Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6012,2,Mod(1,6012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6012, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6012.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6012 = 2^{2} \cdot 3^{2} \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6012.a (trivial) |
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: | yes |
Analytic conductor: | \(48.0060616952\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - x^{8} - 31x^{7} + 24x^{6} + 293x^{5} - 101x^{4} - 864x^{3} - 278x^{2} + 24x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2004) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.25977\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6012.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(5\) | −3.25977 | −1.45781 | −0.728906 | − | 0.684613i | \(-0.759971\pi\) | ||||
−0.728906 | + | 0.684613i | \(0.759971\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.95900 | 0.740431 | 0.370216 | − | 0.928946i | \(-0.379284\pi\) | ||||
0.370216 | + | 0.928946i | \(0.379284\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.86584 | −0.562572 | −0.281286 | − | 0.959624i | \(-0.590761\pi\) | ||||
−0.281286 | + | 0.959624i | \(0.590761\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.83769 | 1.34173 | 0.670867 | − | 0.741578i | \(-0.265922\pi\) | ||||
0.670867 | + | 0.741578i | \(0.265922\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.17274 | 1.01204 | 0.506019 | − | 0.862523i | \(-0.331117\pi\) | ||||
0.506019 | + | 0.862523i | \(0.331117\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.05426 | 1.15953 | 0.579764 | − | 0.814785i | \(-0.303145\pi\) | ||||
0.579764 | + | 0.814785i | \(0.303145\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.26074 | 0.262883 | 0.131441 | − | 0.991324i | \(-0.458039\pi\) | ||||
0.131441 | + | 0.991324i | \(0.458039\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.62609 | 1.12522 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −10.5500 | −1.95909 | −0.979543 | − | 0.201233i | \(-0.935505\pi\) | ||||
−0.979543 | + | 0.201233i | \(0.935505\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.26256 | −1.12479 | −0.562394 | − | 0.826869i | \(-0.690120\pi\) | ||||
−0.562394 | + | 0.826869i | \(0.690120\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.38588 | −1.07941 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.409655 | 0.0673469 | 0.0336734 | − | 0.999433i | \(-0.489279\pi\) | ||||
0.0336734 | + | 0.999433i | \(0.489279\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.65442 | 0.414550 | 0.207275 | − | 0.978283i | \(-0.433540\pi\) | ||||
0.207275 | + | 0.978283i | \(0.433540\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.317178 | 0.0483692 | 0.0241846 | − | 0.999708i | \(-0.492301\pi\) | ||||
0.0241846 | + | 0.999708i | \(0.492301\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.08939 | 0.596499 | 0.298249 | − | 0.954488i | \(-0.403597\pi\) | ||||
0.298249 | + | 0.954488i | \(0.403597\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.16233 | −0.451761 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.15844 | 0.983287 | 0.491644 | − | 0.870796i | \(-0.336396\pi\) | ||||
0.491644 | + | 0.870796i | \(0.336396\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.08221 | 0.820125 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.72693 | 1.13615 | 0.568074 | − | 0.822977i | \(-0.307689\pi\) | ||||
0.568074 | + | 0.822977i | \(0.307689\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.89631 | 1.26709 | 0.633546 | − | 0.773705i | \(-0.281599\pi\) | ||||
0.633546 | + | 0.773705i | \(0.281599\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −15.7697 | −1.95600 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.55284 | −0.800557 | −0.400278 | − | 0.916394i | \(-0.631087\pi\) | ||||
−0.400278 | + | 0.916394i | \(0.631087\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.0764 | 1.19585 | 0.597927 | − | 0.801550i | \(-0.295991\pi\) | ||||
0.597927 | + | 0.801550i | \(0.295991\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.8701 | −1.38929 | −0.694647 | − | 0.719351i | \(-0.744439\pi\) | ||||
−0.694647 | + | 0.719351i | \(0.744439\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.65518 | −0.416546 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.70687 | −0.304547 | −0.152273 | − | 0.988338i | \(-0.548659\pi\) | ||||
−0.152273 | + | 0.988338i | \(0.548659\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.18316 | −0.678690 | −0.339345 | − | 0.940662i | \(-0.610205\pi\) | ||||
−0.339345 | + | 0.940662i | \(0.610205\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13.6022 | −1.47536 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.6820 | −1.55629 | −0.778147 | − | 0.628082i | \(-0.783840\pi\) | ||||
−0.778147 | + | 0.628082i | \(0.783840\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.47702 | 0.993461 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −16.4757 | −1.69037 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.3373 | 1.04959 | 0.524796 | − | 0.851228i | \(-0.324142\pi\) | ||||
0.524796 | + | 0.851228i | \(0.324142\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.40969 | −0.737292 | −0.368646 | − | 0.929570i | \(-0.620178\pi\) | ||||
−0.368646 | + | 0.929570i | \(0.620178\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.02321 | 0.199353 | 0.0996763 | − | 0.995020i | \(-0.468219\pi\) | ||||
0.0996763 | + | 0.995020i | \(0.468219\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.1811 | −0.984240 | −0.492120 | − | 0.870527i | \(-0.663778\pi\) | ||||
−0.492120 | + | 0.870527i | \(0.663778\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.0121 | 1.62946 | 0.814730 | − | 0.579840i | \(-0.196885\pi\) | ||||
0.814730 | + | 0.579840i | \(0.196885\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.94341 | −0.276892 | −0.138446 | − | 0.990370i | \(-0.544211\pi\) | ||||
−0.138446 | + | 0.990370i | \(0.544211\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.10973 | −0.383234 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.17438 | 0.749344 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.51863 | −0.683512 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.04091 | −0.182545 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.1274 | −1.25360 | −0.626802 | − | 0.779179i | \(-0.715636\pi\) | ||||
−0.626802 | + | 0.779179i | \(0.715636\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.26678 | 0.722272 | 0.361136 | − | 0.932513i | \(-0.382389\pi\) | ||||
0.361136 | + | 0.932513i | \(0.382389\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.90129 | 0.858550 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.27285 | 0.535926 | 0.267963 | − | 0.963429i | \(-0.413650\pi\) | ||||
0.267963 | + | 0.963429i | \(0.413650\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.3243 | 1.38461 | 0.692304 | − | 0.721606i | \(-0.256596\pi\) | ||||
0.692304 | + | 0.721606i | \(0.256596\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.02636 | −0.754822 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 34.3906 | 2.85598 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.806495 | 0.0660707 | 0.0330353 | − | 0.999454i | \(-0.489483\pi\) | ||||
0.0330353 | + | 0.999454i | \(0.489483\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.6840 | −1.19496 | −0.597482 | − | 0.801882i | \(-0.703832\pi\) | ||||
−0.597482 | + | 0.801882i | \(0.703832\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 20.4145 | 1.63973 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.8590 | 1.18588 | 0.592938 | − | 0.805248i | \(-0.297968\pi\) | ||||
0.592938 | + | 0.805248i | \(0.297968\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.46979 | 0.194647 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.6684 | 0.913942 | 0.456971 | − | 0.889482i | \(-0.348934\pi\) | ||||
0.456971 | + | 0.889482i | \(0.348934\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.4032 | 0.800248 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 24.8278 | 1.88763 | 0.943813 | − | 0.330481i | \(-0.107211\pi\) | ||||
0.943813 | + | 0.330481i | \(0.107211\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.0215 | 0.833147 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 21.8021 | 1.62957 | 0.814783 | − | 0.579766i | \(-0.196856\pi\) | ||||
0.814783 | + | 0.579766i | \(0.196856\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.5477 | 1.37864 | 0.689320 | − | 0.724457i | \(-0.257909\pi\) | ||||
0.689320 | + | 0.724457i | \(0.257909\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.33538 | −0.0981792 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.78566 | −0.569344 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.90014 | 0.643992 | 0.321996 | − | 0.946741i | \(-0.395646\pi\) | ||||
0.321996 | + | 0.946741i | \(0.395646\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 22.4480 | 1.61584 | 0.807921 | − | 0.589291i | \(-0.200593\pi\) | ||||
0.807921 | + | 0.589291i | \(0.200593\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.49823 | 0.605474 | 0.302737 | − | 0.953074i | \(-0.402100\pi\) | ||||
0.302737 | + | 0.953074i | \(0.402100\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.02067 | 0.214129 | 0.107065 | − | 0.994252i | \(-0.465855\pi\) | ||||
0.107065 | + | 0.994252i | \(0.465855\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −20.6674 | −1.45057 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.65279 | −0.604337 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.43045 | −0.652318 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.8920 | 1.16289 | 0.581447 | − | 0.813584i | \(-0.302487\pi\) | ||||
0.581447 | + | 0.813584i | \(0.302487\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.03393 | −0.0705132 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.2683 | −0.832829 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 20.1864 | 1.35788 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.393347 | 0.0263405 | 0.0131702 | − | 0.999913i | \(-0.495808\pi\) | ||||
0.0131702 | + | 0.999913i | \(0.495808\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.13362 | −0.606220 | −0.303110 | − | 0.952956i | \(-0.598025\pi\) | ||||
−0.303110 | + | 0.952956i | \(0.598025\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.86675 | −0.387686 | −0.193843 | − | 0.981033i | \(-0.562095\pi\) | ||||
−0.193843 | + | 0.981033i | \(0.562095\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.0755 | −0.856605 | −0.428302 | − | 0.903635i | \(-0.640888\pi\) | ||||
−0.428302 | + | 0.903635i | \(0.640888\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −13.3305 | −0.869584 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.4797 | −1.00130 | −0.500648 | − | 0.865651i | \(-0.666905\pi\) | ||||
−0.500648 | + | 0.865651i | \(0.666905\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.96592 | 0.641962 | 0.320981 | − | 0.947086i | \(-0.395988\pi\) | ||||
0.320981 | + | 0.947086i | \(0.395988\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 10.3085 | 0.658584 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 24.4509 | 1.55578 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.1882 | 0.769310 | 0.384655 | − | 0.923060i | \(-0.374320\pi\) | ||||
0.384655 | + | 0.923060i | \(0.374320\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.35234 | −0.147891 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.91332 | 0.493619 | 0.246810 | − | 0.969064i | \(-0.420618\pi\) | ||||
0.246810 | + | 0.969064i | \(0.420618\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.802513 | 0.0498658 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.615803 | −0.0379721 | −0.0189860 | − | 0.999820i | \(-0.506044\pi\) | ||||
−0.0189860 | + | 0.999820i | \(0.506044\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −23.3349 | −1.43345 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 24.5177 | 1.49487 | 0.747436 | − | 0.664334i | \(-0.231285\pi\) | ||||
0.747436 | + | 0.664334i | \(0.231285\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.4785 | 1.60846 | 0.804228 | − | 0.594321i | \(-0.202579\pi\) | ||||
0.804228 | + | 0.594321i | \(0.202579\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −10.4974 | −0.633017 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.05737 | −0.303868 | −0.151934 | − | 0.988391i | \(-0.548550\pi\) | ||||
−0.151934 | + | 0.988391i | \(0.548550\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −26.1625 | −1.56073 | −0.780363 | − | 0.625326i | \(-0.784966\pi\) | ||||
−0.780363 | + | 0.625326i | \(0.784966\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −28.9055 | −1.71826 | −0.859128 | − | 0.511761i | \(-0.828993\pi\) | ||||
−0.859128 | + | 0.511761i | \(0.828993\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.20000 | 0.306946 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.411724 | 0.0242191 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 21.3626 | 1.24802 | 0.624009 | − | 0.781417i | \(-0.285503\pi\) | ||||
0.624009 | + | 0.781417i | \(0.285503\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −28.4478 | −1.65629 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.09907 | 0.352719 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.621351 | 0.0358141 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −32.2597 | −1.84718 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.5731 | 1.28832 | 0.644158 | − | 0.764892i | \(-0.277208\pi\) | ||||
0.644158 | + | 0.764892i | \(0.277208\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.9825 | 1.01969 | 0.509846 | − | 0.860266i | \(-0.329702\pi\) | ||||
0.509846 | + | 0.860266i | \(0.329702\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.05074 | −0.0593913 | −0.0296957 | − | 0.999559i | \(-0.509454\pi\) | ||||
−0.0296957 | + | 0.999559i | \(0.509454\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.29356 | 0.0726537 | 0.0363269 | − | 0.999340i | \(-0.488434\pi\) | ||||
0.0363269 | + | 0.999340i | \(0.488434\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 19.6846 | 1.10213 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 21.0901 | 1.17348 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 27.2173 | 1.50974 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.01110 | 0.441666 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.42036 | −0.133035 | −0.0665175 | − | 0.997785i | \(-0.521189\pi\) | ||||
−0.0665175 | + | 0.997785i | \(0.521189\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 21.3607 | 1.16706 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.02901 | −0.491842 | −0.245921 | − | 0.969290i | \(-0.579090\pi\) | ||||
−0.245921 | + | 0.969290i | \(0.579090\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.6849 | 0.632775 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.9080 | −1.07493 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −20.0918 | −1.07858 | −0.539292 | − | 0.842119i | \(-0.681308\pi\) | ||||
−0.539292 | + | 0.842119i | \(0.681308\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.7445 | −0.842782 | −0.421391 | − | 0.906879i | \(-0.638458\pi\) | ||||
−0.421391 | + | 0.906879i | \(0.638458\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.8715 | 0.844757 | 0.422379 | − | 0.906419i | \(-0.361195\pi\) | ||||
0.422379 | + | 0.906419i | \(0.361195\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −32.8469 | −1.74333 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 28.1278 | 1.48453 | 0.742265 | − | 0.670107i | \(-0.233752\pi\) | ||||
0.742265 | + | 0.670107i | \(0.233752\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.54557 | 0.344504 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 38.6939 | 2.02533 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.0328 | −0.993504 | −0.496752 | − | 0.867892i | \(-0.665474\pi\) | ||||
−0.496752 | + | 0.867892i | \(0.665474\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 14.0234 | 0.728057 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.6675 | −0.655899 | −0.327949 | − | 0.944695i | \(-0.606358\pi\) | ||||
−0.327949 | + | 0.944695i | \(0.606358\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −51.0376 | −2.62857 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.31841 | 0.427288 | 0.213644 | − | 0.976912i | \(-0.431467\pi\) | ||||
0.213644 | + | 0.976912i | \(0.431467\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 29.2821 | 1.49624 | 0.748122 | − | 0.663561i | \(-0.230956\pi\) | ||||
0.748122 | + | 0.663561i | \(0.230956\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.9150 | 0.607247 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 16.3851 | 0.830756 | 0.415378 | − | 0.909649i | \(-0.363649\pi\) | ||||
0.415378 | + | 0.909649i | \(0.363649\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.26074 | 0.266047 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.82378 | 0.443972 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.2130 | −0.663140 | −0.331570 | − | 0.943431i | \(-0.607578\pi\) | ||||
−0.331570 | + | 0.943431i | \(0.607578\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.20672 | 0.210074 | 0.105037 | − | 0.994468i | \(-0.466504\pi\) | ||||
0.105037 | + | 0.994468i | \(0.466504\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −30.2963 | −1.50917 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.764352 | −0.0378875 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.6454 | −1.11974 | −0.559871 | − | 0.828580i | \(-0.689149\pi\) | ||||
−0.559871 | + | 0.828580i | \(0.689149\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 17.0960 | 0.841240 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 20.1557 | 0.989404 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.1237 | 0.787693 | 0.393846 | − | 0.919176i | \(-0.371144\pi\) | ||||
0.393846 | + | 0.919176i | \(0.371144\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.3944 | 0.896487 | 0.448244 | − | 0.893911i | \(-0.352050\pi\) | ||||
0.448244 | + | 0.893911i | \(0.352050\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 23.4762 | 1.13876 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 19.3868 | 0.938195 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.3846 | −0.885557 | −0.442779 | − | 0.896631i | \(-0.646007\pi\) | ||||
−0.442779 | + | 0.896631i | \(0.646007\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.7250 | 0.755694 | 0.377847 | − | 0.925868i | \(-0.376664\pi\) | ||||
0.377847 | + | 0.925868i | \(0.376664\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.37212 | 0.304820 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.49754 | 0.310111 | 0.155055 | − | 0.987906i | \(-0.450444\pi\) | ||||
0.155055 | + | 0.987906i | \(0.450444\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.33495 | −0.396005 | −0.198003 | − | 0.980201i | \(-0.563445\pi\) | ||||
−0.198003 | + | 0.980201i | \(0.563445\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 47.8601 | 2.26879 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 37.4466 | 1.76721 | 0.883607 | − | 0.468230i | \(-0.155108\pi\) | ||||
0.883607 | + | 0.468230i | \(0.155108\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.95272 | −0.233215 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −30.8929 | −1.44828 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.9246 | −0.838478 | −0.419239 | − | 0.907876i | \(-0.637703\pi\) | ||||
−0.419239 | + | 0.907876i | \(0.637703\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −38.4054 | −1.78872 | −0.894359 | − | 0.447349i | \(-0.852368\pi\) | ||||
−0.894359 | + | 0.447349i | \(0.852368\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −23.3091 | −1.08327 | −0.541633 | − | 0.840615i | \(-0.682194\pi\) | ||||
−0.541633 | + | 0.840615i | \(0.682194\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 24.1638 | 1.11817 | 0.559084 | − | 0.829111i | \(-0.311153\pi\) | ||||
0.559084 | + | 0.829111i | \(0.311153\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.8370 | −0.592757 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.591804 | −0.0272112 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 28.4357 | 1.30472 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 28.6876 | 1.31077 | 0.655384 | − | 0.755296i | \(-0.272507\pi\) | ||||
0.655384 | + | 0.755296i | \(0.272507\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.98178 | 0.0903616 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −33.6971 | −1.53011 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.6346 | 1.02567 | 0.512835 | − | 0.858487i | \(-0.328595\pi\) | ||||
0.512835 | + | 0.858487i | \(0.328595\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.7912 | −0.802905 | −0.401452 | − | 0.915880i | \(-0.631494\pi\) | ||||
−0.401452 | + | 0.915880i | \(0.631494\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −44.0224 | −1.98267 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 19.7397 | 0.885448 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.0860 | 1.03347 | 0.516736 | − | 0.856145i | \(-0.327147\pi\) | ||||
0.516736 | + | 0.856145i | \(0.327147\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18.9514 | −0.845002 | −0.422501 | − | 0.906362i | \(-0.638848\pi\) | ||||
−0.422501 | + | 0.906362i | \(0.638848\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 24.1539 | 1.07483 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.7388 | 0.741935 | 0.370968 | − | 0.928646i | \(-0.379026\pi\) | ||||
0.370968 | + | 0.928646i | \(0.379026\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −23.2535 | −1.02868 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.59519 | −0.290619 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.63015 | −0.335574 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 39.7522 | 1.74157 | 0.870787 | − | 0.491660i | \(-0.163610\pi\) | ||||
0.870787 | + | 0.491660i | \(0.163610\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.3323 | −1.06398 | −0.531989 | − | 0.846751i | \(-0.678555\pi\) | ||||
−0.531989 | + | 0.846751i | \(0.678555\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −26.1320 | −1.13833 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.4105 | −0.930893 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.8412 | 0.556216 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 33.1879 | 1.43484 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.90041 | 0.254148 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 25.4258 | 1.09314 | 0.546570 | − | 0.837413i | \(-0.315933\pi\) | ||||
0.546570 | + | 0.837413i | \(0.315933\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −55.4554 | −2.37545 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.2511 | 1.03690 | 0.518450 | − | 0.855108i | \(-0.326509\pi\) | ||||
0.518450 | + | 0.855108i | \(0.326509\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −53.3225 | −2.27161 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.30276 | −0.225496 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.0732 | 0.426813 | 0.213407 | − | 0.976963i | \(-0.431544\pi\) | ||||
0.213407 | + | 0.976963i | \(0.431544\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.53441 | 0.0648985 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.79902 | −0.286545 | −0.143272 | − | 0.989683i | \(-0.545762\pi\) | ||||
−0.143272 | + | 0.989683i | \(0.545762\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.59483 | 0.403657 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.1444 | −0.592966 | −0.296483 | − | 0.955038i | \(-0.595814\pi\) | ||||
−0.296483 | + | 0.955038i | \(0.595814\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.33250 | −0.348704 | −0.174352 | − | 0.984683i | \(-0.555783\pi\) | ||||
−0.174352 | + | 0.984683i | \(0.555783\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.09305 | 0.295801 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.87608 | −0.119733 | −0.0598665 | − | 0.998206i | \(-0.519067\pi\) | ||||
−0.0598665 | + | 0.998206i | \(0.519067\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.1128 | −0.502524 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.3565 | −0.553170 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.86013 | 0.241874 | 0.120937 | − | 0.992660i | \(-0.461410\pi\) | ||||
0.120937 | + | 0.992660i | \(0.461410\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −31.6526 | −1.30422 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −33.1853 | −1.36276 | −0.681378 | − | 0.731932i | \(-0.738619\pi\) | ||||
−0.681378 | + | 0.731932i | \(0.738619\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −26.6466 | −1.09240 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.4862 | 0.510174 | 0.255087 | − | 0.966918i | \(-0.417896\pi\) | ||||
0.255087 | + | 0.966918i | \(0.417896\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.1405 | 0.739964 | 0.369982 | − | 0.929039i | \(-0.379364\pi\) | ||||
0.369982 | + | 0.929039i | \(0.379364\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 24.5090 | 0.996433 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 46.7416 | 1.89718 | 0.948591 | − | 0.316506i | \(-0.102510\pi\) | ||||
0.948591 | + | 0.316506i | \(0.102510\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 19.7832 | 0.800342 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26.1419 | −1.05586 | −0.527930 | − | 0.849288i | \(-0.677032\pi\) | ||||
−0.527930 | + | 0.849288i | \(0.677032\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.8947 | 0.438606 | 0.219303 | − | 0.975657i | \(-0.429622\pi\) | ||||
0.219303 | + | 0.975657i | \(0.429622\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.3051 | 0.655355 | 0.327678 | − | 0.944790i | \(-0.393734\pi\) | ||||
0.327678 | + | 0.944790i | \(0.393734\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −28.7621 | −1.15233 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −21.4776 | −0.859102 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.70938 | 0.0681576 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.2613 | −0.926019 | −0.463010 | − | 0.886353i | \(-0.653230\pi\) | ||||
−0.463010 | + | 0.886353i | \(0.653230\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 46.0520 | 1.82752 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.2984 | −0.606143 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.97779 | 0.236108 | 0.118054 | − | 0.993007i | \(-0.462334\pi\) | ||||
0.118054 | + | 0.993007i | \(0.462334\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.0348 | 0.908403 | 0.454202 | − | 0.890899i | \(-0.349925\pi\) | ||||
0.454202 | + | 0.890899i | \(0.349925\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.539846 | 0.0212235 | 0.0106118 | − | 0.999944i | \(-0.496622\pi\) | ||||
0.0106118 | + | 0.999944i | \(0.496622\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16.2831 | −0.639166 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −16.6423 | −0.651262 | −0.325631 | − | 0.945497i | \(-0.605577\pi\) | ||||
−0.325631 | + | 0.945497i | \(0.605577\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −26.9478 | −1.05294 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −34.1742 | −1.33124 | −0.665619 | − | 0.746292i | \(-0.731832\pi\) | ||||
−0.665619 | + | 0.746292i | \(0.731832\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.8130 | −1.19849 | −0.599243 | − | 0.800567i | \(-0.704532\pi\) | ||||
−0.599243 | + | 0.800567i | \(0.704532\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −32.2759 | −1.25161 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.3008 | −0.515010 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −18.4649 | −0.712831 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21.0355 | −0.810859 | −0.405430 | − | 0.914126i | \(-0.632878\pi\) | ||||
−0.405430 | + | 0.914126i | \(0.632878\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.32794 | −0.204769 | −0.102385 | − | 0.994745i | \(-0.532647\pi\) | ||||
−0.102385 | + | 0.994745i | \(0.532647\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20.2507 | 0.777151 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.97577 | 0.305185 | 0.152592 | − | 0.988289i | \(-0.451238\pi\) | ||||
0.152592 | + | 0.988289i | \(0.451238\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −20.4480 | −0.781279 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 34.6303 | 1.31931 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.54471 | 0.287014 | 0.143507 | − | 0.989649i | \(-0.454162\pi\) | ||||
0.143507 | + | 0.989649i | \(0.454162\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −53.2134 | −2.01850 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.0762 | 0.419540 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.7808 | −1.16258 | −0.581288 | − | 0.813698i | \(-0.697451\pi\) | ||||
−0.581288 | + | 0.813698i | \(0.697451\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.07050 | 0.0780906 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −14.5156 | −0.545914 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.62232 | 0.0984834 | 0.0492417 | − | 0.998787i | \(-0.484320\pi\) | ||||
0.0492417 | + | 0.998787i | \(0.484320\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.89547 | −0.295688 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 29.4238 | 1.10039 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.01417 | 0.336172 | 0.168086 | − | 0.985772i | \(-0.446241\pi\) | ||||
0.168086 | + | 0.985772i | \(0.446241\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.96346 | 0.147607 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −59.3553 | −2.20440 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.0515 | −0.817846 | −0.408923 | − | 0.912569i | \(-0.634095\pi\) | ||||
−0.408923 | + | 0.912569i | \(0.634095\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.32350 | 0.0489514 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 51.7621 | 1.91188 | 0.955938 | − | 0.293569i | \(-0.0948429\pi\) | ||||
0.955938 | + | 0.293569i | \(0.0948429\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.2266 | 0.450371 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 46.4176 | 1.70750 | 0.853749 | − | 0.520684i | \(-0.174323\pi\) | ||||
0.853749 | + | 0.520684i | \(0.174323\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 41.9648 | 1.53954 | 0.769770 | − | 0.638321i | \(-0.220371\pi\) | ||||
0.769770 | + | 0.638321i | \(0.220371\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.62899 | −0.0963187 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −19.9447 | −0.728762 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40.9764 | 1.49525 | 0.747625 | − | 0.664121i | \(-0.231194\pi\) | ||||
0.747625 | + | 0.664121i | \(0.231194\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 47.8663 | 1.74203 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.14287 | −0.114230 | −0.0571148 | − | 0.998368i | \(-0.518190\pi\) | ||||
−0.0571148 | + | 0.998368i | \(0.518190\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.9986 | −0.579949 | −0.289974 | − | 0.957034i | \(-0.593647\pi\) | ||||
−0.289974 | + | 0.957034i | \(0.593647\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 33.3266 | 1.20650 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 42.2181 | 1.52441 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34.4686 | −1.24297 | −0.621485 | − | 0.783426i | \(-0.713470\pi\) | ||||
−0.621485 | + | 0.783426i | \(0.713470\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.97582 | −0.214935 | −0.107468 | − | 0.994209i | \(-0.534274\pi\) | ||||
−0.107468 | + | 0.994209i | \(0.534274\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −35.2337 | −1.26563 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 13.4161 | 0.480682 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.8011 | −0.672755 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −48.4368 | −1.72878 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −48.8368 | −1.74084 | −0.870422 | − | 0.492306i | \(-0.836154\pi\) | ||||
−0.870422 | + | 0.492306i | \(0.836154\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.76613 | −0.205020 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 47.8753 | 1.70010 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −40.1178 | −1.42105 | −0.710523 | − | 0.703674i | \(-0.751542\pi\) | ||||
−0.710523 | + | 0.703674i | \(0.751542\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17.0639 | 0.603679 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 22.1478 | 0.781578 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.05094 | −0.283758 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.67223 | 0.199425 | 0.0997126 | − | 0.995016i | \(-0.468208\pi\) | ||||
0.0997126 | + | 0.995016i | \(0.468208\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.49117 | 0.298165 | 0.149083 | − | 0.988825i | \(-0.452368\pi\) | ||||
0.149083 | + | 0.988825i | \(0.452368\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −38.0364 | −1.33236 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.60310 | 0.0560854 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.01425 | −0.279699 | −0.139850 | − | 0.990173i | \(-0.544662\pi\) | ||||
−0.139850 | + | 0.990173i | \(0.544662\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 52.3868 | 1.82609 | 0.913045 | − | 0.407858i | \(-0.133724\pi\) | ||||
0.913045 | + | 0.407858i | \(0.133724\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −0.346898 | −0.0120628 | −0.00603141 | − | 0.999982i | \(-0.501920\pi\) | ||||
−0.00603141 | + | 0.999982i | \(0.501920\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22.4031 | 0.778091 | 0.389046 | − | 0.921218i | \(-0.372805\pi\) | ||||
0.389046 | + | 0.921218i | \(0.372805\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −13.1956 | −0.457199 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.25977 | −0.112809 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.27328 | −0.320149 | −0.160075 | − | 0.987105i | \(-0.551173\pi\) | ||||
−0.160075 | + | 0.987105i | \(0.551173\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 82.3026 | 2.83802 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −33.9121 | −1.16661 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14.7290 | −0.506094 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.516469 | 0.0177043 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −31.6268 | −1.08288 | −0.541440 | − | 0.840739i | \(-0.682121\pi\) | ||||
−0.541440 | + | 0.840739i | \(0.682121\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10.0275 | −0.342533 | −0.171267 | − | 0.985225i | \(-0.554786\pi\) | ||||
−0.171267 | + | 0.985225i | \(0.554786\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24.1534 | −0.824102 | −0.412051 | − | 0.911161i | \(-0.635187\pi\) | ||||
−0.412051 | + | 0.911161i | \(0.635187\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 38.9292 | 1.32516 | 0.662582 | − | 0.748989i | \(-0.269460\pi\) | ||||
0.662582 | + | 0.748989i | \(0.269460\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −80.9330 | −2.75180 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.05059 | 0.171330 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −31.7006 | −1.07413 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.99814 | −0.135162 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −46.1448 | −1.55820 | −0.779100 | − | 0.626900i | \(-0.784324\pi\) | ||||
−0.779100 | + | 0.626900i | \(0.784324\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.41271 | 0.283431 | 0.141716 | − | 0.989907i | \(-0.454738\pi\) | ||||
0.141716 | + | 0.989907i | \(0.454738\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −40.4167 | −1.36013 | −0.680065 | − | 0.733152i | \(-0.738048\pi\) | ||||
−0.680065 | + | 0.733152i | \(0.738048\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 26.8983 | 0.903156 | 0.451578 | − | 0.892232i | \(-0.350861\pi\) | ||||
0.451578 | + | 0.892232i | \(0.350861\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −27.6755 | −0.928208 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 20.6689 | 0.691657 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −71.0699 | −2.37560 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 66.0700 | 2.20356 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 29.8703 | 0.995123 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −60.4612 | −2.00980 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −35.2510 | −1.17049 | −0.585244 | − | 0.810857i | \(-0.699001\pi\) | ||||
−0.585244 | + | 0.810857i | \(0.699001\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.88805 | −0.261343 | −0.130671 | − | 0.991426i | \(-0.541713\pi\) | ||||
−0.130671 | + | 0.991426i | \(0.541713\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.5368 | 0.381813 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 16.1946 | 0.534793 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −22.3691 | −0.737887 | −0.368944 | − | 0.929452i | \(-0.620280\pi\) | ||||
−0.368944 | + | 0.929452i | \(0.620280\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 48.7467 | 1.60452 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.30476 | 0.0757799 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −42.4881 | −1.39399 | −0.696994 | − | 0.717077i | \(-0.745480\pi\) | ||||
−0.696994 | + | 0.717077i | \(0.745480\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.9832 | −0.523830 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 25.3795 | 0.829997 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40.4812 | 1.32246 | 0.661232 | − | 0.750181i | \(-0.270034\pi\) | ||||
0.661232 | + | 0.750181i | \(0.270034\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −43.8361 | −1.42902 | −0.714508 | − | 0.699627i | \(-0.753349\pi\) | ||||
−0.714508 | + | 0.699627i | \(0.753349\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.34653 | 0.108978 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 34.4133 | 1.11828 | 0.559142 | − | 0.829072i | \(-0.311131\pi\) | ||||
0.559142 | + | 0.829072i | \(0.311131\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −57.4240 | −1.86406 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.11149 | −0.0683978 | −0.0341989 | − | 0.999415i | \(-0.510888\pi\) | ||||
−0.0341989 | + | 0.999415i | \(0.510888\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −29.0124 | −0.938819 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12.2885 | 0.396816 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.21961 | 0.265149 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −73.1752 | −2.35559 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.4443 | 0.786076 | 0.393038 | − | 0.919522i | \(-0.371424\pi\) | ||||
0.393038 | + | 0.919522i | \(0.371424\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25.3151 | −0.812401 | −0.406200 | − | 0.913784i | \(-0.633147\pi\) | ||||
−0.406200 | + | 0.913784i | \(0.633147\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 31.9792 | 1.02521 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −0.758388 | −0.0242630 | −0.0121315 | − | 0.999926i | \(-0.503862\pi\) | ||||
−0.0121315 | + | 0.999926i | \(0.503862\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 27.3944 | 0.875528 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −13.4057 | −0.427575 | −0.213787 | − | 0.976880i | \(-0.568580\pi\) | ||||
−0.213787 | + | 0.976880i | \(0.568580\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −27.7023 | −0.882668 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.399879 | 0.0127154 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.74067 | 0.277657 | 0.138828 | − | 0.990316i | \(-0.455666\pi\) | ||||
0.138828 | + | 0.990316i | \(0.455666\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.84667 | −0.312161 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −54.0544 | −1.71192 | −0.855960 | − | 0.517042i | \(-0.827033\pi\) | ||||
−0.855960 | + | 0.517042i | \(0.827033\pi\) | |||||||
\(998\) | 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 | 6012.2.a.i.1.2 | 9 | ||
3.2 | odd | 2 | 2004.2.a.c.1.8 | ✓ | 9 | ||
12.11 | even | 2 | 8016.2.a.bc.1.8 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2004.2.a.c.1.8 | ✓ | 9 | 3.2 | odd | 2 | ||
6012.2.a.i.1.2 | 9 | 1.1 | even | 1 | trivial | ||
8016.2.a.bc.1.8 | 9 | 12.11 | even | 2 |