Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8100,2,Mod(649,8100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8100, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8100.649");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8100 = 2^{2} \cdot 3^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8100.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(64.6788256372\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 649.3 | ||
Root | \(-0.618034i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8100.649 |
Dual form | 8100.2.d.k.649.2 |
$q$-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 \(\left(\mathbb{Z}/8100\mathbb{Z}\right)^\times\).
\(n\) | \(4051\) | \(6401\) | \(7777\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.85410i | 1.07875i | 0.842066 | + | 0.539375i | \(0.181339\pi\) | ||||
−0.842066 | + | 0.539375i | \(0.818661\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.85410 | 0.559033 | 0.279516 | − | 0.960141i | \(-0.409826\pi\) | ||||
0.279516 | + | 0.960141i | \(0.409826\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.854102i | 0.236885i | 0.992961 | + | 0.118443i | \(0.0377902\pi\) | ||||
−0.992961 | + | 0.118443i | \(0.962210\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 1.14590i | − 0.277921i | −0.990298 | − | 0.138961i | \(-0.955624\pi\) | ||||
0.990298 | − | 0.138961i | \(-0.0443761\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.00000 | −0.458831 | −0.229416 | − | 0.973329i | \(-0.573682\pi\) | ||||
−0.229416 | + | 0.973329i | \(0.573682\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 4.85410i | − 1.01215i | −0.862489 | − | 0.506075i | \(-0.831096\pi\) | ||||
0.862489 | − | 0.506075i | \(-0.168904\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.70820 | −0.688596 | −0.344298 | − | 0.938860i | \(-0.611883\pi\) | ||||
−0.344298 | + | 0.938860i | \(0.611883\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.70820 | 0.486408 | 0.243204 | − | 0.969975i | \(-0.421802\pi\) | ||||
0.243204 | + | 0.969975i | \(0.421802\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.85410i | 0.962408i | 0.876609 | + | 0.481204i | \(0.159800\pi\) | ||||
−0.876609 | + | 0.481204i | \(0.840200\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.5623 | −1.80573 | −0.902864 | − | 0.429925i | \(-0.858540\pi\) | ||||
−0.902864 | + | 0.429925i | \(0.858540\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.854102i | 0.130249i | 0.997877 | + | 0.0651247i | \(0.0207445\pi\) | ||||
−0.997877 | + | 0.0651247i | \(0.979255\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.70820i | 0.978492i | 0.872146 | + | 0.489246i | \(0.162728\pi\) | ||||
−0.872146 | + | 0.489246i | \(0.837272\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.14590 | −0.163700 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.85410i | 0.666762i | 0.942792 | + | 0.333381i | \(0.108190\pi\) | ||||
−0.942792 | + | 0.333381i | \(0.891810\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.14590 | −0.149183 | −0.0745916 | − | 0.997214i | \(-0.523765\pi\) | ||||
−0.0745916 | + | 0.997214i | \(0.523765\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.854102 | 0.109357 | 0.0546783 | − | 0.998504i | \(-0.482587\pi\) | ||||
0.0546783 | + | 0.998504i | \(0.482587\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.00000i | 0.855186i | 0.903971 | + | 0.427593i | \(0.140638\pi\) | ||||
−0.903971 | + | 0.427593i | \(0.859362\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.00000 | 1.06810 | 0.534052 | − | 0.845452i | \(-0.320669\pi\) | ||||
0.534052 | + | 0.845452i | \(0.320669\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.70820i | 0.316971i | 0.987361 | + | 0.158486i | \(0.0506612\pi\) | ||||
−0.987361 | + | 0.158486i | \(0.949339\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.29180i | 0.603056i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.7082 | −1.31728 | −0.658638 | − | 0.752460i | \(-0.728867\pi\) | ||||
−0.658638 | + | 0.752460i | \(0.728867\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.70820i | 0.736321i | 0.929762 | + | 0.368161i | \(0.120012\pi\) | ||||
−0.929762 | + | 0.368161i | \(0.879988\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.0000 | 1.27200 | 0.635999 | − | 0.771690i | \(-0.280588\pi\) | ||||
0.635999 | + | 0.771690i | \(0.280588\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.43769 | −0.255540 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.0000i | 1.01535i | 0.861550 | + | 0.507673i | \(0.169494\pi\) | ||||
−0.861550 | + | 0.507673i | \(0.830506\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.85410 | 0.483001 | 0.241501 | − | 0.970401i | \(-0.422360\pi\) | ||||
0.241501 | + | 0.970401i | \(0.422360\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.145898i | 0.0143758i | 0.999974 | + | 0.00718788i | \(0.00228799\pi\) | ||||
−0.999974 | + | 0.00718788i | \(0.997712\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 18.7082i | − 1.80859i | −0.426908 | − | 0.904295i | \(-0.640397\pi\) | ||||
0.426908 | − | 0.904295i | \(-0.359603\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.85410 | −0.369156 | −0.184578 | − | 0.982818i | \(-0.559092\pi\) | ||||
−0.184578 | + | 0.982818i | \(0.559092\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 1.85410i | − 0.174419i | −0.996190 | − | 0.0872096i | \(-0.972205\pi\) | ||||
0.996190 | − | 0.0872096i | \(-0.0277950\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.27051 | 0.299807 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.56231 | −0.687482 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.00000i | 0.621150i | 0.950549 | + | 0.310575i | \(0.100522\pi\) | ||||
−0.950549 | + | 0.310575i | \(0.899478\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.29180 | −0.200235 | −0.100118 | − | 0.994976i | \(-0.531922\pi\) | ||||
−0.100118 | + | 0.994976i | \(0.531922\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 5.70820i | − 0.494964i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 2.56231i | − 0.218913i | −0.993992 | − | 0.109456i | \(-0.965089\pi\) | ||||
0.993992 | − | 0.109456i | \(-0.0349110\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.2705 | −1.46487 | −0.732433 | − | 0.680839i | \(-0.761615\pi\) | ||||
−0.732433 | + | 0.680839i | \(0.761615\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.58359i | 0.132427i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.0000 | −1.22885 | −0.614424 | − | 0.788976i | \(-0.710612\pi\) | ||||
−0.614424 | + | 0.788976i | \(0.710612\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.14590 | −0.662904 | −0.331452 | − | 0.943472i | \(-0.607538\pi\) | ||||
−0.331452 | + | 0.943472i | \(0.607538\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.7082i | 1.33346i | 0.745299 | + | 0.666730i | \(0.232307\pi\) | ||||
−0.745299 | + | 0.666730i | \(0.767693\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 13.8541 | 1.09186 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 14.4164i | − 1.12918i | −0.825371 | − | 0.564590i | \(-0.809034\pi\) | ||||
0.825371 | − | 0.564590i | \(-0.190966\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 22.8541i | 1.76850i | 0.467011 | + | 0.884252i | \(0.345331\pi\) | ||||
−0.467011 | + | 0.884252i | \(0.654669\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.2705 | 0.943885 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 15.7082i | − 1.19427i | −0.802140 | − | 0.597136i | \(-0.796305\pi\) | ||||
0.802140 | − | 0.597136i | \(-0.203695\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.29180 | 0.395527 | 0.197764 | − | 0.980250i | \(-0.436632\pi\) | ||||
0.197764 | + | 0.980250i | \(0.436632\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.4164 | −1.07156 | −0.535782 | − | 0.844357i | \(-0.679983\pi\) | ||||
−0.535782 | + | 0.844357i | \(0.679983\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 2.12461i | − 0.155367i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.4164 | −1.40492 | −0.702461 | − | 0.711722i | \(-0.747915\pi\) | ||||
−0.702461 | + | 0.711722i | \(0.747915\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 16.7082i | − 1.20268i | −0.798992 | − | 0.601341i | \(-0.794633\pi\) | ||||
0.798992 | − | 0.601341i | \(-0.205367\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 25.8541i | − 1.84203i | −0.389529 | − | 0.921014i | \(-0.627362\pi\) | ||||
0.389529 | − | 0.921014i | \(-0.372638\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.8541 | −1.12387 | −0.561934 | − | 0.827182i | \(-0.689942\pi\) | ||||
−0.561934 | + | 0.827182i | \(0.689942\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 10.5836i | − 0.742823i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.70820 | −0.256502 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.7082 | −1.56330 | −0.781649 | − | 0.623719i | \(-0.785621\pi\) | ||||
−0.781649 | + | 0.623719i | \(0.785621\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.72949i | 0.524712i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.978714 | 0.0658354 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 3.29180i | − 0.220435i | −0.993907 | − | 0.110217i | \(-0.964845\pi\) | ||||
0.993907 | − | 0.110217i | \(-0.0351547\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 3.00000i | − 0.199117i | −0.995032 | − | 0.0995585i | \(-0.968257\pi\) | ||||
0.995032 | − | 0.0995585i | \(-0.0317430\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.41641 | 0.556172 | 0.278086 | − | 0.960556i | \(-0.410300\pi\) | ||||
0.278086 | + | 0.960556i | \(0.410300\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 20.1246i | 1.31841i | 0.751965 | + | 0.659204i | \(0.229106\pi\) | ||||
−0.751965 | + | 0.659204i | \(0.770894\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.4164 | −0.867835 | −0.433918 | − | 0.900953i | \(-0.642869\pi\) | ||||
−0.433918 | + | 0.900953i | \(0.642869\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.4164 | −1.12189 | −0.560945 | − | 0.827853i | \(-0.689562\pi\) | ||||
−0.560945 | + | 0.827853i | \(0.689562\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 1.70820i | − 0.108690i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.8541 | 0.685105 | 0.342552 | − | 0.939499i | \(-0.388709\pi\) | ||||
0.342552 | + | 0.939499i | \(0.388709\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 9.00000i | − 0.565825i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 25.4164i | 1.58543i | 0.609591 | + | 0.792716i | \(0.291334\pi\) | ||||
−0.609591 | + | 0.792716i | \(0.708666\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −16.7082 | −1.03820 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.29180i | 0.141318i | 0.997501 | + | 0.0706591i | \(0.0225102\pi\) | ||||
−0.997501 | + | 0.0706591i | \(0.977490\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 27.2705 | 1.66271 | 0.831356 | − | 0.555740i | \(-0.187565\pi\) | ||||
0.831356 | + | 0.555740i | \(0.187565\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.41641 | −0.511260 | −0.255630 | − | 0.966775i | \(-0.582283\pi\) | ||||
−0.255630 | + | 0.966775i | \(0.582283\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.4164i | 1.40696i | 0.710717 | + | 0.703478i | \(0.248371\pi\) | ||||
−0.710717 | + | 0.703478i | \(0.751629\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.70820 | −0.400178 | −0.200089 | − | 0.979778i | \(-0.564123\pi\) | ||||
−0.200089 | + | 0.979778i | \(0.564123\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 11.8541i | − 0.704653i | −0.935877 | − | 0.352327i | \(-0.885391\pi\) | ||||
0.935877 | − | 0.352327i | \(-0.114609\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 33.0000i | − 1.94793i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.6869 | 0.922760 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 20.1246i | 1.17569i | 0.808973 | + | 0.587846i | \(0.200024\pi\) | ||||
−0.808973 | + | 0.587846i | \(0.799976\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.14590 | 0.239763 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.43769 | −0.140506 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.0000i | 0.570730i | 0.958419 | + | 0.285365i | \(0.0921148\pi\) | ||||
−0.958419 | + | 0.285365i | \(0.907885\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.708204 | 0.0401586 | 0.0200793 | − | 0.999798i | \(-0.493608\pi\) | ||||
0.0200793 | + | 0.999798i | \(0.493608\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 20.8541i | − 1.17874i | −0.807862 | − | 0.589372i | \(-0.799375\pi\) | ||||
0.807862 | − | 0.589372i | \(-0.200625\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.58359i | 0.0889434i | 0.999011 | + | 0.0444717i | \(0.0141605\pi\) | ||||
−0.999011 | + | 0.0444717i | \(0.985840\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.87539 | −0.384948 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.29180i | 0.127519i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −19.1459 | −1.05555 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.4164 | −0.957292 | −0.478646 | − | 0.878008i | \(-0.658872\pi\) | ||||
−0.478646 | + | 0.878008i | \(0.658872\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.2918i | 0.996418i | 0.867057 | + | 0.498209i | \(0.166009\pi\) | ||||
−0.867057 | + | 0.498209i | \(0.833991\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.02129 | 0.271918 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.7082i | 0.902158i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 35.5623i | 1.90908i | 0.298075 | + | 0.954542i | \(0.403655\pi\) | ||||
−0.298075 | + | 0.954542i | \(0.596345\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −23.7082 | −1.26907 | −0.634536 | − | 0.772894i | \(-0.718809\pi\) | ||||
−0.634536 | + | 0.772894i | \(0.718809\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 17.5623i | − 0.934747i | −0.884060 | − | 0.467374i | \(-0.845200\pi\) | ||||
0.884060 | − | 0.467374i | \(-0.154800\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.1459 | 0.852148 | 0.426074 | − | 0.904688i | \(-0.359896\pi\) | ||||
0.426074 | + | 0.904688i | \(0.359896\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.56231i | 0.499148i | 0.968356 | + | 0.249574i | \(0.0802906\pi\) | ||||
−0.968356 | + | 0.249574i | \(0.919709\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13.8541 | −0.719269 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.1246i | 0.834901i | 0.908700 | + | 0.417450i | \(0.137076\pi\) | ||||
−0.908700 | + | 0.417450i | \(0.862924\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 3.16718i | − 0.163118i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.2705 | −1.04123 | −0.520613 | − | 0.853793i | \(-0.674297\pi\) | ||||
−0.520613 | + | 0.853793i | \(0.674297\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 30.9787i | − 1.58294i | −0.611209 | − | 0.791469i | \(-0.709317\pi\) | ||||
0.611209 | − | 0.791469i | \(-0.290683\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.70820 | −0.340119 | −0.170060 | − | 0.985434i | \(-0.554396\pi\) | ||||
−0.170060 | + | 0.985434i | \(0.554396\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.56231 | −0.281298 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 31.5410i | 1.58300i | 0.611170 | + | 0.791499i | \(0.290699\pi\) | ||||
−0.611170 | + | 0.791499i | \(0.709301\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −35.1246 | −1.75404 | −0.877020 | − | 0.480454i | \(-0.840472\pi\) | ||||
−0.877020 | + | 0.480454i | \(0.840472\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.31308i | 0.115223i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.8541i | 0.538018i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.2705 | −0.705631 | −0.352816 | − | 0.935693i | \(-0.614776\pi\) | ||||
−0.352816 | + | 0.935693i | \(0.614776\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 3.27051i | − 0.160931i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.14590 | −0.202540 | −0.101270 | − | 0.994859i | \(-0.532291\pi\) | ||||
−0.101270 | + | 0.994859i | \(0.532291\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.70820 | 0.278201 | 0.139100 | − | 0.990278i | \(-0.455579\pi\) | ||||
0.139100 | + | 0.990278i | \(0.455579\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.43769i | 0.117968i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.0000 | 1.01153 | 0.505767 | − | 0.862670i | \(-0.331209\pi\) | ||||
0.505767 | + | 0.862670i | \(0.331209\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 37.7082i | − 1.81214i | −0.423127 | − | 0.906070i | \(-0.639068\pi\) | ||||
0.423127 | − | 0.906070i | \(-0.360932\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.70820i | 0.464406i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.56231 | 0.456384 | 0.228192 | − | 0.973616i | \(-0.426719\pi\) | ||||
0.228192 | + | 0.973616i | \(0.426719\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.1459i | 0.909649i | 0.890581 | + | 0.454825i | \(0.150298\pi\) | ||||
−0.890581 | + | 0.454825i | \(0.849702\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.14590 | 0.337236 | 0.168618 | − | 0.985681i | \(-0.446070\pi\) | ||||
0.168618 | + | 0.985681i | \(0.446070\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −21.4377 | −1.00946 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.0000i | 0.467780i | 0.972263 | + | 0.233890i | \(0.0751456\pi\) | ||||
−0.972263 | + | 0.233890i | \(0.924854\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 23.5623 | 1.09741 | 0.548703 | − | 0.836017i | \(-0.315122\pi\) | ||||
0.548703 | + | 0.836017i | \(0.315122\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.14590i | 0.146202i | 0.997325 | + | 0.0731011i | \(0.0232896\pi\) | ||||
−0.997325 | + | 0.0731011i | \(0.976710\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 12.0000i | − 0.555294i | −0.960683 | − | 0.277647i | \(-0.910445\pi\) | ||||
0.960683 | − | 0.277647i | \(-0.0895545\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −19.9787 | −0.922531 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.58359i | 0.0728136i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16.1459 | −0.737725 | −0.368862 | − | 0.929484i | \(-0.620253\pi\) | ||||
−0.368862 | + | 0.929484i | \(0.620253\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.00000 | −0.227980 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 3.41641i | − 0.154812i | −0.997000 | − | 0.0774061i | \(-0.975336\pi\) | ||||
0.997000 | − | 0.0774061i | \(-0.0246638\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.8328 | −0.804784 | −0.402392 | − | 0.915468i | \(-0.631821\pi\) | ||||
−0.402392 | + | 0.915468i | \(0.631821\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.24922i | 0.191375i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 25.6869i | 1.15222i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.43769 | −0.243425 | −0.121712 | − | 0.992565i | \(-0.538839\pi\) | ||||
−0.121712 | + | 0.992565i | \(0.538839\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.2705i | 1.08217i | 0.840968 | + | 0.541084i | \(0.181986\pi\) | ||||
−0.840968 | + | 0.541084i | \(0.818014\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −21.0000 | −0.930809 | −0.465404 | − | 0.885098i | \(-0.654091\pi\) | ||||
−0.465404 | + | 0.885098i | \(0.654091\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.72949 | −0.341933 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.4377i | 0.547009i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 35.1246 | 1.53884 | 0.769419 | − | 0.638745i | \(-0.220546\pi\) | ||||
0.769419 | + | 0.638745i | \(0.220546\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.4164i | 0.805293i | 0.915355 | + | 0.402647i | \(0.131910\pi\) | ||||
−0.915355 | + | 0.402647i | \(0.868090\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 3.10333i | − 0.135183i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.562306 | −0.0244481 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 9.87539i | − 0.427751i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.12461 | −0.0915135 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 40.3951 | 1.73672 | 0.868361 | − | 0.495933i | \(-0.165174\pi\) | ||||
0.868361 | + | 0.495933i | \(0.165174\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 38.4164i | 1.64257i | 0.570520 | + | 0.821283i | \(0.306742\pi\) | ||||
−0.570520 | + | 0.821283i | \(0.693258\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.41641 | 0.315950 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 33.4164i | − 1.42101i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 40.2492i | − 1.70541i | −0.522389 | − | 0.852707i | \(-0.674959\pi\) | ||||
0.522389 | − | 0.852707i | \(-0.325041\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.729490 | −0.0308541 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 36.7082i | − 1.54707i | −0.633756 | − | 0.773533i | \(-0.718488\pi\) | ||||
0.633756 | − | 0.773533i | \(-0.281512\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.70820 | 0.155456 | 0.0777280 | − | 0.996975i | \(-0.475233\pi\) | ||||
0.0777280 | + | 0.996975i | \(0.475233\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.8328 | 0.453339 | 0.226670 | − | 0.973972i | \(-0.427216\pi\) | ||||
0.226670 | + | 0.973972i | \(0.427216\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 0.416408i | − 0.0173353i | −0.999962 | − | 0.00866764i | \(-0.997241\pi\) | ||||
0.999962 | − | 0.00866764i | \(-0.00275903\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −19.1459 | −0.794306 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.00000i | 0.372742i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 15.0000i | − 0.619116i | −0.950881 | − | 0.309558i | \(-0.899819\pi\) | ||||
0.950881 | − | 0.309558i | \(-0.100181\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.41641 | −0.223179 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 3.27051i | − 0.134304i | −0.997743 | − | 0.0671519i | \(-0.978609\pi\) | ||||
0.997743 | − | 0.0671519i | \(-0.0213912\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20.5623 | 0.840153 | 0.420077 | − | 0.907489i | \(-0.362003\pi\) | ||||
0.420077 | + | 0.907489i | \(0.362003\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.85410 | 0.401957 | 0.200979 | − | 0.979596i | \(-0.435588\pi\) | ||||
0.200979 | + | 0.979596i | \(0.435588\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.5410i | 1.15844i | 0.815170 | + | 0.579222i | \(0.196644\pi\) | ||||
−0.815170 | + | 0.579222i | \(0.803356\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.72949 | −0.231790 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.7082i | 0.472890i | 0.971645 | + | 0.236445i | \(0.0759823\pi\) | ||||
−0.971645 | + | 0.236445i | \(0.924018\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 20.1246i | − 0.810186i | −0.914275 | − | 0.405093i | \(-0.867239\pi\) | ||||
0.914275 | − | 0.405093i | \(-0.132761\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −33.4164 | −1.34312 | −0.671559 | − | 0.740951i | \(-0.734375\pi\) | ||||
−0.671559 | + | 0.740951i | \(0.734375\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 34.2492i | 1.37217i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.70820 | 0.267474 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.145898 | 0.00580811 | 0.00290405 | − | 0.999996i | \(-0.499076\pi\) | ||||
0.00290405 | + | 0.999996i | \(0.499076\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 0.978714i | − 0.0387781i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.5623 | 0.456684 | 0.228342 | − | 0.973581i | \(-0.426670\pi\) | ||||
0.228342 | + | 0.973581i | \(0.426670\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 37.5623i | 1.48131i | 0.671884 | + | 0.740656i | \(0.265485\pi\) | ||||
−0.671884 | + | 0.740656i | \(0.734515\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 24.7082i | − 0.971380i | −0.874131 | − | 0.485690i | \(-0.838568\pi\) | ||||
0.874131 | − | 0.485690i | \(-0.161432\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.12461 | −0.0833983 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.14590i | 0.162242i | 0.996704 | + | 0.0811208i | \(0.0258499\pi\) | ||||
−0.996704 | + | 0.0811208i | \(0.974150\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.2705 | −0.711718 | −0.355859 | − | 0.934540i | \(-0.615812\pi\) | ||||
−0.355859 | + | 0.934540i | \(0.615812\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.8328 | 1.00478 | 0.502390 | − | 0.864641i | \(-0.332454\pi\) | ||||
0.502390 | + | 0.864641i | \(0.332454\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.0000i | 0.696963i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.58359 | 0.0611339 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.70820i | 0.104394i | 0.998637 | + | 0.0521968i | \(0.0166223\pi\) | ||||
−0.998637 | + | 0.0521968i | \(0.983378\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.4164i | 0.630934i | 0.948937 | + | 0.315467i | \(0.102161\pi\) | ||||
−0.948937 | + | 0.315467i | \(0.897839\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −28.5410 | −1.09530 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29.3951i | 1.12477i | 0.826874 | + | 0.562387i | \(0.190117\pi\) | ||||
−0.826874 | + | 0.562387i | \(0.809883\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.14590 | −0.157946 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.1246 | 0.385158 | 0.192579 | − | 0.981281i | \(-0.438315\pi\) | ||||
0.192579 | + | 0.981281i | \(0.438315\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.2492i | 0.501850i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15.7082 | −0.593291 | −0.296645 | − | 0.954988i | \(-0.595868\pi\) | ||||
−0.296645 | + | 0.954988i | \(0.595868\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 11.7082i | − 0.441583i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.8541i | 0.521037i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.0000 | 0.713560 | 0.356780 | − | 0.934188i | \(-0.383875\pi\) | ||||
0.356780 | + | 0.934188i | \(0.383875\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 13.1459i | − 0.492318i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 20.5623 | 0.766845 | 0.383422 | − | 0.923573i | \(-0.374745\pi\) | ||||
0.383422 | + | 0.923573i | \(0.374745\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.416408 | −0.0155078 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 37.5623i | − 1.39311i | −0.717504 | − | 0.696554i | \(-0.754715\pi\) | ||||
0.717504 | − | 0.696554i | \(-0.245285\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.978714 | 0.0361990 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 36.5623i | − 1.35046i | −0.737607 | − | 0.675230i | \(-0.764044\pi\) | ||||
0.737607 | − | 0.675230i | \(-0.235956\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.9787i | 0.478077i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.43769 | −0.200029 | −0.100014 | − | 0.994986i | \(-0.531889\pi\) | ||||
−0.100014 | + | 0.994986i | \(0.531889\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 0.875388i | − 0.0321149i | −0.999871 | − | 0.0160574i | \(-0.994889\pi\) | ||||
0.999871 | − | 0.0160574i | \(-0.00511146\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 53.3951 | 1.95102 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −40.9787 | −1.49533 | −0.747667 | − | 0.664074i | \(-0.768826\pi\) | ||||
−0.747667 | + | 0.664074i | \(0.768826\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.2705i | 1.24558i | 0.782388 | + | 0.622791i | \(0.214001\pi\) | ||||
−0.782388 | + | 0.622791i | \(0.785999\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −34.8541 | −1.26346 | −0.631730 | − | 0.775188i | \(-0.717655\pi\) | ||||
−0.631730 | + | 0.775188i | \(0.717655\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 11.0000i | − 0.398227i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 0.978714i | − 0.0353393i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26.1459 | 0.942845 | 0.471423 | − | 0.881907i | \(-0.343741\pi\) | ||||
0.471423 | + | 0.881907i | \(0.343741\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 33.5410i | − 1.20639i | −0.797595 | − | 0.603193i | \(-0.793895\pi\) | ||||
0.797595 | − | 0.603193i | \(-0.206105\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 23.1246 | 0.828525 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.6869 | 0.597105 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.14590i | 0.0764930i | 0.999268 | + | 0.0382465i | \(0.0121772\pi\) | ||||
−0.999268 | + | 0.0382465i | \(0.987823\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.29180 | 0.188155 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.729490i | 0.0259050i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.27051i | 0.328378i | 0.986429 | + | 0.164189i | \(0.0525007\pi\) | ||||
−0.986429 | + | 0.164189i | \(0.947499\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.68692 | 0.271944 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.02129i | 0.177197i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8.12461 | −0.285646 | −0.142823 | − | 0.989748i | \(-0.545618\pi\) | ||||
−0.142823 | + | 0.989748i | \(0.545618\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.9787 | −0.596203 | −0.298102 | − | 0.954534i | \(-0.596353\pi\) | ||||
−0.298102 | + | 0.954534i | \(0.596353\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 1.70820i | − 0.0597625i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.41641 | 0.154134 | 0.0770668 | − | 0.997026i | \(-0.475445\pi\) | ||||
0.0770668 | + | 0.997026i | \(0.475445\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.5410i | 0.611442i | 0.952121 | + | 0.305721i | \(0.0988974\pi\) | ||||
−0.952121 | + | 0.305721i | \(0.901103\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 44.3951i | 1.54377i | 0.635762 | + | 0.771885i | \(0.280686\pi\) | ||||
−0.635762 | + | 0.771885i | \(0.719314\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.41641 | 0.188120 | 0.0940598 | − | 0.995567i | \(-0.470016\pi\) | ||||
0.0940598 | + | 0.995567i | \(0.470016\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.31308i | 0.0454956i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −53.1246 | −1.83407 | −0.917033 | − | 0.398812i | \(-0.869423\pi\) | ||||
−0.917033 | + | 0.398812i | \(0.869423\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.2492 | −0.525835 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 21.5836i | − 0.741621i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 28.4164 | 0.974102 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 24.1246i | − 0.826011i | −0.910729 | − | 0.413005i | \(-0.864479\pi\) | ||||
0.910729 | − | 0.413005i | \(-0.135521\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.14590i | 0.141621i | 0.997490 | + | 0.0708106i | \(0.0225586\pi\) | ||||
−0.997490 | + | 0.0708106i | \(0.977441\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.58359 | −0.326988 | −0.163494 | − | 0.986544i | \(-0.552276\pi\) | ||||
−0.163494 | + | 0.986544i | \(0.552276\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 15.2705i | 0.519814i | 0.965634 | + | 0.259907i | \(0.0836919\pi\) | ||||
−0.965634 | + | 0.259907i | \(0.916308\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −21.7082 | −0.736400 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.97871 | −0.202581 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 14.2705i | − 0.481881i | −0.970540 | − | 0.240940i | \(-0.922544\pi\) | ||||
0.970540 | − | 0.240940i | \(-0.0774558\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26.1246 | 0.880161 | 0.440080 | − | 0.897958i | \(-0.354950\pi\) | ||||
0.440080 | + | 0.897958i | \(0.354950\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.1246i | 1.04743i | 0.851895 | + | 0.523713i | \(0.175454\pi\) | ||||
−0.851895 | + | 0.523713i | \(0.824546\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.978714i | 0.0328620i | 0.999865 | + | 0.0164310i | \(0.00523038\pi\) | ||||
−0.999865 | + | 0.0164310i | \(0.994770\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −19.9787 | −0.670065 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 13.4164i | − 0.448963i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −10.0426 | −0.334939 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.56231 | 0.185307 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.9787i | 0.464156i | 0.972697 | + | 0.232078i | \(0.0745524\pi\) | ||||
−0.972697 | + | 0.232078i | \(0.925448\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26.1246 | −0.865547 | −0.432774 | − | 0.901503i | \(-0.642465\pi\) | ||||
−0.432774 | + | 0.901503i | \(0.642465\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.4377i | 0.411628i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 6.54102i | − 0.216003i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.5623 | 0.810236 | 0.405118 | − | 0.914264i | \(-0.367230\pi\) | ||||
0.405118 | + | 0.914264i | \(0.367230\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.68692i | 0.253018i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 41.2918 | 1.35474 | 0.677370 | − | 0.735643i | \(-0.263120\pi\) | ||||
0.677370 | + | 0.735643i | \(0.263120\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.29180 | 0.0751106 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 43.8328i | − 1.43196i | −0.698123 | − | 0.715978i | \(-0.745981\pi\) | ||||
0.698123 | − | 0.715978i | \(-0.254019\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 29.3951 | 0.958254 | 0.479127 | − | 0.877746i | \(-0.340953\pi\) | ||||
0.479127 | + | 0.877746i | \(0.340953\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 56.1246i | 1.82767i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 46.4164i | − 1.50833i | −0.656685 | − | 0.754165i | \(-0.728042\pi\) | ||||
0.656685 | − | 0.754165i | \(-0.271958\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.31308 | −0.0750858 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 3.16718i | − 0.102595i | −0.998683 | − | 0.0512976i | \(-0.983664\pi\) | ||||
0.998683 | − | 0.0512976i | \(-0.0163357\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.31308 | 0.236152 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.6656 | −0.763407 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 43.8328i | − 1.40957i | −0.709422 | − | 0.704784i | \(-0.751044\pi\) | ||||
0.709422 | − | 0.704784i | \(-0.248956\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.9787 | −0.705330 | −0.352665 | − | 0.935750i | \(-0.614725\pi\) | ||||
−0.352665 | + | 0.935750i | \(0.614725\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 49.2918i | − 1.58022i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 37.6869i | − 1.20571i | −0.797850 | − | 0.602856i | \(-0.794029\pi\) | ||||
0.797850 | − | 0.602856i | \(-0.205971\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 22.2492 | 0.711088 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 9.54102i | − 0.304311i | −0.988357 | − | 0.152156i | \(-0.951379\pi\) | ||||
0.988357 | − | 0.152156i | \(-0.0486215\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.14590 | 0.131832 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.1459 | −0.735254 | −0.367627 | − | 0.929973i | \(-0.619830\pi\) | ||||
−0.367627 | + | 0.929973i | \(0.619830\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.12461i | 0.0989574i | 0.998775 | + | 0.0494787i | \(0.0157560\pi\) | ||||
−0.998775 | + | 0.0494787i | \(0.984244\pi\) | |||||||
\(998\) | 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 | 8100.2.d.k.649.3 | 4 | ||
3.2 | odd | 2 | 8100.2.d.n.649.3 | 4 | |||
5.2 | odd | 4 | 8100.2.a.q.1.1 | yes | 2 | ||
5.3 | odd | 4 | 8100.2.a.o.1.2 | ✓ | 2 | ||
5.4 | even | 2 | inner | 8100.2.d.k.649.2 | 4 | ||
15.2 | even | 4 | 8100.2.a.r.1.1 | yes | 2 | ||
15.8 | even | 4 | 8100.2.a.p.1.2 | yes | 2 | ||
15.14 | odd | 2 | 8100.2.d.n.649.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8100.2.a.o.1.2 | ✓ | 2 | 5.3 | odd | 4 | ||
8100.2.a.p.1.2 | yes | 2 | 15.8 | even | 4 | ||
8100.2.a.q.1.1 | yes | 2 | 5.2 | odd | 4 | ||
8100.2.a.r.1.1 | yes | 2 | 15.2 | even | 4 | ||
8100.2.d.k.649.2 | 4 | 5.4 | even | 2 | inner | ||
8100.2.d.k.649.3 | 4 | 1.1 | even | 1 | trivial | ||
8100.2.d.n.649.2 | 4 | 15.14 | odd | 2 | |||
8100.2.d.n.649.3 | 4 | 3.2 | odd | 2 |