Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [360,4,Mod(1,360)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(360, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("360.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 360.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(21.2406876021\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 360.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | 0.107990 | 0.0539949 | − | 0.998541i | \(-0.482805\pi\) | ||||
0.0539949 | + | 0.998541i | \(0.482805\pi\) | |||||||
\(8\) | 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 | ||||||||
\(13\) | −68.0000 | −1.45075 | −0.725377 | − | 0.688352i | \(-0.758335\pi\) | ||||
−0.725377 | + | 0.688352i | \(0.758335\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 38.0000 | 0.542138 | 0.271069 | − | 0.962560i | \(-0.412623\pi\) | ||||
0.271069 | + | 0.962560i | \(0.412623\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000 | 0.0482980 | 0.0241490 | − | 0.999708i | \(-0.492312\pi\) | ||||
0.0241490 | + | 0.999708i | \(0.492312\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −152.000 | −1.37801 | −0.689004 | − | 0.724757i | \(-0.741952\pi\) | ||||
−0.689004 | + | 0.724757i | \(0.741952\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 46.0000 | 0.294551 | 0.147276 | − | 0.989095i | \(-0.452950\pi\) | ||||
0.147276 | + | 0.989095i | \(0.452950\pi\) | |||||||
\(30\) | 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 | ||||||||
\(35\) | −10.0000 | −0.0482945 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −312.000 | −1.38628 | −0.693142 | − | 0.720801i | \(-0.743774\pi\) | ||||
−0.693142 | + | 0.720801i | \(0.743774\pi\) | |||||||
\(38\) | 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 | ||||||||
\(43\) | −200.000 | −0.709296 | −0.354648 | − | 0.935000i | \(-0.615399\pi\) | ||||
−0.354648 | + | 0.935000i | \(0.615399\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −104.000 | −0.322765 | −0.161383 | − | 0.986892i | \(-0.551595\pi\) | ||||
−0.161383 | + | 0.986892i | \(0.551595\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −339.000 | −0.988338 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 414.000 | 1.07297 | 0.536484 | − | 0.843911i | \(-0.319752\pi\) | ||||
0.536484 | + | 0.843911i | \(0.319752\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −170.000 | −0.416778 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.00000 | 0.00441318 | 0.00220659 | − | 0.999998i | \(-0.499298\pi\) | ||||
0.00220659 | + | 0.999998i | \(0.499298\pi\) | |||||||
\(60\) | 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 | ||||||||
\(65\) | 340.000 | 0.648797 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −244.000 | −0.444916 | −0.222458 | − | 0.974942i | \(-0.571408\pi\) | ||||
−0.222458 | + | 0.974942i | \(0.571408\pi\) | |||||||
\(68\) | 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 | ||||||||
\(73\) | −378.000 | −0.606049 | −0.303024 | − | 0.952983i | \(-0.597996\pi\) | ||||
−0.303024 | + | 0.952983i | \(0.597996\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 68.0000 | 0.100641 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −852.000 | −1.21339 | −0.606693 | − | 0.794936i | \(-0.707504\pi\) | ||||
−0.606693 | + | 0.794936i | \(0.707504\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −844.000 | −1.11616 | −0.558079 | − | 0.829788i | \(-0.688461\pi\) | ||||
−0.558079 | + | 0.829788i | \(0.688461\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −190.000 | −0.242452 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1380.00 | 1.64359 | 0.821796 | − | 0.569782i | \(-0.192972\pi\) | ||||
0.821796 | + | 0.569782i | \(0.192972\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −136.000 | −0.156667 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −20.0000 | −0.0215995 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 514.000 | 0.538029 | 0.269014 | − | 0.963136i | \(-0.413302\pi\) | ||||
0.269014 | + | 0.963136i | \(0.413302\pi\) | |||||||
\(98\) | 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 | ||||||||
\(103\) | 898.000 | 0.859054 | 0.429527 | − | 0.903054i | \(-0.358680\pi\) | ||||
0.429527 | + | 0.903054i | \(0.358680\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −876.000 | −0.791459 | −0.395730 | − | 0.918367i | \(-0.629508\pi\) | ||||
−0.395730 | + | 0.918367i | \(0.629508\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 602.000 | 0.529001 | 0.264501 | − | 0.964386i | \(-0.414793\pi\) | ||||
0.264501 | + | 0.964386i | \(0.414793\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1350.00 | −1.12387 | −0.561935 | − | 0.827181i | \(-0.689943\pi\) | ||||
−0.561935 | + | 0.827181i | \(0.689943\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 760.000 | 0.616264 | ||||||||
\(116\) | 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 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −366.000 | −0.255726 | −0.127863 | − | 0.991792i | \(-0.540812\pi\) | ||||
−0.127863 | + | 0.991792i | \(0.540812\pi\) | |||||||
\(128\) | 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 | ||||||||
\(133\) | 8.00000 | 0.00521570 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2026.00 | 1.26345 | 0.631726 | − | 0.775192i | \(-0.282347\pi\) | ||||
0.631726 | + | 0.775192i | \(0.282347\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2460.00 | 1.50111 | 0.750556 | − | 0.660807i | \(-0.229786\pi\) | ||||
0.750556 | + | 0.660807i | \(0.229786\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2312.00 | −1.35202 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −230.000 | −0.131727 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3362.00 | 1.84850 | 0.924248 | − | 0.381794i | \(-0.124694\pi\) | ||||
0.924248 | + | 0.381794i | \(0.124694\pi\) | |||||||
\(150\) | 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 | ||||||||
\(155\) | 1300.00 | 0.673668 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2092.00 | 1.06344 | 0.531719 | − | 0.846921i | \(-0.321546\pi\) | ||||
0.531719 | + | 0.846921i | \(0.321546\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −304.000 | −0.148811 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 244.000 | 0.117249 | 0.0586244 | − | 0.998280i | \(-0.481329\pi\) | ||||
0.0586244 | + | 0.998280i | \(0.481329\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2064.00 | −0.956390 | −0.478195 | − | 0.878254i | \(-0.658709\pi\) | ||||
−0.478195 | + | 0.878254i | \(0.658709\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2427.00 | 1.10469 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1258.00 | −0.552855 | −0.276428 | − | 0.961035i | \(-0.589151\pi\) | ||||
−0.276428 | + | 0.961035i | \(0.589151\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 50.0000 | 0.0215980 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3986.00 | 1.66440 | 0.832200 | − | 0.554475i | \(-0.187081\pi\) | ||||
0.832200 | + | 0.554475i | \(0.187081\pi\) | |||||||
\(180\) | 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 | ||||||||
\(185\) | 1560.00 | 0.619965 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1292.00 | 0.505243 | ||||||||
\(188\) | 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 | ||||||||
\(193\) | 214.000 | 0.0798138 | 0.0399069 | − | 0.999203i | \(-0.487294\pi\) | ||||
0.0399069 | + | 0.999203i | \(0.487294\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3014.00 | −1.09004 | −0.545022 | − | 0.838422i | \(-0.683479\pi\) | ||||
−0.545022 | + | 0.838422i | \(0.683479\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1792.00 | −0.638349 | −0.319175 | − | 0.947696i | \(-0.603406\pi\) | ||||
−0.319175 | + | 0.947696i | \(0.603406\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 92.0000 | 0.0318085 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 240.000 | 0.0817674 | ||||||||
\(206\) | 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 | ||||||||
\(215\) | 1000.00 | 0.317207 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −520.000 | −0.162672 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2584.00 | −0.786510 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6506.00 | 1.95369 | 0.976847 | − | 0.213937i | \(-0.0686287\pi\) | ||||
0.976847 | + | 0.213937i | \(0.0686287\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3696.00 | 1.08067 | 0.540335 | − | 0.841450i | \(-0.318297\pi\) | ||||
0.540335 | + | 0.841450i | \(0.318297\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3386.00 | −0.977088 | −0.488544 | − | 0.872539i | \(-0.662472\pi\) | ||||
−0.488544 | + | 0.872539i | \(0.662472\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3306.00 | −0.929542 | −0.464771 | − | 0.885431i | \(-0.653863\pi\) | ||||
−0.464771 | + | 0.885431i | \(0.653863\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 520.000 | 0.144345 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4188.00 | 1.13347 | 0.566735 | − | 0.823900i | \(-0.308206\pi\) | ||||
0.566735 | + | 0.823900i | \(0.308206\pi\) | |||||||
\(240\) | 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 | ||||||||
\(245\) | 1695.00 | 0.441998 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −272.000 | −0.0700686 | ||||||||
\(248\) | 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 | ||||||||
\(253\) | −5168.00 | −1.28423 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1158.00 | −0.281066 | −0.140533 | − | 0.990076i | \(-0.544882\pi\) | ||||
−0.140533 | + | 0.990076i | \(0.544882\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −624.000 | −0.149705 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8304.00 | −1.94695 | −0.973473 | − | 0.228804i | \(-0.926519\pi\) | ||||
−0.973473 | + | 0.228804i | \(0.926519\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2070.00 | −0.479846 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7478.00 | 1.69495 | 0.847475 | − | 0.530835i | \(-0.178122\pi\) | ||||
0.847475 | + | 0.530835i | \(0.178122\pi\) | |||||||
\(270\) | 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 | ||||||||
\(275\) | 850.000 | 0.186389 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2296.00 | −0.498026 | −0.249013 | − | 0.968500i | \(-0.580106\pi\) | ||||
−0.249013 | + | 0.968500i | \(0.580106\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | −1972.00 | −0.414216 | −0.207108 | − | 0.978318i | \(-0.566405\pi\) | ||||
−0.207108 | + | 0.978318i | \(0.566405\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −96.0000 | −0.0197446 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3469.00 | −0.706086 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9254.00 | −1.84513 | −0.922567 | − | 0.385836i | \(-0.873913\pi\) | ||||
−0.922567 | + | 0.385836i | \(0.873913\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.0000 | −0.00197364 | ||||||||
\(296\) | 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 | ||||||||
\(305\) | 190.000 | 0.0356701 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5888.00 | −1.09461 | −0.547306 | − | 0.836933i | \(-0.684347\pi\) | ||||
−0.547306 | + | 0.836933i | \(0.684347\pi\) | |||||||
\(308\) | 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 | ||||||||
\(313\) | −8026.00 | −1.44938 | −0.724691 | − | 0.689074i | \(-0.758017\pi\) | ||||
−0.724691 | + | 0.689074i | \(0.758017\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2838.00 | −0.502833 | −0.251416 | − | 0.967879i | \(-0.580896\pi\) | ||||
−0.251416 | + | 0.967879i | \(0.580896\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1564.00 | 0.274505 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 152.000 | 0.0261842 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1700.00 | −0.290151 | ||||||||
\(326\) | 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 | ||||||||
\(335\) | 1220.00 | 0.198972 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 814.000 | 0.131577 | 0.0657884 | − | 0.997834i | \(-0.479044\pi\) | ||||
0.0657884 | + | 0.997834i | \(0.479044\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8840.00 | −1.40385 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1364.00 | −0.214720 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4544.00 | 0.702982 | 0.351491 | − | 0.936191i | \(-0.385675\pi\) | ||||
0.351491 | + | 0.936191i | \(0.385675\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6978.00 | 1.07027 | 0.535134 | − | 0.844767i | \(-0.320261\pi\) | ||||
0.535134 | + | 0.844767i | \(0.320261\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2818.00 | −0.424892 | −0.212446 | − | 0.977173i | \(-0.568143\pi\) | ||||
−0.212446 | + | 0.977173i | \(0.568143\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3540.00 | 0.529250 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −744.000 | −0.109378 | −0.0546892 | − | 0.998503i | \(-0.517417\pi\) | ||||
−0.0546892 | + | 0.998503i | \(0.517417\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6843.00 | −0.997667 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1890.00 | 0.271033 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6454.00 | −0.917973 | −0.458986 | − | 0.888443i | \(-0.651787\pi\) | ||||
−0.458986 | + | 0.888443i | \(0.651787\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 828.000 | 0.115870 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5900.00 | −0.819009 | −0.409505 | − | 0.912308i | \(-0.634298\pi\) | ||||
−0.409505 | + | 0.912308i | \(0.634298\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3128.00 | −0.427321 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11876.0 | −1.60958 | −0.804788 | − | 0.593563i | \(-0.797721\pi\) | ||||
−0.804788 | + | 0.593563i | \(0.797721\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 552.000 | 0.0736446 | 0.0368223 | − | 0.999322i | \(-0.488276\pi\) | ||||
0.0368223 | + | 0.999322i | \(0.488276\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −340.000 | −0.0450078 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1722.00 | 0.224444 | 0.112222 | − | 0.993683i | \(-0.464203\pi\) | ||||
0.112222 | + | 0.993683i | \(0.464203\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5776.00 | −0.747071 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4260.00 | 0.542643 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4576.00 | 0.578496 | 0.289248 | − | 0.957254i | \(-0.406595\pi\) | ||||
0.289248 | + | 0.957254i | \(0.406595\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | 17680.0 | 2.18537 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10608.0 | −1.29194 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −230.000 | −0.0278063 | −0.0139031 | − | 0.999903i | \(-0.504426\pi\) | ||||
−0.0139031 | + | 0.999903i | \(0.504426\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.00000 | 0.000476579 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4220.00 | 0.499161 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15438.0 | 1.79999 | 0.899995 | − | 0.435901i | \(-0.143570\pi\) | ||||
0.899995 | + | 0.435901i | \(0.143570\pi\) | |||||||
\(420\) | 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 | ||||||||
\(425\) | 950.000 | 0.108428 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −76.0000 | −0.00861334 | ||||||||
\(428\) | 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 | ||||||||
\(433\) | −8698.00 | −0.965356 | −0.482678 | − | 0.875798i | \(-0.660336\pi\) | ||||
−0.482678 | + | 0.875798i | \(0.660336\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −608.000 | −0.0665551 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8536.00 | 0.928021 | 0.464010 | − | 0.885830i | \(-0.346410\pi\) | ||||
0.464010 | + | 0.885830i | \(0.346410\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8712.00 | 0.934356 | 0.467178 | − | 0.884163i | \(-0.345271\pi\) | ||||
0.467178 | + | 0.884163i | \(0.345271\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6900.00 | −0.735037 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5484.00 | 0.576405 | 0.288203 | − | 0.957569i | \(-0.406942\pi\) | ||||
0.288203 | + | 0.957569i | \(0.406942\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1632.00 | −0.170394 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 680.000 | 0.0700635 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19402.0 | 1.98597 | 0.992984 | − | 0.118250i | \(-0.0377283\pi\) | ||||
0.992984 | + | 0.118250i | \(0.0377283\pi\) | |||||||
\(458\) | 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 | ||||||||
\(463\) | 6222.00 | 0.624537 | 0.312269 | − | 0.949994i | \(-0.398911\pi\) | ||||
0.312269 | + | 0.949994i | \(0.398911\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15260.0 | 1.51210 | 0.756048 | − | 0.654516i | \(-0.227128\pi\) | ||||
0.756048 | + | 0.654516i | \(0.227128\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −488.000 | −0.0480464 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6800.00 | −0.661024 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 100.000 | 0.00965961 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9812.00 | −0.935953 | −0.467977 | − | 0.883741i | \(-0.655017\pi\) | ||||
−0.467977 | + | 0.883741i | \(0.655017\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21216.0 | 2.01116 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2570.00 | −0.240614 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7226.00 | −0.672364 | −0.336182 | − | 0.941797i | \(-0.609136\pi\) | ||||
−0.336182 | + | 0.941797i | \(0.609136\pi\) | |||||||
\(488\) | 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 | ||||||||
\(493\) | 1748.00 | 0.159688 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1416.00 | −0.127799 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4156.00 | −0.372842 | −0.186421 | − | 0.982470i | \(-0.559689\pi\) | ||||
−0.186421 | + | 0.982470i | \(0.559689\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14088.0 | −1.24881 | −0.624406 | − | 0.781100i | \(-0.714659\pi\) | ||||
−0.624406 | + | 0.781100i | \(0.714659\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3510.00 | −0.309293 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16970.0 | −1.47776 | −0.738882 | − | 0.673835i | \(-0.764646\pi\) | ||||
−0.738882 | + | 0.673835i | \(0.764646\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −756.000 | −0.0654471 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4490.00 | −0.384181 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3536.00 | −0.300799 | ||||||||
\(518\) | 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 | ||||||||
\(523\) | 20620.0 | 1.72400 | 0.861998 | − | 0.506912i | \(-0.169213\pi\) | ||||
0.861998 | + | 0.506912i | \(0.169213\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9880.00 | −0.816660 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10937.0 | 0.898907 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3264.00 | 0.265252 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4380.00 | 0.353951 | ||||||||
\(536\) | 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 | ||||||||
\(545\) | −3010.00 | −0.236577 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24104.0 | 1.88412 | 0.942059 | − | 0.335447i | \(-0.108887\pi\) | ||||
0.942059 | + | 0.335447i | \(0.108887\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 184.000 | 0.0142262 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1704.00 | −0.131033 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23582.0 | 1.79390 | 0.896949 | − | 0.442134i | \(-0.145778\pi\) | ||||
0.896949 | + | 0.442134i | \(0.145778\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13600.0 | 1.02901 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2680.00 | 0.200619 | 0.100310 | − | 0.994956i | \(-0.468017\pi\) | ||||
0.100310 | + | 0.994956i | \(0.468017\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6750.00 | 0.502610 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25004.0 | 1.84222 | 0.921109 | − | 0.389304i | \(-0.127285\pi\) | ||||
0.921109 | + | 0.389304i | \(0.127285\pi\) | |||||||
\(570\) | 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 | ||||||||
\(575\) | −3800.00 | −0.275602 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15862.0 | −1.14444 | −0.572222 | − | 0.820099i | \(-0.693918\pi\) | ||||
−0.572222 | + | 0.820099i | \(0.693918\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1688.00 | −0.120534 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14076.0 | 0.999946 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15036.0 | −1.05724 | −0.528622 | − | 0.848857i | \(-0.677291\pi\) | ||||
−0.528622 | + | 0.848857i | \(0.677291\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1040.00 | −0.0727546 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12786.0 | 0.885427 | 0.442713 | − | 0.896663i | \(-0.354016\pi\) | ||||
0.442713 | + | 0.896663i | \(0.354016\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −380.000 | −0.0261823 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13464.0 | −0.918404 | −0.459202 | − | 0.888332i | \(-0.651865\pi\) | ||||
−0.459202 | + | 0.888332i | \(0.651865\pi\) | |||||||
\(600\) | 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 | ||||||||
\(605\) | 875.000 | 0.0587997 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11082.0 | −0.741029 | −0.370514 | − | 0.928827i | \(-0.620819\pi\) | ||||
−0.370514 | + | 0.928827i | \(0.620819\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7072.00 | 0.468253 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26568.0 | −1.75052 | −0.875262 | − | 0.483649i | \(-0.839311\pi\) | ||||
−0.875262 | + | 0.483649i | \(0.839311\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3282.00 | −0.214146 | −0.107073 | − | 0.994251i | \(-0.534148\pi\) | ||||
−0.107073 | + | 0.994251i | \(0.534148\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2308.00 | −0.149865 | −0.0749324 | − | 0.997189i | \(-0.523874\pi\) | ||||
−0.0749324 | + | 0.997189i | \(0.523874\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2760.00 | 0.177491 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 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 | ||||||||
\(635\) | 1830.00 | 0.114364 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 23052.0 | 1.43384 | ||||||||
\(638\) | 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 | ||||||||
\(643\) | −5508.00 | −0.337814 | −0.168907 | − | 0.985632i | \(-0.554024\pi\) | ||||
−0.168907 | + | 0.985632i | \(0.554024\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4536.00 | 0.275624 | 0.137812 | − | 0.990458i | \(-0.455993\pi\) | ||||
0.137812 | + | 0.990458i | \(0.455993\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 68.0000 | 0.00411284 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 27914.0 | 1.67283 | 0.836416 | − | 0.548095i | \(-0.184647\pi\) | ||||
0.836416 | + | 0.548095i | \(0.184647\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2490.00 | 0.148538 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22842.0 | −1.35022 | −0.675112 | − | 0.737715i | \(-0.735905\pi\) | ||||
−0.675112 | + | 0.737715i | \(0.735905\pi\) | |||||||
\(660\) | 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 | ||||||||
\(665\) | −40.0000 | −0.00233253 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6992.00 | −0.405894 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1292.00 | −0.0743325 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16050.0 | −0.919290 | −0.459645 | − | 0.888103i | \(-0.652023\pi\) | ||||
−0.459645 | + | 0.888103i | \(0.652023\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5314.00 | 0.301674 | 0.150837 | − | 0.988559i | \(-0.451803\pi\) | ||||
0.150837 | + | 0.988559i | \(0.451803\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1028.00 | 0.0581016 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15876.0 | 0.889426 | 0.444713 | − | 0.895673i | \(-0.353306\pi\) | ||||
0.444713 | + | 0.895673i | \(0.353306\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10130.0 | −0.565033 | ||||||||
\(686\) | 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 | ||||||||
\(695\) | −12300.0 | −0.671317 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1824.00 | −0.0991233 | ||||||||
\(698\) | 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 | ||||||||
\(703\) | −1248.00 | −0.0669548 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1404.00 | 0.0746858 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6154.00 | −0.325978 | −0.162989 | − | 0.986628i | \(-0.552113\pi\) | ||||
−0.162989 | + | 0.986628i | \(0.552113\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 39520.0 | 2.07579 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11560.0 | 0.604643 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −20264.0 | −1.05107 | −0.525535 | − | 0.850772i | \(-0.676135\pi\) | ||||
−0.525535 | + | 0.850772i | \(0.676135\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1796.00 | 0.0927691 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1150.00 | 0.0589102 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25354.0 | −1.29344 | −0.646718 | − | 0.762729i | \(-0.723859\pi\) | ||||
−0.646718 | + | 0.762729i | \(0.723859\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7600.00 | −0.384536 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13344.0 | −0.672404 | −0.336202 | − | 0.941790i | \(-0.609142\pi\) | ||||
−0.336202 | + | 0.941790i | \(0.609142\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8296.00 | −0.414636 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −28452.0 | −1.41627 | −0.708135 | − | 0.706077i | \(-0.750463\pi\) | ||||
−0.708135 | + | 0.706077i | \(0.750463\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5784.00 | 0.285591 | 0.142796 | − | 0.989752i | \(-0.454391\pi\) | ||||
0.142796 | + | 0.989752i | \(0.454391\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16810.0 | −0.826672 | ||||||||
\(746\) | 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 | ||||||||
\(755\) | −10480.0 | −0.505174 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5704.00 | −0.273864 | −0.136932 | − | 0.990580i | \(-0.543724\pi\) | ||||
−0.136932 | + | 0.990580i | \(0.543724\pi\) | |||||||
\(758\) | 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 | ||||||||
\(763\) | 1204.00 | 0.0571268 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −136.000 | −0.00640245 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13298.0 | −0.623587 | −0.311793 | − | 0.950150i | \(-0.600930\pi\) | ||||
−0.311793 | + | 0.950150i | \(0.600930\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 642.000 | 0.0298721 | 0.0149361 | − | 0.999888i | \(-0.495246\pi\) | ||||
0.0149361 | + | 0.999888i | \(0.495246\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6500.00 | −0.301273 | ||||||||
\(776\) | 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 | ||||||||
\(785\) | −10460.0 | −0.475584 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20236.0 | −0.916564 | −0.458282 | − | 0.888807i | \(-0.651535\pi\) | ||||
−0.458282 | + | 0.888807i | \(0.651535\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2700.00 | −0.121367 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2584.00 | 0.115713 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11562.0 | −0.513861 | −0.256930 | − | 0.966430i | \(-0.582711\pi\) | ||||
−0.256930 | + | 0.966430i | \(0.582711\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3952.00 | −0.174983 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12852.0 | −0.564804 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1520.00 | 0.0665503 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −18984.0 | −0.825021 | −0.412510 | − | 0.910953i | \(-0.635348\pi\) | ||||
−0.412510 | + | 0.910953i | \(0.635348\pi\) | |||||||
\(810\) | 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 | ||||||||
\(815\) | −1220.00 | −0.0524353 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −800.000 | −0.0342576 | ||||||||
\(818\) | 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 | ||||||||
\(823\) | 37102.0 | 1.57144 | 0.785720 | − | 0.618583i | \(-0.212293\pi\) | ||||
0.785720 | + | 0.618583i | \(0.212293\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11304.0 | 0.475307 | 0.237653 | − | 0.971350i | \(-0.423622\pi\) | ||||
0.237653 | + | 0.971350i | \(0.423622\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −974.000 | −0.0408063 | −0.0204031 | − | 0.999792i | \(-0.506495\pi\) | ||||
−0.0204031 | + | 0.999792i | \(0.506495\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −12882.0 | −0.535816 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10320.0 | 0.427711 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16480.0 | −0.678132 | −0.339066 | − | 0.940763i | \(-0.610111\pi\) | ||||
−0.339066 | + | 0.940763i | \(0.610111\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22273.0 | −0.913240 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12135.0 | −0.494032 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −350.000 | −0.0141985 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 47424.0 | 1.91031 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11192.0 | 0.449246 | 0.224623 | − | 0.974446i | \(-0.427885\pi\) | ||||
0.224623 | + | 0.974446i | \(0.427885\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 34278.0 | 1.36629 | 0.683147 | − | 0.730281i | \(-0.260611\pi\) | ||||
0.683147 | + | 0.730281i | \(0.260611\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14020.0 | −0.556876 | −0.278438 | − | 0.960454i | \(-0.589817\pi\) | ||||
−0.278438 | + | 0.960454i | \(0.589817\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 30528.0 | 1.20415 | 0.602077 | − | 0.798438i | \(-0.294340\pi\) | ||||
0.602077 | + | 0.798438i | \(0.294340\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6290.00 | 0.247244 | ||||||||
\(866\) | 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 | ||||||||
\(875\) | −250.000 | −0.00965891 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2932.00 | 0.112892 | 0.0564462 | − | 0.998406i | \(-0.482023\pi\) | ||||
0.0564462 | + | 0.998406i | \(0.482023\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | −35140.0 | −1.33925 | −0.669624 | − | 0.742701i | \(-0.733545\pi\) | ||||
−0.669624 | + | 0.742701i | \(0.733545\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20296.0 | 0.768290 | 0.384145 | − | 0.923273i | \(-0.374496\pi\) | ||||
0.384145 | + | 0.923273i | \(0.374496\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −732.000 | −0.0276159 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −416.000 | −0.0155889 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −19930.0 | −0.744342 | ||||||||
\(896\) | 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 | ||||||||
\(905\) | −12850.0 | −0.471987 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19512.0 | 0.714317 | 0.357158 | − | 0.934044i | \(-0.383746\pi\) | ||||
0.357158 | + | 0.934044i | \(0.383746\pi\) | |||||||
\(908\) | 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 | ||||||||
\(913\) | −28696.0 | −1.04020 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −996.000 | −0.0358678 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7340.00 | 0.263465 | 0.131732 | − | 0.991285i | \(-0.457946\pi\) | ||||
0.131732 | + | 0.991285i | \(0.457946\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 48144.0 | 1.71688 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7800.00 | −0.277257 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −48932.0 | −1.72810 | −0.864051 | − | 0.503404i | \(-0.832081\pi\) | ||||
−0.864051 | + | 0.503404i | \(0.832081\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1356.00 | −0.0477348 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6460.00 | −0.225951 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30298.0 | 1.05634 | 0.528171 | − | 0.849138i | \(-0.322878\pi\) | ||||
0.528171 | + | 0.849138i | \(0.322878\pi\) | |||||||
\(938\) | 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 | ||||||||
\(943\) | 7296.00 | 0.251952 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −23912.0 | −0.820523 | −0.410262 | − | 0.911968i | \(-0.634563\pi\) | ||||
−0.410262 | + | 0.911968i | \(0.634563\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 25704.0 | 0.879228 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22866.0 | 0.777232 | 0.388616 | − | 0.921400i | \(-0.372953\pi\) | ||||
0.388616 | + | 0.921400i | \(0.372953\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 23420.0 | 0.793564 | ||||||||
\(956\) | 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 | ||||||||
\(965\) | −1070.00 | −0.0356938 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 738.000 | 0.0245424 | 0.0122712 | − | 0.999925i | \(-0.496094\pi\) | ||||
0.0122712 | + | 0.999925i | \(0.496094\pi\) | |||||||
\(968\) | 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 | ||||||||
\(973\) | 4920.00 | 0.162105 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −34426.0 | −1.12731 | −0.563657 | − | 0.826009i | \(-0.690606\pi\) | ||||
−0.563657 | + | 0.826009i | \(0.690606\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 46920.0 | 1.53174 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 30216.0 | 0.980408 | 0.490204 | − | 0.871608i | \(-0.336922\pi\) | ||||
0.490204 | + | 0.871608i | \(0.336922\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15070.0 | 0.487482 | ||||||||
\(986\) | 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 | ||||||||
\(995\) | 8960.00 | 0.285478 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24276.0 | −0.771142 | −0.385571 | − | 0.922678i | \(-0.625996\pi\) | ||||
−0.385571 | + | 0.922678i | \(0.625996\pi\) | |||||||
\(998\) | 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 | 360.4.a.d.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 360.4.a.k.1.1 | yes | 1 | ||
4.3 | odd | 2 | 720.4.a.g.1.1 | 1 | |||
5.2 | odd | 4 | 1800.4.f.t.649.2 | 2 | |||
5.3 | odd | 4 | 1800.4.f.t.649.1 | 2 | |||
5.4 | even | 2 | 1800.4.a.r.1.1 | 1 | |||
12.11 | even | 2 | 720.4.a.x.1.1 | 1 | |||
15.2 | even | 4 | 1800.4.f.f.649.2 | 2 | |||
15.8 | even | 4 | 1800.4.f.f.649.1 | 2 | |||
15.14 | odd | 2 | 1800.4.a.q.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
360.4.a.d.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
360.4.a.k.1.1 | yes | 1 | 3.2 | odd | 2 | ||
720.4.a.g.1.1 | 1 | 4.3 | odd | 2 | |||
720.4.a.x.1.1 | 1 | 12.11 | even | 2 | |||
1800.4.a.q.1.1 | 1 | 15.14 | odd | 2 | |||
1800.4.a.r.1.1 | 1 | 5.4 | even | 2 | |||
1800.4.f.f.649.1 | 2 | 15.8 | even | 4 | |||
1800.4.f.f.649.2 | 2 | 15.2 | even | 4 | |||
1800.4.f.t.649.1 | 2 | 5.3 | odd | 4 | |||
1800.4.f.t.649.2 | 2 | 5.2 | odd | 4 |