Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,3,Mod(1025,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, 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("1152.1025");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.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: | \(31.3897264543\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{41}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1025.4 | ||
Root | \(-1.22474 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1152.1025 |
Dual form | 1152.3.e.f.1025.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.87832i | 0.975663i | 0.872938 | + | 0.487832i | \(0.162212\pi\) | ||||
−0.872938 | + | 0.487832i | \(0.837788\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 11.7980 | 1.68542 | 0.842711 | − | 0.538366i | \(-0.180958\pi\) | ||||
0.842711 | + | 0.538366i | \(0.180958\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 9.75663i | 0.886966i | 0.896283 | + | 0.443483i | \(0.146257\pi\) | ||||
−0.896283 | + | 0.443483i | \(0.853743\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −22.6969 | −1.74592 | −0.872959 | − | 0.487793i | \(-0.837802\pi\) | ||||
−0.872959 | + | 0.487793i | \(0.837802\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 22.1988i | 1.30581i | 0.757438 | + | 0.652907i | \(0.226451\pi\) | ||||
−0.757438 | + | 0.652907i | \(0.773549\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −17.7980 | −0.936735 | −0.468367 | − | 0.883534i | \(-0.655158\pi\) | ||||
−0.468367 | + | 0.883534i | \(0.655158\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 14.1421i | 0.614875i | 0.951568 | + | 0.307438i | \(0.0994716\pi\) | ||||
−0.951568 | + | 0.307438i | \(0.900528\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.20204 | 0.0480816 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 20.0061i | − 0.689865i | −0.938628 | − | 0.344932i | \(-0.887902\pi\) | ||||
0.938628 | − | 0.344932i | \(-0.112098\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −39.7980 | −1.28381 | −0.641903 | − | 0.766786i | \(-0.721855\pi\) | ||||
−0.641903 | + | 0.766786i | \(0.721855\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 57.5542i | 1.64440i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.40408 | −0.0649752 | −0.0324876 | − | 0.999472i | \(-0.510343\pi\) | ||||
−0.0324876 | + | 0.999472i | \(0.510343\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 64.3395i | − 1.56926i | −0.619967 | − | 0.784628i | \(-0.712854\pi\) | ||||
0.619967 | − | 0.784628i | \(-0.287146\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.19184 | 0.0742287 | 0.0371144 | − | 0.999311i | \(-0.488183\pi\) | ||||
0.0371144 | + | 0.999311i | \(0.488183\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 41.8549i | 0.890531i | 0.895399 | + | 0.445265i | \(0.146891\pi\) | ||||
−0.895399 | + | 0.445265i | \(0.853109\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 90.1918 | 1.84065 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 55.5043i | 1.04725i | 0.851949 | + | 0.523625i | \(0.175421\pi\) | ||||
−0.851949 | + | 0.523625i | \(0.824579\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −47.5959 | −0.865380 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 111.423i | − 1.88852i | −0.329200 | − | 0.944260i | \(-0.606779\pi\) | ||||
0.329200 | − | 0.944260i | \(-0.393221\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.8082 | −0.177183 | −0.0885915 | − | 0.996068i | \(-0.528237\pi\) | ||||
−0.0885915 | + | 0.996068i | \(0.528237\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 110.723i | − 1.70343i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −18.2020 | −0.271672 | −0.135836 | − | 0.990731i | \(-0.543372\pi\) | ||||
−0.135836 | + | 0.990731i | \(0.543372\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 34.7983i | 0.490117i | 0.969508 | + | 0.245059i | \(0.0788072\pi\) | ||||
−0.969508 | + | 0.245059i | \(0.921193\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 87.5959 | 1.19994 | 0.599972 | − | 0.800021i | \(-0.295178\pi\) | ||||
0.599972 | + | 0.800021i | \(0.295178\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 115.108i | 1.49491i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −151.394 | −1.91638 | −0.958189 | − | 0.286136i | \(-0.907629\pi\) | ||||
−0.958189 | + | 0.286136i | \(0.907629\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 61.8112i | 0.744714i | 0.928090 | + | 0.372357i | \(0.121450\pi\) | ||||
−0.928090 | + | 0.372357i | \(0.878550\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −108.293 | −1.27403 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 72.9532i | 0.819699i | 0.912153 | + | 0.409850i | \(0.134419\pi\) | ||||
−0.912153 | + | 0.409850i | \(0.865581\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −267.778 | −2.94261 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 86.8241i | − 0.913937i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −87.3735 | −0.900757 | −0.450379 | − | 0.892838i | \(-0.648711\pi\) | ||||
−0.450379 | + | 0.892838i | \(0.648711\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.63573i | 0.0161953i | 0.999967 | + | 0.00809766i | \(0.00257759\pi\) | ||||
−0.999967 | + | 0.00809766i | \(0.997422\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 38.9898 | 0.378542 | 0.189271 | − | 0.981925i | \(-0.439388\pi\) | ||||
0.189271 | + | 0.981925i | \(0.439388\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 205.303i | 1.91872i | 0.282179 | + | 0.959362i | \(0.408943\pi\) | ||||
−0.282179 | + | 0.959362i | \(0.591057\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −33.3031 | −0.305533 | −0.152766 | − | 0.988262i | \(-0.548818\pi\) | ||||
−0.152766 | + | 0.988262i | \(0.548818\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 93.8951i | − 0.830930i | −0.909609 | − | 0.415465i | \(-0.863619\pi\) | ||||
0.909609 | − | 0.415465i | \(-0.136381\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −68.9898 | −0.599911 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 261.901i | 2.20085i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 25.8082 | 0.213291 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 127.822i | 1.02257i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −45.8184 | −0.360775 | −0.180387 | − | 0.983596i | \(-0.557735\pi\) | ||||
−0.180387 | + | 0.983596i | \(0.557735\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 194.304i | 1.48324i | 0.670821 | + | 0.741619i | \(0.265942\pi\) | ||||
−0.670821 | + | 0.741619i | \(0.734058\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −209.980 | −1.57879 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 90.3668i | − 0.659612i | −0.944049 | − | 0.329806i | \(-0.893017\pi\) | ||||
0.944049 | − | 0.329806i | \(-0.106983\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.22245 | −0.0591543 | −0.0295772 | − | 0.999563i | \(-0.509416\pi\) | ||||
−0.0295772 | + | 0.999563i | \(0.509416\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 221.446i | − 1.54857i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 97.5959 | 0.673075 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 79.2457i | − 0.531851i | −0.963994 | − | 0.265925i | \(-0.914323\pi\) | ||||
0.963994 | − | 0.265925i | \(-0.0856775\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.9898 | −0.0992702 | −0.0496351 | − | 0.998767i | \(-0.515806\pi\) | ||||
−0.0496351 | + | 0.998767i | \(0.515806\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 194.147i | − 1.25256i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −267.576 | −1.70430 | −0.852151 | − | 0.523295i | \(-0.824702\pi\) | ||||
−0.852151 | + | 0.523295i | \(0.824702\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 166.848i | 1.03633i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 261.171 | 1.60228 | 0.801139 | − | 0.598478i | \(-0.204228\pi\) | ||||
0.801139 | + | 0.598478i | \(0.204228\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 300.070i | 1.79683i | 0.439150 | + | 0.898414i | \(0.355280\pi\) | ||||
−0.439150 | + | 0.898414i | \(0.644720\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 346.151 | 2.04823 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 31.2909i | − 0.180872i | −0.995902 | − | 0.0904362i | \(-0.971174\pi\) | ||||
0.995902 | − | 0.0904362i | \(-0.0288261\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 14.1816 | 0.0810379 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 66.4825i | 0.371410i | 0.982606 | + | 0.185705i | \(0.0594570\pi\) | ||||
−0.982606 | + | 0.185705i | \(0.940543\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 235.464 | 1.30091 | 0.650454 | − | 0.759546i | \(-0.274579\pi\) | ||||
0.650454 | + | 0.759546i | \(0.274579\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 11.7279i | − 0.0633939i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −216.586 | −1.15821 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 140.535i | 0.735787i | 0.929868 | + | 0.367893i | \(0.119921\pi\) | ||||
−0.929868 | + | 0.367893i | \(0.880079\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 293.151 | 1.51892 | 0.759459 | − | 0.650556i | \(-0.225464\pi\) | ||||
0.759459 | + | 0.650556i | \(0.225464\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 60.4324i | 0.306763i | 0.988167 | + | 0.153382i | \(0.0490164\pi\) | ||||
−0.988167 | + | 0.153382i | \(0.950984\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −143.757 | −0.722398 | −0.361199 | − | 0.932489i | \(-0.617632\pi\) | ||||
−0.361199 | + | 0.932489i | \(0.617632\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 236.031i | − 1.16271i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 313.868 | 1.53107 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 173.648i | − 0.830852i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 255.778 | 1.21222 | 0.606108 | − | 0.795382i | \(-0.292730\pi\) | ||||
0.606108 | + | 0.795382i | \(0.292730\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 15.5708i | 0.0724222i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −469.535 | −2.16375 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 503.845i | − 2.27984i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −248.969 | −1.11645 | −0.558227 | − | 0.829688i | \(-0.688518\pi\) | ||||
−0.558227 | + | 0.829688i | \(0.688518\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 277.600i | 1.22291i | 0.791280 | + | 0.611454i | \(0.209415\pi\) | ||||
−0.791280 | + | 0.611454i | \(0.790585\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 193.666 | 0.845704 | 0.422852 | − | 0.906199i | \(-0.361029\pi\) | ||||
0.422852 | + | 0.906199i | \(0.361029\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 150.435i | − 0.645643i | −0.946460 | − | 0.322821i | \(-0.895369\pi\) | ||||
0.946460 | − | 0.322821i | \(-0.104631\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −204.182 | −0.868858 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 140.593i | − 0.588255i | −0.955766 | − | 0.294128i | \(-0.904971\pi\) | ||||
0.955766 | − | 0.294128i | \(-0.0950291\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −228.182 | −0.946812 | −0.473406 | − | 0.880844i | \(-0.656976\pi\) | ||||
−0.473406 | + | 0.880844i | \(0.656976\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 439.984i | 1.79585i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 403.959 | 1.63546 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 214.546i | − 0.854766i | −0.904071 | − | 0.427383i | \(-0.859436\pi\) | ||||
0.904071 | − | 0.427383i | \(-0.140564\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −137.980 | −0.545374 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 382.652i | 1.48892i | 0.667669 | + | 0.744458i | \(0.267292\pi\) | ||||
−0.667669 | + | 0.744458i | \(0.732708\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −28.3633 | −0.109511 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 164.563i | − 0.625713i | −0.949800 | − | 0.312856i | \(-0.898714\pi\) | ||||
0.949800 | − | 0.312856i | \(-0.101286\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −270.767 | −1.02176 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 239.480i | 0.890262i | 0.895465 | + | 0.445131i | \(0.146843\pi\) | ||||
−0.895465 | + | 0.445131i | \(0.853157\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −153.778 | −0.567445 | −0.283722 | − | 0.958906i | \(-0.591569\pi\) | ||||
−0.283722 | + | 0.958906i | \(0.591569\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11.7279i | 0.0426468i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −135.242 | −0.488238 | −0.244119 | − | 0.969745i | \(-0.578499\pi\) | ||||
−0.244119 | + | 0.969745i | \(0.578499\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 63.6396i | − 0.226475i | −0.993568 | − | 0.113238i | \(-0.963878\pi\) | ||||
0.993568 | − | 0.113238i | \(-0.0361222\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 333.576 | 1.17871 | 0.589356 | − | 0.807873i | \(-0.299382\pi\) | ||||
0.589356 | + | 0.807873i | \(0.299382\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 759.075i | − 2.64486i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −203.788 | −0.705148 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 278.822i | − 0.951610i | −0.879551 | − | 0.475805i | \(-0.842157\pi\) | ||||
0.879551 | − | 0.475805i | \(-0.157843\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 543.555 | 1.84256 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 320.983i | − 1.07352i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 37.6571 | 0.125107 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 52.7256i | − 0.172871i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −99.7367 | −0.324875 | −0.162438 | − | 0.986719i | \(-0.551936\pi\) | ||||
−0.162438 | + | 0.986719i | \(0.551936\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 313.927i | − 1.00941i | −0.863292 | − | 0.504705i | \(-0.831601\pi\) | ||||
0.863292 | − | 0.504705i | \(-0.168399\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −52.4245 | −0.167490 | −0.0837452 | − | 0.996487i | \(-0.526688\pi\) | ||||
−0.0837452 | + | 0.996487i | \(0.526688\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 68.8888i | 0.217315i | 0.994079 | + | 0.108657i | \(0.0346551\pi\) | ||||
−0.994079 | + | 0.108657i | \(0.965345\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 195.192 | 0.611887 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 395.094i | − 1.22320i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −27.2827 | −0.0839466 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 493.803i | 1.50092i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 114.202 | 0.345021 | 0.172511 | − | 0.985008i | \(-0.444812\pi\) | ||||
0.172511 | + | 0.985008i | \(0.444812\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 88.7953i | − 0.265061i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −203.192 | −0.602943 | −0.301472 | − | 0.953475i | \(-0.597478\pi\) | ||||
−0.301472 | + | 0.953475i | \(0.597478\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 388.294i | − 1.13869i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 485.980 | 1.41685 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 79.5524i | 0.229258i | 0.993408 | + | 0.114629i | \(0.0365679\pi\) | ||||
−0.993408 | + | 0.114629i | \(0.963432\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 479.898 | 1.37507 | 0.687533 | − | 0.726153i | \(-0.258694\pi\) | ||||
0.687533 | + | 0.726153i | \(0.258694\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 132.922i | − 0.376549i | −0.982116 | − | 0.188274i | \(-0.939711\pi\) | ||||
0.982116 | − | 0.188274i | \(-0.0602894\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −169.757 | −0.478189 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 660.308i | 1.83930i | 0.392742 | + | 0.919649i | \(0.371527\pi\) | ||||
−0.392742 | + | 0.919649i | \(0.628473\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −44.2327 | −0.122528 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 427.320i | 1.17074i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 281.373 | 0.766685 | 0.383343 | − | 0.923606i | \(-0.374773\pi\) | ||||
0.383343 | + | 0.923606i | \(0.374773\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 654.837i | 1.76506i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 617.959 | 1.65673 | 0.828364 | − | 0.560191i | \(-0.189272\pi\) | ||||
0.828364 | + | 0.560191i | \(0.189272\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 454.077i | 1.20445i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 695.292 | 1.83454 | 0.917272 | − | 0.398262i | \(-0.130387\pi\) | ||||
0.917272 | + | 0.398262i | \(0.130387\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 315.269i | 0.823156i | 0.911375 | + | 0.411578i | \(0.135022\pi\) | ||||
−0.911375 | + | 0.411578i | \(0.864978\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −561.535 | −1.45853 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 539.364i | − 1.38654i | −0.720677 | − | 0.693270i | \(-0.756169\pi\) | ||||
0.720677 | − | 0.693270i | \(-0.243831\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −313.939 | −0.802912 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 738.547i | − 1.86974i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 490.404 | 1.23527 | 0.617637 | − | 0.786463i | \(-0.288090\pi\) | ||||
0.617637 | + | 0.786463i | \(0.288090\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 460.891i | 1.14935i | 0.818380 | + | 0.574677i | \(0.194872\pi\) | ||||
−0.818380 | + | 0.574677i | \(0.805128\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 903.292 | 2.24142 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 23.4557i | − 0.0576308i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 535.292 | 1.30878 | 0.654391 | − | 0.756156i | \(-0.272925\pi\) | ||||
0.654391 | + | 0.756156i | \(0.272925\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 1314.56i | − 3.18296i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −301.535 | −0.726590 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 405.993i | − 0.968958i | −0.874803 | − | 0.484479i | \(-0.839009\pi\) | ||||
0.874803 | − | 0.484479i | \(-0.160991\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 70.6969 | 0.167926 | 0.0839631 | − | 0.996469i | \(-0.473242\pi\) | ||||
0.0839631 | + | 0.996469i | \(0.473242\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 26.6839i | 0.0627856i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −127.514 | −0.298628 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 334.239i | 0.775497i | 0.921765 | + | 0.387749i | \(0.126747\pi\) | ||||
−0.921765 | + | 0.387749i | \(0.873253\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 88.3429 | 0.204025 | 0.102013 | − | 0.994783i | \(-0.467472\pi\) | ||||
0.102013 | + | 0.994783i | \(0.467472\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 251.701i | − 0.575975i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −231.353 | −0.527000 | −0.263500 | − | 0.964659i | \(-0.584877\pi\) | ||||
−0.263500 | + | 0.964659i | \(0.584877\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 715.091i | 1.61420i | 0.590414 | + | 0.807101i | \(0.298965\pi\) | ||||
−0.590414 | + | 0.807101i | \(0.701035\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −355.889 | −0.799750 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 576.455i | − 1.28386i | −0.766761 | − | 0.641932i | \(-0.778133\pi\) | ||||
0.766761 | − | 0.641932i | \(-0.221867\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 627.737 | 1.39188 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 1306.30i | − 2.87100i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −168.990 | −0.369781 | −0.184890 | − | 0.982759i | \(-0.559193\pi\) | ||||
−0.184890 | + | 0.982759i | \(0.559193\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 772.653i | 1.67604i | 0.545641 | + | 0.838019i | \(0.316286\pi\) | ||||
−0.545641 | + | 0.838019i | \(0.683714\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 461.818 | 0.997448 | 0.498724 | − | 0.866761i | \(-0.333802\pi\) | ||||
0.498724 | + | 0.866761i | \(0.333802\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 516.016i | − 1.10496i | −0.833526 | − | 0.552480i | \(-0.813682\pi\) | ||||
0.833526 | − | 0.552480i | \(-0.186318\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −214.747 | −0.457883 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 31.1416i | 0.0658384i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −21.3939 | −0.0450397 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 175.706i | 0.366818i | 0.983037 | + | 0.183409i | \(0.0587133\pi\) | ||||
−0.983037 | + | 0.183409i | \(0.941287\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 54.5653 | 0.113441 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 426.235i | − 0.878836i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 694.100 | 1.42526 | 0.712628 | − | 0.701542i | \(-0.247505\pi\) | ||||
0.712628 | + | 0.701542i | \(0.247505\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 512.173i | − 1.04312i | −0.853214 | − | 0.521561i | \(-0.825350\pi\) | ||||
0.853214 | − | 0.521561i | \(-0.174650\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 444.111 | 0.900834 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 410.549i | 0.826054i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −132.849 | −0.266230 | −0.133115 | − | 0.991101i | \(-0.542498\pi\) | ||||
−0.133115 | + | 0.991101i | \(0.542498\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 243.986i | 0.485063i | 0.970144 | + | 0.242531i | \(0.0779777\pi\) | ||||
−0.970144 | + | 0.242531i | \(0.922022\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.97959 | −0.0158012 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 396.530i | − 0.779038i | −0.921018 | − | 0.389519i | \(-0.872641\pi\) | ||||
0.921018 | − | 0.389519i | \(-0.127359\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1033.45 | 2.02241 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 190.205i | 0.369329i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −408.363 | −0.789871 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 76.4527i | − 0.146742i | −0.997305 | − | 0.0733711i | \(-0.976624\pi\) | ||||
0.997305 | − | 0.0733711i | \(-0.0233757\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −298.524 | −0.570793 | −0.285396 | − | 0.958410i | \(-0.592125\pi\) | ||||
−0.285396 | + | 0.958410i | \(0.592125\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 883.468i | − 1.67641i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 329.000 | 0.621928 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1460.31i | 2.73979i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1001.53 | −1.87203 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 879.968i | 1.63259i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −566.070 | −1.04634 | −0.523170 | − | 0.852228i | \(-0.675251\pi\) | ||||
−0.523170 | + | 0.852228i | \(0.675251\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 162.463i | − 0.298097i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −500.727 | −0.915405 | −0.457702 | − | 0.889105i | \(-0.651328\pi\) | ||||
−0.457702 | + | 0.889105i | \(0.651328\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 356.067i | 0.646220i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1786.14 | −3.22991 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 224.568i | 0.403174i | 0.979471 | + | 0.201587i | \(0.0646098\pi\) | ||||
−0.979471 | + | 0.201587i | \(0.935390\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −72.4449 | −0.129597 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 708.092i | − 1.25771i | −0.777521 | − | 0.628856i | \(-0.783523\pi\) | ||||
0.777521 | − | 0.628856i | \(-0.216477\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 458.050 | 0.810708 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 627.453i | − 1.10273i | −0.834264 | − | 0.551365i | \(-0.814107\pi\) | ||||
0.834264 | − | 0.551365i | \(-0.185893\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25.2531 | 0.0442260 | 0.0221130 | − | 0.999755i | \(-0.492961\pi\) | ||||
0.0221130 | + | 0.999755i | \(0.492961\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16.9994i | 0.0295642i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 158.000 | 0.273830 | 0.136915 | − | 0.990583i | \(-0.456281\pi\) | ||||
0.136915 | + | 0.990583i | \(0.456281\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 729.246i | 1.25516i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −541.535 | −0.928876 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1060.63i | 1.80687i | 0.428728 | + | 0.903434i | \(0.358962\pi\) | ||||
−0.428728 | + | 0.903434i | \(0.641038\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 708.322 | 1.20258 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1051.50i | 1.77319i | 0.462545 | + | 0.886596i | \(0.346936\pi\) | ||||
−0.462545 | + | 0.886596i | \(0.653064\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1277.63 | −2.14729 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 52.0835i | − 0.0869507i | −0.999054 | − | 0.0434754i | \(-0.986157\pi\) | ||||
0.999054 | − | 0.0434754i | \(-0.0138430\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 66.0000 | 0.109817 | 0.0549085 | − | 0.998491i | \(-0.482513\pi\) | ||||
0.0549085 | + | 0.998491i | \(0.482513\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 125.900i | 0.208100i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 210.627 | 0.346996 | 0.173498 | − | 0.984834i | \(-0.444493\pi\) | ||||
0.173498 | + | 0.984834i | \(0.444493\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 949.979i | − 1.55479i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 320.706 | 0.523175 | 0.261587 | − | 0.965180i | \(-0.415754\pi\) | ||||
0.261587 | + | 0.965180i | \(0.415754\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 233.316i | 0.378146i | 0.981963 | + | 0.189073i | \(0.0605484\pi\) | ||||
−0.981963 | + | 0.189073i | \(0.939452\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −206.020 | −0.332828 | −0.166414 | − | 0.986056i | \(-0.553219\pi\) | ||||
−0.166414 | + | 0.986056i | \(0.553219\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 860.699i | 1.38154i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −593.504 | −0.949607 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 53.3678i | − 0.0848455i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.5857 | 0.0674892 | 0.0337446 | − | 0.999430i | \(-0.489257\pi\) | ||||
0.0337446 | + | 0.999430i | \(0.489257\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 223.516i | − 0.351994i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2047.08 | −3.21362 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 160.021i | − 0.249643i | −0.992179 | − | 0.124821i | \(-0.960164\pi\) | ||||
0.992179 | − | 0.124821i | \(-0.0398358\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −997.980 | −1.55207 | −0.776034 | − | 0.630691i | \(-0.782771\pi\) | ||||
−0.776034 | + | 0.630691i | \(0.782771\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 552.628i | − 0.854140i | −0.904219 | − | 0.427070i | \(-0.859546\pi\) | ||||
0.904219 | − | 0.427070i | \(-0.140454\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1087.11 | 1.67505 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 374.272i | − 0.573158i | −0.958057 | − | 0.286579i | \(-0.907482\pi\) | ||||
0.958057 | − | 0.286579i | \(-0.0925181\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −947.878 | −1.44714 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 251.759i | 0.382032i | 0.981587 | + | 0.191016i | \(0.0611782\pi\) | ||||
−0.981587 | + | 0.191016i | \(0.938822\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 339.535 | 0.513668 | 0.256834 | − | 0.966456i | \(-0.417321\pi\) | ||||
0.256834 | + | 0.966456i | \(0.417321\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 1024.35i | − 1.54037i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 282.929 | 0.424181 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 105.451i | − 0.157155i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1049.03 | 1.55873 | 0.779367 | − | 0.626567i | \(-0.215541\pi\) | ||||
0.779367 | + | 0.626567i | \(0.215541\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 310.390i | − 0.458479i | −0.973370 | − | 0.229240i | \(-0.926376\pi\) | ||||
0.973370 | − | 0.229240i | \(-0.0736239\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1030.83 | −1.51816 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 746.233i | 1.09258i | 0.837596 | + | 0.546291i | \(0.183961\pi\) | ||||
−0.837596 | + | 0.546291i | \(0.816039\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 440.838 | 0.643559 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 1259.78i | − 1.82841i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 776.241 | 1.12336 | 0.561679 | − | 0.827355i | \(-0.310155\pi\) | ||||
0.561679 | + | 0.827355i | \(0.310155\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 40.1117i | − 0.0577147i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1428.26 | 2.04916 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 801.223i | − 1.14297i | −0.820612 | − | 0.571486i | \(-0.806367\pi\) | ||||
0.820612 | − | 0.571486i | \(-0.193633\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 42.7878 | 0.0608645 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 19.2982i | 0.0272959i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1198.25 | −1.69006 | −0.845030 | − | 0.534719i | \(-0.820417\pi\) | ||||
−0.845030 | + | 0.534719i | \(0.820417\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 562.828i | − 0.789380i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1080.28 | 1.51088 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1206.22i | 1.67764i | 0.544409 | + | 0.838820i | \(0.316754\pi\) | ||||
−0.544409 | + | 0.838820i | \(0.683246\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 460.000 | 0.638003 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 24.0481i | − 0.0331698i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −503.394 | −0.692426 | −0.346213 | − | 0.938156i | \(-0.612533\pi\) | ||||
−0.346213 | + | 0.938156i | \(0.612533\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 70.8550i | 0.0969289i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 380.736 | 0.519421 | 0.259711 | − | 0.965687i | \(-0.416373\pi\) | ||||
0.259711 | + | 0.965687i | \(0.416373\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 177.591i | − 0.240964i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 717.775 | 0.971279 | 0.485640 | − | 0.874159i | \(-0.338587\pi\) | ||||
0.485640 | + | 0.874159i | \(0.338587\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 239.675i | − 0.322577i | −0.986907 | − | 0.161288i | \(-0.948435\pi\) | ||||
0.986907 | − | 0.161288i | \(-0.0515649\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 386.586 | 0.518907 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2422.16i | 3.23386i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 481.010 | 0.640493 | 0.320246 | − | 0.947334i | \(-0.396234\pi\) | ||||
0.320246 | + | 0.947334i | \(0.396234\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 73.1249i | − 0.0968542i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −338.656 | −0.447366 | −0.223683 | − | 0.974662i | \(-0.571808\pi\) | ||||
−0.223683 | + | 0.974662i | \(0.571808\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 525.945i | 0.691123i | 0.938396 | + | 0.345561i | \(0.112312\pi\) | ||||
−0.938396 | + | 0.345561i | \(0.887688\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −392.908 | −0.514952 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2528.95i | 3.29720i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 248.506 | 0.323155 | 0.161577 | − | 0.986860i | \(-0.448342\pi\) | ||||
0.161577 | + | 0.986860i | \(0.448342\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 402.701i | − 0.520958i | −0.965479 | − | 0.260479i | \(-0.916119\pi\) | ||||
0.965479 | − | 0.260479i | \(-0.0838806\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −47.8388 | −0.0617275 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1145.11i | 1.46998i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −339.514 | −0.434717 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 1305.32i | − 1.66283i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1258.97 | −1.59971 | −0.799853 | − | 0.600195i | \(-0.795090\pi\) | ||||
−0.799853 | + | 0.600195i | \(0.795090\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 1107.77i | − 1.40047i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 245.312 | 0.309347 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 878.734i | − 1.10255i | −0.834323 | − | 0.551276i | \(-0.814141\pi\) | ||||
0.834323 | − | 0.551276i | \(-0.185859\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −929.131 | −1.16287 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 854.641i | 1.06431i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −813.939 | −1.01110 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1199.39i | 1.48256i | 0.671195 | + | 0.741281i | \(0.265782\pi\) | ||||
−0.671195 | + | 0.741281i | \(0.734218\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −30.2837 | −0.0373412 | −0.0186706 | − | 0.999826i | \(-0.505943\pi\) | ||||
−0.0186706 | + | 0.999826i | \(0.505943\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1274.08i | 1.56328i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −56.8082 | −0.0695326 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 144.441i | − 0.175933i | −0.996123 | − | 0.0879665i | \(-0.971963\pi\) | ||||
0.996123 | − | 0.0879665i | \(-0.0280368\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −795.839 | −0.966997 | −0.483499 | − | 0.875345i | \(-0.660634\pi\) | ||||
−0.483499 | + | 0.875345i | \(0.660634\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 567.541i | − 0.686265i | −0.939287 | − | 0.343133i | \(-0.888512\pi\) | ||||
0.939287 | − | 0.343133i | \(-0.111488\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1188.54 | −1.43370 | −0.716849 | − | 0.697228i | \(-0.754416\pi\) | ||||
−0.716849 | + | 0.697228i | \(0.754416\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2002.15i | 2.40354i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1463.84 | −1.75310 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 598.256i | 0.713058i | 0.934284 | + | 0.356529i | \(0.116040\pi\) | ||||
−0.934284 | + | 0.356529i | \(0.883960\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 440.757 | 0.524087 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1688.63i | 1.99838i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 304.484 | 0.359485 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 33.9989i | − 0.0399517i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 337.192 | 0.395301 | 0.197651 | − | 0.980273i | \(-0.436669\pi\) | ||||
0.197651 | + | 0.980273i | \(0.436669\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 913.497i | − 1.06592i | −0.846139 | − | 0.532962i | \(-0.821079\pi\) | ||||
0.846139 | − | 0.532962i | \(-0.178921\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −748.645 | −0.871531 | −0.435765 | − | 0.900060i | \(-0.643522\pi\) | ||||
−0.435765 | + | 0.900060i | \(0.643522\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 460.632i | − 0.533757i | −0.963730 | − | 0.266879i | \(-0.914008\pi\) | ||||
0.963730 | − | 0.266879i | \(-0.0859923\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 152.647 | 0.176470 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 1477.09i | − 1.69976i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 413.131 | 0.474318 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1508.04i | 1.72347i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1066.32 | 1.21588 | 0.607938 | − | 0.793985i | \(-0.291997\pi\) | ||||
0.607938 | + | 0.793985i | \(0.291997\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 586.899i | − 0.666173i | −0.942896 | − | 0.333087i | \(-0.891910\pi\) | ||||
0.942896 | − | 0.333087i | \(-0.108090\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1242.95 | −1.40764 | −0.703820 | − | 0.710378i | \(-0.748524\pi\) | ||||
−0.703820 | + | 0.710378i | \(0.748524\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 37.8259i | 0.0426447i | 0.999773 | + | 0.0213224i | \(0.00678763\pi\) | ||||
−0.999773 | + | 0.0213224i | \(0.993212\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −540.563 | −0.608058 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 744.933i | − 0.834191i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −324.322 | −0.362371 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 796.201i | 0.885652i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1232.13 | −1.36751 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1148.67i | 1.26925i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 763.837 | 0.842157 | 0.421079 | − | 0.907024i | \(-0.361652\pi\) | ||||
0.421079 | + | 0.907024i | \(0.361652\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 378.008i | − 0.414937i | −0.978242 | − | 0.207469i | \(-0.933478\pi\) | ||||
0.978242 | − | 0.207469i | \(-0.0665225\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −603.069 | −0.660536 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2292.39i | 2.49988i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 206.141 | 0.224310 | 0.112155 | − | 0.993691i | \(-0.464225\pi\) | ||||
0.112155 | + | 0.993691i | \(0.464225\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 789.815i | − 0.855704i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.88981 | −0.00312411 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 1793.22i | − 1.93027i | −0.261752 | − | 0.965135i | \(-0.584300\pi\) | ||||
0.261752 | − | 0.965135i | \(-0.415700\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1605.23 | −1.72420 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 1056.57i | − 1.13002i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 322.767 | 0.344469 | 0.172234 | − | 0.985056i | \(-0.444901\pi\) | ||||
0.172234 | + | 0.985056i | \(0.444901\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 805.965i | 0.856499i | 0.903661 | + | 0.428249i | \(0.140870\pi\) | ||||
−0.903661 | + | 0.428249i | \(0.859130\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 909.898 | 0.964897 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 1197.31i | − 1.26432i | −0.774839 | − | 0.632158i | \(-0.782169\pi\) | ||||
0.774839 | − | 0.632158i | \(-0.217831\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1988.16 | −2.09500 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1109.71i | 1.16444i | 0.813030 | + | 0.582222i | \(0.197816\pi\) | ||||
−0.813030 | + | 0.582222i | \(0.802184\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −685.576 | −0.717880 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 1066.14i | − 1.11172i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 622.878 | 0.648156 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1430.08i | 1.48195i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1075.72 | −1.11243 | −0.556213 | − | 0.831040i | \(-0.687746\pi\) | ||||
−0.556213 | + | 0.831040i | \(0.687746\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 958.163i | 0.986779i | 0.869808 | + | 0.493390i | \(0.164242\pi\) | ||||
−0.869808 | + | 0.493390i | \(0.835758\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −97.0081 | −0.0997000 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 116.792i | − 0.119542i | −0.998212 | − | 0.0597709i | \(-0.980963\pi\) | ||||
0.998212 | − | 0.0597709i | \(-0.0190370\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −711.778 | −0.727046 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 209.817i | 0.213446i | 0.994289 | + | 0.106723i | \(0.0340358\pi\) | ||||
−0.994289 | + | 0.106723i | \(0.965964\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −294.808 | −0.299298 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 45.1394i | 0.0456414i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −359.798 | −0.363066 | −0.181533 | − | 0.983385i | \(-0.558106\pi\) | ||||
−0.181533 | + | 0.983385i | \(0.558106\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 701.293i | − 0.704817i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1628.06 | 1.63296 | 0.816478 | − | 0.577377i | \(-0.195924\pi\) | ||||
0.816478 | + | 0.577377i | \(0.195924\pi\) | |||||||
\(998\) | 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 | 1152.3.e.f.1025.4 | yes | 4 | |
3.2 | odd | 2 | inner | 1152.3.e.f.1025.1 | yes | 4 | |
4.3 | odd | 2 | 1152.3.e.b.1025.4 | yes | 4 | ||
8.3 | odd | 2 | 1152.3.e.d.1025.1 | yes | 4 | ||
8.5 | even | 2 | 1152.3.e.h.1025.1 | yes | 4 | ||
12.11 | even | 2 | 1152.3.e.b.1025.1 | ✓ | 4 | ||
16.3 | odd | 4 | 2304.3.h.k.2177.7 | 8 | |||
16.5 | even | 4 | 2304.3.h.i.2177.2 | 8 | |||
16.11 | odd | 4 | 2304.3.h.k.2177.2 | 8 | |||
16.13 | even | 4 | 2304.3.h.i.2177.7 | 8 | |||
24.5 | odd | 2 | 1152.3.e.h.1025.4 | yes | 4 | ||
24.11 | even | 2 | 1152.3.e.d.1025.4 | yes | 4 | ||
48.5 | odd | 4 | 2304.3.h.i.2177.8 | 8 | |||
48.11 | even | 4 | 2304.3.h.k.2177.8 | 8 | |||
48.29 | odd | 4 | 2304.3.h.i.2177.1 | 8 | |||
48.35 | even | 4 | 2304.3.h.k.2177.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1152.3.e.b.1025.1 | ✓ | 4 | 12.11 | even | 2 | ||
1152.3.e.b.1025.4 | yes | 4 | 4.3 | odd | 2 | ||
1152.3.e.d.1025.1 | yes | 4 | 8.3 | odd | 2 | ||
1152.3.e.d.1025.4 | yes | 4 | 24.11 | even | 2 | ||
1152.3.e.f.1025.1 | yes | 4 | 3.2 | odd | 2 | inner | |
1152.3.e.f.1025.4 | yes | 4 | 1.1 | even | 1 | trivial | |
1152.3.e.h.1025.1 | yes | 4 | 8.5 | even | 2 | ||
1152.3.e.h.1025.4 | yes | 4 | 24.5 | odd | 2 | ||
2304.3.h.i.2177.1 | 8 | 48.29 | odd | 4 | |||
2304.3.h.i.2177.2 | 8 | 16.5 | even | 4 | |||
2304.3.h.i.2177.7 | 8 | 16.13 | even | 4 | |||
2304.3.h.i.2177.8 | 8 | 48.5 | odd | 4 | |||
2304.3.h.k.2177.1 | 8 | 48.35 | even | 4 | |||
2304.3.h.k.2177.2 | 8 | 16.11 | odd | 4 | |||
2304.3.h.k.2177.7 | 8 | 16.3 | odd | 4 | |||
2304.3.h.k.2177.8 | 8 | 48.11 | even | 4 |