Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8016,2,Mod(1,8016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8016, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8016 = 2^{4} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8016.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: | \(64.0080822603\) |
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: | \( x^{9} - 29x^{7} - 7x^{6} + 266x^{5} + 69x^{4} - 901x^{3} - 199x^{2} + 875x + 391 \) |
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 | 1.9 | ||
Root | \(-3.21153\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8016.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.21153 | 1.88345 | 0.941726 | − | 0.336380i | \(-0.109203\pi\) | ||||
0.941726 | + | 0.336380i | \(0.109203\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.13720 | 1.94168 | 0.970840 | − | 0.239730i | \(-0.0770590\pi\) | ||||
0.970840 | + | 0.239730i | \(0.0770590\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.59181 | 0.479949 | 0.239974 | − | 0.970779i | \(-0.422861\pi\) | ||||
0.239974 | + | 0.970779i | \(0.422861\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.05424 | 1.40179 | 0.700897 | − | 0.713263i | \(-0.252783\pi\) | ||||
0.700897 | + | 0.713263i | \(0.252783\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.21153 | −1.08741 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.754874 | 0.183084 | 0.0915419 | − | 0.995801i | \(-0.470820\pi\) | ||||
0.0915419 | + | 0.995801i | \(0.470820\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.66875 | 0.382836 | 0.191418 | − | 0.981509i | \(-0.438691\pi\) | ||||
0.191418 | + | 0.981509i | \(0.438691\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.13720 | −1.12103 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.04218 | −1.25988 | −0.629941 | − | 0.776643i | \(-0.716921\pi\) | ||||
−0.629941 | + | 0.776643i | \(0.716921\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.7370 | 2.54739 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.24703 | −0.788654 | −0.394327 | − | 0.918970i | \(-0.629022\pi\) | ||||
−0.394327 | + | 0.918970i | \(0.629022\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.07105 | 0.192367 | 0.0961834 | − | 0.995364i | \(-0.469336\pi\) | ||||
0.0961834 | + | 0.995364i | \(0.469336\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.59181 | −0.277098 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 21.6355 | 3.65706 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.94651 | 0.813201 | 0.406600 | − | 0.913606i | \(-0.366714\pi\) | ||||
0.406600 | + | 0.913606i | \(0.366714\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.05424 | −0.809326 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.04535 | 0.475603 | 0.237802 | − | 0.971314i | \(-0.423573\pi\) | ||||
0.237802 | + | 0.971314i | \(0.423573\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12.5625 | −1.91577 | −0.957884 | − | 0.287154i | \(-0.907291\pi\) | ||||
−0.957884 | + | 0.287154i | \(0.907291\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.21153 | 0.627818 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.35819 | −1.36503 | −0.682516 | − | 0.730871i | \(-0.739114\pi\) | ||||
−0.682516 | + | 0.730871i | \(0.739114\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 19.3908 | 2.77012 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.754874 | −0.105704 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.52323 | −1.17076 | −0.585378 | − | 0.810761i | \(-0.699054\pi\) | ||||
−0.585378 | + | 0.810761i | \(0.699054\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.70395 | 0.903961 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.66875 | −0.221031 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.98059 | 0.518229 | 0.259115 | − | 0.965847i | \(-0.416569\pi\) | ||||
0.259115 | + | 0.965847i | \(0.416569\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.18677 | 1.04821 | 0.524104 | − | 0.851654i | \(-0.324400\pi\) | ||||
0.524104 | + | 0.851654i | \(0.324400\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.13720 | 0.647226 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 21.2861 | 2.64021 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.99504 | 0.610242 | 0.305121 | − | 0.952314i | \(-0.401303\pi\) | ||||
0.305121 | + | 0.952314i | \(0.401303\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.04218 | 0.727393 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.73050 | −0.798763 | −0.399382 | − | 0.916785i | \(-0.630775\pi\) | ||||
−0.399382 | + | 0.916785i | \(0.630775\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.06414 | −0.709754 | −0.354877 | − | 0.934913i | \(-0.615477\pi\) | ||||
−0.354877 | + | 0.934913i | \(0.615477\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −12.7370 | −1.47074 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.17744 | 0.931906 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.5695 | 1.52669 | 0.763345 | − | 0.645991i | \(-0.223556\pi\) | ||||
0.763345 | + | 0.645991i | \(0.223556\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.95533 | 0.653683 | 0.326841 | − | 0.945079i | \(-0.394016\pi\) | ||||
0.326841 | + | 0.945079i | \(0.394016\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.17917 | 0.344830 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.24703 | 0.455330 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.83467 | 0.830473 | 0.415237 | − | 0.909713i | \(-0.363699\pi\) | ||||
0.415237 | + | 0.909713i | \(0.363699\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 25.9646 | 2.72183 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.07105 | −0.111063 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.02797 | 0.721054 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.42397 | 0.347652 | 0.173826 | − | 0.984776i | \(-0.444387\pi\) | ||||
0.173826 | + | 0.984776i | \(0.444387\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.59181 | 0.159983 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −17.3384 | −1.72523 | −0.862617 | − | 0.505858i | \(-0.831176\pi\) | ||||
−0.862617 | + | 0.505858i | \(0.831176\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.2605 | −1.01100 | −0.505498 | − | 0.862828i | \(-0.668691\pi\) | ||||
−0.505498 | + | 0.862828i | \(0.668691\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −21.6355 | −2.11140 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.1324 | −1.26955 | −0.634777 | − | 0.772696i | \(-0.718908\pi\) | ||||
−0.634777 | + | 0.772696i | \(0.718908\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.53965 | −0.434820 | −0.217410 | − | 0.976080i | \(-0.569761\pi\) | ||||
−0.217410 | + | 0.976080i | \(0.569761\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.94651 | −0.469502 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −20.4713 | −1.92578 | −0.962889 | − | 0.269897i | \(-0.913010\pi\) | ||||
−0.962889 | + | 0.269897i | \(0.913010\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −25.4468 | −2.37293 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.05424 | 0.467264 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.87794 | 0.355490 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.46614 | −0.769649 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.04535 | −0.274590 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 32.5845 | 2.91444 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.7560 | 1.57559 | 0.787795 | − | 0.615937i | \(-0.211222\pi\) | ||||
0.787795 | + | 0.615937i | \(0.211222\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.5625 | 1.10607 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19.4096 | 1.69582 | 0.847912 | − | 0.530137i | \(-0.177859\pi\) | ||||
0.847912 | + | 0.530137i | \(0.177859\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.57268 | 0.743345 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.21153 | −0.362471 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.29492 | 0.794118 | 0.397059 | − | 0.917793i | \(-0.370031\pi\) | ||||
0.397059 | + | 0.917793i | \(0.370031\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.0428 | −1.10628 | −0.553140 | − | 0.833089i | \(-0.686570\pi\) | ||||
−0.553140 | + | 0.833089i | \(0.686570\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.35819 | 0.788101 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.04538 | 0.672789 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −17.8865 | −1.48539 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −19.3908 | −1.59933 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.33359 | 0.436945 | 0.218473 | − | 0.975843i | \(-0.429893\pi\) | ||||
0.218473 | + | 0.975843i | \(0.429893\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.2184 | 1.48259 | 0.741294 | − | 0.671180i | \(-0.234212\pi\) | ||||
0.741294 | + | 0.671180i | \(0.234212\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.754874 | 0.0610280 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.51077 | 0.362314 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.86754 | −0.787516 | −0.393758 | − | 0.919214i | \(-0.628825\pi\) | ||||
−0.393758 | + | 0.919214i | \(0.628825\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.52323 | 0.675936 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −31.0399 | −2.44629 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.64582 | 0.598867 | 0.299433 | − | 0.954117i | \(-0.403202\pi\) | ||||
0.299433 | + | 0.954117i | \(0.403202\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.70395 | −0.521902 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.5453 | 0.965024 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.66875 | 0.127612 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.13111 | 0.162025 | 0.0810127 | − | 0.996713i | \(-0.474185\pi\) | ||||
0.0810127 | + | 0.996713i | \(0.474185\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 65.4324 | 4.94622 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.98059 | −0.299200 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.2841 | −0.918155 | −0.459078 | − | 0.888396i | \(-0.651820\pi\) | ||||
−0.459078 | + | 0.888396i | \(0.651820\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.6588 | −0.940924 | −0.470462 | − | 0.882420i | \(-0.655913\pi\) | ||||
−0.470462 | + | 0.882420i | \(0.655913\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.18677 | −0.605183 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 20.8324 | 1.53163 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.20162 | 0.0878709 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.13720 | −0.373676 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.9840 | −1.08420 | −0.542101 | − | 0.840313i | \(-0.682371\pi\) | ||||
−0.542101 | + | 0.840313i | \(0.682371\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.2434 | −1.38517 | −0.692586 | − | 0.721335i | \(-0.743529\pi\) | ||||
−0.692586 | + | 0.721335i | \(0.743529\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −21.2861 | −1.52433 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.73605 | −0.266182 | −0.133091 | − | 0.991104i | \(-0.542490\pi\) | ||||
−0.133091 | + | 0.991104i | \(0.542490\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.3082 | −1.22694 | −0.613472 | − | 0.789717i | \(-0.710228\pi\) | ||||
−0.613472 | + | 0.789717i | \(0.710228\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.99504 | −0.352323 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −21.8179 | −1.53131 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.8256 | 0.895776 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.04218 | −0.419961 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.65632 | 0.183742 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.3219 | −0.710587 | −0.355293 | − | 0.934755i | \(-0.615619\pi\) | ||||
−0.355293 | + | 0.934755i | \(0.615619\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.73050 | 0.461166 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −52.9075 | −3.60826 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.50221 | 0.373514 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.06414 | 0.409777 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.81531 | 0.256646 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.3854 | −1.16421 | −0.582107 | − | 0.813113i | \(-0.697771\pi\) | ||||
−0.582107 | + | 0.813113i | \(0.697771\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 12.7370 | 0.849131 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −22.0068 | −1.46065 | −0.730323 | − | 0.683102i | \(-0.760630\pi\) | ||||
−0.730323 | + | 0.683102i | \(0.760630\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.2875 | −0.679815 | −0.339907 | − | 0.940459i | \(-0.610396\pi\) | ||||
−0.339907 | + | 0.940459i | \(0.610396\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.17744 | −0.538036 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.06675 | −0.331934 | −0.165967 | − | 0.986131i | \(-0.553074\pi\) | ||||
−0.165967 | + | 0.986131i | \(0.553074\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −39.4123 | −2.57097 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −13.5695 | −0.881434 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.30330 | −0.148988 | −0.0744939 | − | 0.997221i | \(-0.523734\pi\) | ||||
−0.0744939 | + | 0.997221i | \(0.523734\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.625570 | −0.0402965 | −0.0201483 | − | 0.999797i | \(-0.506414\pi\) | ||||
−0.0201483 | + | 0.999797i | \(0.506414\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 81.6650 | 5.21739 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.43423 | 0.536657 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.95533 | −0.377404 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 22.4644 | 1.41794 | 0.708970 | − | 0.705238i | \(-0.249160\pi\) | ||||
0.708970 | + | 0.705238i | \(0.249160\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.61800 | −0.604678 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.17917 | −0.199088 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.6816 | −0.853436 | −0.426718 | − | 0.904385i | \(-0.640330\pi\) | ||||
−0.426718 | + | 0.904385i | \(0.640330\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 25.4112 | 1.57897 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.24703 | −0.262885 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.63785 | −0.285982 | −0.142991 | − | 0.989724i | \(-0.545672\pi\) | ||||
−0.142991 | + | 0.989724i | \(0.545672\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −35.8958 | −2.20506 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.83467 | −0.479474 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 24.6489 | 1.50287 | 0.751434 | − | 0.659808i | \(-0.229363\pi\) | ||||
0.751434 | + | 0.659808i | \(0.229363\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.6032 | −0.704844 | −0.352422 | − | 0.935841i | \(-0.614642\pi\) | ||||
−0.352422 | + | 0.935841i | \(0.614642\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −25.9646 | −1.57145 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 20.2748 | 1.22262 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.516066 | −0.0310074 | −0.0155037 | − | 0.999880i | \(-0.504935\pi\) | ||||
−0.0155037 | + | 0.999880i | \(0.504935\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.07105 | 0.0641222 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.67914 | −0.458099 | −0.229050 | − | 0.973415i | \(-0.573562\pi\) | ||||
−0.229050 | + | 0.973415i | \(0.573562\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.5410 | 0.923819 | 0.461909 | − | 0.886927i | \(-0.347165\pi\) | ||||
0.461909 | + | 0.886927i | \(0.347165\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.02797 | −0.416301 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 15.6445 | 0.923469 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.4302 | −0.966480 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.42397 | −0.200717 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.27759 | 0.425161 | 0.212581 | − | 0.977144i | \(-0.431813\pi\) | ||||
0.212581 | + | 0.977144i | \(0.431813\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 16.7644 | 0.976060 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.59181 | −0.0923662 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −30.5386 | −1.76609 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −64.5363 | −3.71981 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 17.3384 | 0.996064 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 34.4788 | 1.97425 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.121465 | 0.00693237 | 0.00346619 | − | 0.999994i | \(-0.498897\pi\) | ||||
0.00346619 | + | 0.999994i | \(0.498897\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.2605 | 0.583699 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.6650 | 0.944984 | 0.472492 | − | 0.881335i | \(-0.343355\pi\) | ||||
0.472492 | + | 0.881335i | \(0.343355\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −33.1709 | −1.87493 | −0.937464 | − | 0.348083i | \(-0.886833\pi\) | ||||
−0.937464 | + | 0.348083i | \(0.886833\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 21.6355 | 1.21902 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 23.8173 | 1.33771 | 0.668856 | − | 0.743392i | \(-0.266784\pi\) | ||||
0.668856 | + | 0.743392i | \(0.266784\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.76047 | −0.378513 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.1324 | 0.732977 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.25969 | 0.0700912 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 64.3757 | 3.57092 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.53965 | 0.251043 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −48.0749 | −2.65045 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.84876 | −0.101617 | −0.0508085 | − | 0.998708i | \(-0.516180\pi\) | ||||
−0.0508085 | + | 0.998708i | \(0.516180\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.94651 | 0.271067 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 21.0368 | 1.14936 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.0656 | 0.657256 | 0.328628 | − | 0.944460i | \(-0.393414\pi\) | ||||
0.328628 | + | 0.944460i | \(0.393414\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 20.4713 | 1.11185 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.70491 | 0.0923261 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 63.6541 | 3.43700 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 25.4468 | 1.37001 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.33156 | 0.286213 | 0.143106 | − | 0.989707i | \(-0.454291\pi\) | ||||
0.143106 | + | 0.989707i | \(0.454291\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.1869 | 0.919994 | 0.459997 | − | 0.887920i | \(-0.347850\pi\) | ||||
0.459997 | + | 0.887920i | \(0.347850\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.05424 | −0.269775 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −36.7612 | −1.95660 | −0.978301 | − | 0.207189i | \(-0.933568\pi\) | ||||
−0.978301 | + | 0.207189i | \(0.933568\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −28.3457 | −1.50443 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.87794 | −0.205242 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −16.2669 | −0.858536 | −0.429268 | − | 0.903177i | \(-0.641228\pi\) | ||||
−0.429268 | + | 0.903177i | \(0.641228\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.2153 | −0.853436 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.46614 | 0.444357 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −25.5393 | −1.33679 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 24.3923 | 1.27327 | 0.636633 | − | 0.771167i | \(-0.280327\pi\) | ||||
0.636633 | + | 0.771167i | \(0.280327\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.04535 | 0.158534 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −43.7855 | −2.27323 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.3889 | −1.00392 | −0.501959 | − | 0.864892i | \(-0.667387\pi\) | ||||
−0.501959 | + | 0.864892i | \(0.667387\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −32.5845 | −1.68265 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −21.4655 | −1.10553 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.6031 | −0.647375 | −0.323688 | − | 0.946164i | \(-0.604923\pi\) | ||||
−0.323688 | + | 0.946164i | \(0.604923\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −17.7560 | −0.909668 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.7144 | 0.598576 | 0.299288 | − | 0.954163i | \(-0.403251\pi\) | ||||
0.299288 | + | 0.954163i | \(0.403251\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 34.4395 | 1.75520 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −12.5625 | −0.638590 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.63603 | −0.285758 | −0.142879 | − | 0.989740i | \(-0.545636\pi\) | ||||
−0.142879 | + | 0.989740i | \(0.545636\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.56109 | −0.230664 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −19.4096 | −0.979085 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 57.1484 | 2.87545 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −29.3054 | −1.47080 | −0.735399 | − | 0.677634i | \(-0.763005\pi\) | ||||
−0.735399 | + | 0.677634i | \(0.763005\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8.57268 | −0.429171 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 21.4310 | 1.07021 | 0.535106 | − | 0.844785i | \(-0.320271\pi\) | ||||
0.535106 | + | 0.844785i | \(0.320271\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.41335 | 0.269658 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.21153 | 0.209273 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.87390 | 0.390295 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.9959 | 0.741498 | 0.370749 | − | 0.928733i | \(-0.379101\pi\) | ||||
0.370749 | + | 0.928733i | \(0.379101\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.29492 | −0.458484 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 20.4491 | 1.00623 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 25.0811 | 1.23118 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.0428 | 0.638710 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 27.7911 | 1.35769 | 0.678843 | − | 0.734283i | \(-0.262482\pi\) | ||||
0.678843 | + | 0.734283i | \(0.262482\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.1443 | 0.884300 | 0.442150 | − | 0.896941i | \(-0.354216\pi\) | ||||
0.442150 | + | 0.896941i | \(0.354216\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.35819 | −0.455011 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.61481 | 0.466387 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 42.0571 | 2.03528 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.04538 | −0.388435 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.8731 | 0.571905 | 0.285952 | − | 0.958244i | \(-0.407690\pi\) | ||||
0.285952 | + | 0.958244i | \(0.407690\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.57113 | 0.363845 | 0.181923 | − | 0.983313i | \(-0.441768\pi\) | ||||
0.181923 | + | 0.983313i | \(0.441768\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 17.8865 | 0.857592 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −10.0829 | −0.482328 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −26.3797 | −1.25904 | −0.629518 | − | 0.776986i | \(-0.716748\pi\) | ||||
−0.629518 | + | 0.776986i | \(0.716748\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.3908 | 0.923372 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 22.2140 | 1.05542 | 0.527709 | − | 0.849425i | \(-0.323051\pi\) | ||||
0.527709 | + | 0.849425i | \(0.323051\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 32.9959 | 1.56416 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.33359 | −0.252270 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.2554 | 0.531176 | 0.265588 | − | 0.964087i | \(-0.414434\pi\) | ||||
0.265588 | + | 0.964087i | \(0.414434\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.84761 | 0.228265 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −18.2184 | −0.855973 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 109.351 | 5.12644 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.97107 | 0.466427 | 0.233213 | − | 0.972426i | \(-0.425076\pi\) | ||||
0.233213 | + | 0.972426i | \(0.425076\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.754874 | −0.0352345 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −19.6426 | −0.914847 | −0.457423 | − | 0.889249i | \(-0.651228\pi\) | ||||
−0.457423 | + | 0.889249i | \(0.651228\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.5210 | −1.13959 | −0.569793 | − | 0.821788i | \(-0.692977\pi\) | ||||
−0.569793 | + | 0.821788i | \(0.692977\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.51077 | −0.209182 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14.0943 | −0.652205 | −0.326102 | − | 0.945334i | \(-0.605735\pi\) | ||||
−0.326102 | + | 0.945334i | \(0.605735\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 25.6605 | 1.18489 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.86754 | 0.454672 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −19.9972 | −0.919471 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 21.2548 | 0.975235 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.52323 | −0.390252 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.44493 | −0.248785 | −0.124393 | − | 0.992233i | \(-0.539698\pi\) | ||||
−0.124393 | + | 0.992233i | \(0.539698\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 25.0008 | 1.13994 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 31.0399 | 1.41236 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 14.4201 | 0.654785 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 30.1077 | 1.36431 | 0.682155 | − | 0.731208i | \(-0.261043\pi\) | ||||
0.682155 | + | 0.731208i | \(0.261043\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.64582 | −0.345756 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.44218 | −0.110214 | −0.0551070 | − | 0.998480i | \(-0.517550\pi\) | ||||
−0.0551070 | + | 0.998480i | \(0.517550\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.20597 | −0.144390 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.70395 | 0.301320 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −34.5759 | −1.55094 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.782658 | 0.0350366 | 0.0175183 | − | 0.999847i | \(-0.494423\pi\) | ||||
0.0175183 | + | 0.999847i | \(0.494423\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.00000 | 0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.28226 | −0.413876 | −0.206938 | − | 0.978354i | \(-0.566350\pi\) | ||||
−0.206938 | + | 0.978354i | \(0.566350\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −73.0211 | −3.24940 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.5453 | −0.557157 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.573049 | −0.0254000 | −0.0127000 | − | 0.999919i | \(-0.504043\pi\) | ||||
−0.0127000 | + | 0.999919i | \(0.504043\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −31.1527 | −1.37812 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.66875 | −0.0736769 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −43.2123 | −1.90416 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14.8964 | −0.655145 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.13111 | −0.0935454 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −33.0780 | −1.44918 | −0.724588 | − | 0.689183i | \(-0.757970\pi\) | ||||
−0.724588 | + | 0.689183i | \(0.757970\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 29.7761 | 1.30202 | 0.651010 | − | 0.759069i | \(-0.274346\pi\) | ||||
0.651010 | + | 0.759069i | \(0.274346\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −65.4324 | −2.85570 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.808510 | 0.0352192 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.5079 | 0.587301 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.98059 | 0.172743 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15.3919 | 0.666697 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −55.3073 | −2.39114 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12.2841 | 0.530097 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 30.8665 | 1.32951 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 35.6923 | 1.53453 | 0.767266 | − | 0.641329i | \(-0.221616\pi\) | ||||
0.767266 | + | 0.641329i | \(0.221616\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.6588 | 0.543243 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −19.1189 | −0.818962 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.440380 | −0.0188293 | −0.00941464 | − | 0.999956i | \(-0.502997\pi\) | ||||
−0.00941464 | + | 0.999956i | \(0.502997\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.18677 | 0.349403 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.08721 | −0.301925 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 69.7093 | 2.96434 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −20.8324 | −0.884284 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.81205 | −0.246264 | −0.123132 | − | 0.992390i | \(-0.539294\pi\) | ||||
−0.123132 | + | 0.992390i | \(0.539294\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −63.4940 | −2.68551 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.20162 | −0.0507323 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.04845 | −0.170622 | −0.0853109 | − | 0.996354i | \(-0.527188\pi\) | ||||
−0.0853109 | + | 0.996354i | \(0.527188\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −86.2155 | −3.62711 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.13720 | 0.215742 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 23.2702 | 0.975538 | 0.487769 | − | 0.872973i | \(-0.337811\pi\) | ||||
0.487769 | + | 0.872973i | \(0.337811\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.8512 | 1.33293 | 0.666466 | − | 0.745536i | \(-0.267806\pi\) | ||||
0.666466 | + | 0.745536i | \(0.267806\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14.9840 | 0.625964 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −76.9591 | −3.20941 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.0290 | −0.500773 | −0.250387 | − | 0.968146i | \(-0.580558\pi\) | ||||
−0.250387 | + | 0.968146i | \(0.580558\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 19.2434 | 0.799730 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 30.5937 | 1.26924 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.5674 | −0.561902 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 21.2861 | 0.880070 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.88626 | −0.201678 | −0.100839 | − | 0.994903i | \(-0.532153\pi\) | ||||
−0.100839 | + | 0.994903i | \(0.532153\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.78731 | 0.0736450 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.73605 | 0.153680 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −19.0611 | −0.782746 | −0.391373 | − | 0.920232i | \(-0.628000\pi\) | ||||
−0.391373 | + | 0.920232i | \(0.628000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 16.3321 | 0.669549 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 17.3082 | 0.708376 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.2482 | 0.500447 | 0.250224 | − | 0.968188i | \(-0.419496\pi\) | ||||
0.250224 | + | 0.968188i | \(0.419496\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.87869 | 0.158215 | 0.0791076 | − | 0.996866i | \(-0.474793\pi\) | ||||
0.0791076 | + | 0.996866i | \(0.474793\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.99504 | 0.203414 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −35.6554 | −1.44960 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.6407 | 0.513071 | 0.256535 | − | 0.966535i | \(-0.417419\pi\) | ||||
0.256535 | + | 0.966535i | \(0.417419\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 21.8179 | 0.884104 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −47.2985 | −1.91349 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.03966 | −0.163160 | −0.0815802 | − | 0.996667i | \(-0.525997\pi\) | ||||
−0.0815802 | + | 0.996667i | \(0.525997\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −12.8256 | −0.517176 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 42.8979 | 1.72700 | 0.863502 | − | 0.504345i | \(-0.168266\pi\) | ||||
0.863502 | + | 0.504345i | \(0.168266\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.22024 | 0.370593 | 0.185296 | − | 0.982683i | \(-0.440676\pi\) | ||||
0.185296 | + | 0.982683i | \(0.440676\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.04218 | 0.242464 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 40.2483 | 1.61251 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 73.5456 | 2.94182 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.65632 | −0.106083 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.73399 | 0.148884 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.58214 | 0.142603 | 0.0713014 | − | 0.997455i | \(-0.477285\pi\) | ||||
0.0713014 | + | 0.997455i | \(0.477285\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10.3219 | 0.410258 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 74.7799 | 2.96755 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 98.0058 | 3.88313 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.73050 | −0.266254 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.55994 | −0.140609 | −0.0703046 | − | 0.997526i | \(-0.522397\pi\) | ||||
−0.0703046 | + | 0.997526i | \(0.522397\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.3558 | 0.605573 | 0.302787 | − | 0.953058i | \(-0.402083\pi\) | ||||
0.302787 | + | 0.953058i | \(0.402083\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 52.9075 | 2.08323 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25.8947 | 1.01803 | 0.509013 | − | 0.860759i | \(-0.330011\pi\) | ||||
0.509013 | + | 0.860759i | \(0.330011\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.33635 | 0.248723 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.50221 | −0.215649 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.96529 | 0.389972 | 0.194986 | − | 0.980806i | \(-0.437534\pi\) | ||||
0.194986 | + | 0.980806i | \(0.437534\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 81.7441 | 3.19400 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.06414 | −0.236585 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −23.3366 | −0.909065 | −0.454533 | − | 0.890730i | \(-0.650194\pi\) | ||||
−0.454533 | + | 0.890730i | \(0.650194\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.7943 | 0.847702 | 0.423851 | − | 0.905732i | \(-0.360678\pi\) | ||||
0.423851 | + | 0.905732i | \(0.360678\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.81531 | −0.148174 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 36.1041 | 1.40006 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 25.6613 | 0.993611 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 17.3854 | 0.672159 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.0318 | 0.503086 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.8535 | −0.958034 | −0.479017 | − | 0.877806i | \(-0.659007\pi\) | ||||
−0.479017 | + | 0.877806i | \(0.659007\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −12.7370 | −0.490246 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11.6686 | −0.448459 | −0.224229 | − | 0.974536i | \(-0.571987\pi\) | ||||
−0.224229 | + | 0.974536i | \(0.571987\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17.5896 | 0.675028 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 22.0068 | 0.843304 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 40.3092 | 1.54239 | 0.771195 | − | 0.636599i | \(-0.219659\pi\) | ||||
0.771195 | + | 0.636599i | \(0.219659\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 39.1458 | 1.49568 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.2875 | 0.392491 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −43.0784 | −1.64116 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.648820 | 0.0246823 | 0.0123411 | − | 0.999924i | \(-0.496072\pi\) | ||||
0.0123411 | + | 0.999924i | \(0.496072\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.17744 | 0.310635 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −54.9303 | −2.08362 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.29885 | 0.0870753 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.06675 | 0.191642 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.2448 | −0.538017 | −0.269009 | − | 0.963138i | \(-0.586696\pi\) | ||||
−0.269009 | + | 0.963138i | \(0.586696\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.25446 | 0.311323 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 39.4123 | 1.48435 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −89.0707 | −3.34985 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 33.6480 | 1.26368 | 0.631839 | − | 0.775100i | \(-0.282300\pi\) | ||||
0.631839 | + | 0.775100i | \(0.282300\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.5695 | 0.508896 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.47149 | −0.242359 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 33.8834 | 1.26717 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.30330 | 0.0860182 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17.0334 | −0.635239 | −0.317619 | − | 0.948218i | \(-0.602883\pi\) | ||||
−0.317619 | + | 0.948218i | \(0.602883\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −52.7102 | −1.96303 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.625570 | 0.0232652 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −54.0943 | −2.00901 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.31178 | −0.271179 | −0.135589 | − | 0.990765i | \(-0.543293\pi\) | ||||
−0.135589 | + | 0.990765i | \(0.543293\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.48313 | −0.350746 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.4158 | 0.643267 | 0.321634 | − | 0.946864i | \(-0.395768\pi\) | ||||
0.321634 | + | 0.946864i | \(0.395768\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −81.6650 | −3.01226 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.95116 | 0.292885 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27.3162 | 1.00484 | 0.502421 | − | 0.864623i | \(-0.332443\pi\) | ||||
0.502421 | + | 0.864623i | \(0.332443\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.43423 | −0.309839 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33.4574 | −1.22743 | −0.613716 | − | 0.789526i | \(-0.710326\pi\) | ||||
−0.613716 | + | 0.789526i | \(0.710326\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 22.4626 | 0.822965 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.95533 | 0.217894 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −67.4636 | −2.46506 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.04026 | 0.329884 | 0.164942 | − | 0.986303i | \(-0.447256\pi\) | ||||
0.164942 | + | 0.986303i | \(0.447256\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −22.4644 | −0.818649 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 76.7271 | 2.79239 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −29.0912 | −1.05734 | −0.528669 | − | 0.848828i | \(-0.677309\pi\) | ||||
−0.528669 | + | 0.848828i | \(0.677309\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9.61800 | 0.349111 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25.4421 | 0.922274 | 0.461137 | − | 0.887329i | \(-0.347442\pi\) | ||||
0.461137 | + | 0.887329i | \(0.347442\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −23.3211 | −0.844280 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.17917 | 0.114943 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 20.1189 | 0.726450 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.4143 | −0.591915 | −0.295958 | − | 0.955201i | \(-0.595639\pi\) | ||||
−0.295958 | + | 0.955201i | \(0.595639\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.6816 | 0.492731 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 46.6409 | 1.67756 | 0.838778 | − | 0.544474i | \(-0.183271\pi\) | ||||
0.838778 | + | 0.544474i | \(0.183271\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13.6420 | 0.490034 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −25.4112 | −0.911621 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.08191 | 0.182078 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.7137 | −0.383365 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.24703 | 0.151777 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −41.5574 | −1.48325 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.52468 | −0.161287 | −0.0806437 | − | 0.996743i | \(-0.525698\pi\) | ||||
−0.0806437 | + | 0.996743i | \(0.525698\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.63785 | 0.165112 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −105.165 | −3.73924 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 41.3779 | 1.46937 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 35.8958 | 1.27309 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.76977 | −0.204376 | −0.102188 | − | 0.994765i | \(-0.532584\pi\) | ||||
−0.102188 | + | 0.994765i | \(0.532584\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.06425 | −0.249915 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.83467 | 0.276824 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.65296 | −0.340646 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −130.725 | −4.60746 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −24.6489 | −0.867681 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.89016 | −0.101613 | −0.0508063 | − | 0.998709i | \(-0.516179\pi\) | ||||
−0.0508063 | + | 0.998709i | \(0.516179\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.7963 | 0.835600 | 0.417800 | − | 0.908539i | \(-0.362801\pi\) | ||||
0.417800 | + | 0.908539i | \(0.362801\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11.6032 | 0.406942 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 32.2006 | 1.12794 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −20.9637 | −0.733426 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 25.9646 | 0.907277 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.4083 | 0.537752 | 0.268876 | − | 0.963175i | \(-0.413348\pi\) | ||||
0.268876 | + | 0.963175i | \(0.413348\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 53.0392 | 1.84883 | 0.924416 | − | 0.381386i | \(-0.124553\pi\) | ||||
0.924416 | + | 0.381386i | \(0.124553\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −20.2748 | −0.705879 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 37.1164 | 1.29066 | 0.645332 | − | 0.763902i | \(-0.276719\pi\) | ||||
0.645332 | + | 0.763902i | \(0.276719\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −33.9601 | −1.17948 | −0.589742 | − | 0.807592i | \(-0.700771\pi\) | ||||
−0.589742 | + | 0.807592i | \(0.700771\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.516066 | 0.0179021 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14.6376 | 0.507164 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.21153 | −0.145746 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.07105 | −0.0370210 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −22.1451 | −0.764533 | −0.382267 | − | 0.924052i | \(-0.624856\pi\) | ||||
−0.382267 | + | 0.924052i | \(0.624856\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.9627 | −0.378025 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.67914 | 0.264484 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 52.8349 | 1.81758 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −43.4923 | −1.49441 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −15.5410 | −0.533367 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −29.8877 | −1.02454 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.8091 | 0.780970 | 0.390485 | − | 0.920609i | \(-0.372307\pi\) | ||||
0.390485 | + | 0.920609i | \(0.372307\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.02797 | 0.240351 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 53.9748 | 1.84374 | 0.921872 | − | 0.387493i | \(-0.126659\pi\) | ||||
0.921872 | + | 0.387493i | \(0.126659\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −36.9731 | −1.26151 | −0.630754 | − | 0.775983i | \(-0.717254\pi\) | ||||
−0.630754 | + | 0.775983i | \(0.717254\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −15.6445 | −0.533165 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −20.2798 | −0.690331 | −0.345165 | − | 0.938542i | \(-0.612177\pi\) | ||||
−0.345165 | + | 0.938542i | \(0.612177\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.97524 | 0.305167 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.4302 | 0.557998 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 21.6001 | 0.732732 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 25.2461 | 0.855432 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.42397 | 0.115884 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 167.393 | 5.65891 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 38.8159 | 1.31072 | 0.655360 | − | 0.755317i | \(-0.272517\pi\) | ||||
0.655360 | + | 0.755317i | \(0.272517\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.27759 | −0.245467 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25.0400 | −0.843618 | −0.421809 | − | 0.906685i | \(-0.638605\pi\) | ||||
−0.421809 | + | 0.906685i | \(0.638605\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.66634 | 0.325298 | 0.162649 | − | 0.986684i | \(-0.447996\pi\) | ||||
0.162649 | + | 0.986684i | \(0.447996\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −16.7644 | −0.563529 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 22.8139 | 0.766015 | 0.383008 | − | 0.923745i | \(-0.374888\pi\) | ||||
0.383008 | + | 0.923745i | \(0.374888\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 91.2162 | 3.05929 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.59181 | 0.0533276 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −15.6164 | −0.522584 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −51.7347 | −1.72930 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 30.5386 | 1.01965 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.54879 | −0.151711 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.43396 | −0.214346 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 64.5363 | 2.14763 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −53.3130 | −1.77219 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −43.6100 | −1.44805 | −0.724023 | − | 0.689775i | \(-0.757709\pi\) | ||||
−0.724023 | + | 0.689775i | \(0.757709\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −17.3384 | −0.575078 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −47.3364 | −1.56832 | −0.784162 | − | 0.620556i | \(-0.786907\pi\) | ||||
−0.784162 | + | 0.620556i | \(0.786907\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.47976 | 0.313734 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −34.4788 | −1.13983 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 99.7110 | 3.29275 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.69738 | −0.121965 | −0.0609826 | − | 0.998139i | \(-0.519423\pi\) | ||||
−0.0609826 | + | 0.998139i | \(0.519423\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.121465 | −0.00400241 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −34.0175 | −1.11970 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 63.0035 | 2.07154 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −10.2605 | −0.336999 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −19.5929 | −0.642821 | −0.321410 | − | 0.946940i | \(-0.604157\pi\) | ||||
−0.321410 | + | 0.946940i | \(0.604157\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 32.3583 | 1.06050 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −16.6650 | −0.545587 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.06064 | 0.165501 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −46.2138 | −1.50974 | −0.754869 | − | 0.655875i | \(-0.772300\pi\) | ||||
−0.754869 | + | 0.655875i | \(0.772300\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 33.1709 | 1.08249 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16.1732 | −0.527231 | −0.263616 | − | 0.964628i | \(-0.584915\pi\) | ||||
−0.263616 | + | 0.964628i | \(0.584915\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18.4005 | −0.599204 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −21.6355 | −0.703802 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19.7305 | 0.641154 | 0.320577 | − | 0.947223i | \(-0.396123\pi\) | ||||
0.320577 | + | 0.947223i | \(0.396123\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −30.6496 | −0.994929 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −23.8173 | −0.772329 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 44.2858 | 1.43456 | 0.717279 | − | 0.696786i | \(-0.245387\pi\) | ||||
0.717279 | + | 0.696786i | \(0.245387\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −63.1054 | −2.04204 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.76047 | 0.218535 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 47.7498 | 1.54192 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.8528 | −0.962995 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13.1324 | −0.423184 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −81.0443 | −2.60891 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19.9140 | 0.640391 | 0.320195 | − | 0.947352i | \(-0.396251\pi\) | ||||
0.320195 | + | 0.947352i | \(0.396251\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.25969 | −0.0404672 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 30.1118 | 0.966334 | 0.483167 | − | 0.875528i | \(-0.339486\pi\) | ||||
0.483167 | + | 0.875528i | \(0.339486\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −67.0037 | −2.14804 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −64.3757 | −2.06167 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10.6796 | 0.341672 | 0.170836 | − | 0.985299i | \(-0.445353\pi\) | ||||
0.170836 | + | 0.985299i | \(0.445353\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.4713 | 0.398585 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.53965 | −0.144940 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 43.7358 | 1.39496 | 0.697478 | − | 0.716606i | \(-0.254305\pi\) | ||||
0.697478 | + | 0.716606i | \(0.254305\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15.7345 | −0.501342 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 48.0749 | 1.53024 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 75.9051 | 2.41364 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.5304 | 0.620402 | 0.310201 | − | 0.950671i | \(-0.399604\pi\) | ||||
0.310201 | + | 0.950671i | \(0.399604\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.84876 | 0.0586685 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −72.8938 | −2.31089 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.72889 | −0.181436 | −0.0907179 | − | 0.995877i | \(-0.528916\pi\) | ||||
−0.0907179 | + | 0.995877i | \(0.528916\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.94651 | −0.156501 |
(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 | 8016.2.a.bb.1.9 | 9 | ||
4.3 | odd | 2 | 2004.2.a.d.1.9 | ✓ | 9 | ||
12.11 | even | 2 | 6012.2.a.h.1.1 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2004.2.a.d.1.9 | ✓ | 9 | 4.3 | odd | 2 | ||
6012.2.a.h.1.1 | 9 | 12.11 | even | 2 | |||
8016.2.a.bb.1.9 | 9 | 1.1 | even | 1 | trivial |