Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1900,3,Mod(1101,1900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1900.1101");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1900.e (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: | \(51.7712502285\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} + 89x^{12} + 3026x^{10} + 49092x^{8} + 390297x^{6} + 1440495x^{4} + 1994425x^{2} + 151875 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1101.7 | ||
Root | \(-0.284180i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1900.1101 |
Dual form | 1900.3.e.h.1101.8 |
$q$-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 \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) | \(951\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | − | 0.284180i | − | 0.0947267i | −0.998878 | − | 0.0473633i | \(-0.984918\pi\) | ||
0.998878 | − | 0.0473633i | \(-0.0150819\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.19606 | −0.313722 | −0.156861 | − | 0.987621i | \(-0.550137\pi\) | ||||
−0.156861 | + | 0.987621i | \(0.550137\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.91924 | 0.991027 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.14967 | −0.195425 | −0.0977124 | − | 0.995215i | \(-0.531153\pi\) | ||||
−0.0977124 | + | 0.995215i | \(0.531153\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.91448i | − | 0.454960i | −0.973783 | − | 0.227480i | \(-0.926951\pi\) | ||
0.973783 | − | 0.227480i | \(-0.0730486\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 21.3302 | 1.25472 | 0.627358 | − | 0.778731i | \(-0.284136\pi\) | ||||
0.627358 | + | 0.778731i | \(0.284136\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −12.8601 | − | 13.9863i | −0.676850 | − | 0.736121i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.624075i | 0.0297178i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 9.06199 | 0.394000 | 0.197000 | − | 0.980404i | \(-0.436880\pi\) | ||||
0.197000 | + | 0.980404i | \(0.436880\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.09229i | − | 0.188603i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 33.2891i | 1.14790i | 0.818891 | + | 0.573950i | \(0.194589\pi\) | ||||
−0.818891 | + | 0.573950i | \(0.805411\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 44.1498i | 1.42419i | 0.702085 | + | 0.712093i | \(0.252253\pi\) | ||||
−0.702085 | + | 0.712093i | \(0.747747\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.610894i | 0.0185119i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 50.0133i | − | 1.35171i | −0.737035 | − | 0.675855i | \(-0.763775\pi\) | ||
0.737035 | − | 0.675855i | \(-0.236225\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.68078 | −0.0430968 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 61.1061i | − | 1.49039i | −0.666845 | − | 0.745196i | \(-0.732356\pi\) | ||
0.666845 | − | 0.745196i | \(-0.267644\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.39704 | 0.125513 | 0.0627563 | − | 0.998029i | \(-0.480011\pi\) | ||||
0.0627563 | + | 0.998029i | \(0.480011\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.02253 | −0.191969 | −0.0959844 | − | 0.995383i | \(-0.530600\pi\) | ||||
−0.0959844 | + | 0.995383i | \(0.530600\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −44.1773 | −0.901578 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 6.06161i | − | 0.118855i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 62.0535i | − | 1.17082i | −0.810737 | − | 0.585411i | \(-0.800933\pi\) | ||
0.810737 | − | 0.585411i | \(-0.199067\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.97463 | + | 3.65460i | −0.0697303 | + | 0.0641157i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 37.5680i | 0.636746i | 0.947966 | + | 0.318373i | \(0.103136\pi\) | ||||
−0.947966 | + | 0.318373i | \(0.896864\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 58.0153 | 0.951071 | 0.475535 | − | 0.879697i | \(-0.342254\pi\) | ||||
0.475535 | + | 0.879697i | \(0.342254\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −19.5871 | −0.310907 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 121.549i | 1.81416i | 0.420958 | + | 0.907080i | \(0.361694\pi\) | ||||
−0.420958 | + | 0.907080i | \(0.638306\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 2.57524i | − | 0.0373223i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 103.884i | − | 1.46315i | −0.681759 | − | 0.731576i | \(-0.738785\pi\) | ||
0.681759 | − | 0.731576i | \(-0.261215\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 120.816 | 1.65501 | 0.827507 | − | 0.561456i | \(-0.189759\pi\) | ||||
0.827507 | + | 0.561456i | \(0.189759\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.72080 | 0.0613091 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 57.1212i | 0.723053i | 0.932362 | + | 0.361526i | \(0.117744\pi\) | ||||
−0.932362 | + | 0.361526i | \(0.882256\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 78.8260 | 0.973161 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 47.3469 | 0.570445 | 0.285222 | − | 0.958461i | \(-0.407933\pi\) | ||||
0.285222 | + | 0.958461i | \(0.407933\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.46009 | 0.108737 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 68.2779i | − | 0.767168i | −0.923506 | − | 0.383584i | \(-0.874690\pi\) | ||
0.923506 | − | 0.383584i | \(-0.125310\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.9885i | 0.142731i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 12.5465 | 0.134908 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 22.7712i | − | 0.234755i | −0.993087 | − | 0.117378i | \(-0.962551\pi\) | ||
0.993087 | − | 0.117378i | \(-0.0374488\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −19.1735 | −0.193671 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 37.0879 | 0.367207 | 0.183603 | − | 0.983000i | \(-0.441224\pi\) | ||||
0.183603 | + | 0.983000i | \(0.441224\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 167.221i | − | 1.62350i | −0.584003 | − | 0.811752i | \(-0.698514\pi\) | ||
0.584003 | − | 0.811752i | \(-0.301486\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 82.4568i | − | 0.770624i | −0.922786 | − | 0.385312i | \(-0.874094\pi\) | ||
0.922786 | − | 0.385312i | \(-0.125906\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 137.915i | 1.26528i | 0.774448 | + | 0.632638i | \(0.218028\pi\) | ||||
−0.774448 | + | 0.632638i | \(0.781972\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −14.2128 | −0.128043 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 156.892i | − | 1.38842i | −0.719772 | − | 0.694211i | \(-0.755753\pi\) | ||
0.719772 | − | 0.694211i | \(-0.244247\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 52.7527i | − | 0.450877i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −46.8422 | −0.393632 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −116.379 | −0.961809 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −17.3651 | −0.141180 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 160.978i | − | 1.26754i | −0.773521 | − | 0.633771i | \(-0.781506\pi\) | ||
0.773521 | − | 0.633771i | \(-0.218494\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 1.53373i | − | 0.0118894i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 200.942 | 1.53391 | 0.766954 | − | 0.641703i | \(-0.221772\pi\) | ||||
0.766954 | + | 0.641703i | \(0.221772\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 28.2416 | + | 30.7147i | 0.212343 | + | 0.230938i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 181.728 | 1.32648 | 0.663240 | − | 0.748406i | \(-0.269181\pi\) | ||||
0.663240 | + | 0.748406i | \(0.269181\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −49.6249 | −0.357013 | −0.178507 | − | 0.983939i | \(-0.557127\pi\) | ||||
−0.178507 | + | 0.983939i | \(0.557127\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.56402i | 0.0181846i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.7142i | 0.0889104i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 12.5543i | 0.0854035i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −197.358 | −1.32455 | −0.662276 | − | 0.749260i | \(-0.730409\pi\) | ||||
−0.662276 | + | 0.749260i | \(0.730409\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 76.4718i | − | 0.506436i | −0.967409 | − | 0.253218i | \(-0.918511\pi\) | ||
0.967409 | − | 0.253218i | \(-0.0814890\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 190.249 | 1.24346 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 163.139 | 1.03910 | 0.519550 | − | 0.854440i | \(-0.326100\pi\) | ||||
0.519550 | + | 0.854440i | \(0.326100\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −17.6344 | −0.110908 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −19.9006 | −0.123606 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 287.890 | 1.76620 | 0.883100 | − | 0.469185i | \(-0.155452\pi\) | ||||
0.883100 | + | 0.469185i | \(0.155452\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 47.3144i | − | 0.283320i | −0.989915 | − | 0.141660i | \(-0.954756\pi\) | ||
0.989915 | − | 0.141660i | \(-0.0452439\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 134.019 | 0.793012 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −114.703 | − | 124.747i | −0.670776 | − | 0.729516i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 64.2813i | − | 0.371568i | −0.982591 | − | 0.185784i | \(-0.940518\pi\) | ||
0.982591 | − | 0.185784i | \(-0.0594825\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.6761 | 0.0603168 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 276.531i | 1.54487i | 0.635097 | + | 0.772433i | \(0.280960\pi\) | ||||
−0.635097 | + | 0.772433i | \(0.719040\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 95.9988i | − | 0.530380i | −0.964196 | − | 0.265190i | \(-0.914565\pi\) | ||
0.964196 | − | 0.265190i | \(-0.0854347\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 16.4868i | − | 0.0900918i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −45.8529 | −0.245203 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 11.1829i | 0.0591690i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 235.317 | 1.23203 | 0.616013 | − | 0.787736i | \(-0.288747\pi\) | ||||
0.616013 | + | 0.787736i | \(0.288747\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 311.842i | − | 1.61576i | −0.589344 | − | 0.807882i | \(-0.700614\pi\) | ||
0.589344 | − | 0.807882i | \(-0.299386\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −212.226 | −1.07729 | −0.538644 | − | 0.842533i | \(-0.681063\pi\) | ||||
−0.538644 | + | 0.842533i | \(0.681063\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −63.8764 | −0.320987 | −0.160493 | − | 0.987037i | \(-0.551309\pi\) | ||||
−0.160493 | + | 0.987037i | \(0.551309\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 34.5417 | 0.171849 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 73.1046i | − | 0.360121i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 80.8261 | 0.390464 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 27.6451 | + | 30.0660i | 0.132273 | + | 0.143856i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 153.634i | − | 0.728125i | −0.931375 | − | 0.364063i | \(-0.881389\pi\) | ||
0.931375 | − | 0.364063i | \(-0.118611\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −29.5217 | −0.138600 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 96.9553i | − | 0.446799i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 34.3335i | − | 0.156774i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 126.157i | − | 0.570845i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 64.1517i | − | 0.287676i | −0.989601 | − | 0.143838i | \(-0.954056\pi\) | ||
0.989601 | − | 0.143838i | \(-0.0459444\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 185.129i | 0.815546i | 0.913083 | + | 0.407773i | \(0.133694\pi\) | ||||
−0.913083 | + | 0.407773i | \(0.866306\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −244.498 | −1.06768 | −0.533838 | − | 0.845587i | \(-0.679251\pi\) | ||||
−0.533838 | + | 0.845587i | \(0.679251\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 1.34156i | − | 0.00580761i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 76.4331 | 0.328039 | 0.164019 | − | 0.986457i | \(-0.447554\pi\) | ||||
0.164019 | + | 0.986457i | \(0.447554\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 16.2327 | 0.0684924 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −221.151 | −0.925317 | −0.462659 | − | 0.886537i | \(-0.653104\pi\) | ||||
−0.462659 | + | 0.886537i | \(0.653104\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.4423i | 0.0599266i | 0.999551 | + | 0.0299633i | \(0.00953904\pi\) | ||||
−0.999551 | + | 0.0299633i | \(0.990461\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 68.2314i | − | 0.280788i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −82.7217 | + | 76.0610i | −0.334906 | + | 0.307939i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 13.4550i | − | 0.0540363i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 120.711 | 0.480920 | 0.240460 | − | 0.970659i | \(-0.422702\pi\) | ||||
0.240460 | + | 0.970659i | \(0.422702\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −19.4803 | −0.0769973 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 396.891i | − | 1.54432i | −0.635426 | − | 0.772161i | \(-0.719176\pi\) | ||
0.635426 | − | 0.772161i | \(-0.280824\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 109.832i | 0.424061i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 296.913i | 1.13760i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 435.465 | 1.65576 | 0.827880 | − | 0.560905i | \(-0.189547\pi\) | ||||
0.827880 | + | 0.560905i | \(0.189547\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −19.4032 | −0.0726713 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 59.6306i | − | 0.221675i | −0.993839 | − | 0.110838i | \(-0.964647\pi\) | ||
0.993839 | − | 0.110838i | \(-0.0353533\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 419.450 | 1.54779 | 0.773893 | − | 0.633317i | \(-0.218307\pi\) | ||||
0.773893 | + | 0.633317i | \(0.218307\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.69108 | 0.0135204 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 262.373 | 0.947196 | 0.473598 | − | 0.880741i | \(-0.342955\pi\) | ||||
0.473598 | + | 0.880741i | \(0.342955\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 393.783i | 1.41141i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 223.815i | − | 0.796495i | −0.917278 | − | 0.398247i | \(-0.869619\pi\) | ||
0.917278 | − | 0.398247i | \(-0.130381\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −240.958 | −0.851441 | −0.425721 | − | 0.904855i | \(-0.639979\pi\) | ||||
−0.425721 | + | 0.904855i | \(0.639979\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 134.192i | 0.467569i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 165.976 | 0.574312 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.47113 | −0.0222376 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 418.683i | 1.42895i | 0.699660 | + | 0.714476i | \(0.253335\pi\) | ||||
−0.699660 | + | 0.714476i | \(0.746665\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 10.9468i | 0.0368578i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 53.5969i | − | 0.179254i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.8522 | −0.0393761 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 10.5396i | − | 0.0347843i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 31.3393i | 0.102082i | 0.998697 | + | 0.0510412i | \(0.0162540\pi\) | ||||
−0.998697 | + | 0.0510412i | \(0.983746\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −47.5208 | −0.153789 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −475.395 | −1.52860 | −0.764301 | − | 0.644860i | \(-0.776916\pi\) | ||||
−0.764301 | + | 0.644860i | \(0.776916\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −97.9348 | −0.312891 | −0.156445 | − | 0.987687i | \(-0.550004\pi\) | ||||
−0.156445 | + | 0.987687i | \(0.550004\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 491.774i | 1.55134i | 0.631140 | + | 0.775669i | \(0.282587\pi\) | ||||
−0.631140 | + | 0.775669i | \(0.717413\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 71.5606i | − | 0.224328i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −23.4326 | −0.0729987 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −274.309 | − | 298.330i | −0.849254 | − | 0.923623i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 39.1927 | 0.119855 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 19.8140 | 0.0602249 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 329.980i | − | 0.996919i | −0.866913 | − | 0.498460i | \(-0.833899\pi\) | ||
0.866913 | − | 0.498460i | \(-0.166101\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 446.080i | − | 1.33958i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 548.629i | − | 1.62798i | −0.580879 | − | 0.813990i | \(-0.697291\pi\) | ||
0.580879 | − | 0.813990i | \(-0.302709\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −44.5855 | −0.131521 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 94.9076i | − | 0.278321i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 204.623 | 0.596567 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −225.865 | −0.650907 | −0.325454 | − | 0.945558i | \(-0.605517\pi\) | ||||
−0.325454 | + | 0.945558i | \(0.605517\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 236.046 | 0.676350 | 0.338175 | − | 0.941083i | \(-0.390190\pi\) | ||||
0.338175 | + | 0.941083i | \(0.390190\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −30.1182 | −0.0858069 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 205.291 | 0.581560 | 0.290780 | − | 0.956790i | \(-0.406085\pi\) | ||||
0.290780 | + | 0.956790i | \(0.406085\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 13.3116i | 0.0372875i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −132.769 | −0.369830 | −0.184915 | − | 0.982755i | \(-0.559201\pi\) | ||||
−0.184915 | + | 0.982755i | \(0.559201\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −30.2334 | + | 359.732i | −0.0837490 | + | 0.996487i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 33.0726i | 0.0911090i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −314.585 | −0.857181 | −0.428590 | − | 0.903499i | \(-0.640990\pi\) | ||||
−0.428590 | + | 0.903499i | \(0.640990\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 545.020i | − | 1.47702i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 136.273i | 0.367313i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 79.5881i | − | 0.213373i | −0.994293 | − | 0.106687i | \(-0.965976\pi\) | ||
0.994293 | − | 0.106687i | \(-0.0340241\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 196.887 | 0.522248 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 212.412i | − | 0.560454i | −0.959934 | − | 0.280227i | \(-0.909590\pi\) | ||
0.959934 | − | 0.280227i | \(-0.0904098\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −45.7467 | −0.120070 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 709.304i | 1.85197i | 0.377563 | + | 0.925984i | \(0.376762\pi\) | ||||
−0.377563 | + | 0.925984i | \(0.623238\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 48.1375 | 0.124386 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 604.145 | 1.55307 | 0.776536 | − | 0.630073i | \(-0.216975\pi\) | ||||
0.776536 | + | 0.630073i | \(0.216975\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 193.294 | 0.494358 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 57.1036i | − | 0.145302i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 374.253 | 0.942703 | 0.471352 | − | 0.881945i | \(-0.343766\pi\) | ||||
0.471352 | + | 0.881945i | \(0.343766\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.72850 | − | 8.02569i | 0.0218759 | − | 0.0201145i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 298.430i | 0.744215i | 0.928190 | + | 0.372108i | \(0.121365\pi\) | ||||
−0.928190 | + | 0.372108i | \(0.878635\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 261.123 | 0.647948 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 107.512i | 0.264158i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 290.042i | − | 0.709150i | −0.935028 | − | 0.354575i | \(-0.884626\pi\) | ||
0.935028 | − | 0.354575i | \(-0.115374\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 51.6434i | − | 0.125653i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 82.5014i | − | 0.199761i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 14.1024i | 0.0338187i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −44.1734 | −0.105426 | −0.0527129 | − | 0.998610i | \(-0.516787\pi\) | ||||
−0.0527129 | + | 0.998610i | \(0.516787\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 326.685i | 0.775975i | 0.921665 | + | 0.387987i | \(0.126830\pi\) | ||||
−0.921665 | + | 0.387987i | \(0.873170\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −80.4742 | −0.190246 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −127.405 | −0.298372 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.61312 | 0.00842219 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 152.204i | − | 0.353141i | −0.984288 | − | 0.176571i | \(-0.943500\pi\) | ||
0.984288 | − | 0.176571i | \(-0.0565004\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 223.747i | 0.516736i | 0.966047 | + | 0.258368i | \(0.0831848\pi\) | ||||
−0.966047 | + | 0.258368i | \(0.916815\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −116.539 | − | 126.744i | −0.266679 | − | 0.290031i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 253.627i | 0.577737i | 0.957369 | + | 0.288869i | \(0.0932791\pi\) | ||||
−0.957369 | + | 0.288869i | \(0.906721\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −394.028 | −0.893488 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −471.418 | −1.06415 | −0.532075 | − | 0.846697i | \(-0.678587\pi\) | ||||
−0.532075 | + | 0.846697i | \(0.678587\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 56.0852i | 0.125470i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 546.839i | 1.21790i | 0.793207 | + | 0.608952i | \(0.208410\pi\) | ||||
−0.793207 | + | 0.608952i | \(0.791590\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 131.358i | 0.291260i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −21.7318 | −0.0479730 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 166.467 | 0.364261 | 0.182130 | − | 0.983274i | \(-0.441701\pi\) | ||||
0.182130 | + | 0.983274i | \(0.441701\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 108.619i | − | 0.236644i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −258.722 | −0.561220 | −0.280610 | − | 0.959822i | \(-0.590537\pi\) | ||||
−0.280610 | + | 0.959822i | \(0.590537\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −629.974 | −1.36064 | −0.680318 | − | 0.732917i | \(-0.738158\pi\) | ||||
−0.680318 | + | 0.732917i | \(0.738158\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −151.843 | −0.325145 | −0.162573 | − | 0.986697i | \(-0.551979\pi\) | ||||
−0.162573 | + | 0.986697i | \(0.551979\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 266.928i | − | 0.569142i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 46.3608i | − | 0.0984305i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.6019 | −0.0245283 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 553.470i | − | 1.16032i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −15.2726 | −0.0318843 | −0.0159421 | − | 0.999873i | \(-0.505075\pi\) | ||||
−0.0159421 | + | 0.999873i | \(0.505075\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −295.802 | −0.614974 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.65536i | 0.0117088i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 279.446i | 0.573812i | 0.957959 | + | 0.286906i | \(0.0926267\pi\) | ||||
−0.957959 | + | 0.286906i | \(0.907373\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 81.8127i | − | 0.167306i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 641.107 | 1.30572 | 0.652859 | − | 0.757480i | \(-0.273569\pi\) | ||||
0.652859 | + | 0.757480i | \(0.273569\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 710.062i | 1.44029i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 228.135i | 0.459023i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −102.056 | −0.204521 | −0.102261 | − | 0.994758i | \(-0.532608\pi\) | ||||
−0.102261 | + | 0.994758i | \(0.532608\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.4458 | −0.0268379 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −889.366 | −1.76812 | −0.884061 | − | 0.467371i | \(-0.845201\pi\) | ||||
−0.884061 | + | 0.467371i | \(0.845201\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 38.0855i | − | 0.0751193i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 35.5445i | 0.0698320i | 0.999390 | + | 0.0349160i | \(0.0111164\pi\) | ||||
−0.999390 | + | 0.0349160i | \(0.988884\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −265.319 | −0.519214 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −71.2223 | + | 65.4876i | −0.138835 | + | 0.127656i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 19.3955 | 0.0375155 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −18.2674 | −0.0351974 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 747.135i | 1.43404i | 0.697053 | + | 0.717020i | \(0.254494\pi\) | ||||
−0.697053 | + | 0.717020i | \(0.745506\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 677.562i | 1.29553i | 0.761840 | + | 0.647765i | \(0.224296\pi\) | ||||
−0.761840 | + | 0.647765i | \(0.775704\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 941.722i | 1.78695i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −446.880 | −0.844764 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 335.078i | 0.631032i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −361.411 | −0.678069 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 78.5845 | 0.146340 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 94.9668 | 0.176191 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −362.237 | −0.669569 | −0.334784 | − | 0.942295i | \(-0.608663\pi\) | ||||
−0.334784 | + | 0.942295i | \(0.608663\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −27.2809 | −0.0502411 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 585.353i | 1.07011i | 0.844816 | + | 0.535057i | \(0.179710\pi\) | ||||
−0.844816 | + | 0.535057i | \(0.820290\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 517.453 | 0.942537 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 465.591 | − | 428.102i | 0.844993 | − | 0.776955i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 125.441i | − | 0.226838i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1040.06 | −1.86725 | −0.933623 | − | 0.358257i | \(-0.883371\pi\) | ||||
−0.933623 | + | 0.358257i | \(0.883371\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 31.9207i | − | 0.0571032i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.0305i | 0.0232272i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 421.015i | 0.747807i | 0.927468 | + | 0.373903i | \(0.121981\pi\) | ||||
−0.927468 | + | 0.373903i | \(0.878019\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −173.106 | −0.305302 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24.7446i | 0.0434879i | 0.999764 | + | 0.0217440i | \(0.00692187\pi\) | ||||
−0.999764 | + | 0.0217440i | \(0.993078\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −283.521 | −0.496534 | −0.248267 | − | 0.968692i | \(-0.579861\pi\) | ||||
−0.248267 | + | 0.968692i | \(0.579861\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 66.8723i | − | 0.116706i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 147.592 | 0.255792 | 0.127896 | − | 0.991788i | \(-0.459178\pi\) | ||||
0.127896 | + | 0.991788i | \(0.459178\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −88.6194 | −0.153056 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −103.976 | −0.178961 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 133.395i | 0.228808i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −876.849 | −1.49378 | −0.746890 | − | 0.664948i | \(-0.768454\pi\) | ||||
−0.746890 | + | 0.664948i | \(0.768454\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 617.492 | − | 567.772i | 1.04837 | − | 0.963960i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 60.3103i | 0.102048i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 205.974 | 0.347343 | 0.173671 | − | 0.984804i | \(-0.444437\pi\) | ||||
0.173671 | + | 0.984804i | \(0.444437\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 18.1524i | 0.0304060i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 631.341i | 1.05399i | 0.849868 | + | 0.526996i | \(0.176682\pi\) | ||||
−0.849868 | + | 0.526996i | \(0.823318\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 139.903i | 0.232784i | 0.993203 | + | 0.116392i | \(0.0371328\pi\) | ||||
−0.993203 | + | 0.116392i | \(0.962867\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1084.12i | 1.79788i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.9312i | 0.0311881i | 0.999878 | + | 0.0155940i | \(0.00496394\pi\) | ||||
−0.999878 | + | 0.0155940i | \(0.995036\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −20.7749 | −0.0341131 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 53.3636i | 0.0873381i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −86.8754 | −0.141722 | −0.0708608 | − | 0.997486i | \(-0.522575\pi\) | ||||
−0.0708608 | + | 0.997486i | \(0.522575\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 664.265 | 1.07660 | 0.538302 | − | 0.842752i | \(-0.319066\pi\) | ||||
0.538302 | + | 0.842752i | \(0.319066\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1120.54 | 1.81024 | 0.905122 | − | 0.425151i | \(-0.139779\pi\) | ||||
0.905122 | + | 0.425151i | \(0.139779\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 46.1463i | − | 0.0743096i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 149.942i | 0.240678i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.54415 | − | 7.85618i | 0.0136270 | − | 0.0125298i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1066.79i | − | 1.69601i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −940.484 | −1.49047 | −0.745233 | − | 0.666804i | \(-0.767662\pi\) | ||||
−0.745233 | + | 0.666804i | \(0.767662\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −43.6598 | −0.0689729 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 261.286i | 0.410182i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 926.565i | − | 1.45002i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 585.344i | − | 0.913174i | −0.889679 | − | 0.456587i | \(-0.849072\pi\) | ||
0.889679 | − | 0.456587i | \(-0.150928\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −562.853 | −0.875354 | −0.437677 | − | 0.899132i | \(-0.644199\pi\) | ||||
−0.437677 | + | 0.899132i | \(0.644199\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −723.636 | −1.11845 | −0.559224 | − | 0.829017i | \(-0.688901\pi\) | ||||
−0.559224 | + | 0.829017i | \(0.688901\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 80.7589i | − | 0.124436i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −27.5528 | −0.0423238 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −211.465 | −0.323836 | −0.161918 | − | 0.986804i | \(-0.551768\pi\) | ||||
−0.161918 | + | 0.986804i | \(0.551768\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1077.59 | 1.64016 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 692.365i | − | 1.05063i | −0.850908 | − | 0.525315i | \(-0.823948\pi\) | ||
0.850908 | − | 0.525315i | \(-0.176052\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1121.07i | 1.69602i | 0.529978 | + | 0.848011i | \(0.322200\pi\) | ||||
−0.529978 | + | 0.848011i | \(0.677800\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −35.8512 | −0.0540743 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 301.665i | 0.452272i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −18.2306 | −0.0272506 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −124.714 | −0.185863 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 536.583i | − | 0.797301i | −0.917103 | − | 0.398650i | \(-0.869479\pi\) | ||
0.917103 | − | 0.398650i | \(-0.130521\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 234.317i | − | 0.346110i | −0.984912 | − | 0.173055i | \(-0.944636\pi\) | ||
0.984912 | − | 0.173055i | \(-0.0553639\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 50.0069i | 0.0736478i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 52.6099 | 0.0772539 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 545.339i | − | 0.798447i | −0.916854 | − | 0.399223i | \(-0.869280\pi\) | ||
0.916854 | − | 0.399223i | \(-0.130720\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 69.4814i | 0.101137i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −367.014 | −0.532677 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −225.173 | −0.325865 | −0.162933 | − | 0.986637i | \(-0.552095\pi\) | ||||
−0.162933 | + | 0.986637i | \(0.552095\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 42.1060 | 0.0607590 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 1303.40i | − | 1.87002i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 21.7207i | − | 0.0310740i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −517.342 | −0.738005 | −0.369003 | − | 0.929428i | \(-0.620301\pi\) | ||||
−0.369003 | + | 0.929428i | \(0.620301\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −699.501 | + | 643.178i | −0.995022 | + | 0.914905i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −81.4471 | −0.115201 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 272.183 | 0.383897 | 0.191948 | − | 0.981405i | \(-0.438519\pi\) | ||||
0.191948 | + | 0.981405i | \(0.438519\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 509.478i | 0.716565i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 400.085i | 0.561129i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 62.8466i | 0.0876522i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 547.539 | 0.761528 | 0.380764 | − | 0.924672i | \(-0.375661\pi\) | ||||
0.380764 | + | 0.924672i | \(0.375661\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 367.226i | 0.509329i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.10421 | 0.00567664 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1211.49 | −1.66642 | −0.833210 | − | 0.552957i | \(-0.813499\pi\) | ||||
−0.833210 | + | 0.552957i | \(0.813499\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 690.044 | 0.946563 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 115.120 | 0.157483 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.28014 | 0.00447495 | 0.00223748 | − | 0.999997i | \(-0.499288\pi\) | ||||
0.00223748 | + | 0.999997i | \(0.499288\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 261.290i | − | 0.354532i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −848.413 | −1.14806 | −0.574028 | − | 0.818836i | \(-0.694620\pi\) | ||||
−0.574028 | + | 0.818836i | \(0.694620\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 21.6150 | + | 23.5078i | 0.0291701 | + | 0.0317245i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 620.675i | 0.835363i | 0.908593 | + | 0.417682i | \(0.137157\pi\) | ||||
−0.908593 | + | 0.417682i | \(0.862843\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 422.298 | 0.565326 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 181.080i | 0.241762i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 88.8695i | − | 0.118335i | −0.998248 | − | 0.0591674i | \(-0.981155\pi\) | ||
0.998248 | − | 0.0591674i | \(-0.0188446\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 34.3036i | − | 0.0455559i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 389.621 | 0.514692 | 0.257346 | − | 0.966319i | \(-0.417152\pi\) | ||||
0.257346 | + | 0.966319i | \(0.417152\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.53592i | 0.00729370i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 183.315 | 0.240887 | 0.120444 | − | 0.992720i | \(-0.461568\pi\) | ||||
0.120444 | + | 0.992720i | \(0.461568\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 302.869i | − | 0.396945i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 222.195 | 0.289694 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 839.391 | 1.09154 | 0.545768 | − | 0.837936i | \(-0.316238\pi\) | ||||
0.545768 | + | 0.837936i | \(0.316238\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −112.788 | −0.146289 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1149.34i | 1.48685i | 0.668819 | + | 0.743425i | \(0.266800\pi\) | ||||
−0.668819 | + | 0.743425i | \(0.733200\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 31.2120 | 0.0401699 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −854.649 | + | 785.833i | −1.09711 | + | 1.00877i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 223.316i | 0.285936i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 169.518 | 0.216498 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 500.800i | 0.636341i | 0.948034 | + | 0.318170i | \(0.103068\pi\) | ||||
−0.948034 | + | 0.318170i | \(0.896932\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 123.750i | − | 0.156845i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 344.543i | 0.435579i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 343.130i | − | 0.432699i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 481.090i | − | 0.603626i | −0.953367 | − | 0.301813i | \(-0.902408\pi\) | ||
0.953367 | − | 0.301813i | \(-0.0975918\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −192.452 | −0.240866 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 608.988i | − | 0.760284i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −259.715 | −0.323431 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −16.9458 | −0.0209985 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −16.0970 | −0.0198974 | −0.00994869 | − | 0.999951i | \(-0.503167\pi\) | ||||
−0.00994869 | + | 0.999951i | \(0.503167\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 744.398i | 0.917876i | 0.888468 | + | 0.458938i | \(0.151770\pi\) | ||||
−0.888468 | + | 0.458938i | \(0.848230\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 119.199i | − | 0.146617i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −69.4067 | − | 75.4846i | −0.0849531 | − | 0.0923925i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 115.848i | 0.141450i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −817.427 | −0.995648 | −0.497824 | − | 0.867278i | \(-0.665868\pi\) | ||||
−0.497824 | + | 0.867278i | \(0.665868\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 447.054 | 0.543201 | 0.271600 | − | 0.962410i | \(-0.412447\pi\) | ||||
0.271600 | + | 0.962410i | \(0.412447\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1387.55i | 1.67782i | 0.544274 | + | 0.838908i | \(0.316805\pi\) | ||||
−0.544274 | + | 0.838908i | \(0.683195\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 1076.73i | − | 1.29883i | −0.760433 | − | 0.649416i | \(-0.775013\pi\) | ||
0.760433 | − | 0.649416i | \(-0.224987\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 74.5613i | − | 0.0897247i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −942.310 | −1.13122 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 224.823 | 0.268606 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 606.394i | 0.722758i | 0.932419 | + | 0.361379i | \(0.117694\pi\) | ||||
−0.932419 | + | 0.361379i | \(0.882306\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −267.163 | −0.317673 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −63.6038 | −0.0754493 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 255.574 | 0.301741 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 68.4754i | 0.0806542i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 453.220i | − | 0.532573i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −99.5618 | −0.116720 | −0.0583598 | − | 0.998296i | \(-0.518587\pi\) | ||||
−0.0583598 | + | 0.998296i | \(0.518587\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1591.90i | 1.85753i | 0.370669 | + | 0.928765i | \(0.379128\pi\) | ||||
−0.370669 | + | 0.928765i | \(0.620872\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 974.586 | 1.13456 | 0.567279 | − | 0.823525i | \(-0.307996\pi\) | ||||
0.567279 | + | 0.823525i | \(0.307996\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 38.1348 | 0.0442913 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 270.696i | 0.313669i | 0.987625 | + | 0.156834i | \(0.0501289\pi\) | ||||
−0.987625 | + | 0.156834i | \(0.949871\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 47.1671i | − | 0.0544027i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 122.792i | − | 0.141302i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 718.897 | 0.825370 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 203.102i | − | 0.232649i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 868.510i | − | 0.990319i | −0.868802 | − | 0.495160i | \(-0.835110\pi\) | ||
0.868802 | − | 0.495160i | \(-0.164890\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 118.981 | 0.135360 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 916.787 | 1.04062 | 0.520311 | − | 0.853977i | \(-0.325816\pi\) | ||||
0.520311 | + | 0.853977i | \(0.325816\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 878.004 | 0.994342 | 0.497171 | − | 0.867653i | \(-0.334372\pi\) | ||||
0.497171 | + | 0.867653i | \(0.334372\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1351.53i | 1.52371i | 0.647747 | + | 0.761856i | \(0.275711\pi\) | ||||
−0.647747 | + | 0.761856i | \(0.724289\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 353.516i | 0.397656i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −169.450 | −0.190180 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 116.031 | + | 126.192i | 0.129934 | + | 0.141312i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −15.2312 | −0.0169801 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1469.71 | −1.63482 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 1323.61i | − | 1.46905i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.36816i | 0.00372996i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 872.623i | − | 0.962098i | −0.876694 | − | 0.481049i | \(-0.840256\pi\) | ||
0.876694 | − | 0.481049i | \(-0.159744\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 330.796 | 0.363912 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 885.104i | − | 0.971574i | −0.874077 | − | 0.485787i | \(-0.838533\pi\) | ||
0.874077 | − | 0.485787i | \(-0.161467\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −101.780 | −0.111479 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −441.279 | −0.481221 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −446.590 | −0.485952 | −0.242976 | − | 0.970032i | \(-0.578124\pi\) | ||||
−0.242976 | + | 0.970032i | \(0.578124\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.90600 | 0.00966992 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −614.419 | −0.665676 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 1491.48i | − | 1.60894i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 534.036 | 0.574850 | 0.287425 | − | 0.957803i | \(-0.407201\pi\) | ||||
0.287425 | + | 0.957803i | \(0.407201\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 568.127 | + | 617.878i | 0.610233 | + | 0.663671i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 135.098i | 0.144799i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1157.99 | −1.23585 | −0.617926 | − | 0.786236i | \(-0.712027\pi\) | ||||
−0.617926 | + | 0.786236i | \(0.712027\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 27.8311i | 0.0296391i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 868.034i | 0.922459i | 0.887281 | + | 0.461230i | \(0.152592\pi\) | ||||
−0.887281 | + | 0.461230i | \(0.847408\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 553.743i | − | 0.587214i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1754.37 | −1.85255 | −0.926276 | − | 0.376845i | \(-0.877009\pi\) | ||||
−0.926276 | + | 0.376845i | \(0.877009\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 714.563i | − | 0.752965i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 139.752 | 0.146953 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 541.232i | 0.567924i | 0.958836 | + | 0.283962i | \(0.0916490\pi\) | ||||
−0.958836 | + | 0.283962i | \(0.908351\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −20.3361 | −0.0212498 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −399.084 | −0.416146 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −988.203 | −1.02831 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 735.452i | − | 0.763709i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 632.276 | 0.653853 | 0.326927 | − | 0.945050i | \(-0.393987\pi\) | ||||
0.326927 | + | 0.945050i | \(0.393987\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −84.7795 | + | 77.9531i | −0.0874917 | + | 0.0804470i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1326.62i | − | 1.36624i | −0.730305 | − | 0.683122i | \(-0.760622\pi\) | ||
0.730305 | − | 0.683122i | \(-0.239378\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 108.979 | 0.112003 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 250.280i | − | 0.256172i | −0.991763 | − | 0.128086i | \(-0.959117\pi\) | ||
0.991763 | − | 0.128086i | \(-0.0408833\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 146.775i | 0.149924i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1230.10i | 1.25392i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 1291.69i | − | 1.31403i | −0.753879 | − | 0.657014i | \(-0.771819\pi\) | ||
0.753879 | − | 0.657014i | \(-0.228181\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 5.63074i | − | 0.00570490i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 48.9079 | 0.0494519 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 468.338i | − | 0.472592i | −0.971681 | − | 0.236296i | \(-0.924067\pi\) | ||
0.971681 | − | 0.236296i | \(-0.0759335\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −93.7738 | −0.0944348 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1592.68 | 1.59747 | 0.798735 | − | 0.601683i | \(-0.205503\pi\) | ||||
0.798735 | + | 0.601683i | \(0.205503\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −254.682 | −0.254937 |
(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 | 1900.3.e.h.1101.7 | yes | 14 | |
5.2 | odd | 4 | 1900.3.g.d.949.14 | 28 | |||
5.3 | odd | 4 | 1900.3.g.d.949.15 | 28 | |||
5.4 | even | 2 | 1900.3.e.g.1101.8 | yes | 14 | ||
19.18 | odd | 2 | inner | 1900.3.e.h.1101.8 | yes | 14 | |
95.18 | even | 4 | 1900.3.g.d.949.13 | 28 | |||
95.37 | even | 4 | 1900.3.g.d.949.16 | 28 | |||
95.94 | odd | 2 | 1900.3.e.g.1101.7 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1900.3.e.g.1101.7 | ✓ | 14 | 95.94 | odd | 2 | ||
1900.3.e.g.1101.8 | yes | 14 | 5.4 | even | 2 | ||
1900.3.e.h.1101.7 | yes | 14 | 1.1 | even | 1 | trivial | |
1900.3.e.h.1101.8 | yes | 14 | 19.18 | odd | 2 | inner | |
1900.3.g.d.949.13 | 28 | 95.18 | even | 4 | |||
1900.3.g.d.949.14 | 28 | 5.2 | odd | 4 | |||
1900.3.g.d.949.15 | 28 | 5.3 | odd | 4 | |||
1900.3.g.d.949.16 | 28 | 95.37 | even | 4 |