Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1800,4,Mod(649,1800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1800.649");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1800.f (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: | \(106.203438010\) |
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 360) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 649.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1800.649 |
Dual form | 1800.4.f.t.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 \(\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1001\) | \(1351\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 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 | ||||||||
\(11\) | 34.0000 | 0.931944 | 0.465972 | − | 0.884799i | \(-0.345705\pi\) | ||||
0.465972 | + | 0.884799i | \(0.345705\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 68.0000i | − 1.45075i | −0.688352 | − | 0.725377i | \(-0.741665\pi\) | ||||
0.688352 | − | 0.725377i | \(-0.258335\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 38.0000i | − 0.542138i | −0.962560 | − | 0.271069i | \(-0.912623\pi\) | ||||
0.962560 | − | 0.271069i | \(-0.0873772\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.00000 | −0.0482980 | −0.0241490 | − | 0.999708i | \(-0.507688\pi\) | ||||
−0.0241490 | + | 0.999708i | \(0.507688\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 152.000i | − 1.37801i | −0.724757 | − | 0.689004i | \(-0.758048\pi\) | ||||
0.724757 | − | 0.689004i | \(-0.241952\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −46.0000 | −0.294551 | −0.147276 | − | 0.989095i | \(-0.547050\pi\) | ||||
−0.147276 | + | 0.989095i | \(0.547050\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −260.000 | −1.50637 | −0.753184 | − | 0.657810i | \(-0.771483\pi\) | ||||
−0.753184 | + | 0.657810i | \(0.771483\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 312.000i | 1.38628i | 0.720801 | + | 0.693142i | \(0.243774\pi\) | ||||
−0.720801 | + | 0.693142i | \(0.756226\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −48.0000 | −0.182838 | −0.0914188 | − | 0.995813i | \(-0.529140\pi\) | ||||
−0.0914188 | + | 0.995813i | \(0.529140\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 200.000i | − 0.709296i | −0.935000 | − | 0.354648i | \(-0.884601\pi\) | ||||
0.935000 | − | 0.354648i | \(-0.115399\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 104.000i | 0.322765i | 0.986892 | + | 0.161383i | \(0.0515953\pi\) | ||||
−0.986892 | + | 0.161383i | \(0.948405\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 339.000 | 0.988338 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 414.000i | 1.07297i | 0.843911 | + | 0.536484i | \(0.180248\pi\) | ||||
−0.843911 | + | 0.536484i | \(0.819752\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.00000 | −0.00441318 | −0.00220659 | − | 0.999998i | \(-0.500702\pi\) | ||||
−0.00220659 | + | 0.999998i | \(0.500702\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −38.0000 | −0.0797607 | −0.0398803 | − | 0.999204i | \(-0.512698\pi\) | ||||
−0.0398803 | + | 0.999204i | \(0.512698\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 244.000i | 0.444916i | 0.974942 | + | 0.222458i | \(0.0714080\pi\) | ||||
−0.974942 | + | 0.222458i | \(0.928592\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −708.000 | −1.18344 | −0.591719 | − | 0.806144i | \(-0.701551\pi\) | ||||
−0.591719 | + | 0.806144i | \(0.701551\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 378.000i | − 0.606049i | −0.952983 | − | 0.303024i | \(-0.902004\pi\) | ||||
0.952983 | − | 0.303024i | \(-0.0979963\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 68.0000i | − 0.100641i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 852.000 | 1.21339 | 0.606693 | − | 0.794936i | \(-0.292496\pi\) | ||||
0.606693 | + | 0.794936i | \(0.292496\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 844.000i | − 1.11616i | −0.829788 | − | 0.558079i | \(-0.811539\pi\) | ||||
0.829788 | − | 0.558079i | \(-0.188461\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1380.00 | −1.64359 | −0.821796 | − | 0.569782i | \(-0.807028\pi\) | ||||
−0.821796 | + | 0.569782i | \(0.807028\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −136.000 | −0.156667 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 514.000i | − 0.538029i | −0.963136 | − | 0.269014i | \(-0.913302\pi\) | ||||
0.963136 | − | 0.269014i | \(-0.0866979\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 702.000 | 0.691600 | 0.345800 | − | 0.938308i | \(-0.387608\pi\) | ||||
0.345800 | + | 0.938308i | \(0.387608\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 898.000i | 0.859054i | 0.903054 | + | 0.429527i | \(0.141320\pi\) | ||||
−0.903054 | + | 0.429527i | \(0.858680\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 876.000i | 0.791459i | 0.918367 | + | 0.395730i | \(0.129508\pi\) | ||||
−0.918367 | + | 0.395730i | \(0.870492\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −602.000 | −0.529001 | −0.264501 | − | 0.964386i | \(-0.585207\pi\) | ||||
−0.264501 | + | 0.964386i | \(0.585207\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 1350.00i | − 1.12387i | −0.827181 | − | 0.561935i | \(-0.810057\pi\) | ||||
0.827181 | − | 0.561935i | \(-0.189943\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −76.0000 | −0.0585455 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −175.000 | −0.131480 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 366.000i | 0.255726i | 0.991792 | + | 0.127863i | \(0.0408118\pi\) | ||||
−0.991792 | + | 0.127863i | \(0.959188\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −498.000 | −0.332141 | −0.166070 | − | 0.986114i | \(-0.553108\pi\) | ||||
−0.166070 | + | 0.986114i | \(0.553108\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.00000i | 0.00521570i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 2026.00i | − 1.26345i | −0.775192 | − | 0.631726i | \(-0.782347\pi\) | ||||
0.775192 | − | 0.631726i | \(-0.217653\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2460.00 | −1.50111 | −0.750556 | − | 0.660807i | \(-0.770214\pi\) | ||||
−0.750556 | + | 0.660807i | \(0.770214\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 2312.00i | − 1.35202i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3362.00 | −1.84850 | −0.924248 | − | 0.381794i | \(-0.875306\pi\) | ||||
−0.924248 | + | 0.381794i | \(0.875306\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2096.00 | 1.12960 | 0.564802 | − | 0.825227i | \(-0.308953\pi\) | ||||
0.564802 | + | 0.825227i | \(0.308953\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 2092.00i | − 1.06344i | −0.846921 | − | 0.531719i | \(-0.821546\pi\) | ||||
0.846921 | − | 0.531719i | \(-0.178454\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −304.000 | −0.148811 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 244.000i | 0.117249i | 0.998280 | + | 0.0586244i | \(0.0186714\pi\) | ||||
−0.998280 | + | 0.0586244i | \(0.981329\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2064.00i | 0.956390i | 0.878254 | + | 0.478195i | \(0.158709\pi\) | ||||
−0.878254 | + | 0.478195i | \(0.841291\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2427.00 | −1.10469 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 1258.00i | − 0.552855i | −0.961035 | − | 0.276428i | \(-0.910849\pi\) | ||||
0.961035 | − | 0.276428i | \(-0.0891506\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3986.00 | −1.66440 | −0.832200 | − | 0.554475i | \(-0.812919\pi\) | ||||
−0.832200 | + | 0.554475i | \(0.812919\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2570.00 | 1.05540 | 0.527698 | − | 0.849432i | \(-0.323055\pi\) | ||||
0.527698 | + | 0.849432i | \(0.323055\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 1292.00i | − 0.505243i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4684.00 | −1.77446 | −0.887231 | − | 0.461325i | \(-0.847374\pi\) | ||||
−0.887231 | + | 0.461325i | \(0.847374\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 214.000i | 0.0798138i | 0.999203 | + | 0.0399069i | \(0.0127061\pi\) | ||||
−0.999203 | + | 0.0399069i | \(0.987294\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3014.00i | 1.09004i | 0.838422 | + | 0.545022i | \(0.183479\pi\) | ||||
−0.838422 | + | 0.545022i | \(0.816521\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1792.00 | 0.638349 | 0.319175 | − | 0.947696i | \(-0.396594\pi\) | ||||
0.319175 | + | 0.947696i | \(0.396594\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 92.0000i | 0.0318085i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −136.000 | −0.0450111 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4540.00 | −1.48126 | −0.740631 | − | 0.671911i | \(-0.765474\pi\) | ||||
−0.740631 | + | 0.671911i | \(0.765474\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 520.000i | 0.162672i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2584.00 | −0.786510 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6506.00i | 1.95369i | 0.213937 | + | 0.976847i | \(0.431371\pi\) | ||||
−0.213937 | + | 0.976847i | \(0.568629\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 3696.00i | − 1.08067i | −0.841450 | − | 0.540335i | \(-0.818297\pi\) | ||||
0.841450 | − | 0.540335i | \(-0.181703\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3386.00 | 0.977088 | 0.488544 | − | 0.872539i | \(-0.337528\pi\) | ||||
0.488544 | + | 0.872539i | \(0.337528\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 3306.00i | − 0.929542i | −0.885431 | − | 0.464771i | \(-0.846137\pi\) | ||||
0.885431 | − | 0.464771i | \(-0.153863\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4188.00 | −1.13347 | −0.566735 | − | 0.823900i | \(-0.691794\pi\) | ||||
−0.566735 | + | 0.823900i | \(0.691794\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5462.00 | 1.45991 | 0.729955 | − | 0.683495i | \(-0.239541\pi\) | ||||
0.729955 | + | 0.683495i | \(0.239541\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 272.000i | 0.0700686i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3366.00 | 0.846454 | 0.423227 | − | 0.906024i | \(-0.360897\pi\) | ||||
0.423227 | + | 0.906024i | \(0.360897\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 5168.00i | − 1.28423i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1158.00i | 0.281066i | 0.990076 | + | 0.140533i | \(0.0448817\pi\) | ||||
−0.990076 | + | 0.140533i | \(0.955118\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 624.000 | 0.149705 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 8304.00i | − 1.94695i | −0.228804 | − | 0.973473i | \(-0.573481\pi\) | ||||
0.228804 | − | 0.973473i | \(-0.426519\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7478.00 | −1.69495 | −0.847475 | − | 0.530835i | \(-0.821878\pi\) | ||||
−0.847475 | + | 0.530835i | \(0.821878\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6792.00 | −1.52245 | −0.761226 | − | 0.648486i | \(-0.775402\pi\) | ||||
−0.761226 | + | 0.648486i | \(0.775402\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2296.00i | 0.498026i | 0.968500 | + | 0.249013i | \(0.0801062\pi\) | ||||
−0.968500 | + | 0.249013i | \(0.919894\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3980.00 | −0.844936 | −0.422468 | − | 0.906378i | \(-0.638836\pi\) | ||||
−0.422468 | + | 0.906378i | \(0.638836\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 1972.00i | − 0.414216i | −0.978318 | − | 0.207108i | \(-0.933595\pi\) | ||||
0.978318 | − | 0.207108i | \(-0.0664052\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 96.0000i | 0.0197446i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3469.00 | 0.706086 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 9254.00i | − 1.84513i | −0.385836 | − | 0.922567i | \(-0.626087\pi\) | ||||
0.385836 | − | 0.922567i | \(-0.373913\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10336.0 | −1.99915 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −400.000 | −0.0765967 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5888.00i | 1.09461i | 0.836933 | + | 0.547306i | \(0.184347\pi\) | ||||
−0.836933 | + | 0.547306i | \(0.815653\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4604.00 | 0.839450 | 0.419725 | − | 0.907651i | \(-0.362127\pi\) | ||||
0.419725 | + | 0.907651i | \(0.362127\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 8026.00i | − 1.44938i | −0.689074 | − | 0.724691i | \(-0.741983\pi\) | ||||
0.689074 | − | 0.724691i | \(-0.258017\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2838.00i | 0.502833i | 0.967879 | + | 0.251416i | \(0.0808963\pi\) | ||||
−0.967879 | + | 0.251416i | \(0.919104\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1564.00 | −0.274505 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 152.000i | 0.0261842i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 208.000 | 0.0348554 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1020.00 | −0.169378 | −0.0846892 | − | 0.996407i | \(-0.526990\pi\) | ||||
−0.0846892 | + | 0.996407i | \(0.526990\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 814.000i | − 0.131577i | −0.997834 | − | 0.0657884i | \(-0.979044\pi\) | ||||
0.997834 | − | 0.0657884i | \(-0.0209562\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8840.00 | −1.40385 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1364.00i | − 0.214720i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 4544.00i | − 0.702982i | −0.936191 | − | 0.351491i | \(-0.885675\pi\) | ||||
0.936191 | − | 0.351491i | \(-0.114325\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6978.00 | −1.07027 | −0.535134 | − | 0.844767i | \(-0.679739\pi\) | ||||
−0.535134 | + | 0.844767i | \(0.679739\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 2818.00i | − 0.424892i | −0.977173 | − | 0.212446i | \(-0.931857\pi\) | ||||
0.977173 | − | 0.212446i | \(-0.0681430\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 744.000 | 0.109378 | 0.0546892 | − | 0.998503i | \(-0.482583\pi\) | ||||
0.0546892 | + | 0.998503i | \(0.482583\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6843.00 | −0.997667 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6454.00i | 0.917973i | 0.888443 | + | 0.458986i | \(0.151787\pi\) | ||||
−0.888443 | + | 0.458986i | \(0.848213\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 828.000 | 0.115870 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 5900.00i | − 0.819009i | −0.912308 | − | 0.409505i | \(-0.865702\pi\) | ||||
0.912308 | − | 0.409505i | \(-0.134298\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3128.00i | 0.427321i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11876.0 | 1.60958 | 0.804788 | − | 0.593563i | \(-0.202279\pi\) | ||||
0.804788 | + | 0.593563i | \(0.202279\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 552.000i | 0.0736446i | 0.999322 | + | 0.0368223i | \(0.0117236\pi\) | ||||
−0.999322 | + | 0.0368223i | \(0.988276\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1722.00 | −0.224444 | −0.112222 | − | 0.993683i | \(-0.535797\pi\) | ||||
−0.112222 | + | 0.993683i | \(0.535797\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5776.00 | −0.747071 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 4576.00i | − 0.578496i | −0.957254 | − | 0.289248i | \(-0.906595\pi\) | ||||
0.957254 | − | 0.289248i | \(-0.0934052\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2892.00 | −0.360149 | −0.180074 | − | 0.983653i | \(-0.557634\pi\) | ||||
−0.180074 | + | 0.983653i | \(0.557634\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 17680.0i | 2.18537i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10608.0i | 1.29194i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 230.000 | 0.0278063 | 0.0139031 | − | 0.999903i | \(-0.495574\pi\) | ||||
0.0139031 | + | 0.999903i | \(0.495574\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.00000i | 0 0.000476579i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15438.0 | −1.79999 | −0.899995 | − | 0.435901i | \(-0.856430\pi\) | ||||
−0.899995 | + | 0.435901i | \(0.856430\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12294.0 | 1.42321 | 0.711607 | − | 0.702578i | \(-0.247968\pi\) | ||||
0.711607 | + | 0.702578i | \(0.247968\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 76.0000i | 0.00861334i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17488.0 | −1.95445 | −0.977224 | − | 0.212209i | \(-0.931934\pi\) | ||||
−0.977224 | + | 0.212209i | \(0.931934\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 8698.00i | − 0.965356i | −0.875798 | − | 0.482678i | \(-0.839664\pi\) | ||||
0.875798 | − | 0.482678i | \(-0.160336\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 608.000i | 0.0665551i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8536.00 | −0.928021 | −0.464010 | − | 0.885830i | \(-0.653590\pi\) | ||||
−0.464010 | + | 0.885830i | \(0.653590\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8712.00i | 0.934356i | 0.884163 | + | 0.467178i | \(0.154729\pi\) | ||||
−0.884163 | + | 0.467178i | \(0.845271\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5484.00 | −0.576405 | −0.288203 | − | 0.957569i | \(-0.593058\pi\) | ||||
−0.288203 | + | 0.957569i | \(0.593058\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1632.00 | −0.170394 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 19402.0i | − 1.98597i | −0.118250 | − | 0.992984i | \(-0.537728\pi\) | ||||
0.118250 | − | 0.992984i | \(-0.462272\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13578.0 | 1.37178 | 0.685890 | − | 0.727705i | \(-0.259413\pi\) | ||||
0.685890 | + | 0.727705i | \(0.259413\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6222.00i | 0.624537i | 0.949994 | + | 0.312269i | \(0.101089\pi\) | ||||
−0.949994 | + | 0.312269i | \(0.898911\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 15260.0i | − 1.51210i | −0.654516 | − | 0.756048i | \(-0.727128\pi\) | ||||
0.654516 | − | 0.756048i | \(-0.272872\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 488.000 | 0.0480464 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 6800.00i | − 0.661024i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9812.00 | 0.935953 | 0.467977 | − | 0.883741i | \(-0.344983\pi\) | ||||
0.467977 | + | 0.883741i | \(0.344983\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21216.0 | 2.01116 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7226.00i | 0.672364i | 0.941797 | + | 0.336182i | \(0.109136\pi\) | ||||
−0.941797 | + | 0.336182i | \(0.890864\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6750.00 | 0.620414 | 0.310207 | − | 0.950669i | \(-0.399602\pi\) | ||||
0.310207 | + | 0.950669i | \(0.399602\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1748.00i | 0.159688i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1416.00i | 0.127799i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4156.00 | 0.372842 | 0.186421 | − | 0.982470i | \(-0.440311\pi\) | ||||
0.186421 | + | 0.982470i | \(0.440311\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 14088.0i | − 1.24881i | −0.781100 | − | 0.624406i | \(-0.785341\pi\) | ||||
0.781100 | − | 0.624406i | \(-0.214659\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16970.0 | 1.47776 | 0.738882 | − | 0.673835i | \(-0.235354\pi\) | ||||
0.738882 | + | 0.673835i | \(0.235354\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −756.000 | −0.0654471 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3536.00i | 0.300799i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8500.00 | 0.714763 | 0.357382 | − | 0.933958i | \(-0.383670\pi\) | ||||
0.357382 | + | 0.933958i | \(0.383670\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20620.0i | 1.72400i | 0.506912 | + | 0.861998i | \(0.330787\pi\) | ||||
−0.506912 | + | 0.861998i | \(0.669213\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9880.00i | 0.816660i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10937.0 | −0.898907 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3264.00i | 0.265252i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11526.0 | 0.921076 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5314.00 | 0.422304 | 0.211152 | − | 0.977453i | \(-0.432278\pi\) | ||||
0.211152 | + | 0.977453i | \(0.432278\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 24104.0i | − 1.88412i | −0.335447 | − | 0.942059i | \(-0.608887\pi\) | ||||
0.335447 | − | 0.942059i | \(-0.391113\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 184.000 | 0.0142262 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 1704.00i | − 0.131033i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 23582.0i | − 1.79390i | −0.442134 | − | 0.896949i | \(-0.645778\pi\) | ||||
0.442134 | − | 0.896949i | \(-0.354222\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13600.0 | −1.02901 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2680.00i | 0.200619i | 0.994956 | + | 0.100310i | \(0.0319833\pi\) | ||||
−0.994956 | + | 0.100310i | \(0.968017\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −25004.0 | −1.84222 | −0.921109 | − | 0.389304i | \(-0.872715\pi\) | ||||
−0.921109 | + | 0.389304i | \(0.872715\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11180.0 | −0.819384 | −0.409692 | − | 0.912224i | \(-0.634364\pi\) | ||||
−0.409692 | + | 0.912224i | \(0.634364\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15862.0i | 1.14444i | 0.820099 | + | 0.572222i | \(0.193918\pi\) | ||||
−0.820099 | + | 0.572222i | \(0.806082\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1688.00 | −0.120534 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14076.0i | 0.999946i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15036.0i | 1.05724i | 0.848857 | + | 0.528622i | \(0.177291\pi\) | ||||
−0.848857 | + | 0.528622i | \(0.822709\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1040.00 | 0.0727546 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12786.0i | 0.885427i | 0.896663 | + | 0.442713i | \(0.145984\pi\) | ||||
−0.896663 | + | 0.442713i | \(0.854016\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13464.0 | 0.918404 | 0.459202 | − | 0.888332i | \(-0.348135\pi\) | ||||
0.459202 | + | 0.888332i | \(0.348135\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8518.00 | 0.578131 | 0.289065 | − | 0.957309i | \(-0.406656\pi\) | ||||
0.289065 | + | 0.957309i | \(0.406656\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11082.0i | 0.741029i | 0.928827 | + | 0.370514i | \(0.120819\pi\) | ||||
−0.928827 | + | 0.370514i | \(0.879181\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7072.00 | 0.468253 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 26568.0i | − 1.75052i | −0.483649 | − | 0.875262i | \(-0.660689\pi\) | ||||
0.483649 | − | 0.875262i | \(-0.339311\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3282.00i | 0.214146i | 0.994251 | + | 0.107073i | \(0.0341479\pi\) | ||||
−0.994251 | + | 0.107073i | \(0.965852\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2308.00 | 0.149865 | 0.0749324 | − | 0.997189i | \(-0.476126\pi\) | ||||
0.0749324 | + | 0.997189i | \(0.476126\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2760.00i | 0.177491i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11856.0 | 0.751558 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24572.0 | −1.55023 | −0.775116 | − | 0.631819i | \(-0.782308\pi\) | ||||
−0.775116 | + | 0.631819i | \(0.782308\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 23052.0i | − 1.43384i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2136.00 | −0.131618 | −0.0658088 | − | 0.997832i | \(-0.520963\pi\) | ||||
−0.0658088 | + | 0.997832i | \(0.520963\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 5508.00i | − 0.337814i | −0.985632 | − | 0.168907i | \(-0.945976\pi\) | ||||
0.985632 | − | 0.168907i | \(-0.0540237\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 4536.00i | − 0.275624i | −0.990458 | − | 0.137812i | \(-0.955993\pi\) | ||||
0.990458 | − | 0.137812i | \(-0.0440069\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −68.0000 | −0.00411284 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 27914.0i | 1.67283i | 0.548095 | + | 0.836416i | \(0.315353\pi\) | ||||
−0.548095 | + | 0.836416i | \(0.684647\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22842.0 | 1.35022 | 0.675112 | − | 0.737715i | \(-0.264095\pi\) | ||||
0.675112 | + | 0.737715i | \(0.264095\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16458.0 | 0.968445 | 0.484222 | − | 0.874945i | \(-0.339103\pi\) | ||||
0.484222 | + | 0.874945i | \(0.339103\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6992.00i | 0.405894i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1292.00 | −0.0743325 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 16050.0i | − 0.919290i | −0.888103 | − | 0.459645i | \(-0.847977\pi\) | ||||
0.888103 | − | 0.459645i | \(-0.152023\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 5314.00i | − 0.301674i | −0.988559 | − | 0.150837i | \(-0.951803\pi\) | ||||
0.988559 | − | 0.150837i | \(-0.0481969\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1028.00 | −0.0581016 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15876.0i | 0.889426i | 0.895673 | + | 0.444713i | \(0.146694\pi\) | ||||
−0.895673 | + | 0.444713i | \(0.853306\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 28152.0 | 1.55661 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13372.0 | −0.736172 | −0.368086 | − | 0.929792i | \(-0.619987\pi\) | ||||
−0.368086 | + | 0.929792i | \(0.619987\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1824.00i | 0.0991233i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3230.00 | 0.174031 | 0.0870153 | − | 0.996207i | \(-0.472267\pi\) | ||||
0.0870153 | + | 0.996207i | \(0.472267\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 1248.00i | − 0.0669548i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 1404.00i | − 0.0746858i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6154.00 | 0.325978 | 0.162989 | − | 0.986628i | \(-0.447887\pi\) | ||||
0.162989 | + | 0.986628i | \(0.447887\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 39520.0i | 2.07579i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 20264.0 | 1.05107 | 0.525535 | − | 0.850772i | \(-0.323865\pi\) | ||||
0.525535 | + | 0.850772i | \(0.323865\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1796.00 | 0.0927691 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25354.0i | 1.29344i | 0.762729 | + | 0.646718i | \(0.223859\pi\) | ||||
−0.762729 | + | 0.646718i | \(0.776141\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7600.00 | −0.384536 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 13344.0i | − 0.672404i | −0.941790 | − | 0.336202i | \(-0.890858\pi\) | ||||
0.941790 | − | 0.336202i | \(-0.109142\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8296.00i | 0.414636i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28452.0 | 1.41627 | 0.708135 | − | 0.706077i | \(-0.249537\pi\) | ||||
0.708135 | + | 0.706077i | \(0.249537\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5784.00i | 0.285591i | 0.989752 | + | 0.142796i | \(0.0456092\pi\) | ||||
−0.989752 | + | 0.142796i | \(0.954391\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1752.00 | 0.0854695 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 852.000 | 0.0413980 | 0.0206990 | − | 0.999786i | \(-0.493411\pi\) | ||||
0.0206990 | + | 0.999786i | \(0.493411\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5704.00i | 0.273864i | 0.990580 | + | 0.136932i | \(0.0437243\pi\) | ||||
−0.990580 | + | 0.136932i | \(0.956276\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24828.0 | 1.18267 | 0.591337 | − | 0.806425i | \(-0.298600\pi\) | ||||
0.591337 | + | 0.806425i | \(0.298600\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1204.00i | 0.0571268i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 136.000i | 0.00640245i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13298.0 | 0.623587 | 0.311793 | − | 0.950150i | \(-0.399070\pi\) | ||||
0.311793 | + | 0.950150i | \(0.399070\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 642.000i | 0.0298721i | 0.999888 | + | 0.0149361i | \(0.00475447\pi\) | ||||
−0.999888 | + | 0.0149361i | \(0.995246\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 192.000 | 0.00883070 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24072.0 | −1.10290 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20236.0i | 0.916564i | 0.888807 | + | 0.458282i | \(0.151535\pi\) | ||||
−0.888807 | + | 0.458282i | \(0.848465\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2700.00 | −0.121367 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2584.00i | 0.115713i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11562.0i | 0.513861i | 0.966430 | + | 0.256930i | \(0.0827111\pi\) | ||||
−0.966430 | + | 0.256930i | \(0.917289\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3952.00 | 0.174983 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 12852.0i | − 0.564804i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18984.0 | 0.825021 | 0.412510 | − | 0.910953i | \(-0.364652\pi\) | ||||
0.412510 | + | 0.910953i | \(0.364652\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2332.00 | −0.100971 | −0.0504856 | − | 0.998725i | \(-0.516077\pi\) | ||||
−0.0504856 | + | 0.998725i | \(0.516077\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 800.000i | 0.0342576i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19126.0 | 0.813035 | 0.406518 | − | 0.913643i | \(-0.366743\pi\) | ||||
0.406518 | + | 0.913643i | \(0.366743\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 37102.0i | 1.57144i | 0.618583 | + | 0.785720i | \(0.287707\pi\) | ||||
−0.618583 | + | 0.785720i | \(0.712293\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 11304.0i | − 0.475307i | −0.971350 | − | 0.237653i | \(-0.923622\pi\) | ||||
0.971350 | − | 0.237653i | \(-0.0763782\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 974.000 | 0.0408063 | 0.0204031 | − | 0.999792i | \(-0.493505\pi\) | ||||
0.0204031 | + | 0.999792i | \(0.493505\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 12882.0i | − 0.535816i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16480.0 | 0.678132 | 0.339066 | − | 0.940763i | \(-0.389889\pi\) | ||||
0.339066 | + | 0.940763i | \(0.389889\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22273.0 | −0.913240 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 350.000i | 0.0141985i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 47424.0 | 1.91031 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11192.0i | 0.449246i | 0.974446 | + | 0.224623i | \(0.0721150\pi\) | ||||
−0.974446 | + | 0.224623i | \(0.927885\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 34278.0i | − 1.36629i | −0.730281 | − | 0.683147i | \(-0.760611\pi\) | ||||
0.730281 | − | 0.683147i | \(-0.239389\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14020.0 | 0.556876 | 0.278438 | − | 0.960454i | \(-0.410183\pi\) | ||||
0.278438 | + | 0.960454i | \(0.410183\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 30528.0i | 1.20415i | 0.798438 | + | 0.602077i | \(0.205660\pi\) | ||||
−0.798438 | + | 0.602077i | \(0.794340\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 28968.0 | 1.13081 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16592.0 | 0.645463 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 2932.00i | − 0.112892i | −0.998406 | − | 0.0564462i | \(-0.982023\pi\) | ||||
0.998406 | − | 0.0564462i | \(-0.0179769\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7116.00 | −0.272127 | −0.136064 | − | 0.990700i | \(-0.543445\pi\) | ||||
−0.136064 | + | 0.990700i | \(0.543445\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 35140.0i | − 1.33925i | −0.742701 | − | 0.669624i | \(-0.766455\pi\) | ||||
0.742701 | − | 0.669624i | \(-0.233545\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 20296.0i | − 0.768290i | −0.923273 | − | 0.384145i | \(-0.874496\pi\) | ||||
0.923273 | − | 0.384145i | \(-0.125504\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 732.000 | 0.0276159 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 416.000i | − 0.0155889i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11960.0 | 0.443702 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15732.0 | 0.581697 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 19512.0i | − 0.714317i | −0.934044 | − | 0.357158i | \(-0.883746\pi\) | ||||
0.934044 | − | 0.357158i | \(-0.116254\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16720.0 | 0.608077 | 0.304039 | − | 0.952660i | \(-0.401665\pi\) | ||||
0.304039 | + | 0.952660i | \(0.401665\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 28696.0i | − 1.04020i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 996.000i | 0.0358678i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7340.00 | −0.263465 | −0.131732 | − | 0.991285i | \(-0.542054\pi\) | ||||
−0.131732 | + | 0.991285i | \(0.542054\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 48144.0i | 1.71688i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 48932.0 | 1.72810 | 0.864051 | − | 0.503404i | \(-0.167919\pi\) | ||||
0.864051 | + | 0.503404i | \(0.167919\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1356.00 | −0.0477348 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 30298.0i | − 1.05634i | −0.849138 | − | 0.528171i | \(-0.822878\pi\) | ||||
0.849138 | − | 0.528171i | \(-0.177122\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8414.00 | −0.291486 | −0.145743 | − | 0.989322i | \(-0.546557\pi\) | ||||
−0.145743 | + | 0.989322i | \(0.546557\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7296.00i | 0.251952i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23912.0i | 0.820523i | 0.911968 | + | 0.410262i | \(0.134563\pi\) | ||||
−0.911968 | + | 0.410262i | \(0.865437\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −25704.0 | −0.879228 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22866.0i | 0.777232i | 0.921400 | + | 0.388616i | \(0.127047\pi\) | ||||
−0.921400 | + | 0.388616i | \(0.872953\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4052.00 | −0.136440 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 37809.0 | 1.26914 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 738.000i | − 0.0245424i | −0.999925 | − | 0.0122712i | \(-0.996094\pi\) | ||||
0.999925 | − | 0.0122712i | \(-0.00390614\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −44098.0 | −1.45744 | −0.728719 | − | 0.684813i | \(-0.759884\pi\) | ||||
−0.728719 | + | 0.684813i | \(0.759884\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4920.00i | 0.162105i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 34426.0i | 1.12731i | 0.826009 | + | 0.563657i | \(0.190606\pi\) | ||||
−0.826009 | + | 0.563657i | \(0.809394\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −46920.0 | −1.53174 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 30216.0i | 0.980408i | 0.871608 | + | 0.490204i | \(0.163078\pi\) | ||||
−0.871608 | + | 0.490204i | \(0.836922\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −30400.0 | −0.977415 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4592.00 | 0.147194 | 0.0735972 | − | 0.997288i | \(-0.476552\pi\) | ||||
0.0735972 | + | 0.997288i | \(0.476552\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24276.0i | 0.771142i | 0.922678 | + | 0.385571i | \(0.125996\pi\) | ||||
−0.922678 | + | 0.385571i | \(0.874004\pi\) | |||||||
\(998\) | 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 | 1800.4.f.t.649.1 | 2 | ||
3.2 | odd | 2 | 1800.4.f.f.649.1 | 2 | |||
5.2 | odd | 4 | 360.4.a.d.1.1 | ✓ | 1 | ||
5.3 | odd | 4 | 1800.4.a.r.1.1 | 1 | |||
5.4 | even | 2 | inner | 1800.4.f.t.649.2 | 2 | ||
15.2 | even | 4 | 360.4.a.k.1.1 | yes | 1 | ||
15.8 | even | 4 | 1800.4.a.q.1.1 | 1 | |||
15.14 | odd | 2 | 1800.4.f.f.649.2 | 2 | |||
20.7 | even | 4 | 720.4.a.g.1.1 | 1 | |||
60.47 | odd | 4 | 720.4.a.x.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
360.4.a.d.1.1 | ✓ | 1 | 5.2 | odd | 4 | ||
360.4.a.k.1.1 | yes | 1 | 15.2 | even | 4 | ||
720.4.a.g.1.1 | 1 | 20.7 | even | 4 | |||
720.4.a.x.1.1 | 1 | 60.47 | odd | 4 | |||
1800.4.a.q.1.1 | 1 | 15.8 | even | 4 | |||
1800.4.a.r.1.1 | 1 | 5.3 | odd | 4 | |||
1800.4.f.f.649.1 | 2 | 3.2 | odd | 2 | |||
1800.4.f.f.649.2 | 2 | 15.14 | odd | 2 | |||
1800.4.f.t.649.1 | 2 | 1.1 | even | 1 | trivial | ||
1800.4.f.t.649.2 | 2 | 5.4 | even | 2 | inner |