Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4032,3,Mod(449,4032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4032, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4032.449");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 4032.d (of order \(2\), degree \(1\), not 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: | \(109.864042590\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 44x^{10} + 719x^{8} + 5356x^{6} + 17809x^{4} + 20000x^{2} + 144 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{13} \) |
Twist minimal: | no (minimal twist has level 2016) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.4 | ||
Root | \(3.75209i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4032.449 |
Dual form | 4032.3.d.o.449.9 |
$q$-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 \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1793\) | \(3781\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 3.85589i | − 0.771179i | −0.922670 | − | 0.385589i | \(-0.873998\pi\) | ||||
0.922670 | − | 0.385589i | \(-0.126002\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.64575 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.89341i | 0.626673i | 0.949642 | + | 0.313337i | \(0.101447\pi\) | ||||
−0.949642 | + | 0.313337i | \(0.898553\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −20.9186 | −1.60912 | −0.804562 | − | 0.593869i | \(-0.797600\pi\) | ||||
−0.804562 | + | 0.593869i | \(0.797600\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 3.42256i | − 0.201327i | −0.994921 | − | 0.100664i | \(-0.967903\pi\) | ||||
0.994921 | − | 0.100664i | \(-0.0320966\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 11.1466 | 0.586666 | 0.293333 | − | 0.956010i | \(-0.405236\pi\) | ||||
0.293333 | + | 0.956010i | \(0.405236\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 25.1631i | 1.09405i | 0.837117 | + | 0.547023i | \(0.184239\pi\) | ||||
−0.837117 | + | 0.547023i | \(0.815761\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 10.1321 | 0.405283 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.948063i | 0.0326918i | 0.999866 | + | 0.0163459i | \(0.00520330\pi\) | ||||
−0.999866 | + | 0.0163459i | \(0.994797\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.63987 | −0.214189 | −0.107095 | − | 0.994249i | \(-0.534155\pi\) | ||||
−0.107095 | + | 0.994249i | \(0.534155\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 10.2017i | 0.291478i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.63459 | −0.152286 | −0.0761430 | − | 0.997097i | \(-0.524261\pi\) | ||||
−0.0761430 | + | 0.997097i | \(0.524261\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 30.2404i | − 0.737570i | −0.929515 | − | 0.368785i | \(-0.879774\pi\) | ||||
0.929515 | − | 0.368785i | \(-0.120226\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −16.6926 | −0.388201 | −0.194100 | − | 0.980982i | \(-0.562179\pi\) | ||||
−0.194100 | + | 0.980982i | \(0.562179\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 9.40243i | − 0.200052i | −0.994985 | − | 0.100026i | \(-0.968107\pi\) | ||||
0.994985 | − | 0.100026i | \(-0.0318925\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 44.4345i | 0.838387i | 0.907897 | + | 0.419194i | \(0.137687\pi\) | ||||
−0.907897 | + | 0.419194i | \(0.862313\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 26.5802 | 0.483277 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 52.2908i | 0.886285i | 0.896451 | + | 0.443143i | \(0.146137\pi\) | ||||
−0.896451 | + | 0.443143i | \(0.853863\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −48.5469 | −0.795852 | −0.397926 | − | 0.917418i | \(-0.630270\pi\) | ||||
−0.397926 | + | 0.917418i | \(0.630270\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 80.6599i | 1.24092i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 63.5263 | 0.948154 | 0.474077 | − | 0.880483i | \(-0.342782\pi\) | ||||
0.474077 | + | 0.880483i | \(0.342782\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 35.6768i | − 0.502490i | −0.967924 | − | 0.251245i | \(-0.919160\pi\) | ||||
0.967924 | − | 0.251245i | \(-0.0808400\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 19.4279 | 0.266135 | 0.133068 | − | 0.991107i | \(-0.457517\pi\) | ||||
0.133068 | + | 0.991107i | \(0.457517\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 18.2382i | − 0.236860i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 152.405 | 1.92918 | 0.964588 | − | 0.263760i | \(-0.0849627\pi\) | ||||
0.964588 | + | 0.263760i | \(0.0849627\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 97.7442i | − 1.17764i | −0.808264 | − | 0.588821i | \(-0.799592\pi\) | ||||
0.808264 | − | 0.588821i | \(-0.200408\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13.1970 | −0.155259 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 99.3657i | 1.11647i | 0.829684 | + | 0.558234i | \(0.188521\pi\) | ||||
−0.829684 | + | 0.558234i | \(0.811479\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 55.3454 | 0.608192 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 42.9803i | − 0.452424i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 133.405 | 1.37531 | 0.687657 | − | 0.726036i | \(-0.258639\pi\) | ||||
0.687657 | + | 0.726036i | \(0.258639\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 161.774i | − 1.60172i | −0.598852 | − | 0.800860i | \(-0.704376\pi\) | ||||
0.598852 | − | 0.800860i | \(-0.295624\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −88.2106 | −0.856414 | −0.428207 | − | 0.903681i | \(-0.640855\pi\) | ||||
−0.428207 | + | 0.903681i | \(0.640855\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 128.321i | − 1.19926i | −0.800276 | − | 0.599632i | \(-0.795314\pi\) | ||||
0.800276 | − | 0.599632i | \(-0.204686\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −158.797 | −1.45686 | −0.728429 | − | 0.685122i | \(-0.759749\pi\) | ||||
−0.728429 | + | 0.685122i | \(0.759749\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.63061i | 0.0852266i | 0.999092 | + | 0.0426133i | \(0.0135684\pi\) | ||||
−0.999092 | + | 0.0426133i | \(0.986432\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 97.0261 | 0.843705 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.05525i | 0.0760946i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 73.4809 | 0.607280 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 135.466i | − 1.08372i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 187.202 | 1.47403 | 0.737017 | − | 0.675875i | \(-0.236234\pi\) | ||||
0.737017 | + | 0.675875i | \(0.236234\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 103.874i | − 0.792928i | −0.918050 | − | 0.396464i | \(-0.870237\pi\) | ||||
0.918050 | − | 0.396464i | \(-0.129763\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −29.4913 | −0.221739 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 198.199i | 1.44671i | 0.690476 | + | 0.723356i | \(0.257401\pi\) | ||||
−0.690476 | + | 0.723356i | \(0.742599\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −59.7079 | −0.429554 | −0.214777 | − | 0.976663i | \(-0.568902\pi\) | ||||
−0.214777 | + | 0.976663i | \(0.568902\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 144.200i | − 1.00839i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.65563 | 0.0252112 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 56.1968i | − 0.377160i | −0.982058 | − | 0.188580i | \(-0.939612\pi\) | ||||
0.982058 | − | 0.188580i | \(-0.0603884\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.98303 | −0.0594903 | −0.0297451 | − | 0.999558i | \(-0.509470\pi\) | ||||
−0.0297451 | + | 0.999558i | \(0.509470\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 25.6026i | 0.165178i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.3517 | 0.0850424 | 0.0425212 | − | 0.999096i | \(-0.486461\pi\) | ||||
0.0425212 | + | 0.999096i | \(0.486461\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 66.5752i | − 0.413511i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 136.711 | 0.838715 | 0.419358 | − | 0.907821i | \(-0.362255\pi\) | ||||
0.419358 | + | 0.907821i | \(0.362255\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 45.5297i | − 0.272633i | −0.990665 | − | 0.136316i | \(-0.956474\pi\) | ||||
0.990665 | − | 0.136316i | \(-0.0435264\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 268.588 | 1.58928 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 38.8939i | − 0.224820i | −0.993662 | − | 0.112410i | \(-0.964143\pi\) | ||||
0.993662 | − | 0.112410i | \(-0.0358570\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −26.8070 | −0.153183 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 68.6751i | 0.383660i | 0.981428 | + | 0.191830i | \(0.0614422\pi\) | ||||
−0.981428 | + | 0.191830i | \(0.938558\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 104.985 | 0.580026 | 0.290013 | − | 0.957023i | \(-0.406340\pi\) | ||||
0.290013 | + | 0.957023i | \(0.406340\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 21.7264i | 0.117440i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 23.5931 | 0.126166 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 43.1970i | − 0.226162i | −0.993586 | − | 0.113081i | \(-0.963928\pi\) | ||||
0.993586 | − | 0.113081i | \(-0.0360720\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −92.0404 | −0.476893 | −0.238447 | − | 0.971156i | \(-0.576638\pi\) | ||||
−0.238447 | + | 0.971156i | \(0.576638\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 86.2740i | − 0.437939i | −0.975732 | − | 0.218969i | \(-0.929730\pi\) | ||||
0.975732 | − | 0.218969i | \(-0.0702695\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.93405 | 0.0197691 | 0.00988456 | − | 0.999951i | \(-0.496854\pi\) | ||||
0.00988456 | + | 0.999951i | \(0.496854\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 2.50834i | − 0.0123563i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −116.604 | −0.568798 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 76.8384i | 0.367648i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −94.1420 | −0.446171 | −0.223085 | − | 0.974799i | \(-0.571613\pi\) | ||||
−0.223085 | + | 0.974799i | \(0.571613\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 64.3650i | 0.299372i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 17.5675 | 0.0809560 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 71.5953i | 0.323961i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −149.630 | −0.670986 | −0.335493 | − | 0.942043i | \(-0.608903\pi\) | ||||
−0.335493 | + | 0.942043i | \(0.608903\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 24.5021i | − 0.107939i | −0.998543 | − | 0.0539693i | \(-0.982813\pi\) | ||||
0.998543 | − | 0.0539693i | \(-0.0171873\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −335.268 | −1.46405 | −0.732027 | − | 0.681276i | \(-0.761425\pi\) | ||||
−0.732027 | + | 0.681276i | \(0.761425\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 60.9364i | 0.261530i | 0.991413 | + | 0.130765i | \(0.0417433\pi\) | ||||
−0.991413 | + | 0.130765i | \(0.958257\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −36.2548 | −0.154276 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 319.472i | − 1.33670i | −0.743846 | − | 0.668351i | \(-0.767000\pi\) | ||||
0.743846 | − | 0.668351i | \(-0.233000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 274.230 | 1.13789 | 0.568943 | − | 0.822377i | \(-0.307353\pi\) | ||||
0.568943 | + | 0.822377i | \(0.307353\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 26.9913i | − 0.110168i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −233.172 | −0.944017 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 455.650i | − 1.81534i | −0.419687 | − | 0.907669i | \(-0.637860\pi\) | ||||
0.419687 | − | 0.907669i | \(-0.362140\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −173.459 | −0.685610 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 86.2818i | − 0.335727i | −0.985810 | − | 0.167863i | \(-0.946313\pi\) | ||||
0.985810 | − | 0.167863i | \(-0.0536868\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.9077 | 0.0575587 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 290.234i | − 1.10355i | −0.833992 | − | 0.551776i | \(-0.813950\pi\) | ||||
0.833992 | − | 0.551776i | \(-0.186050\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 171.335 | 0.646546 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 309.859i | − 1.15189i | −0.817488 | − | 0.575945i | \(-0.804634\pi\) | ||||
0.817488 | − | 0.575945i | \(-0.195366\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 475.422 | 1.75432 | 0.877162 | − | 0.480195i | \(-0.159434\pi\) | ||||
0.877162 | + | 0.480195i | \(0.159434\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 69.8446i | 0.253980i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −399.021 | −1.44051 | −0.720254 | − | 0.693710i | \(-0.755975\pi\) | ||||
−0.720254 | + | 0.693710i | \(0.755975\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 57.9182i | 0.206115i | 0.994675 | + | 0.103057i | \(0.0328625\pi\) | ||||
−0.994675 | + | 0.103057i | \(0.967137\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −187.466 | −0.662423 | −0.331211 | − | 0.943557i | \(-0.607457\pi\) | ||||
−0.331211 | + | 0.943557i | \(0.607457\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 80.0085i | 0.278775i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 277.286 | 0.959467 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 59.4001i | − 0.202731i | −0.994849 | − | 0.101365i | \(-0.967679\pi\) | ||||
0.994849 | − | 0.101365i | \(-0.0323211\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 201.628 | 0.683485 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 526.376i | − 1.76046i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 44.1646 | 0.146726 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 187.192i | 0.613744i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 230.365 | 0.750374 | 0.375187 | − | 0.926949i | \(-0.377579\pi\) | ||||
0.375187 | + | 0.926949i | \(0.377579\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 285.635i | − 0.918440i | −0.888323 | − | 0.459220i | \(-0.848129\pi\) | ||||
0.888323 | − | 0.459220i | \(-0.151871\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −158.225 | −0.505513 | −0.252756 | − | 0.967530i | \(-0.581337\pi\) | ||||
−0.252756 | + | 0.967530i | \(0.581337\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 398.409i | 1.25681i | 0.777887 | + | 0.628405i | \(0.216292\pi\) | ||||
−0.777887 | + | 0.628405i | \(0.783708\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.53538 | −0.0204871 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 38.1501i | − 0.118112i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −211.949 | −0.652151 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 24.8765i | 0.0756124i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 625.718 | 1.89039 | 0.945193 | − | 0.326511i | \(-0.105873\pi\) | ||||
0.945193 | + | 0.326511i | \(0.105873\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 244.951i | − 0.731196i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −62.6776 | −0.185987 | −0.0929934 | − | 0.995667i | \(-0.529644\pi\) | ||||
−0.0929934 | + | 0.995667i | \(0.529644\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 45.7713i | − 0.134227i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.5203 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 470.894i | − 1.35704i | −0.734580 | − | 0.678522i | \(-0.762621\pi\) | ||||
0.734580 | − | 0.678522i | \(-0.237379\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −99.3869 | −0.284776 | −0.142388 | − | 0.989811i | \(-0.545478\pi\) | ||||
−0.142388 | + | 0.989811i | \(0.545478\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 606.481i | − 1.71808i | −0.511911 | − | 0.859039i | \(-0.671062\pi\) | ||||
0.511911 | − | 0.859039i | \(-0.328938\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −137.566 | −0.387510 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 572.425i | − 1.59450i | −0.603651 | − | 0.797249i | \(-0.706288\pi\) | ||||
0.603651 | − | 0.797249i | \(-0.293712\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −236.752 | −0.655823 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 74.9118i | − 0.205238i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 384.530 | 1.04777 | 0.523883 | − | 0.851790i | \(-0.324483\pi\) | ||||
0.523883 | + | 0.851790i | \(0.324483\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 117.563i | − 0.316881i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 579.800 | 1.55442 | 0.777212 | − | 0.629239i | \(-0.216633\pi\) | ||||
0.777212 | + | 0.629239i | \(0.216633\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 19.8322i | − 0.0526052i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 128.966 | 0.340280 | 0.170140 | − | 0.985420i | \(-0.445578\pi\) | ||||
0.170140 | + | 0.985420i | \(0.445578\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 525.916i | 1.37315i | 0.727059 | + | 0.686575i | \(0.240887\pi\) | ||||
−0.727059 | + | 0.686575i | \(0.759113\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −70.3247 | −0.182662 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 134.120i | 0.344781i | 0.985029 | + | 0.172391i | \(0.0551491\pi\) | ||||
−0.985029 | + | 0.172391i | \(0.944851\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 86.1222 | 0.220261 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 587.657i | − 1.48774i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 275.606 | 0.694222 | 0.347111 | − | 0.937824i | \(-0.387163\pi\) | ||||
0.347111 | + | 0.937824i | \(0.387163\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 387.895i | 0.967320i | 0.875256 | + | 0.483660i | \(0.160693\pi\) | ||||
−0.875256 | + | 0.483660i | \(0.839307\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 138.897 | 0.344657 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 38.8415i | − 0.0954336i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −261.605 | −0.639622 | −0.319811 | − | 0.947481i | \(-0.603619\pi\) | ||||
−0.319811 | + | 0.947481i | \(0.603619\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 138.349i | − 0.334984i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −376.891 | −0.908172 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 345.798i | 0.825293i | 0.910891 | + | 0.412646i | \(0.135395\pi\) | ||||
−0.910891 | + | 0.412646i | \(0.864605\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 484.947 | 1.15189 | 0.575947 | − | 0.817487i | \(-0.304633\pi\) | ||||
0.575947 | + | 0.817487i | \(0.304633\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 34.6777i | − 0.0815946i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 128.443 | 0.300804 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 727.249i | − 1.68735i | −0.536851 | − | 0.843677i | \(-0.680386\pi\) | ||||
0.536851 | − | 0.843677i | \(-0.319614\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −211.148 | −0.487640 | −0.243820 | − | 0.969821i | \(-0.578401\pi\) | ||||
−0.243820 | + | 0.969821i | \(0.578401\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 280.484i | 0.641840i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 759.909 | 1.73100 | 0.865500 | − | 0.500908i | \(-0.167001\pi\) | ||||
0.865500 | + | 0.500908i | \(0.167001\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 121.346i | 0.273919i | 0.990577 | + | 0.136959i | \(0.0437330\pi\) | ||||
−0.990577 | + | 0.136959i | \(0.956267\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 383.143 | 0.860996 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 409.519i | 0.912068i | 0.889962 | + | 0.456034i | \(0.150730\pi\) | ||||
−0.889962 | + | 0.456034i | \(0.849270\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 208.459 | 0.462215 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 213.406i | − 0.469024i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 375.001 | 0.820570 | 0.410285 | − | 0.911957i | \(-0.365429\pi\) | ||||
0.410285 | + | 0.911957i | \(0.365429\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 713.233i | 1.54714i | 0.633709 | + | 0.773571i | \(0.281532\pi\) | ||||
−0.633709 | + | 0.773571i | \(0.718468\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 642.413 | 1.38750 | 0.693751 | − | 0.720215i | \(-0.255957\pi\) | ||||
0.693751 | + | 0.720215i | \(0.255957\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 251.943i | − 0.539492i | −0.962932 | − | 0.269746i | \(-0.913060\pi\) | ||||
0.962932 | − | 0.269746i | \(-0.0869397\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −168.075 | −0.358369 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 115.069i | − 0.243275i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 112.939 | 0.237766 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 174.575i | − 0.364458i | −0.983256 | − | 0.182229i | \(-0.941669\pi\) | ||||
0.983256 | − | 0.182229i | \(-0.0583312\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 117.868 | 0.245047 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 514.397i | − 1.06061i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −169.624 | −0.348304 | −0.174152 | − | 0.984719i | \(-0.555718\pi\) | ||||
−0.174152 | + | 0.984719i | \(0.555718\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 56.9134i | 0.115913i | 0.998319 | + | 0.0579566i | \(0.0184585\pi\) | ||||
−0.998319 | + | 0.0579566i | \(0.981541\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.24481 | 0.00658176 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 94.3919i | 0.189923i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21.0923 | 0.0422691 | 0.0211345 | − | 0.999777i | \(-0.493272\pi\) | ||||
0.0211345 | + | 0.999777i | \(0.493272\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 420.228i | 0.835444i | 0.908575 | + | 0.417722i | \(0.137171\pi\) | ||||
−0.908575 | + | 0.417722i | \(0.862829\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −623.782 | −1.23521 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 242.312i | − 0.476055i | −0.971258 | − | 0.238028i | \(-0.923499\pi\) | ||||
0.971258 | − | 0.238028i | \(-0.0765009\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −51.4013 | −0.100590 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 340.131i | 0.660448i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 64.8148 | 0.125367 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 52.9968i | − 0.101721i | −0.998706 | − | 0.0508607i | \(-0.983804\pi\) | ||||
0.998706 | − | 0.0508607i | \(-0.0161965\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −136.510 | −0.261013 | −0.130506 | − | 0.991447i | \(-0.541660\pi\) | ||||
−0.130506 | + | 0.991447i | \(0.541660\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 22.7254i | 0.0431222i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −104.180 | −0.196938 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 632.586i | 1.18684i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −494.793 | −0.924847 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 48.2538i | 0.0895248i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 305.615 | 0.564908 | 0.282454 | − | 0.959281i | \(-0.408852\pi\) | ||||
0.282454 | + | 0.959281i | \(0.408852\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 612.306i | 1.12350i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −102.020 | −0.186508 | −0.0932542 | − | 0.995642i | \(-0.529727\pi\) | ||||
−0.0932542 | + | 0.995642i | \(0.529727\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.5677i | 0.0191792i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −403.226 | −0.729160 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 403.429i | − 0.724289i | −0.932122 | − | 0.362145i | \(-0.882045\pi\) | ||||
0.932122 | − | 0.362145i | \(-0.117955\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 349.187 | 0.624663 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 813.539i | 1.44501i | 0.691367 | + | 0.722503i | \(0.257009\pi\) | ||||
−0.691367 | + | 0.722503i | \(0.742991\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 37.1346 | 0.0657250 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 1045.50i | − 1.83743i | −0.394923 | − | 0.918714i | \(-0.629229\pi\) | ||||
0.394923 | − | 0.918714i | \(-0.370771\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 939.318 | 1.64504 | 0.822521 | − | 0.568735i | \(-0.192567\pi\) | ||||
0.822521 | + | 0.568735i | \(0.192567\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 254.954i | 0.443399i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −456.546 | −0.791241 | −0.395620 | − | 0.918414i | \(-0.629470\pi\) | ||||
−0.395620 | + | 0.918414i | \(0.629470\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 258.607i | 0.445107i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −306.305 | −0.525395 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 555.407i | − 0.946178i | −0.881015 | − | 0.473089i | \(-0.843139\pi\) | ||||
0.881015 | − | 0.473089i | \(-0.156861\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −74.0123 | −0.125658 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 506.971i | − 0.854925i | −0.904033 | − | 0.427463i | \(-0.859408\pi\) | ||||
0.904033 | − | 0.427463i | \(-0.140592\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 34.9161 | 0.0586825 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 730.835i | 1.22009i | 0.792366 | + | 0.610046i | \(0.208849\pi\) | ||||
−0.792366 | + | 0.610046i | \(0.791151\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −196.232 | −0.326510 | −0.163255 | − | 0.986584i | \(-0.552199\pi\) | ||||
−0.163255 | + | 0.986584i | \(0.552199\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 283.335i | − 0.468322i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 655.779 | 1.08036 | 0.540180 | − | 0.841549i | \(-0.318356\pi\) | ||||
0.540180 | + | 0.841549i | \(0.318356\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 196.686i | 0.321908i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 341.221 | 0.556641 | 0.278320 | − | 0.960488i | \(-0.410222\pi\) | ||||
0.278320 | + | 0.960488i | \(0.410222\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 246.010i | − 0.398720i | −0.979926 | − | 0.199360i | \(-0.936114\pi\) | ||||
0.979926 | − | 0.199360i | \(-0.0638863\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 760.921 | 1.22928 | 0.614638 | − | 0.788810i | \(-0.289302\pi\) | ||||
0.614638 | + | 0.788810i | \(0.289302\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 262.897i | − 0.421985i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −269.039 | −0.430462 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 19.2847i | 0.0306594i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −70.2909 | −0.111396 | −0.0556980 | − | 0.998448i | \(-0.517738\pi\) | ||||
−0.0556980 | + | 0.998448i | \(0.517738\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 721.832i | − 1.13674i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −146.430 | −0.229875 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 1116.18i | − 1.74130i | −0.491900 | − | 0.870652i | \(-0.663697\pi\) | ||||
0.491900 | − | 0.870652i | \(-0.336303\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −513.359 | −0.798381 | −0.399191 | − | 0.916868i | \(-0.630709\pi\) | ||||
−0.399191 | + | 0.916868i | \(0.630709\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 249.620i | − 0.385812i | −0.981217 | − | 0.192906i | \(-0.938209\pi\) | ||||
0.981217 | − | 0.192906i | \(-0.0617912\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −360.462 | −0.555412 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 916.213i | 1.40308i | 0.712629 | + | 0.701541i | \(0.247504\pi\) | ||||
−0.712629 | + | 0.701541i | \(0.752496\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −400.525 | −0.611489 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 1080.96i | − 1.64030i | −0.572149 | − | 0.820149i | \(-0.693890\pi\) | ||||
0.572149 | − | 0.820149i | \(-0.306110\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 449.943 | 0.680701 | 0.340350 | − | 0.940299i | \(-0.389454\pi\) | ||||
0.340350 | + | 0.940299i | \(0.389454\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 113.715i | 0.171000i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −23.8562 | −0.0357664 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 334.654i | − 0.498739i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −614.341 | −0.912840 | −0.456420 | − | 0.889764i | \(-0.650869\pi\) | ||||
−0.456420 | + | 0.889764i | \(0.650869\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 211.920i | 0.313029i | 0.987676 | + | 0.156514i | \(0.0500258\pi\) | ||||
−0.987676 | + | 0.156514i | \(0.949974\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −352.957 | −0.519820 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 816.178i | 1.19499i | 0.801873 | + | 0.597495i | \(0.203837\pi\) | ||||
−0.801873 | + | 0.597495i | \(0.796163\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 764.236 | 1.11567 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 929.508i | − 1.34907i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1070.12 | −1.54866 | −0.774330 | − | 0.632782i | \(-0.781913\pi\) | ||||
−0.774330 | + | 0.632782i | \(0.781913\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 230.227i | 0.331263i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −103.500 | −0.148493 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 600.000i | 0.855920i | 0.903798 | + | 0.427960i | \(0.140768\pi\) | ||||
−0.903798 | + | 0.427960i | \(0.859232\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −62.8067 | −0.0893410 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 428.013i | 0.605393i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 911.547 | 1.28568 | 0.642840 | − | 0.766001i | \(-0.277756\pi\) | ||||
0.642840 | + | 0.766001i | \(0.277756\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 167.080i | − 0.234333i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −556.022 | −0.777653 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 515.213i | − 0.716569i | −0.933612 | − | 0.358284i | \(-0.883362\pi\) | ||||
0.933612 | − | 0.358284i | \(-0.116638\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 233.383 | 0.323694 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.60586i | 0.0132495i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1223.59 | 1.68307 | 0.841534 | − | 0.540204i | \(-0.181653\pi\) | ||||
0.841534 | + | 0.540204i | \(0.181653\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 57.1316i | 0.0781554i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 376.404 | 0.513512 | 0.256756 | − | 0.966476i | \(-0.417346\pi\) | ||||
0.256756 | + | 0.966476i | \(0.417346\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 437.913i | 0.594183i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 504.166 | 0.682228 | 0.341114 | − | 0.940022i | \(-0.389196\pi\) | ||||
0.341114 | + | 0.940022i | \(0.389196\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1134.40i | 1.52679i | 0.645934 | + | 0.763393i | \(0.276468\pi\) | ||||
−0.645934 | + | 0.763393i | \(0.723532\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −216.689 | −0.290857 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 339.506i | 0.453279i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 949.876 | 1.26481 | 0.632407 | − | 0.774636i | \(-0.282067\pi\) | ||||
0.632407 | + | 0.774636i | \(0.282067\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 34.6376i | 0.0458777i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −750.370 | −0.991241 | −0.495621 | − | 0.868539i | \(-0.665059\pi\) | ||||
−0.495621 | + | 0.868539i | \(0.665059\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 1100.48i | − 1.44610i | −0.690794 | − | 0.723052i | \(-0.742739\pi\) | ||||
0.690794 | − | 0.723052i | \(-0.257261\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 420.139 | 0.550640 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 1093.85i | − 1.42614i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −525.202 | −0.682968 | −0.341484 | − | 0.939888i | \(-0.610929\pi\) | ||||
−0.341484 | + | 0.939888i | \(0.610929\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 211.562i | − 0.273689i | −0.990593 | − | 0.136845i | \(-0.956304\pi\) | ||||
0.990593 | − | 0.136845i | \(-0.0436961\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −67.2758 | −0.0868074 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 337.079i | − 0.432707i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 245.935 | 0.314897 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 51.4826i | − 0.0655829i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1219.20 | 1.54917 | 0.774585 | − | 0.632470i | \(-0.217959\pi\) | ||||
0.774585 | + | 0.632470i | \(0.217959\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 25.4802i | − 0.0322126i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1015.53 | 1.28062 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1096.10i | 1.37528i | 0.726053 | + | 0.687639i | \(0.241353\pi\) | ||||
−0.726053 | + | 0.687639i | \(0.758647\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −32.1804 | −0.0402759 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 133.924i | 0.166780i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −256.707 | −0.318891 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 213.728i | 0.264188i | 0.991237 | + | 0.132094i | \(0.0421701\pi\) | ||||
−0.991237 | + | 0.132094i | \(0.957830\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −263.712 | −0.325169 | −0.162585 | − | 0.986695i | \(-0.551983\pi\) | ||||
−0.162585 | + | 0.986695i | \(0.551983\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 527.141i | − 0.646799i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −186.067 | −0.227744 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 401.805i | − 0.489409i | −0.969598 | − | 0.244705i | \(-0.921309\pi\) | ||||
0.969598 | − | 0.244705i | \(-0.0786910\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −682.384 | −0.829142 | −0.414571 | − | 0.910017i | \(-0.636068\pi\) | ||||
−0.414571 | + | 0.910017i | \(0.636068\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 964.623i | − 1.16641i | −0.812324 | − | 0.583206i | \(-0.801798\pi\) | ||||
0.812324 | − | 0.583206i | \(-0.198202\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 379.477 | 0.457753 | 0.228877 | − | 0.973455i | \(-0.426495\pi\) | ||||
0.228877 | + | 0.973455i | \(0.426495\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 23.9580i | − 0.0287610i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −175.558 | −0.210249 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 616.642i | 0.734973i | 0.930029 | + | 0.367487i | \(0.119782\pi\) | ||||
−0.930029 | + | 0.367487i | \(0.880218\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 840.101 | 0.998931 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 1035.65i | − 1.22562i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −194.412 | −0.229530 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 141.783i | − 0.166608i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −411.601 | −0.482533 | −0.241267 | − | 0.970459i | \(-0.577563\pi\) | ||||
−0.241267 | + | 0.970459i | \(0.577563\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 564.267i | 0.658421i | 0.944256 | + | 0.329211i | \(0.106783\pi\) | ||||
−0.944256 | + | 0.329211i | \(0.893217\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1196.28 | −1.39265 | −0.696324 | − | 0.717728i | \(-0.745182\pi\) | ||||
−0.696324 | + | 0.717728i | \(0.745182\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 1171.34i | − 1.35729i | −0.734468 | − | 0.678644i | \(-0.762568\pi\) | ||||
0.734468 | − | 0.678644i | \(-0.237432\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −149.971 | −0.173377 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1050.59i | 1.20896i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1328.88 | −1.52570 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 358.408i | 0.409609i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 239.563 | 0.273162 | 0.136581 | − | 0.990629i | \(-0.456389\pi\) | ||||
0.136581 | + | 0.990629i | \(0.456389\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1004.79i | 1.14051i | 0.821468 | + | 0.570255i | \(0.193156\pi\) | ||||
−0.821468 | + | 0.570255i | \(0.806844\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1469.24 | −1.66391 | −0.831957 | − | 0.554841i | \(-0.812779\pi\) | ||||
−0.831957 | + | 0.554841i | \(0.812779\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1327.12i | 1.49619i | 0.663591 | + | 0.748096i | \(0.269032\pi\) | ||||
−0.663591 | + | 0.748096i | \(0.730968\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −495.290 | −0.557132 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 104.806i | − 0.117363i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 264.804 | 0.295870 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 6.29502i | − 0.00700224i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 152.080 | 0.168790 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 404.810i | − 0.447304i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1238.98 | 1.36602 | 0.683010 | − | 0.730409i | \(-0.260671\pi\) | ||||
0.683010 | + | 0.730409i | \(0.260671\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 302.136i | − 0.331653i | −0.986155 | − | 0.165826i | \(-0.946971\pi\) | ||||
0.986155 | − | 0.165826i | \(-0.0530292\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 673.791 | 0.737996 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 274.824i | 0.299699i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1023.81 | −1.11404 | −0.557022 | − | 0.830498i | \(-0.688056\pi\) | ||||
−0.557022 | + | 0.830498i | \(0.688056\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 746.309i | 0.808569i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −57.0901 | −0.0617190 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 330.204i | − 0.355441i | −0.984081 | − | 0.177720i | \(-0.943128\pi\) | ||||
0.984081 | − | 0.177720i | \(-0.0568722\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 78.0265 | 0.0838094 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 90.9726i | − 0.0972969i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −320.286 | −0.341821 | −0.170910 | − | 0.985287i | \(-0.554671\pi\) | ||||
−0.170910 | + | 0.985287i | \(0.554671\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 1473.27i | − 1.56565i | −0.622244 | − | 0.782823i | \(-0.713779\pi\) | ||||
0.622244 | − | 0.782823i | \(-0.286221\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 760.940 | 0.806936 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1058.79i | 1.11805i | 0.829152 | + | 0.559023i | \(0.188824\pi\) | ||||
−0.829152 | + | 0.559023i | \(0.811176\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −406.404 | −0.428245 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1683.17i | 1.76619i | 0.469199 | + | 0.883093i | \(0.344543\pi\) | ||||
−0.469199 | + | 0.883093i | \(0.655457\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −166.563 | −0.174412 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 524.387i | − 0.546806i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −916.912 | −0.954123 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 354.898i | 0.367770i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −764.881 | −0.790983 | −0.395492 | − | 0.918470i | \(-0.629426\pi\) | ||||
−0.395492 | + | 0.918470i | \(0.629426\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 631.310i | − 0.650165i | −0.945686 | − | 0.325082i | \(-0.894608\pi\) | ||||
0.945686 | − | 0.325082i | \(-0.105392\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 157.972 | 0.162356 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 367.900i | − 0.376560i | −0.982115 | − | 0.188280i | \(-0.939709\pi\) | ||||
0.982115 | − | 0.188280i | \(-0.0602913\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −684.968 | −0.699661 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1678.27i | 1.70729i | 0.520852 | + | 0.853647i | \(0.325614\pi\) | ||||
−0.520852 | + | 0.853647i | \(0.674386\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −332.663 | −0.337729 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 420.038i | − 0.424710i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1079.56 | −1.08936 | −0.544681 | − | 0.838644i | \(-0.683349\pi\) | ||||
−0.544681 | + | 0.838644i | \(0.683349\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 15.1693i | − 0.0152455i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 677.368 | 0.679406 | 0.339703 | − | 0.940533i | \(-0.389673\pi\) | ||||
0.339703 | + | 0.940533i | \(0.389673\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4032.3.d.o.449.4 | 12 | ||
3.2 | odd | 2 | inner | 4032.3.d.o.449.9 | 12 | ||
4.3 | odd | 2 | 4032.3.d.n.449.4 | 12 | |||
8.3 | odd | 2 | 2016.3.d.f.449.9 | yes | 12 | ||
8.5 | even | 2 | 2016.3.d.e.449.9 | yes | 12 | ||
12.11 | even | 2 | 4032.3.d.n.449.9 | 12 | |||
24.5 | odd | 2 | 2016.3.d.e.449.4 | ✓ | 12 | ||
24.11 | even | 2 | 2016.3.d.f.449.4 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2016.3.d.e.449.4 | ✓ | 12 | 24.5 | odd | 2 | ||
2016.3.d.e.449.9 | yes | 12 | 8.5 | even | 2 | ||
2016.3.d.f.449.4 | yes | 12 | 24.11 | even | 2 | ||
2016.3.d.f.449.9 | yes | 12 | 8.3 | odd | 2 | ||
4032.3.d.n.449.4 | 12 | 4.3 | odd | 2 | |||
4032.3.d.n.449.9 | 12 | 12.11 | even | 2 | |||
4032.3.d.o.449.4 | 12 | 1.1 | even | 1 | trivial | ||
4032.3.d.o.449.9 | 12 | 3.2 | odd | 2 | inner |