Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,4,Mod(895,1344)]
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([1, 0, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1344.895");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(79.2985670477\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 672) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 895.12 | ||
Character | \(\chi\) | \(=\) | 1344.895 |
Dual form | 1344.4.b.j.895.13 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 2.14586i | − | 0.191932i | −0.995385 | − | 0.0959659i | \(-0.969406\pi\) | ||
0.995385 | − | 0.0959659i | \(-0.0305940\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 17.7853 | + | 5.16554i | 0.960316 | + | 0.278913i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 22.4578i | 0.615571i | 0.951456 | + | 0.307785i | \(0.0995879\pi\) | ||||
−0.951456 | + | 0.307785i | \(0.900412\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 45.2827i | 0.966090i | 0.875596 | + | 0.483045i | \(0.160469\pi\) | ||||
−0.875596 | + | 0.483045i | \(0.839531\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 6.43759i | − | 0.110812i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 33.9461i | 0.484303i | 0.970238 | + | 0.242151i | \(0.0778530\pi\) | ||||
−0.970238 | + | 0.242151i | \(0.922147\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 43.2405 | 0.522108 | 0.261054 | − | 0.965324i | \(-0.415930\pi\) | ||||
0.261054 | + | 0.965324i | \(0.415930\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 53.3559 | + | 15.4966i | 0.554439 | + | 0.161030i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 42.1194i | − | 0.381848i | −0.981605 | − | 0.190924i | \(-0.938852\pi\) | ||
0.981605 | − | 0.190924i | \(-0.0611483\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 120.395 | 0.963162 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 65.2787 | 0.417998 | 0.208999 | − | 0.977916i | \(-0.432979\pi\) | ||||
0.208999 | + | 0.977916i | \(0.432979\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −188.898 | −1.09442 | −0.547211 | − | 0.836994i | \(-0.684311\pi\) | ||||
−0.547211 | + | 0.836994i | \(0.684311\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 67.3734i | 0.355400i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 11.0845 | − | 38.1648i | 0.0535322 | − | 0.184315i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −165.117 | −0.733653 | −0.366826 | − | 0.930289i | \(-0.619556\pi\) | ||||
−0.366826 | + | 0.930289i | \(0.619556\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 135.848i | 0.557772i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 210.591i | 0.802167i | 0.916041 | + | 0.401084i | \(0.131366\pi\) | ||||
−0.916041 | + | 0.401084i | \(0.868634\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 322.736i | 1.14458i | 0.820053 | + | 0.572288i | \(0.193944\pi\) | ||||
−0.820053 | + | 0.572288i | \(0.806056\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 19.3128i | − | 0.0639773i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −189.974 | −0.589586 | −0.294793 | − | 0.955561i | \(-0.595251\pi\) | ||||
−0.294793 | + | 0.955561i | \(0.595251\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 289.634 | + | 183.741i | 0.844415 | + | 0.535689i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 101.838i | 0.279612i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −511.728 | −1.32625 | −0.663124 | − | 0.748509i | \(-0.730770\pi\) | ||||
−0.663124 | + | 0.748509i | \(0.730770\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 48.1913 | 0.118148 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 129.722 | 0.301439 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −17.9855 | −0.0396866 | −0.0198433 | − | 0.999803i | \(-0.506317\pi\) | ||||
−0.0198433 | + | 0.999803i | \(0.506317\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 472.581i | 0.991932i | 0.868342 | + | 0.495966i | \(0.165186\pi\) | ||||
−0.868342 | + | 0.495966i | \(0.834814\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 160.068 | + | 46.4898i | 0.320105 | + | 0.0929709i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 97.1705 | 0.185423 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 565.144i | 1.03050i | 0.857041 | + | 0.515249i | \(0.172301\pi\) | ||||
−0.857041 | + | 0.515249i | \(0.827699\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 126.358i | − | 0.220460i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 595.510i | − | 0.995409i | −0.867347 | − | 0.497704i | \(-0.834176\pi\) | ||
0.867347 | − | 0.497704i | \(-0.165824\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 412.203i | − | 0.660887i | −0.943826 | − | 0.330443i | \(-0.892802\pi\) | ||
0.943826 | − | 0.330443i | \(-0.107198\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 361.186 | 0.556082 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −116.007 | + | 399.419i | −0.171691 | + | 0.591143i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 377.133i | − | 0.537099i | −0.963266 | − | 0.268549i | \(-0.913456\pi\) | ||
0.963266 | − | 0.268549i | \(-0.0865442\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 238.431 | 0.315316 | 0.157658 | − | 0.987494i | \(-0.449606\pi\) | ||||
0.157658 | + | 0.987494i | \(0.449606\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 72.8437 | 0.0929531 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 195.836 | 0.241331 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 585.905i | − | 0.697818i | −0.937157 | − | 0.348909i | \(-0.886552\pi\) | ||
0.937157 | − | 0.348909i | \(-0.113448\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −233.910 | + | 805.367i | −0.269455 | + | 0.927752i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −566.694 | −0.631865 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 92.7882i | − | 0.100209i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 601.047i | − | 0.629146i | −0.949233 | − | 0.314573i | \(-0.898139\pi\) | ||
0.949233 | − | 0.314573i | \(-0.101861\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 202.120i | 0.205190i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 56.3229i | 0.0554885i | 0.999615 | + | 0.0277442i | \(0.00883240\pi\) | ||||
−0.999615 | + | 0.0277442i | \(0.991168\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1434.44 | 1.37223 | 0.686113 | − | 0.727495i | \(-0.259315\pi\) | ||||
0.686113 | + | 0.727495i | \(0.259315\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 33.2536 | − | 114.495i | 0.0309068 | − | 0.106414i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2180.73i | 1.97027i | 0.171774 | + | 0.985136i | \(0.445050\pi\) | ||||
−0.171774 | + | 0.985136i | \(0.554950\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −713.382 | −0.626877 | −0.313439 | − | 0.949608i | \(-0.601481\pi\) | ||||
−0.313439 | + | 0.949608i | \(0.601481\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −495.352 | −0.423575 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1090.97 | 0.908227 | 0.454114 | − | 0.890944i | \(-0.349956\pi\) | ||||
0.454114 | + | 0.890944i | \(0.349956\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −90.3824 | −0.0732887 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 407.544i | 0.322030i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −175.350 | + | 603.742i | −0.135078 | + | 0.465084i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 826.648 | 0.621073 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 631.774i | 0.463131i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 526.585i | − | 0.376793i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1748.59i | 1.22175i | 0.791726 | + | 0.610876i | \(0.209183\pi\) | ||||
−0.791726 | + | 0.610876i | \(0.790817\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 968.207i | 0.660821i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1109.66 | 0.740084 | 0.370042 | − | 0.929015i | \(-0.379343\pi\) | ||||
0.370042 | + | 0.929015i | \(0.379343\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 769.046 | + | 223.360i | 0.501389 | + | 0.145623i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 57.9383i | − | 0.0369373i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 495.842 | 0.309216 | 0.154608 | − | 0.987976i | \(-0.450589\pi\) | ||||
0.154608 | + | 0.987976i | \(0.450589\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 323.217 | 0.197230 | 0.0986148 | − | 0.995126i | \(-0.468559\pi\) | ||||
0.0986148 | + | 0.995126i | \(0.468559\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −569.922 | −0.340398 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1016.95 | −0.594696 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 140.079i | − | 0.0802271i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 868.903 | + | 551.224i | 0.487523 | + | 0.309280i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2009.92 | −1.10509 | −0.552546 | − | 0.833482i | \(-0.686344\pi\) | ||||
−0.552546 | + | 0.833482i | \(0.686344\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 357.813i | − | 0.192837i | −0.995341 | − | 0.0964185i | \(-0.969261\pi\) | ||
0.995341 | − | 0.0964185i | \(-0.0307387\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 305.515i | 0.161434i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 405.350i | 0.210055i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2794.84i | 1.42071i | 0.703841 | + | 0.710357i | \(0.251467\pi\) | ||||
−0.703841 | + | 0.710357i | \(0.748533\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1535.18 | −0.765710 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 217.569 | − | 749.106i | 0.106502 | − | 0.366695i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3205.38i | 1.54028i | 0.637877 | + | 0.770138i | \(0.279813\pi\) | ||||
−0.637877 | + | 0.770138i | \(0.720187\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 144.574 | 0.0682125 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 146.770 | 0.0680084 | 0.0340042 | − | 0.999422i | \(-0.489174\pi\) | ||||
0.0340042 | + | 0.999422i | \(0.489174\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 146.475 | 0.0666706 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 389.165 | 0.174036 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 4019.32i | − | 1.76638i | −0.469019 | − | 0.883188i | \(-0.655393\pi\) | ||
0.469019 | − | 0.883188i | \(-0.344607\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2141.27 | + | 621.906i | 0.924940 | + | 0.268638i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −53.9564 | −0.0229131 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 737.398i | 0.307909i | 0.988078 | + | 0.153955i | \(0.0492010\pi\) | ||||
−0.988078 | + | 0.153955i | \(0.950799\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 209.250i | 0.0859305i | 0.999077 | + | 0.0429653i | \(0.0136805\pi\) | ||||
−0.999077 | + | 0.0429653i | \(0.986320\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1417.74i | 0.572692i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 354.319i | 0.140811i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −762.355 | −0.298122 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 480.203 | + | 139.469i | 0.184813 | + | 0.0536768i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2950.47i | 1.11774i | 0.829254 | + | 0.558871i | \(0.188765\pi\) | ||||
−0.829254 | + | 0.558871i | \(0.811235\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −945.388 | −0.352593 | −0.176297 | − | 0.984337i | \(-0.556412\pi\) | ||||
−0.176297 | + | 0.984337i | \(0.556412\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 291.512 | 0.107054 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2000.29 | 0.723426 | 0.361713 | − | 0.932290i | \(-0.382192\pi\) | ||||
0.361713 | + | 0.932290i | \(0.382192\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2976.34 | 1.06024 | 0.530118 | − | 0.847924i | \(-0.322148\pi\) | ||||
0.530118 | + | 0.847924i | \(0.322148\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1695.43i | 0.594958i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1161.00 | + | 337.199i | 0.401410 | + | 0.116585i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 451.900 | 0.153961 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 379.074i | − | 0.127283i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 971.086i | 0.321394i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1535.80i | 0.501085i | 0.968106 | + | 0.250543i | \(0.0806091\pi\) | ||||
−0.968106 | + | 0.250543i | \(0.919391\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 1786.53i | − | 0.574699i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 692.547 | 0.219680 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3359.61 | − | 975.760i | −1.05099 | − | 0.305248i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 1236.61i | − | 0.381563i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1537.17 | −0.467880 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1762.27 | −0.529195 | −0.264598 | − | 0.964359i | \(-0.585239\pi\) | ||||
−0.264598 | + | 0.964359i | \(0.585239\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1083.56 | 0.321054 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2216.72 | −0.648145 | −0.324072 | − | 0.946032i | \(-0.605052\pi\) | ||||
−0.324072 | + | 0.946032i | \(0.605052\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 266.103i | 0.0767887i | 0.999263 | + | 0.0383943i | \(0.0122243\pi\) | ||||
−0.999263 | + | 0.0383943i | \(0.987776\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −348.020 | + | 1198.26i | −0.0991256 | + | 0.341296i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1336.76 | −0.375854 | −0.187927 | − | 0.982183i | \(-0.560177\pi\) | ||||
−0.187927 | + | 0.982183i | \(0.560177\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 407.658i | 0.113160i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 1131.40i | − | 0.310094i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5020.39i | 1.35875i | 0.733790 | + | 0.679377i | \(0.237750\pi\) | ||||
−0.733790 | + | 0.679377i | \(0.762250\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 5225.18i | − | 1.39661i | −0.715799 | − | 0.698306i | \(-0.753937\pi\) | ||
0.715799 | − | 0.698306i | \(-0.246063\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 394.284 | − | 621.516i | 0.102816 | − | 0.162070i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1958.05i | 0.504403i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 715.293 | 0.182048 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7419.77 | 1.86586 | 0.932932 | − | 0.360052i | \(-0.117241\pi\) | ||||
0.932932 | + | 0.360052i | \(0.117241\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 945.908 | 0.235054 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 218.531 | 0.0536665 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 2328.28i | − | 0.565112i | −0.959251 | − | 0.282556i | \(-0.908818\pi\) | ||
0.959251 | − | 0.282556i | \(-0.0911823\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2936.67 | − | 852.920i | −0.704539 | − | 0.204625i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 587.508 | 0.139333 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5075.60i | 1.19002i | 0.803719 | + | 0.595009i | \(0.202852\pi\) | ||||
−0.803719 | + | 0.595009i | \(0.797148\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1098.10i | 0.254549i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 1757.72i | − | 0.402886i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 3183.37i | − | 0.721536i | −0.932655 | − | 0.360768i | \(-0.882515\pi\) | ||
0.932655 | − | 0.360768i | \(-0.117485\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2852.11 | 0.639310 | 0.319655 | − | 0.947534i | \(-0.396433\pi\) | ||||
0.319655 | + | 0.947534i | \(0.396433\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −701.729 | + | 2416.10i | −0.155570 | + | 0.535638i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2703.81i | 0.592894i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5373.67 | 1.16560 | 0.582802 | − | 0.812614i | \(-0.301956\pi\) | ||||
0.582802 | + | 0.812614i | \(0.301956\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1700.08 | −0.364808 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9082.79 | −1.92823 | −0.964117 | − | 0.265479i | \(-0.914470\pi\) | ||||
−0.964117 | + | 0.265479i | \(0.914470\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3175.47 | −0.667003 | −0.333501 | − | 0.942750i | \(-0.608230\pi\) | ||||
−0.333501 | + | 0.942750i | \(0.608230\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − | 278.365i | − | 0.0578558i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1087.82 | + | 3745.43i | −0.223735 | + | 0.770334i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3760.66 | 0.765451 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 1803.14i | − | 0.363237i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 7132.20i | − | 1.42207i | −0.703154 | − | 0.711037i | \(-0.748226\pi\) | ||
0.703154 | − | 0.711037i | \(-0.251774\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 38.5944i | 0.00761712i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 606.360i | 0.118467i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1907.28 | 0.368899 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1667.10 | + | 5739.95i | −0.319237 | + | 1.09915i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 168.969i | 0.0320363i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1014.10 | 0.190383 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6900.58 | −1.28286 | −0.641428 | − | 0.767183i | \(-0.721658\pi\) | ||||
−0.641428 | + | 0.767183i | \(0.721658\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4303.31 | 0.792255 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3871.19 | 0.705837 | 0.352918 | − | 0.935654i | \(-0.385189\pi\) | ||||
0.352918 | + | 0.935654i | \(0.385189\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 1658.29i | − | 0.299463i | −0.988727 | − | 0.149732i | \(-0.952159\pi\) | ||
0.988727 | − | 0.149732i | \(-0.0478410\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 99.7608 | − | 343.484i | 0.0178441 | − | 0.0614384i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 987.422 | 0.174950 | 0.0874750 | − | 0.996167i | \(-0.472120\pi\) | ||||
0.0874750 | + | 0.996167i | \(0.472120\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1466.01i | 0.257307i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6542.19i | 1.13754i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1467.85i | 0.252858i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5451.83i | 0.930501i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2140.15 | −0.361928 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3378.75 | − | 981.317i | −0.566189 | − | 0.164443i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2313.90i | 0.384240i | 0.981371 | + | 0.192120i | \(0.0615362\pi\) | ||||
−0.981371 | + | 0.192120i | \(0.938464\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1486.06 | −0.244551 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1212.72 | 0.197785 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6416.44 | −1.03717 | −0.518584 | − | 0.855026i | \(-0.673541\pi\) | ||||
−0.518584 | + | 0.855026i | \(0.673541\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3272.90 | 0.524365 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 4242.23i | − | 0.673695i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4202.12 | + | 4764.01i | 0.661495 | + | 0.749949i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −271.147 | −0.0423133 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 3589.22i | − | 0.555272i | −0.960686 | − | 0.277636i | \(-0.910449\pi\) | ||
0.960686 | − | 0.277636i | \(-0.0895508\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5875.58i | 0.901183i | 0.892730 | + | 0.450591i | \(0.148787\pi\) | ||||
−0.892730 | + | 0.450591i | \(0.851213\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1222.63i | 0.185924i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 5263.01i | − | 0.793546i | −0.917917 | − | 0.396773i | \(-0.870130\pi\) | ||
0.917917 | − | 0.396773i | \(-0.129870\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1277.88 | −0.191051 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −526.050 | + | 1811.23i | −0.0779874 | + | 0.268516i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1668.09i | 0.245233i | 0.992454 | + | 0.122616i | \(0.0391284\pi\) | ||||
−0.992454 | + | 0.122616i | \(0.960872\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4989.26 | −0.727403 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2479.94 | 0.358577 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −884.531 | −0.126845 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9459.64 | 1.34547 | 0.672737 | − | 0.739882i | \(-0.265119\pi\) | ||||
0.672737 | + | 0.739882i | \(0.265119\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1895.32i | 0.267389i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9101.23 | − | 2643.35i | −1.27362 | − | 0.369908i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9759.34 | 1.35474 | 0.677372 | − | 0.735641i | \(-0.263119\pi\) | ||||
0.677372 | + | 0.735641i | \(0.263119\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 1579.75i | − | 0.217542i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2956.00i | 0.403824i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 6429.32i | − | 0.871377i | −0.900098 | − | 0.435688i | \(-0.856505\pi\) | ||
0.900098 | − | 0.435688i | \(-0.143495\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5245.78i | 0.705379i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5874.11 | −0.783689 | −0.391845 | − | 0.920031i | \(-0.628163\pi\) | ||||
−0.391845 | + | 0.920031i | \(0.628163\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 857.098 | + | 248.934i | 0.113459 | + | 0.0329529i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2904.62i | 0.381525i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2826.87 | 0.368452 | 0.184226 | − | 0.982884i | \(-0.441022\pi\) | ||||
0.184226 | + | 0.982884i | \(0.441022\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1429.79 | 0.184930 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3328.97 | 0.427288 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −809.276 | −0.103086 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4224.05i | 0.534002i | 0.963696 | + | 0.267001i | \(0.0860328\pi\) | ||||
−0.963696 | + | 0.267001i | \(0.913967\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2307.14 | + | 670.081i | 0.289477 | + | 0.0840753i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3689.69 | 0.459487 | 0.229743 | − | 0.973251i | \(-0.426211\pi\) | ||||
0.229743 | + | 0.973251i | \(0.426211\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 8553.82i | − | 1.05731i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 173.815i | − | 0.0213258i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 3708.17i | − | 0.451615i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3417.91i | 0.413214i | 0.978424 | + | 0.206607i | \(0.0662422\pi\) | ||||
−0.978424 | + | 0.206607i | \(0.933758\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1487.52 | 0.178526 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −319.877 | − | 92.9047i | −0.0381117 | − | 0.0110691i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 511.640i | − | 0.0605191i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 969.651 | 0.113871 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15173.0 | 1.76909 | 0.884547 | − | 0.466452i | \(-0.154468\pi\) | ||||
0.884547 | + | 0.466452i | \(0.154468\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3284.80 | 0.380264 | 0.190132 | − | 0.981759i | \(-0.439108\pi\) | ||||
0.190132 | + | 0.981759i | \(0.439108\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1709.77 | −0.196529 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4086.95i | 0.466462i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2441.14 | + | 8405.01i | −0.276663 | + | 0.952569i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3050.85 | −0.343348 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 15962.8i | − | 1.78399i | −0.452044 | − | 0.891995i | \(-0.649305\pi\) | ||
0.452044 | − | 0.891995i | \(-0.350695\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15565.2i | 1.72752i | 0.503901 | + | 0.863761i | \(0.331897\pi\) | ||||
−0.503901 | + | 0.863761i | \(0.668103\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 420.237i | − | 0.0463191i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 1821.26i | − | 0.199366i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5475.98 | −0.595340 | −0.297670 | − | 0.954669i | \(-0.596209\pi\) | ||||
−0.297670 | + | 0.954669i | \(0.596209\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2606.71 | + | 1653.67i | 0.281472 | + | 0.178563i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 7171.60i | − | 0.769149i | −0.923094 | − | 0.384574i | \(-0.874348\pi\) | ||
0.923094 | − | 0.384574i | \(-0.125652\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1257.27 | −0.133934 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6029.75 | −0.638026 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16309.6 | 1.71425 | 0.857123 | − | 0.515112i | \(-0.172250\pi\) | ||||
0.857123 | + | 0.515112i | \(0.172250\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4729.42 | −0.493791 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 1073.44i | − | 0.111334i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1728.21 | + | 501.938i | 0.178065 | + | 0.0517169i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 611.848 | 0.0626281 | 0.0313140 | − | 0.999510i | \(-0.490031\pi\) | ||||
0.0313140 | + | 0.999510i | \(0.490031\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 916.545i | 0.0932041i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 9345.40i | − | 0.944162i | −0.881555 | − | 0.472081i | \(-0.843503\pi\) | ||
0.881555 | − | 0.472081i | \(-0.156497\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 4461.44i | − | 0.447820i | −0.974610 | − | 0.223910i | \(-0.928118\pi\) | ||
0.974610 | − | 0.223910i | \(-0.0718822\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1216.05i | 0.121275i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4705.53 | −0.466266 | −0.233133 | − | 0.972445i | \(-0.574898\pi\) | ||||
−0.233133 | + | 0.972445i | \(0.574898\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2919.27 | + | 10051.3i | −0.287419 | + | 0.989604i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8384.51i | 0.820250i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7247.93 | −0.704567 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5205.95 | 0.502875 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4605.55 | −0.442083 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6801.17 | −0.648754 | −0.324377 | − | 0.945928i | \(-0.605155\pi\) | ||||
−0.324377 | + | 0.945928i | \(0.605155\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 7476.97i | − | 0.708774i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 652.707 | − | 2247.32i | 0.0614891 | − | 0.211711i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1289.77 | −0.120753 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 9205.87i | − | 0.856587i | −0.903640 | − | 0.428293i | \(-0.859115\pi\) | ||
0.903640 | − | 0.428293i | \(-0.140885\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9616.15i | 0.889279i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 9457.66i | − | 0.869283i | −0.900603 | − | 0.434642i | \(-0.856875\pi\) | ||
0.900603 | − | 0.434642i | \(-0.143125\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2215.96i | 0.202438i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 433.722 | 0.0393825 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3076.13 | − | 10591.3i | 0.277632 | − | 0.955907i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2381.97i | 0.213691i | 0.994276 | + | 0.106845i | \(0.0340750\pi\) | ||||
−0.994276 | + | 0.106845i | \(0.965925\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 440.310 | 0.0392647 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20001.0 | −1.77297 | −0.886483 | − | 0.462760i | \(-0.846859\pi\) | ||||
−0.886483 | + | 0.462760i | \(0.846859\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 120.861 | 0.0106500 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 439.426 | 0.0384923 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 17010.3i | − | 1.48127i | −0.671907 | − | 0.740636i | \(-0.734524\pi\) | ||
0.671907 | − | 0.740636i | \(-0.265476\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2129.25 | − | 7331.16i | 0.184330 | − | 0.634660i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1167.49 | 0.100480 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 3078.11i | − | 0.263374i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 4266.39i | − | 0.362932i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 12058.0i | − | 1.01982i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 19855.6i | − | 1.66965i | −0.550514 | − | 0.834826i | \(-0.685568\pi\) | ||
0.550514 | − | 0.834826i | \(-0.314432\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6014.00 | 0.502818 | 0.251409 | − | 0.967881i | \(-0.419106\pi\) | ||||
0.251409 | + | 0.967881i | \(0.419106\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6423.80 | + | 1865.72i | 0.534015 | + | 0.155098i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 6412.36i | − | 0.530032i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10393.0 | 0.854192 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −161.869 | −0.0132289 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9536.15 | −0.774965 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4679.55 | 0.378158 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2212.20i | 0.177771i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4126.42 | + | 6504.55i | −0.329754 | + | 0.519797i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18092.6 | −1.43782 | −0.718911 | − | 0.695102i | \(-0.755359\pi\) | ||||
−0.718911 | + | 0.695102i | \(0.755359\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 627.750i | 0.0496120i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1530.82i | 0.120318i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 2206.48i | − | 0.172472i | −0.996275 | − | 0.0862360i | \(-0.972516\pi\) | ||
0.996275 | − | 0.0862360i | \(-0.0274839\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4253.23i | 0.330644i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2822.68 | 0.218240 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1948.10 | − | 6707.43i | 0.149804 | − | 0.515785i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1062.96i | 0.0812974i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18990.1 | −1.44459 | −0.722294 | − | 0.691586i | \(-0.756912\pi\) | ||||
−0.722294 | + | 0.691586i | \(0.756912\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14614.4 | −1.10576 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2287.06 | −0.172121 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7744.41 | −0.579730 | −0.289865 | − | 0.957068i | \(-0.593610\pi\) | ||||
−0.289865 | + | 0.957068i | \(0.593610\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 2341.07i | − | 0.174318i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1440.61 | + | 418.408i | 0.106702 | + | 0.0309903i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14284.6 | −1.05245 | −0.526224 | − | 0.850346i | \(-0.676393\pi\) | ||||
−0.526224 | + | 0.850346i | \(0.676393\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1831.70i | 0.134246i | 0.997745 | + | 0.0671229i | \(0.0213820\pi\) | ||||
−0.997745 | + | 0.0671229i | \(0.978618\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8851.42i | 0.645329i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 5070.97i | − | 0.367781i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 11057.8i | − | 0.797822i | −0.916990 | − | 0.398911i | \(-0.869388\pi\) | ||
0.916990 | − | 0.398911i | \(-0.130612\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2836.17 | −0.203570 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4240.57 | + | 1231.62i | 0.302803 | + | 0.0879456i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 11492.3i | − | 0.816400i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 874.535 | 0.0618078 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6826.40 | −0.479992 | −0.239996 | − | 0.970774i | \(-0.577146\pi\) | ||||
−0.239996 | + | 0.970774i | \(0.577146\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8168.05 | −0.571407 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6000.87 | 0.417670 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 27637.4i | − | 1.91388i | −0.290283 | − | 0.956941i | \(-0.593750\pi\) | ||
0.290283 | − | 0.956941i | \(-0.406250\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1295.55 | + | 376.277i | 0.0892644 | + | 0.0259258i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8929.02 | 0.612128 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 21755.3i | − | 1.48397i | −0.670415 | − | 0.741986i | \(-0.733884\pi\) | ||
0.670415 | − | 0.741986i | \(-0.266116\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18589.8i | 1.26172i | 0.775896 | + | 0.630861i | \(0.217298\pi\) | ||||
−0.775896 | + | 0.630861i | \(0.782702\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5086.30i | 0.343499i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 1773.87i | − | 0.119204i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −765.817 | −0.0512085 | −0.0256042 | − | 0.999672i | \(-0.508151\pi\) | ||||
−0.0256042 | + | 0.999672i | \(0.508151\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3483.00 | + | 1011.60i | 0.231754 | + | 0.0673104i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 8602.54i | − | 0.569593i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7598.18 | 0.500633 | 0.250316 | − | 0.968164i | \(-0.419465\pi\) | ||||
0.250316 | + | 0.968164i | \(0.419465\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1355.70 | 0.0888896 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −562.905 | −0.0367289 | −0.0183644 | − | 0.999831i | \(-0.505846\pi\) | ||||
−0.0183644 | + | 0.999831i | \(0.505846\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22585.7 | −1.46655 | −0.733276 | − | 0.679931i | \(-0.762010\pi\) | ||||
−0.733276 | + | 0.679931i | \(0.762010\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 1137.22i | − | 0.0734866i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3026.51 | − | 10420.5i | 0.194630 | − | 0.670126i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13919.4 | 0.890844 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2913.26i | 0.185557i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 5605.10i | − | 0.355310i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 19524.7i | − | 1.23180i | −0.787825 | − | 0.615899i | \(-0.788793\pi\) | ||
0.787825 | − | 0.615899i | \(-0.211207\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4607.41i | 0.289302i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3752.24 | 0.234493 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8320.31 | + | 13115.4i | −0.517524 | + | 0.815781i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 5359.59i | − | 0.331803i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −848.601 | −0.0522898 | −0.0261449 | − | 0.999658i | \(-0.508323\pi\) | ||||
−0.0261449 | + | 0.999658i | \(0.508323\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31852.2 | 1.95354 | 0.976772 | − | 0.214279i | \(-0.0687403\pi\) | ||||
0.976772 | + | 0.214279i | \(0.0687403\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2077.64 | 0.126833 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18585.6 | 1.12933 | 0.564664 | − | 0.825321i | \(-0.309006\pi\) | ||||
0.564664 | + | 0.825321i | \(0.309006\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 403.914i | − | 0.0244299i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10078.8 | − | 2927.28i | −0.606791 | − | 0.176235i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18107.5 | −1.08514 | −0.542572 | − | 0.840009i | \(-0.682550\pi\) | ||||
−0.542572 | + | 0.840009i | \(0.682550\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 2381.17i | − | 0.142046i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 3709.83i | − | 0.220296i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11989.2i | 0.708699i | 0.935113 | + | 0.354350i | \(0.115298\pi\) | ||||
−0.935113 | + | 0.354350i | \(0.884702\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10534.7i | 0.619896i | 0.950754 | + | 0.309948i | \(0.100312\pi\) | ||||
−0.950754 | + | 0.309948i | \(0.899688\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4611.52 | −0.270131 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 479.301 | − | 1650.27i | 0.0279496 | − | 0.0962325i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 2749.50i | − | 0.159612i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5286.82 | −0.305531 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10613.1 | −0.610604 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18223.8 | 1.04380 | 0.521900 | − | 0.853007i | \(-0.325224\pi\) | ||||
0.521900 | + | 0.853007i | \(0.325224\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3250.67 | 0.185361 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 30533.9i | − | 1.73340i | −0.498830 | − | 0.866700i | \(-0.666237\pi\) | ||
0.498830 | − | 0.866700i | \(-0.333763\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3104.73 | − | 10689.8i | 0.175477 | − | 0.604179i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6650.16 | −0.374207 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 16410.7i | − | 0.919381i | −0.888079 | − | 0.459690i | \(-0.847960\pi\) | ||
0.888079 | − | 0.459690i | \(-0.152040\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 1064.01i | − | 0.0593484i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 798.310i | 0.0443340i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 23172.4i | − | 1.28128i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3517.34 | 0.193641 | 0.0968205 | − | 0.995302i | \(-0.469133\pi\) | ||||
0.0968205 | + | 0.995302i | \(0.469133\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1044.06 | + | 3594.77i | −0.0572302 | + | 0.197048i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 693.579i | − | 0.0378546i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7148.76 | −0.388492 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4010.28 | −0.216999 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7231.67 | −0.389638 | −0.194819 | − | 0.980839i | \(-0.562412\pi\) | ||||
−0.194819 | + | 0.980839i | \(0.562412\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7139.77 | −0.383046 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1222.97i | 0.0653332i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −290.938 | + | 1001.72i | −0.0154764 | + | 0.0532865i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12722.9 | 0.673933 | 0.336967 | − | 0.941517i | \(-0.390599\pi\) | ||||
0.336967 | + | 0.941517i | \(0.390599\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 3394.20i | − | 0.179033i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7956.27i | 0.417903i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2182.23i | 0.114141i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15061.2i | 0.784476i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1736.00 | 0.0900442 | 0.0450221 | − | 0.998986i | \(-0.485664\pi\) | ||||
0.0450221 | + | 0.998986i | \(0.485664\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 25511.9 | + | 7409.64i | 1.31777 | + | 0.382731i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 15675.6i | − | 0.806335i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7859.24 | 0.402600 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28120.7 | −1.43458 | −0.717290 | − | 0.696774i | \(-0.754618\pi\) | ||||
−0.717290 | + | 0.696774i | \(0.754618\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10955.6 | −0.554321 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 30570.1i | − | 1.54042i | −0.637788 | − | 0.770212i | \(-0.720150\pi\) | ||
0.637788 | − | 0.770212i | \(-0.279850\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1182.85 | − | 1864.55i | 0.0593607 | − | 0.0935713i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12691.9 | −0.634344 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 30930.9i | − | 1.53966i | −0.638248 | − | 0.769831i | \(-0.720340\pi\) | ||
0.638248 | − | 0.769831i | \(-0.279660\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5874.15i | 0.291217i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 3045.97i | − | 0.150398i | −0.997169 | − | 0.0751991i | \(-0.976041\pi\) | ||
0.997169 | − | 0.0751991i | \(-0.0239592\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4313.01i | 0.212102i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2145.88 | 0.105105 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11264.6 | + | 38785.0i | −0.549534 | + | 1.89209i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6453.80i | 0.313585i | 0.987632 | + | 0.156793i | \(0.0501155\pi\) | ||||
−0.987632 | + | 0.156793i | \(0.949885\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 22259.3 | 1.07726 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −767.817 | −0.0370116 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12161.0 | 0.583882 | 0.291941 | − | 0.956436i | \(-0.405699\pi\) | ||||
0.291941 | + | 0.956436i | \(0.405699\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2837.72 | 0.135709 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 8701.33i | − | 0.414485i | −0.978290 | − | 0.207243i | \(-0.933551\pi\) | ||
0.978290 | − | 0.207243i | \(-0.0664489\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12687.7 | − | 3685.00i | −0.602000 | − | 0.174844i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 655.594 | 0.0309844 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 814.432i | − | 0.0383408i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32329.2i | 1.51602i | 0.652243 | + | 0.758010i | \(0.273828\pi\) | ||||
−0.652243 | + | 0.758010i | \(0.726172\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 6984.83i | − | 0.326268i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 10932.6i | − | 0.508691i | −0.967113 | − | 0.254345i | \(-0.918140\pi\) | ||
0.967113 | − | 0.254345i | \(-0.0818600\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −22742.4 | −1.05411 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8810.00 | − | 2558.76i | −0.406766 | − | 0.118140i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9106.08i | 0.418818i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13373.8 | 0.612744 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1762.52 | 0.0804438 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5997.34 | 0.272680 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1491.34 | −0.0675484 | −0.0337742 | − | 0.999429i | \(-0.510753\pi\) | ||||
−0.0337742 | + | 0.999429i | \(0.510753\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 15226.8i | 0.687058i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 19403.2 | + | 5635.44i | 0.872185 | + | 0.253316i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −21399.8 | −0.958295 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3294.29i | 0.146964i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 15439.9i | − | 0.686211i | −0.939297 | − | 0.343106i | \(-0.888521\pi\) | ||
0.939297 | − | 0.343106i | \(-0.111479\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 6448.88i | − | 0.285538i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 5273.15i | − | 0.232606i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9257.17 | 0.406822 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1607.48 | − | 466.874i | −0.0703803 | − | 0.0204412i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 9550.10i | − | 0.416579i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3257.49 | 0.141567 | 0.0707833 | − | 0.997492i | \(-0.477450\pi\) | ||||
0.0707833 | + | 0.997492i | \(0.477450\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12540.0 | 0.542959 | 0.271479 | − | 0.962444i | \(-0.412487\pi\) | ||||
0.271479 | + | 0.962444i | \(0.412487\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8556.32 | 0.369106 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6878.31 | 0.295628 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13955.3i | 0.597592i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2105.19 | + | 7248.30i | −0.0898183 | + | 0.309251i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 34789.9 | 1.47890 | 0.739450 | − | 0.673212i | \(-0.235086\pi\) | ||||
0.739450 | + | 0.673212i | \(0.235086\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 31049.4i | 1.31508i | 0.753418 | + | 0.657542i | \(0.228404\pi\) | ||||
−0.753418 | + | 0.657542i | \(0.771596\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8111.43i | 0.342308i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7640.76i | 0.321276i | 0.987013 | + | 0.160638i | \(0.0513551\pi\) | ||||
−0.987013 | + | 0.160638i | \(0.948645\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10612.1i | 0.444598i | 0.974979 | + | 0.222299i | \(0.0713561\pi\) | ||||
−0.974979 | + | 0.222299i | \(0.928644\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 16121.0 | 0.672962 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6237.31 | + | 9831.97i | −0.259436 | + | 0.408953i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 314.948i | − | 0.0130530i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5100.25 | −0.210622 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4130.16 | 0.169951 | 0.0849755 | − | 0.996383i | \(-0.472919\pi\) | ||||
0.0849755 | + | 0.996383i | \(0.472919\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20127.7 | −0.825278 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −27248.4 | −1.11327 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 314.316i | − | 0.0127962i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14702.2 | + | 4270.08i | 0.596426 | + | 0.173225i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9526.40 | −0.385094 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6954.64i | 0.280143i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 26371.3i | − | 1.05854i | −0.848453 | − | 0.529270i | \(-0.822466\pi\) | ||
0.848453 | − | 0.529270i | \(-0.177534\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 835.094i | − | 0.0334031i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 44766.4i | − | 1.78435i | −0.451685 | − | 0.892177i | \(-0.649177\pi\) | ||
0.451685 | − | 0.892177i | \(-0.350823\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8343.09 | 0.331388 | 0.165694 | − | 0.986177i | \(-0.447014\pi\) | ||||
0.165694 | + | 0.986177i | \(0.447014\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3263.45 | + | 11236.3i | −0.129173 | + | 0.444753i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 28104.1i | 1.10855i | 0.832335 | + | 0.554273i | \(0.187004\pi\) | ||||
−0.832335 | + | 0.554273i | \(0.812996\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8624.90 | −0.339024 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 11282.0 | 0.441933 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8469.58 | 0.330622 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −25591.3 | −0.995553 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 5409.43i | − | 0.209715i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2720.09 | − | 9365.47i | 0.105092 | − | 0.361841i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18277.6 | −0.703753 | −0.351876 | − | 0.936047i | \(-0.614456\pi\) | ||||
−0.351876 | + | 0.936047i | \(0.614456\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 21396.6i | − | 0.821035i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 23503.1i | 0.898796i | 0.893332 | + | 0.449398i | \(0.148362\pi\) | ||||
−0.893332 | + | 0.449398i | \(0.851638\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 14588.2i | − | 0.555982i | −0.960584 | − | 0.277991i | \(-0.910332\pi\) | ||
0.960584 | − | 0.277991i | \(-0.0896685\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 115.783i | 0.00439775i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9514.11 | −0.360149 | −0.180075 | − | 0.983653i | \(-0.557634\pi\) | ||||
−0.180075 | + | 0.983653i | \(0.557634\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9032.42 | + | 31099.3i | −0.340762 | + | 1.17327i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1819.08i | 0.0683967i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8214.57 | −0.307828 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1582.36 | 0.0590976 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5721.84 | 0.212984 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −12331.0 | −0.457467 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 17371.2i | − | 0.642306i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5001.31 | + | 17219.9i | −0.184311 | + | 0.634597i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 449.022 | 0.0164928 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 36132.0i | − | 1.32276i | −0.750051 | − | 0.661381i | \(-0.769971\pi\) | ||
0.750051 | − | 0.661381i | \(-0.230029\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 506.906i | 0.0184962i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9475.15i | 0.344595i | 0.985045 | + | 0.172297i | \(0.0551190\pi\) | ||||
−0.985045 | + | 0.172297i | \(0.944881\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5354.63i | 0.194099i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3042.29 | 0.109918 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 19735.6 | + | 5731.96i | 0.710715 | + | 0.206419i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6230.48i | 0.223639i | 0.993729 | + | 0.111820i | \(0.0356679\pi\) | ||||
−0.993729 | + | 0.111820i | \(0.964332\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20701.7 | −0.740657 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 26966.3 | 0.961654 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19879.4 | −0.706626 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 12909.9 | 0.457409 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 47363.5i | − | 1.67271i | −0.548189 | − | 0.836354i | \(-0.684683\pi\) | ||
0.548189 | − | 0.836354i | \(-0.315317\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12523.9 | + | 7945.07i | 0.440876 | + | 0.279688i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11613.6 | 0.407515 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1635.91i | 0.0572192i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42614.5i | 1.48576i | 0.669427 | + | 0.742878i | \(0.266540\pi\) | ||||
−0.669427 | + | 0.742878i | \(0.733460\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 4974.87i | − | 0.172895i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1348.67i | − | 0.0467219i | −0.999727 | − | 0.0233609i | \(-0.992563\pi\) | ||
0.999727 | − | 0.0233609i | \(-0.00743669\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8869.98 | 0.306306 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 299.282 | − | 1030.45i | 0.0103023 | − | 0.0354715i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 9182.47i | − | 0.315090i | −0.987512 | − | 0.157545i | \(-0.949642\pi\) | ||
0.987512 | − | 0.157545i | \(-0.0503579\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18665.7 | 0.638476 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2962.27 | 0.101007 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −56268.6 | −1.91261 | −0.956306 | − | 0.292367i | \(-0.905557\pi\) | ||||
−0.956306 | + | 0.292367i | \(0.905557\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6331.31 | 0.214530 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4398.04i | 0.148556i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8818.70 | + | 2561.29i | 0.296945 | + | 0.0862443i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5891.51 | 0.197761 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 19626.6i | 0.656758i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2028.67i | 0.0676739i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 57083.0i | 1.89831i | 0.314812 | + | 0.949154i | \(0.398059\pi\) | ||||
−0.314812 | + | 0.949154i | \(0.601941\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4403.54i | 0.145988i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10206.5 | −0.337325 | −0.168663 | − | 0.985674i | \(-0.553945\pi\) | ||||
−0.168663 | + | 0.985674i | \(0.553945\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5748.51 | + | 1669.59i | 0.189403 | + | 0.0550098i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 16355.5i | 0.537225i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 29142.9 | 0.954313 | 0.477156 | − | 0.878818i | \(-0.341668\pi\) | ||||
0.477156 | + | 0.878818i | \(0.341668\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13158.1 | 0.429556 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6420.44 | −0.208959 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 48767.5 | 1.58234 | 0.791171 | − | 0.611595i | \(-0.209472\pi\) | ||||
0.791171 | + | 0.611595i | \(0.209472\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 4292.35i | − | 0.138848i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −10136.2 | − | 2943.95i | −0.326890 | − | 0.0949413i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13593.4 | 0.437053 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37756.7i | 1.21027i | 0.796122 | + | 0.605137i | \(0.206882\pi\) | ||||
−0.796122 | + | 0.605137i | \(0.793118\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6941.69i | 0.221841i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 6386.81i | − | 0.203493i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 12731.7i | − | 0.404429i | −0.979341 | − | 0.202215i | \(-0.935186\pi\) | ||
0.979341 | − | 0.202215i | \(-0.0648139\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4458.17 | −0.141192 |
(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.b.j.895.12 | 24 | ||
4.3 | odd | 2 | 1344.4.b.i.895.12 | 24 | |||
7.6 | odd | 2 | 1344.4.b.i.895.13 | 24 | |||
8.3 | odd | 2 | 672.4.b.b.223.13 | yes | 24 | ||
8.5 | even | 2 | 672.4.b.a.223.13 | yes | 24 | ||
28.27 | even | 2 | inner | 1344.4.b.j.895.13 | 24 | ||
56.13 | odd | 2 | 672.4.b.b.223.12 | yes | 24 | ||
56.27 | even | 2 | 672.4.b.a.223.12 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.4.b.a.223.12 | ✓ | 24 | 56.27 | even | 2 | ||
672.4.b.a.223.13 | yes | 24 | 8.5 | even | 2 | ||
672.4.b.b.223.12 | yes | 24 | 56.13 | odd | 2 | ||
672.4.b.b.223.13 | yes | 24 | 8.3 | odd | 2 | ||
1344.4.b.i.895.12 | 24 | 4.3 | odd | 2 | |||
1344.4.b.i.895.13 | 24 | 7.6 | odd | 2 | |||
1344.4.b.j.895.12 | 24 | 1.1 | even | 1 | trivial | ||
1344.4.b.j.895.13 | 24 | 28.27 | even | 2 | inner |