Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,4,Mod(673,1344)]
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, 1, 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("1344.673");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.c (of order \(2\), degree \(1\), 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: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 386x^{10} + 54793x^{8} + 3447408x^{6} + 90154296x^{4} + 707138208x^{2} + 525876624 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{22} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 673.10 | ||
Root | \(-10.8906i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.673 |
Dual form | 1344.4.c.e.673.3 |
$q$-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 | ||||||||
\(3\) | 3.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.28149i | 0.114620i | 0.998356 | + | 0.0573099i | \(0.0182523\pi\) | ||||
−0.998356 | + | 0.0573099i | \(0.981748\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 58.8368i | 1.61272i | 0.591422 | + | 0.806362i | \(0.298567\pi\) | ||||
−0.591422 | + | 0.806362i | \(0.701433\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 11.2921i | 0.240913i | 0.992719 | + | 0.120456i | \(0.0384358\pi\) | ||||
−0.992719 | + | 0.120456i | \(0.961564\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.84446 | −0.0661757 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −104.187 | −1.48642 | −0.743208 | − | 0.669060i | \(-0.766697\pi\) | ||||
−0.743208 | + | 0.669060i | \(0.766697\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 51.5021i | 0.621863i | 0.950432 | + | 0.310932i | \(0.100641\pi\) | ||||
−0.950432 | + | 0.310932i | \(0.899359\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 21.0000i | − 0.218218i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −131.383 | −1.19110 | −0.595549 | − | 0.803319i | \(-0.703066\pi\) | ||||
−0.595549 | + | 0.803319i | \(0.703066\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 123.358 | 0.986862 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 27.0000i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 32.6564i | − 0.209108i | −0.994519 | − | 0.104554i | \(-0.966658\pi\) | ||||
0.994519 | − | 0.104554i | \(-0.0333415\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 108.814 | 0.630440 | 0.315220 | − | 0.949019i | \(-0.397922\pi\) | ||||
0.315220 | + | 0.949019i | \(0.397922\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −176.510 | −0.931107 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 8.97041i | − 0.0433222i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 5.75772i | − 0.0255828i | −0.999918 | − | 0.0127914i | \(-0.995928\pi\) | ||||
0.999918 | − | 0.0127914i | \(-0.00407174\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −33.8763 | −0.139091 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −198.587 | −0.756442 | −0.378221 | − | 0.925715i | \(-0.623464\pi\) | ||||
−0.378221 | + | 0.925715i | \(0.623464\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 97.7382i | − 0.346626i | −0.984867 | − | 0.173313i | \(-0.944553\pi\) | ||||
0.984867 | − | 0.173313i | \(-0.0554473\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 11.5334i | − 0.0382066i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 422.128 | 1.31008 | 0.655039 | − | 0.755595i | \(-0.272652\pi\) | ||||
0.655039 | + | 0.755595i | \(0.272652\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 312.561i | − 0.858183i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 209.333i | − 0.542530i | −0.962505 | − | 0.271265i | \(-0.912558\pi\) | ||||
0.962505 | − | 0.271265i | \(-0.0874420\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −75.3986 | −0.184850 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −154.506 | −0.359033 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 74.8335i | − 0.165127i | −0.996586 | − | 0.0825635i | \(-0.973689\pi\) | ||||
0.996586 | − | 0.0825635i | \(-0.0263107\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 447.218i | 0.938694i | 0.883014 | + | 0.469347i | \(0.155511\pi\) | ||||
−0.883014 | + | 0.469347i | \(0.844489\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 63.0000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −14.4707 | −0.0276134 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 328.017i | 0.598115i | 0.954235 | + | 0.299057i | \(0.0966722\pi\) | ||||
−0.954235 | + | 0.299057i | \(0.903328\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 394.149i | − 0.687681i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 148.641 | 0.248457 | 0.124228 | − | 0.992254i | \(-0.460354\pi\) | ||||
0.124228 | + | 0.992254i | \(0.460354\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −35.9094 | −0.0575737 | −0.0287868 | − | 0.999586i | \(-0.509164\pi\) | ||||
−0.0287868 | + | 0.999586i | \(0.509164\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 370.073i | 0.569765i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 411.858i | − 0.609552i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1302.70 | −1.85526 | −0.927628 | − | 0.373505i | \(-0.878156\pi\) | ||||
−0.927628 | + | 0.373505i | \(0.878156\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 393.931i | − 0.520958i | −0.965479 | − | 0.260479i | \(-0.916119\pi\) | ||||
0.965479 | − | 0.260479i | \(-0.0838805\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 133.514i | − 0.170373i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 97.9692 | 0.120729 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −480.693 | −0.572509 | −0.286255 | − | 0.958154i | \(-0.592410\pi\) | ||||
−0.286255 | + | 0.958154i | \(0.592410\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 79.0448i | − 0.0910565i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 326.443i | 0.363985i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −65.9994 | −0.0712778 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1278.12 | −1.33787 | −0.668936 | − | 0.743320i | \(-0.733250\pi\) | ||||
−0.668936 | + | 0.743320i | \(0.733250\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 529.531i | − 0.537575i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 1506.28i | − 1.48397i | −0.670417 | − | 0.741985i | \(-0.733885\pi\) | ||||
0.670417 | − | 0.741985i | \(-0.266115\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1101.07 | 1.05331 | 0.526656 | − | 0.850078i | \(-0.323446\pi\) | ||||
0.526656 | + | 0.850078i | \(0.323446\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 26.9112 | 0.0250121 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 837.935i | − 0.757068i | −0.925587 | − | 0.378534i | \(-0.876428\pi\) | ||||
0.925587 | − | 0.378534i | \(-0.123572\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 1278.36i | − 1.12334i | −0.827361 | − | 0.561671i | \(-0.810159\pi\) | ||||
0.827361 | − | 0.561671i | \(-0.189841\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 17.2732 | 0.0147702 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1523.07 | −1.26795 | −0.633976 | − | 0.773353i | \(-0.718578\pi\) | ||||
−0.633976 | + | 0.773353i | \(0.718578\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 168.366i | − 0.136523i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 101.629i | − 0.0803043i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 729.309 | 0.561812 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2130.77 | −1.60088 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 595.762i | − 0.436732i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 318.267i | 0.227734i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 451.549 | 0.315500 | 0.157750 | − | 0.987479i | \(-0.449576\pi\) | ||||
0.157750 | + | 0.987479i | \(0.449576\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 293.215 | 0.200125 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 946.680i | 0.631388i | 0.948861 | + | 0.315694i | \(0.102237\pi\) | ||||
−0.948861 | + | 0.315694i | \(0.897763\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 360.515i | − 0.235042i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 34.6002 | 0.0220586 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −467.626 | −0.291621 | −0.145810 | − | 0.989313i | \(-0.546579\pi\) | ||||
−0.145810 | + | 0.989313i | \(0.546579\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 962.541i | − 0.587350i | −0.955905 | − | 0.293675i | \(-0.905122\pi\) | ||||
0.955905 | − | 0.293675i | \(-0.0948784\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1266.38i | 0.756374i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −664.392 | −0.388526 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 41.8488 | 0.0239679 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 147.000i | 0.0824786i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1466.66i | 0.806399i | 0.915112 | + | 0.403200i | \(0.132102\pi\) | ||||
−0.915112 | + | 0.403200i | \(0.867898\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3483.73 | 1.87750 | 0.938749 | − | 0.344603i | \(-0.111986\pi\) | ||||
0.938749 | + | 0.344603i | \(0.111986\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 937.683 | 0.495472 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 139.444i | 0.0722609i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 2687.47i | − 1.36614i | −0.730353 | − | 0.683070i | \(-0.760645\pi\) | ||||
0.730353 | − | 0.683070i | \(-0.239355\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 627.999 | 0.313230 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 919.681 | 0.450193 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 2442.97i | − 1.17391i | −0.809618 | − | 0.586957i | \(-0.800326\pi\) | ||||
0.809618 | − | 0.586957i | \(-0.199674\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 226.196i | − 0.106723i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1671.70 | −0.774610 | −0.387305 | − | 0.921952i | \(-0.626594\pi\) | ||||
−0.387305 | + | 0.921952i | \(0.626594\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2069.49 | 0.941961 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 463.519i | − 0.207288i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 2590.55i | − 1.13847i | −0.822173 | − | 0.569237i | \(-0.807239\pi\) | ||||
0.822173 | − | 0.569237i | \(-0.192761\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −863.505 | −0.372999 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 224.501 | 0.0953361 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 1898.74i | − 0.792840i | −0.918069 | − | 0.396420i | \(-0.870252\pi\) | ||||
0.918069 | − | 0.396420i | \(-0.129748\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4009.08i | 1.64637i | 0.567776 | + | 0.823183i | \(0.307804\pi\) | ||||
−0.567776 | + | 0.823183i | \(0.692196\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1341.65 | −0.541955 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.37845 | 0.00293229 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 6130.03i | − 2.39718i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 189.000i | 0.0727393i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4203.58 | 1.59246 | 0.796232 | − | 0.604991i | \(-0.206823\pi\) | ||||
0.796232 | + | 0.604991i | \(0.206823\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3161.70 | −1.17919 | −0.589597 | − | 0.807698i | \(-0.700713\pi\) | ||||
−0.589597 | + | 0.807698i | \(0.700713\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 43.4121i | − 0.0159426i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.8747i | 0.00827287i | 0.999991 | + | 0.00413643i | \(0.00131667\pi\) | ||||
−0.999991 | + | 0.00413643i | \(0.998683\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4942.15 | 1.76050 | 0.880251 | − | 0.474509i | \(-0.157374\pi\) | ||||
0.880251 | + | 0.474509i | \(0.157374\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −984.051 | −0.345322 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 228.595i | 0.0790355i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 254.487i | − 0.0867032i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1182.45 | 0.397033 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3030.22 | −1.00289 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 5076.99i | − 1.65647i | −0.560384 | − | 0.828233i | \(-0.689346\pi\) | ||||
0.560384 | − | 0.828233i | \(-0.310654\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 445.922i | 0.143446i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 125.250 | 0.0397302 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −761.701 | −0.238284 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 107.728i | − 0.0332402i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 1176.49i | − 0.358097i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2689.06 | 0.807500 | 0.403750 | − | 0.914869i | \(-0.367707\pi\) | ||||
0.403750 | + | 0.914869i | \(0.367707\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1110.22 | −0.328954 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 1351.24i | − 0.395086i | −0.980294 | − | 0.197543i | \(-0.936704\pi\) | ||||
0.980294 | − | 0.197543i | \(-0.0632963\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1017.83i | 0.293714i | 0.989158 | + | 0.146857i | \(0.0469156\pi\) | ||||
−0.989158 | + | 0.146857i | \(0.953084\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1235.57 | 0.351925 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5123.55 | −1.44058 | −0.720290 | − | 0.693673i | \(-0.755991\pi\) | ||||
−0.720290 | + | 0.693673i | \(0.755991\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 540.951i | 0.150161i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 3908.10i | − 1.07113i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3568.88 | −0.965906 | −0.482953 | − | 0.875646i | \(-0.660436\pi\) | ||||
−0.482953 | + | 0.875646i | \(0.660436\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1056.55 | −0.282399 | −0.141200 | − | 0.989981i | \(-0.545096\pi\) | ||||
−0.141200 | + | 0.989981i | \(0.545096\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 62.7929i | 0.0163742i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −581.568 | −0.149815 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1181.79 | 0.300775 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 4004.08i | − 1.00691i | −0.864020 | − | 0.503457i | \(-0.832061\pi\) | ||||
0.864020 | − | 0.503457i | \(-0.167939\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 7730.16i | − 1.92091i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 400.543 | 0.0983647 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2498.49 | −0.606425 | −0.303213 | − | 0.952923i | \(-0.598059\pi\) | ||||
−0.303213 | + | 0.952923i | \(0.598059\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 40.3040i | 0.00966939i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 293.907i | 0.0697027i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 51.9986 | 0.0121915 | 0.00609577 | − | 0.999981i | \(-0.498060\pi\) | ||||
0.00609577 | + | 0.999981i | \(0.498060\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 268.258 | 0.0621846 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 1442.08i | − 0.330538i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 99.8880i | 0.0226404i | 0.999936 | + | 0.0113202i | \(0.00360341\pi\) | ||||
−0.999936 | + | 0.0113202i | \(0.996397\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7653.72 | −1.71561 | −0.857806 | − | 0.513974i | \(-0.828173\pi\) | ||||
−0.857806 | + | 0.513974i | \(0.828173\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 237.134 | 0.0525715 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7257.98i | 1.59154i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3373.81i | 0.731814i | 0.930651 | + | 0.365907i | \(0.119241\pi\) | ||||
−0.930651 | + | 0.365907i | \(0.880759\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −979.330 | −0.210147 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4769.05 | −1.01245 | −0.506224 | − | 0.862402i | \(-0.668959\pi\) | ||||
−0.506224 | + | 0.862402i | \(0.668959\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4315.56i | 0.906480i | 0.891389 | + | 0.453240i | \(0.149732\pi\) | ||||
−0.891389 | + | 0.453240i | \(0.850268\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 197.998i | − 0.0411523i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1390.11 | 0.285908 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5941.94 | 1.20943 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 3834.36i | − 0.772421i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 6184.45i | − 1.23310i | −0.787314 | − | 0.616552i | \(-0.788529\pi\) | ||||
0.787314 | − | 0.616552i | \(-0.211471\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 95.8982 | 0.0189268 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1588.59 | 0.310369 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 1483.59i | − 0.286951i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 684.167i | 0.131012i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4518.85 | 0.856770 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −573.104 | −0.107593 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 997.239i | 0.185392i | 0.995694 | + | 0.0926962i | \(0.0295485\pi\) | ||||
−0.995694 | + | 0.0926962i | \(0.970451\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3303.20i | 0.608130i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1979.15 | −0.360860 | −0.180430 | − | 0.983588i | \(-0.557749\pi\) | ||||
−0.180430 | + | 0.983588i | \(0.557749\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3819.96 | −0.689830 | −0.344915 | − | 0.938634i | \(-0.612092\pi\) | ||||
−0.344915 | + | 0.938634i | \(0.612092\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 80.7337i | 0.0144407i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 5469.80i | − 0.969132i | −0.874755 | − | 0.484566i | \(-0.838978\pi\) | ||||
0.874755 | − | 0.484566i | \(-0.161022\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1921.40 | 0.337234 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2513.81 | 0.437093 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 5365.86i | − 0.924347i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1392.97i | 0.237748i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3835.07 | 0.648562 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2954.89 | −0.495163 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 1451.21i | − 0.240983i | −0.992714 | − | 0.120492i | \(-0.961553\pi\) | ||||
0.992714 | − | 0.120492i | \(-0.0384471\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 51.8195i | 0.00852760i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −420.350 | −0.0685557 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6599.01 | 1.06668 | 0.533340 | − | 0.845901i | \(-0.320937\pi\) | ||||
0.533340 | + | 0.845901i | \(0.320937\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 4569.21i | − 0.732052i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6402.29i | 1.01673i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 505.097 | 0.0788218 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6659.56i | 1.03027i | 0.857109 | + | 0.515135i | \(0.172258\pi\) | ||||
−0.857109 | + | 0.515135i | \(0.827742\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7006.27i | 1.07460i | 0.843390 | + | 0.537302i | \(0.180557\pi\) | ||||
−0.843390 | + | 0.537302i | \(0.819443\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 304.887 | 0.0463637 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9955.17 | −1.50102 | −0.750510 | − | 0.660859i | \(-0.770192\pi\) | ||||
−0.750510 | + | 0.660859i | \(0.770192\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 190.481i | 0.0284780i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2187.93i | 0.324363i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5535.13 | 0.813741 | 0.406870 | − | 0.913486i | \(-0.366620\pi\) | ||||
0.406870 | + | 0.913486i | \(0.366620\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4206.53 | 0.613286 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 6392.31i | − 0.924268i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 46.0175i | − 0.00659908i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3303.44 | −0.469859 | −0.234930 | − | 0.972012i | \(-0.575486\pi\) | ||||
−0.234930 | + | 0.972012i | \(0.575486\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1787.29 | 0.252147 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1465.33i | 0.205057i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 12293.9i | − 1.70658i | −0.521435 | − | 0.853291i | \(-0.674603\pi\) | ||||
0.521435 | − | 0.853291i | \(-0.325397\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −954.802 | −0.131482 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 368.760 | 0.0503769 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5187.37i | 0.703054i | 0.936178 | + | 0.351527i | \(0.114337\pi\) | ||||
−0.936178 | + | 0.351527i | \(0.885663\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1354.65i | 0.182154i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8112.41 | −1.08231 | −0.541155 | − | 0.840923i | \(-0.682013\pi\) | ||||
−0.541155 | + | 0.840923i | \(0.682013\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 527.790 | 0.0698667 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 879.644i | 0.115542i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 6411.90i | − 0.835723i | −0.908511 | − | 0.417861i | \(-0.862780\pi\) | ||||
0.908511 | − | 0.417861i | \(-0.137220\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13688.4 | 1.77047 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2840.04 | −0.364532 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 1669.39i | − 0.212649i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11946.9i | 1.51032i | 0.655540 | + | 0.755160i | \(0.272441\pi\) | ||||
−0.655540 | + | 0.755160i | \(0.727559\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1081.55 | 0.135702 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2194.25 | 0.273256 | 0.136628 | − | 0.990622i | \(-0.456374\pi\) | ||||
0.136628 | + | 0.990622i | \(0.456374\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1228.74i | 0.151881i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 103.800i | 0.0127355i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 338.766 | 0.0412580 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1599.68 | 0.193396 | 0.0966982 | − | 0.995314i | \(-0.469172\pi\) | ||||
0.0966982 | + | 0.995314i | \(0.469172\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 1402.88i | − 0.168367i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 523.835i | 0.0624121i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 504.818 | 0.0597121 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2887.62 | 0.339107 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16378.8i | 1.90969i | 0.297109 | + | 0.954843i | \(0.403977\pi\) | ||||
−0.297109 | + | 0.954843i | \(0.596023\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 6202.51i | − 0.718033i | −0.933331 | − | 0.359016i | \(-0.883112\pi\) | ||||
0.933331 | − | 0.359016i | \(-0.116888\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3799.15 | −0.436693 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −12852.3 | −1.46689 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 3130.52i | − 0.354793i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 1993.18i | − 0.224316i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10846.2 | −1.21217 | −0.606084 | − | 0.795400i | \(-0.707261\pi\) | ||||
−0.606084 | + | 0.795400i | \(0.707261\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11096.6 | −1.23156 | −0.615782 | − | 0.787917i | \(-0.711160\pi\) | ||||
−0.615782 | + | 0.787917i | \(0.711160\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 125.546i | 0.0138379i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 6766.51i | − 0.740700i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3308.76 | −0.359723 | −0.179862 | − | 0.983692i | \(-0.557565\pi\) | ||||
−0.179862 | + | 0.983692i | \(0.557565\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −441.000 | −0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9065.37i | 0.972254i | 0.873888 | + | 0.486127i | \(0.161591\pi\) | ||||
−0.873888 | + | 0.486127i | \(0.838409\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 616.002i | − 0.0656209i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4399.98 | −0.465575 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1298.44 | 0.136475 | 0.0682374 | − | 0.997669i | \(-0.478262\pi\) | ||||
0.0682374 | + | 0.997669i | \(0.478262\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 11684.2i | − 1.21993i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10451.2i | 1.08397i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 101.295 | 0.0104369 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8174.80 | 0.836764 | 0.418382 | − | 0.908271i | \(-0.362597\pi\) | ||||
0.418382 | + | 0.908271i | \(0.362597\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2813.05i | 0.286061i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 4936.55i | − 0.498738i | −0.968409 | − | 0.249369i | \(-0.919777\pi\) | ||||
0.968409 | − | 0.249369i | \(-0.0802231\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12083.1 | −1.21285 | −0.606425 | − | 0.795141i | \(-0.707397\pi\) | ||||
−0.606425 | + | 0.795141i | \(0.707397\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −418.333 | −0.0417198 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14461.5i | 1.43298i | 0.697599 | + | 0.716488i | \(0.254252\pi\) | ||||
−0.697599 | + | 0.716488i | \(0.745748\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 2296.12i | − 0.226066i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8062.42 | 0.788741 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5750.60 | 0.559013 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6353.19i | 0.613693i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1884.00i | 0.180843i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −15170.7 | −1.44711 | −0.723555 | − | 0.690266i | \(-0.757493\pi\) | ||||
−0.723555 | + | 0.690266i | \(0.757493\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 65.0168 | 0.00616323 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2759.04i | 0.259919i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 1637.90i | − 0.153347i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4020.50 | 0.374099 | 0.187050 | − | 0.982350i | \(-0.440108\pi\) | ||||
0.187050 | + | 0.982350i | \(0.440108\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7328.90 | 0.677759 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18396.4i | 1.69087i | 0.534078 | + | 0.845435i | \(0.320659\pi\) | ||||
−0.534078 | + | 0.845435i | \(0.679341\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3402.37i | 0.310822i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 678.588 | 0.0616167 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1040.49 | −0.0939078 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4588.93i | 0.411681i | 0.978586 | + | 0.205840i | \(0.0659927\pi\) | ||||
−0.978586 | + | 0.205840i | \(0.934007\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 5015.09i | − 0.447221i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6342.89 | 0.562257 | 0.281129 | − | 0.959670i | \(-0.409291\pi\) | ||||
0.281129 | + | 0.959670i | \(0.409291\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1930.28 | 0.170092 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6208.46i | 0.543841i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16127.4i | 1.40439i | 0.711984 | + | 0.702196i | \(0.247797\pi\) | ||||
−0.711984 | + | 0.702196i | \(0.752203\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 251.366 | 0.0217608 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1390.56 | 0.119678 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1411.00i | 0.120730i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 24836.6i | 2.11279i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7771.66 | 0.657298 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10521.2 | 0.884723 | 0.442362 | − | 0.896837i | \(-0.354141\pi\) | ||||
0.442362 | + | 0.896837i | \(0.354141\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 4897.33i | − 0.409455i | −0.978819 | − | 0.204728i | \(-0.934369\pi\) | ||||
0.978819 | − | 0.204728i | \(-0.0656309\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 2590.51i | − 0.215351i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −11337.1 | −0.937096 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5094.51 | 0.418715 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 673.502i | 0.0550423i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 2242.47i | − 0.182237i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1073.80 | 0.0867749 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5696.22 | 0.457746 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2883.00i | 0.230389i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3638.72i | 0.289170i | 0.989492 | + | 0.144585i | \(0.0461847\pi\) | ||||
−0.989492 | + | 0.144585i | \(0.953815\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −12027.2 | −0.950530 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1638.20 | 0.128757 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 18255.3i | − 1.42695i | −0.700681 | − | 0.713475i | \(-0.747120\pi\) | ||||
0.700681 | − | 0.713475i | \(-0.252880\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 4024.96i | − 0.312898i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1681.87 | 0.130037 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9118.90 | 0.701221 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 22.1353i | 0.00169296i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 18481.5i | − 1.40590i | −0.711240 | − | 0.702950i | \(-0.751866\pi\) | ||||
0.711240 | − | 0.702950i | \(-0.248134\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1103.67 | 0.0835068 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 18390.1 | 1.38401 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20507.1i | 1.53512i | 0.640980 | + | 0.767558i | \(0.278528\pi\) | ||||
−0.640980 | + | 0.767558i | \(0.721472\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 1951.80i | − 0.145332i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −567.000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7707.00 | −0.567828 | −0.283914 | − | 0.958850i | \(-0.591633\pi\) | ||||
−0.283914 | + | 0.958850i | \(0.591633\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 21912.4i | − 1.60596i | −0.596005 | − | 0.802981i | \(-0.703246\pi\) | ||||
0.596005 | − | 0.802981i | \(-0.296754\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12610.8i | 0.919410i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −16207.1 | −1.17545 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21547.3 | 1.55464 | 0.777319 | − | 0.629107i | \(-0.216579\pi\) | ||||
0.777319 | + | 0.629107i | \(0.216579\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 9485.11i | − 0.680808i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2757.52i | 0.196904i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12316.5 | 0.874951 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 130.236 | 0.00920446 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2902.83i | 0.204110i | 0.994779 | + | 0.102055i | \(0.0325418\pi\) | ||||
−0.994779 | + | 0.102055i | \(0.967458\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5604.18i | 0.392048i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −68.6241 | −0.00477634 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7451.82 | −0.516036 | −0.258018 | − | 0.966140i | \(-0.583069\pi\) | ||||
−0.258018 | + | 0.966140i | \(0.583069\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 934.601i | 0.0643948i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14826.5i | 1.01643i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3734.85 | 0.254761 | 0.127381 | − | 0.991854i | \(-0.459343\pi\) | ||||
0.127381 | + | 0.991854i | \(0.459343\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5577.40 | 0.378547 | 0.189274 | − | 0.981924i | \(-0.439387\pi\) | ||||
0.189274 | + | 0.981924i | \(0.439387\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 2952.15i | − 0.199372i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 2730.56i | − 0.183492i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10660.7 | 0.712858 | 0.356429 | − | 0.934322i | \(-0.383994\pi\) | ||||
0.356429 | + | 0.934322i | \(0.383994\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −685.784 | −0.0456312 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4766.71i | 0.315615i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 634.143i | − 0.0417827i | −0.999782 | − | 0.0208914i | \(-0.993350\pi\) | ||||
0.999782 | − | 0.0208914i | \(-0.00665041\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 763.461 | 0.0500581 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7716.38 | 0.503484 | 0.251742 | − | 0.967794i | \(-0.418997\pi\) | ||||
0.251742 | + | 0.967794i | \(0.418997\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6849.48i | 0.444756i | 0.974961 | + | 0.222378i | \(0.0713819\pi\) | ||||
−0.974961 | + | 0.222378i | \(0.928618\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3547.34i | 0.229227i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3364.85 | 0.216388 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15011.9 | 0.960760 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 9090.67i | − 0.579021i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 599.880i | 0.0380267i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27119.1 | −1.71092 | −0.855462 | − | 0.517866i | \(-0.826727\pi\) | ||||
−0.855462 | + | 0.517866i | \(0.826727\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 15231.0 | 0.956361 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 578.655i | 0.0361625i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 553.313i | 0.0344161i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1337.77 | −0.0828189 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1587.63 | 0.0978275 | 0.0489137 | − | 0.998803i | \(-0.484424\pi\) | ||||
0.0489137 | + | 0.998803i | \(0.484424\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16849.4i | 1.03340i | 0.856167 | + | 0.516699i | \(0.172839\pi\) | ||||
−0.856167 | + | 0.516699i | \(0.827161\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 375.751i | 0.0229383i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3808.51 | 0.231419 | 0.115709 | − | 0.993283i | \(-0.463086\pi\) | ||||
0.115709 | + | 0.993283i | \(0.463086\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4402.96 | 0.266304 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 2285.10i | − 0.137573i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 17569.4i | 1.05290i | 0.850206 | + | 0.526451i | \(0.176477\pi\) | ||||
−0.850206 | + | 0.526451i | \(0.823523\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1213.16 | −0.0723695 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 323.185 | 0.0191912 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 16528.3i | − 0.977011i | −0.872561 | − | 0.488506i | \(-0.837542\pi\) | ||||
0.872561 | − | 0.488506i | \(-0.162458\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5472.10i | 0.321997i | 0.986955 | + | 0.160999i | \(0.0514714\pi\) | ||||
−0.986955 | + | 0.160999i | \(0.948529\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3529.48 | 0.206747 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 461.995 | 0.0269405 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4290.50i | 0.249068i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8067.17i | 0.466210i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −26312.9 | −1.51385 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4565.96 | 0.261523 | 0.130761 | − | 0.991414i | \(-0.458258\pi\) | ||||
0.130761 | + | 0.991414i | \(0.458258\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 3330.66i | − 0.189922i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11267.7i | 0.639667i | 0.947474 | + | 0.319834i | \(0.103627\pi\) | ||||
−0.947474 | + | 0.319834i | \(0.896373\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8946.85 | 0.505668 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4053.71 | 0.228103 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 33282.6i | 1.86460i | 0.361680 | + | 0.932302i | \(0.382203\pi\) | ||||
−0.361680 | + | 0.932302i | \(0.617797\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 599.257i | − 0.0334255i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3053.50 | −0.169576 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2363.81 | 0.130702 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26803.4i | 1.47561i | 0.675012 | + | 0.737807i | \(0.264139\pi\) | ||||
−0.675012 | + | 0.737807i | \(0.735861\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3706.72i | 0.203184i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1233.48 | 0.0673219 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20690.2 | 1.12439 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 15370.7i | − 0.831719i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 15482.4i | − 0.834185i | −0.908864 | − | 0.417093i | \(-0.863049\pi\) | ||||
0.908864 | − | 0.417093i | \(-0.136951\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 296.535 | 0.0159090 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1622.85 | −0.0866953 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10544.0i | 0.560888i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21219.1i | 1.12398i | 0.827144 | + | 0.561989i | \(0.189964\pi\) | ||||
−0.827144 | + | 0.561989i | \(0.810036\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11724.3 | 0.618419 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −14296.4 | −0.750916 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 851.410i | − 0.0445328i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 10706.6i | − 0.557666i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −298.549 | −0.0154854 | −0.00774270 | − | 0.999970i | \(-0.502465\pi\) | ||||
−0.00774270 | + | 0.999970i | \(0.502465\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7707.46 | −0.398115 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 3169.65i | − 0.163043i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 4028.42i | − 0.206361i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1760.30 | 0.0898021 | 0.0449010 | − | 0.998991i | \(-0.485703\pi\) | ||||
0.0449010 | + | 0.998991i | \(0.485703\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10183.1i | 0.515231i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 13537.8i | − 0.682170i | −0.940032 | − | 0.341085i | \(-0.889206\pi\) | ||||
0.940032 | − | 0.341085i | \(-0.110794\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −188.379 | −0.00945368 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −19299.5 | −0.964594 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32498.8i | 1.61771i | 0.588008 | + | 0.808855i | \(0.299912\pi\) | ||||
−0.588008 | + | 0.808855i | \(0.700088\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 1744.70i | − 0.0864957i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18031.9 | −0.890344 | −0.445172 | − | 0.895445i | \(-0.646858\pi\) | ||||
−0.445172 | + | 0.895445i | \(0.646858\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1879.51 | −0.0924293 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3545.38i | 0.173653i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5865.55i | 0.286145i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4040.23 | −0.196312 | −0.0981559 | − | 0.995171i | \(-0.531294\pi\) | ||||
−0.0981559 | + | 0.995171i | \(0.531294\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12012.2 | 0.581342 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4464.36i | 0.215198i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13359.2i | 0.641413i | 0.947179 | + | 0.320706i | \(0.103920\pi\) | ||||
−0.947179 | + | 0.320706i | \(0.896080\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 23190.5 | 1.10904 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12534.3 | 0.597066 | 0.298533 | − | 0.954399i | \(-0.403503\pi\) | ||||
0.298533 | + | 0.954399i | \(0.403503\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8948.49i | 0.424583i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1201.63i | 0.0567909i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 845.028 | 0.0397812 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6633.90 | 0.311085 | 0.155543 | − | 0.987829i | \(-0.450287\pi\) | ||||
0.155543 | + | 0.987829i | \(0.450287\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 7495.46i | − 0.350120i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 26826.6i | − 1.24824i | −0.781330 | − | 0.624118i | \(-0.785458\pi\) | ||||
0.781330 | − | 0.624118i | \(-0.214542\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13423.1 | 0.622158 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −120.912 | −0.00558262 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 10227.7i | − 0.470403i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8745.55i | 0.400692i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −881.722 | −0.0402429 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3443.97 | 0.156586 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 17011.8i | − 0.770527i | −0.922807 | − | 0.385264i | \(-0.874111\pi\) | ||||
0.922807 | − | 0.385264i | \(-0.125889\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 155.996i | 0.00703878i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10661.5 | 0.479240 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5050.03 | −0.226144 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 804.773i | 0.0359023i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 32459.1i | 1.44261i | 0.692617 | + | 0.721306i | \(0.256458\pi\) | ||||
−0.692617 | + | 0.721306i | \(0.743542\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −43980.2 | −1.94732 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4326.23 | 0.190836 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 2112.80i | − 0.0928505i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1178.56i | 0.0516010i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −299.664 | −0.0130715 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −26684.3 | −1.15966 | −0.579832 | − | 0.814736i | \(-0.696882\pi\) | ||||
−0.579832 | + | 0.814736i | \(0.696882\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 6621.72i | − 0.286708i | −0.989672 | − | 0.143354i | \(-0.954211\pi\) | ||||
0.989672 | − | 0.143354i | \(-0.0457887\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 22961.2i | − 0.990509i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3130.63 | 0.134554 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5033.73 | 0.215554 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 711.403i | 0.0303522i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 3728.98i | − 0.158517i | −0.996854 | − | 0.0792583i | \(-0.974745\pi\) | ||||
0.996854 | − | 0.0792583i | \(-0.0252552\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4227.28 | 0.179045 | 0.0895224 | − | 0.995985i | \(-0.471466\pi\) | ||||
0.0895224 | + | 0.995985i | \(0.471466\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −21773.9 | −0.918874 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13173.2i | 0.553903i | 0.960884 | + | 0.276951i | \(0.0893241\pi\) | ||||
−0.960884 | + | 0.276951i | \(0.910676\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 30108.2i | − 1.26140i | −0.776026 | − | 0.630701i | \(-0.782767\pi\) | ||||
0.776026 | − | 0.630701i | \(-0.217233\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10121.4 | −0.422513 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5105.17 | −0.212345 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 2142.26i | − 0.0887855i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 2937.99i | − 0.121328i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19630.4 | 0.807769 | 0.403885 | − | 0.914810i | \(-0.367660\pi\) | ||||
0.403885 | + | 0.914810i | \(0.367660\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23322.6 | 0.956274 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 14307.2i | − 0.584537i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2652.02i | 0.107967i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14915.4 | 0.605075 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −12946.7 | −0.523356 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 756.467i | 0.0304716i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5126.66i | 0.205784i | 0.994693 | + | 0.102892i | \(0.0328096\pi\) | ||||
−0.994693 | + | 0.102892i | \(0.967190\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 593.994 | 0.0237593 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9742.87 | −0.388343 | −0.194172 | − | 0.980968i | \(-0.562202\pi\) | ||||
−0.194172 | + | 0.980968i | \(0.562202\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4584.46i | 0.182095i | 0.995847 | + | 0.0910475i | \(0.0290215\pi\) | ||||
−0.995847 | + | 0.0910475i | \(0.970978\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4170.33i | 0.165069i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −47428.1 | −1.87076 | −0.935382 | − | 0.353638i | \(-0.884944\pi\) | ||||
−0.935382 | + | 0.353638i | \(0.884944\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3319.76 | 0.130492 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 17825.8i | 0.698266i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 76646.7i | − 2.99202i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3704.01 | −0.144094 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11503.1 | 0.445957 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 2227.87i | − 0.0860752i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32425.1i | 1.24848i | 0.781232 | + | 0.624241i | \(0.214592\pi\) | ||||
−0.781232 | + | 0.624241i | \(0.785408\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 18553.3 | 0.711932 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13989.5 | −0.534982 | −0.267491 | − | 0.963560i | \(-0.586195\pi\) | ||||
−0.267491 | + | 0.963560i | \(0.586195\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 44760.1i | − 1.70589i | −0.522003 | − | 0.852944i | \(-0.674815\pi\) | ||||
0.522003 | − | 0.852944i | \(-0.325185\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 287.695i | 0.0109274i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8460.71 | 0.320274 | 0.160137 | − | 0.987095i | \(-0.448806\pi\) | ||||
0.160137 | + | 0.987095i | \(0.448806\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3160.84 | −0.119248 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4765.78i | 0.179192i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 21740.5i | 0.814689i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2433.21 | 0.0908751 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4450.78 | 0.165671 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 3553.49i | − 0.131830i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21809.8i | 0.806425i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2052.50 | −0.0756401 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5137.58 | −0.188706 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 19962.9i | − 0.730825i | −0.930846 | − | 0.365412i | \(-0.880928\pi\) | ||||
0.930846 | − | 0.365412i | \(-0.119072\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 13556.6i | 0.494656i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −33633.5 | −1.22319 | −0.611596 | − | 0.791170i | \(-0.709472\pi\) | ||||
−0.611596 | + | 0.791170i | \(0.709472\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 23177.6 | 0.840162 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 1719.31i | − 0.0621188i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 6626.76i | − 0.238642i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36166.7 | 1.29818 | 0.649092 | − | 0.760710i | \(-0.275149\pi\) | ||||
0.649092 | + | 0.760710i | \(0.275149\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2991.72 | −0.107036 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1678.47i | 0.0598564i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 710.260i | − 0.0252467i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9909.59 | −0.351104 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −24869.0 | −0.878282 | −0.439141 | − | 0.898418i | \(-0.644717\pi\) | ||||
−0.439141 | + | 0.898418i | \(0.644717\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2523.61i | 0.0888376i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 5937.45i | − 0.208342i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7855.56 | 0.274764 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 13606.6 | 0.474396 | 0.237198 | − | 0.971461i | \(-0.423771\pi\) | ||||
0.237198 | + | 0.971461i | \(0.423771\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 11459.9i | − 0.398274i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24937.2i | 0.863899i | 0.901898 | + | 0.431949i | \(0.142174\pi\) | ||||
−0.901898 | + | 0.431949i | \(0.857826\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 26091.0 | 0.900997 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −242.201 | −0.00833736 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 21167.6i | 0.726351i | 0.931721 | + | 0.363176i | \(0.118308\pi\) | ||||
−0.931721 | + | 0.363176i | \(0.881692\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 405.493i | − 0.0138702i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16409.4 | 0.559528 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 16473.2 | 0.559937 | 0.279968 | − | 0.960009i | \(-0.409676\pi\) | ||||
0.279968 | + | 0.960009i | \(0.409676\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5386.84i | 0.182528i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5764.19i | 0.194702i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3273.38 | 0.110222 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17950.4 | −0.602545 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7541.42i | 0.252356i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 4051.68i | − 0.135159i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14680.9 | 0.488219 | 0.244109 | − | 0.969748i | \(-0.421504\pi\) | ||||
0.244109 | + | 0.969748i | \(0.421504\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 16097.6 | 0.533672 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 49712.5i | 1.64300i | 0.570211 | + | 0.821498i | \(0.306862\pi\) | ||||
−0.570211 | + | 0.821498i | \(0.693138\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6737.79i | 0.221998i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4178.91 | −0.137264 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15124.5 | 0.495266 | 0.247633 | − | 0.968854i | \(-0.420347\pi\) | ||||
0.247633 | + | 0.968854i | \(0.420347\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 28282.4i | − 0.923300i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11505.2i | 0.374447i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −43510.2 | −1.41176 | −0.705881 | − | 0.708331i | \(-0.749448\pi\) | ||||
−0.705881 | + | 0.708331i | \(0.749448\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −29.3136 | −0.000948234 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 8864.68i | − 0.285882i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12841.1i | 0.412866i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −50363.6 | −1.61438 | −0.807191 | − | 0.590291i | \(-0.799013\pi\) | ||||
−0.807191 | + | 0.590291i | \(0.799013\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4353.62 | 0.139132 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6333.30i | 0.201788i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 39782.3i | − 1.26371i | −0.775087 | − | 0.631855i | \(-0.782294\pi\) | ||||
0.775087 | − | 0.631855i | \(-0.217706\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −155.458 | −0.00492341 |
(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.c.e.673.10 | yes | 12 | |
4.3 | odd | 2 | 1344.4.c.h.673.4 | yes | 12 | ||
8.3 | odd | 2 | 1344.4.c.h.673.9 | yes | 12 | ||
8.5 | even | 2 | inner | 1344.4.c.e.673.3 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1344.4.c.e.673.3 | ✓ | 12 | 8.5 | even | 2 | inner | |
1344.4.c.e.673.10 | yes | 12 | 1.1 | even | 1 | trivial | |
1344.4.c.h.673.4 | yes | 12 | 4.3 | odd | 2 | ||
1344.4.c.h.673.9 | yes | 12 | 8.3 | odd | 2 |