Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1900,2,Mod(493,1900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1900, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1900.493");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1900.l (of order \(4\), degree \(2\), 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: | \(15.1715763840\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 48 x^{14} - 184 x^{13} + 588 x^{12} - 1440 x^{11} + 3064 x^{10} - 5344 x^{9} + \cdots + 5800 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{17} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1557.1 | ||
Root | \(0.870982 - 0.924776i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1900.1557 |
Dual form | 1900.2.l.c.493.1 |
$q$-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 \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) | \(951\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −1.79576 | − | 1.79576i | −1.03678 | − | 1.03678i | −0.999297 | − | 0.0374838i | \(-0.988066\pi\) |
−0.0374838 | − | 0.999297i | \(-0.511934\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.30136 | − | 3.30136i | −1.24780 | − | 1.24780i | −0.956691 | − | 0.291106i | \(-0.905977\pi\) |
−0.291106 | − | 0.956691i | \(-0.594023\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.44949i | 1.14983i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.44949 | 0.738549 | 0.369274 | − | 0.929320i | \(-0.379606\pi\) | ||||
0.369274 | + | 0.929320i | \(0.379606\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.60293 | − | 2.60293i | −0.721923 | − | 0.721923i | 0.247073 | − | 0.968997i | \(-0.420531\pi\) |
−0.968997 | + | 0.247073i | \(0.920531\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.48393 | − | 1.48393i | −0.359905 | − | 0.359905i | 0.503873 | − | 0.863778i | \(-0.331908\pi\) |
−0.863778 | + | 0.503873i | \(0.831908\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.66477 | − | 3.44949i | −0.611341 | − | 0.791367i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 11.8569i | 2.58738i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.78529 | − | 4.78529i | 0.997801 | − | 0.997801i | −0.00219610 | − | 0.999998i | \(-0.500699\pi\) |
0.999998 | + | 0.00219610i | \(0.000699042\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.807175 | − | 0.807175i | 0.155341 | − | 0.155341i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.32955 | −0.989672 | −0.494836 | − | 0.868986i | \(-0.664772\pi\) | ||||
−0.494836 | + | 0.868986i | \(0.664772\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 6.52734i | − | 1.17234i | −0.810187 | − | 0.586172i | \(-0.800634\pi\) | ||
0.810187 | − | 0.586172i | \(-0.199366\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.39869 | − | 4.39869i | −0.765714 | − | 0.765714i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.00162 | + | 7.00162i | −1.15106 | + | 1.15106i | −0.164719 | + | 0.986341i | \(0.552672\pi\) |
−0.986341 | + | 0.164719i | \(0.947328\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9.34847i | 1.49695i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 11.8569i | − | 1.85173i | −0.377849 | − | 0.925867i | \(-0.623336\pi\) | ||
0.377849 | − | 0.925867i | \(-0.376664\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.81743 | + | 1.81743i | −0.277156 | + | 0.277156i | −0.831973 | − | 0.554817i | \(-0.812788\pi\) |
0.554817 | + | 0.831973i | \(0.312788\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.30136 | + | 3.30136i | 0.481553 | + | 0.481553i | 0.905627 | − | 0.424074i | \(-0.139401\pi\) |
−0.424074 | + | 0.905627i | \(0.639401\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14.7980i | 2.11399i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.32955i | 0.746286i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.41011 | + | 3.41011i | 0.468414 | + | 0.468414i | 0.901400 | − | 0.432986i | \(-0.142540\pi\) |
−0.432986 | + | 0.901400i | \(0.642540\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.40916 | + | 10.9797i | −0.186648 | + | 1.45430i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.52734 | 0.849787 | 0.424893 | − | 0.905243i | \(-0.360312\pi\) | ||||
0.424893 | + | 0.905243i | \(0.360312\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.34847 | 0.684801 | 0.342401 | − | 0.939554i | \(-0.388760\pi\) | ||||
0.342401 | + | 0.939554i | \(0.388760\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 11.3880 | − | 11.3880i | 1.43475 | − | 1.43475i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.58010 | − | 4.58010i | 0.559548 | − | 0.559548i | −0.369631 | − | 0.929179i | \(-0.620516\pi\) |
0.929179 | + | 0.369631i | \(0.120516\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −17.1864 | −2.06900 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.8569i | 1.40715i | 0.710619 | + | 0.703577i | \(0.248415\pi\) | ||||
−0.710619 | + | 0.703577i | \(0.751585\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.96786 | + | 2.96786i | −0.347361 | + | 0.347361i | −0.859126 | − | 0.511765i | \(-0.828992\pi\) |
0.511765 | + | 0.859126i | \(0.328992\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.08665 | − | 8.08665i | −0.921559 | − | 0.921559i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.8569 | −1.33400 | −0.667002 | − | 0.745056i | \(-0.732423\pi\) | ||||
−0.667002 | + | 0.745056i | \(0.732423\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.44949 | 0.827721 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.93623 | − | 6.93623i | 0.761350 | − | 0.761350i | −0.215217 | − | 0.976566i | \(-0.569046\pi\) |
0.976566 | + | 0.215217i | \(0.0690458\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.57058 | + | 9.57058i | 1.02607 | + | 1.02607i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.32955 | −0.564931 | −0.282465 | − | 0.959277i | \(-0.591152\pi\) | ||||
−0.282465 | + | 0.959277i | \(0.591152\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 17.1864i | 1.80163i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −11.7215 | + | 11.7215i | −1.21546 | + | 1.21546i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.77292 | + | 3.77292i | −0.383082 | + | 0.383082i | −0.872211 | − | 0.489129i | \(-0.837315\pi\) |
0.489129 | + | 0.872211i | \(0.337315\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.44949i | 0.849206i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.34847 | −0.134178 | −0.0670889 | − | 0.997747i | \(-0.521371\pi\) | ||||
−0.0670889 | + | 0.997747i | \(0.521371\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.58010 | + | 4.58010i | 0.451290 | + | 0.451290i | 0.895783 | − | 0.444492i | \(-0.146616\pi\) |
−0.444492 | + | 0.895783i | \(0.646616\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.80880 | − | 7.80880i | 0.754905 | − | 0.754905i | −0.220485 | − | 0.975390i | \(-0.570764\pi\) |
0.975390 | + | 0.220485i | \(0.0707642\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.52734 | 0.625205 | 0.312603 | − | 0.949884i | \(-0.398799\pi\) | ||||
0.312603 | + | 0.949884i | \(0.398799\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 25.1464 | 2.38679 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.78596 | + | 9.78596i | 0.920586 | + | 0.920586i | 0.997071 | − | 0.0764849i | \(-0.0243697\pi\) |
−0.0764849 | + | 0.997071i | \(0.524370\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 8.97879 | − | 8.97879i | 0.830089 | − | 0.830089i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.79796i | 0.898177i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.00000 | −0.454545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −21.2921 | + | 21.2921i | −1.91984 | + | 1.91984i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.79576 | + | 1.79576i | −0.159348 | + | 0.159348i | −0.782278 | − | 0.622930i | \(-0.785942\pi\) |
0.622930 | + | 0.782278i | \(0.285942\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.52734 | 0.574700 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.79796 | 0.856052 | 0.428026 | − | 0.903767i | \(-0.359209\pi\) | ||||
0.428026 | + | 0.903767i | \(0.359209\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.59063 | + | 20.1854i | −0.224636 | + | 1.75030i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.08665 | − | 8.08665i | −0.690889 | − | 0.690889i | 0.271539 | − | 0.962428i | \(-0.412468\pi\) |
−0.962428 | + | 0.271539i | \(0.912468\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 5.55051i | − | 0.470788i | −0.971900 | − | 0.235394i | \(-0.924362\pi\) | ||
0.971900 | − | 0.235394i | \(-0.0756381\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 11.8569i | − | 0.998530i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.37586 | − | 6.37586i | −0.533176 | − | 0.533176i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 26.5735 | − | 26.5735i | 2.19175 | − | 2.19175i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 23.1464i | 1.89623i | 0.317929 | + | 0.948115i | \(0.397013\pi\) | ||||
−0.317929 | + | 0.948115i | \(0.602987\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.32955i | 0.433712i | 0.976204 | + | 0.216856i | \(0.0695803\pi\) | ||||
−0.976204 | + | 0.216856i | \(0.930420\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.11879 | − | 5.11879i | 0.413830 | − | 0.413830i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.7215 | + | 11.7215i | 0.935479 | + | 0.935479i | 0.998041 | − | 0.0625624i | \(-0.0199273\pi\) |
−0.0625624 | + | 0.998041i | \(0.519927\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 12.2474i | − | 0.971286i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −31.5959 | −2.49011 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.78529 | + | 4.78529i | −0.374813 | + | 0.374813i | −0.869227 | − | 0.494414i | \(-0.835383\pi\) |
0.494414 | + | 0.869227i | \(0.335383\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.43294 | + | 1.43294i | −0.110884 | + | 0.110884i | −0.760372 | − | 0.649488i | \(-0.774983\pi\) |
0.649488 | + | 0.760372i | \(0.274983\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.550510i | 0.0423469i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 11.8990 | − | 9.19211i | 0.909938 | − | 0.702938i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.7631 | + | 11.7631i | 0.894334 | + | 0.894334i | 0.994928 | − | 0.100594i | \(-0.0320742\pi\) |
−0.100594 | + | 0.994928i | \(0.532074\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −11.7215 | − | 11.7215i | −0.881043 | − | 0.881043i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −17.1864 | −1.28457 | −0.642287 | − | 0.766464i | \(-0.722014\pi\) | ||||
−0.642287 | + | 0.766464i | \(0.722014\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.32955i | 0.396142i | 0.980188 | + | 0.198071i | \(0.0634677\pi\) | ||||
−0.980188 | + | 0.198071i | \(0.936532\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.60455 | − | 9.60455i | −0.709989 | − | 0.709989i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.63487 | − | 3.63487i | −0.265808 | − | 0.265808i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.32955 | −0.387668 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.10102 | 0.0796670 | 0.0398335 | − | 0.999206i | \(-0.487317\pi\) | ||||
0.0398335 | + | 0.999206i | \(0.487317\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.181408 | − | 0.181408i | −0.0130581 | − | 0.0130581i | 0.700548 | − | 0.713606i | \(-0.252939\pi\) |
−0.713606 | + | 0.700548i | \(0.752939\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.7215 | − | 11.7215i | −0.835123 | − | 0.835123i | 0.153089 | − | 0.988212i | \(-0.451078\pi\) |
−0.988212 | + | 0.153089i | \(0.951078\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 16.6969i | − | 1.18361i | −0.806079 | − | 0.591807i | \(-0.798415\pi\) | ||
0.806079 | − | 0.591807i | \(-0.201585\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −16.4495 | −1.16026 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 17.5948 | + | 17.5948i | 1.23491 | + | 1.23491i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 16.5068 | + | 16.5068i | 1.14730 | + | 1.14730i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.52734 | − | 8.44949i | −0.451505 | − | 0.584463i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 18.3842i | − | 1.26562i | −0.774306 | − | 0.632811i | \(-0.781901\pi\) | ||
0.774306 | − | 0.632811i | \(-0.218099\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 21.2921 | − | 21.2921i | 1.45891 | − | 1.45891i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −21.5491 | + | 21.5491i | −1.46285 | + | 1.46285i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.6591 | 0.720275 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.72513i | 0.519648i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.5703 | − | 12.5703i | −0.841770 | − | 0.841770i | 0.147319 | − | 0.989089i | \(-0.452936\pi\) |
−0.989089 | + | 0.147319i | \(0.952936\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.7631 | + | 11.7631i | −0.780746 | + | 0.780746i | −0.979957 | − | 0.199211i | \(-0.936162\pi\) |
0.199211 | + | 0.979957i | \(0.436162\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.2474i | 0.677170i | 0.940936 | + | 0.338585i | \(0.109948\pi\) | ||||
−0.940936 | + | 0.338585i | \(0.890052\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 29.0433i | 1.91091i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.6894 | + | 14.6894i | −0.962333 | + | 0.962333i | −0.999316 | − | 0.0369834i | \(-0.988225\pi\) |
0.0369834 | + | 0.999316i | \(0.488225\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 21.2921 | + | 21.2921i | 1.38307 | + | 1.38307i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.0000i | 0.776215i | 0.921614 | + | 0.388108i | \(0.126871\pi\) | ||||
−0.921614 | + | 0.388108i | \(0.873129\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 4.13176i | − | 0.266150i | −0.991106 | − | 0.133075i | \(-0.957515\pi\) | ||
0.991106 | − | 0.133075i | \(-0.0424851\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.7990 | − | 15.7990i | −1.01351 | − | 1.01351i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.04256 | + | 15.9150i | −0.129965 | + | 1.01265i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −24.9116 | −1.57871 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.1010 | −0.826929 | −0.413465 | − | 0.910520i | \(-0.635681\pi\) | ||||
−0.413465 | + | 0.910520i | \(0.635681\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.7215 | − | 11.7215i | 0.736925 | − | 0.736925i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.1390 | − | 18.1390i | 1.13148 | − | 1.13148i | 0.141547 | − | 0.989932i | \(-0.454792\pi\) |
0.989932 | − | 0.141547i | \(-0.0452077\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 46.2297 | 2.87258 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 18.3842i | − | 1.13795i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.75314 | − | 7.75314i | 0.478079 | − | 0.478079i | −0.426438 | − | 0.904517i | \(-0.640232\pi\) |
0.904517 | + | 0.426438i | \(0.140232\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.57058 | + | 9.57058i | 0.585710 | + | 0.585710i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 24.9116 | 1.51888 | 0.759442 | − | 0.650575i | \(-0.225472\pi\) | ||||
0.759442 | + | 0.650575i | \(0.225472\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 27.3485 | 1.66130 | 0.830651 | − | 0.556794i | \(-0.187969\pi\) | ||||
0.830651 | + | 0.556794i | \(0.187969\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 30.8627 | − | 30.8627i | 1.86789 | − | 1.86789i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.6251 | − | 20.6251i | −1.23924 | − | 1.23924i | −0.960312 | − | 0.278929i | \(-0.910021\pi\) |
−0.278929 | − | 0.960312i | \(-0.589979\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 22.5160 | 1.34800 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 27.8455i | − | 1.66112i | −0.556925 | − | 0.830562i | \(-0.688019\pi\) | ||
0.556925 | − | 0.830562i | \(-0.311981\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.90408 | + | 9.90408i | −0.588736 | + | 0.588736i | −0.937289 | − | 0.348553i | \(-0.886673\pi\) |
0.348553 | + | 0.937289i | \(0.386673\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −39.1438 | + | 39.1438i | −2.31059 | + | 2.31059i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 12.5959i | − | 0.740936i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 13.5505 | 0.794345 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.41011 | − | 3.41011i | −0.199221 | − | 0.199221i | 0.600445 | − | 0.799666i | \(-0.294990\pi\) |
−0.799666 | + | 0.600445i | \(0.794990\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.97717 | − | 1.97717i | 0.114727 | − | 0.114727i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −24.9116 | −1.44067 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.0000 | 0.691669 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.42152 | + | 2.42152i | 0.139113 | + | 0.139113i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.55726 | − | 6.55726i | 0.374243 | − | 0.374243i | −0.494777 | − | 0.869020i | \(-0.664750\pi\) |
0.869020 | + | 0.494777i | \(0.164750\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 16.4495i | − | 0.935779i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −29.1464 | −1.65274 | −0.826371 | − | 0.563126i | \(-0.809599\pi\) | ||||
−0.826371 | + | 0.563126i | \(0.809599\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.15094 | + | 2.15094i | −0.121578 | + | 0.121578i | −0.765278 | − | 0.643700i | \(-0.777399\pi\) |
0.643700 | + | 0.765278i | \(0.277399\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.7631 | + | 11.7631i | −0.660683 | + | 0.660683i | −0.955541 | − | 0.294858i | \(-0.904728\pi\) |
0.294858 | + | 0.955541i | \(0.404728\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.0547 | −0.730921 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −28.0454 | −1.56534 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.16446 | + | 9.07312i | −0.0647924 | + | 0.504842i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −11.7215 | − | 11.7215i | −0.648201 | − | 0.648201i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 21.7980i | − | 1.20176i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 34.3729i | 1.88930i | 0.328075 | + | 0.944652i | \(0.393600\pi\) | ||||
−0.328075 | + | 0.944652i | \(0.606400\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −24.1520 | − | 24.1520i | −1.32352 | − | 1.32352i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.9462 | − | 18.9462i | 1.03206 | − | 1.03206i | 0.0325943 | − | 0.999469i | \(-0.489623\pi\) |
0.999469 | − | 0.0325943i | \(-0.0103769\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 35.1464i | − | 1.90889i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 15.9886i | − | 0.865834i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 25.7439 | − | 25.7439i | 1.39004 | − | 1.39004i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.0229 | − | 15.0229i | −0.806470 | − | 0.806470i | 0.177628 | − | 0.984098i | \(-0.443158\pi\) |
−0.984098 | + | 0.177628i | \(0.943158\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 13.7980i | − | 0.738588i | −0.929313 | − | 0.369294i | \(-0.879600\pi\) | ||
0.929313 | − | 0.369294i | \(-0.120400\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.20204 | −0.224288 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.7215 | + | 11.7215i | −0.623873 | + | 0.623873i | −0.946520 | − | 0.322646i | \(-0.895428\pi\) |
0.322646 | + | 0.946520i | \(0.395428\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 17.5948 | − | 17.5948i | 0.931213 | − | 0.931213i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 24.2474i | − | 1.27973i | −0.768487 | − | 0.639866i | \(-0.778990\pi\) | ||
0.768487 | − | 0.639866i | \(-0.221010\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.79796 | + | 18.3842i | −0.252524 | + | 0.967591i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.97879 | + | 8.97879i | 0.471264 | + | 0.471264i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.9264 | − | 23.9264i | −1.24895 | − | 1.24895i | −0.956184 | − | 0.292766i | \(-0.905424\pi\) |
−0.292766 | − | 0.956184i | \(-0.594576\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 40.9002 | 2.12918 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 22.5160i | − | 1.16897i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.00162 | + | 7.00162i | 0.362530 | + | 0.362530i | 0.864744 | − | 0.502213i | \(-0.167481\pi\) |
−0.502213 | + | 0.864744i | \(0.667481\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.8725 | + | 13.8725i | 0.714468 | + | 0.714468i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.32955 | 0.273760 | 0.136880 | − | 0.990588i | \(-0.456292\pi\) | ||||
0.136880 | + | 0.990588i | \(0.456292\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.44949 | 0.330417 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −27.3807 | − | 27.3807i | −1.39909 | − | 1.39909i | −0.802681 | − | 0.596408i | \(-0.796594\pi\) |
−0.596408 | − | 0.802681i | \(-0.703406\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.26922 | − | 6.26922i | −0.318682 | − | 0.318682i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 27.7980i | 1.40941i | 0.709499 | + | 0.704706i | \(0.248921\pi\) | ||||
−0.709499 | + | 0.704706i | \(0.751079\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.2020 | −0.718228 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −17.5948 | − | 17.5948i | −0.887538 | − | 0.887538i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.90357 | + | 8.90357i | 0.446857 | + | 0.446857i | 0.894308 | − | 0.447451i | \(-0.147668\pi\) |
−0.447451 | + | 0.894308i | \(0.647668\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 40.9002 | − | 31.5959i | 2.04757 | − | 1.58177i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 34.3729i | − | 1.71650i | −0.513233 | − | 0.858249i | \(-0.671552\pi\) | ||
0.513233 | − | 0.858249i | \(-0.328448\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16.9902 | + | 16.9902i | −0.846343 | + | 0.846343i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −17.1504 | + | 17.1504i | −0.850114 | + | 0.850114i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.19779 | −0.0592268 | −0.0296134 | − | 0.999561i | \(-0.509428\pi\) | ||||
−0.0296134 | + | 0.999561i | \(0.509428\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 29.0433i | 1.43260i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −21.5491 | − | 21.5491i | −1.06036 | − | 1.06036i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.96737 | + | 9.96737i | −0.488104 | + | 0.488104i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 9.79796i | − | 0.478662i | −0.970938 | − | 0.239331i | \(-0.923072\pi\) | ||
0.970938 | − | 0.239331i | \(-0.0769280\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.19779i | 0.0583766i | 0.999574 | + | 0.0291883i | \(0.00929225\pi\) | ||||
−0.999574 | + | 0.0291883i | \(0.990708\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −11.3880 | + | 11.3880i | −0.553704 | + | 0.553704i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −17.6572 | − | 17.6572i | −0.854493 | − | 0.854493i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 22.8990i | 1.10557i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 18.3842i | − | 0.885537i | −0.896636 | − | 0.442768i | \(-0.853996\pi\) | ||
0.896636 | − | 0.442768i | \(-0.146004\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.58010 | − | 4.58010i | −0.220105 | − | 0.220105i | 0.588437 | − | 0.808543i | \(-0.299743\pi\) |
−0.808543 | + | 0.588437i | \(0.799743\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −29.2585 | − | 3.75509i | −1.39962 | − | 0.179630i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.5160 | 1.07463 | 0.537315 | − | 0.843382i | \(-0.319439\pi\) | ||||
0.537315 | + | 0.843382i | \(0.319439\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −51.0454 | −2.43073 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.0550 | − | 12.0550i | 0.572751 | − | 0.572751i | −0.360145 | − | 0.932896i | \(-0.617273\pi\) |
0.932896 | + | 0.360145i | \(0.117273\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 41.5654 | − | 41.5654i | 1.96597 | − | 1.96597i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.52734 | −0.308044 | −0.154022 | − | 0.988067i | \(-0.549223\pi\) | ||||
−0.154022 | + | 0.988067i | \(0.549223\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 29.0433i | − | 1.36760i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.57058 | − | 9.57058i | 0.449665 | − | 0.449665i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.63487 | − | 3.63487i | −0.170032 | − | 0.170032i | 0.616962 | − | 0.786993i | \(-0.288363\pi\) |
−0.786993 | + | 0.616962i | \(0.788363\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.39558 | −0.111816 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −23.3939 | −1.08956 | −0.544781 | − | 0.838579i | \(-0.683387\pi\) | ||||
−0.544781 | + | 0.838579i | \(0.683387\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.75314 | − | 7.75314i | 0.360319 | − | 0.360319i | −0.503611 | − | 0.863930i | \(-0.667996\pi\) |
0.863930 | + | 0.503611i | \(0.167996\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.9907 | + | 17.9907i | 0.832512 | + | 0.832512i | 0.987860 | − | 0.155348i | \(-0.0496499\pi\) |
−0.155348 | + | 0.987860i | \(0.549650\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −30.2411 | −1.39640 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 42.0980i | − | 1.93977i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.45178 | + | 4.45178i | −0.204693 | + | 0.204693i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −11.7631 | + | 11.7631i | −0.538597 | + | 0.538597i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 29.1464i | 1.33173i | 0.746070 | + | 0.665867i | \(0.231938\pi\) | ||||
−0.746070 | + | 0.665867i | \(0.768062\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 36.4495 | 1.66195 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 56.7386 | + | 56.7386i | 2.58170 | + | 2.58170i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.1977 | + | 20.1977i | −0.915245 | + | 0.915245i | −0.996679 | − | 0.0814340i | \(-0.974050\pi\) |
0.0814340 | + | 0.996679i | \(0.474050\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 17.1864 | 0.777197 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −28.2929 | −1.27684 | −0.638419 | − | 0.769689i | \(-0.720411\pi\) | ||||
−0.638419 | + | 0.769689i | \(0.720411\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.90866 | + | 7.90866i | 0.356188 | + | 0.356188i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 39.1438 | − | 39.1438i | 1.75584 | − | 1.75584i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 42.9444i | − | 1.92245i | −0.275757 | − | 0.961227i | \(-0.588928\pi\) | ||
0.275757 | − | 0.961227i | \(-0.411072\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.14643 | 0.229925 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14.3559 | + | 14.3559i | −0.640096 | + | 0.640096i | −0.950579 | − | 0.310483i | \(-0.899509\pi\) |
0.310483 | + | 0.950579i | \(0.399509\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.988583 | − | 0.988583i | 0.0439045 | − | 0.0439045i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −23.7138 | −1.05109 | −0.525547 | − | 0.850764i | \(-0.676139\pi\) | ||||
−0.525547 | + | 0.850764i | \(0.676139\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19.5959 | 0.866872 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.93528 | − | 0.633403i | −0.217898 | − | 0.0279654i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.08665 | + | 8.08665i | 0.355650 | + | 0.355650i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 42.2474i | − | 1.85446i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 2.93397i | − | 0.128540i | −0.997933 | − | 0.0642698i | \(-0.979528\pi\) | ||
0.997933 | − | 0.0642698i | \(-0.0204718\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.15857 | − | 2.15857i | −0.0943879 | − | 0.0943879i | 0.658336 | − | 0.752724i | \(-0.271261\pi\) |
−0.752724 | + | 0.658336i | \(0.771261\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.68609 | + | 9.68609i | −0.421933 | + | 0.421933i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 22.7980i | − | 0.991216i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 22.5160i | 0.977110i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −30.8627 | + | 30.8627i | −1.33681 | + | 1.33681i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 30.8627 | + | 30.8627i | 1.33182 | + | 1.33182i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 36.2474i | 1.56129i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.6515 | −0.629919 | −0.314959 | − | 0.949105i | \(-0.601991\pi\) | ||||
−0.314959 | + | 0.949105i | \(0.601991\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.57058 | − | 9.57058i | 0.410713 | − | 0.410713i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.1651 | − | 30.1651i | 1.28976 | − | 1.28976i | 0.354836 | − | 0.934928i | \(-0.384537\pi\) |
0.934928 | − | 0.354836i | \(-0.115463\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 18.4495i | 0.787405i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.2020 | + | 18.3842i | 0.605027 | + | 0.783194i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 39.1438 | + | 39.1438i | 1.66457 | + | 1.66457i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 27.2278 | + | 27.2278i | 1.15368 | + | 1.15368i | 0.985809 | + | 0.167870i | \(0.0536888\pi\) |
0.167870 | + | 0.985809i | \(0.446311\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.46131 | 0.400171 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.0547i | 0.551169i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.25315 | + | 8.25315i | 0.347829 | + | 0.347829i | 0.859300 | − | 0.511471i | \(-0.170899\pi\) |
−0.511471 | + | 0.859300i | \(0.670899\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −24.5934 | − | 24.5934i | −1.03283 | − | 1.03283i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 27.8455 | 1.16735 | 0.583673 | − | 0.811989i | \(-0.301615\pi\) | ||||
0.583673 | + | 0.811989i | \(0.301615\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.2474 | 0.847329 | 0.423665 | − | 0.905819i | \(-0.360743\pi\) | ||||
0.423665 | + | 0.905819i | \(0.360743\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.97717 | − | 1.97717i | −0.0825973 | − | 0.0825973i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.6572 | + | 17.6572i | 0.735080 | + | 0.735080i | 0.971621 | − | 0.236542i | \(-0.0760139\pi\) |
−0.236542 | + | 0.971621i | \(0.576014\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.651531i | 0.0270767i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −45.7980 | −1.90002 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.35302 | + | 8.35302i | 0.345947 | + | 0.345947i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20.1417 | + | 20.1417i | 0.831336 | + | 0.831336i | 0.987700 | − | 0.156364i | \(-0.0499773\pi\) |
−0.156364 | + | 0.987700i | \(0.549977\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −22.5160 | + | 17.3939i | −0.927755 | + | 0.716702i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 42.0980i | 1.73168i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −29.9837 | + | 29.9837i | −1.22715 | + | 1.22715i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.2525 | 0.582340 | 0.291170 | − | 0.956671i | \(-0.405956\pi\) | ||||
0.291170 | + | 0.956671i | \(0.405956\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 19.5820i | − | 0.798767i | −0.916784 | − | 0.399383i | \(-0.869224\pi\) | ||
0.916784 | − | 0.399383i | \(-0.130776\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 15.7990 | + | 15.7990i | 0.643385 | + | 0.643385i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.53443 | + | 8.53443i | −0.346402 | + | 0.346402i | −0.858767 | − | 0.512366i | \(-0.828769\pi\) |
0.512366 | + | 0.858767i | \(0.328769\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 63.1918i | − | 2.56066i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 17.1864i | − | 0.695289i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.4752 | − | 20.4752i | 0.826984 | − | 0.826984i | −0.160114 | − | 0.987099i | \(-0.551186\pi\) |
0.987099 | + | 0.160114i | \(0.0511862\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.7760 | + | 22.7760i | 0.916928 | + | 0.916928i | 0.996805 | − | 0.0798768i | \(-0.0254527\pi\) |
−0.0798768 | + | 0.996805i | \(0.525453\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 14.0454i | − | 0.564533i | −0.959336 | − | 0.282266i | \(-0.908914\pi\) | ||
0.959336 | − | 0.282266i | \(-0.0910862\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 7.72513i | − | 0.309999i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 17.5948 | + | 17.5948i | 0.704919 | + | 0.704919i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.45172 | + | 26.8947i | −0.137848 | + | 1.07407i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 20.7798 | 0.828545 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.5505 | −0.698675 | −0.349337 | − | 0.936997i | \(-0.613593\pi\) | ||||
−0.349337 | + | 0.936997i | \(0.613593\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −33.0136 | + | 33.0136i | −1.31217 | + | 1.31217i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 38.5181 | − | 38.5181i | 1.52614 | − | 1.52614i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −40.9002 | −1.61799 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.92291i | 0.352434i | 0.984351 | + | 0.176217i | \(0.0563860\pi\) | ||||
−0.984351 | + | 0.176217i | \(0.943614\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21.6256 | + | 21.6256i | −0.852830 | + | 0.852830i | −0.990481 | − | 0.137651i | \(-0.956045\pi\) |
0.137651 | + | 0.990481i | \(0.456045\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.26922 | − | 6.26922i | −0.246468 | − | 0.246468i | 0.573051 | − | 0.819520i | \(-0.305760\pi\) |
−0.819520 | + | 0.573051i | \(0.805760\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.9886 | 0.627609 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 77.3939 | 3.03331 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −26.4109 | + | 26.4109i | −1.03354 | + | 1.03354i | −0.0341199 | + | 0.999418i | \(0.510863\pi\) |
−0.999418 | + | 0.0341199i | \(0.989137\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −10.2376 | − | 10.2376i | −0.399406 | − | 0.399406i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.19779 | 0.0466592 | 0.0233296 | − | 0.999728i | \(-0.492573\pi\) | ||||
0.0233296 | + | 0.999728i | \(0.492573\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 33.1751i | 1.29036i | 0.764030 | + | 0.645180i | \(0.223218\pi\) | ||||
−0.764030 | + | 0.645180i | \(0.776782\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 13.8725 | − | 13.8725i | 0.538761 | − | 0.538761i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −25.5034 | + | 25.5034i | −0.987496 | + | 0.987496i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 45.1464i | 1.74546i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.1010 | 0.505759 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.58010 | − | 4.58010i | −0.176550 | − | 0.176550i | 0.613300 | − | 0.789850i | \(-0.289842\pi\) |
−0.789850 | + | 0.613300i | \(0.789842\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14.1847 | − | 14.1847i | 0.545160 | − | 0.545160i | −0.379877 | − | 0.925037i | \(-0.624034\pi\) |
0.925037 | + | 0.379877i | \(0.124034\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 24.9116 | 0.956018 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 42.2474 | 1.61893 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.38727 | + | 5.38727i | 0.206138 | + | 0.206138i | 0.802624 | − | 0.596486i | \(-0.203437\pi\) |
−0.596486 | + | 0.802624i | \(0.703437\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 18.4019 | − | 18.4019i | 0.702078 | − | 0.702078i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 17.7526i | − | 0.676318i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.4495 | −0.397517 | −0.198759 | − | 0.980048i | \(-0.563691\pi\) | ||||
−0.198759 | + | 0.980048i | \(0.563691\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 27.8948 | − | 27.8948i | 1.05964 | − | 1.05964i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −17.5948 | + | 17.5948i | −0.666449 | + | 0.666449i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 52.7571 | 1.99546 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −32.9444 | −1.24429 | −0.622146 | − | 0.782901i | \(-0.713739\pi\) | ||||
−0.622146 | + | 0.782901i | \(0.713739\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 42.8098 | + | 5.49428i | 1.61460 | + | 0.207221i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.45178 | + | 4.45178i | 0.167427 | + | 0.167427i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 4.00000i | − | 0.150223i | −0.997175 | − | 0.0751116i | \(-0.976069\pi\) | ||
0.997175 | − | 0.0751116i | \(-0.0239313\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 40.9002i | − | 1.53388i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −31.2352 | − | 31.2352i | −1.16977 | − | 1.16977i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 21.5491 | − | 21.5491i | 0.804765 | − | 0.804765i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.247449i | 0.00922828i | 0.999989 | + | 0.00461414i | \(0.00146873\pi\) | ||||
−0.999989 | + | 0.00461414i | \(0.998531\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 30.2411i | − | 1.12624i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7.41964 | + | 7.41964i | −0.275939 | + | 0.275939i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.9907 | − | 17.9907i | −0.667239 | − | 0.667239i | 0.289837 | − | 0.957076i | \(-0.406399\pi\) |
−0.957076 | + | 0.289837i | \(0.906399\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 34.3939i | 1.27385i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.39388 | 0.199500 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.7215 | − | 11.7215i | 0.432944 | − | 0.432944i | −0.456685 | − | 0.889629i | \(-0.650963\pi\) |
0.889629 | + | 0.456685i | \(0.150963\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.2189 | − | 11.2189i | 0.413254 | − | 0.413254i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32.2929i | 1.18791i | 0.804498 | + | 0.593956i | \(0.202435\pi\) | ||||
−0.804498 | + | 0.593956i | \(0.797565\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 32.2474 | − | 24.9116i | 1.18464 | − | 0.915149i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −22.9820 | − | 22.9820i | −0.843129 | − | 0.843129i | 0.146136 | − | 0.989265i | \(-0.453316\pi\) |
−0.989265 | + | 0.146136i | \(0.953316\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 23.9264 | + | 23.9264i | 0.875423 | + | 0.875423i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −51.5593 | −1.88394 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 50.3615i | 1.83772i | 0.394587 | + | 0.918859i | \(0.370888\pi\) | ||||
−0.394587 | + | 0.918859i | \(0.629112\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 23.5263 | + | 23.5263i | 0.857344 | + | 0.857344i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.0545 | + | 11.0545i | 0.401783 | + | 0.401783i | 0.878861 | − | 0.477078i | \(-0.158304\pi\) |
−0.477078 | + | 0.878861i | \(0.658304\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −42.0980 | −1.52806 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13.3485 | −0.483882 | −0.241941 | − | 0.970291i | \(-0.577784\pi\) | ||||
−0.241941 | + | 0.970291i | \(0.577784\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −21.5491 | − | 21.5491i | −0.780129 | − | 0.780129i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −16.9902 | − | 16.9902i | −0.613481 | − | 0.613481i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.6515i | 0.672591i | 0.941756 | + | 0.336296i | \(0.109174\pi\) | ||||
−0.941756 | + | 0.336296i | \(0.890826\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −65.1464 | −2.34619 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.83163 | + | 5.83163i | 0.209749 | + | 0.209749i | 0.804161 | − | 0.594412i | \(-0.202615\pi\) |
−0.594412 | + | 0.804161i | \(0.702615\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −83.0174 | − | 83.0174i | −2.97823 | − | 2.97823i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −40.9002 | + | 31.5959i | −1.46540 | + | 1.13204i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 29.0433i | 1.03925i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.30188 | + | 4.30188i | −0.153736 | + | 0.153736i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.3905 | + | 19.3905i | −0.691197 | + | 0.691197i | −0.962495 | − | 0.271298i | \(-0.912547\pi\) |
0.271298 | + | 0.962495i | \(0.412547\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −27.8455 | −0.991327 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 64.6140i | − | 2.29741i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.9217 | − | 13.9217i | −0.494374 | − | 0.494374i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14.1847 | − | 14.1847i | 0.502446 | − | 0.502446i | −0.409751 | − | 0.912197i | \(-0.634384\pi\) |
0.912197 | + | 0.409751i | \(0.134384\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 9.79796i | − | 0.346627i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 18.3842i | − | 0.649575i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.26973 | + | 7.26973i | −0.256543 | + | 0.256543i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −44.7351 | − | 44.7351i | −1.57475 | − | 1.57475i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 5.39388i | − | 0.189639i | −0.995494 | − | 0.0948193i | \(-0.969773\pi\) | ||
0.995494 | − | 0.0948193i | \(-0.0302273\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 35.5707i | 1.24905i | 0.781003 | + | 0.624527i | \(0.214708\pi\) | ||||
−0.781003 | + | 0.624527i | \(0.785292\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −49.1112 | − | 49.1112i | −1.72241 | − | 1.72241i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.1123 | + | 1.42617i | 0.388769 | + | 0.0498953i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −59.2844 | −2.07157 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −51.7980 | −1.80776 | −0.903881 | − | 0.427785i | \(-0.859294\pi\) | ||||
−0.903881 | + | 0.427785i | \(0.859294\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15.6899 | + | 15.6899i | −0.546915 | + | 0.546915i | −0.925547 | − | 0.378632i | \(-0.876395\pi\) |
0.378632 | + | 0.925547i | \(0.376395\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.34160 | − | 9.34160i | 0.324839 | − | 0.324839i | −0.525781 | − | 0.850620i | \(-0.676227\pi\) |
0.850620 | + | 0.525781i | \(0.176227\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.13176 | −0.143502 | −0.0717510 | − | 0.997423i | \(-0.522859\pi\) | ||||
−0.0717510 | + | 0.997423i | \(0.522859\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 74.0753i | 2.56964i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 21.9591 | − | 21.9591i | 0.760838 | − | 0.760838i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.26870 | − | 5.26870i | −0.182113 | − | 0.182113i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14.7909 | −0.510637 | −0.255319 | − | 0.966857i | \(-0.582180\pi\) | ||||
−0.255319 | + | 0.966857i | \(0.582180\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.595918 | −0.0205489 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −50.0038 | + | 50.0038i | −1.72222 | + | 1.72222i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16.5068 | + | 16.5068i | 0.567180 | + | 0.567180i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 35.5707 | 1.22078 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 67.0095i | 2.29706i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13.8725 | + | 13.8725i | −0.474984 | + | 0.474984i | −0.903523 | − | 0.428539i | \(-0.859028\pi\) |
0.428539 | + | 0.903523i | \(0.359028\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −21.0049 | + | 21.0049i | −0.717513 | + | 0.717513i | −0.968095 | − | 0.250583i | \(-0.919378\pi\) |
0.250583 | + | 0.968095i | \(0.419378\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32.0000i | 1.09183i | 0.837842 | + | 0.545913i | \(0.183817\pi\) | ||||
−0.837842 | + | 0.545913i | \(0.816183\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 140.586 | 4.79115 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −8.25315 | − | 8.25315i | −0.280941 | − | 0.280941i | 0.552543 | − | 0.833484i | \(-0.313657\pi\) |
−0.833484 | + | 0.552543i | \(0.813657\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −22.6192 | + | 22.6192i | −0.768189 | + | 0.768189i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −29.0433 | −0.985227 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −23.8434 | −0.807902 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −13.0147 | − | 13.0147i | −0.440480 | − | 0.440480i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.181408 | − | 0.181408i | 0.00612572 | − | 0.00612572i | −0.704037 | − | 0.710163i | \(-0.748621\pi\) |
0.710163 | + | 0.704037i | \(0.248621\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 12.2474i | 0.413096i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.1464 | 0.375533 | 0.187766 | − | 0.982214i | \(-0.439875\pi\) | ||||
0.187766 | + | 0.982214i | \(0.439875\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.0452 | − | 29.0452i | 0.977450 | − | 0.977450i | −0.0223014 | − | 0.999751i | \(-0.507099\pi\) |
0.999751 | + | 0.0223014i | \(0.00709935\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 25.4036 | − | 25.4036i | 0.852968 | − | 0.852968i | −0.137530 | − | 0.990498i | \(-0.543916\pi\) |
0.990498 | + | 0.137530i | \(0.0439163\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.8569 | 0.397667 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 18.2474 | 0.611313 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.59063 | − | 20.1854i | 0.0866921 | − | 0.675478i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 44.7351 | + | 44.7351i | 1.49366 | + | 1.49366i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 34.7878i | 1.16024i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 10.1207i | − | 0.337169i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −21.5491 | − | 21.5491i | −0.717109 | − | 0.717109i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.1977 | − | 20.1977i | 0.670653 | − | 0.670653i | −0.287213 | − | 0.957867i | \(-0.592729\pi\) |
0.957867 | + | 0.287213i | \(0.0927289\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 4.65153i | − | 0.154282i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 15.9886i | − | 0.529727i | −0.964286 | − | 0.264864i | \(-0.914673\pi\) | ||
0.964286 | − | 0.264864i | \(-0.0853270\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.9902 | − | 16.9902i | 0.562294 | − | 0.562294i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −32.3466 | − | 32.3466i | −1.06818 | − | 1.06818i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 47.5959i | 1.57004i | 0.619468 | + | 0.785022i | \(0.287349\pi\) | ||||
−0.619468 | + | 0.785022i | \(0.712651\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −23.5505 | −0.776016 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 30.8627 | − | 30.8627i | 1.01586 | − | 1.01586i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −15.7990 | + | 15.7990i | −0.518907 | + | 0.518907i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 21.7980i | 0.715168i | 0.933881 | + | 0.357584i | \(0.116399\pi\) | ||||
−0.933881 | + | 0.357584i | \(0.883601\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 51.0454 | − | 39.4332i | 1.67295 | − | 1.29237i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 52.3399 | + | 52.3399i | 1.71353 | + | 1.71353i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.5063 | − | 15.5063i | −0.506568 | − | 0.506568i | 0.406903 | − | 0.913471i | \(-0.366609\pi\) |
−0.913471 | + | 0.406903i | \(0.866609\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.72513 | 0.252100 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 34.3729i | − | 1.12052i | −0.828316 | − | 0.560262i | \(-0.810701\pi\) | ||
0.828316 | − | 0.560262i | \(-0.189299\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −56.7386 | − | 56.7386i | −1.84766 | − | 1.84766i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.78529 | + | 4.78529i | 0.155501 | + | 0.155501i | 0.780570 | − | 0.625069i | \(-0.214929\pi\) |
−0.625069 | + | 0.780570i | \(0.714929\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15.4503 | 0.501536 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 42.2474 | 1.36997 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.0049 | + | 21.0049i | 0.680414 | + | 0.680414i | 0.960094 | − | 0.279679i | \(-0.0902281\pi\) |
−0.279679 | + | 0.960094i | \(0.590228\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 23.4430 | + | 23.4430i | 0.757805 | + | 0.757805i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 53.3939i | 1.72418i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.6061 | −0.374391 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 26.9364 | + | 26.9364i | 0.868012 | + | 0.868012i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.93623 | − | 6.93623i | −0.223054 | − | 0.223054i | 0.586729 | − | 0.809783i | \(-0.300415\pi\) |
−0.809783 | + | 0.586729i | \(0.800415\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 18.3842 | − | 14.2020i | 0.590586 | − | 0.456235i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1.19779i | − | 0.0384389i | −0.999815 | − | 0.0192194i | \(-0.993882\pi\) | ||
0.999815 | − | 0.0192194i | \(-0.00611811\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18.3242 | + | 18.3242i | −0.587448 | + | 0.587448i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −35.2894 | + | 35.2894i | −1.12901 | + | 1.12901i | −0.138669 | + | 0.990339i | \(0.544282\pi\) |
−0.990339 | + | 0.138669i | \(0.955718\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13.0547 | −0.417229 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 22.5160i | 0.718880i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −27.3807 | − | 27.3807i | −0.873309 | − | 0.873309i | 0.119522 | − | 0.992832i | \(-0.461864\pi\) |
−0.992832 | + | 0.119522i | \(0.961864\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −39.1438 | + | 39.1438i | −1.24596 | + | 1.24596i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 17.3939i | 0.553093i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 31.4389i | − | 0.998689i | −0.866403 | − | 0.499345i | \(-0.833574\pi\) | ||
0.866403 | − | 0.499345i | \(-0.166426\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 61.7253 | − | 61.7253i | 1.95879 | − | 1.95879i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.08665 | − | 8.08665i | −0.256107 | − | 0.256107i | 0.567362 | − | 0.823469i | \(-0.307964\pi\) |
−0.823469 | + | 0.567362i | \(0.807964\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 11.3031i | 0.357613i |
(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 | 1900.2.l.c.1557.1 | yes | 16 | |
5.2 | odd | 4 | inner | 1900.2.l.c.493.2 | yes | 16 | |
5.3 | odd | 4 | inner | 1900.2.l.c.493.7 | yes | 16 | |
5.4 | even | 2 | inner | 1900.2.l.c.1557.8 | yes | 16 | |
19.18 | odd | 2 | inner | 1900.2.l.c.1557.7 | yes | 16 | |
95.18 | even | 4 | inner | 1900.2.l.c.493.1 | ✓ | 16 | |
95.37 | even | 4 | inner | 1900.2.l.c.493.8 | yes | 16 | |
95.94 | odd | 2 | inner | 1900.2.l.c.1557.2 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1900.2.l.c.493.1 | ✓ | 16 | 95.18 | even | 4 | inner | |
1900.2.l.c.493.2 | yes | 16 | 5.2 | odd | 4 | inner | |
1900.2.l.c.493.7 | yes | 16 | 5.3 | odd | 4 | inner | |
1900.2.l.c.493.8 | yes | 16 | 95.37 | even | 4 | inner | |
1900.2.l.c.1557.1 | yes | 16 | 1.1 | even | 1 | trivial | |
1900.2.l.c.1557.2 | yes | 16 | 95.94 | odd | 2 | inner | |
1900.2.l.c.1557.7 | yes | 16 | 19.18 | odd | 2 | inner | |
1900.2.l.c.1557.8 | yes | 16 | 5.4 | even | 2 | inner |