Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,3,Mod(244,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.244");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.0163796583\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 244.2 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.244 |
Dual form | 441.3.d.b.244.1 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.500000 | −0.250000 | − | 0.968246i | \(-0.580431\pi\) | ||||
−0.250000 | + | 0.968246i | \(0.580431\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.00000 | −0.750000 | ||||||||
\(5\) | 5.19615i | 1.03923i | 0.854400 | + | 0.519615i | \(0.173925\pi\) | ||||
−0.854400 | + | 0.519615i | \(0.826075\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 7.00000 | 0.875000 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − 5.19615i | − 0.519615i | ||||||||
\(11\) | 11.0000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 6.92820i | − 0.532939i | −0.963843 | − | 0.266469i | \(-0.914143\pi\) | ||||
0.963843 | − | 0.266469i | \(-0.0858571\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 5.00000 | 0.312500 | ||||||||
\(17\) | 24.2487i | 1.42639i | 0.700963 | + | 0.713197i | \(0.252754\pi\) | ||||
−0.700963 | + | 0.713197i | \(0.747246\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 3.46410i | − 0.182321i | −0.995836 | − | 0.0911606i | \(-0.970942\pi\) | ||||
0.995836 | − | 0.0911606i | \(-0.0290577\pi\) | |||||||
\(20\) | − 15.5885i | − 0.779423i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −11.0000 | −0.500000 | ||||||||
\(23\) | −28.0000 | −1.21739 | −0.608696 | − | 0.793404i | \(-0.708307\pi\) | ||||
−0.608696 | + | 0.793404i | \(0.708307\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.00000 | −0.0800000 | ||||||||
\(26\) | 6.92820i | 0.266469i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −25.0000 | −0.862069 | −0.431034 | − | 0.902335i | \(-0.641851\pi\) | ||||
−0.431034 | + | 0.902335i | \(0.641851\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 32.9090i | 1.06158i | 0.847504 | + | 0.530790i | \(0.178105\pi\) | ||||
−0.847504 | + | 0.530790i | \(0.821895\pi\) | |||||||
\(32\) | −33.0000 | −1.03125 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − 24.2487i | − 0.713197i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −58.0000 | −1.56757 | −0.783784 | − | 0.621034i | \(-0.786713\pi\) | ||||
−0.783784 | + | 0.621034i | \(0.786713\pi\) | |||||||
\(38\) | 3.46410i | 0.0911606i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 36.3731i | 0.909327i | ||||||||
\(41\) | 3.46410i | 0.0844903i | 0.999107 | + | 0.0422451i | \(0.0134510\pi\) | ||||
−0.999107 | + | 0.0422451i | \(0.986549\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 26.0000 | 0.604651 | 0.302326 | − | 0.953205i | \(-0.402237\pi\) | ||||
0.302326 | + | 0.953205i | \(0.402237\pi\) | |||||||
\(44\) | −33.0000 | −0.750000 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 28.0000 | 0.608696 | ||||||||
\(47\) | 76.2102i | 1.62149i | 0.585396 | + | 0.810747i | \(0.300939\pi\) | ||||
−0.585396 | + | 0.810747i | \(0.699061\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.00000 | 0.0400000 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 20.7846i | 0.399704i | ||||||||
\(53\) | −31.0000 | −0.584906 | −0.292453 | − | 0.956280i | \(-0.594471\pi\) | ||||
−0.292453 | + | 0.956280i | \(0.594471\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 57.1577i | 1.03923i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 25.0000 | 0.431034 | ||||||||
\(59\) | − 8.66025i | − 0.146784i | −0.997303 | − | 0.0733920i | \(-0.976618\pi\) | ||||
0.997303 | − | 0.0733920i | \(-0.0233824\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.8564i | 0.227154i | 0.993529 | + | 0.113577i | \(0.0362309\pi\) | ||||
−0.993529 | + | 0.113577i | \(0.963769\pi\) | |||||||
\(62\) | − 32.9090i | − 0.530790i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 13.0000 | 0.203125 | ||||||||
\(65\) | 36.0000 | 0.553846 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −52.0000 | −0.776119 | −0.388060 | − | 0.921634i | \(-0.626855\pi\) | ||||
−0.388060 | + | 0.921634i | \(0.626855\pi\) | |||||||
\(68\) | − 72.7461i | − 1.06980i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −64.0000 | −0.901408 | −0.450704 | − | 0.892673i | \(-0.648827\pi\) | ||||
−0.450704 | + | 0.892673i | \(0.648827\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 6.92820i | − 0.0949069i | −0.998873 | − | 0.0474534i | \(-0.984889\pi\) | ||||
0.998873 | − | 0.0474534i | \(-0.0151106\pi\) | |||||||
\(74\) | 58.0000 | 0.783784 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 10.3923i | 0.136741i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 17.0000 | 0.215190 | 0.107595 | − | 0.994195i | \(-0.465685\pi\) | ||||
0.107595 | + | 0.994195i | \(0.465685\pi\) | |||||||
\(80\) | 25.9808i | 0.324760i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − 3.46410i | − 0.0422451i | ||||||||
\(83\) | 53.6936i | 0.646911i | 0.946243 | + | 0.323455i | \(0.104845\pi\) | ||||
−0.946243 | + | 0.323455i | \(0.895155\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −126.000 | −1.48235 | ||||||||
\(86\) | −26.0000 | −0.302326 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 77.0000 | 0.875000 | ||||||||
\(89\) | 79.6743i | 0.895217i | 0.894230 | + | 0.447609i | \(0.147724\pi\) | ||||
−0.894230 | + | 0.447609i | \(0.852276\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 84.0000 | 0.913043 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − 76.2102i | − 0.810747i | ||||||||
\(95\) | 18.0000 | 0.189474 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 91.7987i | − 0.946378i | −0.880961 | − | 0.473189i | \(-0.843103\pi\) | ||||
0.880961 | − | 0.473189i | \(-0.156897\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.00000 | 0.0600000 | ||||||||
\(101\) | − 20.7846i | − 0.205788i | −0.994692 | − | 0.102894i | \(-0.967190\pi\) | ||||
0.994692 | − | 0.102894i | \(-0.0328103\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(104\) | − 48.4974i | − 0.466321i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 31.0000 | 0.292453 | ||||||||
\(107\) | −31.0000 | −0.289720 | −0.144860 | − | 0.989452i | \(-0.546273\pi\) | ||||
−0.144860 | + | 0.989452i | \(0.546273\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −136.000 | −1.24771 | −0.623853 | − | 0.781542i | \(-0.714434\pi\) | ||||
−0.623853 | + | 0.781542i | \(0.714434\pi\) | |||||||
\(110\) | − 57.1577i | − 0.519615i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 74.0000 | 0.654867 | 0.327434 | − | 0.944874i | \(-0.393816\pi\) | ||||
0.327434 | + | 0.944874i | \(0.393816\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 145.492i | − 1.26515i | ||||||||
\(116\) | 75.0000 | 0.646552 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8.66025i | 0.0733920i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | − 13.8564i | − 0.113577i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − 98.7269i | − 0.796185i | ||||||||
\(125\) | 119.512i | 0.956092i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.00787402 | −0.00393701 | − | 0.999992i | \(-0.501253\pi\) | ||||
−0.00393701 | + | 0.999992i | \(0.501253\pi\) | |||||||
\(128\) | 119.000 | 0.929688 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −36.0000 | −0.276923 | ||||||||
\(131\) | − 181.865i | − 1.38828i | −0.719838 | − | 0.694142i | \(-0.755784\pi\) | ||||
0.719838 | − | 0.694142i | \(-0.244216\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 52.0000 | 0.388060 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 169.741i | 1.24810i | ||||||||
\(137\) | −88.0000 | −0.642336 | −0.321168 | − | 0.947022i | \(-0.604075\pi\) | ||||
−0.321168 | + | 0.947022i | \(0.604075\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 190.526i | 1.37069i | 0.728220 | + | 0.685344i | \(0.240348\pi\) | ||||
−0.728220 | + | 0.685344i | \(0.759652\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 64.0000 | 0.450704 | ||||||||
\(143\) | − 76.2102i | − 0.532939i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 129.904i | − 0.895888i | ||||||||
\(146\) | 6.92820i | 0.0474534i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 174.000 | 1.17568 | ||||||||
\(149\) | 230.000 | 1.54362 | 0.771812 | − | 0.635851i | \(-0.219351\pi\) | ||||
0.771812 | + | 0.635851i | \(0.219351\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 227.000 | 1.50331 | 0.751656 | − | 0.659556i | \(-0.229256\pi\) | ||||
0.751656 | + | 0.659556i | \(0.229256\pi\) | |||||||
\(152\) | − 24.2487i | − 0.159531i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −171.000 | −1.10323 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 48.4974i | 0.308901i | 0.988001 | + | 0.154450i | \(0.0493607\pi\) | ||||
−0.988001 | + | 0.154450i | \(0.950639\pi\) | |||||||
\(158\) | −17.0000 | −0.107595 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − 171.473i | − 1.07171i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 212.000 | 1.30061 | 0.650307 | − | 0.759672i | \(-0.274640\pi\) | ||||
0.650307 | + | 0.759672i | \(0.274640\pi\) | |||||||
\(164\) | − 10.3923i | − 0.0633677i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − 53.6936i | − 0.323455i | ||||||||
\(167\) | 96.9948i | 0.580807i | 0.956904 | + | 0.290404i | \(0.0937896\pi\) | ||||
−0.956904 | + | 0.290404i | \(0.906210\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 121.000 | 0.715976 | ||||||||
\(170\) | 126.000 | 0.741176 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −78.0000 | −0.453488 | ||||||||
\(173\) | − 214.774i | − 1.24147i | −0.784020 | − | 0.620735i | \(-0.786834\pi\) | ||||
0.784020 | − | 0.620735i | \(-0.213166\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 55.0000 | 0.312500 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 79.6743i | − 0.447609i | ||||||||
\(179\) | −46.0000 | −0.256983 | −0.128492 | − | 0.991711i | \(-0.541014\pi\) | ||||
−0.128492 | + | 0.991711i | \(0.541014\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 31.1769i | 0.172248i | 0.996284 | + | 0.0861241i | \(0.0274481\pi\) | ||||
−0.996284 | + | 0.0861241i | \(0.972552\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −196.000 | −1.06522 | ||||||||
\(185\) | − 301.377i | − 1.62906i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 266.736i | 1.42639i | ||||||||
\(188\) | − 228.631i | − 1.21612i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −18.0000 | −0.0947368 | ||||||||
\(191\) | −208.000 | −1.08901 | −0.544503 | − | 0.838759i | \(-0.683282\pi\) | ||||
−0.544503 | + | 0.838759i | \(0.683282\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 239.000 | 1.23834 | 0.619171 | − | 0.785256i | \(-0.287469\pi\) | ||||
0.619171 | + | 0.785256i | \(0.287469\pi\) | |||||||
\(194\) | 91.7987i | 0.473189i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 26.0000 | 0.131980 | 0.0659898 | − | 0.997820i | \(-0.478980\pi\) | ||||
0.0659898 | + | 0.997820i | \(0.478980\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 242.487i | 1.21853i | 0.792967 | + | 0.609264i | \(0.208535\pi\) | ||||
−0.792967 | + | 0.609264i | \(0.791465\pi\) | |||||||
\(200\) | −14.0000 | −0.0700000 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 20.7846i | 0.102894i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −18.0000 | −0.0878049 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 34.6410i | − 0.166543i | ||||||||
\(209\) | − 38.1051i | − 0.182321i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −52.0000 | −0.246445 | −0.123223 | − | 0.992379i | \(-0.539323\pi\) | ||||
−0.123223 | + | 0.992379i | \(0.539323\pi\) | |||||||
\(212\) | 93.0000 | 0.438679 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 31.0000 | 0.144860 | ||||||||
\(215\) | 135.100i | 0.628372i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 136.000 | 0.623853 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − 171.473i | − 0.779423i | ||||||||
\(221\) | 168.000 | 0.760181 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.5167i | 0.100972i | 0.998725 | + | 0.0504858i | \(0.0160770\pi\) | ||||
−0.998725 | + | 0.0504858i | \(0.983923\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −74.0000 | −0.327434 | ||||||||
\(227\) | 67.5500i | 0.297577i | 0.988869 | + | 0.148789i | \(0.0475374\pi\) | ||||
−0.988869 | + | 0.148789i | \(0.952463\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 31.1769i | − 0.136144i | −0.997680 | − | 0.0680719i | \(-0.978315\pi\) | ||||
0.997680 | − | 0.0680719i | \(-0.0216847\pi\) | |||||||
\(230\) | 145.492i | 0.632575i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −175.000 | −0.754310 | ||||||||
\(233\) | −262.000 | −1.12446 | −0.562232 | − | 0.826980i | \(-0.690057\pi\) | ||||
−0.562232 | + | 0.826980i | \(0.690057\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −396.000 | −1.68511 | ||||||||
\(236\) | 25.9808i | 0.110088i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −160.000 | −0.669456 | −0.334728 | − | 0.942315i | \(-0.608644\pi\) | ||||
−0.334728 | + | 0.942315i | \(0.608644\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 472.850i | − 1.96203i | −0.193925 | − | 0.981016i | \(-0.562122\pi\) | ||||
0.193925 | − | 0.981016i | \(-0.437878\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − 41.5692i | − 0.170366i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −24.0000 | −0.0971660 | ||||||||
\(248\) | 230.363i | 0.928882i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − 119.512i | − 0.478046i | ||||||||
\(251\) | − 67.5500i | − 0.269123i | −0.990905 | − | 0.134562i | \(-0.957037\pi\) | ||||
0.990905 | − | 0.134562i | \(-0.0429626\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −308.000 | −1.21739 | ||||||||
\(254\) | 1.00000 | 0.00393701 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −171.000 | −0.667969 | ||||||||
\(257\) | 405.300i | 1.57704i | 0.615008 | + | 0.788521i | \(0.289153\pi\) | ||||
−0.615008 | + | 0.788521i | \(0.710847\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −108.000 | −0.415385 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 181.865i | 0.694142i | ||||||||
\(263\) | −106.000 | −0.403042 | −0.201521 | − | 0.979484i | \(-0.564588\pi\) | ||||
−0.201521 | + | 0.979484i | \(0.564588\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 161.081i | − 0.607852i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 156.000 | 0.582090 | ||||||||
\(269\) | 434.745i | 1.61615i | 0.589079 | + | 0.808076i | \(0.299491\pi\) | ||||
−0.589079 | + | 0.808076i | \(0.700509\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 126.440i | 0.466567i | 0.972409 | + | 0.233284i | \(0.0749470\pi\) | ||||
−0.972409 | + | 0.233284i | \(0.925053\pi\) | |||||||
\(272\) | 121.244i | 0.445748i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 88.0000 | 0.321168 | ||||||||
\(275\) | −22.0000 | −0.0800000 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 236.000 | 0.851986 | 0.425993 | − | 0.904727i | \(-0.359925\pi\) | ||||
0.425993 | + | 0.904727i | \(0.359925\pi\) | |||||||
\(278\) | − 190.526i | − 0.685344i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 116.000 | 0.412811 | 0.206406 | − | 0.978466i | \(-0.433823\pi\) | ||||
0.206406 | + | 0.978466i | \(0.433823\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 370.659i | 1.30975i | 0.755738 | + | 0.654874i | \(0.227278\pi\) | ||||
−0.755738 | + | 0.654874i | \(0.772722\pi\) | |||||||
\(284\) | 192.000 | 0.676056 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 76.2102i | 0.266469i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −299.000 | −1.03460 | ||||||||
\(290\) | 129.904i | 0.447944i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 20.7846i | 0.0711802i | ||||||||
\(293\) | 19.0526i | 0.0650258i | 0.999471 | + | 0.0325129i | \(0.0103510\pi\) | ||||
−0.999471 | + | 0.0325129i | \(0.989649\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 45.0000 | 0.152542 | ||||||||
\(296\) | −406.000 | −1.37162 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −230.000 | −0.771812 | ||||||||
\(299\) | 193.990i | 0.648795i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −227.000 | −0.751656 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − 17.3205i | − 0.0569754i | ||||||||
\(305\) | −72.0000 | −0.236066 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 457.261i | 1.48945i | 0.667371 | + | 0.744725i | \(0.267420\pi\) | ||||
−0.667371 | + | 0.744725i | \(0.732580\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 171.000 | 0.551613 | ||||||||
\(311\) | 329.090i | 1.05817i | 0.848570 | + | 0.529083i | \(0.177464\pi\) | ||||
−0.848570 | + | 0.529083i | \(0.822536\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 549.060i | 1.75419i | 0.480321 | + | 0.877093i | \(0.340520\pi\) | ||||
−0.480321 | + | 0.877093i | \(0.659480\pi\) | |||||||
\(314\) | − 48.4974i | − 0.154450i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −51.0000 | −0.161392 | ||||||||
\(317\) | −187.000 | −0.589905 | −0.294953 | − | 0.955512i | \(-0.595304\pi\) | ||||
−0.294953 | + | 0.955512i | \(0.595304\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −275.000 | −0.862069 | ||||||||
\(320\) | 67.5500i | 0.211094i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 84.0000 | 0.260062 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 13.8564i | 0.0426351i | ||||||||
\(326\) | −212.000 | −0.650307 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 24.2487i | 0.0739290i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.0000 | −0.0483384 | −0.0241692 | − | 0.999708i | \(-0.507694\pi\) | ||||
−0.0241692 | + | 0.999708i | \(0.507694\pi\) | |||||||
\(332\) | − 161.081i | − 0.485183i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − 96.9948i | − 0.290404i | ||||||||
\(335\) | − 270.200i | − 0.806567i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 83.0000 | 0.246291 | 0.123145 | − | 0.992389i | \(-0.460702\pi\) | ||||
0.123145 | + | 0.992389i | \(0.460702\pi\) | |||||||
\(338\) | −121.000 | −0.357988 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 378.000 | 1.11176 | ||||||||
\(341\) | 361.999i | 1.06158i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 182.000 | 0.529070 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 214.774i | 0.620735i | ||||||||
\(347\) | −358.000 | −1.03170 | −0.515850 | − | 0.856679i | \(-0.672524\pi\) | ||||
−0.515850 | + | 0.856679i | \(0.672524\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 678.964i | − 1.94546i | −0.231950 | − | 0.972728i | \(-0.574511\pi\) | ||||
0.231950 | − | 0.972728i | \(-0.425489\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −363.000 | −1.03125 | ||||||||
\(353\) | − 644.323i | − 1.82528i | −0.408767 | − | 0.912639i | \(-0.634041\pi\) | ||||
0.408767 | − | 0.912639i | \(-0.365959\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 332.554i | − 0.936771i | ||||||||
\(356\) | − 239.023i | − 0.671413i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 46.0000 | 0.128492 | ||||||||
\(359\) | 284.000 | 0.791086 | 0.395543 | − | 0.918447i | \(-0.370556\pi\) | ||||
0.395543 | + | 0.918447i | \(0.370556\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 349.000 | 0.966759 | ||||||||
\(362\) | − 31.1769i | − 0.0861241i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 36.0000 | 0.0986301 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 275.396i | − 0.750398i | −0.926944 | − | 0.375199i | \(-0.877574\pi\) | ||||
0.926944 | − | 0.375199i | \(-0.122426\pi\) | |||||||
\(368\) | −140.000 | −0.380435 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 301.377i | 0.814532i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 50.0000 | 0.134048 | 0.0670241 | − | 0.997751i | \(-0.478650\pi\) | ||||
0.0670241 | + | 0.997751i | \(0.478650\pi\) | |||||||
\(374\) | − 266.736i | − 0.713197i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 533.472i | 1.41881i | ||||||||
\(377\) | 173.205i | 0.459430i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 458.000 | 1.20844 | 0.604222 | − | 0.796816i | \(-0.293484\pi\) | ||||
0.604222 | + | 0.796816i | \(0.293484\pi\) | |||||||
\(380\) | −54.0000 | −0.142105 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 208.000 | 0.544503 | ||||||||
\(383\) | − 405.300i | − 1.05822i | −0.848552 | − | 0.529112i | \(-0.822525\pi\) | ||||
0.848552 | − | 0.529112i | \(-0.177475\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −239.000 | −0.619171 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 275.396i | 0.709784i | ||||||||
\(389\) | 698.000 | 1.79434 | 0.897172 | − | 0.441681i | \(-0.145618\pi\) | ||||
0.897172 | + | 0.441681i | \(0.145618\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 678.964i | − 1.73648i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −26.0000 | −0.0659898 | ||||||||
\(395\) | 88.3346i | 0.223632i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 575.041i | − 1.44847i | −0.689556 | − | 0.724233i | \(-0.742194\pi\) | ||||
0.689556 | − | 0.724233i | \(-0.257806\pi\) | |||||||
\(398\) | − 242.487i | − 0.609264i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −10.0000 | −0.0250000 | ||||||||
\(401\) | 284.000 | 0.708229 | 0.354115 | − | 0.935202i | \(-0.384782\pi\) | ||||
0.354115 | + | 0.935202i | \(0.384782\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 228.000 | 0.565757 | ||||||||
\(404\) | 62.3538i | 0.154341i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −638.000 | −1.56757 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 209.578i | 0.512416i | 0.966622 | + | 0.256208i | \(0.0824732\pi\) | ||||
−0.966622 | + | 0.256208i | \(0.917527\pi\) | |||||||
\(410\) | 18.0000 | 0.0439024 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −279.000 | −0.672289 | ||||||||
\(416\) | 228.631i | 0.549593i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 38.1051i | 0.0911606i | ||||||||
\(419\) | − 131.636i | − 0.314167i | −0.987585 | − | 0.157083i | \(-0.949791\pi\) | ||||
0.987585 | − | 0.157083i | \(-0.0502091\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.0000 | −0.0665083 | −0.0332542 | − | 0.999447i | \(-0.510587\pi\) | ||||
−0.0332542 | + | 0.999447i | \(0.510587\pi\) | |||||||
\(422\) | 52.0000 | 0.123223 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −217.000 | −0.511792 | ||||||||
\(425\) | − 48.4974i | − 0.114112i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 93.0000 | 0.217290 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − 135.100i | − 0.314186i | ||||||||
\(431\) | −118.000 | −0.273782 | −0.136891 | − | 0.990586i | \(-0.543711\pi\) | ||||
−0.136891 | + | 0.990586i | \(0.543711\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 561.184i | 1.29604i | 0.761624 | + | 0.648019i | \(0.224402\pi\) | ||||
−0.761624 | + | 0.648019i | \(0.775598\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 408.000 | 0.935780 | ||||||||
\(437\) | 96.9948i | 0.221956i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 739.586i | − 1.68471i | −0.538927 | − | 0.842353i | \(-0.681170\pi\) | ||||
0.538927 | − | 0.842353i | \(-0.318830\pi\) | |||||||
\(440\) | 400.104i | 0.909327i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −168.000 | −0.380090 | ||||||||
\(443\) | 155.000 | 0.349887 | 0.174944 | − | 0.984578i | \(-0.444026\pi\) | ||||
0.174944 | + | 0.984578i | \(0.444026\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −414.000 | −0.930337 | ||||||||
\(446\) | − 22.5167i | − 0.0504858i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 368.000 | 0.819599 | 0.409800 | − | 0.912176i | \(-0.365599\pi\) | ||||
0.409800 | + | 0.912176i | \(0.365599\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 38.1051i | 0.0844903i | ||||||||
\(452\) | −222.000 | −0.491150 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − 67.5500i | − 0.148789i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 341.000 | 0.746171 | 0.373085 | − | 0.927797i | \(-0.378300\pi\) | ||||
0.373085 | + | 0.927797i | \(0.378300\pi\) | |||||||
\(458\) | 31.1769i | 0.0680719i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 436.477i | 0.948863i | ||||||||
\(461\) | − 55.4256i | − 0.120229i | −0.998191 | − | 0.0601146i | \(-0.980853\pi\) | ||||
0.998191 | − | 0.0601146i | \(-0.0191466\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −178.000 | −0.384449 | −0.192225 | − | 0.981351i | \(-0.561570\pi\) | ||||
−0.192225 | + | 0.981351i | \(0.561570\pi\) | |||||||
\(464\) | −125.000 | −0.269397 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 262.000 | 0.562232 | ||||||||
\(467\) | − 658.179i | − 1.40938i | −0.709517 | − | 0.704689i | \(-0.751087\pi\) | ||||
0.709517 | − | 0.704689i | \(-0.248913\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 396.000 | 0.842553 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − 60.6218i | − 0.128436i | ||||||||
\(473\) | 286.000 | 0.604651 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.92820i | 0.0145857i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 160.000 | 0.334728 | ||||||||
\(479\) | 509.223i | 1.06310i | 0.847028 | + | 0.531548i | \(0.178389\pi\) | ||||
−0.847028 | + | 0.531548i | \(0.821611\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 401.836i | 0.835417i | ||||||||
\(482\) | 472.850i | 0.981016i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 477.000 | 0.983505 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −841.000 | −1.72690 | −0.863450 | − | 0.504435i | \(-0.831701\pi\) | ||||
−0.863450 | + | 0.504435i | \(0.831701\pi\) | |||||||
\(488\) | 96.9948i | 0.198760i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 959.000 | 1.95316 | 0.976578 | − | 0.215162i | \(-0.0690279\pi\) | ||||
0.976578 | + | 0.215162i | \(0.0690279\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 606.218i | − 1.22965i | ||||||||
\(494\) | 24.0000 | 0.0485830 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 164.545i | 0.331744i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −118.000 | −0.236473 | −0.118236 | − | 0.992985i | \(-0.537724\pi\) | ||||
−0.118236 | + | 0.992985i | \(0.537724\pi\) | |||||||
\(500\) | − 358.535i | − 0.717069i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 67.5500i | 0.134562i | ||||||||
\(503\) | 363.731i | 0.723123i | 0.932348 | + | 0.361561i | \(0.117756\pi\) | ||||
−0.932348 | + | 0.361561i | \(0.882244\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 108.000 | 0.213861 | ||||||||
\(506\) | 308.000 | 0.608696 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.00000 | 0.00590551 | ||||||||
\(509\) | − 441.673i | − 0.867727i | −0.900979 | − | 0.433863i | \(-0.857150\pi\) | ||||
0.900979 | − | 0.433863i | \(-0.142850\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −305.000 | −0.595703 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − 405.300i | − 0.788521i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 838.313i | 1.62149i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 252.000 | 0.484615 | ||||||||
\(521\) | − 973.413i | − 1.86835i | −0.356810 | − | 0.934177i | \(-0.616136\pi\) | ||||
0.356810 | − | 0.934177i | \(-0.383864\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 471.118i | − 0.900799i | −0.892827 | − | 0.450399i | \(-0.851282\pi\) | ||||
0.892827 | − | 0.450399i | \(-0.148718\pi\) | |||||||
\(524\) | 545.596i | 1.04121i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 106.000 | 0.201521 | ||||||||
\(527\) | −798.000 | −1.51423 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 255.000 | 0.482042 | ||||||||
\(530\) | 161.081i | 0.303926i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 24.0000 | 0.0450281 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 161.081i | − 0.301085i | ||||||||
\(536\) | −364.000 | −0.679104 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 434.745i | − 0.808076i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 806.000 | 1.48983 | 0.744917 | − | 0.667157i | \(-0.232489\pi\) | ||||
0.744917 | + | 0.667157i | \(0.232489\pi\) | |||||||
\(542\) | − 126.440i | − 0.233284i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − 800.207i | − 1.47097i | ||||||||
\(545\) | − 706.677i | − 1.29665i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −154.000 | −0.281536 | −0.140768 | − | 0.990043i | \(-0.544957\pi\) | ||||
−0.140768 | + | 0.990043i | \(0.544957\pi\) | |||||||
\(548\) | 264.000 | 0.481752 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 22.0000 | 0.0400000 | ||||||||
\(551\) | 86.6025i | 0.157173i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −236.000 | −0.425993 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − 571.577i | − 1.02802i | ||||||||
\(557\) | 851.000 | 1.52783 | 0.763914 | − | 0.645318i | \(-0.223275\pi\) | ||||
0.763914 | + | 0.645318i | \(0.223275\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 180.133i | − 0.322242i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −116.000 | −0.206406 | ||||||||
\(563\) | 427.817i | 0.759887i | 0.925010 | + | 0.379944i | \(0.124057\pi\) | ||||
−0.925010 | + | 0.379944i | \(0.875943\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 384.515i | 0.680558i | ||||||||
\(566\) | − 370.659i | − 0.654874i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −448.000 | −0.788732 | ||||||||
\(569\) | 818.000 | 1.43761 | 0.718805 | − | 0.695212i | \(-0.244689\pi\) | ||||
0.718805 | + | 0.695212i | \(0.244689\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 284.000 | 0.497373 | 0.248687 | − | 0.968584i | \(-0.420001\pi\) | ||||
0.248687 | + | 0.968584i | \(0.420001\pi\) | |||||||
\(572\) | 228.631i | 0.399704i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 56.0000 | 0.0973913 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 756.906i | 1.31180i | 0.754850 | + | 0.655898i | \(0.227710\pi\) | ||||
−0.754850 | + | 0.655898i | \(0.772290\pi\) | |||||||
\(578\) | 299.000 | 0.517301 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 389.711i | 0.671916i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −341.000 | −0.584906 | ||||||||
\(584\) | − 48.4974i | − 0.0830435i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − 19.0526i | − 0.0325129i | ||||||||
\(587\) | 947.432i | 1.61402i | 0.590535 | + | 0.807012i | \(0.298917\pi\) | ||||
−0.590535 | + | 0.807012i | \(0.701083\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 114.000 | 0.193548 | ||||||||
\(590\) | −45.0000 | −0.0762712 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −290.000 | −0.489865 | ||||||||
\(593\) | − 408.764i | − 0.689315i | −0.938728 | − | 0.344658i | \(-0.887995\pi\) | ||||
0.938728 | − | 0.344658i | \(-0.112005\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −690.000 | −1.15772 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − 193.990i | − 0.324397i | ||||||||
\(599\) | −556.000 | −0.928214 | −0.464107 | − | 0.885779i | \(-0.653625\pi\) | ||||
−0.464107 | + | 0.885779i | \(0.653625\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 580.237i | − 0.965453i | −0.875771 | − | 0.482726i | \(-0.839647\pi\) | ||||
0.875771 | − | 0.482726i | \(-0.160353\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −681.000 | −1.12748 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 659.911i | 1.08717i | 0.839355 | + | 0.543584i | \(0.182933\pi\) | ||||
−0.839355 | + | 0.543584i | \(0.817067\pi\) | |||||||
\(608\) | 114.315i | 0.188019i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 72.0000 | 0.118033 | ||||||||
\(611\) | 528.000 | 0.864157 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 320.000 | 0.522023 | 0.261011 | − | 0.965336i | \(-0.415944\pi\) | ||||
0.261011 | + | 0.965336i | \(0.415944\pi\) | |||||||
\(614\) | − 457.261i | − 0.744725i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −652.000 | −1.05673 | −0.528363 | − | 0.849019i | \(-0.677194\pi\) | ||||
−0.528363 | + | 0.849019i | \(0.677194\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 644.323i | 1.04091i | 0.853889 | + | 0.520455i | \(0.174238\pi\) | ||||
−0.853889 | + | 0.520455i | \(0.825762\pi\) | |||||||
\(620\) | 513.000 | 0.827419 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 329.090i | − 0.529083i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −671.000 | −1.07360 | ||||||||
\(626\) | − 549.060i | − 0.877093i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 145.492i | − 0.231676i | ||||||||
\(629\) | − 1406.43i | − 2.23597i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −97.0000 | −0.153724 | −0.0768621 | − | 0.997042i | \(-0.524490\pi\) | ||||
−0.0768621 | + | 0.997042i | \(0.524490\pi\) | |||||||
\(632\) | 119.000 | 0.188291 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 187.000 | 0.294953 | ||||||||
\(635\) | − 5.19615i | − 0.00818292i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 275.000 | 0.431034 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 618.342i | 0.966160i | ||||||||
\(641\) | −700.000 | −1.09204 | −0.546022 | − | 0.837771i | \(-0.683858\pi\) | ||||
−0.546022 | + | 0.837771i | \(0.683858\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 325.626i | 0.506416i | 0.967412 | + | 0.253208i | \(0.0814857\pi\) | ||||
−0.967412 | + | 0.253208i | \(0.918514\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −84.0000 | −0.130031 | ||||||||
\(647\) | − 360.267i | − 0.556826i | −0.960461 | − | 0.278413i | \(-0.910192\pi\) | ||||
0.960461 | − | 0.278413i | \(-0.0898084\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − 95.2628i | − 0.146784i | ||||||||
\(650\) | − 13.8564i | − 0.0213175i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −636.000 | −0.975460 | ||||||||
\(653\) | −373.000 | −0.571210 | −0.285605 | − | 0.958347i | \(-0.592194\pi\) | ||||
−0.285605 | + | 0.958347i | \(0.592194\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 945.000 | 1.44275 | ||||||||
\(656\) | 17.3205i | 0.0264032i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 818.000 | 1.24127 | 0.620637 | − | 0.784098i | \(-0.286874\pi\) | ||||
0.620637 | + | 0.784098i | \(0.286874\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 377.587i | − 0.571236i | −0.958344 | − | 0.285618i | \(-0.907801\pi\) | ||||
0.958344 | − | 0.285618i | \(-0.0921989\pi\) | |||||||
\(662\) | 16.0000 | 0.0241692 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 375.855i | 0.566047i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 700.000 | 1.04948 | ||||||||
\(668\) | − 290.985i | − 0.435606i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 270.200i | 0.403283i | ||||||||
\(671\) | 152.420i | 0.227154i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1205.00 | 1.79049 | 0.895245 | − | 0.445574i | \(-0.147000\pi\) | ||||
0.895245 | + | 0.445574i | \(0.147000\pi\) | |||||||
\(674\) | −83.0000 | −0.123145 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −363.000 | −0.536982 | ||||||||
\(677\) | 538.668i | 0.795669i | 0.917457 | + | 0.397834i | \(0.130238\pi\) | ||||
−0.917457 | + | 0.397834i | \(0.869762\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −882.000 | −1.29706 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 361.999i | − 0.530790i | ||||||||
\(683\) | −949.000 | −1.38946 | −0.694729 | − | 0.719271i | \(-0.744476\pi\) | ||||
−0.694729 | + | 0.719271i | \(0.744476\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 457.261i | − 0.667535i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 130.000 | 0.188953 | ||||||||
\(689\) | 214.774i | 0.311719i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 308.305i | − 0.446172i | −0.974799 | − | 0.223086i | \(-0.928387\pi\) | ||||
0.974799 | − | 0.223086i | \(-0.0716131\pi\) | |||||||
\(692\) | 644.323i | 0.931102i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 358.000 | 0.515850 | ||||||||
\(695\) | −990.000 | −1.42446 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −84.0000 | −0.120516 | ||||||||
\(698\) | 678.964i | 0.972728i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 413.000 | 0.589158 | 0.294579 | − | 0.955627i | \(-0.404821\pi\) | ||||
0.294579 | + | 0.955627i | \(0.404821\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 200.918i | 0.285801i | ||||||||
\(704\) | 143.000 | 0.203125 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 644.323i | 0.912639i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 890.000 | 1.25529 | 0.627645 | − | 0.778500i | \(-0.284019\pi\) | ||||
0.627645 | + | 0.778500i | \(0.284019\pi\) | |||||||
\(710\) | 332.554i | 0.468386i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 557.720i | 0.783315i | ||||||||
\(713\) | − 921.451i | − 1.29236i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 396.000 | 0.553846 | ||||||||
\(716\) | 138.000 | 0.192737 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −284.000 | −0.395543 | ||||||||
\(719\) | − 668.572i | − 0.929863i | −0.885347 | − | 0.464932i | \(-0.846079\pi\) | ||||
0.885347 | − | 0.464932i | \(-0.153921\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −349.000 | −0.483380 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − 93.5307i | − 0.129186i | ||||||||
\(725\) | 50.0000 | 0.0689655 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 417.424i | 0.574174i | 0.957905 | + | 0.287087i | \(0.0926868\pi\) | ||||
−0.957905 | + | 0.287087i | \(0.907313\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −36.0000 | −0.0493151 | ||||||||
\(731\) | 630.466i | 0.862471i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 197.454i | 0.269378i | 0.990888 | + | 0.134689i | \(0.0430035\pi\) | ||||
−0.990888 | + | 0.134689i | \(0.956997\pi\) | |||||||
\(734\) | 275.396i | 0.375199i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 924.000 | 1.25543 | ||||||||
\(737\) | −572.000 | −0.776119 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −310.000 | −0.419486 | −0.209743 | − | 0.977757i | \(-0.567263\pi\) | ||||
−0.209743 | + | 0.977757i | \(0.567263\pi\) | |||||||
\(740\) | 904.131i | 1.22180i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 812.000 | 1.09287 | 0.546433 | − | 0.837503i | \(-0.315985\pi\) | ||||
0.546433 | + | 0.837503i | \(0.315985\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1195.12i | 1.60418i | ||||||||
\(746\) | −50.0000 | −0.0670241 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − 800.207i | − 1.06980i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1075.00 | −1.43142 | −0.715712 | − | 0.698395i | \(-0.753898\pi\) | ||||
−0.715712 | + | 0.698395i | \(0.753898\pi\) | |||||||
\(752\) | 381.051i | 0.506717i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − 173.205i | − 0.229715i | ||||||||
\(755\) | 1179.53i | 1.56229i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −484.000 | −0.639366 | −0.319683 | − | 0.947525i | \(-0.603576\pi\) | ||||
−0.319683 | + | 0.947525i | \(0.603576\pi\) | |||||||
\(758\) | −458.000 | −0.604222 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 126.000 | 0.165789 | ||||||||
\(761\) | − 166.277i | − 0.218498i | −0.994014 | − | 0.109249i | \(-0.965155\pi\) | ||||
0.994014 | − | 0.109249i | \(-0.0348446\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 624.000 | 0.816754 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 405.300i | 0.529112i | ||||||||
\(767\) | −60.0000 | −0.0782269 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 594.093i | − 0.772553i | −0.922383 | − | 0.386277i | \(-0.873761\pi\) | ||||
0.922383 | − | 0.386277i | \(-0.126239\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −717.000 | −0.928756 | ||||||||
\(773\) | 1032.30i | 1.33545i | 0.744408 | + | 0.667725i | \(0.232732\pi\) | ||||
−0.744408 | + | 0.667725i | \(0.767268\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 65.8179i | − 0.0849264i | ||||||||
\(776\) | − 642.591i | − 0.828081i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −698.000 | −0.897172 | ||||||||
\(779\) | 12.0000 | 0.0154044 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −704.000 | −0.901408 | ||||||||
\(782\) | 678.964i | 0.868240i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −252.000 | −0.321019 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 408.764i | − 0.519395i | −0.965690 | − | 0.259698i | \(-0.916377\pi\) | ||||
0.965690 | − | 0.259698i | \(-0.0836229\pi\) | |||||||
\(788\) | −78.0000 | −0.0989848 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − 88.3346i | − 0.111816i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 96.0000 | 0.121059 | ||||||||
\(794\) | 575.041i | 0.724233i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − 727.461i | − 0.913896i | ||||||||
\(797\) | − 625.270i | − 0.784530i | −0.919852 | − | 0.392265i | \(-0.871692\pi\) | ||||
0.919852 | − | 0.392265i | \(-0.128308\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1848.00 | −2.31289 | ||||||||
\(800\) | 66.0000 | 0.0825000 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −284.000 | −0.354115 | ||||||||
\(803\) | − 76.2102i | − 0.0949069i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −228.000 | −0.282878 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 145.492i | − 0.180065i | ||||||||
\(809\) | 752.000 | 0.929543 | 0.464771 | − | 0.885431i | \(-0.346137\pi\) | ||||
0.464771 | + | 0.885431i | \(0.346137\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 270.200i | − 0.333169i | −0.986027 | − | 0.166584i | \(-0.946726\pi\) | ||||
0.986027 | − | 0.166584i | \(-0.0532738\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 638.000 | 0.783784 | ||||||||
\(815\) | 1101.58i | 1.35164i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 90.0666i | − 0.110241i | ||||||||
\(818\) | − 209.578i | − 0.256208i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 54.0000 | 0.0658537 | ||||||||
\(821\) | −883.000 | −1.07552 | −0.537759 | − | 0.843099i | \(-0.680729\pi\) | ||||
−0.537759 | + | 0.843099i | \(0.680729\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −490.000 | −0.595383 | −0.297691 | − | 0.954662i | \(-0.596217\pi\) | ||||
−0.297691 | + | 0.954662i | \(0.596217\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1279.00 | −1.54655 | −0.773277 | − | 0.634068i | \(-0.781384\pi\) | ||||
−0.773277 | + | 0.634068i | \(0.781384\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 1513.81i | − 1.82607i | −0.407881 | − | 0.913035i | \(-0.633732\pi\) | ||||
0.407881 | − | 0.913035i | \(-0.366268\pi\) | |||||||
\(830\) | 279.000 | 0.336145 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − 90.0666i | − 0.108253i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −504.000 | −0.603593 | ||||||||
\(836\) | 114.315i | 0.136741i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 131.636i | 0.157083i | ||||||||
\(839\) | − 523.079i | − 0.623456i | −0.950171 | − | 0.311728i | \(-0.899092\pi\) | ||||
0.950171 | − | 0.311728i | \(-0.100908\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −216.000 | −0.256837 | ||||||||
\(842\) | 28.0000 | 0.0332542 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 156.000 | 0.184834 | ||||||||
\(845\) | 628.734i | 0.744064i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −155.000 | −0.182783 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 48.4974i | 0.0570558i | ||||||||
\(851\) | 1624.00 | 1.90834 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 387.979i | − 0.454841i | −0.973797 | − | 0.227421i | \(-0.926971\pi\) | ||||
0.973797 | − | 0.227421i | \(-0.0730292\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −217.000 | −0.253505 | ||||||||
\(857\) | − 831.384i | − 0.970110i | −0.874484 | − | 0.485055i | \(-0.838800\pi\) | ||||
0.874484 | − | 0.485055i | \(-0.161200\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1132.76i | 1.31870i | 0.751837 | + | 0.659349i | \(0.229168\pi\) | ||||
−0.751837 | + | 0.659349i | \(0.770832\pi\) | |||||||
\(860\) | − 405.300i | − 0.471279i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 118.000 | 0.136891 | ||||||||
\(863\) | −22.0000 | −0.0254925 | −0.0127462 | − | 0.999919i | \(-0.504057\pi\) | ||||
−0.0127462 | + | 0.999919i | \(0.504057\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1116.00 | 1.29017 | ||||||||
\(866\) | − 561.184i | − 0.648019i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 187.000 | 0.215190 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 360.267i | 0.413624i | ||||||||
\(872\) | −952.000 | −1.09174 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − 96.9948i | − 0.110978i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −40.0000 | −0.0456100 | −0.0228050 | − | 0.999740i | \(-0.507260\pi\) | ||||
−0.0228050 | + | 0.999740i | \(0.507260\pi\) | |||||||
\(878\) | 739.586i | 0.842353i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 285.788i | 0.324760i | ||||||||
\(881\) | 20.7846i | 0.0235921i | 0.999930 | + | 0.0117960i | \(0.00375488\pi\) | ||||
−0.999930 | + | 0.0117960i | \(0.996245\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 386.000 | 0.437146 | 0.218573 | − | 0.975821i | \(-0.429860\pi\) | ||||
0.218573 | + | 0.975821i | \(0.429860\pi\) | |||||||
\(884\) | −504.000 | −0.570136 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −155.000 | −0.174944 | ||||||||
\(887\) | 1725.12i | 1.94490i | 0.233120 | + | 0.972448i | \(0.425106\pi\) | ||||
−0.233120 | + | 0.972448i | \(0.574894\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 414.000 | 0.465169 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − 67.5500i | − 0.0757287i | ||||||||
\(893\) | 264.000 | 0.295633 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 239.023i | − 0.267065i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −368.000 | −0.409800 | ||||||||
\(899\) | − 822.724i | − 0.915155i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 751.710i | − 0.834306i | ||||||||
\(902\) | − 38.1051i | − 0.0422451i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 518.000 | 0.573009 | ||||||||
\(905\) | −162.000 | −0.179006 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −592.000 | −0.652701 | −0.326351 | − | 0.945249i | \(-0.605819\pi\) | ||||
−0.326351 | + | 0.945249i | \(0.605819\pi\) | |||||||
\(908\) | − 202.650i | − 0.223183i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 416.000 | 0.456641 | 0.228321 | − | 0.973586i | \(-0.426677\pi\) | ||||
0.228321 | + | 0.973586i | \(0.426677\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 590.629i | 0.646911i | ||||||||
\(914\) | −341.000 | −0.373085 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 93.5307i | 0.102108i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 50.0000 | 0.0544070 | 0.0272035 | − | 0.999630i | \(-0.491340\pi\) | ||||
0.0272035 | + | 0.999630i | \(0.491340\pi\) | |||||||
\(920\) | − 1018.45i | − 1.10701i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 55.4256i | 0.0601146i | ||||||||
\(923\) | 443.405i | 0.480395i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 116.000 | 0.125405 | ||||||||
\(926\) | 178.000 | 0.192225 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 825.000 | 0.889009 | ||||||||
\(929\) | − 412.228i | − 0.443733i | −0.975077 | − | 0.221867i | \(-0.928785\pi\) | ||||
0.975077 | − | 0.221867i | \(-0.0712149\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 786.000 | 0.843348 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 658.179i | 0.704689i | ||||||||
\(935\) | −1386.00 | −1.48235 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1605.61i | 1.71357i | 0.515677 | + | 0.856783i | \(0.327540\pi\) | ||||
−0.515677 | + | 0.856783i | \(0.672460\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1188.00 | 1.26383 | ||||||||
\(941\) | − 1328.48i | − 1.41178i | −0.708323 | − | 0.705889i | \(-0.750548\pi\) | ||||
0.708323 | − | 0.705889i | \(-0.249452\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 96.9948i | − 0.102858i | ||||||||
\(944\) | − 43.3013i | − 0.0458700i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −286.000 | −0.302326 | ||||||||
\(947\) | 1370.00 | 1.44667 | 0.723337 | − | 0.690495i | \(-0.242607\pi\) | ||||
0.723337 | + | 0.690495i | \(0.242607\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −48.0000 | −0.0505796 | ||||||||
\(950\) | − 6.92820i | − 0.00729285i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1150.00 | −1.20672 | −0.603358 | − | 0.797471i | \(-0.706171\pi\) | ||||
−0.603358 | + | 0.797471i | \(0.706171\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 1080.80i | − 1.13173i | ||||||||
\(956\) | 480.000 | 0.502092 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − 509.223i | − 0.531548i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −122.000 | −0.126951 | ||||||||
\(962\) | − 401.836i | − 0.417709i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1418.55i | 1.47152i | ||||||||
\(965\) | 1241.88i | 1.28692i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.00000 | 0.00517063 | 0.00258532 | − | 0.999997i | \(-0.499177\pi\) | ||||
0.00258532 | + | 0.999997i | \(0.499177\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −477.000 | −0.491753 | ||||||||
\(971\) | − 445.137i | − 0.458432i | −0.973376 | − | 0.229216i | \(-0.926384\pi\) | ||||
0.973376 | − | 0.229216i | \(-0.0736161\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 841.000 | 0.863450 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 69.2820i | 0.0709857i | ||||||||
\(977\) | −958.000 | −0.980553 | −0.490276 | − | 0.871567i | \(-0.663104\pi\) | ||||
−0.490276 | + | 0.871567i | \(0.663104\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 876.418i | 0.895217i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −959.000 | −0.976578 | ||||||||
\(983\) | 280.592i | 0.285445i | 0.989763 | + | 0.142722i | \(0.0455856\pi\) | ||||
−0.989763 | + | 0.142722i | \(0.954414\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 135.100i | 0.137157i | ||||||||
\(986\) | 606.218i | 0.614825i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 72.0000 | 0.0728745 | ||||||||
\(989\) | −728.000 | −0.736097 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 923.000 | 0.931382 | 0.465691 | − | 0.884947i | \(-0.345806\pi\) | ||||
0.465691 | + | 0.884947i | \(0.345806\pi\) | |||||||
\(992\) | − 1086.00i | − 1.09475i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1260.00 | −1.26633 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 20.7846i | − 0.0208472i | −0.999946 | − | 0.0104236i | \(-0.996682\pi\) | ||||
0.999946 | − | 0.0104236i | \(-0.00331799\pi\) | |||||||
\(998\) | 118.000 | 0.118236 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 441.3.d.b.244.2 | 2 | ||
3.2 | odd | 2 | 147.3.d.b.97.1 | 2 | |||
7.2 | even | 3 | 63.3.m.c.10.1 | 2 | |||
7.3 | odd | 6 | 63.3.m.c.19.1 | 2 | |||
7.4 | even | 3 | 441.3.m.e.19.1 | 2 | |||
7.5 | odd | 6 | 441.3.m.e.325.1 | 2 | |||
7.6 | odd | 2 | inner | 441.3.d.b.244.1 | 2 | ||
12.11 | even | 2 | 2352.3.f.d.97.2 | 2 | |||
21.2 | odd | 6 | 21.3.f.b.10.1 | ✓ | 2 | ||
21.5 | even | 6 | 147.3.f.c.31.1 | 2 | |||
21.11 | odd | 6 | 147.3.f.c.19.1 | 2 | |||
21.17 | even | 6 | 21.3.f.b.19.1 | yes | 2 | ||
21.20 | even | 2 | 147.3.d.b.97.2 | 2 | |||
28.3 | even | 6 | 1008.3.cg.g.145.1 | 2 | |||
28.23 | odd | 6 | 1008.3.cg.g.577.1 | 2 | |||
84.23 | even | 6 | 336.3.bh.a.241.1 | 2 | |||
84.59 | odd | 6 | 336.3.bh.a.145.1 | 2 | |||
84.83 | odd | 2 | 2352.3.f.d.97.1 | 2 | |||
105.2 | even | 12 | 525.3.s.c.199.2 | 4 | |||
105.17 | odd | 12 | 525.3.s.c.124.1 | 4 | |||
105.23 | even | 12 | 525.3.s.c.199.1 | 4 | |||
105.38 | odd | 12 | 525.3.s.c.124.2 | 4 | |||
105.44 | odd | 6 | 525.3.o.g.451.1 | 2 | |||
105.59 | even | 6 | 525.3.o.g.376.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.3.f.b.10.1 | ✓ | 2 | 21.2 | odd | 6 | ||
21.3.f.b.19.1 | yes | 2 | 21.17 | even | 6 | ||
63.3.m.c.10.1 | 2 | 7.2 | even | 3 | |||
63.3.m.c.19.1 | 2 | 7.3 | odd | 6 | |||
147.3.d.b.97.1 | 2 | 3.2 | odd | 2 | |||
147.3.d.b.97.2 | 2 | 21.20 | even | 2 | |||
147.3.f.c.19.1 | 2 | 21.11 | odd | 6 | |||
147.3.f.c.31.1 | 2 | 21.5 | even | 6 | |||
336.3.bh.a.145.1 | 2 | 84.59 | odd | 6 | |||
336.3.bh.a.241.1 | 2 | 84.23 | even | 6 | |||
441.3.d.b.244.1 | 2 | 7.6 | odd | 2 | inner | ||
441.3.d.b.244.2 | 2 | 1.1 | even | 1 | trivial | ||
441.3.m.e.19.1 | 2 | 7.4 | even | 3 | |||
441.3.m.e.325.1 | 2 | 7.5 | odd | 6 | |||
525.3.o.g.376.1 | 2 | 105.59 | even | 6 | |||
525.3.o.g.451.1 | 2 | 105.44 | odd | 6 | |||
525.3.s.c.124.1 | 4 | 105.17 | odd | 12 | |||
525.3.s.c.124.2 | 4 | 105.38 | odd | 12 | |||
525.3.s.c.199.1 | 4 | 105.23 | even | 12 | |||
525.3.s.c.199.2 | 4 | 105.2 | even | 12 | |||
1008.3.cg.g.145.1 | 2 | 28.3 | even | 6 | |||
1008.3.cg.g.577.1 | 2 | 28.23 | odd | 6 | |||
2352.3.f.d.97.1 | 2 | 84.83 | odd | 2 | |||
2352.3.f.d.97.2 | 2 | 12.11 | even | 2 |