Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5184,2,Mod(2591,5184)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5184, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5184.2591");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5184 = 2^{6} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5184.f (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: | \(41.3944484078\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8x^{14} + 49x^{12} - 104x^{10} + 160x^{8} - 104x^{6} + 49x^{4} - 8x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{37}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2591.6 | ||
Root | \(0.670418 + 0.387066i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5184.2591 |
Dual form | 5184.2.f.b.2591.5 |
$q$-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 \(\left(\mathbb{Z}/5184\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1217\) | \(2431\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(5\) | −1.59733 | −0.714347 | −0.357174 | − | 0.934038i | \(-0.616260\pi\) | ||||
−0.357174 | + | 0.934038i | \(0.616260\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.16418i | 0.440018i | 0.975498 | + | 0.220009i | \(0.0706086\pi\) | ||||
−0.975498 | + | 0.220009i | \(0.929391\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.98092i | 0.597269i | 0.954368 | + | 0.298635i | \(0.0965312\pi\) | ||||
−0.954368 | + | 0.298635i | \(0.903469\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.164177i | 0.0455345i | 0.999741 | + | 0.0227672i | \(0.00724766\pi\) | ||||
−0.999741 | + | 0.0227672i | \(0.992752\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.57825i | 0.867852i | 0.900948 | + | 0.433926i | \(0.142872\pi\) | ||||
−0.900948 | + | 0.433926i | \(0.857128\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.16418 | −0.725912 | −0.362956 | − | 0.931806i | \(-0.618232\pi\) | ||||
−0.362956 | + | 0.931806i | \(0.618232\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.21374 | 0.253082 | 0.126541 | − | 0.991961i | \(-0.459612\pi\) | ||||
0.126541 | + | 0.991961i | \(0.459612\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.44854 | −0.489708 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.98396 | −0.925499 | −0.462749 | − | 0.886489i | \(-0.653137\pi\) | ||||
−0.462749 | + | 0.886489i | \(0.653137\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 6.64469i | − 1.19342i | −0.802456 | − | 0.596711i | \(-0.796474\pi\) | ||||
0.802456 | − | 0.596711i | \(-0.203526\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 1.85957i | − 0.314325i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 1.10377i | − 0.181459i | −0.995876 | − | 0.0907295i | \(-0.971080\pi\) | ||||
0.995876 | − | 0.0907295i | \(-0.0289199\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.02533i | 0.316304i | 0.987415 | + | 0.158152i | \(0.0505536\pi\) | ||||
−0.987415 | + | 0.158152i | \(0.949446\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.34477 | −1.27257 | −0.636283 | − | 0.771456i | \(-0.719529\pi\) | ||||
−0.636283 | + | 0.771456i | \(0.719529\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.21731 | −0.323428 | −0.161714 | − | 0.986838i | \(-0.551702\pi\) | ||||
−0.161714 | + | 0.986838i | \(0.551702\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.64469 | 0.806385 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.65461 | 1.32616 | 0.663081 | − | 0.748548i | \(-0.269248\pi\) | ||||
0.663081 | + | 0.748548i | \(0.269248\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 3.16418i | − 0.426658i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 0.888520i | − 0.115675i | −0.998326 | − | 0.0578377i | \(-0.981579\pi\) | ||||
0.998326 | − | 0.0578377i | \(-0.0184206\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 9.74846i | − 1.24816i | −0.781359 | − | 0.624081i | \(-0.785473\pi\) | ||||
0.781359 | − | 0.624081i | \(-0.214527\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 0.262245i | − 0.0325274i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.98359 | −0.486673 | −0.243336 | − | 0.969942i | \(-0.578242\pi\) | ||||
−0.243336 | + | 0.969942i | \(0.578242\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.8049 | 1.51966 | 0.759828 | − | 0.650124i | \(-0.225283\pi\) | ||||
0.759828 | + | 0.650124i | \(0.225283\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.879814 | 0.102974 | 0.0514872 | − | 0.998674i | \(-0.483604\pi\) | ||||
0.0514872 | + | 0.998674i | \(0.483604\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.30614 | −0.262809 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 2.91179i | − 0.327602i | −0.986493 | − | 0.163801i | \(-0.947625\pi\) | ||||
0.986493 | − | 0.163801i | \(-0.0523755\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.9298i | 1.52899i | 0.644630 | + | 0.764495i | \(0.277012\pi\) | ||||
−0.644630 | + | 0.764495i | \(0.722988\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 5.71564i | − 0.619948i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.41501i | 0.891990i | 0.895036 | + | 0.445995i | \(0.147150\pi\) | ||||
−0.895036 | + | 0.445995i | \(0.852850\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.191131 | −0.0200360 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.05423 | 0.518553 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.31634 | 0.438258 | 0.219129 | − | 0.975696i | \(-0.429678\pi\) | ||||
0.219129 | + | 0.975696i | \(0.429678\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.3103 | −1.12542 | −0.562709 | − | 0.826655i | \(-0.690241\pi\) | ||||
−0.562709 | + | 0.826655i | \(0.690241\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.00000i | 0.197066i | 0.995134 | + | 0.0985329i | \(0.0314150\pi\) | ||||
−0.995134 | + | 0.0985329i | \(0.968585\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 19.4306i | − 1.87842i | −0.343339 | − | 0.939211i | \(-0.611558\pi\) | ||||
0.343339 | − | 0.939211i | \(-0.388442\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 10.7760i | − 1.03216i | −0.856541 | − | 0.516079i | \(-0.827391\pi\) | ||||
0.856541 | − | 0.516079i | \(-0.172609\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 4.46677i | − 0.420198i | −0.977680 | − | 0.210099i | \(-0.932621\pi\) | ||||
0.977680 | − | 0.210099i | \(-0.0673786\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.93874 | −0.180789 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.16571 | −0.381870 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.07597 | 0.643270 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.8978 | 1.06417 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 9.22813i | − 0.818864i | −0.912341 | − | 0.409432i | \(-0.865727\pi\) | ||||
0.912341 | − | 0.409432i | \(-0.134273\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.6764i | 0.932799i | 0.884574 | + | 0.466399i | \(0.154449\pi\) | ||||
−0.884574 | + | 0.466399i | \(0.845551\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 3.68366i | − 0.319414i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 20.2163i | − 1.72719i | −0.504182 | − | 0.863597i | \(-0.668206\pi\) | ||||
0.504182 | − | 0.863597i | \(-0.331794\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.1686 | −1.11694 | −0.558472 | − | 0.829523i | \(-0.688612\pi\) | ||||
−0.558472 | + | 0.829523i | \(0.688612\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.325221 | −0.0271963 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.96103 | 0.661128 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.99383 | 0.491033 | 0.245517 | − | 0.969392i | \(-0.421042\pi\) | ||||
0.245517 | + | 0.969392i | \(0.421042\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 2.32835i | − 0.189479i | −0.995502 | − | 0.0947394i | \(-0.969798\pi\) | ||||
0.995502 | − | 0.0947394i | \(-0.0302018\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.6138i | 0.852518i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 9.14861i | − 0.730139i | −0.930980 | − | 0.365069i | \(-0.881045\pi\) | ||||
0.930980 | − | 0.365069i | \(-0.118955\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.41301i | 0.111361i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −22.1416 | −1.73427 | −0.867133 | − | 0.498077i | \(-0.834040\pi\) | ||||
−0.867133 | + | 0.498077i | \(0.834040\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −21.4440 | −1.65939 | −0.829693 | − | 0.558220i | \(-0.811484\pi\) | ||||
−0.829693 | + | 0.558220i | \(0.811484\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.9730 | 0.997927 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −16.7481 | −1.27334 | −0.636668 | − | 0.771138i | \(-0.719688\pi\) | ||||
−0.636668 | + | 0.771138i | \(0.719688\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 2.85053i | − 0.215480i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 16.1146i | − 1.20446i | −0.798323 | − | 0.602229i | \(-0.794279\pi\) | ||||
0.798323 | − | 0.602229i | \(-0.205721\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 16.3612i | − 1.21612i | −0.793892 | − | 0.608059i | \(-0.791949\pi\) | ||||
0.793892 | − | 0.608059i | \(-0.208051\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.76309i | 0.129625i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.08821 | −0.518341 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.6326 | −1.34820 | −0.674102 | − | 0.738638i | \(-0.735469\pi\) | ||||
−0.674102 | + | 0.738638i | \(0.735469\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.65671 | −0.119252 | −0.0596262 | − | 0.998221i | \(-0.518991\pi\) | ||||
−0.0596262 | + | 0.998221i | \(0.518991\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.8978 | 0.847681 | 0.423840 | − | 0.905737i | \(-0.360682\pi\) | ||||
0.423840 | + | 0.905737i | \(0.360682\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.32835i | 0.590381i | 0.955438 | + | 0.295191i | \(0.0953832\pi\) | ||||
−0.955438 | + | 0.295191i | \(0.904617\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 5.80222i | − 0.407236i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 3.23512i | − 0.225951i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 6.26797i | − 0.433565i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.77187 | −0.328509 | −0.164255 | − | 0.986418i | \(-0.552522\pi\) | ||||
−0.164255 | + | 0.986418i | \(0.552522\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 13.3293 | 0.909053 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.73560 | 0.525127 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.587465 | −0.0395172 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 24.4415i | − 1.63673i | −0.574701 | − | 0.818363i | \(-0.694882\pi\) | ||||
0.574701 | − | 0.818363i | \(-0.305118\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.9107i | 1.05603i | 0.849235 | + | 0.528014i | \(0.177063\pi\) | ||||
−0.849235 | + | 0.528014i | \(0.822937\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 25.1700i | − 1.66328i | −0.555312 | − | 0.831642i | \(-0.687401\pi\) | ||||
0.555312 | − | 0.831642i | \(-0.312599\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.87605i | 0.450465i | 0.974305 | + | 0.225233i | \(0.0723142\pi\) | ||||
−0.974305 | + | 0.225233i | \(0.927686\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.54177 | 0.231040 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.8300 | 1.08864 | 0.544322 | − | 0.838876i | \(-0.316787\pi\) | ||||
0.544322 | + | 0.838876i | \(0.316787\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.1692 | 0.783887 | 0.391943 | − | 0.919989i | \(-0.371803\pi\) | ||||
0.391943 | + | 0.919989i | \(0.371803\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.01643 | −0.576039 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 0.519485i | − 0.0330540i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 22.1787i | − 1.39990i | −0.714190 | − | 0.699952i | \(-0.753205\pi\) | ||||
0.714190 | − | 0.699952i | \(-0.246795\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.40432i | 0.151158i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 4.86892i | − 0.303715i | −0.988402 | − | 0.151857i | \(-0.951475\pi\) | ||||
0.988402 | − | 0.151857i | \(-0.0485254\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.28499 | 0.0798452 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −17.1807 | −1.05941 | −0.529705 | − | 0.848182i | \(-0.677697\pi\) | ||||
−0.529705 | + | 0.848182i | \(0.677697\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −15.4216 | −0.947340 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 28.1844 | 1.71843 | 0.859216 | − | 0.511613i | \(-0.170952\pi\) | ||||
0.859216 | + | 0.511613i | \(0.170952\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 17.6324i | − 1.07109i | −0.844505 | − | 0.535547i | \(-0.820105\pi\) | ||||
0.844505 | − | 0.535547i | \(-0.179895\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 4.85035i | − 0.292487i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 20.0968i | − 1.20750i | −0.797174 | − | 0.603749i | \(-0.793673\pi\) | ||||
0.797174 | − | 0.603749i | \(-0.206327\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.06089i | 0.301908i | 0.988541 | + | 0.150954i | \(0.0482345\pi\) | ||||
−0.988541 | + | 0.150954i | \(0.951766\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.55208 | −0.567812 | −0.283906 | − | 0.958852i | \(-0.591630\pi\) | ||||
−0.283906 | + | 0.958852i | \(0.591630\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.35784 | −0.139179 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.19615 | 0.246832 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.33095 | −0.369858 | −0.184929 | − | 0.982752i | \(-0.559206\pi\) | ||||
−0.184929 | + | 0.982752i | \(0.559206\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.41926i | 0.0826324i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.199268i | 0.0115240i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 9.71479i | − 0.559951i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 15.5715i | 0.891622i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.58074 | −0.261437 | −0.130718 | − | 0.991420i | \(-0.541728\pi\) | ||||
−0.130718 | + | 0.991420i | \(0.541728\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.0707 | −1.36493 | −0.682463 | − | 0.730920i | \(-0.739091\pi\) | ||||
−0.682463 | + | 0.730920i | \(0.739091\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.07597 | 0.173864 | 0.0869320 | − | 0.996214i | \(-0.472294\pi\) | ||||
0.0869320 | + | 0.996214i | \(0.472294\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.37060 | −0.470140 | −0.235070 | − | 0.971978i | \(-0.575532\pi\) | ||||
−0.235070 | + | 0.971978i | \(0.575532\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 9.87282i | − 0.552772i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 11.3222i | − 0.629984i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 0.401994i | − 0.0222986i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 2.58134i | − 0.142314i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −25.6445 | −1.40955 | −0.704774 | − | 0.709432i | \(-0.748951\pi\) | ||||
−0.704774 | + | 0.709432i | \(0.748951\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.36310 | 0.347653 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.4043 | 0.566759 | 0.283380 | − | 0.959008i | \(-0.408544\pi\) | ||||
0.283380 | + | 0.959008i | \(0.408544\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.1626 | 0.712794 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.7207i | 0.794841i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.971054i | 0.0521289i | 0.999660 | + | 0.0260644i | \(0.00829751\pi\) | ||||
−0.999660 | + | 0.0260644i | \(0.991702\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.57290i | 0.512425i | 0.966620 | + | 0.256213i | \(0.0824747\pi\) | ||||
−0.966620 | + | 0.256213i | \(0.917525\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 21.3671i | − 1.13725i | −0.822596 | − | 0.568627i | \(-0.807475\pi\) | ||||
0.822596 | − | 0.568627i | \(-0.192525\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −20.4536 | −1.08556 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.5074 | 1.24068 | 0.620338 | − | 0.784335i | \(-0.286996\pi\) | ||||
0.620338 | + | 0.784335i | \(0.286996\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.98798 | −0.473052 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.40535 | −0.0735595 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 10.4683i | − 0.546439i | −0.961952 | − | 0.273220i | \(-0.911911\pi\) | ||||
0.961952 | − | 0.273220i | \(-0.0880886\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.2397i | 0.583535i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 28.6668i | 1.48431i | 0.670229 | + | 0.742154i | \(0.266196\pi\) | ||||
−0.670229 | + | 0.742154i | \(0.733804\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 0.818252i | − 0.0421421i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.5729 | −1.10813 | −0.554063 | − | 0.832475i | \(-0.686923\pi\) | ||||
−0.554063 | + | 0.832475i | \(0.686923\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 22.9975 | 1.17512 | 0.587560 | − | 0.809181i | \(-0.300089\pi\) | ||||
0.587560 | + | 0.809181i | \(0.300089\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.68366 | 0.187737 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −19.0980 | −0.968309 | −0.484155 | − | 0.874982i | \(-0.660873\pi\) | ||||
−0.484155 | + | 0.874982i | \(0.660873\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.34306i | 0.219638i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.65109i | 0.234022i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 11.1366i | − 0.558930i | −0.960156 | − | 0.279465i | \(-0.909843\pi\) | ||||
0.960156 | − | 0.279465i | \(-0.0901571\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.65161i | 0.132415i | 0.997806 | + | 0.0662075i | \(0.0210899\pi\) | ||||
−0.997806 | + | 0.0662075i | \(0.978910\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.09091 | 0.0543419 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.18648 | 0.108380 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.8139 | 1.32586 | 0.662931 | − | 0.748681i | \(-0.269312\pi\) | ||||
0.662931 | + | 0.748681i | \(0.269312\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.03439 | 0.0508992 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 22.2504i | − 1.09223i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.92291i | 0.0939405i | 0.998896 | + | 0.0469703i | \(0.0149566\pi\) | ||||
−0.998896 | + | 0.0469703i | \(0.985043\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.272971i | 0.0133038i | 0.999978 | + | 0.00665189i | \(0.00211738\pi\) | ||||
−0.999978 | + | 0.00665189i | \(0.997883\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 8.76148i | − 0.424994i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.3489 | 0.549214 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −33.5705 | −1.61703 | −0.808517 | − | 0.588473i | \(-0.799729\pi\) | ||||
−0.808517 | + | 0.588473i | \(0.799729\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.11494 | 0.197751 | 0.0988756 | − | 0.995100i | \(-0.468475\pi\) | ||||
0.0988756 | + | 0.995100i | \(0.468475\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.84049 | −0.183716 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.2624i | 1.06253i | 0.847206 | + | 0.531264i | \(0.178283\pi\) | ||||
−0.847206 | + | 0.531264i | \(0.821717\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 25.8199i | 1.22674i | 0.789796 | + | 0.613370i | \(0.210186\pi\) | ||||
−0.789796 | + | 0.613370i | \(0.789814\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 13.4415i | − 0.637190i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.4688i | 0.541245i | 0.962686 | + | 0.270622i | \(0.0872295\pi\) | ||||
−0.962686 | + | 0.270622i | \(0.912771\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.01202 | −0.188918 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.305299 | 0.0143126 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −20.5096 | −0.959397 | −0.479699 | − | 0.877433i | \(-0.659254\pi\) | ||||
−0.479699 | + | 0.877433i | \(0.659254\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.0821 | 0.562719 | 0.281359 | − | 0.959602i | \(-0.409215\pi\) | ||||
0.281359 | + | 0.959602i | \(0.409215\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 21.6937i | − 1.00819i | −0.863648 | − | 0.504096i | \(-0.831826\pi\) | ||||
0.863648 | − | 0.504096i | \(-0.168174\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.38932i | 0.295662i | 0.989013 | + | 0.147831i | \(0.0472292\pi\) | ||||
−0.989013 | + | 0.147831i | \(0.952771\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 4.63760i | − 0.214144i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 16.5303i | − 0.760064i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.74761 | 0.355485 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.15743 | −0.0528841 | −0.0264421 | − | 0.999650i | \(-0.508418\pi\) | ||||
−0.0264421 | + | 0.999650i | \(0.508418\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.181214 | 0.00826264 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.89461 | −0.313068 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 8.18844i | − 0.371053i | −0.982639 | − | 0.185527i | \(-0.940601\pi\) | ||||
0.982639 | − | 0.185527i | \(-0.0593991\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.86944i | 0.129496i | 0.997902 | + | 0.0647479i | \(0.0206243\pi\) | ||||
−0.997902 | + | 0.0647479i | \(0.979376\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 17.8339i | − 0.803196i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 14.9071i | 0.668675i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.07327 | 0.0928124 | 0.0464062 | − | 0.998923i | \(-0.485223\pi\) | ||||
0.0464062 | + | 0.998923i | \(0.485223\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 39.0342 | 1.74045 | 0.870224 | − | 0.492657i | \(-0.163974\pi\) | ||||
0.870224 | + | 0.492657i | \(0.163974\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.0663 | 0.803939 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.65838 | −0.206479 | −0.103239 | − | 0.994657i | \(-0.532921\pi\) | ||||
−0.103239 | + | 0.994657i | \(0.532921\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.02426i | 0.0453106i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 3.19466i | − 0.140773i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 4.39230i | − 0.193173i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.42555i | 0.237698i | 0.992912 | + | 0.118849i | \(0.0379204\pi\) | ||||
−0.992912 | + | 0.118849i | \(0.962080\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.8280 | 0.867017 | 0.433508 | − | 0.901149i | \(-0.357275\pi\) | ||||
0.433508 | + | 0.901149i | \(0.357275\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 23.7763 | 1.03571 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.5268 | −0.935949 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.332513 | −0.0144027 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 31.0370i | 1.34185i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11.1817i | 0.481629i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 14.5116i | − 0.623904i | −0.950098 | − | 0.311952i | \(-0.899017\pi\) | ||||
0.950098 | − | 0.311952i | \(-0.100983\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 17.2129i | 0.737319i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.8295 | −0.976117 | −0.488058 | − | 0.872811i | \(-0.662295\pi\) | ||||
−0.488058 | + | 0.872811i | \(0.662295\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.7701 | 0.671831 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.38984 | 0.144151 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10.4848 | −0.444254 | −0.222127 | − | 0.975018i | \(-0.571300\pi\) | ||||
−0.222127 | + | 0.975018i | \(0.571300\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 1.37002i | − 0.0579456i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.69923i | 0.155904i | 0.996957 | + | 0.0779519i | \(0.0248381\pi\) | ||||
−0.996957 | + | 0.0779519i | \(0.975162\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.13490i | 0.300167i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25.8719i | 1.08461i | 0.840182 | + | 0.542304i | \(0.182448\pi\) | ||||
−0.840182 | + | 0.542304i | \(0.817552\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.21171 | −0.218103 | −0.109052 | − | 0.994036i | \(-0.534781\pi\) | ||||
−0.109052 | + | 0.994036i | \(0.534781\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.97189 | −0.123936 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24.9341 | −1.03802 | −0.519010 | − | 0.854768i | \(-0.673699\pi\) | ||||
−0.519010 | + | 0.854768i | \(0.673699\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.2167 | −0.672782 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19.1250i | 0.792076i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 12.0894i | − 0.498982i | −0.968377 | − | 0.249491i | \(-0.919737\pi\) | ||||
0.968377 | − | 0.249491i | \(-0.0802633\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 21.0250i | 0.866319i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 21.3992i | − 0.878760i | −0.898301 | − | 0.439380i | \(-0.855198\pi\) | ||||
0.898301 | − | 0.439380i | \(-0.144802\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.65401 | 0.272788 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −32.8504 | −1.34223 | −0.671116 | − | 0.741353i | \(-0.734185\pi\) | ||||
−0.671116 | + | 0.741353i | \(0.734185\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.7086 | 0.967096 | 0.483548 | − | 0.875318i | \(-0.339348\pi\) | ||||
0.483548 | + | 0.875318i | \(0.339348\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −11.3026 | −0.459518 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 41.4026i | − 1.68048i | −0.542216 | − | 0.840239i | \(-0.682414\pi\) | ||||
0.542216 | − | 0.840239i | \(-0.317586\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 0.364031i | − 0.0147271i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 32.4820i | 1.31194i | 0.754789 | + | 0.655968i | \(0.227739\pi\) | ||||
−0.754789 | + | 0.655968i | \(0.772261\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 30.1842i | 1.21517i | 0.794254 | + | 0.607586i | \(0.207862\pi\) | ||||
−0.794254 | + | 0.607586i | \(0.792138\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.8535 | 0.998946 | 0.499473 | − | 0.866329i | \(-0.333527\pi\) | ||||
0.499473 | + | 0.866329i | \(0.333527\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.79656 | −0.392491 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.76196 | −0.270478 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.94957 | 0.157480 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 31.5937i | 1.25773i | 0.777516 | + | 0.628863i | \(0.216479\pi\) | ||||
−0.777516 | + | 0.628863i | \(0.783521\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14.7404i | 0.584953i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.926728i | 0.0367183i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.48328i | 0.0585859i | 0.999571 | + | 0.0292930i | \(0.00932558\pi\) | ||||
−0.999571 | + | 0.0292930i | \(0.990674\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 45.3533 | 1.78856 | 0.894280 | − | 0.447507i | \(-0.147688\pi\) | ||||
0.894280 | + | 0.447507i | \(0.147688\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.0785 | 0.592796 | 0.296398 | − | 0.955065i | \(-0.404215\pi\) | ||||
0.296398 | + | 0.955065i | \(0.404215\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.76008 | 0.0690894 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 34.3187 | 1.34300 | 0.671498 | − | 0.741006i | \(-0.265651\pi\) | ||||
0.671498 | + | 0.741006i | \(0.265651\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 17.0537i | − 0.666342i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 29.5778i | − 1.15219i | −0.817383 | − | 0.576094i | \(-0.804576\pi\) | ||||
0.817383 | − | 0.576094i | \(-0.195424\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.36203i | 0.247454i | 0.992316 | + | 0.123727i | \(0.0394848\pi\) | ||||
−0.992316 | + | 0.123727i | \(0.960515\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.88402i | 0.228173i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.04924 | −0.234228 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19.3109 | 0.745489 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21.3043 | −0.821221 | −0.410611 | − | 0.911811i | \(-0.634684\pi\) | ||||
−0.410611 | + | 0.911811i | \(0.634684\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.4279 | 0.631375 | 0.315687 | − | 0.948863i | \(-0.397765\pi\) | ||||
0.315687 | + | 0.948863i | \(0.397765\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.02498i | 0.192841i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 1.01447i | − 0.0388177i | −0.999812 | − | 0.0194089i | \(-0.993822\pi\) | ||||
0.999812 | − | 0.0194089i | \(-0.00617842\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 32.2921i | 1.23382i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.58506i | 0.0603861i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.91349 | −0.339085 | −0.169543 | − | 0.985523i | \(-0.554229\pi\) | ||||
−0.169543 | + | 0.985523i | \(0.554229\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 21.0345 | 0.797886 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.24714 | −0.274505 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29.3401 | −1.10816 | −0.554080 | − | 0.832463i | \(-0.686930\pi\) | ||||
−0.554080 | + | 0.832463i | \(0.686930\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.49253i | 0.131723i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 13.1672i | − 0.495203i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 19.6175i | − 0.736751i | −0.929677 | − | 0.368376i | \(-0.879914\pi\) | ||||
0.929677 | − | 0.368376i | \(-0.120086\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 8.06493i | − 0.302034i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.519485 | 0.0194276 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −51.5446 | −1.92229 | −0.961145 | − | 0.276044i | \(-0.910977\pi\) | ||||
−0.961145 | + | 0.276044i | \(0.910977\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.32835 | −0.0867124 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 12.2034 | 0.453224 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27.3801i | 1.01547i | 0.861513 | + | 0.507735i | \(0.169517\pi\) | ||||
−0.861513 | + | 0.507735i | \(0.830483\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 29.8596i | − 1.10440i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 6.21759i | − 0.229652i | −0.993386 | − | 0.114826i | \(-0.963369\pi\) | ||||
0.993386 | − | 0.114826i | \(-0.0366310\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 7.89116i | − 0.290674i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 48.1637 | 1.77173 | 0.885865 | − | 0.463943i | \(-0.153566\pi\) | ||||
0.885865 | + | 0.463943i | \(0.153566\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −29.5198 | −1.08298 | −0.541489 | − | 0.840708i | \(-0.682139\pi\) | ||||
−0.541489 | + | 0.840708i | \(0.682139\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.57411 | −0.350768 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 22.6206 | 0.826539 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.01224i | 0.0369373i | 0.999829 | + | 0.0184686i | \(0.00587909\pi\) | ||||
−0.999829 | + | 0.0184686i | \(0.994121\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.71915i | 0.135354i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 32.3712i | − 1.17655i | −0.808660 | − | 0.588276i | \(-0.799807\pi\) | ||||
0.808660 | − | 0.588276i | \(-0.200193\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 38.1317i | − 1.38227i | −0.722724 | − | 0.691136i | \(-0.757110\pi\) | ||||
0.722724 | − | 0.691136i | \(-0.242890\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.5452 | 0.454167 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.145874 | 0.00526722 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.45626 | −0.341001 | −0.170501 | − | 0.985358i | \(-0.554538\pi\) | ||||
−0.170501 | + | 0.985358i | \(0.554538\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −39.7374 | −1.42925 | −0.714627 | − | 0.699506i | \(-0.753404\pi\) | ||||
−0.714627 | + | 0.699506i | \(0.753404\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 16.2698i | 0.584428i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 6.40851i | − 0.229609i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 25.3654i | 0.907644i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.6133i | 0.521573i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.8010 | −0.385015 | −0.192507 | − | 0.981296i | \(-0.561662\pi\) | ||||
−0.192507 | + | 0.981296i | \(0.561662\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.20011 | 0.184894 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.60047 | 0.0568345 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −13.2916 | −0.470812 | −0.235406 | − | 0.971897i | \(-0.575642\pi\) | ||||
−0.235406 | + | 0.971897i | \(0.575642\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 7.93408i | − 0.280687i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.74284i | 0.0615035i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 2.25704i | − 0.0795502i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 16.5163i | − 0.580684i | −0.956923 | − | 0.290342i | \(-0.906231\pi\) | ||||
0.956923 | − | 0.290342i | \(-0.0937690\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −34.5560 | −1.21342 | −0.606712 | − | 0.794921i | \(-0.707512\pi\) | ||||
−0.606712 | + | 0.794921i | \(0.707512\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 35.3675 | 1.23887 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 26.4043 | 0.923770 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 46.5813 | 1.62570 | 0.812849 | − | 0.582475i | \(-0.197915\pi\) | ||||
0.812849 | + | 0.582475i | \(0.197915\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 35.4173i | 1.23457i | 0.786740 | + | 0.617284i | \(0.211767\pi\) | ||||
−0.786740 | + | 0.617284i | \(0.788233\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34.7146i | 1.20714i | 0.797308 | + | 0.603572i | \(0.206257\pi\) | ||||
−0.797308 | + | 0.603572i | \(0.793743\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.9120i | 0.413721i | 0.978370 | + | 0.206861i | \(0.0663247\pi\) | ||||
−0.978370 | + | 0.206861i | \(0.933675\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 20.1981i | 0.699823i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 34.2531 | 1.18538 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.50962 | 0.259261 | 0.129630 | − | 0.991562i | \(-0.458621\pi\) | ||||
0.129630 | + | 0.991562i | \(0.458621\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.16011 | −0.143452 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −20.7222 | −0.712866 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.23768i | 0.283050i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 1.33969i | − 0.0459241i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 47.0179i | 1.60986i | 0.593369 | + | 0.804931i | \(0.297798\pi\) | ||||
−0.593369 | + | 0.804931i | \(0.702202\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 29.4641i | 1.00648i | 0.864148 | + | 0.503238i | \(0.167858\pi\) | ||||
−0.864148 | + | 0.503238i | \(0.832142\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 35.7888 | 1.22110 | 0.610549 | − | 0.791979i | \(-0.290949\pi\) | ||||
0.610549 | + | 0.791979i | \(0.290949\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −47.0404 | −1.60127 | −0.800636 | − | 0.599151i | \(-0.795505\pi\) | ||||
−0.800636 | + | 0.599151i | \(0.795505\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 26.7523 | 0.909604 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.76801 | 0.195666 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 0.654013i | − 0.0221604i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 13.8511i | 0.468253i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.4500i | 0.623013i | 0.950244 | + | 0.311506i | \(0.100834\pi\) | ||||
−0.950244 | + | 0.311506i | \(0.899166\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 14.0647i | − 0.473852i | −0.971528 | − | 0.236926i | \(-0.923860\pi\) | ||||
0.971528 | − | 0.236926i | \(-0.0761398\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.2404 | 0.613837 | 0.306919 | − | 0.951736i | \(-0.400702\pi\) | ||||
0.306919 | + | 0.951736i | \(0.400702\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −37.7362 | −1.26706 | −0.633529 | − | 0.773719i | \(-0.718394\pi\) | ||||
−0.633529 | + | 0.773719i | \(0.718394\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.7432 | 0.360314 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.01596 | 0.234780 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 25.7403i | 0.860402i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 33.1169i | 1.10451i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 34.5466i | 1.15091i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 26.1342i | 0.868730i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 38.1744 | 1.26756 | 0.633781 | − | 0.773513i | \(-0.281502\pi\) | ||||
0.633781 | + | 0.773513i | \(0.281502\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.9190 | 0.626813 | 0.313407 | − | 0.949619i | \(-0.398530\pi\) | ||||
0.313407 | + | 0.949619i | \(0.398530\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −27.5937 | −0.913218 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −12.4292 | −0.410448 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 4.03920i | − 0.133241i | −0.997778 | − | 0.0666204i | \(-0.978778\pi\) | ||||
0.997778 | − | 0.0666204i | \(-0.0212217\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.10226i | 0.0691968i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.70263i | 0.0888619i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 23.4245i | − 0.768534i | −0.923222 | − | 0.384267i | \(-0.874454\pi\) | ||||
0.923222 | − | 0.384267i | \(-0.125546\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17.8608 | −0.585364 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 11.3222 | 0.370276 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −41.0860 | −1.34222 | −0.671111 | − | 0.741357i | \(-0.734182\pi\) | ||||
−0.671111 | + | 0.741357i | \(0.734182\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.5313 | −0.799696 | −0.399848 | − | 0.916581i | \(-0.630937\pi\) | ||||
−0.399848 | + | 0.916581i | \(0.630937\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.45823i | 0.0800509i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 47.0862i | − 1.53010i | −0.643973 | − | 0.765048i | \(-0.722715\pi\) | ||||
0.643973 | − | 0.765048i | \(-0.277285\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.144445i | 0.00468889i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 47.3929i | − 1.53521i | −0.640926 | − | 0.767603i | \(-0.721449\pi\) | ||||
0.640926 | − | 0.767603i | \(-0.278551\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 29.7623 | 0.963086 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 23.5353 | 0.759996 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.1519 | −0.424256 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.64631 | 0.0851876 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40.0248i | 1.28711i | 0.765400 | + | 0.643555i | \(0.222541\pi\) | ||||
−0.765400 | + | 0.643555i | \(0.777459\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 36.5162i | 1.17186i | 0.810362 | + | 0.585930i | \(0.199271\pi\) | ||||
−0.810362 | + | 0.585930i | \(0.800729\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 15.3306i | − 0.491475i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 43.4028i | − 1.38858i | −0.719697 | − | 0.694289i | \(-0.755719\pi\) | ||||
0.719697 | − | 0.694289i | \(-0.244281\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16.6694 | −0.532758 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.34326 | −0.0747384 | −0.0373692 | − | 0.999302i | \(-0.511898\pi\) | ||||
−0.0373692 | + | 0.999302i | \(0.511898\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −19.0047 | −0.605539 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −10.1284 | −0.322064 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 44.6280i | − 1.41766i | −0.705382 | − | 0.708828i | \(-0.749224\pi\) | ||||
0.705382 | − | 0.708828i | \(-0.250776\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 13.3031i | − 0.421737i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 53.4194i | 1.69181i | 0.533334 | + | 0.845904i | \(0.320939\pi\) | ||||
−0.533334 | + | 0.845904i | \(0.679061\pi\) | |||||||
\(998\) | 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 | 5184.2.f.b.2591.6 | yes | 16 | |
3.2 | odd | 2 | inner | 5184.2.f.b.2591.12 | yes | 16 | |
4.3 | odd | 2 | 5184.2.f.e.2591.5 | yes | 16 | ||
8.3 | odd | 2 | inner | 5184.2.f.b.2591.11 | yes | 16 | |
8.5 | even | 2 | 5184.2.f.e.2591.12 | yes | 16 | ||
12.11 | even | 2 | 5184.2.f.e.2591.11 | yes | 16 | ||
24.5 | odd | 2 | 5184.2.f.e.2591.6 | yes | 16 | ||
24.11 | even | 2 | inner | 5184.2.f.b.2591.5 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5184.2.f.b.2591.5 | ✓ | 16 | 24.11 | even | 2 | inner | |
5184.2.f.b.2591.6 | yes | 16 | 1.1 | even | 1 | trivial | |
5184.2.f.b.2591.11 | yes | 16 | 8.3 | odd | 2 | inner | |
5184.2.f.b.2591.12 | yes | 16 | 3.2 | odd | 2 | inner | |
5184.2.f.e.2591.5 | yes | 16 | 4.3 | odd | 2 | ||
5184.2.f.e.2591.6 | yes | 16 | 24.5 | odd | 2 | ||
5184.2.f.e.2591.11 | yes | 16 | 12.11 | even | 2 | ||
5184.2.f.e.2591.12 | yes | 16 | 8.5 | even | 2 |