Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8040,2,Mod(1,8040)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8040, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8040.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8040 = 2^{3} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8040.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: | \(64.1997232251\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - x^{6} - 15x^{5} + 3x^{4} + 43x^{3} - 6x^{2} - 29x + 6 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.05266\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8040.1 |
$q$-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 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.670274 | 0.253340 | 0.126670 | − | 0.991945i | \(-0.459571\pi\) | ||||
0.126670 | + | 0.991945i | \(0.459571\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.78339 | 1.14073 | 0.570367 | − | 0.821390i | \(-0.306801\pi\) | ||||
0.570367 | + | 0.821390i | \(0.306801\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.11429 | 1.14110 | 0.570550 | − | 0.821263i | \(-0.306730\pi\) | ||||
0.570550 | + | 0.821263i | \(0.306730\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.83923 | 0.446080 | 0.223040 | − | 0.974809i | \(-0.428402\pi\) | ||||
0.223040 | + | 0.974809i | \(0.428402\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.73969 | 1.31677 | 0.658387 | − | 0.752679i | \(-0.271239\pi\) | ||||
0.658387 | + | 0.752679i | \(0.271239\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.670274 | 0.146266 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.13944 | 1.48868 | 0.744338 | − | 0.667803i | \(-0.232765\pi\) | ||||
0.744338 | + | 0.667803i | \(0.232765\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.82187 | −0.338313 | −0.169156 | − | 0.985589i | \(-0.554104\pi\) | ||||
−0.169156 | + | 0.985589i | \(0.554104\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.12208 | −0.919952 | −0.459976 | − | 0.887931i | \(-0.652142\pi\) | ||||
−0.459976 | + | 0.887931i | \(0.652142\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.78339 | 0.658603 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.670274 | −0.113297 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.09121 | 0.343793 | 0.171896 | − | 0.985115i | \(-0.445011\pi\) | ||||
0.171896 | + | 0.985115i | \(0.445011\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.11429 | 0.658814 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.12208 | 1.11228 | 0.556141 | − | 0.831088i | \(-0.312282\pi\) | ||||
0.556141 | + | 0.831088i | \(0.312282\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.02515 | −0.461331 | −0.230665 | − | 0.973033i | \(-0.574090\pi\) | ||||
−0.230665 | + | 0.973033i | \(0.574090\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.47041 | −0.797941 | −0.398971 | − | 0.916964i | \(-0.630632\pi\) | ||||
−0.398971 | + | 0.916964i | \(0.630632\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.55073 | −0.935819 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.83923 | 0.257544 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.86073 | 0.942393 | 0.471197 | − | 0.882028i | \(-0.343822\pi\) | ||||
0.471197 | + | 0.882028i | \(0.343822\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.78339 | −0.510152 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.73969 | 0.760240 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.63478 | 0.212830 | 0.106415 | − | 0.994322i | \(-0.466063\pi\) | ||||
0.106415 | + | 0.994322i | \(0.466063\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.50889 | 0.705341 | 0.352671 | − | 0.935748i | \(-0.385274\pi\) | ||||
0.352671 | + | 0.935748i | \(0.385274\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.670274 | 0.0844466 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.11429 | −0.510315 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.00000 | 0.122169 | ||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.13944 | 0.859488 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.4491 | −1.47744 | −0.738718 | − | 0.674015i | \(-0.764568\pi\) | ||||
−0.738718 | + | 0.674015i | \(0.764568\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.4317 | −1.22093 | −0.610467 | − | 0.792042i | \(-0.709018\pi\) | ||||
−0.610467 | + | 0.792042i | \(0.709018\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.53591 | 0.288993 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.01717 | 0.789493 | 0.394746 | − | 0.918790i | \(-0.370832\pi\) | ||||
0.394746 | + | 0.918790i | \(0.370832\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.16000 | −0.566383 | −0.283192 | − | 0.959063i | \(-0.591393\pi\) | ||||
−0.283192 | + | 0.959063i | \(0.591393\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.83923 | −0.199493 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.82187 | −0.195325 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.63153 | 0.596941 | 0.298470 | − | 0.954419i | \(-0.403524\pi\) | ||||
0.298470 | + | 0.954419i | \(0.403524\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.75770 | 0.289086 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.12208 | −0.531135 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.73969 | −0.588879 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.80937 | −0.995991 | −0.497995 | − | 0.867180i | \(-0.665930\pi\) | ||||
−0.497995 | + | 0.867180i | \(0.665930\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.78339 | 0.380245 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.47407 | 0.345683 | 0.172842 | − | 0.984950i | \(-0.444705\pi\) | ||||
0.172842 | + | 0.984950i | \(0.444705\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.1717 | 1.59345 | 0.796723 | − | 0.604345i | \(-0.206565\pi\) | ||||
0.796723 | + | 0.604345i | \(0.206565\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.670274 | −0.0654121 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −17.9034 | −1.73079 | −0.865393 | − | 0.501093i | \(-0.832931\pi\) | ||||
−0.865393 | + | 0.501093i | \(0.832931\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.3694 | 1.66369 | 0.831844 | − | 0.555009i | \(-0.187285\pi\) | ||||
0.831844 | + | 0.555009i | \(0.187285\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.09121 | 0.198489 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −19.3577 | −1.82102 | −0.910508 | − | 0.413491i | \(-0.864309\pi\) | ||||
−0.910508 | + | 0.413491i | \(0.864309\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.13944 | −0.665756 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.11429 | 0.380366 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.23279 | 0.113010 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.31401 | 0.301274 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.12208 | 0.642176 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.6572 | 1.12315 | 0.561573 | − | 0.827427i | \(-0.310196\pi\) | ||||
0.561573 | + | 0.827427i | \(0.310196\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.02515 | −0.266349 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.7384 | −1.20033 | −0.600166 | − | 0.799876i | \(-0.704899\pi\) | ||||
−0.600166 | + | 0.799876i | \(0.704899\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.84716 | 0.333591 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.2004 | −0.871476 | −0.435738 | − | 0.900074i | \(-0.643513\pi\) | ||||
−0.435738 | + | 0.900074i | \(0.643513\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.0665 | −1.02347 | −0.511733 | − | 0.859144i | \(-0.670996\pi\) | ||||
−0.511733 | + | 0.859144i | \(0.670996\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.47041 | −0.460691 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 15.5660 | 1.30169 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.82187 | 0.151298 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.55073 | −0.540295 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.31188 | −0.107474 | −0.0537368 | − | 0.998555i | \(-0.517113\pi\) | ||||
−0.0537368 | + | 0.998555i | \(0.517113\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.61324 | 0.294041 | 0.147021 | − | 0.989133i | \(-0.453032\pi\) | ||||
0.147021 | + | 0.989133i | \(0.453032\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.83923 | 0.148693 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.12208 | 0.411415 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.72452 | 0.456867 | 0.228433 | − | 0.973560i | \(-0.426640\pi\) | ||||
0.228433 | + | 0.973560i | \(0.426640\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.86073 | 0.544091 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.78538 | 0.377141 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.8151 | 1.16041 | 0.580204 | − | 0.814471i | \(-0.302973\pi\) | ||||
0.580204 | + | 0.814471i | \(0.302973\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.78339 | −0.294536 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.97042 | −0.307240 | −0.153620 | − | 0.988130i | \(-0.549093\pi\) | ||||
−0.153620 | + | 0.988130i | \(0.549093\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.92740 | 0.302107 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.73969 | 0.438925 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 24.2043 | 1.84022 | 0.920109 | − | 0.391662i | \(-0.128100\pi\) | ||||
0.920109 | + | 0.391662i | \(0.128100\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.670274 | 0.0506680 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.63478 | 0.122877 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.26827 | −0.692743 | −0.346371 | − | 0.938097i | \(-0.612586\pi\) | ||||
−0.346371 | + | 0.938097i | \(0.612586\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −24.7538 | −1.83994 | −0.919969 | − | 0.391991i | \(-0.871786\pi\) | ||||
−0.919969 | + | 0.391991i | \(0.871786\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.50889 | 0.407229 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.09121 | −0.153749 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.95853 | 0.508858 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.670274 | 0.0487553 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.65532 | 0.119775 | 0.0598875 | − | 0.998205i | \(-0.480926\pi\) | ||||
0.0598875 | + | 0.998205i | \(0.480926\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.2421 | −0.953191 | −0.476595 | − | 0.879123i | \(-0.658129\pi\) | ||||
−0.476595 | + | 0.879123i | \(0.658129\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.11429 | −0.294631 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.51881 | −0.250705 | −0.125352 | − | 0.992112i | \(-0.540006\pi\) | ||||
−0.125352 | + | 0.992112i | \(0.540006\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.9365 | 0.987933 | 0.493966 | − | 0.869481i | \(-0.335547\pi\) | ||||
0.493966 | + | 0.869481i | \(0.335547\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.00000 | 0.0705346 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.22115 | −0.0857081 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.12208 | −0.497427 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.13944 | 0.496225 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 21.7154 | 1.50209 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.8657 | 1.71183 | 0.855914 | − | 0.517118i | \(-0.172995\pi\) | ||||
0.855914 | + | 0.517118i | \(0.172995\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −12.4491 | −0.852998 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.02515 | 0.206313 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.43320 | −0.233060 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10.4317 | −0.704906 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.56715 | 0.509021 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.60254 | −0.643033 | −0.321517 | − | 0.946904i | \(-0.604193\pi\) | ||||
−0.321517 | + | 0.946904i | \(0.604193\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.6064 | 0.903089 | 0.451545 | − | 0.892249i | \(-0.350873\pi\) | ||||
0.451545 | + | 0.892249i | \(0.350873\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.78622 | 0.250200 | 0.125100 | − | 0.992144i | \(-0.460075\pi\) | ||||
0.125100 | + | 0.992144i | \(0.460075\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.53591 | 0.166850 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.4793 | 0.883059 | 0.441530 | − | 0.897247i | \(-0.354436\pi\) | ||||
0.441530 | + | 0.897247i | \(0.354436\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.47041 | 0.356850 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.01717 | 0.455814 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.81123 | −0.505266 | −0.252633 | − | 0.967562i | \(-0.581297\pi\) | ||||
−0.252633 | + | 0.967562i | \(0.581297\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.8308 | 0.890923 | 0.445462 | − | 0.895301i | \(-0.353040\pi\) | ||||
0.445462 | + | 0.895301i | \(0.353040\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.55073 | 0.418511 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 23.6147 | 1.50257 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.16000 | −0.327001 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.7731 | −0.869352 | −0.434676 | − | 0.900587i | \(-0.643137\pi\) | ||||
−0.434676 | + | 0.900587i | \(0.643137\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 27.0113 | 1.69818 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.83923 | −0.115177 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.1620 | 1.25767 | 0.628837 | − | 0.777538i | \(-0.283531\pi\) | ||||
0.628837 | + | 0.777538i | \(0.283531\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.40168 | 0.0870964 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.82187 | −0.112771 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.295696 | 0.0182334 | 0.00911671 | − | 0.999958i | \(-0.497098\pi\) | ||||
0.00911671 | + | 0.999958i | \(0.497098\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.86073 | −0.421451 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.63153 | 0.344644 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −19.4531 | −1.18608 | −0.593038 | − | 0.805175i | \(-0.702071\pi\) | ||||
−0.593038 | + | 0.805175i | \(0.702071\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.8772 | −0.660743 | −0.330372 | − | 0.943851i | \(-0.607174\pi\) | ||||
−0.330372 | + | 0.943851i | \(0.607174\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.75770 | 0.166904 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.78339 | 0.228147 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25.1608 | 1.51177 | 0.755883 | − | 0.654707i | \(-0.227208\pi\) | ||||
0.755883 | + | 0.654707i | \(0.227208\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.12208 | −0.306651 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.91436 | 0.531786 | 0.265893 | − | 0.964003i | \(-0.414333\pi\) | ||||
0.265893 | + | 0.964003i | \(0.414333\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −19.4711 | −1.15744 | −0.578720 | − | 0.815526i | \(-0.696447\pi\) | ||||
−0.578720 | + | 0.815526i | \(0.696447\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.73969 | −0.339990 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.77374 | 0.281785 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.6172 | −0.801013 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.80937 | −0.575035 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.3591 | −0.605185 | −0.302592 | − | 0.953120i | \(-0.597852\pi\) | ||||
−0.302592 | + | 0.953120i | \(0.597852\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.63478 | −0.0951803 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.78339 | 0.219534 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 29.3737 | 1.69873 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.02768 | −0.116873 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.47407 | 0.199580 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.50889 | −0.315438 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.7029 | 1.46694 | 0.733470 | − | 0.679721i | \(-0.237899\pi\) | ||||
0.733470 | + | 0.679721i | \(0.237899\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 16.1717 | 0.919976 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.07146 | −0.117462 | −0.0587308 | − | 0.998274i | \(-0.518705\pi\) | ||||
−0.0587308 | + | 0.998274i | \(0.518705\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.9262 | 0.674110 | 0.337055 | − | 0.941485i | \(-0.390569\pi\) | ||||
0.337055 | + | 0.941485i | \(0.390569\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.670274 | −0.0377657 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −32.0644 | −1.80092 | −0.900458 | − | 0.434943i | \(-0.856769\pi\) | ||||
−0.900458 | + | 0.434943i | \(0.856769\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.89284 | −0.385925 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −17.9034 | −0.999270 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.5566 | 0.587386 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.11429 | 0.228220 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 17.3694 | 0.960531 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.66667 | −0.202150 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.3465 | 0.568697 | 0.284349 | − | 0.958721i | \(-0.408223\pi\) | ||||
0.284349 | + | 0.958721i | \(0.408223\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.09121 | 0.114598 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.00000 | −0.0546358 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.03793 | 0.165486 | 0.0827432 | − | 0.996571i | \(-0.473632\pi\) | ||||
0.0827432 | + | 0.996571i | \(0.473632\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −19.3577 | −1.05136 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −19.3788 | −1.04942 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.08271 | −0.490420 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7.13944 | −0.384375 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −14.1956 | −0.762058 | −0.381029 | − | 0.924563i | \(-0.624430\pi\) | ||||
−0.381029 | + | 0.924563i | \(0.624430\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 29.5421 | 1.58135 | 0.790677 | − | 0.612234i | \(-0.209729\pi\) | ||||
0.790677 | + | 0.612234i | \(0.209729\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.11429 | 0.219605 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 32.2119 | 1.71447 | 0.857234 | − | 0.514927i | \(-0.172181\pi\) | ||||
0.857234 | + | 0.514927i | \(0.172181\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.4491 | 0.660729 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.23279 | 0.0652462 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 30.8548 | 1.62845 | 0.814226 | − | 0.580548i | \(-0.197162\pi\) | ||||
0.814226 | + | 0.580548i | \(0.197162\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.9440 | 0.733894 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.31401 | 0.173941 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.4317 | 0.546018 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −30.8580 | −1.61077 | −0.805386 | − | 0.592750i | \(-0.798042\pi\) | ||||
−0.805386 | + | 0.592750i | \(0.798042\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.12208 | 0.370760 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.59857 | 0.238746 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.4483 | 0.799881 | 0.399940 | − | 0.916541i | \(-0.369031\pi\) | ||||
0.399940 | + | 0.916541i | \(0.369031\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.49570 | −0.386048 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.9680 | 0.974320 | 0.487160 | − | 0.873313i | \(-0.338033\pi\) | ||||
0.487160 | + | 0.873313i | \(0.338033\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.6572 | 0.648449 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.5529 | −0.539230 | −0.269615 | − | 0.962968i | \(-0.586896\pi\) | ||||
−0.269615 | + | 0.962968i | \(0.586896\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.53591 | −0.129242 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.02515 | −0.153777 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.90885 | −0.299591 | −0.149795 | − | 0.988717i | \(-0.547861\pi\) | ||||
−0.149795 | + | 0.988717i | \(0.547861\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.1311 | 0.664068 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −13.7384 | −0.693012 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.01717 | −0.353072 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.2533 | 0.966295 | 0.483148 | − | 0.875539i | \(-0.339493\pi\) | ||||
0.483148 | + | 0.875539i | \(0.339493\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.84716 | 0.192599 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.05547 | 0.202520 | 0.101260 | − | 0.994860i | \(-0.467713\pi\) | ||||
0.101260 | + | 0.994860i | \(0.467713\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −21.0737 | −1.04976 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.91185 | 0.392176 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.26712 | 0.0626550 | 0.0313275 | − | 0.999509i | \(-0.490027\pi\) | ||||
0.0313275 | + | 0.999509i | \(0.490027\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.2004 | −0.503147 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.09575 | 0.0539182 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.16000 | 0.253294 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12.0665 | −0.590899 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 31.0552 | 1.51714 | 0.758572 | − | 0.651589i | \(-0.225897\pi\) | ||||
0.758572 | + | 0.651589i | \(0.225897\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.9337 | −1.11772 | −0.558859 | − | 0.829263i | \(-0.688761\pi\) | ||||
−0.558859 | + | 0.829263i | \(0.688761\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.47041 | −0.265980 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.83923 | 0.0892160 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.69247 | 0.178691 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 15.5660 | 0.751531 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.8073 | −0.520568 | −0.260284 | − | 0.965532i | \(-0.583816\pi\) | ||||
−0.260284 | + | 0.965532i | \(0.583816\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −39.1113 | −1.87957 | −0.939785 | − | 0.341766i | \(-0.888975\pi\) | ||||
−0.939785 | + | 0.341766i | \(0.888975\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.82187 | 0.0873519 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 40.9781 | 1.96025 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.92985 | −0.187561 | −0.0937807 | − | 0.995593i | \(-0.529895\pi\) | ||||
−0.0937807 | + | 0.995593i | \(0.529895\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.55073 | −0.311940 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −21.6585 | −1.02903 | −0.514513 | − | 0.857483i | \(-0.672027\pi\) | ||||
−0.514513 | + | 0.857483i | \(0.672027\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.63153 | −0.266960 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.31188 | −0.0620499 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.5401 | −0.827770 | −0.413885 | − | 0.910329i | \(-0.635828\pi\) | ||||
−0.413885 | + | 0.910329i | \(0.635828\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 26.9456 | 1.26882 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.61324 | 0.169765 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.75770 | −0.129283 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.1088 | −0.566424 | −0.283212 | − | 0.959057i | \(-0.591400\pi\) | ||||
−0.283212 | + | 0.959057i | \(0.591400\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.83923 | 0.0858481 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −26.6861 | −1.24290 | −0.621448 | − | 0.783455i | \(-0.713455\pi\) | ||||
−0.621448 | + | 0.783455i | \(0.713455\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.7128 | 1.14850 | 0.574250 | − | 0.818680i | \(-0.305294\pi\) | ||||
0.574250 | + | 0.818680i | \(0.305294\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.12208 | 0.237531 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.926018 | 0.0428510 | 0.0214255 | − | 0.999770i | \(-0.493180\pi\) | ||||
0.0214255 | + | 0.999770i | \(0.493180\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.670274 | 0.0309504 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.72452 | 0.263772 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.4453 | −0.526256 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.73969 | 0.263355 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.86073 | 0.314131 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 31.8360 | 1.45462 | 0.727312 | − | 0.686307i | \(-0.240769\pi\) | ||||
0.727312 | + | 0.686307i | \(0.240769\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.60384 | 0.392302 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.78538 | 0.217742 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.80937 | 0.445421 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.2782 | 1.14547 | 0.572733 | − | 0.819742i | \(-0.305883\pi\) | ||||
0.572733 | + | 0.819742i | \(0.305883\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 14.8151 | 0.669962 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.9319 | −0.718997 | −0.359499 | − | 0.933146i | \(-0.617052\pi\) | ||||
−0.359499 | + | 0.933146i | \(0.617052\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.35084 | −0.150914 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.78339 | −0.170051 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.34430 | −0.374293 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.67237 | −0.253930 | −0.126965 | − | 0.991907i | \(-0.540524\pi\) | ||||
−0.126965 | + | 0.991907i | \(0.540524\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.97042 | −0.177385 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15.2206 | −0.678654 | −0.339327 | − | 0.940668i | \(-0.610199\pi\) | ||||
−0.339327 | + | 0.940668i | \(0.610199\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.47407 | −0.154594 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.92740 | 0.174422 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.30717 | −0.412533 | −0.206266 | − | 0.978496i | \(-0.566131\pi\) | ||||
−0.206266 | + | 0.978496i | \(0.566131\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.99207 | −0.309311 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.73969 | 0.253413 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −16.1717 | −0.712610 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −20.6967 | −0.910238 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 24.2043 | 1.06245 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.3936 | −0.499162 | −0.249581 | − | 0.968354i | \(-0.580293\pi\) | ||||
−0.249581 | + | 0.968354i | \(0.580293\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.3201 | 0.932261 | 0.466130 | − | 0.884716i | \(-0.345648\pi\) | ||||
0.466130 | + | 0.884716i | \(0.345648\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.670274 | 0.0292532 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.42070 | −0.410372 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 27.9716 | 1.21616 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.63478 | 0.0709432 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 29.3023 | 1.26922 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 17.9034 | 0.774031 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.26827 | −0.399955 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −24.7840 | −1.06752 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.2004 | −1.25542 | −0.627712 | − | 0.778446i | \(-0.716008\pi\) | ||||
−0.627712 | + | 0.778446i | \(0.716008\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −24.7538 | −1.06229 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −17.3694 | −0.744024 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.0743 | 1.45691 | 0.728455 | − | 0.685093i | \(-0.240239\pi\) | ||||
0.728455 | + | 0.685093i | \(0.240239\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.50889 | 0.235114 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.4570 | −0.445481 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.70342 | 0.200010 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.09121 | −0.0887669 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 37.7922 | 1.60131 | 0.800654 | − | 0.599127i | \(-0.204486\pi\) | ||||
0.800654 | + | 0.599127i | \(0.204486\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.4463 | −0.526424 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.95853 | 0.293789 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 26.1466 | 1.10195 | 0.550974 | − | 0.834522i | \(-0.314256\pi\) | ||||
0.550974 | + | 0.834522i | \(0.314256\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19.3577 | 0.814383 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.670274 | 0.0281489 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −37.3200 | −1.56454 | −0.782268 | − | 0.622942i | \(-0.785937\pi\) | ||||
−0.782268 | + | 0.622942i | \(0.785937\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.81060 | 0.0757713 | 0.0378856 | − | 0.999282i | \(-0.487938\pi\) | ||||
0.0378856 | + | 0.999282i | \(0.487938\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.65532 | 0.0691521 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.13944 | 0.297735 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.7019 | −0.778568 | −0.389284 | − | 0.921118i | \(-0.627278\pi\) | ||||
−0.389284 | + | 0.921118i | \(0.627278\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13.2421 | −0.550325 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.45861 | −0.143487 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 25.9568 | 1.07502 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.11429 | −0.170105 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.91146 | −0.0788944 | −0.0394472 | − | 0.999222i | \(-0.512560\pi\) | ||||
−0.0394472 | + | 0.999222i | \(0.512560\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −29.3991 | −1.21137 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.51881 | −0.144744 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.36025 | 0.0558588 | 0.0279294 | − | 0.999610i | \(-0.491109\pi\) | ||||
0.0279294 | + | 0.999610i | \(0.491109\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.23279 | −0.0505395 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13.9365 | 0.570383 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 30.3993 | 1.24208 | 0.621040 | − | 0.783779i | \(-0.286710\pi\) | ||||
0.621040 | + | 0.783779i | \(0.286710\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25.6037 | −1.04439 | −0.522197 | − | 0.852825i | \(-0.674888\pi\) | ||||
−0.522197 | + | 0.852825i | \(0.674888\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.00000 | 0.0407231 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.31401 | −0.134734 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.07196 | 0.0435094 | 0.0217547 | − | 0.999763i | \(-0.493075\pi\) | ||||
0.0217547 | + | 0.999763i | \(0.493075\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.22115 | −0.0494836 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −22.5069 | −0.910530 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.7022 | 0.795765 | 0.397883 | − | 0.917436i | \(-0.369745\pi\) | ||||
0.397883 | + | 0.917436i | \(0.369745\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.12208 | −0.287190 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.84791 | −0.396462 | −0.198231 | − | 0.980155i | \(-0.563520\pi\) | ||||
−0.198231 | + | 0.980155i | \(0.563520\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.39967 | 0.217031 | 0.108516 | − | 0.994095i | \(-0.465390\pi\) | ||||
0.108516 | + | 0.994095i | \(0.465390\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.13944 | 0.286496 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.77467 | 0.151229 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 21.7154 | 0.867232 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.84622 | 0.153359 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 45.8600 | 1.82566 | 0.912829 | − | 0.408343i | \(-0.133893\pi\) | ||||
0.912829 | + | 0.408343i | \(0.133893\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 24.8657 | 0.988324 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −12.6572 | −0.502286 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −26.9516 | −1.06786 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12.4491 | −0.492478 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −33.9181 | −1.33969 | −0.669843 | − | 0.742503i | \(-0.733639\pi\) | ||||
−0.669843 | + | 0.742503i | \(0.733639\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.51361 | −0.0991272 | −0.0495636 | − | 0.998771i | \(-0.515783\pi\) | ||||
−0.0495636 | + | 0.998771i | \(0.515783\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.02515 | 0.119115 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 27.6877 | 1.08852 | 0.544259 | − | 0.838917i | \(-0.316811\pi\) | ||||
0.544259 | + | 0.838917i | \(0.316811\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.18499 | 0.242782 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.43320 | −0.134558 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −39.6926 | −1.55329 | −0.776645 | − | 0.629938i | \(-0.783080\pi\) | ||||
−0.776645 | + | 0.629938i | \(0.783080\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.7384 | 0.536805 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −10.4317 | −0.406978 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16.4133 | −0.639370 | −0.319685 | − | 0.947524i | \(-0.603577\pi\) | ||||
−0.319685 | + | 0.947524i | \(0.603577\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.56972 | 0.138846 | 0.0694230 | − | 0.997587i | \(-0.477884\pi\) | ||||
0.0694230 | + | 0.997587i | \(0.477884\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7.56715 | 0.293884 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.84716 | −0.149187 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.0071 | −0.503638 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.60254 | −0.371256 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 20.8423 | 0.804607 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.07992 | −0.234364 | −0.117182 | − | 0.993110i | \(-0.537386\pi\) | ||||
−0.117182 | + | 0.993110i | \(0.537386\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −32.9303 | −1.26561 | −0.632807 | − | 0.774310i | \(-0.718097\pi\) | ||||
−0.632807 | + | 0.774310i | \(0.718097\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.57497 | −0.252324 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.6064 | 0.521399 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.7093 | 0.830685 | 0.415342 | − | 0.909665i | \(-0.363662\pi\) | ||||
0.415342 | + | 0.909665i | \(0.363662\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.2004 | 0.389736 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.78622 | 0.144453 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 28.2270 | 1.07536 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 48.7214 | 1.85345 | 0.926724 | − | 0.375742i | \(-0.122612\pi\) | ||||
0.926724 | + | 0.375742i | \(0.122612\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.53591 | 0.0963311 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.0665 | 0.457708 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.0992 | 0.496166 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13.4793 | 0.509835 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11.2299 | −0.424146 | −0.212073 | − | 0.977254i | \(-0.568021\pi\) | ||||
−0.212073 | + | 0.977254i | \(0.568021\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.0029 | 0.452697 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.47041 | 0.206027 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.32858 | 0.0875753 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.42425 | −0.241268 | −0.120634 | − | 0.992697i | \(-0.538493\pi\) | ||||
−0.120634 | + | 0.992697i | \(0.538493\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.01717 | 0.263164 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −36.5688 | −1.36951 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15.5660 | −0.582134 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7.81123 | −0.291716 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14.1488 | −0.527662 | −0.263831 | − | 0.964569i | \(-0.584986\pi\) | ||||
−0.263831 | + | 0.964569i | \(0.584986\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.8395 | 0.403683 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 13.8308 | 0.514375 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.82187 | −0.0676625 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.0186600 | 0.000692059 0 | 0.000346030 | − | 1.00000i | \(-0.499890\pi\) | ||||
0.000346030 | 1.00000i | \(0.499890\pi\) | ||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.56396 | −0.205790 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −38.2015 | −1.41101 | −0.705503 | − | 0.708707i | \(-0.749279\pi\) | ||||
−0.705503 | + | 0.708707i | \(0.749279\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.55073 | 0.241627 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.78339 | 0.139363 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.1980 | −0.632640 | −0.316320 | − | 0.948653i | \(-0.602447\pi\) | ||||
−0.316320 | + | 0.948653i | \(0.602447\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 23.6147 | 0.867509 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33.1297 | −1.21541 | −0.607705 | − | 0.794163i | \(-0.707910\pi\) | ||||
−0.607705 | + | 0.794163i | \(0.707910\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.31188 | 0.0480636 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.16000 | −0.188794 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.0002 | −0.438477 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −31.0531 | −1.13314 | −0.566572 | − | 0.824012i | \(-0.691731\pi\) | ||||
−0.566572 | + | 0.824012i | \(0.691731\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −13.7731 | −0.501920 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.61324 | −0.131499 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23.1862 | −0.842716 | −0.421358 | − | 0.906894i | \(-0.638446\pi\) | ||||
−0.421358 | + | 0.906894i | \(0.638446\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 27.0113 | 0.980447 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.58898 | −0.0938503 | −0.0469251 | − | 0.998898i | \(-0.514942\pi\) | ||||
−0.0469251 | + | 0.998898i | \(0.514942\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.6423 | 0.421479 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.83923 | −0.0664976 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.72594 | 0.242860 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −23.4029 | −0.843929 | −0.421964 | − | 0.906612i | \(-0.638659\pi\) | ||||
−0.421964 | + | 0.906612i | \(0.638659\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20.1620 | 0.726118 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −30.9422 | −1.11292 | −0.556458 | − | 0.830876i | \(-0.687840\pi\) | ||||
−0.556458 | + | 0.830876i | \(0.687840\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.12208 | −0.183990 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.40168 | 0.0502851 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 40.8785 | 1.46462 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −47.0997 | −1.68536 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.82187 | −0.0651083 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.72452 | −0.204317 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −44.1093 | −1.57233 | −0.786163 | − | 0.618019i | \(-0.787935\pi\) | ||||
−0.786163 | + | 0.618019i | \(0.787935\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.295696 | 0.0105271 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.9749 | −0.461336 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 22.6652 | 0.804864 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6.86073 | −0.243325 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −30.2678 | −1.07214 | −0.536070 | − | 0.844173i | \(-0.680092\pi\) | ||||
−0.536070 | + | 0.844173i | \(0.680092\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.0614 | −0.355945 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.63153 | 0.198980 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −39.4670 | −1.39276 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.78538 | −0.168663 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −19.4531 | −0.684781 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −20.5517 | −0.722561 | −0.361280 | − | 0.932457i | \(-0.617660\pi\) | ||||
−0.361280 | + | 0.932457i | \(0.617660\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23.4426 | −0.823182 | −0.411591 | − | 0.911369i | \(-0.635027\pi\) | ||||
−0.411591 | + | 0.911369i | \(0.635027\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10.8772 | −0.381480 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −14.8151 | −0.518951 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −17.3634 | −0.607469 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.75770 | 0.0963620 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27.1275 | −0.946755 | −0.473377 | − | 0.880860i | \(-0.656965\pi\) | ||||
−0.473377 | + | 0.880860i | \(0.656965\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.6446 | −0.475622 | −0.237811 | − | 0.971311i | \(-0.576430\pi\) | ||||
−0.237811 | + | 0.971311i | \(0.576430\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.78339 | 0.131721 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −37.5205 | −1.30472 | −0.652358 | − | 0.757911i | \(-0.726220\pi\) | ||||
−0.652358 | + | 0.757911i | \(0.726220\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.84587 | −0.341961 | −0.170981 | − | 0.985274i | \(-0.554694\pi\) | ||||
−0.170981 | + | 0.985274i | \(0.554694\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 25.1608 | 0.872818 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −12.0483 | −0.417450 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.97042 | 0.137402 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.12208 | −0.177045 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0.762629 | 0.0263289 | 0.0131644 | − | 0.999913i | \(-0.495810\pi\) | ||||
0.0131644 | + | 0.999913i | \(0.495810\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.6808 | −0.885545 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8.91436 | 0.307027 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.92740 | −0.135107 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.22130 | 0.0763247 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −19.4711 | −0.668248 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.9301 | 0.511796 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 42.8841 | 1.46832 | 0.734162 | − | 0.678974i | \(-0.237575\pi\) | ||||
0.734162 | + | 0.678974i | \(0.237575\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.73969 | −0.196293 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 35.6280 | 1.21703 | 0.608514 | − | 0.793543i | \(-0.291766\pi\) | ||||
0.608514 | + | 0.793543i | \(0.291766\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.95039 | 0.271264 | 0.135632 | − | 0.990759i | \(-0.456694\pi\) | ||||
0.135632 | + | 0.990759i | \(0.456694\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.77374 | 0.162689 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 54.3602 | 1.85044 | 0.925221 | − | 0.379430i | \(-0.123880\pi\) | ||||
0.925221 | + | 0.379430i | \(0.123880\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −24.2043 | −0.822971 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −13.6172 | −0.462465 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 26.5486 | 0.900601 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.11429 | 0.139407 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9.80937 | −0.331997 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.670274 | −0.0226594 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.3772 | 0.350413 | 0.175207 | − | 0.984532i | \(-0.443941\pi\) | ||||
0.175207 | + | 0.984532i | \(0.443941\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −10.3591 | −0.349404 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25.8167 | 0.869786 | 0.434893 | − | 0.900482i | \(-0.356786\pi\) | ||||
0.434893 | + | 0.900482i | \(0.356786\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.52466 | 0.0513088 | 0.0256544 | − | 0.999671i | \(-0.491833\pi\) | ||||
0.0256544 | + | 0.999671i | \(0.491833\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.63478 | −0.0549524 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13.2881 | 0.446172 | 0.223086 | − | 0.974799i | \(-0.428387\pi\) | ||||
0.223086 | + | 0.974799i | \(0.428387\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.48380 | 0.284538 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.78339 | 0.126748 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −31.3984 | −1.05071 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.26827 | 0.309804 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 29.3737 | 0.980761 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.33175 | 0.311231 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.6185 | 0.420383 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.02768 | −0.0674769 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 24.7538 | 0.822845 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −38.0633 | −1.26387 | −0.631936 | − | 0.775021i | \(-0.717739\pi\) | ||||
−0.631936 | + | 0.775021i | \(0.717739\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.47407 | 0.115228 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.9805 | −0.562589 | −0.281295 | − | 0.959621i | \(-0.590764\pi\) | ||||
−0.281295 | + | 0.959621i | \(0.590764\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −19.5223 | −0.646093 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.50889 | −0.182118 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.20851 | −0.304092 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19.4705 | 0.642272 | 0.321136 | − | 0.947033i | \(-0.395935\pi\) | ||||
0.321136 | + | 0.947033i | \(0.395935\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 25.7029 | 0.846939 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −51.2192 | −1.68590 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.09121 | 0.0687585 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 16.1717 | 0.531148 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −43.5080 | −1.42745 | −0.713725 | − | 0.700426i | \(-0.752993\pi\) | ||||
−0.713725 | + | 0.700426i | \(0.752993\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −37.5991 | −1.23226 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.07146 | −0.0678165 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.95853 | −0.227568 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.6446 | 0.543756 | 0.271878 | − | 0.962332i | \(-0.412355\pi\) | ||||
0.271878 | + | 0.962332i | \(0.412355\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11.9262 | 0.389198 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.64480 | 0.184015 | 0.0920077 | − | 0.995758i | \(-0.470672\pi\) | ||||
0.0920077 | + | 0.995758i | \(0.470672\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 50.8476 | 1.65583 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.670274 | −0.0218040 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −44.4840 | −1.44553 | −0.722767 | − | 0.691092i | \(-0.757130\pi\) | ||||
−0.722767 | + | 0.691092i | \(0.757130\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −42.9189 | −1.39321 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −32.0644 | −1.03976 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −10.4655 | −0.339012 | −0.169506 | − | 0.985529i | \(-0.554217\pi\) | ||||
−0.169506 | + | 0.985529i | \(0.554217\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.65532 | −0.0535650 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.89284 | −0.222814 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.83704 | −0.220779 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.76434 | −0.153688 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −17.9034 | −0.576929 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 13.2421 | 0.426280 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 47.4772 | 1.52676 | 0.763382 | − | 0.645948i | \(-0.223538\pi\) | ||||
0.763382 | + | 0.645948i | \(0.223538\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 10.5566 | 0.339128 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 38.5501 | 1.23713 | 0.618567 | − | 0.785732i | \(-0.287714\pi\) | ||||
0.618567 | + | 0.785732i | \(0.287714\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.08786 | −0.259285 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.11429 | 0.131763 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18.3124 | 0.585866 | 0.292933 | − | 0.956133i | \(-0.405369\pi\) | ||||
0.292933 | + | 0.956133i | \(0.405369\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21.3063 | 0.680951 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17.3694 | 0.554563 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16.1671 | 0.515650 | 0.257825 | − | 0.966192i | \(-0.416994\pi\) | ||||
0.257825 | + | 0.966192i | \(0.416994\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.51881 | 0.112118 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.66667 | −0.116711 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −21.5979 | −0.686772 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 57.2685 | 1.81919 | 0.909597 | − | 0.415492i | \(-0.136391\pi\) | ||||
0.909597 | + | 0.415492i | \(0.136391\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 10.3465 | 0.328337 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −13.9365 | −0.441817 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 43.2429 | 1.36952 | 0.684758 | − | 0.728771i | \(-0.259908\pi\) | ||||
0.684758 | + | 0.728771i | \(0.259908\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.09121 | 0.0661629 |
(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 | 8040.2.a.t.1.4 | ✓ | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8040.2.a.t.1.4 | ✓ | 7 | 1.1 | even | 1 | trivial |