Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(865,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.865");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.s (of order \(3\), 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: | \(12.0733807856\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.9391935744.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 5x^{6} + 12x^{5} - 76x^{4} + 84x^{3} + 245x^{2} - 1372x + 2401 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1297.3 | ||
Root | \(1.57052 - 2.12920i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1512.1297 |
Dual form | 1512.2.s.m.865.3 |
$q$-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 \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.366025 | − | 0.633975i | 0.163692 | − | 0.283522i | −0.772498 | − | 0.635017i | \(-0.780993\pi\) |
0.936190 | + | 0.351495i | \(0.114326\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.62920 | − | 0.295509i | −0.993743 | − | 0.111692i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.55868 | − | 2.69971i | −0.469960 | − | 0.813994i | 0.529450 | − | 0.848341i | \(-0.322398\pi\) |
−0.999410 | + | 0.0343469i | \(0.989065\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.32307 | −0.644303 | −0.322152 | − | 0.946688i | \(-0.604406\pi\) | ||||
−0.322152 | + | 0.946688i | \(0.604406\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.09808 | + | 5.36603i | 0.751394 | + | 1.30145i | 0.947147 | + | 0.320799i | \(0.103951\pi\) |
−0.195753 | + | 0.980653i | \(0.562715\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.36125 | − | 5.82185i | 0.771123 | − | 1.33562i | −0.165825 | − | 0.986155i | \(-0.553029\pi\) |
0.936948 | − | 0.349469i | \(-0.113638\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.33369 | + | 4.04207i | −0.486608 | + | 0.842829i | −0.999881 | − | 0.0153959i | \(-0.995099\pi\) |
0.513274 | + | 0.858225i | \(0.328432\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.23205 | + | 3.86603i | 0.446410 | + | 0.773205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.24884 | −1.71747 | −0.858733 | − | 0.512423i | \(-0.828748\pi\) | ||||
−0.858733 | + | 0.512423i | \(0.828748\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.326629 | − | 0.565738i | −0.0586643 | − | 0.101610i | 0.835202 | − | 0.549944i | \(-0.185351\pi\) |
−0.893866 | + | 0.448334i | \(0.852018\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.14970 | + | 1.55868i | −0.194334 | + | 0.263465i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.41993 | + | 9.38759i | −0.891031 | + | 1.54331i | −0.0523889 | + | 0.998627i | \(0.516684\pi\) |
−0.838642 | + | 0.544683i | \(0.816650\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −12.4309 | −1.94138 | −0.970688 | − | 0.240343i | \(-0.922740\pi\) | ||||
−0.970688 | + | 0.240343i | \(0.922740\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.77062 | 0.270017 | 0.135008 | − | 0.990844i | \(-0.456894\pi\) | ||||
0.135008 | + | 0.990844i | \(0.456894\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.50706 | + | 9.53850i | −0.803287 | + | 1.39133i | 0.114154 | + | 0.993463i | \(0.463584\pi\) |
−0.917441 | + | 0.397871i | \(0.869749\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.82535 | + | 1.55390i | 0.975050 | + | 0.221986i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.398363 | − | 0.689985i | −0.0547194 | − | 0.0947768i | 0.837368 | − | 0.546639i | \(-0.184093\pi\) |
−0.892088 | + | 0.451863i | \(0.850760\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.28207 | −0.307714 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.290731 | − | 0.503561i | −0.0378499 | − | 0.0655580i | 0.846480 | − | 0.532421i | \(-0.178718\pi\) |
−0.884330 | + | 0.466863i | \(0.845384\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.264389 | − | 0.457934i | 0.0338515 | − | 0.0586325i | −0.848603 | − | 0.529030i | \(-0.822556\pi\) |
0.882455 | + | 0.470397i | \(0.155889\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.850302 | + | 1.47277i | −0.105467 | + | 0.182674i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.59330 | − | 9.68788i | −0.683330 | − | 1.18356i | −0.973958 | − | 0.226726i | \(-0.927198\pi\) |
0.290628 | − | 0.956836i | \(-0.406136\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.34674 | 0.753220 | 0.376610 | − | 0.926372i | \(-0.377090\pi\) | ||||
0.376610 | + | 0.926372i | \(0.377090\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.48816 | − | 2.57757i | −0.174176 | − | 0.301682i | 0.765700 | − | 0.643198i | \(-0.222393\pi\) |
−0.939876 | + | 0.341516i | \(0.889060\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.30029 | + | 7.55868i | 0.376103 | + | 0.861392i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.68788 | − | 8.11964i | 0.527427 | − | 0.913531i | −0.472062 | − | 0.881566i | \(-0.656490\pi\) |
0.999489 | − | 0.0319654i | \(-0.0101766\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.0527 | −1.21319 | −0.606595 | − | 0.795011i | \(-0.707465\pi\) | ||||
−0.606595 | + | 0.795011i | \(0.707465\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.53590 | 0.491987 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.89237 | + | 10.2059i | −0.624590 | + | 1.08182i | 0.364030 | + | 0.931387i | \(0.381400\pi\) |
−0.988620 | + | 0.150434i | \(0.951933\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.10780 | + | 0.686487i | 0.640272 | + | 0.0719634i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.46060 | − | 4.26189i | −0.252453 | − | 0.437261i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.77062 | −0.179779 | −0.0898895 | − | 0.995952i | \(-0.528651\pi\) | ||||
−0.0898895 | + | 0.995952i | \(0.528651\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.67604 | − | 8.09914i | −0.465283 | − | 0.805894i | 0.533931 | − | 0.845528i | \(-0.320714\pi\) |
−0.999214 | + | 0.0396337i | \(0.987381\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.30257 | + | 9.18432i | −0.522477 | + | 0.904958i | 0.477180 | + | 0.878805i | \(0.341659\pi\) |
−0.999658 | + | 0.0261522i | \(0.991675\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.44043 | + | 9.42310i | −0.525946 | + | 0.910965i | 0.473597 | + | 0.880742i | \(0.342955\pi\) |
−0.999543 | + | 0.0302237i | \(0.990378\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.73561 | + | 3.00617i | 0.166241 | + | 0.287939i | 0.937095 | − | 0.349073i | \(-0.113504\pi\) |
−0.770854 | + | 0.637012i | \(0.780170\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.3276 | 1.15969 | 0.579843 | − | 0.814728i | \(-0.303114\pi\) | ||||
0.579843 | + | 0.814728i | \(0.303114\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.70838 | + | 2.95900i | 0.159307 | + | 0.275928i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.55974 | − | 15.0238i | −0.601331 | − | 1.37723i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.641033 | − | 1.11030i | 0.0582757 | − | 0.100937i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.92820 | 0.619677 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.1174 | −0.897771 | −0.448885 | − | 0.893589i | \(-0.648179\pi\) | ||||
−0.448885 | + | 0.893589i | \(0.648179\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.65676 | + | 8.06574i | −0.406863 | + | 0.704707i | −0.994536 | − | 0.104391i | \(-0.966711\pi\) |
0.587674 | + | 0.809098i | \(0.300044\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.5578 | + | 14.3135i | −0.915476 | + | 1.24114i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.71900 | − | 11.6376i | −0.574043 | − | 0.994271i | −0.996145 | − | 0.0877228i | \(-0.972041\pi\) |
0.422102 | − | 0.906548i | \(-0.361292\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.90453 | 0.755272 | 0.377636 | − | 0.925954i | \(-0.376737\pi\) | ||||
0.377636 | + | 0.925954i | \(0.376737\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.62092 | + | 6.27162i | 0.302797 | + | 0.524459i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.38531 | + | 5.86353i | −0.281135 | + | 0.486939i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.63397 | + | 2.83013i | −0.133860 | + | 0.231853i | −0.925162 | − | 0.379574i | \(-0.876071\pi\) |
0.791301 | + | 0.611427i | \(0.209404\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.79073 | − | 6.56574i | −0.308485 | − | 0.534312i | 0.669546 | − | 0.742771i | \(-0.266489\pi\) |
−0.978031 | + | 0.208458i | \(0.933155\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.478218 | −0.0384114 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.31351 | + | 9.20327i | 0.424064 | + | 0.734501i | 0.996333 | − | 0.0855654i | \(-0.0272697\pi\) |
−0.572268 | + | 0.820067i | \(0.693936\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.33019 | − | 9.93776i | 0.577700 | − | 0.783205i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.75839 | − | 16.9020i | 0.764336 | − | 1.32387i | −0.176260 | − | 0.984344i | \(-0.556400\pi\) |
0.940597 | − | 0.339526i | \(-0.110267\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.2156 | 0.945272 | 0.472636 | − | 0.881258i | \(-0.343303\pi\) | ||||
0.472636 | + | 0.881258i | \(0.343303\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.60335 | −0.584873 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.80735 | + | 15.2548i | −0.669610 | + | 1.15980i | 0.308403 | + | 0.951256i | \(0.400205\pi\) |
−0.978013 | + | 0.208543i | \(0.933128\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.72606 | − | 10.8241i | −0.357256 | − | 0.818227i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.37558 | − | 2.38258i | −0.102816 | − | 0.178082i | 0.810028 | − | 0.586391i | \(-0.199452\pi\) |
−0.912844 | + | 0.408309i | \(0.866119\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.07636 | 0.600311 | 0.300155 | − | 0.953890i | \(-0.402961\pi\) | ||||
0.300155 | + | 0.953890i | \(0.402961\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.96766 | + | 6.87219i | 0.291708 | + | 0.505254i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.65782 | − | 16.7278i | 0.706250 | − | 1.22326i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.712767 | + | 1.23455i | −0.0515740 | + | 0.0893288i | −0.890660 | − | 0.454670i | \(-0.849757\pi\) |
0.839086 | + | 0.543999i | \(0.183090\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.24656 | + | 3.89115i | 0.161711 | + | 0.280091i | 0.935482 | − | 0.353374i | \(-0.114966\pi\) |
−0.773772 | + | 0.633465i | \(0.781632\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.8706 | 1.13074 | 0.565368 | − | 0.824838i | \(-0.308734\pi\) | ||||
0.565368 | + | 0.824838i | \(0.308734\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.24528 | − | 10.8171i | −0.442716 | − | 0.766806i | 0.555174 | − | 0.831734i | \(-0.312652\pi\) |
−0.997890 | + | 0.0649277i | \(0.979318\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 24.3170 | + | 2.73311i | 1.70672 | + | 0.191827i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.55002 | + | 7.88086i | −0.317787 | + | 0.550423i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −20.9564 | −1.44959 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.9091 | −1.78366 | −0.891828 | − | 0.452375i | \(-0.850577\pi\) | ||||
−0.891828 | + | 0.452375i | \(0.850577\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.648091 | − | 1.12253i | 0.0441995 | − | 0.0765557i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.691592 | + | 1.58396i | 0.0469483 | + | 0.107526i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.19704 | − | 12.4656i | −0.484126 | − | 0.838530i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.05268 | 0.338353 | 0.169176 | − | 0.985586i | \(-0.445889\pi\) | ||||
0.169176 | + | 0.985586i | \(0.445889\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.45105 | − | 9.44149i | −0.361799 | − | 0.626654i | 0.626458 | − | 0.779455i | \(-0.284504\pi\) |
−0.988257 | + | 0.152801i | \(0.951171\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.35030 | − | 7.53494i | 0.287476 | − | 0.497923i | −0.685731 | − | 0.727855i | \(-0.740517\pi\) |
0.973207 | + | 0.229932i | \(0.0738505\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.35736 | − | 4.08307i | 0.154436 | − | 0.267491i | −0.778418 | − | 0.627747i | \(-0.783977\pi\) |
0.932853 | + | 0.360256i | \(0.117311\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.03145 | + | 6.98267i | 0.262983 | + | 0.455499i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.8232 | −1.34694 | −0.673470 | − | 0.739215i | \(-0.735197\pi\) | ||||
−0.673470 | + | 0.739215i | \(0.735197\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.42577 | + | 12.8618i | 0.478336 | + | 0.828502i | 0.999692 | − | 0.0248376i | \(-0.00790685\pi\) |
−0.521356 | + | 0.853339i | \(0.674574\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.48339 | − | 3.75833i | 0.222545 | − | 0.240111i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.80841 | + | 13.5246i | −0.496837 | + | 0.860547i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.13148 | 0.387015 | 0.193508 | − | 0.981099i | \(-0.438014\pi\) | ||||
0.193508 | + | 0.981099i | \(0.438014\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.5499 | 0.914744 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.52634 | − | 9.57191i | 0.344724 | − | 0.597079i | −0.640580 | − | 0.767892i | \(-0.721306\pi\) |
0.985304 | + | 0.170813i | \(0.0546393\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 17.0242 | − | 23.0802i | 1.05783 | − | 1.43413i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.04645 | − | 15.6689i | −0.557828 | − | 0.966187i | −0.997677 | − | 0.0681153i | \(-0.978301\pi\) |
0.439849 | − | 0.898072i | \(-0.355032\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.583244 | −0.0358284 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.43087 | + | 14.6027i | 0.514039 | + | 0.890342i | 0.999867 | + | 0.0162879i | \(0.00518482\pi\) |
−0.485828 | + | 0.874054i | \(0.661482\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.13504 | + | 12.3582i | −0.433423 | + | 0.750710i | −0.997165 | − | 0.0752403i | \(-0.976028\pi\) |
0.563743 | + | 0.825950i | \(0.309361\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.95811 | − | 12.0518i | 0.419590 | − | 0.726750i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.17604 | − | 3.76901i | −0.130746 | − | 0.226458i | 0.793219 | − | 0.608937i | \(-0.208404\pi\) |
−0.923964 | + | 0.382479i | \(0.875070\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.6917 | 1.59229 | 0.796147 | − | 0.605104i | \(-0.206868\pi\) | ||||
0.796147 | + | 0.605104i | \(0.206868\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.23205 | + | 3.86603i | 0.132682 | + | 0.229811i | 0.924709 | − | 0.380674i | \(-0.124308\pi\) |
−0.792028 | + | 0.610485i | \(0.790975\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 32.6832 | + | 3.67343i | 1.92923 | + | 0.216836i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.6962 | + | 18.5263i | −0.629185 | + | 1.08978i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.86353 | 0.167289 | 0.0836445 | − | 0.996496i | \(-0.473344\pi\) | ||||
0.0836445 | + | 0.996496i | \(0.473344\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.425660 | −0.0247829 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.42132 | − | 9.39000i | 0.313523 | − | 0.543037i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.65530 | − | 0.523234i | −0.268327 | − | 0.0301587i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.193546 | − | 0.335231i | −0.0110824 | − | 0.0191953i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.17717 | 0.238403 | 0.119202 | − | 0.992870i | \(-0.461966\pi\) | ||||
0.119202 | + | 0.992870i | \(0.461966\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.1401 | + | 24.4914i | 0.801814 | + | 1.38878i | 0.918421 | + | 0.395604i | \(0.129465\pi\) |
−0.116607 | + | 0.993178i | \(0.537202\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.96638 | + | 13.7982i | −0.450287 | + | 0.779919i | −0.998404 | − | 0.0564825i | \(-0.982011\pi\) |
0.548117 | + | 0.836402i | \(0.315345\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.62792 | − | 16.6760i | 0.540758 | − | 0.936620i | −0.458103 | − | 0.888899i | \(-0.651471\pi\) |
0.998861 | − | 0.0477206i | \(-0.0151957\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 14.4160 | + | 24.9692i | 0.807140 | + | 1.39801i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 41.6536 | 2.31767 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.18521 | − | 8.98104i | −0.287624 | − | 0.498179i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 17.2979 | − | 23.4512i | 0.953661 | − | 1.29291i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.44716 | − | 12.8989i | 0.409333 | − | 0.708986i | −0.585482 | − | 0.810685i | \(-0.699095\pi\) |
0.994815 | + | 0.101700i | \(0.0324281\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.18916 | −0.447421 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 34.8279 | 1.89719 | 0.948597 | − | 0.316486i | \(-0.102503\pi\) | ||||
0.948597 | + | 0.316486i | \(0.102503\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.01822 | + | 1.76361i | −0.0551398 | + | 0.0955049i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.4860 | − | 6.10247i | −0.944155 | − | 0.329502i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.4641 | − | 26.7846i | −0.830156 | − | 1.43787i | −0.897914 | − | 0.440171i | \(-0.854918\pi\) |
0.0677573 | − | 0.997702i | \(-0.478416\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −32.8971 | −1.76094 | −0.880471 | − | 0.474101i | \(-0.842773\pi\) | ||||
−0.880471 | + | 0.474101i | \(0.842773\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.89676 | − | 6.74938i | −0.207403 | − | 0.359233i | 0.743492 | − | 0.668744i | \(-0.233168\pi\) |
−0.950896 | + | 0.309511i | \(0.899835\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.32307 | − | 4.02367i | 0.123296 | − | 0.213554i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.44043 | − | 9.42310i | 0.287135 | − | 0.497332i | −0.685990 | − | 0.727611i | \(-0.740631\pi\) |
0.973125 | + | 0.230279i | \(0.0739639\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.0960 | − | 22.6829i | −0.689261 | − | 1.19384i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.17882 | −0.114045 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.83491 | + | 13.5705i | 0.408979 | + | 0.708372i | 0.994776 | − | 0.102086i | \(-0.0325517\pi\) |
−0.585797 | + | 0.810458i | \(0.699218\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.843478 | + | 1.93183i | 0.0437912 | + | 0.100295i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.0119 | − | 32.9297i | 0.984401 | − | 1.70503i | 0.339834 | − | 0.940486i | \(-0.389629\pi\) |
0.644568 | − | 0.764547i | \(-0.277037\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 21.4857 | 1.10657 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.8663 | 1.07183 | 0.535915 | − | 0.844272i | \(-0.319967\pi\) | ||||
0.535915 | + | 0.844272i | \(0.319967\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.48777 | − | 12.9692i | 0.382607 | − | 0.662695i | −0.608827 | − | 0.793303i | \(-0.708360\pi\) |
0.991434 | + | 0.130608i | \(0.0416929\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.00000 | + | 0.674371i | 0.305788 | + | 0.0343691i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.6235 | − | 30.5248i | −0.893548 | − | 1.54767i | −0.835591 | − | 0.549352i | \(-0.814875\pi\) |
−0.0579573 | − | 0.998319i | \(-0.518459\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −28.9198 | −1.46254 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.43176 | − | 5.94399i | −0.172671 | − | 0.299075i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.85297 | − | 13.6017i | 0.394129 | − | 0.682652i | −0.598860 | − | 0.800854i | \(-0.704380\pi\) |
0.992990 | + | 0.118201i | \(0.0377129\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.6760 | + | 18.4914i | −0.533136 | + | 0.923419i | 0.466115 | + | 0.884724i | \(0.345653\pi\) |
−0.999251 | + | 0.0386945i | \(0.987680\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.758782 | + | 1.31425i | 0.0377976 | + | 0.0654674i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 33.7917 | 1.67499 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.3158 | − | 28.2598i | −0.806764 | − | 1.39736i | −0.915094 | − | 0.403241i | \(-0.867884\pi\) |
0.108330 | − | 0.994115i | \(-0.465450\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.615582 | + | 1.40987i | 0.0302908 | + | 0.0693753i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.04556 | + | 7.00712i | −0.198589 | + | 0.343966i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −28.1770 | −1.37654 | −0.688269 | − | 0.725455i | \(-0.741629\pi\) | ||||
−0.688269 | + | 0.725455i | \(0.741629\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.62246 | 0.371496 | 0.185748 | − | 0.982597i | \(-0.440529\pi\) | ||||
0.185748 | + | 0.982597i | \(0.440529\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −13.8301 | + | 23.9545i | −0.670860 | + | 1.16196i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.830453 | + | 1.12587i | −0.0401884 | + | 0.0544847i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.73294 | − | 6.46565i | −0.179809 | − | 0.311439i | 0.762006 | − | 0.647570i | \(-0.224215\pi\) |
−0.941815 | + | 0.336131i | \(0.890881\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.3348 | −0.592770 | −0.296385 | − | 0.955069i | \(-0.595781\pi\) | ||||
−0.296385 | + | 0.955069i | \(0.595781\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 15.6882 | + | 27.1728i | 0.750469 | + | 1.29985i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.0360 | + | 27.7752i | −0.765357 | + | 1.32564i | 0.174701 | + | 0.984622i | \(0.444104\pi\) |
−0.940058 | + | 0.341015i | \(0.889229\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.52028 | + | 13.0255i | −0.357299 | + | 0.618861i | −0.987509 | − | 0.157565i | \(-0.949636\pi\) |
0.630209 | + | 0.776425i | \(0.282969\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.31351 | + | 7.47122i | 0.204480 | + | 0.354170i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.60757 | 0.406216 | 0.203108 | − | 0.979156i | \(-0.434896\pi\) | ||||
0.203108 | + | 0.979156i | \(0.434896\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.3758 | + | 33.5598i | 0.912369 | + | 1.58027i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.67083 | − | 3.62092i | 0.125210 | − | 0.169751i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.0027 | + | 19.0572i | −0.514683 | + | 0.891457i | 0.485172 | + | 0.874419i | \(0.338757\pi\) |
−0.999855 | + | 0.0170385i | \(0.994576\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.4766 | 0.627666 | 0.313833 | − | 0.949478i | \(-0.398387\pi\) | ||||
0.313833 | + | 0.949478i | \(0.398387\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −36.6560 | −1.70355 | −0.851775 | − | 0.523907i | \(-0.824474\pi\) | ||||
−0.851775 | + | 0.523907i | \(0.824474\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17.5632 | + | 30.4204i | −0.812730 | + | 1.40769i | 0.0982167 | + | 0.995165i | \(0.468686\pi\) |
−0.910947 | + | 0.412524i | \(0.864647\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.8430 | + | 27.1242i | 0.546860 | + | 1.25248i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.75983 | − | 4.78016i | −0.126897 | − | 0.219792i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 30.0099 | 1.37695 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.03340 | − | 12.1822i | −0.321364 | − | 0.556619i | 0.659406 | − | 0.751787i | \(-0.270808\pi\) |
−0.980770 | + | 0.195168i | \(0.937475\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.5909 | − | 21.8080i | 0.574094 | − | 0.994360i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.648091 | + | 1.12253i | −0.0294283 | + | 0.0509713i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.66064 | − | 9.80452i | −0.256508 | − | 0.444285i | 0.708796 | − | 0.705414i | \(-0.249239\pi\) |
−0.965304 | + | 0.261128i | \(0.915905\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.0720 | 1.17661 | 0.588307 | − | 0.808638i | \(-0.299795\pi\) | ||||
0.588307 | + | 0.808638i | \(0.299795\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −28.6536 | − | 49.6295i | −1.29049 | − | 2.23520i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −16.6868 | − | 1.87552i | −0.748507 | − | 0.0841285i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.21793 | + | 2.10952i | −0.0545222 | + | 0.0944352i | −0.891998 | − | 0.452039i | \(-0.850697\pi\) |
0.837476 | + | 0.546474i | \(0.184030\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −27.8161 | −1.24026 | −0.620128 | − | 0.784500i | \(-0.712919\pi\) | ||||
−0.620128 | + | 0.784500i | \(0.712919\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.84620 | −0.304652 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.50510 | − | 6.07102i | 0.155361 | − | 0.269093i | −0.777829 | − | 0.628475i | \(-0.783679\pi\) |
0.933190 | + | 0.359382i | \(0.117013\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.15098 | + | 7.21672i | 0.139391 | + | 0.319249i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.88175 | + | 6.72339i | 0.171050 | + | 0.296268i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 34.3350 | 1.51005 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.02189 | − | 10.4302i | −0.263824 | − | 0.456956i | 0.703431 | − | 0.710764i | \(-0.251650\pi\) |
−0.967255 | + | 0.253807i | \(0.918317\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.47350 | − | 9.48039i | 0.239340 | − | 0.414548i | −0.721185 | − | 0.692742i | \(-0.756402\pi\) |
0.960525 | + | 0.278194i | \(0.0897357\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.02384 | − | 3.50540i | 0.0881601 | − | 0.152698i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.607804 | + | 1.05275i | 0.0264263 | + | 0.0457716i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 28.8778 | 1.25084 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.98267 | + | 6.89819i | 0.172186 | + | 0.298235i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.44345 | − | 20.8485i | −0.277539 | − | 0.898009i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.21066 | − | 3.82897i | 0.0950436 | − | 0.164620i | −0.814583 | − | 0.580047i | \(-0.803034\pi\) |
0.909627 | + | 0.415426i | \(0.136368\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.54111 | 0.108849 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.2438 | 0.651780 | 0.325890 | − | 0.945408i | \(-0.394336\pi\) | ||||
0.325890 | + | 0.945408i | \(0.394336\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −31.0876 | + | 53.8454i | −1.32438 | + | 2.29389i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14.7248 | + | 19.9628i | −0.626161 | + | 0.848906i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15.1436 | − | 26.2296i | −0.641657 | − | 1.11138i | −0.985063 | − | 0.172195i | \(-0.944914\pi\) |
0.343406 | − | 0.939187i | \(-0.388419\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.11327 | −0.173973 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.94838 | + | 17.2311i | 0.419274 | + | 0.726204i | 0.995867 | − | 0.0908278i | \(-0.0289513\pi\) |
−0.576592 | + | 0.817032i | \(0.695618\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.51223 | − | 7.81540i | 0.189831 | − | 0.328797i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.54912 | − | 7.87931i | 0.190709 | − | 0.330318i | −0.754776 | − | 0.655982i | \(-0.772255\pi\) |
0.945485 | + | 0.325664i | \(0.105588\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.65287 | + | 6.32696i | 0.152868 | + | 0.264775i | 0.932281 | − | 0.361736i | \(-0.117816\pi\) |
−0.779413 | + | 0.626511i | \(0.784482\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −20.8356 | −0.868906 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21.5215 | − | 37.2763i | −0.895952 | − | 1.55183i | −0.832622 | − | 0.553841i | \(-0.813161\pi\) |
−0.0633297 | − | 0.997993i | \(-0.520172\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 29.0597 | + | 3.26617i | 1.20560 | + | 0.135503i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.24184 | + | 2.15093i | −0.0514318 | + | 0.0890825i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16.8705 | 0.696321 | 0.348161 | − | 0.937435i | \(-0.386806\pi\) | ||||
0.348161 | + | 0.937435i | \(0.386806\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.39153 | −0.180950 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.64703 | + | 6.31684i | −0.149766 | + | 0.259401i | −0.931141 | − | 0.364660i | \(-0.881185\pi\) |
0.781375 | + | 0.624062i | \(0.214519\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.9258 | − | 1.34040i | −0.488909 | − | 0.0549510i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.99650 | − | 12.1183i | −0.285869 | − | 0.495140i | 0.686950 | − | 0.726704i | \(-0.258949\pi\) |
−0.972820 | + | 0.231564i | \(0.925616\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.8953 | 0.933919 | 0.466960 | − | 0.884279i | \(-0.345349\pi\) | ||||
0.466960 | + | 0.884279i | \(0.345349\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.469269 | − | 0.812797i | −0.0190785 | − | 0.0330449i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.9017 | + | 34.4708i | −0.807785 | + | 1.39913i | 0.106609 | + | 0.994301i | \(0.466001\pi\) |
−0.914395 | + | 0.404824i | \(0.867333\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.7933 | − | 22.1586i | 0.517560 | − | 0.896441i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.2934 | + | 23.0248i | 0.536915 | + | 0.929965i | 0.999068 | + | 0.0431643i | \(0.0137439\pi\) |
−0.462153 | + | 0.886800i | \(0.652923\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −37.7444 | −1.51953 | −0.759766 | − | 0.650197i | \(-0.774686\pi\) | ||||
−0.759766 | + | 0.650197i | \(0.774686\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.26311 | − | 14.3121i | −0.332122 | − | 0.575253i | 0.650805 | − | 0.759245i | \(-0.274431\pi\) |
−0.982928 | + | 0.183992i | \(0.941098\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 18.5081 | − | 25.0920i | 0.741512 | − | 1.00529i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.62436 | + | 14.9378i | −0.344974 | + | 0.597513i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −67.1654 | −2.67806 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.9880 | −0.556854 | −0.278427 | − | 0.960457i | \(-0.589813\pi\) | ||||
−0.278427 | + | 0.960457i | \(0.589813\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.70321 | + | 6.41415i | −0.146957 | + | 0.254538i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.8558 | − | 3.60982i | −0.628228 | − | 0.143026i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.6604 | + | 27.1247i | 0.618550 | + | 1.07136i | 0.989751 | + | 0.142807i | \(0.0456128\pi\) |
−0.371201 | + | 0.928553i | \(0.621054\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25.2347 | 0.995160 | 0.497580 | − | 0.867418i | \(-0.334222\pi\) | ||||
0.497580 | + | 0.867418i | \(0.334222\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.346742 | + | 0.600574i | 0.0136318 | + | 0.0236110i | 0.872761 | − | 0.488148i | \(-0.162327\pi\) |
−0.859129 | + | 0.511759i | \(0.828994\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.906313 | + | 1.56978i | −0.0355759 | + | 0.0616192i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.17598 | + | 15.8933i | −0.359084 | + | 0.621951i | −0.987808 | − | 0.155677i | \(-0.950244\pi\) |
0.628724 | + | 0.777628i | \(0.283577\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.40898 | + | 5.90453i | 0.133200 | + | 0.230709i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.41641 | 0.0551756 | 0.0275878 | − | 0.999619i | \(-0.491217\pi\) | ||||
0.0275878 | + | 0.999619i | \(0.491217\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.57229 | + | 11.3835i | 0.255633 | + | 0.442769i | 0.965067 | − | 0.262003i | \(-0.0843829\pi\) |
−0.709435 | + | 0.704771i | \(0.751050\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.20998 | + | 11.9325i | 0.202035 | + | 0.462722i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 21.5839 | − | 37.3844i | 0.835732 | − | 1.44753i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.64839 | −0.0636353 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 42.8801 | 1.65291 | 0.826453 | − | 0.563006i | \(-0.190355\pi\) | ||||
0.826453 | + | 0.563006i | \(0.190355\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.2418 | + | 22.9355i | −0.508925 | + | 0.881484i | 0.491021 | + | 0.871148i | \(0.336624\pi\) |
−0.999947 | + | 0.0103369i | \(0.996710\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.65530 | + | 0.523234i | 0.178654 | + | 0.0200799i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.45787 | + | 2.52511i | 0.0557839 | + | 0.0966206i | 0.892569 | − | 0.450911i | \(-0.148901\pi\) |
−0.836785 | + | 0.547532i | \(0.815568\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.83729 | −0.375864 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.925425 | + | 1.60288i | 0.0352559 | + | 0.0610650i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.6078 | + | 20.1053i | −0.441582 | + | 0.764842i | −0.997807 | − | 0.0661896i | \(-0.978916\pi\) |
0.556225 | + | 0.831031i | \(0.312249\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.25928 | − | 5.64525i | 0.123632 | − | 0.214136i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −38.5118 | − | 66.7044i | −1.45874 | − | 2.52661i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.05056 | 0.190757 | 0.0953785 | − | 0.995441i | \(-0.469594\pi\) | ||||
0.0953785 | + | 0.995441i | \(0.469594\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 36.4354 | + | 63.1080i | 1.37419 | + | 2.38016i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.90086 | + | 22.6760i | 0.372360 | + | 0.852820i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.0106 | + | 17.3388i | −0.375954 | + | 0.651172i | −0.990469 | − | 0.137733i | \(-0.956018\pi\) |
0.614515 | + | 0.788905i | \(0.289352\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.04900 | 0.114186 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.30140 | 0.198261 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17.8022 | + | 30.8343i | −0.663909 | + | 1.14992i | 0.315671 | + | 0.948869i | \(0.397771\pi\) |
−0.979580 | + | 0.201056i | \(0.935563\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.6555 | − | 22.5804i | 0.620285 | − | 0.840939i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −20.6439 | − | 35.7562i | −0.766694 | − | 1.32795i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.634146 | −0.0235192 | −0.0117596 | − | 0.999931i | \(-0.503743\pi\) | ||||
−0.0117596 | + | 0.999931i | \(0.503743\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.48551 | + | 9.50118i | 0.202889 | + | 0.351414i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.3817 | − | 21.4458i | 0.457330 | − | 0.792119i | −0.541489 | − | 0.840708i | \(-0.682139\pi\) |
0.998819 | + | 0.0485888i | \(0.0154724\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −17.4363 | + | 30.2006i | −0.642275 | + | 1.11245i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.35897 | − | 4.08585i | −0.0867760 | − | 0.150300i | 0.819371 | − | 0.573264i | \(-0.194323\pi\) |
−0.906147 | + | 0.422964i | \(0.860990\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20.5554 | −0.754103 | −0.377051 | − | 0.926192i | \(-0.623062\pi\) | ||||
−0.377051 | + | 0.926192i | \(0.623062\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.19615 | + | 2.07180i | 0.0438236 | + | 0.0759048i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17.0886 | − | 23.1675i | 0.624403 | − | 0.846521i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.777351 | + | 1.34641i | −0.0283659 | + | 0.0491312i | −0.879860 | − | 0.475233i | \(-0.842364\pi\) |
0.851494 | + | 0.524364i | \(0.175697\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.55002 | −0.201986 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.9305 | 0.397274 | 0.198637 | − | 0.980073i | \(-0.436349\pi\) | ||||
0.198637 | + | 0.980073i | \(0.436349\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.35386 | − | 12.7373i | 0.266577 | − | 0.461725i | −0.701398 | − | 0.712769i | \(-0.747441\pi\) |
0.967976 | + | 0.251044i | \(0.0807739\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.67491 | − | 8.41669i | −0.133041 | − | 0.304705i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.675388 | + | 1.16981i | 0.0243868 | + | 0.0422392i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24.3159 | −0.876855 | −0.438428 | − | 0.898766i | \(-0.644464\pi\) | ||||
−0.438428 | + | 0.898766i | \(0.644464\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.0106190 | + | 0.0183927i | 0.000381939 | + | 0.000661538i | 0.866216 | − | 0.499669i | \(-0.166545\pi\) |
−0.865834 | + | 0.500331i | \(0.833212\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.45811 | − | 2.52551i | 0.0523767 | − | 0.0907191i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −41.7832 | + | 72.3707i | −1.49704 | + | 2.59295i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.89254 | − | 17.1344i | −0.353983 | − | 0.613116i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.77952 | 0.277663 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.00510 | + | 10.4011i | 0.214059 | + | 0.370761i | 0.952981 | − | 0.303030i | \(-0.0979982\pi\) |
−0.738922 | + | 0.673791i | \(0.764665\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −32.4118 | − | 3.64292i | −1.15243 | − | 0.129527i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.614193 | + | 1.06381i | −0.0218106 | + | 0.0377771i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −30.5623 | −1.08257 | −0.541287 | − | 0.840838i | \(-0.682063\pi\) | ||||
−0.541287 | + | 0.840838i | \(0.682063\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −68.2451 | −2.41434 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.63914 | + | 8.03523i | −0.163712 | + | 0.283557i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.61725 | − | 8.28463i | −0.127491 | − | 0.291995i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −20.6246 | − | 35.7228i | −0.725122 | − | 1.25595i | −0.958924 | − | 0.283664i | \(-0.908450\pi\) |
0.233802 | − | 0.972284i | \(-0.424883\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.9000 | −0.382750 | −0.191375 | − | 0.981517i | \(-0.561295\pi\) | ||||
−0.191375 | + | 0.981517i | \(0.561295\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.14364 | − | 12.3731i | −0.250231 | − | 0.433412i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.95149 | − | 10.3083i | 0.208216 | − | 0.360641i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27.1201 | + | 46.9735i | −0.946499 | + | 1.63938i | −0.193778 | + | 0.981045i | \(0.562074\pi\) |
−0.752721 | + | 0.658340i | \(0.771259\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.24784 | + | 12.5536i | 0.252644 | + | 0.437592i | 0.964253 | − | 0.264984i | \(-0.0853666\pi\) |
−0.711609 | + | 0.702576i | \(0.752033\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −48.4452 | −1.68460 | −0.842302 | − | 0.539005i | \(-0.818800\pi\) | ||||
−0.842302 | + | 0.539005i | \(0.818800\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.0573 | − | 17.4197i | −0.349304 | − | 0.605013i | 0.636822 | − | 0.771011i | \(-0.280249\pi\) |
−0.986126 | + | 0.165998i | \(0.946915\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 12.8072 | + | 41.4391i | 0.443742 | + | 1.43578i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.47122 | − | 7.74439i | 0.154733 | − | 0.268005i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −0.439651 | −0.0151784 | −0.00758921 | − | 0.999971i | \(-0.502416\pi\) | ||||
−0.00758921 | + | 0.999971i | \(0.502416\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 56.5410 | 1.94969 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.78302 | + | 4.82033i | −0.0957388 | + | 0.165824i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.01351 | + | 2.72977i | −0.0691849 | + | 0.0937960i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −25.2968 | − | 43.8154i | −0.867164 | − | 1.50197i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −23.1148 | −0.791436 | −0.395718 | − | 0.918372i | \(-0.629504\pi\) | ||||
−0.395718 | + | 0.918372i | \(0.629504\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11.7910 | + | 20.4226i | 0.402772 | + | 0.697621i | 0.994059 | − | 0.108840i | \(-0.0347135\pi\) |
−0.591288 | + | 0.806461i | \(0.701380\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.8976 | + | 34.4637i | −0.678899 | + | 1.17589i | 0.296414 | + | 0.955060i | \(0.404209\pi\) |
−0.975313 | + | 0.220828i | \(0.929124\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.83879 | + | 10.1131i | −0.198755 | + | 0.344253i | −0.948125 | − | 0.317898i | \(-0.897023\pi\) |
0.749370 | + | 0.662151i | \(0.230356\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.44742 | + | 11.1673i | 0.219219 | + | 0.379698i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −29.2276 | −0.991478 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.9936 | + | 22.5056i | 0.440272 | + | 0.762573i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −18.2156 | − | 2.04735i | −0.615800 | − | 0.0692129i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.78361 | + | 8.28545i | −0.161531 | + | 0.279780i | −0.935418 | − | 0.353544i | \(-0.884977\pi\) |
0.773887 | + | 0.633324i | \(0.218310\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.14572 | −0.139673 | −0.0698364 | − | 0.997558i | \(-0.522248\pi\) | ||||
−0.0698364 | + | 0.997558i | \(0.522248\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14.6609 | −0.493379 | −0.246689 | − | 0.969095i | \(-0.579343\pi\) | ||||
−0.246689 | + | 0.969095i | \(0.579343\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 22.6680 | − | 39.2622i | 0.761118 | − | 1.31829i | −0.181157 | − | 0.983454i | \(-0.557984\pi\) |
0.942275 | − | 0.334841i | \(-0.108682\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 26.6005 | + | 2.98977i | 0.892153 | + | 0.100274i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 37.0212 | + | 64.1225i | 1.23887 | + | 2.14578i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.01399 | −0.0673203 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.02094 | + | 5.23242i | 0.100754 | + | 0.174511i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.46832 | − | 4.27525i | 0.0822316 | − | 0.142429i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.95615 | − | 5.12021i | 0.0982658 | − | 0.170201i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.8350 | + | 49.9437i | 0.957451 | + | 1.65835i | 0.728657 | + | 0.684879i | \(0.240145\pi\) |
0.228794 | + | 0.973475i | \(0.426522\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 45.9423 | 1.52214 | 0.761068 | − | 0.648672i | \(-0.224675\pi\) | ||||
0.761068 | + | 0.648672i | \(0.224675\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.2276 | + | 29.8391i | 0.570150 | + | 0.987529i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14.6270 | − | 19.8303i | 0.483027 | − | 0.654854i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.85285 | + | 13.6015i | −0.259041 | + | 0.448673i | −0.965985 | − | 0.258597i | \(-0.916740\pi\) |
0.706944 | + | 0.707270i | \(0.250073\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −14.7439 | −0.485302 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −48.3902 | −1.59106 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −20.7820 | + | 35.9955i | −0.681835 | + | 1.18097i | 0.292585 | + | 0.956240i | \(0.405485\pi\) |
−0.974420 | + | 0.224734i | \(0.927849\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 31.9883 | − | 34.5131i | 1.04837 | − | 1.13112i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.07001 | − | 12.2456i | −0.231214 | − | 0.400475i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −41.5740 | −1.35816 | −0.679082 | − | 0.734062i | \(-0.737622\pi\) | ||||
−0.679082 | + | 0.734062i | \(0.737622\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.55091 | + | 4.41830i | 0.0831572 | + | 0.144032i | 0.904604 | − | 0.426252i | \(-0.140166\pi\) |
−0.821447 | + | 0.570284i | \(0.806833\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 29.0098 | − | 50.2464i | 0.944688 | − | 1.63625i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.99483 | − | 12.1154i | 0.227302 | − | 0.393698i | −0.729706 | − | 0.683761i | \(-0.760343\pi\) |
0.957007 | + | 0.290063i | \(0.0936764\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.45711 | + | 5.98788i | 0.112222 | + | 0.194375i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.30864 | −0.171964 | −0.0859819 | − | 0.996297i | \(-0.527403\pi\) | ||||
−0.0859819 | + | 0.996297i | \(0.527403\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.521782 | + | 0.903752i | 0.0168845 | + | 0.0292447i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 14.2265 | + | 32.5832i | 0.459399 | + | 1.05217i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.2866 | − | 26.4772i | 0.493117 | − | 0.854104i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.28919 | 0.105883 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −33.1799 | −1.06700 | −0.533498 | − | 0.845802i | \(-0.679123\pi\) | ||||
−0.533498 | + | 0.845802i | \(0.679123\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.87415 | − | 15.3705i | 0.284785 | − | 0.493262i | −0.687772 | − | 0.725927i | \(-0.741411\pi\) |
0.972557 | + | 0.232665i | \(0.0747445\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −23.4118 | − | 2.63137i | −0.750547 | − | 0.0843578i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18.8872 | − | 32.7136i | −0.604255 | − | 1.04660i | −0.992169 | − | 0.124905i | \(-0.960137\pi\) |
0.387914 | − | 0.921696i | \(-0.373196\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 36.7373 | 1.17413 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 20.1280 | + | 34.8628i | 0.641984 | + | 1.11195i | 0.984989 | + | 0.172616i | \(0.0552219\pi\) |
−0.343005 | + | 0.939334i | \(0.611445\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.80906 | − | 10.0616i | 0.185092 | − | 0.320589i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.13207 | + | 7.15696i | −0.131392 | + | 0.227578i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.872347 | − | 1.51095i | −0.0277110 | − | 0.0479969i | 0.851837 | − | 0.523806i | \(-0.175488\pi\) |
−0.879548 | + | 0.475810i | \(0.842155\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.14372 | −0.289875 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.35274 | − | 5.80711i | −0.106182 | − | 0.183913i | 0.808038 | − | 0.589130i | \(-0.200529\pi\) |
−0.914221 | + | 0.405217i | \(0.867196\pi\) | |||||||
\(998\) | 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 | 1512.2.s.m.1297.3 | yes | 8 | |
3.2 | odd | 2 | 1512.2.s.p.1297.1 | yes | 8 | ||
7.4 | even | 3 | inner | 1512.2.s.m.865.3 | ✓ | 8 | |
21.11 | odd | 6 | 1512.2.s.p.865.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.s.m.865.3 | ✓ | 8 | 7.4 | even | 3 | inner | |
1512.2.s.m.1297.3 | yes | 8 | 1.1 | even | 1 | trivial | |
1512.2.s.p.865.1 | yes | 8 | 21.11 | odd | 6 | ||
1512.2.s.p.1297.1 | yes | 8 | 3.2 | odd | 2 |