Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,4,Mod(649,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.649");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.d (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: | \(53.1017190052\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 180) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 649.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 900.649 |
Dual form | 900.4.d.i.649.2 |
$q$-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 \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 2.00000i | − 0.107990i | −0.998541 | − | 0.0539949i | \(-0.982805\pi\) | ||||
0.998541 | − | 0.0539949i | \(-0.0171955\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 30.0000 | 0.822304 | 0.411152 | − | 0.911567i | \(-0.365127\pi\) | ||||
0.411152 | + | 0.911567i | \(0.365127\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 4.00000i | − 0.0853385i | −0.999089 | − | 0.0426692i | \(-0.986414\pi\) | ||||
0.999089 | − | 0.0426692i | \(-0.0135862\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 90.0000i | − 1.28401i | −0.766700 | − | 0.642006i | \(-0.778102\pi\) | ||||
0.766700 | − | 0.642006i | \(-0.221898\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 28.0000 | 0.338086 | 0.169043 | − | 0.985609i | \(-0.445932\pi\) | ||||
0.169043 | + | 0.985609i | \(0.445932\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 120.000i | 1.08790i | 0.839117 | + | 0.543951i | \(0.183072\pi\) | ||||
−0.839117 | + | 0.543951i | \(0.816928\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −210.000 | −1.34469 | −0.672345 | − | 0.740238i | \(-0.734713\pi\) | ||||
−0.672345 | + | 0.740238i | \(0.734713\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | −0.0231749 | −0.0115874 | − | 0.999933i | \(-0.503688\pi\) | ||||
−0.0115874 | + | 0.999933i | \(0.503688\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 200.000i | − 0.888643i | −0.895867 | − | 0.444322i | \(-0.853445\pi\) | ||||
0.895867 | − | 0.444322i | \(-0.146555\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 240.000 | 0.914188 | 0.457094 | − | 0.889418i | \(-0.348890\pi\) | ||||
0.457094 | + | 0.889418i | \(0.348890\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 136.000i | − 0.482321i | −0.970485 | − | 0.241161i | \(-0.922472\pi\) | ||||
0.970485 | − | 0.241161i | \(-0.0775280\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 120.000i | 0.372421i | 0.982510 | + | 0.186211i | \(0.0596207\pi\) | ||||
−0.982510 | + | 0.186211i | \(0.940379\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 339.000 | 0.988338 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 30.0000i | − 0.0777513i | −0.999244 | − | 0.0388756i | \(-0.987622\pi\) | ||||
0.999244 | − | 0.0388756i | \(-0.0123776\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 450.000 | 0.992966 | 0.496483 | − | 0.868046i | \(-0.334624\pi\) | ||||
0.496483 | + | 0.868046i | \(0.334624\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −166.000 | −0.348428 | −0.174214 | − | 0.984708i | \(-0.555738\pi\) | ||||
−0.174214 | + | 0.984708i | \(0.555738\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 908.000i | − 1.65567i | −0.560972 | − | 0.827835i | \(-0.689572\pi\) | ||||
0.560972 | − | 0.827835i | \(-0.310428\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1020.00 | −1.70495 | −0.852477 | − | 0.522765i | \(-0.824901\pi\) | ||||
−0.852477 | + | 0.522765i | \(0.824901\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 250.000i | − 0.400826i | −0.979712 | − | 0.200413i | \(-0.935772\pi\) | ||||
0.979712 | − | 0.200413i | \(-0.0642284\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 60.0000i | − 0.0888004i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 916.000 | 1.30453 | 0.652266 | − | 0.757990i | \(-0.273818\pi\) | ||||
0.652266 | + | 0.757990i | \(0.273818\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 1140.00i | − 1.50761i | −0.657101 | − | 0.753803i | \(-0.728217\pi\) | ||||
0.657101 | − | 0.753803i | \(-0.271783\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 420.000 | 0.500224 | 0.250112 | − | 0.968217i | \(-0.419533\pi\) | ||||
0.250112 | + | 0.968217i | \(0.419533\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.00000 | −0.00921569 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 1538.00i | − 1.60990i | −0.593343 | − | 0.804950i | \(-0.702192\pi\) | ||||
0.593343 | − | 0.804950i | \(-0.297808\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 450.000 | 0.443333 | 0.221667 | − | 0.975122i | \(-0.428850\pi\) | ||||
0.221667 | + | 0.975122i | \(0.428850\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 1150.00i | − 1.10012i | −0.835124 | − | 0.550062i | \(-0.814604\pi\) | ||||
0.835124 | − | 0.550062i | \(-0.185396\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1620.00i | 1.46366i | 0.681489 | + | 0.731829i | \(0.261333\pi\) | ||||
−0.681489 | + | 0.731829i | \(0.738667\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1702.00 | 1.49561 | 0.747807 | − | 0.663916i | \(-0.231107\pi\) | ||||
0.747807 | + | 0.663916i | \(0.231107\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1350.00i | 1.12387i | 0.827181 | + | 0.561935i | \(0.189943\pi\) | ||||
−0.827181 | + | 0.561935i | \(0.810057\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −180.000 | −0.138660 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −431.000 | −0.323817 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 2450.00i | − 1.71183i | −0.517117 | − | 0.855915i | \(-0.672995\pi\) | ||||
0.517117 | − | 0.855915i | \(-0.327005\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 690.000 | 0.460195 | 0.230098 | − | 0.973168i | \(-0.426095\pi\) | ||||
0.230098 | + | 0.973168i | \(0.426095\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 56.0000i | − 0.0365099i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 2070.00i | − 1.29089i | −0.763806 | − | 0.645445i | \(-0.776672\pi\) | ||||
0.763806 | − | 0.645445i | \(-0.223328\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1924.00 | 1.17404 | 0.587020 | − | 0.809572i | \(-0.300301\pi\) | ||||
0.587020 | + | 0.809572i | \(0.300301\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 120.000i | − 0.0701742i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2910.00 | −1.59998 | −0.799988 | − | 0.600016i | \(-0.795161\pi\) | ||||
−0.799988 | + | 0.600016i | \(0.795161\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 176.000 | 0.0948522 | 0.0474261 | − | 0.998875i | \(-0.484898\pi\) | ||||
0.0474261 | + | 0.998875i | \(0.484898\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 2348.00i | − 1.19357i | −0.802400 | − | 0.596786i | \(-0.796444\pi\) | ||||
0.802400 | − | 0.596786i | \(-0.203556\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 240.000 | 0.117482 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 1996.00i | − 0.959134i | −0.877505 | − | 0.479567i | \(-0.840794\pi\) | ||||
0.877505 | − | 0.479567i | \(-0.159206\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 3120.00i | − 1.44571i | −0.691002 | − | 0.722853i | \(-0.742830\pi\) | ||||
0.691002 | − | 0.722853i | \(-0.257170\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2181.00 | 0.992717 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1770.00i | 0.777865i | 0.921266 | + | 0.388932i | \(0.127156\pi\) | ||||
−0.921266 | + | 0.388932i | \(0.872844\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2130.00 | 0.889406 | 0.444703 | − | 0.895678i | \(-0.353309\pi\) | ||||
0.444703 | + | 0.895678i | \(0.353309\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1654.00 | −0.679231 | −0.339616 | − | 0.940564i | \(-0.610297\pi\) | ||||
−0.339616 | + | 0.940564i | \(0.610297\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 2700.00i | − 1.05585i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1740.00 | 0.659173 | 0.329586 | − | 0.944125i | \(-0.393091\pi\) | ||||
0.329586 | + | 0.944125i | \(0.393091\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 86.0000i | 0.0320747i | 0.999871 | + | 0.0160373i | \(0.00510506\pi\) | ||||
−0.999871 | + | 0.0160373i | \(0.994895\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2490.00i | 0.900534i | 0.892894 | + | 0.450267i | \(0.148671\pi\) | ||||
−0.892894 | + | 0.450267i | \(0.851329\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 832.000 | 0.296376 | 0.148188 | − | 0.988959i | \(-0.452656\pi\) | ||||
0.148188 | + | 0.988959i | \(0.452656\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 420.000i | 0.145213i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 840.000 | 0.278010 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2084.00 | 0.679945 | 0.339973 | − | 0.940435i | \(-0.389582\pi\) | ||||
0.339973 | + | 0.940435i | \(0.389582\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.00000i | 0.00250265i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −360.000 | −0.109576 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 1174.00i | − 0.352542i | −0.984342 | − | 0.176271i | \(-0.943597\pi\) | ||||
0.984342 | − | 0.176271i | \(-0.0564035\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3120.00i | 0.912254i | 0.889915 | + | 0.456127i | \(0.150764\pi\) | ||||
−0.889915 | + | 0.456127i | \(0.849236\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 58.0000 | 0.0167369 | 0.00836845 | − | 0.999965i | \(-0.497336\pi\) | ||||
0.00836845 | + | 0.999965i | \(0.497336\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 5910.00i | − 1.66170i | −0.556494 | − | 0.830852i | \(-0.687854\pi\) | ||||
0.556494 | − | 0.830852i | \(-0.312146\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3300.00 | −0.893135 | −0.446567 | − | 0.894750i | \(-0.647354\pi\) | ||||
−0.446567 | + | 0.894750i | \(0.647354\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2986.00 | −0.798113 | −0.399056 | − | 0.916926i | \(-0.630662\pi\) | ||||
−0.399056 | + | 0.916926i | \(0.630662\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 112.000i | − 0.0288518i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6630.00 | −1.66726 | −0.833629 | − | 0.552324i | \(-0.813741\pi\) | ||||
−0.833629 | + | 0.552324i | \(0.813741\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3600.00i | 0.894585i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1530.00i | 0.371357i | 0.982611 | + | 0.185679i | \(0.0594483\pi\) | ||||
−0.982611 | + | 0.185679i | \(0.940552\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −400.000 | −0.0959644 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2640.00i | 0.618971i | 0.950904 | + | 0.309486i | \(0.100157\pi\) | ||||
−0.950904 | + | 0.309486i | \(0.899843\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7350.00 | 1.66594 | 0.832969 | − | 0.553319i | \(-0.186639\pi\) | ||||
0.832969 | + | 0.553319i | \(0.186639\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3512.00 | 0.787228 | 0.393614 | − | 0.919276i | \(-0.371225\pi\) | ||||
0.393614 | + | 0.919276i | \(0.371225\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5368.00i | 1.16437i | 0.813055 | + | 0.582187i | \(0.197803\pi\) | ||||
−0.813055 | + | 0.582187i | \(0.802197\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3060.00 | −0.649624 | −0.324812 | − | 0.945779i | \(-0.605301\pi\) | ||||
−0.324812 | + | 0.945779i | \(0.605301\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 5044.00i | − 1.05949i | −0.848158 | − | 0.529743i | \(-0.822288\pi\) | ||||
0.848158 | − | 0.529743i | \(-0.177712\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 480.000i | − 0.0987230i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3187.00 | −0.648687 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 2010.00i | − 0.400769i | −0.979717 | − | 0.200385i | \(-0.935781\pi\) | ||||
0.979717 | − | 0.200385i | \(-0.0642192\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 480.000 | 0.0928399 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −272.000 | −0.0520858 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2752.00i | 0.511612i | 0.966728 | + | 0.255806i | \(0.0823409\pi\) | ||||
−0.966728 | + | 0.255806i | \(0.917659\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9540.00 | 1.73943 | 0.869717 | − | 0.493551i | \(-0.164301\pi\) | ||||
0.869717 | + | 0.493551i | \(0.164301\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9254.00i | 1.67114i | 0.549384 | + | 0.835570i | \(0.314863\pi\) | ||||
−0.549384 | + | 0.835570i | \(0.685137\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 150.000i | − 0.0265768i | −0.999912 | − | 0.0132884i | \(-0.995770\pi\) | ||||
0.999912 | − | 0.0132884i | \(-0.00422995\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6300.00 | −1.10574 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 2520.00i | − 0.434107i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 240.000 | 0.0402177 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1892.00 | 0.314180 | 0.157090 | − | 0.987584i | \(-0.449789\pi\) | ||||
0.157090 | + | 0.987584i | \(0.449789\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7378.00i | 1.19260i | 0.802763 | + | 0.596299i | \(0.203363\pi\) | ||||
−0.802763 | + | 0.596299i | \(0.796637\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −120.000 | −0.0190568 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1364.00i | − 0.214720i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 6720.00i | − 1.03962i | −0.854282 | − | 0.519811i | \(-0.826003\pi\) | ||||
0.854282 | − | 0.519811i | \(-0.173997\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5186.00 | −0.795416 | −0.397708 | − | 0.917512i | \(-0.630194\pi\) | ||||
−0.397708 | + | 0.917512i | \(0.630194\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3330.00i | 0.502091i | 0.967975 | + | 0.251045i | \(0.0807743\pi\) | ||||
−0.967975 | + | 0.251045i | \(0.919226\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9000.00 | −1.32312 | −0.661562 | − | 0.749890i | \(-0.730106\pi\) | ||||
−0.661562 | + | 0.749890i | \(0.730106\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6075.00 | −0.885698 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8758.00i | 1.24568i | 0.782350 | + | 0.622839i | \(0.214021\pi\) | ||||
−0.782350 | + | 0.622839i | \(0.785979\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −60.0000 | −0.00839635 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4724.00i | 0.655763i | 0.944719 | + | 0.327881i | \(0.106335\pi\) | ||||
−0.944719 | + | 0.327881i | \(0.893665\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 840.000i | 0.114754i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7292.00 | −0.988298 | −0.494149 | − | 0.869377i | \(-0.664520\pi\) | ||||
−0.494149 | + | 0.869377i | \(0.664520\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14520.0i | 1.93717i | 0.248676 | + | 0.968587i | \(0.420004\pi\) | ||||
−0.248676 | + | 0.968587i | \(0.579996\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7110.00 | −0.926713 | −0.463356 | − | 0.886172i | \(-0.653355\pi\) | ||||
−0.463356 | + | 0.886172i | \(0.653355\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10800.0 | 1.39688 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11488.0i | 1.45231i | 0.687532 | + | 0.726154i | \(0.258694\pi\) | ||||
−0.687532 | + | 0.726154i | \(0.741306\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 780.000 | 0.0971355 | 0.0485678 | − | 0.998820i | \(-0.484534\pi\) | ||||
0.0485678 | + | 0.998820i | \(0.484534\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.0000i | 0.00197771i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 6000.00i | − 0.730735i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5402.00 | −0.653085 | −0.326542 | − | 0.945183i | \(-0.605884\pi\) | ||||
−0.326542 | + | 0.945183i | \(0.605884\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 900.000i | − 0.107230i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2190.00 | 0.255342 | 0.127671 | − | 0.991817i | \(-0.459250\pi\) | ||||
0.127671 | + | 0.991817i | \(0.459250\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7162.00 | −0.829108 | −0.414554 | − | 0.910025i | \(-0.636062\pi\) | ||||
−0.414554 | + | 0.910025i | \(0.636062\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 332.000i | 0.0376267i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9360.00 | 1.04607 | 0.523034 | − | 0.852312i | \(-0.324800\pi\) | ||||
0.523034 | + | 0.852312i | \(0.324800\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12806.0i | 1.42129i | 0.703552 | + | 0.710643i | \(0.251596\pi\) | ||||
−0.703552 | + | 0.710643i | \(0.748404\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3360.00i | 0.367805i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11288.0 | −1.22721 | −0.613607 | − | 0.789612i | \(-0.710282\pi\) | ||||
−0.613607 | + | 0.789612i | \(0.710282\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 8520.00i | − 0.913764i | −0.889527 | − | 0.456882i | \(-0.848966\pi\) | ||||
0.889527 | − | 0.456882i | \(-0.151034\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1260.00 | 0.132434 | 0.0662172 | − | 0.997805i | \(-0.478907\pi\) | ||||
0.0662172 | + | 0.997805i | \(0.478907\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7200.00 | 0.751740 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13750.0i | 1.40744i | 0.710480 | + | 0.703718i | \(0.248478\pi\) | ||||
−0.710480 | + | 0.703718i | \(0.751522\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3210.00 | −0.324305 | −0.162152 | − | 0.986766i | \(-0.551844\pi\) | ||||
−0.162152 | + | 0.986766i | \(0.551844\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 12850.0i | − 1.28983i | −0.764255 | − | 0.644914i | \(-0.776893\pi\) | ||||
0.764255 | − | 0.644914i | \(-0.223107\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8220.00i | 0.814510i | 0.913314 | + | 0.407255i | \(0.133514\pi\) | ||||
−0.913314 | + | 0.407255i | \(0.866486\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1816.00 | −0.178795 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 4080.00i | − 0.396614i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7020.00 | 0.669628 | 0.334814 | − | 0.942284i | \(-0.391326\pi\) | ||||
0.334814 | + | 0.942284i | \(0.391326\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −800.000 | −0.0758355 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8122.00i | 0.755735i | 0.925860 | + | 0.377868i | \(0.123343\pi\) | ||||
−0.925860 | + | 0.377868i | \(0.876657\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13470.0 | −1.23807 | −0.619035 | − | 0.785363i | \(-0.712476\pi\) | ||||
−0.619035 | + | 0.785363i | \(0.712476\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18900.0i | 1.72660i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2040.00i | 0.184118i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2468.00 | −0.221409 | −0.110704 | − | 0.993853i | \(-0.535311\pi\) | ||||
−0.110704 | + | 0.993853i | \(0.535311\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 4440.00i | − 0.393578i | −0.980446 | − | 0.196789i | \(-0.936949\pi\) | ||||
0.980446 | − | 0.196789i | \(-0.0630514\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11190.0 | 0.974436 | 0.487218 | − | 0.873280i | \(-0.338012\pi\) | ||||
0.487218 | + | 0.873280i | \(0.338012\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −500.000 | −0.0432851 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3600.00i | 0.306243i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4020.00 | −0.338041 | −0.169021 | − | 0.985613i | \(-0.554060\pi\) | ||||
−0.169021 | + | 0.985613i | \(0.554060\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 9076.00i | − 0.758826i | −0.925228 | − | 0.379413i | \(-0.876126\pi\) | ||||
0.925228 | − | 0.379413i | \(-0.123874\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 360.000i | 0.0297568i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2233.00 | −0.183529 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 960.000i | − 0.0780154i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10170.0 | 0.812714 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7486.00 | −0.594914 | −0.297457 | − | 0.954735i | \(-0.596138\pi\) | ||||
−0.297457 | + | 0.954735i | \(0.596138\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 7400.00i | − 0.578430i | −0.957264 | − | 0.289215i | \(-0.906606\pi\) | ||||
0.957264 | − | 0.289215i | \(-0.0933942\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5880.00 | −0.454621 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 1832.00i | − 0.140876i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 11490.0i | − 0.874052i | −0.899449 | − | 0.437026i | \(-0.856032\pi\) | ||||
0.899449 | − | 0.437026i | \(-0.143968\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −544.000 | −0.0411606 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 19320.0i | − 1.44625i | −0.690715 | − | 0.723127i | \(-0.742704\pi\) | ||||
0.690715 | − | 0.723127i | \(-0.257296\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8340.00 | −0.614466 | −0.307233 | − | 0.951634i | \(-0.599403\pi\) | ||||
−0.307233 | + | 0.951634i | \(0.599403\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21044.0 | 1.54232 | 0.771159 | − | 0.636642i | \(-0.219677\pi\) | ||||
0.771159 | + | 0.636642i | \(0.219677\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 1418.00i | − 0.102309i | −0.998691 | − | 0.0511543i | \(-0.983710\pi\) | ||||
0.998691 | − | 0.0511543i | \(-0.0162900\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2280.00 | −0.162806 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 900.000i | − 0.0639351i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22020.0i | 1.54832i | 0.632991 | + | 0.774159i | \(0.281827\pi\) | ||||
−0.632991 | + | 0.774159i | \(0.718173\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −112.000 | −0.00783511 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 25230.0i | 1.74717i | 0.486671 | + | 0.873585i | \(0.338211\pi\) | ||||
−0.486671 | + | 0.873585i | \(0.661789\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8280.00 | −0.564794 | −0.282397 | − | 0.959298i | \(-0.591130\pi\) | ||||
−0.282397 | + | 0.959298i | \(0.591130\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18874.0 | −1.28101 | −0.640505 | − | 0.767954i | \(-0.721275\pi\) | ||||
−0.640505 | + | 0.767954i | \(0.721275\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 10550.0i | − 0.705455i | −0.935726 | − | 0.352728i | \(-0.885254\pi\) | ||||
0.935726 | − | 0.352728i | \(-0.114746\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 480.000 | 0.0317819 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11000.0i | 0.724773i | 0.932028 | + | 0.362386i | \(0.118038\pi\) | ||||
−0.932028 | + | 0.362386i | \(0.881962\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11310.0i | 0.737963i | 0.929437 | + | 0.368982i | \(0.120294\pi\) | ||||
−0.929437 | + | 0.368982i | \(0.879706\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17572.0 | 1.14100 | 0.570499 | − | 0.821298i | \(-0.306750\pi\) | ||||
0.570499 | + | 0.821298i | \(0.306750\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 840.000i | − 0.0540191i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −18000.0 | −1.14103 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1604.00 | 0.101195 | 0.0505976 | − | 0.998719i | \(-0.483887\pi\) | ||||
0.0505976 | + | 0.998719i | \(0.483887\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 1356.00i | − 0.0843433i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 31320.0 | 1.92990 | 0.964950 | − | 0.262435i | \(-0.0845254\pi\) | ||||
0.964950 | + | 0.262435i | \(0.0845254\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 31300.0i | − 1.91968i | −0.280555 | − | 0.959838i | \(-0.590519\pi\) | ||||
0.280555 | − | 0.959838i | \(-0.409481\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 10920.0i | − 0.663539i | −0.943361 | − | 0.331769i | \(-0.892354\pi\) | ||||
0.943361 | − | 0.331769i | \(-0.107646\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13500.0 | 0.816520 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 3210.00i | − 0.192369i | −0.995364 | − | 0.0961845i | \(-0.969336\pi\) | ||||
0.995364 | − | 0.0961845i | \(-0.0306639\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11910.0 | 0.704018 | 0.352009 | − | 0.935997i | \(-0.385499\pi\) | ||||
0.352009 | + | 0.935997i | \(0.385499\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3382.00 | −0.199008 | −0.0995042 | − | 0.995037i | \(-0.531726\pi\) | ||||
−0.0995042 | + | 0.995037i | \(0.531726\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 25200.0i | − 1.46289i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4980.00 | −0.286514 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15950.0i | 0.913562i | 0.889579 | + | 0.456781i | \(0.150998\pi\) | ||||
−0.889579 | + | 0.456781i | \(0.849002\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 32190.0i | − 1.82742i | −0.406369 | − | 0.913709i | \(-0.633205\pi\) | ||||
0.406369 | − | 0.913709i | \(-0.366795\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3076.00 | −0.173853 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22140.0i | 1.24036i | 0.784461 | + | 0.620178i | \(0.212940\pi\) | ||||
−0.784461 | + | 0.620178i | \(0.787060\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −120.000 | −0.00663518 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6172.00 | −0.339789 | −0.169894 | − | 0.985462i | \(-0.554343\pi\) | ||||
−0.169894 | + | 0.985462i | \(0.554343\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 21600.0i | − 1.17383i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19170.0 | 1.03287 | 0.516434 | − | 0.856327i | \(-0.327259\pi\) | ||||
0.516434 | + | 0.856327i | \(0.327259\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 5600.00i | − 0.300438i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 900.000i | − 0.0478755i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21898.0 | 1.15994 | 0.579969 | − | 0.814638i | \(-0.303064\pi\) | ||||
0.579969 | + | 0.814638i | \(0.303064\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 480.000i | − 0.0252120i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16680.0 | −0.865173 | −0.432586 | − | 0.901593i | \(-0.642399\pi\) | ||||
−0.432586 | + | 0.901593i | \(0.642399\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2300.00 | −0.118802 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 6518.00i | − 0.332516i | −0.986082 | − | 0.166258i | \(-0.946832\pi\) | ||||
0.986082 | − | 0.166258i | \(-0.0531685\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12240.0 | −0.619306 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 23200.0i | − 1.16905i | −0.811377 | − | 0.584524i | \(-0.801281\pi\) | ||||
0.811377 | − | 0.584524i | \(-0.198719\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 27240.0i | − 1.36146i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16324.0 | 0.812568 | 0.406284 | − | 0.913747i | \(-0.366824\pi\) | ||||
0.406284 | + | 0.913747i | \(0.366824\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 120.000i | − 0.00592513i | −0.999996 | − | 0.00296257i | \(-0.999057\pi\) | ||||
0.999996 | − | 0.00296257i | \(-0.000943015\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3240.00 | 0.158060 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30548.0 | 1.48430 | 0.742152 | − | 0.670232i | \(-0.233805\pi\) | ||||
0.742152 | + | 0.670232i | \(0.233805\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 16952.0i | − 0.813911i | −0.913448 | − | 0.406956i | \(-0.866590\pi\) | ||||
0.913448 | − | 0.406956i | \(-0.133410\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20220.0 | −0.963173 | −0.481586 | − | 0.876399i | \(-0.659939\pi\) | ||||
−0.481586 | + | 0.876399i | \(0.659939\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 3404.00i | − 0.161511i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 1800.00i | − 0.0847382i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20722.0 | 0.971722 | 0.485861 | − | 0.874036i | \(-0.338506\pi\) | ||||
0.485861 | + | 0.874036i | \(0.338506\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4350.00i | 0.202404i | 0.994866 | + | 0.101202i | \(0.0322689\pi\) | ||||
−0.994866 | + | 0.101202i | \(0.967731\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6720.00 | 0.309074 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −30600.0 | −1.40199 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 41972.0i | − 1.90107i | −0.310621 | − | 0.950534i | \(-0.600537\pi\) | ||||
0.310621 | − | 0.950534i | \(-0.399463\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2700.00 | 0.121367 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 664.000i | 0.0297343i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 39510.0i | 1.75598i | 0.478679 | + | 0.877990i | \(0.341116\pi\) | ||||
−0.478679 | + | 0.877990i | \(0.658884\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10800.0 | 0.478193 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 7500.00i | − 0.329601i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −16680.0 | −0.724892 | −0.362446 | − | 0.932005i | \(-0.618058\pi\) | ||||
−0.362446 | + | 0.932005i | \(0.618058\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15484.0 | −0.670428 | −0.335214 | − | 0.942142i | \(-0.608809\pi\) | ||||
−0.335214 | + | 0.942142i | \(0.608809\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 3808.00i | − 0.163066i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4170.00 | 0.177264 | 0.0886322 | − | 0.996064i | \(-0.471750\pi\) | ||||
0.0886322 | + | 0.996064i | \(0.471750\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 30226.0i | − 1.28021i | −0.768288 | − | 0.640105i | \(-0.778891\pi\) | ||||
0.768288 | − | 0.640105i | \(-0.221109\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14760.0i | 0.620623i | 0.950635 | + | 0.310312i | \(0.100433\pi\) | ||||
−0.950635 | + | 0.310312i | \(0.899567\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9934.00 | 0.416191 | 0.208095 | − | 0.978109i | \(-0.433274\pi\) | ||||
0.208095 | + | 0.978109i | \(0.433274\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 30510.0i | − 1.26904i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 23520.0 | 0.967820 | 0.483910 | − | 0.875118i | \(-0.339216\pi\) | ||||
0.483910 | + | 0.875118i | \(0.339216\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19711.0 | 0.808192 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 862.000i | 0.0349689i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 24000.0 | 0.966756 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29816.0i | 1.19681i | 0.801193 | + | 0.598406i | \(0.204199\pi\) | ||||
−0.801193 | + | 0.598406i | \(0.795801\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 35430.0i | 1.41221i | 0.708106 | + | 0.706106i | \(0.249550\pi\) | ||||
−0.708106 | + | 0.706106i | \(0.750450\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 36196.0 | 1.43771 | 0.718854 | − | 0.695161i | \(-0.244667\pi\) | ||||
0.718854 | + | 0.695161i | \(0.244667\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 480.000i | 0.0189332i | 0.999955 | + | 0.00946662i | \(0.00301336\pi\) | ||||
−0.999955 | + | 0.00946662i | \(0.996987\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 27480.0 | 1.07272 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3632.00 | −0.141292 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 28532.0i | − 1.09858i | −0.835631 | − | 0.549291i | \(-0.814898\pi\) | ||||
0.835631 | − | 0.549291i | \(-0.185102\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20340.0 | −0.777834 | −0.388917 | − | 0.921273i | \(-0.627151\pi\) | ||||
−0.388917 | + | 0.921273i | \(0.627151\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 10756.0i | − 0.409930i | −0.978769 | − | 0.204965i | \(-0.934292\pi\) | ||||
0.978769 | − | 0.204965i | \(-0.0657081\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 600.000i | − 0.0227125i | −0.999936 | − | 0.0113563i | \(-0.996385\pi\) | ||||
0.999936 | − | 0.0113563i | \(-0.00361489\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4900.00 | −0.184860 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3360.00i | 0.125911i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 840.000 | 0.0311630 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2700.00 | −0.0998336 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 25400.0i | − 0.929871i | −0.885345 | − | 0.464936i | \(-0.846077\pi\) | ||||
0.885345 | − | 0.464936i | \(-0.153923\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36240.0 | −1.31799 | −0.658993 | − | 0.752149i | \(-0.729017\pi\) | ||||
−0.658993 | + | 0.752149i | \(0.729017\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 34200.0i | − 1.23971i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 1380.00i | − 0.0496964i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6572.00 | −0.235898 | −0.117949 | − | 0.993020i | \(-0.537632\pi\) | ||||
−0.117949 | + | 0.993020i | \(0.537632\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4080.00i | 0.145498i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2340.00 | −0.0826404 | −0.0413202 | − | 0.999146i | \(-0.513156\pi\) | ||||
−0.0413202 | + | 0.999146i | \(0.513156\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9492.00 | 0.334144 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 2522.00i | − 0.0879297i | −0.999033 | − | 0.0439649i | \(-0.986001\pi\) | ||||
0.999033 | − | 0.0439649i | \(-0.0139990\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −52770.0 | −1.82811 | −0.914056 | − | 0.405589i | \(-0.867067\pi\) | ||||
−0.914056 | + | 0.405589i | \(0.867067\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 28800.0i | 0.994546i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 28200.0i | − 0.967663i | −0.875161 | − | 0.483832i | \(-0.839245\pi\) | ||||
0.875161 | − | 0.483832i | \(-0.160755\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1000.00 | −0.0342059 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 15570.0i | − 0.529236i | −0.964353 | − | 0.264618i | \(-0.914754\pi\) | ||||
0.964353 | − | 0.264618i | \(-0.0852458\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4140.00 | −0.139403 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29775.0 | −0.999463 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8350.00i | 0.277681i | 0.990315 | + | 0.138841i | \(0.0443376\pi\) | ||||
−0.990315 | + | 0.138841i | \(0.955662\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 43650.0 | 1.44263 | 0.721316 | − | 0.692606i | \(-0.243538\pi\) | ||||
0.721316 | + | 0.692606i | \(0.243538\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 3848.00i | − 0.126784i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 18810.0i | − 0.615952i | −0.951394 | − | 0.307976i | \(-0.900348\pi\) | ||||
0.951394 | − | 0.307976i | \(-0.0996517\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12600.0 | 0.411336 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 25320.0i | − 0.821549i | −0.911737 | − | 0.410774i | \(-0.865258\pi\) | ||||
0.911737 | − | 0.410774i | \(-0.134742\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16320.0 | 0.524718 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6736.00 | −0.215919 | −0.107960 | − | 0.994155i | \(-0.534432\pi\) | ||||
−0.107960 | + | 0.994155i | \(0.534432\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20500.0i | 0.651195i | 0.945508 | + | 0.325598i | \(0.105565\pi\) | ||||
−0.945508 | + | 0.325598i | \(0.894435\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 900.4.d.i.649.1 | 2 | ||
3.2 | odd | 2 | 900.4.d.d.649.1 | 2 | |||
5.2 | odd | 4 | 180.4.a.e.1.1 | yes | 1 | ||
5.3 | odd | 4 | 900.4.a.j.1.1 | 1 | |||
5.4 | even | 2 | inner | 900.4.d.i.649.2 | 2 | ||
15.2 | even | 4 | 180.4.a.b.1.1 | ✓ | 1 | ||
15.8 | even | 4 | 900.4.a.i.1.1 | 1 | |||
15.14 | odd | 2 | 900.4.d.d.649.2 | 2 | |||
20.7 | even | 4 | 720.4.a.w.1.1 | 1 | |||
45.2 | even | 12 | 1620.4.i.i.1081.1 | 2 | |||
45.7 | odd | 12 | 1620.4.i.c.1081.1 | 2 | |||
45.22 | odd | 12 | 1620.4.i.c.541.1 | 2 | |||
45.32 | even | 12 | 1620.4.i.i.541.1 | 2 | |||
60.47 | odd | 4 | 720.4.a.h.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
180.4.a.b.1.1 | ✓ | 1 | 15.2 | even | 4 | ||
180.4.a.e.1.1 | yes | 1 | 5.2 | odd | 4 | ||
720.4.a.h.1.1 | 1 | 60.47 | odd | 4 | |||
720.4.a.w.1.1 | 1 | 20.7 | even | 4 | |||
900.4.a.i.1.1 | 1 | 15.8 | even | 4 | |||
900.4.a.j.1.1 | 1 | 5.3 | odd | 4 | |||
900.4.d.d.649.1 | 2 | 3.2 | odd | 2 | |||
900.4.d.d.649.2 | 2 | 15.14 | odd | 2 | |||
900.4.d.i.649.1 | 2 | 1.1 | even | 1 | trivial | ||
900.4.d.i.649.2 | 2 | 5.4 | even | 2 | inner | ||
1620.4.i.c.541.1 | 2 | 45.22 | odd | 12 | |||
1620.4.i.c.1081.1 | 2 | 45.7 | odd | 12 | |||
1620.4.i.i.541.1 | 2 | 45.32 | even | 12 | |||
1620.4.i.i.1081.1 | 2 | 45.2 | even | 12 |