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 | 1101.8 | ||
Root | \(0.284180i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1900.1101 |
Dual form | 1900.3.e.g.1101.7 |
$q$-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 | \(0.0150819\pi\) | ||||
−0.998878 | + | 0.0473633i | \(0.984918\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.19606 | 0.313722 | 0.156861 | − | 0.987621i | \(-0.449863\pi\) | ||||
0.156861 | + | 0.987621i | \(0.449863\pi\) | |||||||
\(8\) | 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 | \(0.0730486\pi\) | ||||
−0.973783 | + | 0.227480i | \(0.926951\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −21.3302 | −1.25472 | −0.627358 | − | 0.778731i | \(-0.715864\pi\) | ||||
−0.627358 | + | 0.778731i | \(0.715864\pi\) | |||||||
\(18\) | 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 | \(-0.563120\pi\) | ||||
−0.197000 | + | 0.980404i | \(0.563120\pi\) | |||||||
\(24\) | 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 | \(0.236225\pi\) | ||||
−0.737035 | + | 0.675855i | \(0.763775\pi\) | |||||||
\(38\) | 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 | \(-0.519989\pi\) | ||||
−0.0627563 | + | 0.998029i | \(0.519989\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.02253 | 0.191969 | 0.0959844 | − | 0.995383i | \(-0.469400\pi\) | ||||
0.0959844 | + | 0.995383i | \(0.469400\pi\) | |||||||
\(48\) | 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 | \(0.199067\pi\) | ||||
−0.810737 | + | 0.585411i | \(0.800933\pi\) | |||||||
\(54\) | 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 | \(-0.638306\pi\) | ||
0.420958 | − | 0.907080i | \(-0.361694\pi\) | |||||||
\(68\) | 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 | \(-0.810241\pi\) | ||||
−0.827507 | + | 0.561456i | \(0.810241\pi\) | |||||||
\(74\) | 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 | \(-0.592067\pi\) | ||||
−0.285222 | + | 0.958461i | \(0.592067\pi\) | |||||||
\(84\) | 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 | \(0.0374488\pi\) | ||||
−0.993087 | + | 0.117378i | \(0.962551\pi\) | |||||||
\(98\) | 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 | \(0.301486\pi\) | ||||
−0.584003 | + | 0.811752i | \(0.698514\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 82.4568i | 0.770624i | 0.922786 | + | 0.385312i | \(0.125906\pi\) | ||||
−0.922786 | + | 0.385312i | \(0.874094\pi\) | |||||||
\(108\) | 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 | \(0.244247\pi\) | ||||
−0.719772 | + | 0.694211i | \(0.755753\pi\) | |||||||
\(114\) | 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 | \(0.218494\pi\) | ||||
−0.773521 | + | 0.633771i | \(0.781506\pi\) | |||||||
\(128\) | 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 | \(-0.730819\pi\) | ||||
−0.663240 | + | 0.748406i | \(0.730819\pi\) | |||||||
\(138\) | 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 | \(-0.673900\pi\) | ||||
−0.519550 | + | 0.854440i | \(0.673900\pi\) | |||||||
\(158\) | 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 | \(-0.844548\pi\) | ||||
−0.883100 | + | 0.469185i | \(0.844548\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 47.3144i | 0.283320i | 0.989915 | + | 0.141660i | \(0.0452439\pi\) | ||||
−0.989915 | + | 0.141660i | \(0.954756\pi\) | |||||||
\(168\) | 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 | \(0.0594825\pi\) | ||||
−0.982591 | + | 0.185784i | \(0.940518\pi\) | |||||||
\(174\) | 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 | \(0.299386\pi\) | ||||
−0.589344 | + | 0.807882i | \(0.700614\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 212.226 | 1.07729 | 0.538644 | − | 0.842533i | \(-0.318937\pi\) | ||||
0.538644 | + | 0.842533i | \(0.318937\pi\) | |||||||
\(198\) | 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 | \(0.0459444\pi\) | ||||
−0.989601 | + | 0.143838i | \(0.954056\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 185.129i | − | 0.815546i | −0.913083 | − | 0.407773i | \(-0.866306\pi\) | ||
0.913083 | − | 0.407773i | \(-0.133694\pi\) | |||||||
\(228\) | 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 | \(-0.552446\pi\) | ||||
−0.164019 | + | 0.986457i | \(0.552446\pi\) | |||||||
\(234\) | 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 | \(0.280824\pi\) | ||||
−0.635426 | + | 0.772161i | \(0.719176\pi\) | |||||||
\(258\) | 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 | \(-0.810453\pi\) | ||||
−0.827880 | + | 0.560905i | \(0.810453\pi\) | |||||||
\(264\) | 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 | \(-0.657045\pi\) | ||||
−0.473598 | + | 0.880741i | \(0.657045\pi\) | |||||||
\(278\) | 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 | \(-0.360021\pi\) | ||||
0.425721 | + | 0.904855i | \(0.360021\pi\) | |||||||
\(284\) | 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 | \(-0.746665\pi\) | ||
0.699660 | − | 0.714476i | \(-0.253335\pi\) | |||||||
\(294\) | 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 | \(-0.983746\pi\) | ||
0.998697 | − | 0.0510412i | \(-0.0162540\pi\) | |||||||
\(308\) | 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 | \(-0.449996\pi\) | ||||
0.156445 | + | 0.987687i | \(0.449996\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 491.774i | − | 1.55134i | −0.631140 | − | 0.775669i | \(-0.717413\pi\) | ||
0.631140 | − | 0.775669i | \(-0.282587\pi\) | |||||||
\(318\) | 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 | \(0.302709\pi\) | ||||
−0.580879 | + | 0.813990i | \(0.697291\pi\) | |||||||
\(338\) | 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 | \(-0.394483\pi\) | ||||
0.325454 | + | 0.945558i | \(0.394483\pi\) | |||||||
\(348\) | 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 | \(-0.593915\pi\) | ||||
−0.290780 | + | 0.956790i | \(0.593915\pi\) | |||||||
\(354\) | 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 | \(-0.359010\pi\) | ||||
0.428590 | + | 0.903499i | \(0.359010\pi\) | |||||||
\(368\) | 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 | \(0.0340241\pi\) | ||||
−0.994293 | + | 0.106687i | \(0.965976\pi\) | |||||||
\(374\) | 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 | \(-0.623238\pi\) | ||
0.377563 | − | 0.925984i | \(-0.376762\pi\) | |||||||
\(384\) | 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 | \(-0.656234\pi\) | ||||
−0.471352 | + | 0.881945i | \(0.656234\pi\) | |||||||
\(398\) | 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 | \(-0.916815\pi\) | ||
0.966047 | − | 0.258368i | \(-0.0831848\pi\) | |||||||
\(434\) | 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 | \(-0.321413\pi\) | ||||
0.532075 | + | 0.846697i | \(0.321413\pi\) | |||||||
\(444\) | 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 | \(-0.558299\pi\) | ||||
−0.182130 | + | 0.983274i | \(0.558299\pi\) | |||||||
\(458\) | 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 | \(-0.261842\pi\) | ||||
0.680318 | + | 0.732917i | \(0.261842\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 151.843 | 0.325145 | 0.162573 | − | 0.986697i | \(-0.448021\pi\) | ||||
0.162573 | + | 0.986697i | \(0.448021\pi\) | |||||||
\(468\) | 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 | \(-0.907373\pi\) | ||
0.957959 | − | 0.286906i | \(-0.0926267\pi\) | |||||||
\(488\) | 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 | \(-0.154799\pi\) | ||||
0.884061 | + | 0.467371i | \(0.154799\pi\) | |||||||
\(504\) | 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 | \(-0.775704\pi\) | ||
0.761840 | − | 0.647765i | \(-0.224296\pi\) | |||||||
\(524\) | 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 | \(-0.820290\pi\) | ||
0.844816 | − | 0.535057i | \(-0.179710\pi\) | |||||||
\(548\) | 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 | \(-0.116629\pi\) | ||||
0.933623 | + | 0.358257i | \(0.116629\pi\) | |||||||
\(558\) | 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 | \(-0.878019\pi\) | ||
0.927468 | − | 0.373903i | \(-0.121981\pi\) | |||||||
\(564\) | 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 | \(-0.540822\pi\) | ||||
−0.127896 | + | 0.991788i | \(0.540822\pi\) | |||||||
\(578\) | 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 | \(-0.231546\pi\) | ||||
0.746890 | + | 0.664948i | \(0.231546\pi\) | |||||||
\(588\) | 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 | \(-0.555563\pi\) | ||||
−0.173671 | + | 0.984804i | \(0.555563\pi\) | |||||||
\(594\) | 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 | \(-0.995036\pi\) | ||
0.999878 | − | 0.0155940i | \(-0.00496394\pi\) | |||||||
\(608\) | 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 | \(-0.477425\pi\) | ||||
0.0708608 | + | 0.997486i | \(0.477425\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −664.265 | −1.07660 | −0.538302 | − | 0.842752i | \(-0.680934\pi\) | ||||
−0.538302 | + | 0.842752i | \(0.680934\pi\) | |||||||
\(618\) | 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 | \(-0.355801\pi\) | ||||
0.437677 | + | 0.899132i | \(0.355801\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 723.636 | 1.11845 | 0.559224 | − | 0.829017i | \(-0.311099\pi\) | ||||
0.559224 | + | 0.829017i | \(0.311099\pi\) | |||||||
\(648\) | 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 | \(-0.448232\pi\) | ||||
0.161918 | + | 0.986804i | \(0.448232\pi\) | |||||||
\(654\) | 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 | \(0.130521\pi\) | ||||
−0.917103 | + | 0.398650i | \(0.869479\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 234.317i | 0.346110i | 0.984912 | + | 0.173055i | \(0.0553639\pi\) | ||||
−0.984912 | + | 0.173055i | \(0.944636\pi\) | |||||||
\(678\) | 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 | \(0.130720\pi\) | ||||
−0.916854 | + | 0.399223i | \(0.869280\pi\) | |||||||
\(684\) | 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 | \(-0.186501\pi\) | ||||
0.833210 | + | 0.552957i | \(0.186501\pi\) | |||||||
\(728\) | 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 | \(-0.500712\pi\) | ||||
−0.00223748 | + | 0.999997i | \(0.500712\pi\) | |||||||
\(734\) | 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 | \(-0.862843\pi\) | ||
0.908593 | − | 0.417682i | \(-0.137157\pi\) | |||||||
\(744\) | 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 | \(-0.582848\pi\) | ||||
−0.257346 | + | 0.966319i | \(0.582848\pi\) | |||||||
\(758\) | 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 | \(-0.733200\pi\) | ||
0.668819 | − | 0.743425i | \(-0.266800\pi\) | |||||||
\(774\) | 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 | \(-0.896932\pi\) | ||
0.948034 | − | 0.318170i | \(-0.103068\pi\) | |||||||
\(788\) | 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 | \(0.0975918\pi\) | ||||
−0.953367 | + | 0.301813i | \(0.902408\pi\) | |||||||
\(798\) | 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 | \(-0.587553\pi\) | ||||
−0.271600 | + | 0.962410i | \(0.587553\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 1387.55i | − | 1.67782i | −0.544274 | − | 0.838908i | \(-0.683195\pi\) | ||
0.544274 | − | 0.838908i | \(-0.316805\pi\) | |||||||
\(828\) | 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 | \(-0.481413\pi\) | ||||
0.0583598 | + | 0.998296i | \(0.481413\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1591.90i | − | 1.85753i | −0.370669 | − | 0.928765i | \(-0.620872\pi\) | ||
0.370669 | − | 0.928765i | \(-0.379128\pi\) | |||||||
\(858\) | 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 | \(-0.949871\pi\) | ||
0.987625 | − | 0.156834i | \(-0.0501289\pi\) | |||||||
\(864\) | 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 | \(0.164890\pi\) | ||||
−0.868802 | + | 0.495160i | \(0.835110\pi\) | |||||||
\(878\) | 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 | \(-0.665628\pi\) | ||||
−0.497171 | + | 0.867653i | \(0.665628\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 1351.53i | − | 1.52371i | −0.647747 | − | 0.761856i | \(-0.724289\pi\) | ||
0.647747 | − | 0.761856i | \(-0.275711\pi\) | |||||||
\(888\) | 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 | \(0.159744\pi\) | ||||
−0.876694 | + | 0.481049i | \(0.840256\pi\) | |||||||
\(908\) | 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 | \(-0.287973\pi\) | ||||
0.617926 | + | 0.786236i | \(0.287973\pi\) | |||||||
\(938\) | 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 | \(-0.122991\pi\) | ||||
0.926276 | + | 0.376845i | \(0.122991\pi\) | |||||||
\(948\) | 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 | \(-0.908351\pi\) | ||
0.958836 | − | 0.283962i | \(-0.0916490\pi\) | |||||||
\(954\) | 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 | \(-0.606013\pi\) | ||||
−0.326927 | + | 0.945050i | \(0.606013\pi\) | |||||||
\(968\) | 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 | \(0.0408833\pi\) | ||||
−0.991763 | + | 0.128086i | \(0.959117\pi\) | |||||||
\(978\) | 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 | \(0.228181\pi\) | ||||
−0.753879 | + | 0.657014i | \(0.771819\pi\) | |||||||
\(984\) | 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 | \(-0.794497\pi\) | ||||
−0.798735 | + | 0.601683i | \(0.794497\pi\) | |||||||
\(998\) | 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.g.1101.8 | yes | 14 | |
5.2 | odd | 4 | 1900.3.g.d.949.15 | 28 | |||
5.3 | odd | 4 | 1900.3.g.d.949.14 | 28 | |||
5.4 | even | 2 | 1900.3.e.h.1101.7 | yes | 14 | ||
19.18 | odd | 2 | inner | 1900.3.e.g.1101.7 | ✓ | 14 | |
95.18 | even | 4 | 1900.3.g.d.949.16 | 28 | |||
95.37 | even | 4 | 1900.3.g.d.949.13 | 28 | |||
95.94 | odd | 2 | 1900.3.e.h.1101.8 | yes | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1900.3.e.g.1101.7 | ✓ | 14 | 19.18 | odd | 2 | inner | |
1900.3.e.g.1101.8 | yes | 14 | 1.1 | even | 1 | trivial | |
1900.3.e.h.1101.7 | yes | 14 | 5.4 | even | 2 | ||
1900.3.e.h.1101.8 | yes | 14 | 95.94 | odd | 2 | ||
1900.3.g.d.949.13 | 28 | 95.37 | even | 4 | |||
1900.3.g.d.949.14 | 28 | 5.3 | odd | 4 | |||
1900.3.g.d.949.15 | 28 | 5.2 | odd | 4 | |||
1900.3.g.d.949.16 | 28 | 95.18 | even | 4 |