Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7200,2,Mod(1151,7200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7200, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7200.1151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7200 = 2^{5} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7200.h (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: | \(57.4922894553\) |
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: | \(\Z[a_1, \ldots, a_{41}]\) |
Coefficient ring index: | \( 2^{15} \) |
Twist minimal: | no (minimal twist has level 1440) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1151.11 | ||
Root | \(-1.35818 - 0.394157i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7200.1151 |
Dual form | 7200.2.h.m.1151.1 |
$q$-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 \(\left(\mathbb{Z}/7200\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(6401\) | \(6751\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(-1\) |
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 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.50466i | 1.32464i | 0.749222 | + | 0.662319i | \(0.230428\pi\) | ||||
−0.749222 | + | 0.662319i | \(0.769572\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.92804 | −0.581325 | −0.290663 | − | 0.956826i | \(-0.593876\pi\) | ||||
−0.290663 | + | 0.956826i | \(0.593876\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.50466 | 1.52672 | 0.763360 | − | 0.645974i | \(-0.223548\pi\) | ||||
0.763360 | + | 0.645974i | \(0.223548\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 4.44252i | − 1.07747i | −0.842475 | − | 0.538735i | \(-0.818903\pi\) | ||||
0.842475 | − | 0.538735i | \(-0.181097\pi\) | |||||||
\(18\) | 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 | ||||||||
\(23\) | 1.10027 | 0.229422 | 0.114711 | − | 0.993399i | \(-0.463406\pi\) | ||||
0.114711 | + | 0.993399i | \(0.463406\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.47017i | 1.01578i | 0.861421 | + | 0.507892i | \(0.169575\pi\) | ||||
−0.861421 | + | 0.507892i | \(0.830425\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 8.28267i | − 1.48761i | −0.668396 | − | 0.743806i | \(-0.733019\pi\) | ||||
0.668396 | − | 0.743806i | \(-0.266981\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.778008 | −0.127904 | −0.0639519 | − | 0.997953i | \(-0.520370\pi\) | ||||
−0.0639519 | + | 0.997953i | \(0.520370\pi\) | |||||||
\(38\) | 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 | ||||||||
\(43\) | − 9.55602i | − 1.45728i | −0.684898 | − | 0.728639i | \(-0.740153\pi\) | ||||
0.684898 | − | 0.728639i | \(-0.259847\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.7135 | −1.70858 | −0.854292 | − | 0.519793i | \(-0.826009\pi\) | ||||
−0.854292 | + | 0.519793i | \(0.826009\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.28267 | −0.754667 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.5268i | 1.58333i | 0.610959 | + | 0.791663i | \(0.290784\pi\) | ||||
−0.610959 | + | 0.791663i | \(0.709216\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 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 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 5.45331i | − 0.666228i | −0.942887 | − | 0.333114i | \(-0.891901\pi\) | ||||
0.942887 | − | 0.333114i | \(-0.108099\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.25583 | −0.505075 | −0.252537 | − | 0.967587i | \(-0.581265\pi\) | ||||
−0.252537 | + | 0.967587i | \(0.581265\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.27334 | 0.851280 | 0.425640 | − | 0.904892i | \(-0.360049\pi\) | ||||
0.425640 | + | 0.904892i | \(0.360049\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 6.75712i | − 0.770046i | ||||||||
\(78\) | 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 | ||||||||
\(83\) | 4.25583 | 0.467138 | 0.233569 | − | 0.972340i | \(-0.424959\pi\) | ||||
0.233569 | + | 0.972340i | \(0.424959\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 0.386566i | − 0.0409759i | −0.999790 | − | 0.0204880i | \(-0.993478\pi\) | ||||
0.999790 | − | 0.0204880i | \(-0.00652198\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 19.2920i | 2.02235i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.29200 | −0.943460 | −0.471730 | − | 0.881743i | \(-0.656370\pi\) | ||||
−0.471730 | + | 0.881743i | \(0.656370\pi\) | |||||||
\(98\) | 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 | ||||||||
\(103\) | − 16.9580i | − 1.67092i | −0.549552 | − | 0.835460i | \(-0.685202\pi\) | ||||
0.549552 | − | 0.835460i | \(-0.314798\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.91269 | −0.958296 | −0.479148 | − | 0.877734i | \(-0.659054\pi\) | ||||
−0.479148 | + | 0.877734i | \(0.659054\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.28267 | −0.793336 | −0.396668 | − | 0.917962i | \(-0.629834\pi\) | ||||
−0.396668 | + | 0.917962i | \(0.629834\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 17.8115i | − 1.67557i | −0.546002 | − | 0.837784i | \(-0.683851\pi\) | ||||
0.546002 | − | 0.837784i | \(-0.316149\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 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 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.957977i | 0.0850067i | 0.999096 | + | 0.0425034i | \(0.0135333\pi\) | ||||
−0.999096 | + | 0.0425034i | \(0.986467\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.38441 | 0.732549 | 0.366275 | − | 0.930507i | \(-0.380633\pi\) | ||||
0.366275 | + | 0.930507i | \(0.380633\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 24.5653 | 2.13009 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 11.1270i | − 0.950646i | −0.879811 | − | 0.475323i | \(-0.842331\pi\) | ||||
0.879811 | − | 0.475323i | \(-0.157669\pi\) | |||||||
\(138\) | 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 | ||||||||
\(143\) | −10.6132 | −0.887520 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 11.5268i | − 0.944311i | −0.881515 | − | 0.472155i | \(-0.843476\pi\) | ||||
0.881515 | − | 0.472155i | \(-0.156524\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 10.8294i | − 0.881281i | −0.897684 | − | 0.440640i | \(-0.854751\pi\) | ||||
0.897684 | − | 0.440640i | \(-0.145249\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.3340 | 0.824745 | 0.412372 | − | 0.911015i | \(-0.364700\pi\) | ||||
0.412372 | + | 0.911015i | \(0.364700\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.85607i | 0.303901i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 8.99067i | − 0.704204i | −0.935962 | − | 0.352102i | \(-0.885467\pi\) | ||||
0.935962 | − | 0.352102i | \(-0.114533\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.0683 | 1.01125 | 0.505626 | − | 0.862753i | \(-0.331262\pi\) | ||||
0.505626 | + | 0.862753i | \(0.331262\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 17.3013 | 1.33087 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 19.6123i | − 1.49110i | −0.666452 | − | 0.745548i | \(-0.732188\pi\) | ||||
0.666452 | − | 0.745548i | \(-0.267812\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 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 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.56534i | 0.626360i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.1698 | 1.09765 | 0.548823 | − | 0.835938i | \(-0.315076\pi\) | ||||
0.548823 | + | 0.835938i | \(0.315076\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.565344 | −0.0406944 | −0.0203472 | − | 0.999793i | \(-0.506477\pi\) | ||||
−0.0203472 | + | 0.999793i | \(0.506477\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.37122i | 0.596424i | 0.954500 | + | 0.298212i | \(0.0963903\pi\) | ||||
−0.954500 | + | 0.298212i | \(0.903610\pi\) | |||||||
\(198\) | 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 | ||||||||
\(203\) | −19.1711 | −1.34555 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 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 | \(0.170520\pi\) | ||||
−0.859909 | + | 0.510448i | \(0.829480\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 29.0280 | 1.97055 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 24.4546i | − 1.64499i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 19.5047i | − 1.30613i | −0.757302 | − | 0.653064i | \(-0.773483\pi\) | ||||
0.757302 | − | 0.653064i | \(-0.226517\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.45637 | 0.428524 | 0.214262 | − | 0.976776i | \(-0.431265\pi\) | ||||
0.214262 | + | 0.976776i | \(0.431265\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24.8480 | 1.64200 | 0.821002 | − | 0.570926i | \(-0.193416\pi\) | ||||
0.821002 | + | 0.570926i | \(0.193416\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 8.04408i | − 0.526985i | −0.964661 | − | 0.263493i | \(-0.915126\pi\) | ||||
0.964661 | − | 0.263493i | \(-0.0848745\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 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 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 38.5840i | − 2.45504i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −26.7560 | −1.68882 | −0.844412 | − | 0.535695i | \(-0.820050\pi\) | ||||
−0.844412 | + | 0.535695i | \(0.820050\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.12136 | −0.133369 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.69835i | 0.542588i | 0.962496 | + | 0.271294i | \(0.0874516\pi\) | ||||
−0.962496 | + | 0.271294i | \(0.912548\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 2.72666i | − 0.169426i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −18.0708 | −1.11430 | −0.557148 | − | 0.830413i | \(-0.688104\pi\) | ||||
−0.557148 | + | 0.830413i | \(0.688104\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 9.95413i | − 0.606914i | −0.952845 | − | 0.303457i | \(-0.901859\pi\) | ||||
0.952845 | − | 0.303457i | \(-0.0981409\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 27.1893i | − 1.65163i | −0.563939 | − | 0.825816i | \(-0.690715\pi\) | ||||
0.563939 | − | 0.825816i | \(-0.309285\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.40196 | 0.564909 | 0.282455 | − | 0.959281i | \(-0.408851\pi\) | ||||
0.282455 | + | 0.959281i | \(0.408851\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | 14.5840i | 0.866929i | 0.901171 | + | 0.433464i | \(0.142709\pi\) | ||||
−0.901171 | + | 0.433464i | \(0.857291\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.55790 | 0.505157 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.73599 | −0.160940 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 21.8855i | − 1.27856i | −0.768973 | − | 0.639281i | \(-0.779232\pi\) | ||||
0.768973 | − | 0.639281i | \(-0.220768\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 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 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 25.1307i | − 1.43428i | −0.696927 | − | 0.717142i | \(-0.745450\pi\) | ||||
0.696927 | − | 0.717142i | \(-0.254550\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.8819 | 1.29752 | 0.648758 | − | 0.760995i | \(-0.275289\pi\) | ||||
0.648758 | + | 0.760995i | \(0.275289\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 32.5653 | 1.84070 | 0.920351 | − | 0.391093i | \(-0.127903\pi\) | ||||
0.920351 | + | 0.391093i | \(0.127903\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 1.91484i | − 0.107548i | −0.998553 | − | 0.0537742i | \(-0.982875\pi\) | ||||
0.998553 | − | 0.0537742i | \(-0.0171251\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 10.5467i | − 0.590501i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −31.1391 | −1.73262 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 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 | \(0.0566705\pi\) | ||||
−0.984193 | + | 0.177097i | \(0.943329\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.93206 | 0.486560 | 0.243280 | − | 0.969956i | \(-0.421777\pi\) | ||||
0.243280 | + | 0.969956i | \(0.421777\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.9693i | 0.864786i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.01866i | 0.324977i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −23.2817 | −1.24983 | −0.624913 | − | 0.780694i | \(-0.714866\pi\) | ||||
−0.624913 | + | 0.780694i | \(0.714866\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.1120 | −0.915986 | −0.457993 | − | 0.888956i | \(-0.651432\pi\) | ||||
−0.457993 | + | 0.888956i | \(0.651432\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 14.7286i | − 0.783923i | −0.919982 | − | 0.391962i | \(-0.871797\pi\) | ||||
0.919982 | − | 0.391962i | \(-0.128203\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 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 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.0700i | 0.630049i | 0.949083 | + | 0.315025i | \(0.102013\pi\) | ||||
−0.949083 | + | 0.315025i | \(0.897987\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −40.3975 | −2.09733 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.8153 | −0.663552 | −0.331776 | − | 0.943358i | \(-0.607648\pi\) | ||||
−0.331776 | + | 0.943358i | \(0.607648\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 30.1114i | 1.55082i | ||||||||
\(378\) | 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 | ||||||||
\(383\) | −25.0825 | −1.28165 | −0.640827 | − | 0.767685i | \(-0.721408\pi\) | ||||
−0.640827 | + | 0.767685i | \(0.721408\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 23.4684i | 1.18989i | 0.803765 | + | 0.594947i | \(0.202827\pi\) | ||||
−0.803765 | + | 0.594947i | \(0.797173\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 4.88797i | − 0.247195i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.69396 | −0.135206 | −0.0676031 | − | 0.997712i | \(-0.521535\pi\) | ||||
−0.0676031 | + | 0.997712i | \(0.521535\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | − 45.5933i | − 2.27117i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.50003 | 0.0743536 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.6426 | −1.02071 | −0.510356 | − | 0.859963i | \(-0.670486\pi\) | ||||
−0.510356 | + | 0.859963i | \(0.670486\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 34.2946i | − 1.68753i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 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 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 12.1027i | − 0.585691i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 26.6287 | 1.28266 | 0.641331 | − | 0.767265i | \(-0.278383\pi\) | ||||
0.641331 | + | 0.767265i | \(0.278383\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.3693 | 1.12306 | 0.561528 | − | 0.827458i | \(-0.310214\pi\) | ||||
0.561528 | + | 0.827458i | \(0.310214\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 7.71215i | − 0.368922i | ||||||||
\(438\) | 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 | ||||||||
\(443\) | −23.2817 | −1.10615 | −0.553073 | − | 0.833133i | \(-0.686545\pi\) | ||||
−0.553073 | + | 0.833133i | \(0.686545\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 29.3251i | 1.38394i | 0.721927 | + | 0.691969i | \(0.243256\pi\) | ||||
−0.721927 | + | 0.691969i | \(0.756744\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.70800i | 0.221691i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18.9507 | −0.886477 | −0.443239 | − | 0.896404i | \(-0.646171\pi\) | ||||
−0.443239 | + | 0.896404i | \(0.646171\pi\) | |||||||
\(458\) | 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 | ||||||||
\(463\) | 3.07934i | 0.143109i | 0.997437 | + | 0.0715545i | \(0.0227960\pi\) | ||||
−0.997437 | + | 0.0715545i | \(0.977204\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 40.9065 | 1.89293 | 0.946464 | − | 0.322809i | \(-0.104627\pi\) | ||||
0.946464 | + | 0.322809i | \(0.104627\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 19.1120 | 0.882512 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 18.4244i | 0.847153i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 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 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 0.957977i | − 0.0434101i | −0.999764 | − | 0.0217050i | \(-0.993091\pi\) | ||||
0.999764 | − | 0.0217050i | \(-0.00690947\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.8395 | 0.489178 | 0.244589 | − | 0.969627i | \(-0.421347\pi\) | ||||
0.244589 | + | 0.969627i | \(0.421347\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 24.3013 | 1.09448 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 14.9153i | − 0.669041i | ||||||||
\(498\) | 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 | ||||||||
\(503\) | 15.8241 | 0.705560 | 0.352780 | − | 0.935706i | \(-0.385236\pi\) | ||||
0.352780 | + | 0.935706i | \(0.385236\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10.1258i | 0.448816i | 0.974495 | + | 0.224408i | \(0.0720449\pi\) | ||||
−0.974495 | + | 0.224408i | \(0.927955\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 25.4906i | 1.12764i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22.5840 | 0.993243 | ||||||||
\(518\) | 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 | ||||||||
\(523\) | − 25.9160i | − 1.13323i | −0.823984 | − | 0.566613i | \(-0.808254\pi\) | ||||
0.823984 | − | 0.566613i | \(-0.191746\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −36.7959 | −1.60286 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.7894 | −0.947366 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 13.4416i | − 0.582221i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 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 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.57467i | 0.323870i | 0.986801 | + | 0.161935i | \(0.0517734\pi\) | ||||
−0.986801 | + | 0.161935i | \(0.948227\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 38.3422 | 1.63343 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.91595 | −0.421669 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 1.38596i | − 0.0587252i | −0.999569 | − | 0.0293626i | \(-0.990652\pi\) | ||||
0.999569 | − | 0.0293626i | \(-0.00934774\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 52.6027i | − 2.22486i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 31.7934 | 1.33993 | 0.669965 | − | 0.742393i | \(-0.266309\pi\) | ||||
0.669965 | + | 0.742393i | \(0.266309\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 11.3005i | − 0.473742i | −0.971541 | − | 0.236871i | \(-0.923878\pi\) | ||||
0.971541 | − | 0.236871i | \(-0.0761219\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 13.5933i | − 0.568863i | −0.958696 | − | 0.284432i | \(-0.908195\pi\) | ||||
0.958696 | − | 0.284432i | \(-0.0918049\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 43.0466 | 1.79206 | 0.896028 | − | 0.443998i | \(-0.146440\pi\) | ||||
0.896028 | + | 0.443998i | \(0.146440\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.9153i | 0.618790i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 22.2241i | − 0.920427i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.80210 | −0.239478 | −0.119739 | − | 0.992805i | \(-0.538206\pi\) | ||||
−0.119739 | + | 0.992805i | \(0.538206\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −58.0560 | −2.39215 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.9015i | 0.652995i | 0.945198 | + | 0.326498i | \(0.105869\pi\) | ||||
−0.945198 | + | 0.326498i | \(0.894131\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 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 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.60737i | 0.308774i | 0.988010 | + | 0.154387i | \(0.0493402\pi\) | ||||
−0.988010 | + | 0.154387i | \(0.950660\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −64.4787 | −2.60853 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.418069 | 0.0168856 | 0.00844282 | − | 0.999964i | \(-0.497313\pi\) | ||||
0.00844282 | + | 0.999964i | \(0.497313\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 44.3214i | − 1.78431i | −0.451727 | − | 0.892156i | \(-0.649192\pi\) | ||||
0.451727 | − | 0.892156i | \(-0.350808\pi\) | |||||||
\(618\) | 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 | ||||||||
\(623\) | 1.35478 | 0.0542783 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 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 | \(-0.950910\pi\) | ||||
0.988131 | − | 0.153611i | \(-0.0490903\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −29.0793 | −1.15217 | ||||||||
\(638\) | 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 | ||||||||
\(643\) | 26.1214i | 1.03013i | 0.857152 | + | 0.515063i | \(0.172231\pi\) | ||||
−0.857152 | + | 0.515063i | \(0.827769\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.20180 | 0.125876 | 0.0629379 | − | 0.998017i | \(-0.479953\pi\) | ||||
0.0629379 | + | 0.998017i | \(0.479953\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18.8667 | 0.740582 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.4568i | 0.761403i | 0.924698 | + | 0.380702i | \(0.124317\pi\) | ||||
−0.924698 | + | 0.380702i | \(0.875683\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 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 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.01866i | 0.233043i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.65812 | 0.257034 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.6867 | 1.33707 | 0.668537 | − | 0.743679i | \(-0.266921\pi\) | ||||
0.668537 | + | 0.743679i | \(0.266921\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 45.1672i | − 1.73591i | −0.496639 | − | 0.867957i | \(-0.665433\pi\) | ||||
0.496639 | − | 0.867957i | \(-0.334567\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 32.5653i | − 1.24974i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 44.7986 | 1.71417 | 0.857085 | − | 0.515175i | \(-0.172273\pi\) | ||||
0.857085 | + | 0.515175i | \(0.172273\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 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 | \(0.0413105\pi\) | ||||
−0.991590 | + | 0.129417i | \(0.958690\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.8480 | −0.410898 | ||||||||
\(698\) | 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 | ||||||||
\(703\) | 5.45331i | 0.205676i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −25.4822 | −0.958358 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27.1893 | 1.02112 | 0.510558 | − | 0.859843i | \(-0.329439\pi\) | ||||
0.510558 | + | 0.859843i | \(0.329439\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 9.11317i | − 0.341291i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 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 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.1820i | 1.15648i | 0.815867 | + | 0.578239i | \(0.196260\pi\) | ||||
−0.815867 | + | 0.578239i | \(0.803740\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −42.4528 | −1.57017 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.41129 | 0.162935 | 0.0814674 | − | 0.996676i | \(-0.474039\pi\) | ||||
0.0814674 | + | 0.996676i | \(0.474039\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.5142i | 0.387295i | ||||||||
\(738\) | 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 | ||||||||
\(743\) | 9.65817 | 0.354324 | 0.177162 | − | 0.984182i | \(-0.443308\pi\) | ||||
0.177162 | + | 0.984182i | \(0.443308\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 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 | \(-0.926132\pi\) | ||||
0.973194 | − | 0.229987i | \(-0.0738683\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −36.0887 | −1.31166 | −0.655832 | − | 0.754906i | \(-0.727682\pi\) | ||||
−0.655832 | + | 0.754906i | \(0.727682\pi\) | |||||||
\(758\) | 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 | ||||||||
\(763\) | − 29.0280i | − 1.05088i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −53.8655 | −1.94497 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 54.3200 | 1.95883 | 0.979414 | − | 0.201860i | \(-0.0646986\pi\) | ||||
0.979414 | + | 0.201860i | \(0.0646986\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.17068i | 0.221944i | 0.993824 | + | 0.110972i | \(0.0353964\pi\) | ||||
−0.993824 | + | 0.110972i | \(0.964604\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 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 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 2.12136i | − 0.0756183i | −0.999285 | − | 0.0378092i | \(-0.987962\pi\) | ||||
0.999285 | − | 0.0378092i | \(-0.0120379\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 62.4234 | 2.21952 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19.0093 | −0.675041 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.92522i | 0.280726i | 0.990100 | + | 0.140363i | \(0.0448269\pi\) | ||||
−0.990100 | + | 0.140363i | \(0.955173\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 52.0373i | 1.84095i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −14.0233 | −0.494871 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 29.2158i | − 1.02717i | −0.858037 | − | 0.513587i | \(-0.828316\pi\) | ||||
0.858037 | − | 0.513587i | \(-0.171684\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 10.3013i | − 0.361729i | −0.983508 | − | 0.180864i | \(-0.942111\pi\) | ||||
0.983508 | − | 0.180864i | \(-0.0578895\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −66.9813 | −2.34338 | ||||||||
\(818\) | 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 | ||||||||
\(823\) | − 35.6447i | − 1.24250i | −0.783614 | − | 0.621248i | \(-0.786626\pi\) | ||||
0.783614 | − | 0.621248i | \(-0.213374\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.11317 | 0.316896 | 0.158448 | − | 0.987367i | \(-0.449351\pi\) | ||||
0.158448 | + | 0.987367i | \(0.449351\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.2640 | −0.356484 | −0.178242 | − | 0.983987i | \(-0.557041\pi\) | ||||
−0.178242 | + | 0.983987i | \(0.557041\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 23.4684i | 0.813131i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 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 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 25.5233i | − 0.876992i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.856018 | −0.0293439 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.3620 | 0.525985 | 0.262993 | − | 0.964798i | \(-0.415291\pi\) | ||||
0.262993 | + | 0.964798i | \(0.415291\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.4105i | 0.560572i | 0.959917 | + | 0.280286i | \(0.0904293\pi\) | ||||
−0.959917 | + | 0.280286i | \(0.909571\pi\) | |||||||
\(858\) | 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 | ||||||||
\(863\) | 24.3820 | 0.829972 | 0.414986 | − | 0.909828i | \(-0.363787\pi\) | ||||
0.414986 | + | 0.909828i | \(0.363787\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 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 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.6846 | 0.664703 | 0.332351 | − | 0.943156i | \(-0.392158\pi\) | ||||
0.332351 | + | 0.943156i | \(0.392158\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | 8.99067i | 0.302560i | 0.988491 | + | 0.151280i | \(0.0483395\pi\) | ||||
−0.988491 | + | 0.151280i | \(0.951660\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8.66717 | 0.291015 | 0.145508 | − | 0.989357i | \(-0.453518\pi\) | ||||
0.145508 | + | 0.989357i | \(0.453518\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.35739 | −0.112603 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 82.1035i | 2.74749i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 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 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 39.5747i | 1.31406i | 0.753866 | + | 0.657028i | \(0.228187\pi\) | ||||
−0.753866 | + | 0.657028i | \(0.771813\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.60156 | 0.119325 | 0.0596625 | − | 0.998219i | \(-0.480998\pi\) | ||||
0.0596625 | + | 0.998219i | \(0.480998\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.20541 | −0.271559 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 29.3845i | 0.970363i | ||||||||
\(918\) | 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 | ||||||||
\(923\) | −23.4269 | −0.771107 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 44.6929i | − 1.46633i | −0.680053 | − | 0.733163i | \(-0.738043\pi\) | ||||
0.680053 | − | 0.733163i | \(-0.261957\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 37.0280i | 1.21354i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17.9813 | −0.587425 | −0.293712 | − | 0.955894i | \(-0.594891\pi\) | ||||
−0.293712 | + | 0.955894i | \(0.594891\pi\) | |||||||
\(938\) | 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 | ||||||||
\(943\) | − 2.68670i | − 0.0874911i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −43.8538 | −1.42506 | −0.712529 | − | 0.701643i | \(-0.752450\pi\) | ||||
−0.712529 | + | 0.701643i | \(0.752450\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 40.0373 | 1.29967 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 20.4382i | − 0.662058i | −0.943621 | − | 0.331029i | \(-0.892604\pi\) | ||||
0.943621 | − | 0.331029i | \(-0.107396\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 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 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 14.6167i | − 0.470041i | −0.971990 | − | 0.235021i | \(-0.924484\pi\) | ||||
0.971990 | − | 0.235021i | \(-0.0755158\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −50.4374 | −1.61861 | −0.809307 | − | 0.587385i | \(-0.800157\pi\) | ||||
−0.809307 | + | 0.587385i | \(0.800157\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.10270 | −0.131527 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 17.0744i | − 0.546257i | −0.961978 | − | 0.273129i | \(-0.911942\pi\) | ||||
0.961978 | − | 0.273129i | \(-0.0880585\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.745314i | 0.0238203i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −13.7688 | −0.439155 | −0.219578 | − | 0.975595i | \(-0.570468\pi\) | ||||
−0.219578 | + | 0.975595i | \(0.570468\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 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 | \(0.0718743\pi\) | ||||
−0.974615 | + | 0.223886i | \(0.928126\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.7126 | 1.03602 | 0.518010 | − | 0.855375i | \(-0.326673\pi\) | ||||
0.518010 | + | 0.855375i | \(0.326673\pi\) | |||||||
\(998\) | 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 | 7200.2.h.m.1151.11 | 12 | ||
3.2 | odd | 2 | inner | 7200.2.h.m.1151.12 | 12 | ||
4.3 | odd | 2 | inner | 7200.2.h.m.1151.2 | 12 | ||
5.2 | odd | 4 | 1440.2.o.a.1439.6 | yes | 12 | ||
5.3 | odd | 4 | 1440.2.o.b.1439.8 | yes | 12 | ||
5.4 | even | 2 | 7200.2.h.l.1151.1 | 12 | |||
12.11 | even | 2 | inner | 7200.2.h.m.1151.1 | 12 | ||
15.2 | even | 4 | 1440.2.o.a.1439.7 | yes | 12 | ||
15.8 | even | 4 | 1440.2.o.b.1439.5 | yes | 12 | ||
15.14 | odd | 2 | 7200.2.h.l.1151.2 | 12 | |||
20.3 | even | 4 | 1440.2.o.a.1439.8 | yes | 12 | ||
20.7 | even | 4 | 1440.2.o.b.1439.6 | yes | 12 | ||
20.19 | odd | 2 | 7200.2.h.l.1151.12 | 12 | |||
40.3 | even | 4 | 2880.2.o.f.2879.5 | 12 | |||
40.13 | odd | 4 | 2880.2.o.e.2879.5 | 12 | |||
40.27 | even | 4 | 2880.2.o.e.2879.7 | 12 | |||
40.37 | odd | 4 | 2880.2.o.f.2879.7 | 12 | |||
60.23 | odd | 4 | 1440.2.o.a.1439.5 | ✓ | 12 | ||
60.47 | odd | 4 | 1440.2.o.b.1439.7 | yes | 12 | ||
60.59 | even | 2 | 7200.2.h.l.1151.11 | 12 | |||
120.53 | even | 4 | 2880.2.o.e.2879.8 | 12 | |||
120.77 | even | 4 | 2880.2.o.f.2879.6 | 12 | |||
120.83 | odd | 4 | 2880.2.o.f.2879.8 | 12 | |||
120.107 | odd | 4 | 2880.2.o.e.2879.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1440.2.o.a.1439.5 | ✓ | 12 | 60.23 | odd | 4 | ||
1440.2.o.a.1439.6 | yes | 12 | 5.2 | odd | 4 | ||
1440.2.o.a.1439.7 | yes | 12 | 15.2 | even | 4 | ||
1440.2.o.a.1439.8 | yes | 12 | 20.3 | even | 4 | ||
1440.2.o.b.1439.5 | yes | 12 | 15.8 | even | 4 | ||
1440.2.o.b.1439.6 | yes | 12 | 20.7 | even | 4 | ||
1440.2.o.b.1439.7 | yes | 12 | 60.47 | odd | 4 | ||
1440.2.o.b.1439.8 | yes | 12 | 5.3 | odd | 4 | ||
2880.2.o.e.2879.5 | 12 | 40.13 | odd | 4 | |||
2880.2.o.e.2879.6 | 12 | 120.107 | odd | 4 | |||
2880.2.o.e.2879.7 | 12 | 40.27 | even | 4 | |||
2880.2.o.e.2879.8 | 12 | 120.53 | even | 4 | |||
2880.2.o.f.2879.5 | 12 | 40.3 | even | 4 | |||
2880.2.o.f.2879.6 | 12 | 120.77 | even | 4 | |||
2880.2.o.f.2879.7 | 12 | 40.37 | odd | 4 | |||
2880.2.o.f.2879.8 | 12 | 120.83 | odd | 4 | |||
7200.2.h.l.1151.1 | 12 | 5.4 | even | 2 | |||
7200.2.h.l.1151.2 | 12 | 15.14 | odd | 2 | |||
7200.2.h.l.1151.11 | 12 | 60.59 | even | 2 | |||
7200.2.h.l.1151.12 | 12 | 20.19 | odd | 2 | |||
7200.2.h.m.1151.1 | 12 | 12.11 | even | 2 | inner | ||
7200.2.h.m.1151.2 | 12 | 4.3 | odd | 2 | inner | ||
7200.2.h.m.1151.11 | 12 | 1.1 | even | 1 | trivial | ||
7200.2.h.m.1151.12 | 12 | 3.2 | odd | 2 | inner |