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 | 1025.1 | ||
Root | \(-1.22474 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1152.1025 |
Dual form | 1152.3.e.f.1025.4 |
$q$-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 | \(-0.837788\pi\) | ||||
0.872938 | − | 0.487832i | \(-0.162212\pi\) | |||||||
\(6\) | 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 | \(-0.853743\pi\) | ||||
0.896283 | − | 0.443483i | \(-0.146257\pi\) | |||||||
\(12\) | 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 | \(-0.773549\pi\) | ||||
0.757438 | − | 0.652907i | \(-0.226451\pi\) | |||||||
\(18\) | 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 | \(-0.900528\pi\) | ||||
0.951568 | − | 0.307438i | \(-0.0994716\pi\) | |||||||
\(24\) | 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 | \(0.112098\pi\) | ||||
−0.938628 | + | 0.344932i | \(0.887902\pi\) | |||||||
\(30\) | 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 | \(0.287146\pi\) | ||||
−0.619967 | + | 0.784628i | \(0.712854\pi\) | |||||||
\(42\) | 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 | \(-0.853109\pi\) | ||||
0.895399 | − | 0.445265i | \(-0.146891\pi\) | |||||||
\(48\) | 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 | \(-0.824579\pi\) | ||||
0.851949 | − | 0.523625i | \(-0.175421\pi\) | |||||||
\(54\) | 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 | \(0.393221\pi\) | ||||
−0.329200 | + | 0.944260i | \(0.606779\pi\) | |||||||
\(60\) | 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 | \(-0.921193\pi\) | ||||
0.969508 | − | 0.245059i | \(-0.0788072\pi\) | |||||||
\(72\) | 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 | \(-0.878550\pi\) | ||||
0.928090 | − | 0.372357i | \(-0.121450\pi\) | |||||||
\(84\) | 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 | \(-0.865581\pi\) | ||||
0.912153 | − | 0.409850i | \(-0.134419\pi\) | |||||||
\(90\) | 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 | \(-0.997422\pi\) | ||||
0.999967 | − | 0.00809766i | \(-0.00257759\pi\) | |||||||
\(102\) | 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 | \(-0.591057\pi\) | ||||
0.282179 | − | 0.959362i | \(-0.408943\pi\) | |||||||
\(108\) | 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 | \(0.136381\pi\) | ||||
−0.909609 | + | 0.415465i | \(0.863619\pi\) | |||||||
\(114\) | 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 | \(-0.734058\pi\) | ||||
0.670821 | − | 0.741619i | \(-0.265942\pi\) | |||||||
\(132\) | 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 | \(0.106983\pi\) | ||||
−0.944049 | + | 0.329806i | \(0.893017\pi\) | |||||||
\(138\) | 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 | \(0.0856775\pi\) | ||||
−0.963994 | + | 0.265925i | \(0.914323\pi\) | |||||||
\(150\) | 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 | \(-0.644720\pi\) | ||||
0.439150 | − | 0.898414i | \(-0.355280\pi\) | |||||||
\(168\) | 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 | \(0.0288261\pi\) | ||||
−0.995902 | + | 0.0904362i | \(0.971174\pi\) | |||||||
\(174\) | 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 | \(-0.940543\pi\) | ||||
0.982606 | − | 0.185705i | \(-0.0594570\pi\) | |||||||
\(180\) | 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 | \(-0.880079\pi\) | ||||
0.929868 | − | 0.367893i | \(-0.119921\pi\) | |||||||
\(192\) | 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 | \(-0.950984\pi\) | ||||
0.988167 | − | 0.153382i | \(-0.0490164\pi\) | |||||||
\(198\) | 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 | \(-0.790585\pi\) | ||||
0.791280 | − | 0.611454i | \(-0.209415\pi\) | |||||||
\(228\) | 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 | \(0.104631\pi\) | ||||
−0.946460 | + | 0.322821i | \(0.895369\pi\) | |||||||
\(234\) | 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 | \(0.0950291\pi\) | ||||
−0.955766 | + | 0.294128i | \(0.904971\pi\) | |||||||
\(240\) | 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 | \(0.140564\pi\) | ||||
−0.904071 | + | 0.427383i | \(0.859436\pi\) | |||||||
\(252\) | 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 | \(-0.732708\pi\) | ||||
0.667669 | − | 0.744458i | \(-0.267292\pi\) | |||||||
\(258\) | 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 | \(0.101286\pi\) | ||||
−0.949800 | + | 0.312856i | \(0.898714\pi\) | |||||||
\(264\) | 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 | \(-0.853157\pi\) | ||||
0.895465 | − | 0.445131i | \(-0.146843\pi\) | |||||||
\(270\) | 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 | \(0.0361222\pi\) | ||||
−0.993568 | + | 0.113238i | \(0.963878\pi\) | |||||||
\(282\) | 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 | \(0.157843\pi\) | ||||
−0.879551 | + | 0.475805i | \(0.842157\pi\) | |||||||
\(294\) | 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 | \(0.168399\pi\) | ||||
−0.863292 | + | 0.504705i | \(0.831601\pi\) | |||||||
\(312\) | 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 | \(-0.965345\pi\) | ||||
0.994079 | − | 0.108657i | \(-0.0346551\pi\) | |||||||
\(318\) | 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 | \(-0.963432\pi\) | ||||
0.993408 | − | 0.114629i | \(-0.0365679\pi\) | |||||||
\(348\) | 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 | \(0.0602894\pi\) | ||||
−0.982116 | + | 0.188274i | \(0.939711\pi\) | |||||||
\(354\) | 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 | \(-0.628473\pi\) | ||||
0.392742 | − | 0.919649i | \(-0.371527\pi\) | |||||||
\(360\) | 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 | \(-0.864978\pi\) | ||||
0.911375 | − | 0.411578i | \(-0.135022\pi\) | |||||||
\(384\) | 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 | \(0.243831\pi\) | ||||
−0.720677 | + | 0.693270i | \(0.756169\pi\) | |||||||
\(390\) | 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 | \(-0.805128\pi\) | ||||
0.818380 | − | 0.574677i | \(-0.194872\pi\) | |||||||
\(402\) | 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 | \(0.160991\pi\) | ||||
−0.874803 | + | 0.484479i | \(0.839009\pi\) | |||||||
\(420\) | 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 | \(-0.873253\pi\) | ||||
0.921765 | − | 0.387749i | \(-0.126747\pi\) | |||||||
\(432\) | 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 | \(-0.701035\pi\) | ||||
0.590414 | − | 0.807101i | \(-0.298965\pi\) | |||||||
\(444\) | 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 | \(0.221867\pi\) | ||||
−0.766761 | + | 0.641932i | \(0.778133\pi\) | |||||||
\(450\) | 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 | \(-0.683714\pi\) | ||||
0.545641 | − | 0.838019i | \(-0.316286\pi\) | |||||||
\(462\) | 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 | \(0.186318\pi\) | ||||
−0.833526 | + | 0.552480i | \(0.813682\pi\) | |||||||
\(468\) | 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 | \(-0.941287\pi\) | ||||
0.983037 | − | 0.183409i | \(-0.0587133\pi\) | |||||||
\(480\) | 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 | \(0.174650\pi\) | ||||
−0.853214 | + | 0.521561i | \(0.825350\pi\) | |||||||
\(492\) | 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 | \(-0.922022\pi\) | ||||
0.970144 | − | 0.242531i | \(-0.0779777\pi\) | |||||||
\(504\) | 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 | \(0.127359\pi\) | ||||
−0.921018 | + | 0.389519i | \(0.872641\pi\) | |||||||
\(510\) | 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 | \(0.0233757\pi\) | ||||
−0.997305 | + | 0.0733711i | \(0.976624\pi\) | |||||||
\(522\) | 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 | \(-0.935390\pi\) | ||||
0.979471 | − | 0.201587i | \(-0.0646098\pi\) | |||||||
\(558\) | 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 | \(0.216477\pi\) | ||||
−0.777521 | + | 0.628856i | \(0.783523\pi\) | |||||||
\(564\) | 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 | \(0.185893\pi\) | ||||
−0.834264 | + | 0.551365i | \(0.814107\pi\) | |||||||
\(570\) | 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 | \(-0.641038\pi\) | ||||
0.428728 | − | 0.903434i | \(-0.358962\pi\) | |||||||
\(588\) | 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 | \(-0.653064\pi\) | ||||
0.462545 | − | 0.886596i | \(-0.346936\pi\) | |||||||
\(594\) | 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 | \(0.0138430\pi\) | ||||
−0.999054 | + | 0.0434754i | \(0.986157\pi\) | |||||||
\(600\) | 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 | \(-0.939452\pi\) | ||||
0.981963 | − | 0.189073i | \(-0.0605484\pi\) | |||||||
\(618\) | 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 | \(0.0398358\pi\) | ||||
−0.992179 | + | 0.124821i | \(0.960164\pi\) | |||||||
\(642\) | 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 | \(0.140454\pi\) | ||||
−0.904219 | + | 0.427070i | \(0.859546\pi\) | |||||||
\(648\) | 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 | \(0.0925181\pi\) | ||||
−0.958057 | + | 0.286579i | \(0.907482\pi\) | |||||||
\(654\) | 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 | \(-0.938822\pi\) | ||||
0.981587 | − | 0.191016i | \(-0.0611782\pi\) | |||||||
\(660\) | 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 | \(0.0736239\pi\) | ||||
−0.973370 | + | 0.229240i | \(0.926376\pi\) | |||||||
\(678\) | 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 | \(-0.816039\pi\) | ||||
0.837596 | − | 0.546291i | \(-0.183961\pi\) | |||||||
\(684\) | 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 | \(0.193633\pi\) | ||||
−0.820612 | + | 0.571486i | \(0.806367\pi\) | |||||||
\(702\) | 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 | \(-0.683246\pi\) | ||||
0.544409 | − | 0.838820i | \(-0.316754\pi\) | |||||||
\(720\) | 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 | \(0.0515649\pi\) | ||||
−0.986907 | + | 0.161288i | \(0.948435\pi\) | |||||||
\(744\) | 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 | \(-0.887688\pi\) | ||||
0.938396 | − | 0.345561i | \(-0.112312\pi\) | |||||||
\(762\) | 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 | \(0.0838806\pi\) | ||||
−0.965479 | + | 0.260479i | \(0.916119\pi\) | |||||||
\(774\) | 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 | \(0.185859\pi\) | ||||
−0.834323 | + | 0.551276i | \(0.814141\pi\) | |||||||
\(798\) | 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 | \(-0.734218\pi\) | ||||
0.671195 | − | 0.741281i | \(-0.265782\pi\) | |||||||
\(810\) | 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 | \(0.0280368\pi\) | ||||
−0.996123 | + | 0.0879665i | \(0.971963\pi\) | |||||||
\(822\) | 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 | \(0.111488\pi\) | ||||
−0.939287 | + | 0.343133i | \(0.888512\pi\) | |||||||
\(828\) | 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 | \(-0.883960\pi\) | ||||
0.934284 | − | 0.356529i | \(-0.116040\pi\) | |||||||
\(840\) | 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 | \(0.178921\pi\) | ||||
−0.846139 | + | 0.532962i | \(0.821079\pi\) | |||||||
\(858\) | 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 | \(0.0859923\pi\) | ||||
−0.963730 | + | 0.266879i | \(0.914008\pi\) | |||||||
\(864\) | 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 | \(0.108090\pi\) | ||||
−0.942896 | + | 0.333087i | \(0.891910\pi\) | |||||||
\(882\) | 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 | \(-0.993212\pi\) | ||||
0.999773 | − | 0.0213224i | \(-0.00678763\pi\) | |||||||
\(888\) | 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 | \(0.0665225\pi\) | ||||
−0.978242 | + | 0.207469i | \(0.933478\pi\) | |||||||
\(912\) | 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 | \(0.415700\pi\) | ||||
−0.261752 | + | 0.965135i | \(0.584300\pi\) | |||||||
\(930\) | 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 | \(-0.859130\pi\) | ||||
0.903661 | − | 0.428249i | \(-0.140870\pi\) | |||||||
\(942\) | 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 | \(0.217831\pi\) | ||||
−0.774839 | + | 0.632158i | \(0.782169\pi\) | |||||||
\(948\) | 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 | \(-0.802184\pi\) | ||||
0.813030 | − | 0.582222i | \(-0.197816\pi\) | |||||||
\(954\) | 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 | \(-0.835758\pi\) | ||||
0.869808 | − | 0.493390i | \(-0.164242\pi\) | |||||||
\(972\) | 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 | \(0.0190370\pi\) | ||||
−0.998212 | + | 0.0597709i | \(0.980963\pi\) | |||||||
\(978\) | 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 | \(-0.965964\pi\) | ||||
0.994289 | − | 0.106723i | \(-0.0340358\pi\) | |||||||
\(984\) | 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.1025.1 | yes | 4 | |
3.2 | odd | 2 | inner | 1152.3.e.f.1025.4 | yes | 4 | |
4.3 | odd | 2 | 1152.3.e.b.1025.1 | ✓ | 4 | ||
8.3 | odd | 2 | 1152.3.e.d.1025.4 | yes | 4 | ||
8.5 | even | 2 | 1152.3.e.h.1025.4 | yes | 4 | ||
12.11 | even | 2 | 1152.3.e.b.1025.4 | yes | 4 | ||
16.3 | odd | 4 | 2304.3.h.k.2177.1 | 8 | |||
16.5 | even | 4 | 2304.3.h.i.2177.8 | 8 | |||
16.11 | odd | 4 | 2304.3.h.k.2177.8 | 8 | |||
16.13 | even | 4 | 2304.3.h.i.2177.1 | 8 | |||
24.5 | odd | 2 | 1152.3.e.h.1025.1 | yes | 4 | ||
24.11 | even | 2 | 1152.3.e.d.1025.1 | yes | 4 | ||
48.5 | odd | 4 | 2304.3.h.i.2177.2 | 8 | |||
48.11 | even | 4 | 2304.3.h.k.2177.2 | 8 | |||
48.29 | odd | 4 | 2304.3.h.i.2177.7 | 8 | |||
48.35 | even | 4 | 2304.3.h.k.2177.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1152.3.e.b.1025.1 | ✓ | 4 | 4.3 | odd | 2 | ||
1152.3.e.b.1025.4 | yes | 4 | 12.11 | even | 2 | ||
1152.3.e.d.1025.1 | yes | 4 | 24.11 | even | 2 | ||
1152.3.e.d.1025.4 | yes | 4 | 8.3 | odd | 2 | ||
1152.3.e.f.1025.1 | yes | 4 | 1.1 | even | 1 | trivial | |
1152.3.e.f.1025.4 | yes | 4 | 3.2 | odd | 2 | inner | |
1152.3.e.h.1025.1 | yes | 4 | 24.5 | odd | 2 | ||
1152.3.e.h.1025.4 | yes | 4 | 8.5 | even | 2 | ||
2304.3.h.i.2177.1 | 8 | 16.13 | even | 4 | |||
2304.3.h.i.2177.2 | 8 | 48.5 | odd | 4 | |||
2304.3.h.i.2177.7 | 8 | 48.29 | odd | 4 | |||
2304.3.h.i.2177.8 | 8 | 16.5 | even | 4 | |||
2304.3.h.k.2177.1 | 8 | 16.3 | odd | 4 | |||
2304.3.h.k.2177.2 | 8 | 48.11 | even | 4 | |||
2304.3.h.k.2177.7 | 8 | 48.35 | even | 4 | |||
2304.3.h.k.2177.8 | 8 | 16.11 | odd | 4 |