Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4600,2,Mod(4049,4600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4600, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4600.4049");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4600 = 2^{3} \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4600.e (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(36.7311849298\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.431642176.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 19x^{4} + 97x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 920) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4049.2 | ||
Root | \(-2.95759i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4600.4049 |
Dual form | 4600.2.e.p.4049.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4600\mathbb{Z}\right)^\times\).
\(n\) | \(1151\) | \(1201\) | \(2301\) | \(2577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 2.95759i | − 1.70756i | −0.520631 | − | 0.853782i | \(-0.674303\pi\) | ||||
0.520631 | − | 0.853782i | \(-0.325697\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 3.95759i | − 1.49583i | −0.663796 | − | 0.747914i | \(-0.731056\pi\) | ||||
0.663796 | − | 0.747914i | \(-0.268944\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −5.74732 | −1.91577 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.957587 | −0.288723 | −0.144362 | − | 0.989525i | \(-0.546113\pi\) | ||||
−0.144362 | + | 0.989525i | \(0.546113\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 2.74732i | − 0.761970i | −0.924581 | − | 0.380985i | \(-0.875585\pi\) | ||||
0.924581 | − | 0.380985i | \(-0.124415\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 5.74732i | − 1.39393i | −0.717105 | − | 0.696965i | \(-0.754533\pi\) | ||||
0.717105 | − | 0.696965i | \(-0.245467\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.74732 | 1.54794 | 0.773971 | − | 0.633221i | \(-0.218268\pi\) | ||||
0.773971 | + | 0.633221i | \(0.218268\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −11.7049 | −2.55422 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000i | 0.208514i | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 8.12544i | 1.56374i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.21027 | −0.967522 | −0.483761 | − | 0.875200i | \(-0.660730\pi\) | ||||
−0.483761 | + | 0.875200i | \(0.660730\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.95759 | −1.07001 | −0.535007 | − | 0.844848i | \(-0.679691\pi\) | ||||
−0.535007 | + | 0.844848i | \(0.679691\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.83215i | 0.493013i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 9.12544i | − 1.50021i | −0.661317 | − | 0.750107i | \(-0.730002\pi\) | ||||
0.661317 | − | 0.750107i | \(-0.269998\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −8.12544 | −1.30111 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.252679 | 0.0394619 | 0.0197309 | − | 0.999805i | \(-0.493719\pi\) | ||||
0.0197309 | + | 0.999805i | \(0.493719\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.00000i | 1.21999i | 0.792406 | + | 0.609994i | \(0.208828\pi\) | ||||
−0.792406 | + | 0.609994i | \(0.791172\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 5.49464i | − 0.801476i | −0.916193 | − | 0.400738i | \(-0.868754\pi\) | ||||
0.916193 | − | 0.400738i | \(-0.131246\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −8.66249 | −1.23750 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −16.9982 | −2.38022 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 7.12544i | − 0.978754i | −0.872072 | − | 0.489377i | \(-0.837224\pi\) | ||||
0.872072 | − | 0.489377i | \(-0.162776\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 19.9558i | − 2.64321i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.78973 | 0.623570 | 0.311785 | − | 0.950153i | \(-0.399073\pi\) | ||||
0.311785 | + | 0.950153i | \(0.399073\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.4522 | 1.59434 | 0.797172 | − | 0.603752i | \(-0.206328\pi\) | ||||
0.797172 | + | 0.603752i | \(0.206328\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 22.7455i | 2.86567i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 9.12544i | − 1.11485i | −0.830227 | − | 0.557425i | \(-0.811789\pi\) | ||||
0.830227 | − | 0.557425i | \(-0.188211\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.95759 | 0.356052 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.66249 | 0.197302 | 0.0986509 | − | 0.995122i | \(-0.468547\pi\) | ||||
0.0986509 | + | 0.995122i | \(0.468547\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.3357i | 1.44379i | 0.692005 | + | 0.721893i | \(0.256728\pi\) | ||||
−0.692005 | + | 0.721893i | \(0.743272\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.78973i | 0.431880i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.8303 | −1.33102 | −0.665509 | − | 0.746390i | \(-0.731786\pi\) | ||||
−0.665509 | + | 0.746390i | \(0.731786\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.78973 | 0.754415 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.704908i | 0.0773737i | 0.999251 | + | 0.0386868i | \(0.0123175\pi\) | ||||
−0.999251 | + | 0.0386868i | \(0.987683\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 15.4098i | 1.65211i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.8303 | 1.67801 | 0.839007 | − | 0.544121i | \(-0.183137\pi\) | ||||
0.839007 | + | 0.544121i | \(0.183137\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.8728 | −1.13978 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 17.6201i | 1.82712i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.8728i | 1.10396i | 0.833857 | + | 0.551981i | \(0.186128\pi\) | ||||
−0.833857 | + | 0.551981i | \(0.813872\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.50356 | 0.553129 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.21027 | 0.916456 | 0.458228 | − | 0.888835i | \(-0.348484\pi\) | ||||
0.458228 | + | 0.888835i | \(0.348484\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.4522i | 1.22695i | 0.789712 | + | 0.613477i | \(0.210230\pi\) | ||||
−0.789712 | + | 0.613477i | \(0.789770\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 3.63080i | − 0.351003i | −0.984479 | − | 0.175501i | \(-0.943845\pi\) | ||||
0.984479 | − | 0.175501i | \(-0.0561546\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.6625 | −1.59598 | −0.797989 | − | 0.602672i | \(-0.794103\pi\) | ||||
−0.797989 | + | 0.602672i | \(0.794103\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −26.9893 | −2.56171 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 18.1147i | − 1.70409i | −0.523469 | − | 0.852045i | \(-0.675362\pi\) | ||||
0.523469 | − | 0.852045i | \(-0.324638\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 15.7897i | 1.45976i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −22.7455 | −2.08508 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.0830 | −0.916639 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 0.747321i | − 0.0673836i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.91517i | 0.524887i | 0.964947 | + | 0.262443i | \(0.0845283\pi\) | ||||
−0.964947 | + | 0.262443i | \(0.915472\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 23.6607 | 2.08321 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.40982 | 0.297917 | 0.148958 | − | 0.988843i | \(-0.452408\pi\) | ||||
0.148958 | + | 0.988843i | \(0.452408\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 26.7031i | − 2.31545i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.67321i | 0.142952i | 0.997442 | + | 0.0714761i | \(0.0227710\pi\) | ||||
−0.997442 | + | 0.0714761i | \(0.977229\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.62008 | −0.731146 | −0.365573 | − | 0.930783i | \(-0.619127\pi\) | ||||
−0.365573 | + | 0.930783i | \(0.619127\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −16.2509 | −1.36857 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.63080i | 0.219998i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 25.6201i | 2.11311i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 23.0830 | 1.89104 | 0.945518 | − | 0.325571i | \(-0.105556\pi\) | ||||
0.945518 | + | 0.325571i | \(0.105556\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.7879 | 0.877910 | 0.438955 | − | 0.898509i | \(-0.355349\pi\) | ||||
0.438955 | + | 0.898509i | \(0.355349\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 33.0317i | 2.67045i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 8.19955i | − 0.654395i | −0.944956 | − | 0.327198i | \(-0.893896\pi\) | ||||
0.944956 | − | 0.327198i | \(-0.106104\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −21.0741 | −1.67129 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.95759 | 0.311902 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.6625i | 1.30511i | 0.757743 | + | 0.652554i | \(0.226302\pi\) | ||||
−0.757743 | + | 0.652554i | \(0.773698\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.00000i | 0.619059i | 0.950890 | + | 0.309529i | \(0.100171\pi\) | ||||
−0.950890 | + | 0.309529i | \(0.899829\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.45223 | 0.419402 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −38.7790 | −2.96551 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.87276i | 0.674584i | 0.941400 | + | 0.337292i | \(0.109511\pi\) | ||||
−0.941400 | + | 0.337292i | \(0.890489\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 14.1661i | − 1.06479i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.49464 | −0.111715 | −0.0558574 | − | 0.998439i | \(-0.517789\pi\) | ||||
−0.0558574 | + | 0.998439i | \(0.517789\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.5777 | −0.934891 | −0.467445 | − | 0.884022i | \(-0.654826\pi\) | ||||
−0.467445 | + | 0.884022i | \(0.654826\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 36.8285i | − 2.72244i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.50356i | 0.402460i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 32.1571 | 2.33909 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.9045 | 1.22316 | 0.611582 | − | 0.791181i | \(-0.290534\pi\) | ||||
0.611582 | + | 0.791181i | \(0.290534\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.91517i | 0.713710i | 0.934160 | + | 0.356855i | \(0.116151\pi\) | ||||
−0.934160 | + | 0.356855i | \(0.883849\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 4.53705i | − 0.323252i | −0.986852 | − | 0.161626i | \(-0.948326\pi\) | ||||
0.986852 | − | 0.161626i | \(-0.0516738\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.0000 | 0.992434 | 0.496217 | − | 0.868199i | \(-0.334722\pi\) | ||||
0.496217 | + | 0.868199i | \(0.334722\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −26.9893 | −1.90368 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 20.6201i | 1.44725i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 5.74732i | − 0.399466i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.46115 | −0.446927 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.70491 | 0.599271 | 0.299635 | − | 0.954054i | \(-0.403135\pi\) | ||||
0.299635 | + | 0.954054i | \(0.403135\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 4.91697i | − 0.336905i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 23.5777i | 1.60056i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 36.4839 | 2.46536 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −15.7897 | −1.06213 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 5.40982i | − 0.362268i | −0.983458 | − | 0.181134i | \(-0.942023\pi\) | ||||
0.983458 | − | 0.181134i | \(-0.0579768\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.3250i | 1.14990i | 0.818189 | + | 0.574950i | \(0.194978\pi\) | ||||
−0.818189 | + | 0.574950i | \(0.805022\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.4098 | 0.753982 | 0.376991 | − | 0.926217i | \(-0.376959\pi\) | ||||
0.376991 | + | 0.926217i | \(0.376959\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 11.2085 | 0.737463 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.08483i | 0.136581i | 0.997665 | + | 0.0682907i | \(0.0217546\pi\) | ||||
−0.997665 | + | 0.0682907i | \(0.978245\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 34.9893i | 2.27280i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.5353 | 1.19895 | 0.599473 | − | 0.800395i | \(-0.295377\pi\) | ||||
0.599473 | + | 0.800395i | \(0.295377\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.2509 | 0.660317 | 0.330159 | − | 0.943925i | \(-0.392898\pi\) | ||||
0.330159 | + | 0.943925i | \(0.392898\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4.29509i | 0.275530i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 18.5371i | − 1.17948i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.08483 | 0.132120 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.2527 | −1.08898 | −0.544490 | − | 0.838768i | \(-0.683277\pi\) | ||||
−0.544490 | + | 0.838768i | \(0.683277\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 0.957587i | − 0.0602030i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 28.9045i | − 1.80301i | −0.432768 | − | 0.901505i | \(-0.642463\pi\) | ||||
0.432768 | − | 0.901505i | \(-0.357537\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −36.1147 | −2.24406 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 29.9451 | 1.85355 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.24196i | 0.323233i | 0.986854 | + | 0.161617i | \(0.0516708\pi\) | ||||
−0.986854 | + | 0.161617i | \(0.948329\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 46.8196i | − 2.86531i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.37992 | 0.328019 | 0.164010 | − | 0.986459i | \(-0.447557\pi\) | ||||
0.164010 | + | 0.986459i | \(0.447557\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.5371 | −0.700826 | −0.350413 | − | 0.936595i | \(-0.613959\pi\) | ||||
−0.350413 | + | 0.936595i | \(0.613959\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 32.1571i | 1.94624i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 5.83035i | − 0.350312i | −0.984541 | − | 0.175156i | \(-0.943957\pi\) | ||||
0.984541 | − | 0.175156i | \(-0.0560429\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 34.2402 | 2.04990 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.0741 | 0.660626 | 0.330313 | − | 0.943871i | \(-0.392846\pi\) | ||||
0.330313 | + | 0.943871i | \(0.392846\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 3.86384i | − 0.229682i | −0.993384 | − | 0.114841i | \(-0.963364\pi\) | ||||
0.993384 | − | 0.114841i | \(-0.0366358\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 1.00000i | − 0.0590281i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.0317 | −0.943041 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 32.1571 | 1.88508 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 1.54597i | − 0.0903167i | −0.998980 | − | 0.0451583i | \(-0.985621\pi\) | ||||
0.998980 | − | 0.0451583i | \(-0.0143792\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 7.78082i | − 0.451489i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.74732 | 0.158882 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 31.6607 | 1.82489 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 27.2402i | − 1.56491i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.45223i | 0.368248i | 0.982903 | + | 0.184124i | \(0.0589448\pi\) | ||||
−0.982903 | + | 0.184124i | \(0.941055\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 36.8285 | 2.09510 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.8196 | 1.29398 | 0.646991 | − | 0.762497i | \(-0.276027\pi\) | ||||
0.646991 | + | 0.762497i | \(0.276027\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 16.8620i | − 0.953099i | −0.879148 | − | 0.476550i | \(-0.841887\pi\) | ||||
0.879148 | − | 0.476550i | \(-0.158113\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.33751i | 0.0751218i | 0.999294 | + | 0.0375609i | \(0.0119588\pi\) | ||||
−0.999294 | + | 0.0375609i | \(0.988041\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.98928 | 0.279346 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.7384 | −0.599359 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 38.7790i | − 2.15772i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 49.2808i | 2.72523i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −21.7455 | −1.19887 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −32.2808 | −1.77431 | −0.887156 | − | 0.461470i | \(-0.847322\pi\) | ||||
−0.887156 | + | 0.461470i | \(0.847322\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 52.4468i | 2.87407i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.83215i | 0.263224i | 0.991301 | + | 0.131612i | \(0.0420153\pi\) | ||||
−0.991301 | + | 0.131612i | \(0.957985\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −53.5759 | −2.90984 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.70491 | 0.308938 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.57947i | 0.355258i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 34.6183i | 1.85841i | 0.369569 | + | 0.929203i | \(0.379505\pi\) | ||||
−0.369569 | + | 0.929203i | \(0.620495\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −26.9558 | −1.44291 | −0.721455 | − | 0.692461i | \(-0.756526\pi\) | ||||
−0.721455 | + | 0.692461i | \(0.756526\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 22.3232 | 1.19152 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 8.00000i | − 0.425797i | −0.977074 | − | 0.212899i | \(-0.931710\pi\) | ||||
0.977074 | − | 0.212899i | \(-0.0682904\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 67.2719i | 3.56040i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −0.420532 | −0.0221949 | −0.0110974 | − | 0.999938i | \(-0.503532\pi\) | ||||
−0.0110974 | + | 0.999938i | \(0.503532\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 26.5263 | 1.39612 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 29.8214i | 1.56522i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 11.7156i | − 0.611551i | −0.952104 | − | 0.305775i | \(-0.901084\pi\) | ||||
0.952104 | − | 0.305775i | \(-0.0989156\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.45223 | −0.0756000 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −28.1995 | −1.46405 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 28.1661i | − 1.45838i | −0.684310 | − | 0.729192i | \(-0.739896\pi\) | ||||
0.684310 | − | 0.729192i | \(-0.260104\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14.3143i | 0.737223i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.3781 | −1.40632 | −0.703160 | − | 0.711032i | \(-0.748228\pi\) | ||||
−0.703160 | + | 0.711032i | \(0.748228\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 17.4946 | 0.896278 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 31.7754i | − 1.62365i | −0.583902 | − | 0.811824i | \(-0.698475\pi\) | ||||
0.583902 | − | 0.811824i | \(-0.301525\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 45.9786i | − 2.33722i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.7031 | 0.948285 | 0.474143 | − | 0.880448i | \(-0.342758\pi\) | ||||
0.474143 | + | 0.880448i | \(0.342758\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.74732 | 0.290655 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 10.0848i | − 0.508712i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 39.6924i | 1.99210i | 0.0887714 | + | 0.996052i | \(0.471706\pi\) | ||||
−0.0887714 | + | 0.996052i | \(0.528294\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −78.9768 | −3.95378 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11.3250 | −0.565543 | −0.282771 | − | 0.959187i | \(-0.591254\pi\) | ||||
−0.282771 | + | 0.959187i | \(0.591254\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.3674i | 0.815318i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.73840i | 0.433147i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.45223 | −0.467383 | −0.233691 | − | 0.972311i | \(-0.575081\pi\) | ||||
−0.233691 | + | 0.972311i | \(0.575081\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.94867 | 0.244100 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 18.9558i | − 0.932753i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 25.4946i | 1.24848i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 33.2402 | 1.62389 | 0.811944 | − | 0.583735i | \(-0.198409\pi\) | ||||
0.811944 | + | 0.583735i | \(0.198409\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −38.8285 | −1.89239 | −0.946194 | − | 0.323600i | \(-0.895107\pi\) | ||||
−0.946194 | + | 0.323600i | \(0.895107\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 31.5795i | 1.53545i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 49.2808i | − 2.38486i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.78082 | 0.375661 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.4839 | −0.601329 | −0.300665 | − | 0.953730i | \(-0.597209\pi\) | ||||
−0.300665 | + | 0.953730i | \(0.597209\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 5.78793i | − 0.278150i | −0.990282 | − | 0.139075i | \(-0.955587\pi\) | ||||
0.990282 | − | 0.139075i | \(-0.0444130\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.74732i | 0.322768i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.9241 | 0.569106 | 0.284553 | − | 0.958660i | \(-0.408155\pi\) | ||||
0.284553 | + | 0.958660i | \(0.408155\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 49.7861 | 2.37077 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 39.3973i | 1.87182i | 0.352236 | + | 0.935911i | \(0.385421\pi\) | ||||
−0.352236 | + | 0.935911i | \(0.614579\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 68.2701i | − 3.22906i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −21.3674 | −1.00839 | −0.504195 | − | 0.863590i | \(-0.668211\pi\) | ||||
−0.504195 | + | 0.863590i | \(0.668211\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.241962 | −0.0113936 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 31.9063i | − 1.49909i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.3656i | 0.952663i | 0.879266 | + | 0.476331i | \(0.158034\pi\) | ||||
−0.879266 | + | 0.476331i | \(0.841966\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 46.6995 | 2.17975 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −27.4946 | −1.28055 | −0.640277 | − | 0.768144i | \(-0.721180\pi\) | ||||
−0.640277 | + | 0.768144i | \(0.721180\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 16.8196i | − 0.781675i | −0.920460 | − | 0.390837i | \(-0.872186\pi\) | ||||
0.920460 | − | 0.390837i | \(-0.127814\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 24.4504i | 1.13143i | 0.824601 | + | 0.565715i | \(0.191400\pi\) | ||||
−0.824601 | + | 0.565715i | \(0.808600\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −36.1147 | −1.66762 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −24.2509 | −1.11742 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 7.66070i | − 0.352239i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 40.9522i | 1.87507i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.5688 | −0.482899 | −0.241449 | − | 0.970413i | \(-0.577623\pi\) | ||||
−0.241449 | + | 0.970413i | \(0.577623\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −25.0705 | −1.14312 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 11.7049i | − 0.532592i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.0741i | 0.592444i | 0.955119 | + | 0.296222i | \(0.0957269\pi\) | ||||
−0.955119 | + | 0.296222i | \(0.904273\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 49.2808 | 2.22855 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.22098 | 0.100232 | 0.0501158 | − | 0.998743i | \(-0.484041\pi\) | ||||
0.0501158 | + | 0.998743i | \(0.484041\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 29.9451i | 1.34866i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 6.57947i | − 0.295129i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.87456 | −0.128683 | −0.0643415 | − | 0.997928i | \(-0.520495\pi\) | ||||
−0.0643415 | + | 0.997928i | \(0.520495\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 23.6607 | 1.05708 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.36740i | 0.417672i | 0.977951 | + | 0.208836i | \(0.0669675\pi\) | ||||
−0.977951 | + | 0.208836i | \(0.933033\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 16.1254i | − 0.716156i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 40.5866 | 1.79897 | 0.899484 | − | 0.436953i | \(-0.143942\pi\) | ||||
0.899484 | + | 0.436953i | \(0.143942\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 48.8196 | 2.15965 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 54.8250i | 2.42058i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.26160i | 0.231405i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 26.2420 | 1.15189 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 34.6714 | 1.51898 | 0.759491 | − | 0.650518i | \(-0.225448\pi\) | ||||
0.759491 | + | 0.650518i | \(0.225448\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 35.4098i | 1.54836i | 0.632964 | + | 0.774182i | \(0.281838\pi\) | ||||
−0.632964 | + | 0.774182i | \(0.718162\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 34.2402i | 1.49152i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −27.5281 | −1.19462 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 0.694191i | − 0.0300687i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.42053i | 0.190760i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.29509 | 0.357295 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 37.0705 | 1.59379 | 0.796893 | − | 0.604121i | \(-0.206475\pi\) | ||||
0.796893 | + | 0.604121i | \(0.206475\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 37.1995i | 1.59639i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 21.4187i | − 0.915799i | −0.889004 | − | 0.457899i | \(-0.848602\pi\) | ||||
0.889004 | − | 0.457899i | \(-0.151398\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −71.5670 | −3.05440 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −35.1553 | −1.49767 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 46.8196i | 1.99097i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 20.9558i | − 0.887925i | −0.896045 | − | 0.443963i | \(-0.853572\pi\) | ||||
0.896045 | − | 0.443963i | \(-0.146428\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21.9786 | 0.929594 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16.2773 | 0.687226 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.70491i | 0.282578i | 0.989968 | + | 0.141289i | \(0.0451247\pi\) | ||||
−0.989968 | + | 0.141289i | \(0.954875\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 26.8710i | − 1.12847i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.00000 | −0.251533 | −0.125767 | − | 0.992060i | \(-0.540139\pi\) | ||||
−0.125767 | + | 0.992060i | \(0.540139\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.2933 | 0.556307 | 0.278154 | − | 0.960537i | \(-0.410278\pi\) | ||||
0.278154 | + | 0.960537i | \(0.410278\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 49.9964i | − 2.08863i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 23.2402i | − 0.967501i | −0.875206 | − | 0.483750i | \(-0.839274\pi\) | ||||
0.875206 | − | 0.483750i | \(-0.160726\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 29.3250 | 1.21870 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.78973 | 0.115738 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.82323i | 0.282589i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 17.6112i | − 0.726891i | −0.931616 | − | 0.363445i | \(-0.881600\pi\) | ||||
0.931616 | − | 0.363445i | \(-0.118400\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −40.1978 | −1.65632 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13.4187 | −0.551973 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 41.5759i | − 1.70732i | −0.520834 | − | 0.853658i | \(-0.674379\pi\) | ||||
0.520834 | − | 0.853658i | \(-0.325621\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 41.4062i | − 1.69464i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17.7138 | −0.723767 | −0.361884 | − | 0.932223i | \(-0.617866\pi\) | ||||
−0.361884 | + | 0.932223i | \(0.617866\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −46.7772 | −1.90808 | −0.954041 | − | 0.299675i | \(-0.903122\pi\) | ||||
−0.954041 | + | 0.299675i | \(0.903122\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 52.4468i | 2.13580i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 42.9893i | − 1.74488i | −0.488720 | − | 0.872441i | \(-0.662536\pi\) | ||||
0.488720 | − | 0.872441i | \(-0.337464\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 60.9857 | 2.47126 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.0955 | −0.610700 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 32.6500i | − 1.31872i | −0.751827 | − | 0.659360i | \(-0.770827\pi\) | ||||
0.751827 | − | 0.659360i | \(-0.229173\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.3232i | 0.455854i | 0.973678 | + | 0.227927i | \(0.0731948\pi\) | ||||
−0.973678 | + | 0.227927i | \(0.926805\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.6625 | 0.428562 | 0.214281 | − | 0.976772i | \(-0.431259\pi\) | ||||
0.214281 | + | 0.976772i | \(0.431259\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.12544 | −0.326063 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 62.6500i | − 2.51002i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 19.1094i | 0.763156i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −52.4468 | −2.09119 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.24376 | 0.208751 | 0.104375 | − | 0.994538i | \(-0.466716\pi\) | ||||
0.104375 | + | 0.994538i | \(0.466716\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 25.7455i | − 1.02329i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 23.7987i | 0.942937i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.55489 | −0.377986 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30.4205 | 1.20154 | 0.600769 | − | 0.799422i | \(-0.294861\pi\) | ||||
0.600769 | + | 0.799422i | \(0.294861\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 9.37992i | − 0.369908i | −0.982747 | − | 0.184954i | \(-0.940786\pi\) | ||||
0.982747 | − | 0.184954i | \(-0.0592136\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18.6714i | 0.734049i | 0.930211 | + | 0.367024i | \(0.119623\pi\) | ||||
−0.930211 | + | 0.367024i | \(0.880377\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.58659 | −0.180039 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 69.7330 | 2.73305 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.0723i | 0.472426i | 0.971701 | + | 0.236213i | \(0.0759063\pi\) | ||||
−0.971701 | + | 0.236213i | \(0.924094\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 70.8973i | − 2.76597i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21.2402 | −0.827399 | −0.413700 | − | 0.910413i | \(-0.635764\pi\) | ||||
−0.413700 | + | 0.910413i | \(0.635764\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.9362 | −1.04769 | −0.523847 | − | 0.851812i | \(-0.675504\pi\) | ||||
−0.523847 | + | 0.851812i | \(0.675504\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 46.6995i | 1.81366i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 5.21027i | − 0.201742i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −16.0000 | −0.618596 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11.9241 | −0.460324 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 11.4098i | − 0.439816i | −0.975521 | − | 0.219908i | \(-0.929424\pi\) | ||||
0.975521 | − | 0.219908i | \(-0.0705757\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.8638i | 0.455965i | 0.973665 | + | 0.227982i | \(0.0732128\pi\) | ||||
−0.973665 | + | 0.227982i | \(0.926787\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 43.0299 | 1.65134 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 51.2402 | 1.96353 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10.0723i | 0.385406i | 0.981257 | + | 0.192703i | \(0.0617254\pi\) | ||||
−0.981257 | + | 0.192703i | \(0.938275\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 33.7455i | − 1.28747i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −19.5759 | −0.745781 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −45.9964 | −1.74979 | −0.874893 | − | 0.484317i | \(-0.839068\pi\) | ||||
−0.874893 | + | 0.484317i | \(0.839068\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 21.7808i | − 0.827385i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 1.45223i | − 0.0550071i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.16605 | 0.233222 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21.2312 | −0.801893 | −0.400947 | − | 0.916101i | \(-0.631319\pi\) | ||||
−0.400947 | + | 0.916101i | \(0.631319\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 61.5723i | − 2.32224i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 36.4504i | − 1.37086i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −31.3781 | −1.17843 | −0.589215 | − | 0.807976i | \(-0.700563\pi\) | ||||
−0.589215 | + | 0.807976i | \(0.700563\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 67.9928 | 2.54993 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 5.95759i | − 0.223113i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 54.8196i | − 2.04728i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 20.4629 | 0.763139 | 0.381570 | − | 0.924340i | \(-0.375384\pi\) | ||||
0.381570 | + | 0.924340i | \(0.375384\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 49.2808 | 1.83531 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 30.3179i | − 1.12753i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 14.9875i | − 0.555855i | −0.960602 | − | 0.277928i | \(-0.910352\pi\) | ||||
0.960602 | − | 0.277928i | \(-0.0896475\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 33.0723 | 1.22490 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 45.9786 | 1.70058 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 22.2844i | − 0.823092i | −0.911389 | − | 0.411546i | \(-0.864989\pi\) | ||||
0.911389 | − | 0.411546i | \(-0.135011\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.73840i | 0.321883i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −30.9344 | −1.13794 | −0.568969 | − | 0.822359i | \(-0.692658\pi\) | ||||
−0.568969 | + | 0.822359i | \(0.692658\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −54.8250 | −2.01404 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 44.8285i | − 1.64460i | −0.569054 | − | 0.822300i | \(-0.692691\pi\) | ||||
0.569054 | − | 0.822300i | \(-0.307309\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 4.05133i | − 0.148230i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −14.3692 | −0.525039 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32.1661 | 1.17376 | 0.586878 | − | 0.809675i | \(-0.300357\pi\) | ||||
0.586878 | + | 0.809675i | \(0.300357\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 51.0263i | 1.85950i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 40.6835i | − 1.47867i | −0.673340 | − | 0.739333i | \(-0.735141\pi\) | ||||
0.673340 | − | 0.739333i | \(-0.264859\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.83215 | −0.102800 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.4415 | 1.03100 | 0.515502 | − | 0.856888i | \(-0.327605\pi\) | ||||
0.515502 | + | 0.856888i | \(0.327605\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 65.9433i | 2.38731i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 13.1589i | − 0.475142i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40.4205 | 1.45760 | 0.728801 | − | 0.684726i | \(-0.240078\pi\) | ||||
0.728801 | + | 0.684726i | \(0.240078\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −85.4874 | −3.07876 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24.5688i | 0.883677i | 0.897095 | + | 0.441838i | \(0.145673\pi\) | ||||
−0.897095 | + | 0.441838i | \(0.854327\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 106.812i | 3.83187i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.70491 | 0.0610847 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.59198 | −0.0569656 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 42.3357i | − 1.51295i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.7790i | 0.419877i | 0.977715 | + | 0.209938i | \(0.0673263\pi\) | ||||
−0.977715 | + | 0.209938i | \(0.932674\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 15.5036 | 0.551941 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −71.6906 | −2.54902 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 34.2103i | − 1.21484i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13.8602i | 0.490955i | 0.969402 | + | 0.245478i | \(0.0789448\pi\) | ||||
−0.969402 | + | 0.245478i | \(0.921055\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −31.5795 | −1.11720 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −90.9821 | −3.21469 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 11.8125i | − 0.416854i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 15.9116i | − 0.560114i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 52.0830 | 1.83114 | 0.915571 | − | 0.402157i | \(-0.131739\pi\) | ||||
0.915571 | + | 0.402157i | \(0.131739\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −40.7013 | −1.42922 | −0.714608 | − | 0.699525i | \(-0.753395\pi\) | ||||
−0.714608 | + | 0.699525i | \(0.753395\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 34.1218i | 1.19671i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 53.9786i | 1.88847i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 62.4892 | 2.18355 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.0000 | 0.349002 | 0.174501 | − | 0.984657i | \(-0.444169\pi\) | ||||
0.174501 | + | 0.984657i | \(0.444169\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 42.9009i | − 1.49543i | −0.664020 | − | 0.747715i | \(-0.731151\pi\) | ||||
0.664020 | − | 0.747715i | \(-0.268849\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 39.4397i | − 1.37145i | −0.727859 | − | 0.685727i | \(-0.759485\pi\) | ||||
0.727859 | − | 0.685727i | \(-0.240515\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −29.5460 | −1.02617 | −0.513087 | − | 0.858337i | \(-0.671498\pi\) | ||||
−0.513087 | + | 0.858337i | \(0.671498\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17.2438 | −0.598179 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 49.7861i | 1.72499i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 48.4080i | − 1.67323i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.09554 | 0.0378223 | 0.0189112 | − | 0.999821i | \(-0.493980\pi\) | ||||
0.0189112 | + | 0.999821i | \(0.493980\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.85313 | −0.0639009 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 32.7526i | − 1.12806i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 39.9045i | 1.37113i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −11.4277 | −0.392196 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.12544 | 0.312816 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 10.0937i | − 0.345603i | −0.984957 | − | 0.172802i | \(-0.944718\pi\) | ||||
0.984957 | − | 0.172802i | \(-0.0552819\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 41.8303i | − 1.42890i | −0.699688 | − | 0.714449i | \(-0.746678\pi\) | ||||
0.699688 | − | 0.714449i | \(-0.253322\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.35848 | 0.114590 | 0.0572950 | − | 0.998357i | \(-0.481752\pi\) | ||||
0.0572950 | + | 0.998357i | \(0.481752\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.95759 | −0.100794 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 3.83395i | − 0.130509i | −0.997869 | − | 0.0652545i | \(-0.979214\pi\) | ||||
0.997869 | − | 0.0652545i | \(-0.0207859\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 47.4151i | 1.61030i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.3286 | 0.384296 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −25.0705 | −0.849482 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 62.4892i | − 2.11494i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 15.5263i | − 0.524287i | −0.965029 | − | 0.262144i | \(-0.915571\pi\) | ||||
0.965029 | − | 0.262144i | \(-0.0844294\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.57235 | −0.154221 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26.9893 | 0.909292 | 0.454646 | − | 0.890672i | \(-0.349766\pi\) | ||||
0.454646 | + | 0.890672i | \(0.349766\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.5884i | 0.726507i | 0.931690 | + | 0.363254i | \(0.118334\pi\) | ||||
−0.931690 | + | 0.363254i | \(0.881666\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 49.4098i | − 1.65902i | −0.558492 | − | 0.829510i | \(-0.688620\pi\) | ||||
0.558492 | − | 0.829510i | \(-0.311380\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 23.4098 | 0.785140 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.50176 | −0.217817 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 37.0741i | − 1.24064i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 8.12544i | − 0.271301i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 31.0406 | 1.03526 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −40.9522 | −1.36432 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 93.6393i | − 3.11612i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.54957i | 0.317088i | 0.987352 | + | 0.158544i | \(0.0506800\pi\) | ||||
−0.987352 | + | 0.158544i | \(0.949320\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −52.9344 | −1.75572 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −47.3036 | −1.56724 | −0.783618 | − | 0.621243i | \(-0.786628\pi\) | ||||
−0.783618 | + | 0.621243i | \(0.786628\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 0.675011i | − 0.0223396i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 13.4946i | − 0.445632i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.00000 | −0.263896 | −0.131948 | − | 0.991257i | \(-0.542123\pi\) | ||||
−0.131948 | + | 0.991257i | \(0.542123\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 19.0830 | 0.628807 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 4.56741i | − 0.150338i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 71.5670i | − 2.35057i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 19.6942 | 0.646145 | 0.323073 | − | 0.946374i | \(-0.395284\pi\) | ||||
0.323073 | + | 0.946374i | \(0.395284\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −58.4486 | −1.91558 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 67.4910i | − 2.20956i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 31.8214i | 1.03956i | 0.854300 | + | 0.519780i | \(0.173986\pi\) | ||||
−0.854300 | + | 0.519780i | \(0.826014\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −49.8710 | −1.62748 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.36740 | −0.0771751 | −0.0385876 | − | 0.999255i | \(-0.512286\pi\) | ||||
−0.0385876 | + | 0.999255i | \(0.512286\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.252679i | 0.00822837i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.90266i | 0.321793i | 0.986971 | + | 0.160897i | \(0.0514386\pi\) | ||||
−0.986971 | + | 0.160897i | \(0.948561\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 33.8901 | 1.10012 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.95579 | 0.128275 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 31.5442i | − 1.02182i | −0.859635 | − | 0.510908i | \(-0.829309\pi\) | ||||
0.859635 | − | 0.510908i | \(-0.170691\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 14.7562i | − 0.477001i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.62188 | 0.213832 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.49284 | 0.144930 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 20.8674i | 0.672441i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.5973i | 0.501575i | 0.968042 | + | 0.250788i | \(0.0806896\pi\) | ||||
−0.968042 | + | 0.250788i | \(0.919310\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −114.692 | −3.68445 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −47.1022 | −1.51158 | −0.755791 | − | 0.654813i | \(-0.772747\pi\) | ||||
−0.755791 | + | 0.654813i | \(0.772747\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 34.1147i | 1.09367i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 28.9469i | − 0.926092i | −0.886334 | − | 0.463046i | \(-0.846756\pi\) | ||||
0.886334 | − | 0.463046i | \(-0.153244\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15.1589 | −0.484482 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 95.7647 | 3.05753 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 36.2312i | − 1.15560i | −0.816179 | − | 0.577799i | \(-0.803912\pi\) | ||||
0.816179 | − | 0.577799i | \(-0.196088\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 64.3143i | 2.04715i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.00000 | −0.254385 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −35.1750 | −1.11737 | −0.558685 | − | 0.829380i | \(-0.688694\pi\) | ||||
−0.558685 | + | 0.829380i | \(0.688694\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 95.4732i | 3.02975i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 19.2402i | − 0.609342i | −0.952458 | − | 0.304671i | \(-0.901453\pi\) | ||||
0.952458 | − | 0.304671i | \(-0.0985465\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 74.1482 | 2.34595 |
(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 | 4600.2.e.p.4049.2 | 6 | ||
5.2 | odd | 4 | 920.2.a.h.1.1 | ✓ | 3 | ||
5.3 | odd | 4 | 4600.2.a.x.1.3 | 3 | |||
5.4 | even | 2 | inner | 4600.2.e.p.4049.5 | 6 | ||
15.2 | even | 4 | 8280.2.a.bj.1.3 | 3 | |||
20.3 | even | 4 | 9200.2.a.ce.1.1 | 3 | |||
20.7 | even | 4 | 1840.2.a.s.1.3 | 3 | |||
40.27 | even | 4 | 7360.2.a.cc.1.1 | 3 | |||
40.37 | odd | 4 | 7360.2.a.by.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.2.a.h.1.1 | ✓ | 3 | 5.2 | odd | 4 | ||
1840.2.a.s.1.3 | 3 | 20.7 | even | 4 | |||
4600.2.a.x.1.3 | 3 | 5.3 | odd | 4 | |||
4600.2.e.p.4049.2 | 6 | 1.1 | even | 1 | trivial | ||
4600.2.e.p.4049.5 | 6 | 5.4 | even | 2 | inner | ||
7360.2.a.by.1.3 | 3 | 40.37 | odd | 4 | |||
7360.2.a.cc.1.1 | 3 | 40.27 | even | 4 | |||
8280.2.a.bj.1.3 | 3 | 15.2 | even | 4 | |||
9200.2.a.ce.1.1 | 3 | 20.3 | even | 4 |