Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,4,Mod(1,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, 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("1344.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.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: | \(79.2985670477\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 168) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1344.1 |
$q$-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 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.00000 | 0.178885 | 0.0894427 | − | 0.995992i | \(-0.471491\pi\) | ||||
0.0894427 | + | 0.995992i | \(0.471491\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −52.0000 | −1.42533 | −0.712663 | − | 0.701506i | \(-0.752511\pi\) | ||||
−0.712663 | + | 0.701506i | \(0.752511\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −86.0000 | −1.83478 | −0.917389 | − | 0.397992i | \(-0.869707\pi\) | ||||
−0.917389 | + | 0.397992i | \(0.869707\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.00000 | −0.103280 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −30.0000 | −0.428004 | −0.214002 | − | 0.976833i | \(-0.568650\pi\) | ||||
−0.214002 | + | 0.976833i | \(0.568650\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000 | 0.0482980 | 0.0241490 | − | 0.999708i | \(-0.492312\pi\) | ||||
0.0241490 | + | 0.999708i | \(0.492312\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 21.0000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 120.000 | 1.08790 | 0.543951 | − | 0.839117i | \(-0.316928\pi\) | ||||
0.543951 | + | 0.839117i | \(0.316928\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −121.000 | −0.968000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −246.000 | −1.57521 | −0.787604 | − | 0.616181i | \(-0.788679\pi\) | ||||
−0.787604 | + | 0.616181i | \(0.788679\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 80.0000 | 0.463498 | 0.231749 | − | 0.972776i | \(-0.425555\pi\) | ||||
0.231749 | + | 0.972776i | \(0.425555\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 156.000 | 0.822913 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −14.0000 | −0.0676123 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 290.000 | 1.28853 | 0.644266 | − | 0.764801i | \(-0.277163\pi\) | ||||
0.644266 | + | 0.764801i | \(0.277163\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 258.000 | 1.05931 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −374.000 | −1.42461 | −0.712305 | − | 0.701870i | \(-0.752349\pi\) | ||||
−0.712305 | + | 0.701870i | \(0.752349\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −164.000 | −0.581622 | −0.290811 | − | 0.956780i | \(-0.593925\pi\) | ||||
−0.290811 | + | 0.956780i | \(0.593925\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 18.0000 | 0.0596285 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 464.000 | 1.44003 | 0.720014 | − | 0.693959i | \(-0.244135\pi\) | ||||
0.720014 | + | 0.693959i | \(0.244135\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 90.0000 | 0.247108 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 162.000 | 0.419857 | 0.209928 | − | 0.977717i | \(-0.432677\pi\) | ||||
0.209928 | + | 0.977717i | \(0.432677\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −104.000 | −0.254970 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −12.0000 | −0.0278849 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −180.000 | −0.397187 | −0.198593 | − | 0.980082i | \(-0.563637\pi\) | ||||
−0.198593 | + | 0.980082i | \(0.563637\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 666.000 | 1.39791 | 0.698955 | − | 0.715165i | \(-0.253649\pi\) | ||||
0.698955 | + | 0.715165i | \(0.253649\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −63.0000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −172.000 | −0.328215 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 628.000 | 1.14511 | 0.572555 | − | 0.819866i | \(-0.305952\pi\) | ||||
0.572555 | + | 0.819866i | \(0.305952\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −360.000 | −0.628100 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 296.000 | 0.494771 | 0.247385 | − | 0.968917i | \(-0.420429\pi\) | ||||
0.247385 | + | 0.968917i | \(0.420429\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −518.000 | −0.830511 | −0.415256 | − | 0.909705i | \(-0.636308\pi\) | ||||
−0.415256 | + | 0.909705i | \(0.636308\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 363.000 | 0.558875 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 364.000 | 0.538723 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1184.00 | −1.68621 | −0.843104 | − | 0.537751i | \(-0.819274\pi\) | ||||
−0.843104 | + | 0.537751i | \(0.819274\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −220.000 | −0.290941 | −0.145471 | − | 0.989363i | \(-0.546470\pi\) | ||||
−0.145471 | + | 0.989363i | \(0.546470\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −60.0000 | −0.0765637 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 738.000 | 0.909447 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −774.000 | −0.921841 | −0.460920 | − | 0.887441i | \(-0.652481\pi\) | ||||
−0.460920 | + | 0.887441i | \(0.652481\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 602.000 | 0.693481 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −240.000 | −0.267600 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.00000 | 0.00863982 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1086.00 | −1.13677 | −0.568385 | − | 0.822763i | \(-0.692431\pi\) | ||||
−0.568385 | + | 0.822763i | \(0.692431\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −468.000 | −0.475109 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 290.000 | 0.285704 | 0.142852 | − | 0.989744i | \(-0.454373\pi\) | ||||
0.142852 | + | 0.989744i | \(0.454373\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −88.0000 | −0.0841835 | −0.0420917 | − | 0.999114i | \(-0.513402\pi\) | ||||
−0.0420917 | + | 0.999114i | \(0.513402\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 42.0000 | 0.0390360 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −372.000 | −0.336099 | −0.168050 | − | 0.985779i | \(-0.553747\pi\) | ||||
−0.168050 | + | 0.985779i | \(0.553747\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1430.00 | −1.25660 | −0.628299 | − | 0.777972i | \(-0.716248\pi\) | ||||
−0.628299 | + | 0.777972i | \(0.716248\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −870.000 | −0.743935 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1810.00 | 1.50682 | 0.753409 | − | 0.657552i | \(-0.228408\pi\) | ||||
0.753409 | + | 0.657552i | \(0.228408\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 240.000 | 0.194610 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −774.000 | −0.611593 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 210.000 | 0.161770 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1373.00 | 1.03156 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1122.00 | 0.822499 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −492.000 | −0.352047 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1168.00 | 0.816089 | 0.408044 | − | 0.912962i | \(-0.366211\pi\) | ||||
0.408044 | + | 0.912962i | \(0.366211\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 492.000 | 0.335800 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1268.00 | 0.845692 | 0.422846 | − | 0.906202i | \(-0.361031\pi\) | ||||
0.422846 | + | 0.906202i | \(0.361031\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −28.0000 | −0.0182549 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −54.0000 | −0.0344265 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 474.000 | 0.295595 | 0.147798 | − | 0.989018i | \(-0.452782\pi\) | ||||
0.147798 | + | 0.989018i | \(0.452782\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2684.00 | 1.63780 | 0.818899 | − | 0.573938i | \(-0.194585\pi\) | ||||
0.818899 | + | 0.573938i | \(0.194585\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1392.00 | −0.831401 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4472.00 | 2.61516 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −492.000 | −0.281782 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −147.000 | −0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1314.00 | 0.722464 | 0.361232 | − | 0.932476i | \(-0.382356\pi\) | ||||
0.361232 | + | 0.932476i | \(0.382356\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3000.00 | 1.61680 | 0.808399 | − | 0.588635i | \(-0.200334\pi\) | ||||
0.808399 | + | 0.588635i | \(0.200334\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −270.000 | −0.142668 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 160.000 | 0.0829130 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −774.000 | −0.393452 | −0.196726 | − | 0.980459i | \(-0.563031\pi\) | ||||
−0.196726 | + | 0.980459i | \(0.563031\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −486.000 | −0.242404 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −840.000 | −0.411188 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2292.00 | 1.10137 | 0.550685 | − | 0.834713i | \(-0.314367\pi\) | ||||
0.550685 | + | 0.834713i | \(0.314367\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 312.000 | 0.147207 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1672.00 | −0.774750 | −0.387375 | − | 0.921922i | \(-0.626618\pi\) | ||||
−0.387375 | + | 0.921922i | \(0.626618\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5199.00 | 2.36641 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 36.0000 | 0.0160993 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2730.00 | 1.19976 | 0.599879 | − | 0.800091i | \(-0.295215\pi\) | ||||
0.599879 | + | 0.800091i | \(0.295215\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 847.000 | 0.365870 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 540.000 | 0.229316 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2572.00 | −1.07397 | −0.536984 | − | 0.843592i | \(-0.680436\pi\) | ||||
−0.536984 | + | 0.843592i | \(0.680436\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3214.00 | −1.31986 | −0.659930 | − | 0.751327i | \(-0.729414\pi\) | ||||
−0.659930 | + | 0.751327i | \(0.729414\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1998.00 | −0.807084 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 580.000 | 0.230500 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1560.00 | 0.610045 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 189.000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1520.00 | −0.575829 | −0.287915 | − | 0.957656i | \(-0.592962\pi\) | ||||
−0.287915 | + | 0.957656i | \(0.592962\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −62.0000 | −0.0231236 | −0.0115618 | − | 0.999933i | \(-0.503680\pi\) | ||||
−0.0115618 | + | 0.999933i | \(0.503680\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 516.000 | 0.189495 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1074.00 | 0.388423 | 0.194212 | − | 0.980960i | \(-0.437785\pi\) | ||||
0.194212 | + | 0.980960i | \(0.437785\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 552.000 | 0.196634 | 0.0983172 | − | 0.995155i | \(-0.468654\pi\) | ||||
0.0983172 | + | 0.995155i | \(0.468654\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1884.00 | −0.661130 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1722.00 | 0.595373 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −748.000 | −0.254842 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1080.00 | 0.362634 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −208.000 | −0.0688405 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1692.00 | −0.552048 | −0.276024 | − | 0.961151i | \(-0.589017\pi\) | ||||
−0.276024 | + | 0.961151i | \(0.589017\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −888.000 | −0.285656 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −328.000 | −0.104044 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −560.000 | −0.175186 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1554.00 | 0.479496 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2580.00 | 0.785292 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 528.000 | 0.158554 | 0.0792769 | − | 0.996853i | \(-0.474739\pi\) | ||||
0.0792769 | + | 0.996853i | \(0.474739\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1089.00 | −0.322667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1876.00 | 0.548522 | 0.274261 | − | 0.961655i | \(-0.411567\pi\) | ||||
0.274261 | + | 0.961655i | \(0.411567\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5474.00 | 1.57962 | 0.789808 | − | 0.613354i | \(-0.210180\pi\) | ||||
0.789808 | + | 0.613354i | \(0.210180\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1092.00 | −0.311032 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3418.00 | 0.961033 | 0.480516 | − | 0.876986i | \(-0.340449\pi\) | ||||
0.480516 | + | 0.876986i | \(0.340449\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 928.000 | 0.257600 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3552.00 | 0.973532 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7360.00 | 1.99196 | 0.995981 | − | 0.0895670i | \(-0.0285483\pi\) | ||||
0.995981 | + | 0.0895670i | \(0.0285483\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2126.00 | −0.568248 | −0.284124 | − | 0.958788i | \(-0.591703\pi\) | ||||
−0.284124 | + | 0.958788i | \(0.591703\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 98.0000 | 0.0255551 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −344.000 | −0.0886162 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 660.000 | 0.167975 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7788.00 | 1.95846 | 0.979231 | − | 0.202745i | \(-0.0649864\pi\) | ||||
0.979231 | + | 0.202745i | \(0.0649864\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6240.00 | −1.55061 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 180.000 | 0.0442041 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3470.00 | −0.842228 | −0.421114 | − | 0.907008i | \(-0.638361\pi\) | ||||
−0.421114 | + | 0.907008i | \(0.638361\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2030.00 | −0.487020 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2214.00 | −0.525070 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3096.00 | −0.725884 | −0.362942 | − | 0.931812i | \(-0.618228\pi\) | ||||
−0.362942 | + | 0.931812i | \(0.618228\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 324.000 | 0.0751063 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2322.00 | 0.532225 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3274.00 | 0.742079 | 0.371040 | − | 0.928617i | \(-0.379001\pi\) | ||||
0.371040 | + | 0.928617i | \(0.379001\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 960.000 | 0.215188 | 0.107594 | − | 0.994195i | \(-0.465685\pi\) | ||||
0.107594 | + | 0.994195i | \(0.465685\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1806.00 | −0.400381 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6292.00 | 1.37972 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −910.000 | −0.197388 | −0.0986942 | − | 0.995118i | \(-0.531467\pi\) | ||||
−0.0986942 | + | 0.995118i | \(0.531467\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 720.000 | 0.154499 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6486.00 | −1.37695 | −0.688474 | − | 0.725261i | \(-0.741719\pi\) | ||||
−0.688474 | + | 0.725261i | \(0.741719\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3796.00 | −0.797346 | −0.398673 | − | 0.917093i | \(-0.630529\pi\) | ||||
−0.398673 | + | 0.917093i | \(0.630529\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −24.0000 | −0.00498820 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2618.00 | 0.538452 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4013.00 | −0.816813 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3258.00 | 0.656314 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6882.00 | 1.37219 | 0.686093 | − | 0.727513i | \(-0.259324\pi\) | ||||
0.686093 | + | 0.727513i | \(0.259324\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −360.000 | −0.0710509 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1404.00 | 0.274304 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10320.0 | −1.99606 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1148.00 | 0.219833 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −870.000 | −0.164951 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1332.00 | 0.250066 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7228.00 | −1.34373 | −0.671863 | − | 0.740676i | \(-0.734506\pi\) | ||||
−0.671863 | + | 0.740676i | \(0.734506\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 264.000 | 0.0486034 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7912.00 | 1.44260 | 0.721300 | − | 0.692623i | \(-0.243545\pi\) | ||||
0.721300 | + | 0.692623i | \(0.243545\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2218.00 | 0.400539 | 0.200270 | − | 0.979741i | \(-0.435818\pi\) | ||||
0.200270 | + | 0.979741i | \(0.435818\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −126.000 | −0.0225374 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8118.00 | −1.43834 | −0.719168 | − | 0.694837i | \(-0.755477\pi\) | ||||
−0.719168 | + | 0.694837i | \(0.755477\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12792.0 | 2.24519 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1116.00 | 0.194047 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −120.000 | −0.0206718 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10406.0 | 1.77606 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4290.00 | 0.725497 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3248.00 | −0.544280 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10780.0 | 1.79010 | 0.895049 | − | 0.445968i | \(-0.147140\pi\) | ||||
0.895049 | + | 0.445968i | \(0.147140\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2610.00 | 0.429511 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1256.00 | 0.204844 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3122.00 | 0.504647 | 0.252324 | − | 0.967643i | \(-0.418805\pi\) | ||||
0.252324 | + | 0.967643i | \(0.418805\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5430.00 | −0.869962 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4160.00 | −0.660635 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −720.000 | −0.112358 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 828.000 | 0.128096 | 0.0640481 | − | 0.997947i | \(-0.479599\pi\) | ||||
0.0640481 | + | 0.997947i | \(0.479599\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4614.00 | −0.707684 | −0.353842 | − | 0.935305i | \(-0.615125\pi\) | ||||
−0.353842 | + | 0.935305i | \(0.615125\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2322.00 | 0.353103 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9458.00 | 1.42606 | 0.713029 | − | 0.701134i | \(-0.247323\pi\) | ||||
0.713029 | + | 0.701134i | \(0.247323\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 592.000 | 0.0885073 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −630.000 | −0.0933981 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2952.00 | 0.433985 | 0.216992 | − | 0.976173i | \(-0.430375\pi\) | ||||
0.216992 | + | 0.976173i | \(0.430375\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6843.00 | −0.997667 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4119.00 | −0.595569 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1036.00 | −0.148566 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10592.0 | −1.50653 | −0.753267 | − | 0.657715i | \(-0.771523\pi\) | ||||
−0.753267 | + | 0.657715i | \(0.771523\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3366.00 | −0.474870 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1134.00 | −0.158691 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6478.00 | −0.899244 | −0.449622 | − | 0.893219i | \(-0.648441\pi\) | ||||
−0.449622 | + | 0.893219i | \(0.648441\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1476.00 | 0.203254 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 21156.0 | 2.89016 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5780.00 | −0.783374 | −0.391687 | − | 0.920099i | \(-0.628108\pi\) | ||||
−0.391687 | + | 0.920099i | \(0.628108\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3504.00 | −0.471169 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6912.00 | −0.922158 | −0.461079 | − | 0.887359i | \(-0.652538\pi\) | ||||
−0.461079 | + | 0.887359i | \(0.652538\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 728.000 | 0.0963697 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1476.00 | −0.193874 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9010.00 | 1.17436 | 0.587179 | − | 0.809457i | \(-0.300239\pi\) | ||||
0.587179 | + | 0.809457i | \(0.300239\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3600.00 | −0.465626 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3804.00 | −0.488261 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2368.00 | −0.301638 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10774.0 | −1.36204 | −0.681022 | − | 0.732263i | \(-0.738464\pi\) | ||||
−0.681022 | + | 0.732263i | \(0.738464\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 84.0000 | 0.0105395 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −78.0000 | −0.00971355 | −0.00485678 | − | 0.999988i | \(-0.501546\pi\) | ||||
−0.00485678 | + | 0.999988i | \(0.501546\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6880.00 | −0.850415 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 162.000 | 0.0198762 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −15080.0 | −1.83658 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15254.0 | −1.84416 | −0.922080 | − | 0.386998i | \(-0.873512\pi\) | ||||
−0.922080 | + | 0.386998i | \(0.873512\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1422.00 | −0.170662 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1260.00 | 0.150122 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −440.000 | −0.0520452 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8052.00 | −0.945583 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7316.00 | 0.853007 | 0.426504 | − | 0.904486i | \(-0.359745\pi\) | ||||
0.426504 | + | 0.904486i | \(0.359745\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11330.0 | 1.31162 | 0.655808 | − | 0.754928i | \(-0.272328\pi\) | ||||
0.655808 | + | 0.754928i | \(0.272328\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4176.00 | 0.480010 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3630.00 | 0.414308 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4662.00 | −0.528361 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −13416.0 | −1.50986 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6016.00 | −0.672345 | −0.336172 | − | 0.941801i | \(-0.609132\pi\) | ||||
−0.336172 | + | 0.941801i | \(0.609132\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13550.0 | −1.50386 | −0.751930 | − | 0.659243i | \(-0.770877\pi\) | ||||
−0.751930 | + | 0.659243i | \(0.770877\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1476.00 | 0.162687 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 480.000 | 0.0525435 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2760.00 | −0.300063 | −0.150031 | − | 0.988681i | \(-0.547937\pi\) | ||||
−0.150031 | + | 0.988681i | \(0.547937\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3036.00 | 0.325609 | 0.162804 | − | 0.986658i | \(-0.447946\pi\) | ||||
0.162804 | + | 0.986658i | \(0.447946\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1548.00 | −0.164904 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3942.00 | −0.417115 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12962.0 | 1.36239 | 0.681197 | − | 0.732100i | \(-0.261460\pi\) | ||||
0.681197 | + | 0.732100i | \(0.261460\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19448.0 | 2.03053 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9000.00 | −0.933459 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1204.00 | 0.124054 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11866.0 | 1.21459 | 0.607295 | − | 0.794476i | \(-0.292254\pi\) | ||||
0.607295 | + | 0.794476i | \(0.292254\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 810.000 | 0.0823694 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10998.0 | −1.11112 | −0.555562 | − | 0.831475i | \(-0.687497\pi\) | ||||
−0.555562 | + | 0.831475i | \(0.687497\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9088.00 | −0.912214 | −0.456107 | − | 0.889925i | \(-0.650757\pi\) | ||||
−0.456107 | + | 0.889925i | \(0.650757\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −480.000 | −0.0478698 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18236.0 | −1.80698 | −0.903492 | − | 0.428605i | \(-0.859005\pi\) | ||||
−0.903492 | + | 0.428605i | \(0.859005\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4396.00 | −0.432811 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2322.00 | 0.227159 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8528.00 | 0.829002 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −484.000 | −0.0467525 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1458.00 | 0.139952 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11424.0 | −1.08972 | −0.544860 | − | 0.838527i | \(-0.683417\pi\) | ||||
−0.544860 | + | 0.838527i | \(0.683417\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24940.0 | −2.36417 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2520.00 | 0.237400 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2172.00 | −0.203351 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8536.00 | −0.794257 | −0.397128 | − | 0.917763i | \(-0.629993\pi\) | ||||
−0.397128 | + | 0.917763i | \(0.629993\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6876.00 | −0.635876 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18732.0 | 1.72172 | 0.860859 | − | 0.508844i | \(-0.169927\pi\) | ||||
0.860859 | + | 0.508844i | \(0.169927\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7380.00 | 0.674196 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −936.000 | −0.0849900 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2072.00 | −0.187006 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21700.0 | 1.94674 | 0.973372 | − | 0.229231i | \(-0.0736210\pi\) | ||||
0.973372 | + | 0.229231i | \(0.0736210\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5016.00 | 0.447302 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1048.00 | −0.0928986 | −0.0464493 | − | 0.998921i | \(-0.514791\pi\) | ||||
−0.0464493 | + | 0.998921i | \(0.514791\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 580.000 | 0.0511082 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −15597.0 | −1.36625 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8890.00 | 0.774150 | 0.387075 | − | 0.922048i | \(-0.373485\pi\) | ||||
0.387075 | + | 0.922048i | \(0.373485\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3626.00 | 0.313904 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −108.000 | −0.00929496 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −176.000 | −0.0150592 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −24128.0 | −2.05251 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8190.00 | −0.692680 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13962.0 | 1.17406 | 0.587031 | − | 0.809564i | \(-0.300297\pi\) | ||||
0.587031 | + | 0.809564i | \(0.300297\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16420.0 | −1.37284 | −0.686421 | − | 0.727204i | \(-0.740819\pi\) | ||||
−0.686421 | + | 0.727204i | \(0.740819\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2541.00 | −0.211235 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2400.00 | −0.198379 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2233.00 | 0.183529 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1620.00 | −0.132396 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 32164.0 | 2.61384 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −744.000 | −0.0601232 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7716.00 | 0.620056 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2548.00 | −0.203618 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14554.0 | 1.15661 | 0.578304 | − | 0.815821i | \(-0.303715\pi\) | ||||
0.578304 | + | 0.815821i | \(0.303715\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9642.00 | 0.762022 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2860.00 | −0.224787 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −588.000 | −0.0459617 | −0.0229809 | − | 0.999736i | \(-0.507316\pi\) | ||||
−0.0229809 | + | 0.999736i | \(0.507316\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5994.00 | 0.465970 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −984.000 | −0.0760795 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8288.00 | 0.637327 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1740.00 | −0.133079 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10726.0 | −0.815934 | −0.407967 | − | 0.912997i | \(-0.633762\pi\) | ||||
−0.407967 | + | 0.912997i | \(0.633762\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14104.0 | 1.06715 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4680.00 | −0.352210 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 740.000 | 0.0553948 | 0.0276974 | − | 0.999616i | \(-0.491183\pi\) | ||||
0.0276974 | + | 0.999616i | \(0.491183\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3620.00 | 0.269548 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −567.000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17386.0 | 1.28095 | 0.640474 | − | 0.767980i | \(-0.278738\pi\) | ||||
0.640474 | + | 0.767980i | \(0.278738\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1108.00 | −0.0812055 | −0.0406028 | − | 0.999175i | \(-0.512928\pi\) | ||||
−0.0406028 | + | 0.999175i | \(0.512928\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4560.00 | 0.332455 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −14520.0 | −1.05309 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13694.0 | −0.988022 | −0.494011 | − | 0.869456i | \(-0.664470\pi\) | ||||
−0.494011 | + | 0.869456i | \(0.664470\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 186.000 | 0.0133504 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1540.00 | 0.109966 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8424.00 | −0.598433 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1548.00 | −0.109405 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2844.00 | 0.199973 | 0.0999867 | − | 0.994989i | \(-0.468120\pi\) | ||||
0.0999867 | + | 0.994989i | \(0.468120\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 320.000 | 0.0223860 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3222.00 | −0.224256 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9410.00 | 0.651640 | 0.325820 | − | 0.945432i | \(-0.394360\pi\) | ||||
0.325820 | + | 0.945432i | \(0.394360\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 420.000 | 0.0289384 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1656.00 | −0.113527 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14952.0 | −1.01990 | −0.509952 | − | 0.860203i | \(-0.670337\pi\) | ||||
−0.509952 | + | 0.860203i | \(0.670337\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2570.00 | 0.174430 | 0.0872150 | − | 0.996190i | \(-0.472203\pi\) | ||||
0.0872150 | + | 0.996190i | \(0.472203\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5652.00 | 0.381704 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2746.00 | 0.184530 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8176.00 | −0.546711 | −0.273356 | − | 0.961913i | \(-0.588134\pi\) | ||||
−0.273356 | + | 0.961913i | \(0.588134\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5166.00 | −0.343739 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −39904.0 | −2.64213 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8862.00 | −0.583903 | −0.291952 | − | 0.956433i | \(-0.594305\pi\) | ||||
−0.291952 | + | 0.956433i | \(0.594305\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2244.00 | 0.147133 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1126.00 | −0.0734701 | −0.0367351 | − | 0.999325i | \(-0.511696\pi\) | ||||
−0.0367351 | + | 0.999325i | \(0.511696\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9892.00 | −0.642315 | −0.321158 | − | 0.947026i | \(-0.604072\pi\) | ||||
−0.321158 | + | 0.947026i | \(0.604072\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3240.00 | −0.209367 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5418.00 | 0.348423 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14141.0 | 0.905024 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 624.000 | 0.0397451 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8700.00 | −0.551497 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11256.0 | 0.710134 | 0.355067 | − | 0.934841i | \(-0.384458\pi\) | ||||
0.355067 | + | 0.934841i | \(0.384458\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5076.00 | 0.318725 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2336.00 | 0.145986 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4214.00 | −0.262111 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2664.00 | 0.164924 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5694.00 | −0.350857 | −0.175429 | − | 0.984492i | \(-0.556131\pi\) | ||||
−0.175429 | + | 0.984492i | \(0.556131\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −30028.0 | −1.84166 | −0.920831 | − | 0.389962i | \(-0.872488\pi\) | ||||
−0.920831 | + | 0.389962i | \(0.872488\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 984.000 | 0.0600697 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18680.0 | 1.13506 | 0.567532 | − | 0.823351i | \(-0.307898\pi\) | ||||
0.567532 | + | 0.823351i | \(0.307898\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9360.00 | 0.566120 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1680.00 | 0.101143 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3034.00 | 0.181822 | 0.0909109 | − | 0.995859i | \(-0.471022\pi\) | ||||
0.0909109 | + | 0.995859i | \(0.471022\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2536.00 | 0.151282 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4662.00 | −0.276837 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −26508.0 | −1.56693 | −0.783464 | − | 0.621438i | \(-0.786549\pi\) | ||||
−0.783464 | + | 0.621438i | \(0.786549\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24658.0 | 1.45096 | 0.725480 | − | 0.688243i | \(-0.241618\pi\) | ||||
0.725480 | + | 0.688243i | \(0.241618\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7740.00 | −0.453389 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −56.0000 | −0.00326554 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −29520.0 | −1.71367 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1584.00 | −0.0915411 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −34632.0 | −1.99248 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23266.0 | 1.33260 | 0.666299 | − | 0.745685i | \(-0.267877\pi\) | ||||
0.666299 | + | 0.745685i | \(0.267877\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3267.00 | 0.186292 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5694.00 | −0.323247 | −0.161623 | − | 0.986852i | \(-0.551673\pi\) | ||||
−0.161623 | + | 0.986852i | \(0.551673\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7602.00 | 0.429658 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5628.00 | −0.316689 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14796.0 | 0.828921 | 0.414461 | − | 0.910067i | \(-0.363970\pi\) | ||||
0.414461 | + | 0.910067i | \(0.363970\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 948.000 | 0.0528777 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16422.0 | −0.911992 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −13932.0 | −0.770344 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4540.00 | −0.249942 | −0.124971 | − | 0.992160i | \(-0.539884\pi\) | ||||
−0.124971 | + | 0.992160i | \(0.539884\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3276.00 | 0.179574 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5368.00 | 0.292978 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11220.0 | 0.609739 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10254.0 | −0.554853 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18666.0 | 1.00571 | 0.502857 | − | 0.864370i | \(-0.332282\pi\) | ||||
0.502857 | + | 0.864370i | \(0.332282\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1160.00 | 0.0622336 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2784.00 | −0.148726 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2030.00 | −0.107986 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10974.0 | −0.581294 | −0.290647 | − | 0.956830i | \(-0.593870\pi\) | ||||
−0.290647 | + | 0.956830i | \(0.593870\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10656.0 | −0.562069 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9600.00 | 0.504240 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8944.00 | 0.467813 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −22080.0 | −1.15006 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 28240.0 | 1.46478 | 0.732388 | − | 0.680887i | \(-0.238406\pi\) | ||||
0.732388 | + | 0.680887i | \(0.238406\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 616.000 | 0.0318184 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6378.00 | 0.328078 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 29766.0 | 1.52480 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6232.00 | 0.317926 | 0.158963 | − | 0.987285i | \(-0.449185\pi\) | ||||
0.158963 | + | 0.987285i | \(0.449185\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4920.00 | 0.248937 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21638.0 | −1.09034 | −0.545169 | − | 0.838326i | \(-0.683535\pi\) | ||||
−0.545169 | + | 0.838326i | \(0.683535\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −294.000 | −0.0147542 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −32656.0 | −1.63216 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24364.0 | −1.21278 | −0.606390 | − | 0.795167i | \(-0.707383\pi\) | ||||
−0.606390 | + | 0.795167i | \(0.707383\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1032.00 | 0.0511626 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3112.00 | 0.153658 | 0.0768292 | − | 0.997044i | \(-0.475520\pi\) | ||||
0.0768292 | + | 0.997044i | \(0.475520\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2628.00 | 0.129238 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1980.00 | −0.0969805 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2604.00 | 0.127033 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20576.0 | −0.999772 | −0.499886 | − | 0.866091i | \(-0.666625\pi\) | ||||
−0.499886 | + | 0.866091i | \(0.666625\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −23364.0 | −1.13072 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6000.00 | 0.289222 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4754.00 | 0.228252 | 0.114126 | − | 0.993466i | \(-0.463593\pi\) | ||||
0.114126 | + | 0.993466i | \(0.463593\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 18720.0 | 0.895248 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10950.0 | −0.521599 | −0.260800 | − | 0.965393i | \(-0.583986\pi\) | ||||
−0.260800 | + | 0.965393i | \(0.583986\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10010.0 | 0.474949 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −540.000 | −0.0255212 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 15480.0 | 0.728749 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28798.0 | −1.35043 | −0.675216 | − | 0.737620i | \(-0.735950\pi\) | ||||
−0.675216 | + | 0.737620i | \(0.735950\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10410.0 | 0.486261 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12866.0 | 0.598652 | 0.299326 | − | 0.954151i | \(-0.403238\pi\) | ||||
0.299326 | + | 0.954151i | \(0.403238\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9680.00 | −0.448666 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6090.00 | 0.281181 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1496.00 | −0.0688059 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15392.0 | −0.705210 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6642.00 | 0.303149 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1548.00 | −0.0703828 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13156.0 | 0.595884 | 0.297942 | − | 0.954584i | \(-0.403700\pi\) | ||||
0.297942 | + | 0.954584i | \(0.403700\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9288.00 | 0.419089 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12670.0 | −0.569524 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −57276.0 | −2.56486 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −972.000 | −0.0433626 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −20454.0 | −0.909056 | −0.454528 | − | 0.890732i | \(-0.650192\pi\) | ||||
−0.454528 | + | 0.890732i | \(0.650192\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13920.0 | −0.616338 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6966.00 | −0.307280 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 26936.0 | 1.18375 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1680.00 | −0.0735556 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9822.00 | −0.428440 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 15706.0 | 0.682563 | 0.341282 | − | 0.939961i | \(-0.389139\pi\) | ||||
0.341282 | + | 0.939961i | \(0.389139\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6532.00 | −0.282823 | −0.141412 | − | 0.989951i | \(-0.545164\pi\) | ||||
−0.141412 | + | 0.989951i | \(0.545164\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2880.00 | −0.124239 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4584.00 | 0.197019 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −656.000 | −0.0280912 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5418.00 | 0.231160 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 46754.0 | 1.98749 | 0.993743 | − | 0.111692i | \(-0.0356269\pi\) | ||||
0.993743 | + | 0.111692i | \(0.0356269\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22008.0 | 0.932139 | 0.466070 | − | 0.884748i | \(-0.345670\pi\) | ||||
0.466070 | + | 0.884748i | \(0.345670\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −18876.0 | −0.796579 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −45412.0 | −1.90947 | −0.954734 | − | 0.297461i | \(-0.903860\pi\) | ||||
−0.954734 | + | 0.297461i | \(0.903860\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13670.0 | −0.572713 | −0.286356 | − | 0.958123i | \(-0.592444\pi\) | ||||
−0.286356 | + | 0.958123i | \(0.592444\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2730.00 | 0.113962 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1470.00 | −0.0611434 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3344.00 | −0.138591 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2160.00 | −0.0892001 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −26568.0 | −1.09324 | −0.546621 | − | 0.837380i | \(-0.684086\pi\) | ||||
−0.546621 | + | 0.837380i | \(0.684086\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 36127.0 | 1.48128 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 19458.0 | 0.794981 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10398.0 | 0.423316 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9611.00 | −0.389891 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 11388.0 | 0.460348 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 34800.0 | 1.40180 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1070.00 | −0.0429497 | −0.0214749 | − | 0.999769i | \(-0.506836\pi\) | ||||
−0.0214749 | + | 0.999769i | \(0.506836\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 72.0000 | 0.00287994 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 42906.0 | 1.71020 | 0.855100 | − | 0.518463i | \(-0.173496\pi\) | ||||
0.855100 | + | 0.518463i | \(0.173496\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11252.0 | −0.446930 | −0.223465 | − | 0.974712i | \(-0.571737\pi\) | ||||
−0.223465 | + | 0.974712i | \(0.571737\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7854.00 | −0.310875 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 29264.0 | 1.15430 | 0.577148 | − | 0.816639i | \(-0.304165\pi\) | ||||
0.577148 | + | 0.816639i | \(0.304165\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5460.00 | 0.214619 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 12039.0 | 0.471587 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 61568.0 | 2.40340 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −54008.0 | −2.10102 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9774.00 | −0.378923 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3444.00 | 0.133061 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25782.0 | −0.992698 | −0.496349 | − | 0.868123i | \(-0.665326\pi\) | ||||
−0.496349 | + | 0.868123i | \(0.665326\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −20646.0 | −0.792232 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9054.00 | −0.346240 | −0.173120 | − | 0.984901i | \(-0.555385\pi\) | ||||
−0.173120 | + | 0.984901i | \(0.555385\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8092.00 | −0.308400 | −0.154200 | − | 0.988040i | \(-0.549280\pi\) | ||||
−0.154200 | + | 0.988040i | \(0.549280\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1080.00 | 0.0410212 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11944.0 | 0.452131 | 0.226066 | − | 0.974112i | \(-0.427414\pi\) | ||||
0.226066 | + | 0.974112i | \(0.427414\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8176.00 | −0.308452 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4212.00 | −0.158370 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1856.00 | 0.0695506 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5144.00 | −0.192117 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 30960.0 | 1.15242 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −19680.0 | −0.730105 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4860.00 | −0.179700 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3444.00 | −0.126920 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6428.00 | −0.236104 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 31804.0 | 1.16432 | 0.582158 | − | 0.813076i | \(-0.302209\pi\) | ||||
0.582158 | + | 0.813076i | \(0.302209\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2610.00 | 0.0952346 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27840.0 | 1.01249 | 0.506246 | − | 0.862389i | \(-0.331033\pi\) | ||||
0.506246 | + | 0.862389i | \(0.331033\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11440.0 | 0.414686 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3996.00 | −0.144376 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8876.00 | −0.319642 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12536.0 | 0.449972 | 0.224986 | − | 0.974362i | \(-0.427766\pi\) | ||||
0.224986 | + | 0.974362i | \(0.427766\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 21684.0 | 0.775800 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −25456.0 | −0.907795 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −35090.0 | −1.24730 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −792.000 | −0.0280612 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −25870.0 | −0.913635 | −0.456818 | − | 0.889560i | \(-0.651011\pi\) | ||||
−0.456818 | + | 0.889560i | \(0.651011\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 196.000 | 0.00689972 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −23736.0 | −0.832885 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3120.00 | 0.109128 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6086.00 | −0.212189 | −0.106094 | − | 0.994356i | \(-0.533835\pi\) | ||||
−0.106094 | + | 0.994356i | \(0.533835\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6654.00 | −0.231251 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3894.00 | −0.134900 | −0.0674499 | − | 0.997723i | \(-0.521486\pi\) | ||||
−0.0674499 | + | 0.997723i | \(0.521486\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −44880.0 | −1.54983 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 378.000 | 0.0130120 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 20692.0 | 0.710031 | 0.355016 | − | 0.934860i | \(-0.384476\pi\) | ||||
0.355016 | + | 0.934860i | \(0.384476\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 44548.0 | 1.52380 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 24354.0 | 0.830423 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 46986.0 | 1.59709 | 0.798545 | − | 0.601936i | \(-0.205604\pi\) | ||||
0.798545 | + | 0.601936i | \(0.205604\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3040.00 | −0.103007 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −38376.0 | −1.29626 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3318.00 | −0.111725 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23391.0 | −0.785170 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3348.00 | −0.112033 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −124.000 | −0.00413648 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 53960.0 | 1.79445 | 0.897227 | − | 0.441570i | \(-0.145578\pi\) | ||||
0.897227 | + | 0.441570i | \(0.145578\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 360.000 | 0.0119348 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7068.00 | 0.233597 | 0.116799 | − | 0.993156i | \(-0.462737\pi\) | ||||
0.116799 | + | 0.993156i | \(0.462737\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18788.0 | −0.619029 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −31218.0 | −1.02541 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 54130.0 | 1.77254 | 0.886270 | − | 0.463168i | \(-0.153288\pi\) | ||||
0.886270 | + | 0.463168i | \(0.153288\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 40248.0 | 1.31392 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12870.0 | −0.418866 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −23064.0 | −0.748349 | −0.374175 | − | 0.927358i | \(-0.622074\pi\) | ||||
−0.374175 | + | 0.927358i | \(0.622074\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2148.00 | 0.0694832 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9744.00 | 0.314240 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −19680.0 | −0.632748 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10768.0 | −0.345163 | −0.172582 | − | 0.984995i | \(-0.555211\pi\) | ||||
−0.172582 | + | 0.984995i | \(0.555211\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −32340.0 | −1.03351 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1104.00 | 0.0351750 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12766.0 | −0.405520 | −0.202760 | − | 0.979228i | \(-0.564991\pi\) | ||||
−0.202760 | + | 0.979228i | \(0.564991\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7830.00 | −0.247978 |
(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 | 1344.4.a.g.1.1 | 1 | ||
4.3 | odd | 2 | 1344.4.a.v.1.1 | 1 | |||
8.3 | odd | 2 | 336.4.a.c.1.1 | 1 | |||
8.5 | even | 2 | 168.4.a.f.1.1 | ✓ | 1 | ||
24.5 | odd | 2 | 504.4.a.c.1.1 | 1 | |||
24.11 | even | 2 | 1008.4.a.l.1.1 | 1 | |||
56.13 | odd | 2 | 1176.4.a.e.1.1 | 1 | |||
56.27 | even | 2 | 2352.4.a.bb.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.4.a.f.1.1 | ✓ | 1 | 8.5 | even | 2 | ||
336.4.a.c.1.1 | 1 | 8.3 | odd | 2 | |||
504.4.a.c.1.1 | 1 | 24.5 | odd | 2 | |||
1008.4.a.l.1.1 | 1 | 24.11 | even | 2 | |||
1176.4.a.e.1.1 | 1 | 56.13 | odd | 2 | |||
1344.4.a.g.1.1 | 1 | 1.1 | even | 1 | trivial | ||
1344.4.a.v.1.1 | 1 | 4.3 | odd | 2 | |||
2352.4.a.bb.1.1 | 1 | 56.27 | even | 2 |