | ||
0.955894 | − | 0.293712i | \(-0.0948908\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 13.3276i | − | 0.434466i | −0.976120 | − | 0.217233i | \(-0.930297\pi\) | ||
0.976120 | − | 0.217233i | \(-0.0697032\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.68670 | 0.0874911 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 43.8538i | 1.42506i | 0.701643 | + | 0.712529i | \(0.252450\pi\) | ||||
−0.701643 | + | 0.712529i | \(0.747550\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −40.0373 | −1.29967 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −20.4382 | −0.662058 | −0.331029 | − | 0.943621i | \(-0.607396\pi\) | ||||
−0.331029 | + | 0.943621i | \(0.607396\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.89730 | − | 33.6960i | 0.126114 | − | 1.09038i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 38.9965 | 1.25926 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −37.6027 | −1.21299 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.25578 | − | 0.145244i | −0.0404249 | − | 0.00467556i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14.6167 | −0.470041 | −0.235021 | − | 0.971990i | \(-0.575516\pi\) | ||||
−0.235021 | + | 0.971990i | \(0.575516\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 50.4374 | 1.61861 | 0.809307 | − | 0.587385i | \(-0.199843\pi\) | ||||
0.809307 | + | 0.587385i | \(0.199843\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.10270i | 0.131527i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 17.0744 | 0.546257 | 0.273129 | − | 0.961978i | \(-0.411942\pi\) | ||||
0.273129 | + | 0.961978i | \(0.411942\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.745314i | 0.0238203i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 13.7688i | − | 0.439155i | −0.975595 | − | 0.219578i | \(-0.929532\pi\) | ||
0.975595 | − | 0.219578i | \(-0.0704679\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.15066 | − | 18.5946i | 0.0685259 | − | 0.592475i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10.5142i | 0.334332i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 14.0959i | − | 0.447772i | −0.974615 | − | 0.223886i | \(-0.928126\pi\) | ||
0.974615 | − | 0.223886i | \(-0.0718743\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −43.8802 | − | 5.07520i | −1.39110 | − | 0.160895i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.7126i | 1.03602i | 0.855375 | + | 0.518010i | \(0.173327\pi\) | ||||
−0.855375 | + | 0.518010i | \(0.826673\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1440.2.o.b.1439.6 | yes | 12 | |
3.2 | odd | 2 | inner | 1440.2.o.b.1439.7 | yes | 12 | |
4.3 | odd | 2 | 1440.2.o.a.1439.6 | yes | 12 | ||
5.2 | odd | 4 | 7200.2.h.l.1151.12 | 12 | |||
5.3 | odd | 4 | 7200.2.h.m.1151.2 | 12 | |||
5.4 | even | 2 | 1440.2.o.a.1439.8 | yes | 12 | ||
8.3 | odd | 2 | 2880.2.o.f.2879.7 | 12 | |||
8.5 | even | 2 | 2880.2.o.e.2879.7 | 12 | |||
12.11 | even | 2 | 1440.2.o.a.1439.7 | yes | 12 | ||
15.2 | even | 4 | 7200.2.h.l.1151.11 | 12 | |||
15.8 | even | 4 | 7200.2.h.m.1151.1 | 12 | |||
15.14 | odd | 2 | 1440.2.o.a.1439.5 | ✓ | 12 | ||
20.3 | even | 4 | 7200.2.h.m.1151.11 | 12 | |||
20.7 | even | 4 | 7200.2.h.l.1151.1 | 12 | |||
20.19 | odd | 2 | inner | 1440.2.o.b.1439.8 | yes | 12 | |
24.5 | odd | 2 | 2880.2.o.e.2879.6 | 12 | |||
24.11 | even | 2 | 2880.2.o.f.2879.6 | 12 | |||
40.19 | odd | 2 | 2880.2.o.e.2879.5 | 12 | |||
40.29 | even | 2 | 2880.2.o.f.2879.5 | 12 | |||
60.23 | odd | 4 | 7200.2.h.m.1151.12 | 12 | |||
60.47 | odd | 4 | 7200.2.h.l.1151.2 | 12 | |||
60.59 | even | 2 | inner | 1440.2.o.b.1439.5 | yes | 12 | |
120.29 | odd | 2 | 2880.2.o.f.2879.8 | 12 | |||
120.59 | even | 2 | 2880.2.o.e.2879.8 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1440.2.o.a.1439.5 | ✓ | 12 | 15.14 | odd | 2 | ||
1440.2.o.a.1439.6 | yes | 12 | 4.3 | odd | 2 | ||
1440.2.o.a.1439.7 | yes | 12 | 12.11 | even | 2 | ||
1440.2.o.a.1439.8 | yes | 12 | 5.4 | even | 2 | ||
1440.2.o.b.1439.5 | yes | 12 | 60.59 | even | 2 | inner | |
1440.2.o.b.1439.6 | yes | 12 | 1.1 | even | 1 | trivial | |
1440.2.o.b.1439.7 | yes | 12 | 3.2 | odd | 2 | inner | |
1440.2.o.b.1439.8 | yes | 12 | 20.19 | odd | 2 | inner | |
2880.2.o.e.2879.5 | 12 | 40.19 | odd | 2 | |||
2880.2.o.e.2879.6 | 12 | 24.5 | odd | 2 | |||
2880.2.o.e.2879.7 | 12 | 8.5 | even | 2 | |||
2880.2.o.e.2879.8 | 12 | 120.59 | even | 2 | |||
2880.2.o.f.2879.5 | 12 | 40.29 | even | 2 | |||
2880.2.o.f.2879.6 | 12 | 24.11 | even | 2 | |||
2880.2.o.f.2879.7 | 12 | 8.3 | odd | 2 | |||
2880.2.o.f.2879.8 | 12 | 120.29 | odd | 2 | |||
7200.2.h.l.1151.1 | 12 | 20.7 | even | 4 | |||
7200.2.h.l.1151.2 | 12 | 60.47 | odd | 4 | |||
7200.2.h.l.1151.11 | 12 | 15.2 | even | 4 | |||
7200.2.h.l.1151.12 | 12 | 5.2 | odd | 4 | |||
7200.2.h.m.1151.1 | 12 | 15.8 | even | 4 | |||
7200.2.h.m.1151.2 | 12 | 5.3 | odd | 4 | |||
7200.2.h.m.1151.11 | 12 | 20.3 | even | 4 | |||
7200.2.h.m.1151.12 | 12 | 60.23 | odd | 4 |