Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1792,2,Mod(449,1792)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1792, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1792.449");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1792 = 2^{8} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1792.m (of order \(4\), degree \(2\), 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: | \(14.3091920422\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 449.8 | ||
Root | \(0.339278 + 0.0446668i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1792.449 |
Dual form | 1792.2.m.f.1345.8 |
$q$-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 \(\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times\).
\(n\) | \(1023\) | \(1025\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 | ||||||||
\(3\) | 1.48474 | − | 1.48474i | 0.857214 | − | 0.857214i | −0.133795 | − | 0.991009i | \(-0.542716\pi\) |
0.991009 | + | 0.133795i | \(0.0427163\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.83598 | − | 1.83598i | −0.821077 | − | 0.821077i | 0.165185 | − | 0.986263i | \(-0.447178\pi\) |
−0.986263 | + | 0.165185i | \(0.947178\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 1.40890i | − | 0.469633i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.321444 | + | 0.321444i | 0.0969191 | + | 0.0969191i | 0.753904 | − | 0.656985i | \(-0.228168\pi\) |
−0.656985 | + | 0.753904i | \(0.728168\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.61789 | + | 4.61789i | −1.28077 | + | 1.28077i | −0.340541 | + | 0.940230i | \(0.610610\pi\) |
−0.940230 | + | 0.340541i | \(0.889390\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.45192 | −1.40768 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.84172 | −0.446682 | −0.223341 | − | 0.974740i | \(-0.571696\pi\) | ||||
−0.223341 | + | 0.974740i | \(0.571696\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.88948 | + | 3.88948i | −0.892308 | + | 0.892308i | −0.994740 | − | 0.102432i | \(-0.967338\pi\) |
0.102432 | + | 0.994740i | \(0.467338\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.48474 | − | 1.48474i | −0.323997 | − | 0.323997i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 5.88497i | − | 1.22710i | −0.789656 | − | 0.613550i | \(-0.789741\pi\) | ||
0.789656 | − | 0.613550i | \(-0.210259\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.74168i | 0.348336i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.36237 | + | 2.36237i | 0.454639 | + | 0.454639i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.14570 | + | 6.14570i | −1.14123 | + | 1.14123i | −0.153002 | + | 0.988226i | \(0.548894\pi\) |
−0.988226 | + | 0.153002i | \(0.951106\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.69821 | −1.02343 | −0.511714 | − | 0.859156i | \(-0.670989\pi\) | ||||
−0.511714 | + | 0.859156i | \(0.670989\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.954522 | 0.166161 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.83598 | + | 1.83598i | −0.310338 | + | 0.310338i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.66877 | − | 1.66877i | −0.274344 | − | 0.274344i | 0.556502 | − | 0.830846i | \(-0.312143\pi\) |
−0.830846 | + | 0.556502i | \(0.812143\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 13.7127i | 2.19579i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 10.7333i | − | 1.67626i | −0.545468 | − | 0.838132i | \(-0.683648\pi\) | ||
0.545468 | − | 0.838132i | \(-0.316352\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.533105 | − | 0.533105i | −0.0812978 | − | 0.0812978i | 0.665289 | − | 0.746586i | \(-0.268309\pi\) |
−0.746586 | + | 0.665289i | \(0.768309\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.58672 | + | 2.58672i | −0.385605 | + | 0.385605i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.465401 | 0.0678856 | 0.0339428 | − | 0.999424i | \(-0.489194\pi\) | ||||
0.0339428 | + | 0.999424i | \(0.489194\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.73447 | + | 2.73447i | −0.382902 | + | 0.382902i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.623234 | + | 0.623234i | 0.0856078 | + | 0.0856078i | 0.748614 | − | 0.663006i | \(-0.230720\pi\) |
−0.663006 | + | 0.748614i | \(0.730720\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.18033i | − | 0.159156i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 11.5497i | 1.52980i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.32184 | + | 7.32184i | 0.953223 | + | 0.953223i | 0.998954 | − | 0.0457310i | \(-0.0145617\pi\) |
−0.0457310 | + | 0.998954i | \(0.514562\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.57257 | − | 7.57257i | 0.969569 | − | 0.969569i | −0.0299816 | − | 0.999550i | \(-0.509545\pi\) |
0.999550 | + | 0.0299816i | \(0.00954488\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.40890 | −0.177504 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 16.9567 | 2.10322 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.16327 | + | 6.16327i | −0.752964 | + | 0.752964i | −0.975031 | − | 0.222068i | \(-0.928719\pi\) |
0.222068 | + | 0.975031i | \(0.428719\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −8.73764 | − | 8.73764i | −1.05189 | − | 1.05189i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.162532i | 0.0192890i | 0.999953 | + | 0.00964452i | \(0.00306999\pi\) | ||||
−0.999953 | + | 0.00964452i | \(0.996930\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.49118i | 0.408612i | 0.978907 | + | 0.204306i | \(0.0654938\pi\) | ||||
−0.978907 | + | 0.204306i | \(0.934506\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.58594 | + | 2.58594i | 0.298599 | + | 0.298599i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.321444 | − | 0.321444i | 0.0366320 | − | 0.0366320i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.28703 | −0.932363 | −0.466182 | − | 0.884689i | \(-0.654371\pi\) | ||||
−0.466182 | + | 0.884689i | \(0.654371\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 11.2417 | 1.24908 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.51275 | + | 2.51275i | −0.275810 | + | 0.275810i | −0.831434 | − | 0.555624i | \(-0.812479\pi\) |
0.555624 | + | 0.831434i | \(0.312479\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.38136 | + | 3.38136i | 0.366760 | + | 0.366760i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 18.2495i | 1.95655i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.60040i | 0.169642i | 0.996396 | + | 0.0848209i | \(0.0270318\pi\) | ||||
−0.996396 | + | 0.0848209i | \(0.972968\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.61789 | + | 4.61789i | 0.484086 | + | 0.484086i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.46035 | + | 8.46035i | −0.877297 | + | 0.877297i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 14.2821 | 1.46531 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.88621 | −0.902258 | −0.451129 | − | 0.892459i | \(-0.648979\pi\) | ||||
−0.451129 | + | 0.892459i | \(0.648979\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.452882 | − | 0.452882i | 0.0455164 | − | 0.0455164i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.80533 | − | 9.80533i | −0.975667 | − | 0.975667i | 0.0240439 | − | 0.999711i | \(-0.492346\pi\) |
−0.999711 | + | 0.0240439i | \(0.992346\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.3236i | 1.41135i | 0.708537 | + | 0.705674i | \(0.249356\pi\) | ||||
−0.708537 | + | 0.705674i | \(0.750644\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.45192i | 0.532052i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.6995 | − | 10.6995i | −1.03436 | − | 1.03436i | −0.999388 | − | 0.0349695i | \(-0.988867\pi\) |
−0.0349695 | − | 0.999388i | \(-0.511133\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.38679 | − | 7.38679i | 0.707526 | − | 0.707526i | −0.258488 | − | 0.966014i | \(-0.583224\pi\) |
0.966014 | + | 0.258488i | \(0.0832244\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.95537 | −0.470343 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.05995 | 0.758217 | 0.379108 | − | 0.925352i | \(-0.376231\pi\) | ||||
0.379108 | + | 0.925352i | \(0.376231\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.8047 | + | 10.8047i | −1.00754 | + | 1.00754i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.50613 | + | 6.50613i | 0.601492 | + | 0.601492i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.84172i | 0.168830i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 10.7933i | − | 0.981213i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −15.9362 | − | 15.9362i | −1.43692 | − | 1.43692i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.98222 | + | 5.98222i | −0.535066 | + | 0.535066i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.367471 | −0.0326078 | −0.0163039 | − | 0.999867i | \(-0.505190\pi\) | ||||
−0.0163039 | + | 0.999867i | \(0.505190\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.58304 | −0.139379 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.30850 | + | 9.30850i | −0.813288 | + | 0.813288i | −0.985125 | − | 0.171838i | \(-0.945030\pi\) |
0.171838 | + | 0.985125i | \(0.445030\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.88948 | + | 3.88948i | 0.337261 | + | 0.337261i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 8.67456i | − | 0.746587i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 6.85872i | − | 0.585980i | −0.956115 | − | 0.292990i | \(-0.905350\pi\) | ||
0.956115 | − | 0.292990i | \(-0.0946503\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.1730 | − | 16.1730i | −1.37177 | − | 1.37177i | −0.857814 | − | 0.513961i | \(-0.828178\pi\) |
−0.513961 | − | 0.857814i | \(-0.671822\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.690998 | − | 0.690998i | 0.0581925 | − | 0.0581925i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.96879 | −0.248262 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 22.5668 | 1.87407 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.48474 | + | 1.48474i | −0.122459 | + | 0.122459i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.2009 | + | 15.2009i | 1.24530 | + | 1.24530i | 0.957771 | + | 0.287532i | \(0.0928347\pi\) |
0.287532 | + | 0.957771i | \(0.407165\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.76306i | 0.387612i | 0.981040 | + | 0.193806i | \(0.0620832\pi\) | ||||
−0.981040 | + | 0.193806i | \(0.937917\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.59479i | 0.209776i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.4618 | + | 10.4618i | 0.840314 | + | 0.840314i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.7887 | − | 11.7887i | 0.940844 | − | 0.940844i | −0.0575014 | − | 0.998345i | \(-0.518313\pi\) |
0.998345 | + | 0.0575014i | \(0.0183134\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.85068 | 0.146768 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.88497 | −0.463800 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.68083 | − | 9.68083i | 0.758261 | − | 0.758261i | −0.217745 | − | 0.976006i | \(-0.569870\pi\) |
0.976006 | + | 0.217745i | \(0.0698700\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.75249 | − | 1.75249i | −0.136431 | − | 0.136431i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.1916i | 1.02079i | 0.859939 | + | 0.510397i | \(0.170501\pi\) | ||||
−0.859939 | + | 0.510397i | \(0.829499\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 29.6497i | − | 2.28075i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.47988 | + | 5.47988i | 0.419057 | + | 0.419057i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.40858 | + | 6.40858i | −0.487235 | + | 0.487235i | −0.907433 | − | 0.420198i | \(-0.861961\pi\) |
0.420198 | + | 0.907433i | \(0.361961\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.74168 | 0.131659 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 21.7420 | 1.63423 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.05982 | − | 9.05982i | 0.677163 | − | 0.677163i | −0.282194 | − | 0.959357i | \(-0.591062\pi\) |
0.959357 | + | 0.282194i | \(0.0910623\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.7164 | − | 13.7164i | −1.01953 | − | 1.01953i | −0.999805 | − | 0.0197290i | \(-0.993720\pi\) |
−0.0197290 | − | 0.999805i | \(-0.506280\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 22.4866i | − | 1.66226i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.12766i | 0.450515i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.592009 | − | 0.592009i | −0.0432920 | − | 0.0432920i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.36237 | − | 2.36237i | 0.171837 | − | 0.171837i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.2622 | 1.39376 | 0.696882 | − | 0.717186i | \(-0.254570\pi\) | ||||
0.696882 | + | 0.717186i | \(0.254570\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.38323 | −0.171549 | −0.0857744 | − | 0.996315i | \(-0.527336\pi\) | ||||
−0.0857744 | + | 0.996315i | \(0.527336\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 25.1763 | − | 25.1763i | 1.80291 | − | 1.80291i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.16266 | − | 6.16266i | −0.439072 | − | 0.439072i | 0.452628 | − | 0.891699i | \(-0.350487\pi\) |
−0.891699 | + | 0.452628i | \(0.850487\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 9.33136i | − | 0.661483i | −0.943721 | − | 0.330741i | \(-0.892701\pi\) | ||
0.943721 | − | 0.330741i | \(-0.107299\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 18.3017i | 1.29090i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.14570 | + | 6.14570i | 0.431344 | + | 0.431344i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −19.7062 | + | 19.7062i | −1.37634 | + | 1.37634i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.29132 | −0.576286 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.50050 | −0.172963 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.3372 | + | 19.3372i | −1.33123 | + | 1.33123i | −0.426957 | + | 0.904272i | \(0.640414\pi\) |
−0.904272 | + | 0.426957i | \(0.859586\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.241318 | + | 0.241318i | 0.0165348 | + | 0.0165348i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.95755i | 0.133504i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.69821i | 0.386819i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.18350 | + | 5.18350i | 0.350268 | + | 0.350268i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.50483 | − | 8.50483i | 0.572097 | − | 0.572097i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −19.2604 | −1.28977 | −0.644886 | − | 0.764279i | \(-0.723095\pi\) | ||||
−0.644886 | + | 0.764279i | \(0.723095\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.45385 | 0.163590 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.375264 | + | 0.375264i | −0.0249071 | + | 0.0249071i | −0.719451 | − | 0.694544i | \(-0.755606\pi\) |
0.694544 | + | 0.719451i | \(0.255606\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.34559 | + | 9.34559i | 0.617574 | + | 0.617574i | 0.944909 | − | 0.327334i | \(-0.106150\pi\) |
−0.327334 | + | 0.944909i | \(0.606150\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 0.954522i | − | 0.0628029i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 13.8761i | − | 0.909055i | −0.890733 | − | 0.454527i | \(-0.849808\pi\) | ||
0.890733 | − | 0.454527i | \(-0.150192\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.854468 | − | 0.854468i | −0.0557394 | − | 0.0557394i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −12.3041 | + | 12.3041i | −0.799235 | + | 0.799235i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.2148 | 0.984165 | 0.492082 | − | 0.870549i | \(-0.336236\pi\) | ||||
0.492082 | + | 0.870549i | \(0.336236\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −28.2964 | −1.82273 | −0.911364 | − | 0.411601i | \(-0.864970\pi\) | ||||
−0.911364 | + | 0.411601i | \(0.864970\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.60387 | − | 9.60387i | 0.616089 | − | 0.616089i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.83598 | + | 1.83598i | 0.117297 | + | 0.117297i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 35.9223i | − | 2.28568i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.46154i | 0.472856i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.92064 | − | 8.92064i | −0.563066 | − | 0.563066i | 0.367111 | − | 0.930177i | \(-0.380347\pi\) |
−0.930177 | + | 0.367111i | \(0.880347\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.89169 | − | 1.89169i | 0.118929 | − | 0.118929i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 10.0409 | 0.628784 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −27.4810 | −1.71422 | −0.857110 | − | 0.515133i | \(-0.827742\pi\) | ||||
−0.857110 | + | 0.515133i | \(0.827742\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.66877 | + | 1.66877i | −0.103692 | + | 0.103692i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.65867 | + | 8.65867i | 0.535958 | + | 0.535958i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.9308i | 0.920674i | 0.887744 | + | 0.460337i | \(0.152271\pi\) | ||||
−0.887744 | + | 0.460337i | \(0.847729\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 2.28850i | − | 0.140581i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.37617 | + | 2.37617i | 0.145419 | + | 0.145419i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.00456307 | − | 0.00456307i | 0.000278216 | − | 0.000278216i | −0.706968 | − | 0.707246i | \(-0.749937\pi\) |
0.707246 | + | 0.706968i | \(0.249937\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.74567 | 0.349025 | 0.174512 | − | 0.984655i | \(-0.444165\pi\) | ||||
0.174512 | + | 0.984655i | \(0.444165\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 13.7127 | 0.829931 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.559854 | + | 0.559854i | −0.0337604 | + | 0.0337604i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.2885 | − | 11.2885i | −0.678259 | − | 0.678259i | 0.281347 | − | 0.959606i | \(-0.409219\pi\) |
−0.959606 | + | 0.281347i | \(0.909219\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.02819i | 0.480635i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.71094i | 0.579306i | 0.957132 | + | 0.289653i | \(0.0935399\pi\) | ||||
−0.957132 | + | 0.289653i | \(0.906460\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.6539 | − | 12.6539i | −0.752197 | − | 0.752197i | 0.222692 | − | 0.974889i | \(-0.428516\pi\) |
−0.974889 | + | 0.222692i | \(0.928516\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 21.2051 | − | 21.2051i | 1.25608 | − | 1.25608i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.7333 | −0.633568 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.6081 | −0.800475 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.1937 | + | 13.1937i | −0.773428 | + | 0.773428i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.906335 | − | 0.906335i | −0.0529486 | − | 0.0529486i | 0.680137 | − | 0.733085i | \(-0.261920\pi\) |
−0.733085 | + | 0.680137i | \(0.761920\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 26.8856i | − | 1.56534i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.51874i | 0.0881263i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 27.1761 | + | 27.1761i | 1.57163 | + | 1.57163i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.533105 | + | 0.533105i | −0.0307277 | + | 0.0307277i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −29.1167 | −1.67271 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −27.8063 | −1.59218 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.7928 | − | 14.7928i | 0.844268 | − | 0.844268i | −0.145143 | − | 0.989411i | \(-0.546364\pi\) |
0.989411 | + | 0.145143i | \(0.0463642\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 21.2668 | + | 21.2668i | 1.20983 | + | 1.20983i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.6043i | 0.658022i | 0.944326 | + | 0.329011i | \(0.106715\pi\) | ||||
−0.944326 | + | 0.329011i | \(0.893285\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.5621i | 1.04919i | 0.851351 | + | 0.524596i | \(0.175784\pi\) | ||||
−0.851351 | + | 0.524596i | \(0.824216\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.58672 | + | 2.58672i | 0.145745 | + | 0.145745i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.8863 | − | 15.8863i | 0.892261 | − | 0.892261i | −0.102474 | − | 0.994736i | \(-0.532676\pi\) |
0.994736 | + | 0.102474i | \(0.0326760\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.95100 | −0.221214 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −31.7719 | −1.77333 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.16332 | − | 7.16332i | 0.398578 | − | 0.398578i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.04288 | − | 8.04288i | −0.446139 | − | 0.446139i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 21.9349i | − | 1.21300i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 0.465401i | − | 0.0256584i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.49646 | + | 5.49646i | 0.302113 | + | 0.302113i | 0.841840 | − | 0.539727i | \(-0.181473\pi\) |
−0.539727 | + | 0.841840i | \(0.681473\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.35112 | + | 2.35112i | −0.128841 | + | 0.128841i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 22.6314 | 1.23648 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.73515 | −0.148993 | −0.0744966 | − | 0.997221i | \(-0.523735\pi\) | ||||
−0.0744966 | + | 0.997221i | \(0.523735\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.9669 | − | 11.9669i | 0.649954 | − | 0.649954i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.83166 | − | 1.83166i | −0.0991897 | − | 0.0991897i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 32.0843i | 1.72736i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 25.0209 | + | 25.0209i | 1.34319 | + | 1.34319i | 0.892864 | + | 0.450326i | \(0.148692\pi\) |
0.450326 | + | 0.892864i | \(0.351308\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.72637 | − | 8.72637i | 0.467112 | − | 0.467112i | −0.433866 | − | 0.900978i | \(-0.642851\pi\) |
0.900978 | + | 0.433866i | \(0.142851\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −21.8183 | −1.16458 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −22.2643 | −1.18501 | −0.592504 | − | 0.805567i | \(-0.701861\pi\) | ||||
−0.592504 | + | 0.805567i | \(0.701861\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.298407 | − | 0.298407i | 0.0158378 | − | 0.0158378i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.73447 | + | 2.73447i | 0.144723 | + | 0.144723i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 18.3142i | − | 0.966588i | −0.875458 | − | 0.483294i | \(-0.839440\pi\) | ||
0.875458 | − | 0.483294i | \(-0.160560\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 11.2561i | − | 0.592427i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −16.0253 | − | 16.0253i | −0.841110 | − | 0.841110i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.40976 | − | 6.40976i | 0.335502 | − | 0.335502i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.3398 | 1.00953 | 0.504764 | − | 0.863257i | \(-0.331580\pi\) | ||||
0.504764 | + | 0.863257i | \(0.331580\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −15.1222 | −0.787228 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.623234 | − | 0.623234i | 0.0323567 | − | 0.0323567i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.63668 | + | 5.63668i | 0.291856 | + | 0.291856i | 0.837813 | − | 0.545957i | \(-0.183834\pi\) |
−0.545957 | + | 0.837813i | \(0.683834\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 17.7641i | 0.917333i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 56.7603i | − | 2.92330i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.24191 | + | 3.24191i | 0.166526 | + | 0.166526i | 0.785450 | − | 0.618925i | \(-0.212431\pi\) |
−0.618925 | + | 0.785450i | \(0.712431\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.545598 | + | 0.545598i | −0.0279518 | + | 0.0279518i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.39804 | −0.275827 | −0.137913 | − | 0.990444i | \(-0.544040\pi\) | ||||
−0.137913 | + | 0.990444i | \(0.544040\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.18033 | −0.0601554 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.751091 | + | 0.751091i | −0.0381801 | + | 0.0381801i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.6572 | − | 15.6572i | −0.793854 | − | 0.793854i | 0.188264 | − | 0.982118i | \(-0.439714\pi\) |
−0.982118 | + | 0.188264i | \(0.939714\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.8384i | 0.548123i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 27.6414i | 1.39432i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 15.2149 | + | 15.2149i | 0.765542 | + | 0.765542i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.24563 | + | 2.24563i | −0.112705 | + | 0.112705i | −0.761210 | − | 0.648505i | \(-0.775394\pi\) |
0.648505 | + | 0.761210i | \(0.275394\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 11.5497 | 0.578209 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.3307 | 0.965331 | 0.482665 | − | 0.875805i | \(-0.339669\pi\) | ||||
0.482665 | + | 0.875805i | \(0.339669\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 26.3137 | − | 26.3137i | 1.31078 | − | 1.31078i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −20.6396 | − | 20.6396i | −1.02559 | − | 1.02559i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 1.07283i | − | 0.0531783i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.497591i | 0.0246043i | 0.999924 | + | 0.0123021i | \(0.00391599\pi\) | ||||
−0.999924 | + | 0.0123021i | \(0.996084\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.1834 | − | 10.1834i | −0.502311 | − | 0.502311i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.32184 | − | 7.32184i | 0.360284 | − | 0.360284i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.22673 | 0.452922 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −48.0253 | −2.35181 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.51076 | + | 3.51076i | −0.171512 | + | 0.171512i | −0.787643 | − | 0.616131i | \(-0.788699\pi\) |
0.616131 | + | 0.787643i | \(0.288699\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.35086 | − | 1.35086i | −0.0658368 | − | 0.0658368i | 0.673422 | − | 0.739259i | \(-0.264824\pi\) |
−0.739259 | + | 0.673422i | \(0.764824\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 0.655702i | − | 0.0318813i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 3.20768i | − | 0.155595i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.57257 | − | 7.57257i | −0.366463 | − | 0.366463i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.40787 | + | 4.40787i | −0.212814 | + | 0.212814i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.6166 | 0.944896 | 0.472448 | − | 0.881358i | \(-0.343370\pi\) | ||||
0.472448 | + | 0.881358i | \(0.343370\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.76217 | −0.132741 | −0.0663706 | − | 0.997795i | \(-0.521142\pi\) | ||||
−0.0663706 | + | 0.997795i | \(0.521142\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 33.5058 | − | 33.5058i | 1.60648 | − | 1.60648i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 22.8895 | + | 22.8895i | 1.09495 | + | 1.09495i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 3.05296i | − | 0.145710i | −0.997343 | − | 0.0728550i | \(-0.976789\pi\) | ||
0.997343 | − | 0.0728550i | \(-0.0232110\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.40890i | 0.0670904i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.37047 | + | 1.37047i | 0.0651129 | + | 0.0651129i | 0.738913 | − | 0.673800i | \(-0.235339\pi\) |
−0.673800 | + | 0.738913i | \(0.735339\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.93831 | − | 2.93831i | 0.139289 | − | 0.139289i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 45.1386 | 2.13498 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 38.6173 | 1.82246 | 0.911232 | − | 0.411894i | \(-0.135133\pi\) | ||||
0.911232 | + | 0.411894i | \(0.135133\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.45017 | − | 3.45017i | 0.162462 | − | 0.162462i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.07190 | + | 7.07190i | 0.332267 | + | 0.332267i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 16.9567i | − | 0.794944i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 36.0959i | 1.68849i | 0.535955 | + | 0.844247i | \(0.319952\pi\) | ||||
−0.535955 | + | 0.844247i | \(0.680048\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.35082 | − | 4.35082i | −0.203079 | − | 0.203079i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.29295 | − | 4.29295i | 0.199943 | − | 0.199943i | −0.600033 | − | 0.799975i | \(-0.704846\pi\) |
0.799975 | + | 0.600033i | \(0.204846\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.38348 | −0.157243 | −0.0786217 | − | 0.996905i | \(-0.525052\pi\) | ||||
−0.0786217 | + | 0.996905i | \(0.525052\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 31.0661 | 1.44066 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −21.7747 | + | 21.7747i | −1.00761 | + | 1.00761i | −0.00764098 | + | 0.999971i | \(0.502432\pi\) |
−0.999971 | + | 0.00764098i | \(0.997568\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.16327 | + | 6.16327i | 0.284594 | + | 0.284594i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 35.0064i | − | 1.61301i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 0.342727i | − | 0.0157586i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.77424 | − | 6.77424i | −0.310823 | − | 0.310823i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.878073 | − | 0.878073i | 0.0402042 | − | 0.0402042i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.74054 | 0.307983 | 0.153992 | − | 0.988072i | \(-0.450787\pi\) | ||||
0.153992 | + | 0.988072i | \(0.450787\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.4123 | 0.702743 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −8.73764 | + | 8.73764i | −0.397576 | + | 0.397576i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16.3149 | + | 16.3149i | 0.740823 | + | 0.740823i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 30.4472i | − | 1.37970i | −0.723954 | − | 0.689848i | \(-0.757677\pi\) | ||
0.723954 | − | 0.689848i | \(-0.242323\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 28.7470i | − | 1.29998i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.1585 | − | 11.1585i | −0.503578 | − | 0.503578i | 0.408970 | − | 0.912548i | \(-0.365888\pi\) |
−0.912548 | + | 0.408970i | \(0.865888\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.3186 | − | 11.3186i | 0.509766 | − | 0.509766i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.66297 | −0.0747449 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.162532 | 0.00729057 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.4556 | + | 17.4556i | −0.781420 | + | 0.781420i | −0.980070 | − | 0.198651i | \(-0.936344\pi\) |
0.198651 | + | 0.980070i | \(0.436344\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 19.5860 | + | 19.5860i | 0.875039 | + | 0.875039i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 26.7354i | 1.19207i | 0.802958 | + | 0.596035i | \(0.203258\pi\) | ||||
−0.802958 | + | 0.596035i | \(0.796742\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 36.0049i | 1.60220i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −44.0221 | − | 44.0221i | −1.95509 | − | 1.95509i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.7609 | + | 13.7609i | −0.609942 | + | 0.609942i | −0.942931 | − | 0.332989i | \(-0.891943\pi\) |
0.332989 | + | 0.942931i | \(0.391943\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.49118 | 0.154441 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −18.3768 | −0.811355 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 26.2979 | − | 26.2979i | 1.15883 | − | 1.15883i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.149600 | + | 0.149600i | 0.00657942 | + | 0.00657942i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 19.0301i | 0.835330i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 36.5859i | − | 1.60286i | −0.598091 | − | 0.801428i | \(-0.704074\pi\) | ||
0.598091 | − | 0.801428i | \(-0.295926\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.02294 | + | 4.02294i | 0.175911 | + | 0.175911i | 0.789571 | − | 0.613660i | \(-0.210303\pi\) |
−0.613660 | + | 0.789571i | \(0.710303\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.58594 | − | 2.58594i | 0.112860 | − | 0.112860i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.4945 | 0.457147 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.6328 | −0.505776 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.3157 | − | 10.3157i | 0.447664 | − | 0.447664i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 49.5652 | + | 49.5652i | 2.14691 | + | 2.14691i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 39.2882i | 1.69858i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 26.9029i | − | 1.16095i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.321444 | − | 0.321444i | −0.0138456 | − | 0.0138456i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.9463 | − | 17.9463i | 0.771572 | − | 0.771572i | −0.206809 | − | 0.978381i | \(-0.566308\pi\) |
0.978381 | + | 0.206809i | \(0.0663078\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −40.7306 | −1.74792 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −27.1241 | −1.16187 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18.9329 | + | 18.9329i | −0.809512 | + | 0.809512i | −0.984560 | − | 0.175048i | \(-0.943992\pi\) |
0.175048 | + | 0.984560i | \(0.443992\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −10.6690 | − | 10.6690i | −0.455341 | − | 0.455341i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 47.8072i | − | 2.03665i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.28703i | 0.352400i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9.09798 | + | 9.09798i | 0.386188 | + | 0.386188i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −30.3516 | + | 30.3516i | −1.28604 | + | 1.28604i | −0.348864 | + | 0.937173i | \(0.613432\pi\) |
−0.937173 | + | 0.348864i | \(0.886568\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.92364 | 0.208248 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.75796 | −0.0742210 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.2195 | − | 18.2195i | 0.767858 | − | 0.767858i | −0.209871 | − | 0.977729i | \(-0.567304\pi\) |
0.977729 | + | 0.209871i | \(0.0673043\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14.7980 | − | 14.7980i | −0.622555 | − | 0.622555i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 11.2417i | − | 0.472107i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 40.3261i | − | 1.69056i | −0.534325 | − | 0.845279i | \(-0.679434\pi\) | ||
0.534325 | − | 0.845279i | \(-0.320566\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.1528 | − | 18.1528i | −0.759672 | − | 0.759672i | 0.216591 | − | 0.976262i | \(-0.430506\pi\) |
−0.976262 | + | 0.216591i | \(0.930506\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 28.5993 | − | 28.5993i | 1.19475 | − | 1.19475i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.2497 | 0.427444 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.8535 | 1.20119 | 0.600594 | − | 0.799554i | \(-0.294931\pi\) | ||||
0.600594 | + | 0.799554i | \(0.294931\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.53848 | + | 3.53848i | −0.147054 | + | 0.147054i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.51275 | + | 2.51275i | 0.104246 | + | 0.104246i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.400670i | 0.0165941i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 23.8903i | − | 0.987743i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −22.0073 | − | 22.0073i | −0.908338 | − | 0.908338i | 0.0877997 | − | 0.996138i | \(-0.472016\pi\) |
−0.996138 | + | 0.0877997i | \(0.972016\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22.1631 | − | 22.1631i | 0.913213 | − | 0.913213i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −18.2999 | −0.752757 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 24.6606 | 1.01269 | 0.506344 | − | 0.862331i | \(-0.330996\pi\) | ||||
0.506344 | + | 0.862331i | \(0.330996\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.38136 | − | 3.38136i | 0.138622 | − | 0.138622i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −13.8546 | − | 13.8546i | −0.567033 | − | 0.567033i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 10.8236i | − | 0.442239i | −0.975247 | − | 0.221120i | \(-0.929029\pi\) | ||
0.975247 | − | 0.221120i | \(-0.0709711\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.6417i | 0.678828i | 0.940637 | + | 0.339414i | \(0.110229\pi\) | ||||
−0.940637 | + | 0.339414i | \(0.889771\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.68342 | + | 8.68342i | 0.353616 | + | 0.353616i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −19.8164 | + | 19.8164i | −0.805652 | + | 0.805652i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.3716 | −0.908037 | −0.454019 | − | 0.890992i | \(-0.650010\pi\) | ||||
−0.454019 | + | 0.890992i | \(0.650010\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 18.2495 | 0.739508 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.14917 | + | 2.14917i | −0.0869460 | + | 0.0869460i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −32.7313 | − | 32.7313i | −1.32201 | − | 1.32201i | −0.912150 | − | 0.409857i | \(-0.865579\pi\) |
−0.409857 | − | 0.912150i | \(-0.634421\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 58.5172i | 2.35964i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 3.37531i | − | 0.135885i | −0.997689 | − | 0.0679424i | \(-0.978357\pi\) | ||
0.997689 | − | 0.0679424i | \(-0.0216434\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.57465 | − | 3.57465i | −0.143677 | − | 0.143677i | 0.631609 | − | 0.775287i | \(-0.282395\pi\) |
−0.775287 | + | 0.631609i | \(0.782395\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 13.9025 | − | 13.9025i | 0.557887 | − | 0.557887i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.60040 | 0.0641186 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 30.6750 | 1.22700 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.71259 | + | 3.71259i | −0.148267 | + | 0.148267i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.07340 | + | 3.07340i | 0.122544 | + | 0.122544i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 31.2089i | − | 1.24241i | −0.783649 | − | 0.621204i | \(-0.786644\pi\) | ||
0.783649 | − | 0.621204i | \(-0.213356\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 57.4214i | 2.28230i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.674671 | + | 0.674671i | 0.0267735 | + | 0.0267735i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.61789 | − | 4.61789i | 0.182967 | − | 0.182967i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.228991 | 0.00905876 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25.7829 | 1.01836 | 0.509182 | − | 0.860659i | \(-0.329948\pi\) | ||||
0.509182 | + | 0.860659i | \(0.329948\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.82352 | − | 1.82352i | 0.0719127 | − | 0.0719127i | −0.670236 | − | 0.742148i | \(-0.733807\pi\) |
0.742148 | + | 0.670236i | \(0.233807\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.90645 | + | 2.90645i | 0.114441 | + | 0.114441i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 10.0909i | − | 0.396713i | −0.980130 | − | 0.198356i | \(-0.936440\pi\) | ||
0.980130 | − | 0.198356i | \(-0.0635603\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.70713i | 0.184771i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.46035 | + | 8.46035i | 0.331587 | + | 0.331587i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.8599 | − | 13.8599i | 0.542380 | − | 0.542380i | −0.381846 | − | 0.924226i | \(-0.624712\pi\) |
0.924226 | + | 0.381846i | \(0.124712\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 34.1805 | 1.33554 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.91872 | 0.191898 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13.9075 | + | 13.9075i | −0.541758 | + | 0.541758i | −0.924044 | − | 0.382286i | \(-0.875137\pi\) |
0.382286 | + | 0.924044i | \(0.375137\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.13544 | + | 1.13544i | 0.0441633 | + | 0.0441633i | 0.728844 | − | 0.684680i | \(-0.240058\pi\) |
−0.684680 | + | 0.728844i | \(0.740058\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 25.2549i | − | 0.980820i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 14.2821i | − | 0.553834i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 36.1673 | + | 36.1673i | 1.40040 | + | 1.40040i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −28.5967 | + | 28.5967i | −1.10561 | + | 1.10561i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.86832 | 0.187939 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.91726 | 0.382282 | 0.191141 | − | 0.981563i | \(-0.438781\pi\) | ||||
0.191141 | + | 0.981563i | \(0.438781\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.11450 | + | 4.11450i | −0.158367 | + | 0.158367i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.4673 | + | 16.4673i | 0.632890 | + | 0.632890i | 0.948792 | − | 0.315902i | \(-0.102307\pi\) |
−0.315902 | + | 0.948792i | \(0.602307\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.88621i | 0.341021i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.11434i | 0.0427015i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.51571 | − | 5.51571i | −0.211053 | − | 0.211053i | 0.593662 | − | 0.804715i | \(-0.297682\pi\) |
−0.804715 | + | 0.593662i | \(0.797682\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.5925 | + | 12.5925i | −0.481135 | + | 0.481135i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 27.7515 | 1.05879 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.75605 | −0.219288 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.1271 | − | 31.1271i | 1.18413 | − | 1.18413i | 0.205468 | − | 0.978664i | \(-0.434128\pi\) |
0.978664 | − | 0.205468i | \(-0.0658717\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.452882 | − | 0.452882i | −0.0172036 | − | 0.0172036i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 59.3867i | 2.25267i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.7677i | 0.748756i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −20.6024 | − | 20.6024i | −0.779255 | − | 0.779255i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21.7631 | + | 21.7631i | −0.821981 | + | 0.821981i | −0.986392 | − | 0.164411i | \(-0.947428\pi\) |
0.164411 | + | 0.986392i | \(0.447428\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.9813 | 0.489598 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.53732 | −0.0955612 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.80533 | + | 9.80533i | −0.368767 | + | 0.368767i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.9756 | + | 12.9756i | 0.487309 | + | 0.487309i | 0.907456 | − | 0.420147i | \(-0.138021\pi\) |
−0.420147 | + | 0.907456i | \(0.638021\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.6756i | 0.437868i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 33.5338i | 1.25585i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.45065 | + | 5.45065i | 0.203843 | + | 0.203843i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 22.5900 | − | 22.5900i | 0.843640 | − | 0.843640i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 36.4527 | 1.35946 | 0.679728 | − | 0.733464i | \(-0.262098\pi\) | ||||
0.679728 | + | 0.733464i | \(0.262098\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.3236 | 0.533439 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −42.0127 | + | 42.0127i | −1.56247 | + | 1.56247i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −10.7039 | − | 10.7039i | −0.397531 | − | 0.397531i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 37.9281i | 1.40668i | 0.710855 | + | 0.703338i | \(0.248308\pi\) | ||||
−0.710855 | + | 0.703338i | \(0.751692\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5.20661i | 0.192838i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.981829 | + | 0.981829i | 0.0363143 | + | 0.0363143i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.8899 | + | 12.8899i | −0.476099 | + | 0.476099i | −0.903882 | − | 0.427782i | \(-0.859295\pi\) |
0.427782 | + | 0.903882i | \(0.359295\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.45192 | 0.201097 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.96230 | −0.145953 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.97047 | + | 7.97047i | −0.293199 | + | 0.293199i | −0.838342 | − | 0.545144i | \(-0.816475\pi\) |
0.545144 | + | 0.838342i | \(0.316475\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −53.3353 | − | 53.3353i | −1.95932 | − | 1.95932i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 41.0385i | 1.50556i | 0.658273 | + | 0.752779i | \(0.271287\pi\) | ||||
−0.658273 | + | 0.752779i | \(0.728713\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 55.8171i | − | 2.04498i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.54020 | + | 3.54020i | 0.129529 | + | 0.129529i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.6995 | + | 10.6995i | −0.390951 | + | 0.390951i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.8700 | −0.615594 | −0.307797 | − | 0.951452i | \(-0.599592\pi\) | ||||
−0.307797 | + | 0.951452i | \(0.599592\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −26.4896 | −0.965336 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.74490 | − | 8.74490i | 0.318260 | − | 0.318260i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21.7021 | − | 21.7021i | −0.788778 | − | 0.788778i | 0.192516 | − | 0.981294i | \(-0.438335\pi\) |
−0.981294 | + | 0.192516i | \(0.938335\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 5.61733i | − | 0.203896i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 8.35285i | − | 0.302791i | −0.988473 | − | 0.151395i | \(-0.951623\pi\) | ||
0.988473 | − | 0.151395i | \(-0.0483766\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.38679 | − | 7.38679i | −0.267420 | − | 0.267420i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.76400 | − | 4.76400i | 0.172243 | − | 0.172243i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −67.6229 | −2.44172 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21.8388 | −0.787527 | −0.393764 | − | 0.919212i | \(-0.628827\pi\) | ||||
−0.393764 | + | 0.919212i | \(0.628827\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −40.8022 | + | 40.8022i | −1.46945 | + | 1.46945i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.55450 | + | 6.55450i | 0.235749 | + | 0.235749i | 0.815087 | − | 0.579338i | \(-0.196689\pi\) |
−0.579338 | + | 0.815087i | \(0.696689\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 9.92446i | − | 0.356497i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.95537i | 0.177773i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 41.7470 | + | 41.7470i | 1.49574 | + | 1.49574i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.0522451 | + | 0.0522451i | −0.00186948 | + | 0.00186948i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −29.0369 | −1.03769 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −43.2879 | −1.54501 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.8764 | + | 17.8764i | −0.637224 | + | 0.637224i | −0.949870 | − | 0.312646i | \(-0.898785\pi\) |
0.312646 | + | 0.949870i | \(0.398785\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 22.1684 | + | 22.1684i | 0.789215 | + | 0.789215i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 8.05995i | − | 0.286579i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 69.9386i | 2.48359i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.39782 | − | 3.39782i | −0.120508 | − | 0.120508i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15.9981 | − | 15.9981i | 0.566683 | − | 0.566683i | −0.364515 | − | 0.931198i | \(-0.618765\pi\) |
0.931198 | + | 0.364515i | \(0.118765\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.857136 | −0.0303233 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.25480 | 0.0796694 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.12222 | + | 1.12222i | −0.0396023 | + | 0.0396023i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.8047 | + | 10.8047i | 0.380816 | + | 0.380816i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 0.0135499i | − | 0.000476981i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 13.5401i | − | 0.476046i | −0.971260 | − | 0.238023i | \(-0.923501\pi\) | ||
0.971260 | − | 0.238023i | \(-0.0764993\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.49897 | − | 1.49897i | −0.0526359 | − | 0.0526359i | 0.680299 | − | 0.732935i | \(-0.261850\pi\) |
−0.732935 | + | 0.680299i | \(0.761850\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.53082 | − | 8.53082i | 0.299189 | − | 0.299189i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −35.5477 | −1.24518 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.14701 | 0.145085 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.50613 | − | 6.50613i | 0.227343 | − | 0.227343i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.576655 | − | 0.576655i | −0.0201254 | − | 0.0201254i | 0.696972 | − | 0.717098i | \(-0.254530\pi\) |
−0.717098 | + | 0.696972i | \(0.754530\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.8651i | 0.518164i | 0.965855 | + | 0.259082i | \(0.0834200\pi\) | ||||
−0.965855 | + | 0.259082i | \(0.916580\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.66247i | 0.0578799i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22.5725 | + | 22.5725i | 0.784921 | + | 0.784921i | 0.980657 | − | 0.195736i | \(-0.0627094\pi\) |
−0.195736 | + | 0.980657i | \(0.562709\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.4320 | + | 15.4320i | −0.535975 | + | 0.535975i | −0.922344 | − | 0.386369i | \(-0.873729\pi\) |
0.386369 | + | 0.922344i | \(0.373729\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −33.5209 | −1.16283 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.84172 | 0.0638117 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 24.2195 | − | 24.2195i | 0.838151 | − | 0.838151i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −13.4613 | − | 13.4613i | −0.465290 | − | 0.465290i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 37.1968i | 1.28418i | 0.766630 | + | 0.642089i | \(0.221932\pi\) | ||||
−0.766630 | + | 0.642089i | \(0.778068\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 46.5393i | − | 1.60480i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 14.4182 | + | 14.4182i | 0.496589 | + | 0.496589i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −54.4365 | + | 54.4365i | −1.87267 | + | 1.87267i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.7933 | −0.370864 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −37.5755 | −1.28959 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.82064 | + | 9.82064i | −0.336647 | + | 0.336647i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22.4583 | − | 22.4583i | −0.768958 | − | 0.768958i | 0.208965 | − | 0.977923i | \(-0.432990\pi\) |
−0.977923 | + | 0.208965i | \(0.932990\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 20.1220i | − | 0.688156i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 47.6664i | − | 1.62825i | −0.580688 | − | 0.814126i | \(-0.697216\pi\) | ||
0.580688 | − | 0.814126i | \(-0.302784\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.3609 | + | 22.3609i | 0.762945 | + | 0.762945i | 0.976854 | − | 0.213909i | \(-0.0686195\pi\) |
−0.213909 | + | 0.976854i | \(0.568620\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −15.9362 | + | 15.9362i | −0.543103 | + | 0.543103i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.01295 | 0.204683 | 0.102342 | − | 0.994749i | \(-0.467367\pi\) | ||||
0.102342 | + | 0.994749i | \(0.467367\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23.5321 | 0.800115 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −20.2044 | + | 20.2044i | −0.686179 | + | 0.686179i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.66382 | − | 2.66382i | −0.0903638 | − | 0.0903638i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 56.9226i | − | 1.92875i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12.5198i | 0.423730i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.98222 | + | 5.98222i | 0.202236 | + | 0.202236i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.53722 | − | 7.53722i | 0.254514 | − | 0.254514i | −0.568305 | − | 0.822818i | \(-0.692400\pi\) |
0.822818 | + | 0.568305i | \(0.192400\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.69134 | −0.0907766 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.6023 | −0.626726 | −0.313363 | − | 0.949633i | \(-0.601456\pi\) | ||||
−0.313363 | + | 0.949633i | \(0.601456\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.1111 | + | 15.1111i | −0.508530 | + | 0.508530i | −0.914075 | − | 0.405545i | \(-0.867082\pi\) |
0.405545 | + | 0.914075i | \(0.367082\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −39.9181 | − | 39.9181i | −1.34183 | − | 1.34183i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 56.3410i | 1.89175i | 0.324537 | + | 0.945873i | \(0.394792\pi\) | ||||
−0.324537 | + | 0.945873i | \(0.605208\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.367471i | 0.0123246i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.61358 | + | 3.61358i | 0.121060 | + | 0.121060i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.81017 | + | 1.81017i | −0.0605749 | + | 0.0605749i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −33.2674 | −1.11201 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 80.6988 | 2.69446 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 35.0195 | − | 35.0195i | 1.16796 | − | 1.16796i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.14782 | − | 1.14782i | −0.0382394 | − | 0.0382394i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.58304i | 0.0526804i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 50.3663i | 1.67423i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.23632 | − | 5.23632i | −0.173869 | − | 0.173869i | 0.614808 | − | 0.788677i | \(-0.289234\pi\) |
−0.788677 | + | 0.614808i | \(0.789234\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13.8147 | + | 13.8147i | −0.458205 | + | 0.458205i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.0494 | −0.929319 | −0.464660 | − | 0.885489i | \(-0.653823\pi\) | ||||
−0.464660 | + | 0.885489i | \(0.653823\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.61542 | −0.0534625 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −41.2850 | + | 41.2850i | −1.36484 | + | 1.36484i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.30850 | + | 9.30850i | 0.307394 | + | 0.307394i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36.2282i | 1.19506i | 0.801847 | + | 0.597529i | \(0.203851\pi\) | ||||
−0.801847 | + | 0.597529i | \(0.796149\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 43.9268i | − | 1.44744i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.750555 | − | 0.750555i | −0.0247048 | − | 0.0247048i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.90646 | − | 2.90646i | 0.0955638 | − | 0.0955638i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 20.1805 | 0.662815 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16.6482 | 0.546210 | 0.273105 | − | 0.961984i | \(-0.411949\pi\) | ||||
0.273105 | + | 0.961984i | \(0.411949\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.88948 | − | 3.88948i | 0.127473 | − | 0.127473i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 17.2294 | + | 17.2294i | 0.564066 | + | 0.564066i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.17384i | 0.0710922i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.4319i | 0.536807i | 0.963307 | + | 0.268403i | \(0.0864960\pi\) | ||||
−0.963307 | + | 0.268403i | \(0.913504\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 27.5599 | + | 27.5599i | 0.899382 | + | 0.899382i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.7153 | + | 11.7153i | −0.381907 | + | 0.381907i | −0.871789 | − | 0.489882i | \(-0.837040\pi\) |
0.489882 | + | 0.871789i | \(0.337040\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −63.1652 | −2.05694 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8.67456 | −0.282183 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12.5463 | + | 12.5463i | −0.407699 | + | 0.407699i | −0.880936 | − | 0.473236i | \(-0.843086\pi\) |
0.473236 | + | 0.880936i | \(0.343086\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −16.1219 | − | 16.1219i | −0.523339 | − | 0.523339i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 47.1739i | − | 1.52972i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.9557i | 0.711213i | 0.934636 | + | 0.355607i | \(0.115726\pi\) | ||||
−0.934636 | + | 0.355607i | \(0.884274\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −35.3651 | − | 35.3651i | −1.14439 | − | 1.14439i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.86621 | + | 5.86621i | −0.189627 | + | 0.189627i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.85872 | −0.221480 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.46955 | 0.0474047 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −15.0745 | + | 15.0745i | −0.485768 | + | 0.485768i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.37558 | + | 4.37558i | 0.140855 | + | 0.140855i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 22.2420i | − | 0.715255i | −0.933864 | − | 0.357628i | \(-0.883586\pi\) | ||
0.933864 | − | 0.357628i | \(-0.116414\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 21.2713i | − | 0.683333i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.7865 | − | 18.7865i | −0.602888 | − | 0.602888i | 0.338190 | − | 0.941078i | \(-0.390185\pi\) |
−0.941078 | + | 0.338190i | \(0.890185\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16.1730 | + | 16.1730i | −0.518482 | + | 0.518482i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −23.8832 | −0.764873 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.54985 | 0.305527 | 0.152763 | − | 0.988263i | \(-0.451183\pi\) | ||||
0.152763 | + | 0.988263i | \(0.451183\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.514439 | + | 0.514439i | −0.0164415 | + | 0.0164415i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.4072 | − | 10.4072i | −0.332277 | − | 0.332277i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.65760i | 0.180449i | 0.995921 | + | 0.0902247i | \(0.0287585\pi\) | ||||
−0.995921 | + | 0.0902247i | \(0.971241\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 22.6291i | 0.721023i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.690998 | − | 0.690998i | −0.0219947 | − | 0.0219947i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.13731 | + | 3.13731i | −0.0997606 | + | 0.0997606i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 62.8260 | 1.99573 | 0.997867 | − | 0.0652866i | \(-0.0207962\pi\) | ||||
0.997867 | + | 0.0652866i | \(0.0207962\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 16.3216 | 0.517951 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −17.1322 | + | 17.1322i | −0.543129 | + | 0.543129i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.75899 | − | 5.75899i | −0.182389 | − | 0.182389i | 0.610007 | − | 0.792396i | \(-0.291167\pi\) |
−0.792396 | + | 0.610007i | \(0.791167\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 7.88449i | − | 0.249454i |
(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 | 1792.2.m.f.449.8 | yes | 16 | |
4.3 | odd | 2 | 1792.2.m.h.449.1 | yes | 16 | ||
8.3 | odd | 2 | 1792.2.m.e.449.8 | ✓ | 16 | ||
8.5 | even | 2 | 1792.2.m.g.449.1 | yes | 16 | ||
16.3 | odd | 4 | 1792.2.m.h.1345.1 | yes | 16 | ||
16.5 | even | 4 | 1792.2.m.g.1345.1 | yes | 16 | ||
16.11 | odd | 4 | 1792.2.m.e.1345.8 | yes | 16 | ||
16.13 | even | 4 | inner | 1792.2.m.f.1345.8 | yes | 16 | |
32.3 | odd | 8 | 7168.2.a.bf.1.2 | 8 | |||
32.13 | even | 8 | 7168.2.a.ba.1.2 | 8 | |||
32.19 | odd | 8 | 7168.2.a.bb.1.7 | 8 | |||
32.29 | even | 8 | 7168.2.a.be.1.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1792.2.m.e.449.8 | ✓ | 16 | 8.3 | odd | 2 | ||
1792.2.m.e.1345.8 | yes | 16 | 16.11 | odd | 4 | ||
1792.2.m.f.449.8 | yes | 16 | 1.1 | even | 1 | trivial | |
1792.2.m.f.1345.8 | yes | 16 | 16.13 | even | 4 | inner | |
1792.2.m.g.449.1 | yes | 16 | 8.5 | even | 2 | ||
1792.2.m.g.1345.1 | yes | 16 | 16.5 | even | 4 | ||
1792.2.m.h.449.1 | yes | 16 | 4.3 | odd | 2 | ||
1792.2.m.h.1345.1 | yes | 16 | 16.3 | odd | 4 | ||
7168.2.a.ba.1.2 | 8 | 32.13 | even | 8 | |||
7168.2.a.bb.1.7 | 8 | 32.19 | odd | 8 | |||
7168.2.a.be.1.7 | 8 | 32.29 | even | 8 | |||
7168.2.a.bf.1.2 | 8 | 32.3 | odd | 8 |