Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1296,4,Mod(1,1296)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1296, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1296.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1296 = 2^{4} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1296.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(76.4664753674\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{3}, \sqrt{7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 5x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 324) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.456850\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1296.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −21.0707 | −1.88462 | −0.942309 | − | 0.334746i | \(-0.891350\pi\) | ||||
−0.942309 | + | 0.334746i | \(0.891350\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 31.4955 | 1.70059 | 0.850297 | − | 0.526303i | \(-0.176422\pi\) | ||||
0.850297 | + | 0.526303i | \(0.176422\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 36.6591 | 1.00483 | 0.502415 | − | 0.864626i | \(-0.332445\pi\) | ||||
0.502415 | + | 0.864626i | \(0.332445\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 56.4955 | 1.20531 | 0.602655 | − | 0.798002i | \(-0.294110\pi\) | ||||
0.602655 | + | 0.798002i | \(0.294110\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 35.8010 | 0.510765 | 0.255383 | − | 0.966840i | \(-0.417799\pi\) | ||||
0.255383 | + | 0.966840i | \(0.417799\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −83.4955 | −1.00817 | −0.504083 | − | 0.863655i | \(-0.668170\pi\) | ||||
−0.504083 | + | 0.863655i | \(0.668170\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −69.5523 | −0.630551 | −0.315275 | − | 0.949000i | \(-0.602097\pi\) | ||||
−0.315275 | + | 0.949000i | \(0.602097\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 318.973 | 2.55178 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −81.7082 | −0.523201 | −0.261601 | − | 0.965176i | \(-0.584250\pi\) | ||||
−0.261601 | + | 0.965176i | \(0.584250\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 72.9727 | 0.422783 | 0.211392 | − | 0.977401i | \(-0.432200\pi\) | ||||
0.211392 | + | 0.977401i | \(0.432200\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −663.630 | −3.20497 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −25.4682 | −0.113161 | −0.0565803 | − | 0.998398i | \(-0.518020\pi\) | ||||
−0.0565803 | + | 0.998398i | \(0.518020\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −399.484 | −1.52168 | −0.760841 | − | 0.648938i | \(-0.775213\pi\) | ||||
−0.760841 | + | 0.648938i | \(0.775213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 83.4591 | 0.295986 | 0.147993 | − | 0.988988i | \(-0.452719\pi\) | ||||
0.147993 | + | 0.988988i | \(0.452719\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 311.769 | 0.967579 | 0.483789 | − | 0.875184i | \(-0.339260\pi\) | ||||
0.483789 | + | 0.875184i | \(0.339260\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 648.964 | 1.89202 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.09919 | 0.0106239 | 0.00531196 | − | 0.999986i | \(-0.498309\pi\) | ||||
0.00531196 | + | 0.999986i | \(0.498309\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −772.432 | −1.89372 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 352.194 | 0.777149 | 0.388574 | − | 0.921417i | \(-0.372968\pi\) | ||||
0.388574 | + | 0.921417i | \(0.372968\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.54091 | 0.00743225 | 0.00371613 | − | 0.999993i | \(-0.498817\pi\) | ||||
0.00371613 | + | 0.999993i | \(0.498817\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1190.40 | −2.27155 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −492.432 | −0.897912 | −0.448956 | − | 0.893554i | \(-0.648204\pi\) | ||||
−0.448956 | + | 0.893554i | \(0.648204\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −154.502 | −0.258253 | −0.129126 | − | 0.991628i | \(-0.541217\pi\) | ||||
−0.129126 | + | 0.991628i | \(0.541217\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 305.000 | 0.489008 | 0.244504 | − | 0.969648i | \(-0.421375\pi\) | ||||
0.244504 | + | 0.969648i | \(0.421375\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1154.60 | 1.70881 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −671.386 | −0.956163 | −0.478081 | − | 0.878316i | \(-0.658668\pi\) | ||||
−0.478081 | + | 0.878316i | \(0.658668\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1293.70 | −1.71087 | −0.855434 | − | 0.517912i | \(-0.826710\pi\) | ||||
−0.855434 | + | 0.517912i | \(0.826710\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −754.350 | −0.962597 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1183.91 | 1.41005 | 0.705026 | − | 0.709181i | \(-0.250935\pi\) | ||||
0.705026 | + | 0.709181i | \(0.250935\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1779.35 | 2.04974 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1759.30 | 1.90001 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 615.982 | 0.644778 | 0.322389 | − | 0.946607i | \(-0.395514\pi\) | ||||
0.322389 | + | 0.946607i | \(0.395514\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1187.49 | 1.16990 | 0.584948 | − | 0.811071i | \(-0.301115\pi\) | ||||
0.584948 | + | 0.811071i | \(0.301115\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1386.92 | 1.32677 | 0.663384 | − | 0.748279i | \(-0.269120\pi\) | ||||
0.663384 | + | 0.748279i | \(0.269120\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 678.360 | 0.612893 | 0.306447 | − | 0.951888i | \(-0.400860\pi\) | ||||
0.306447 | + | 0.951888i | \(0.400860\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 945.432 | 0.830788 | 0.415394 | − | 0.909641i | \(-0.363644\pi\) | ||||
0.415394 | + | 0.909641i | \(0.363644\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1986.60 | 1.65384 | 0.826918 | − | 0.562322i | \(-0.190092\pi\) | ||||
0.826918 | + | 0.562322i | \(0.190092\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1465.51 | 1.18835 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1127.57 | 0.868605 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.8909 | 0.00968512 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4087.13 | −2.92451 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1496.54 | 1.04564 | 0.522821 | − | 0.852442i | \(-0.324880\pi\) | ||||
0.522821 | + | 0.852442i | \(0.324880\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 85.2825 | 0.0568791 | 0.0284396 | − | 0.999596i | \(-0.490946\pi\) | ||||
0.0284396 | + | 0.999596i | \(0.490946\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2629.73 | −1.71448 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 899.506 | 0.560949 | 0.280475 | − | 0.959861i | \(-0.409508\pi\) | ||||
0.280475 | + | 0.959861i | \(0.409508\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2000.61 | −1.22079 | −0.610394 | − | 0.792098i | \(-0.708989\pi\) | ||||
−0.610394 | + | 0.792098i | \(0.708989\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2071.07 | 1.21113 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1721.65 | 0.986034 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1474.37 | 0.810639 | 0.405320 | − | 0.914175i | \(-0.367160\pi\) | ||||
0.405320 | + | 0.914175i | \(0.367160\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1092.97 | 0.589039 | 0.294519 | − | 0.955646i | \(-0.404840\pi\) | ||||
0.294519 | + | 0.955646i | \(0.404840\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1537.58 | −0.796785 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 540.514 | 0.274762 | 0.137381 | − | 0.990518i | \(-0.456131\pi\) | ||||
0.137381 | + | 0.990518i | \(0.456131\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2190.58 | −1.07231 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3251.60 | 1.56248 | 0.781242 | − | 0.624228i | \(-0.214586\pi\) | ||||
0.781242 | + | 0.624228i | \(0.214586\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1708.58 | 0.791701 | 0.395850 | − | 0.918315i | \(-0.370450\pi\) | ||||
0.395850 | + | 0.918315i | \(0.370450\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 994.736 | 0.452770 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2629.73 | 1.15569 | 0.577847 | − | 0.816145i | \(-0.303893\pi\) | ||||
0.577847 | + | 0.816145i | \(0.303893\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10046.2 | 4.33955 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4532.77 | −1.89271 | −0.946354 | − | 0.323131i | \(-0.895265\pi\) | ||||
−0.946354 | + | 0.323131i | \(0.895265\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2327.65 | −0.955874 | −0.477937 | − | 0.878394i | \(-0.658615\pi\) | ||||
−0.477937 | + | 0.878394i | \(0.658615\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 536.631 | 0.213264 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1312.43 | 0.513233 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1231.68 | −0.466603 | −0.233302 | − | 0.972404i | \(-0.574953\pi\) | ||||
−0.233302 | + | 0.972404i | \(0.574953\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2143.97 | 0.799619 | 0.399810 | − | 0.916598i | \(-0.369076\pi\) | ||||
0.399810 | + | 0.916598i | \(0.369076\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1984.55 | −0.717733 | −0.358866 | − | 0.933389i | \(-0.616837\pi\) | ||||
−0.358866 | + | 0.933389i | \(0.616837\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 224.400 | 0.0799362 | 0.0399681 | − | 0.999201i | \(-0.487274\pi\) | ||||
0.0399681 | + | 0.999201i | \(0.487274\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2573.44 | −0.889753 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8417.40 | 2.86779 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3060.87 | −1.01304 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3785.22 | −1.23500 | −0.617501 | − | 0.786570i | \(-0.711855\pi\) | ||||
−0.617501 | + | 0.786570i | \(0.711855\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1758.54 | −0.557820 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2298.31 | 0.718983 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2022.59 | 0.615630 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5408.32 | 1.62407 | 0.812036 | − | 0.583607i | \(-0.198359\pi\) | ||||
0.812036 | + | 0.583607i | \(0.198359\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4489.91 | −1.31280 | −0.656400 | − | 0.754413i | \(-0.727922\pi\) | ||||
−0.656400 | + | 0.754413i | \(0.727922\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3117.00 | 0.899462 | 0.449731 | − | 0.893164i | \(-0.351520\pi\) | ||||
0.449731 | + | 0.893164i | \(0.351520\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1675.60 | −0.471124 | −0.235562 | − | 0.971859i | \(-0.575693\pi\) | ||||
−0.235562 | + | 0.971859i | \(0.575693\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6569.18 | −1.82352 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5751.72 | 1.55668 | 0.778342 | − | 0.627840i | \(-0.216061\pi\) | ||||
0.778342 | + | 0.627840i | \(0.216061\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1805.41 | −0.482559 | −0.241279 | − | 0.970456i | \(-0.577567\pi\) | ||||
−0.241279 | + | 0.970456i | \(0.577567\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −13674.1 | −3.56574 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4717.11 | −1.21515 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 32.6596 | 0.00821297 | 0.00410649 | − | 0.999992i | \(-0.498693\pi\) | ||||
0.00410649 | + | 0.999992i | \(0.498693\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2549.73 | −0.633597 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1148.26 | 0.278701 | 0.139351 | − | 0.990243i | \(-0.455499\pi\) | ||||
0.139351 | + | 0.990243i | \(0.455499\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −802.132 | −0.192440 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4634.01 | 1.08648 | 0.543242 | − | 0.839576i | \(-0.317196\pi\) | ||||
0.543242 | + | 0.839576i | \(0.317196\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −86.3727 | −0.0200220 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8134.42 | 1.84373 | 0.921866 | − | 0.387508i | \(-0.126664\pi\) | ||||
0.921866 | + | 0.387508i | \(0.126664\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6891.35 | −1.54472 | −0.772361 | − | 0.635184i | \(-0.780924\pi\) | ||||
−0.772361 | + | 0.635184i | \(0.780924\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11693.3 | 2.56411 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1821.78 | −0.395163 | −0.197582 | − | 0.980286i | \(-0.563309\pi\) | ||||
−0.197582 | + | 0.980286i | \(0.563309\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4541.21 | 0.964077 | 0.482039 | − | 0.876150i | \(-0.339897\pi\) | ||||
0.482039 | + | 0.876150i | \(0.339897\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2757.95 | 0.579303 | 0.289652 | − | 0.957132i | \(-0.406461\pi\) | ||||
0.289652 | + | 0.957132i | \(0.406461\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12581.9 | −2.58777 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3631.29 | −0.739119 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1669.06 | −0.332791 | −0.166396 | − | 0.986059i | \(-0.553213\pi\) | ||||
−0.166396 | + | 0.986059i | \(0.553213\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7420.96 | −1.46463 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3929.39 | −0.760008 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2628.58 | 0.503352 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −74.6094 | −0.0140069 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7500.21 | 1.39433 | 0.697165 | − | 0.716910i | \(-0.254444\pi\) | ||||
0.697165 | + | 0.716910i | \(0.254444\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8486.52 | −1.54735 | −0.773676 | − | 0.633582i | \(-0.781584\pi\) | ||||
−0.773676 | + | 0.633582i | \(0.781584\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9365.66 | 1.69131 | 0.845653 | − | 0.533734i | \(-0.179211\pi\) | ||||
0.845653 | + | 0.533734i | \(0.179211\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 505.887 | 0.0896324 | 0.0448162 | − | 0.998995i | \(-0.485730\pi\) | ||||
0.0448162 | + | 0.998995i | \(0.485730\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2995.35 | −0.525729 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2989.22 | −0.514937 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 18020.5 | 3.07569 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9819.31 | 1.64546 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6598.51 | −1.09573 | −0.547866 | − | 0.836566i | \(-0.684560\pi\) | ||||
−0.547866 | + | 0.836566i | \(0.684560\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10375.9 | 1.69222 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3612.42 | −0.583920 | −0.291960 | − | 0.956431i | \(-0.594307\pi\) | ||||
−0.291960 | + | 0.956431i | \(0.594307\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2675.12 | 0.424826 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9636.46 | 1.51697 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2609.56 | 0.403714 | 0.201857 | − | 0.979415i | \(-0.435302\pi\) | ||||
0.201857 | + | 0.979415i | \(0.435302\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 677.527 | 0.103917 | 0.0519587 | − | 0.998649i | \(-0.483454\pi\) | ||||
0.0519587 | + | 0.998649i | \(0.483454\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1549.88 | −0.233688 | −0.116844 | − | 0.993150i | \(-0.537278\pi\) | ||||
−0.116844 | + | 0.993150i | \(0.537278\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3255.45 | 0.486708 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8381.31 | 1.23217 | 0.616084 | − | 0.787680i | \(-0.288718\pi\) | ||||
0.616084 | + | 0.787680i | \(0.288718\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 112.491 | 0.0164005 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6426.55 | −0.921592 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4205.83 | 0.598208 | 0.299104 | − | 0.954220i | \(-0.403312\pi\) | ||||
0.299104 | + | 0.954220i | \(0.403312\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 129.106 | 0.0180670 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8012.84 | 1.11230 | 0.556151 | − | 0.831081i | \(-0.312277\pi\) | ||||
0.556151 | + | 0.831081i | \(0.312277\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4616.14 | −0.630619 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8049.26 | −1.09093 | −0.545466 | − | 0.838133i | \(-0.683647\pi\) | ||||
−0.545466 | + | 0.838133i | \(0.683647\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3227.47 | −0.430590 | −0.215295 | − | 0.976549i | \(-0.569071\pi\) | ||||
−0.215295 | + | 0.976549i | \(0.569071\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −24328.1 | −3.22045 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8911.93 | 1.16158 | 0.580788 | − | 0.814055i | \(-0.302745\pi\) | ||||
0.580788 | + | 0.814055i | \(0.302745\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2490.04 | −0.322063 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 14146.6 | 1.80200 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2972.50 | 0.375783 | 0.187891 | − | 0.982190i | \(-0.439835\pi\) | ||||
0.187891 | + | 0.982190i | \(0.439835\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12273.2 | −1.52841 | −0.764206 | − | 0.644972i | \(-0.776869\pi\) | ||||
−0.764206 | + | 0.644972i | \(0.776869\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4122.63 | 0.509585 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −933.641 | −0.113707 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2249.30 | −0.271933 | −0.135967 | − | 0.990713i | \(-0.543414\pi\) | ||||
−0.135967 | + | 0.990713i | \(0.543414\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11092.5 | 1.32161 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 27259.1 | 3.22433 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9460.92 | 1.10309 | 0.551547 | − | 0.834144i | \(-0.314038\pi\) | ||||
0.551547 | + | 0.834144i | \(0.314038\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1534.91 | 0.177689 | 0.0888446 | − | 0.996046i | \(-0.471683\pi\) | ||||
0.0888446 | + | 0.996046i | \(0.471683\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 11419.5 | 1.30336 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 111.523 | 0.0126392 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3991.88 | 0.446130 | 0.223065 | − | 0.974804i | \(-0.428394\pi\) | ||||
0.223065 | + | 0.974804i | \(0.428394\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3058.08 | −0.339404 | −0.169702 | − | 0.985495i | \(-0.554281\pi\) | ||||
−0.169702 | + | 0.985495i | \(0.554281\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5807.30 | 0.635700 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14763.8 | 1.60510 | 0.802548 | − | 0.596588i | \(-0.203477\pi\) | ||||
0.802548 | + | 0.596588i | \(0.203477\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11564.7 | 1.24030 | 0.620150 | − | 0.784483i | \(-0.287072\pi\) | ||||
0.620150 | + | 0.784483i | \(0.287072\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −24945.9 | −2.65741 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17266.9 | −1.81486 | −0.907432 | − | 0.420198i | \(-0.861961\pi\) | ||||
−0.907432 | + | 0.420198i | \(0.861961\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14644.7 | −1.52903 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −37492.1 | −3.86298 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12701.5 | 1.30011 | 0.650057 | − | 0.759886i | \(-0.274745\pi\) | ||||
0.650057 | + | 0.759886i | \(0.274745\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16499.8 | 1.66697 | 0.833486 | − | 0.552541i | \(-0.186342\pi\) | ||||
0.833486 | + | 0.552541i | \(0.186342\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1364.84 | 0.136996 | 0.0684982 | − | 0.997651i | \(-0.478179\pi\) | ||||
0.0684982 | + | 0.997651i | \(0.478179\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10333.5 | 1.02393 | 0.511966 | − | 0.859006i | \(-0.328917\pi\) | ||||
0.511966 | + | 0.859006i | \(0.328917\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15509.4 | −1.52698 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3059.54 | 0.297416 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −26632.8 | −2.57262 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12188.6 | −1.16266 | −0.581328 | − | 0.813669i | \(-0.697467\pi\) | ||||
−0.581328 | + | 0.813669i | \(0.697467\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1438.84 | −0.136394 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12979.1 | −1.21516 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9816.46 | −0.913401 | −0.456701 | − | 0.889620i | \(-0.650969\pi\) | ||||
−0.456701 | + | 0.889620i | \(0.650969\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3464.02 | 0.318389 | 0.159195 | − | 0.987247i | \(-0.449110\pi\) | ||||
0.159195 | + | 0.987247i | \(0.449110\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2925.23 | −0.267233 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4866.10 | −0.439184 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12366.9 | 1.10946 | 0.554728 | − | 0.832032i | \(-0.312822\pi\) | ||||
0.554728 | + | 0.832032i | \(0.312822\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6249.98 | −0.554021 | −0.277011 | − | 0.960867i | \(-0.589344\pi\) | ||||
−0.277011 | + | 0.960867i | \(0.589344\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −25021.2 | −2.20481 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7481.43 | 0.651490 | 0.325745 | − | 0.945458i | \(-0.394385\pi\) | ||||
0.325745 | + | 0.945458i | \(0.394385\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9606.11 | 0.831604 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −29223.3 | −2.50045 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11429.2 | 0.972253 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17700.1 | 1.48840 | 0.744200 | − | 0.667957i | \(-0.232831\pi\) | ||||
0.744200 | + | 0.667957i | \(0.232831\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21707.9 | −1.81495 | −0.907475 | − | 0.420107i | \(-0.861993\pi\) | ||||
−0.907475 | + | 0.420107i | \(0.861993\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2612.49 | 0.215943 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7329.47 | −0.602406 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −22569.1 | −1.83410 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14293.5 | −1.15507 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 23790.4 | 1.90116 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19282.0 | −1.53235 | −0.766173 | − | 0.642634i | \(-0.777841\pi\) | ||||
−0.766173 | + | 0.642634i | \(0.777841\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −19920.9 | −1.56572 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7784.53 | 0.608487 | 0.304243 | − | 0.952594i | \(-0.401596\pi\) | ||||
0.304243 | + | 0.952594i | \(0.401596\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6822.26 | 0.527474 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −21145.6 | −1.62605 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8556.03 | −0.650863 | −0.325431 | − | 0.945566i | \(-0.605510\pi\) | ||||
−0.325431 | + | 0.945566i | \(0.605510\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4715.06 | 0.356754 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2963.22 | −0.221821 | −0.110910 | − | 0.993830i | \(-0.535377\pi\) | ||||
−0.110910 | + | 0.993830i | \(0.535377\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −41859.0 | −3.11685 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14484.1 | −1.06714 | −0.533571 | − | 0.845755i | \(-0.679150\pi\) | ||||
−0.533571 | + | 0.845755i | \(0.679150\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16649.8 | −1.22027 | −0.610133 | − | 0.792299i | \(-0.708884\pi\) | ||||
−0.610133 | + | 0.792299i | \(0.708884\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −22185.3 | −1.60903 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14355.4 | 1.03574 | 0.517872 | − | 0.855458i | \(-0.326724\pi\) | ||||
0.517872 | + | 0.855458i | \(0.326724\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −40745.7 | −2.90949 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 150.273 | 0.0106752 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8006.22 | −0.562951 | −0.281475 | − | 0.959568i | \(-0.590824\pi\) | ||||
−0.281475 | + | 0.959568i | \(0.590824\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6092.89 | −0.426236 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17866.7 | 1.23726 | 0.618632 | − | 0.785681i | \(-0.287687\pi\) | ||||
0.618632 | + | 0.785681i | \(0.287687\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −23758.6 | −1.63699 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15812.0 | −1.07857 | −0.539284 | − | 0.842124i | \(-0.681305\pi\) | ||||
−0.539284 | + | 0.842124i | \(0.681305\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22910.3 | 1.55496 | 0.777481 | − | 0.628907i | \(-0.216497\pi\) | ||||
0.777481 | + | 0.628907i | \(0.216497\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −271.620 | −0.0182528 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.7227 | −0.00111821 | −0.000559107 | − | 1.00000i | \(-0.500178\pi\) | ||||
−0.000559107 | 1.00000i | \(0.500178\pi\) | ||||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17613.5 | 1.16623 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 162.745 | 0.0107230 | 0.00536152 | − | 0.999986i | \(-0.498293\pi\) | ||||
0.00536152 | + | 0.999986i | \(0.498293\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8893.18 | −0.580269 | −0.290134 | − | 0.956986i | \(-0.593700\pi\) | ||||
−0.290134 | + | 0.956986i | \(0.593700\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21557.6 | −1.39980 | −0.699898 | − | 0.714242i | \(-0.746771\pi\) | ||||
−0.699898 | + | 0.714242i | \(0.746771\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 37287.9 | 2.39793 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 46247.0 | 2.95981 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −911.785 | −0.0577985 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3085.90 | −0.194687 | −0.0973437 | − | 0.995251i | \(-0.531035\pi\) | ||||
−0.0973437 | + | 0.995251i | \(0.531035\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −31533.1 | −1.97063 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 36663.5 | 2.28047 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12566.5 | 0.774334 | 0.387167 | − | 0.922010i | \(-0.373454\pi\) | ||||
0.387167 | + | 0.922010i | \(0.373454\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −876.227 | −0.0537403 | −0.0268702 | − | 0.999639i | \(-0.508554\pi\) | ||||
−0.0268702 | + | 0.999639i | \(0.508554\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11125.4 | −0.676022 | −0.338011 | − | 0.941142i | \(-0.609754\pi\) | ||||
−0.338011 | + | 0.941142i | \(0.609754\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12911.1 | 0.780903 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 20660.8 | 1.23816 | 0.619080 | − | 0.785328i | \(-0.287506\pi\) | ||||
0.619080 | + | 0.785328i | \(0.287506\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1796.96 | −0.107195 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3653.75 | −0.215978 | −0.107989 | − | 0.994152i | \(-0.534441\pi\) | ||||
−0.107989 | + | 0.994152i | \(0.534441\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13340.8 | −0.785016 | −0.392508 | − | 0.919749i | \(-0.628392\pi\) | ||||
−0.392508 | + | 0.919749i | \(0.628392\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 55410.1 | 3.23114 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5683.00 | 0.329905 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 129.807 | 0.00746816 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4221.95 | −0.241819 | −0.120910 | − | 0.992664i | \(-0.538581\pi\) | ||||
−0.120910 | + | 0.992664i | \(0.538581\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18682.1 | 1.06058 | 0.530288 | − | 0.847818i | \(-0.322084\pi\) | ||||
0.530288 | + | 0.847818i | \(0.322084\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 19400.6 | 1.09651 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −18674.1 | −1.04619 | −0.523093 | − | 0.852275i | \(-0.675222\pi\) | ||||
−0.523093 | + | 0.852275i | \(0.675222\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18953.2 | −1.05717 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 231.586 | 0.0128051 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −35528.3 | −1.95595 | −0.977974 | − | 0.208724i | \(-0.933069\pi\) | ||||
−0.977974 | + | 0.208724i | \(0.933069\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 42154.2 | 2.30072 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14301.9 | −0.777223 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13722.2 | 0.739346 | 0.369673 | − | 0.929162i | \(-0.379470\pi\) | ||||
0.369673 | + | 0.929162i | \(0.379470\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2126.48 | 0.114085 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 37400.5 | 1.98952 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2952.83 | 0.156412 | 0.0782059 | − | 0.996937i | \(-0.475081\pi\) | ||||
0.0782059 | + | 0.996937i | \(0.475081\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5075.42 | −0.266586 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −43638.9 | −2.28252 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8101.57 | −0.420219 | −0.210109 | − | 0.977678i | \(-0.567382\pi\) | ||||
−0.210109 | + | 0.977678i | \(0.567382\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 43681.6 | 2.25629 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −26062.7 | −1.33509 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3400.44 | −0.173474 | −0.0867368 | − | 0.996231i | \(-0.527644\pi\) | ||||
−0.0867368 | + | 0.996231i | \(0.527644\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2987.92 | 0.151179 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20414.0 | −1.02866 | −0.514330 | − | 0.857592i | \(-0.671959\pi\) | ||||
−0.514330 | + | 0.857592i | \(0.671959\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18052.1 | −0.902250 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9505.82 | 0.473176 | 0.236588 | − | 0.971610i | \(-0.423971\pi\) | ||||
0.236588 | + | 0.971610i | \(0.423971\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −37.1606 | −0.00183484 | −0.000917422 | − | 1.00000i | \(-0.500292\pi\) | ||||
−0.000917422 | 1.00000i | \(0.500292\pi\) | ||||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −31066.0 | −1.52774 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 21365.3 | 1.04228 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10177.8 | −0.494532 | −0.247266 | − | 0.968948i | \(-0.579532\pi\) | ||||
−0.247266 | + | 0.968948i | \(0.579532\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −23029.7 | −1.11011 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17129.3 | 0.822425 | 0.411213 | − | 0.911539i | \(-0.365105\pi\) | ||||
0.411213 | + | 0.911539i | \(0.365105\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −22937.8 | −1.09263 | −0.546317 | − | 0.837579i | \(-0.683970\pi\) | ||||
−0.546317 | + | 0.837579i | \(0.683970\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 29776.8 | 1.41283 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 19897.4 | 0.936705 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5270.15 | 0.247135 | 0.123567 | − | 0.992336i | \(-0.460566\pi\) | ||||
0.123567 | + | 0.992336i | \(0.460566\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −31.1847 | −0.00145102 | −0.000725509 | − | 1.00000i | \(-0.500231\pi\) | ||||
−0.000725509 | 1.00000i | \(0.500231\pi\) | ||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 23276.3 | 1.07885 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 33355.1 | 1.53411 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5663.89 | −0.259501 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11389.0 | −0.517822 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23063.1 | −1.04461 | −0.522307 | − | 0.852757i | \(-0.674929\pi\) | ||||
−0.522307 | + | 0.852757i | \(0.674929\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 62568.8 | 2.81251 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 200.045 | 0.00895816 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 34044.1 | 1.51305 | 0.756527 | − | 0.653963i | \(-0.226895\pi\) | ||||
0.756527 | + | 0.653963i | \(0.226895\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11161.6 | 0.494206 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11181.0 | 0.491370 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 46157.0 | 2.02090 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16017.6 | 0.696103 | 0.348052 | − | 0.937475i | \(-0.386843\pi\) | ||||
0.348052 | + | 0.937475i | \(0.386843\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15085.2 | −0.653160 | −0.326580 | − | 0.945170i | \(-0.605896\pi\) | ||||
−0.326580 | + | 0.945170i | \(0.605896\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −68513.4 | −2.94468 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6968.45 | −0.298403 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10695.3 | 0.454651 | 0.227325 | − | 0.973819i | \(-0.427002\pi\) | ||||
0.227325 | + | 0.973819i | \(0.427002\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 29383.7 | 1.24454 | 0.622268 | − | 0.782804i | \(-0.286211\pi\) | ||||
0.622268 | + | 0.782804i | \(0.286211\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5402.42 | 0.227159 | 0.113580 | − | 0.993529i | \(-0.463768\pi\) | ||||
0.113580 | + | 0.993529i | \(0.463768\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25212.9 | 1.05631 | 0.528155 | − | 0.849148i | \(-0.322884\pi\) | ||||
0.528155 | + | 0.849148i | \(0.322884\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 23233.5 | 0.966379 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −36000.9 | −1.49205 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 30316.7 | 1.24750 | 0.623748 | − | 0.781625i | \(-0.285609\pi\) | ||||
0.623748 | + | 0.781625i | \(0.285609\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17712.8 | −0.726261 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −20959.8 | −0.853299 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 406.005 | 0.0164705 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1771.37 | 0.0713535 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −25328.9 | −1.01670 | −0.508350 | − | 0.861150i | \(-0.669744\pi\) | ||||
−0.508350 | + | 0.861150i | \(0.669744\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2010.93 | −0.0801540 | −0.0400770 | − | 0.999197i | \(-0.512760\pi\) | ||||
−0.0400770 | + | 0.999197i | \(0.512760\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6964.49 | −0.276630 | −0.138315 | − | 0.990388i | \(-0.544169\pi\) | ||||
−0.138315 | + | 0.990388i | \(0.544169\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14772.4 | 0.582686 | 0.291343 | − | 0.956619i | \(-0.405898\pi\) | ||||
0.291343 | + | 0.956619i | \(0.405898\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −55410.2 | −2.17804 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −24612.4 | −0.960782 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −27820.2 | −1.08226 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −128726. | −4.97341 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25122.9 | −0.967322 | −0.483661 | − | 0.875255i | \(-0.660693\pi\) | ||||
−0.483661 | + | 0.875255i | \(0.660693\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20881.3 | −0.798533 | −0.399267 | − | 0.916835i | \(-0.630735\pi\) | ||||
−0.399267 | + | 0.916835i | \(0.630735\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 38366.4 | 1.46221 | 0.731106 | − | 0.682264i | \(-0.239005\pi\) | ||||
0.731106 | + | 0.682264i | \(0.239005\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 40986.6 | 1.55152 | 0.775758 | − | 0.631030i | \(-0.217368\pi\) | ||||
0.775758 | + | 0.631030i | \(0.217368\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 47134.2 | 1.77821 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −26031.3 | −0.975481 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 95508.4 | 3.56703 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5962.47 | −0.221201 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 146.755 | 0.00542632 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 49045.2 | 1.80146 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33795.7 | 1.23723 | 0.618616 | − | 0.785694i | \(-0.287694\pi\) | ||||
0.618616 | + | 0.785694i | \(0.287694\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −52137.7 | −1.89616 | −0.948078 | − | 0.318037i | \(-0.896977\pi\) | ||||
−0.948078 | + | 0.318037i | \(0.896977\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −47425.9 | −1.71913 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2686.01 | 0.0967284 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28749.5 | −1.03194 | −0.515972 | − | 0.856605i | \(-0.672569\pi\) | ||||
−0.515972 | + | 0.856605i | \(0.672569\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8728.64 | −0.311275 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8123.65 | −0.288761 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8061.26 | −0.284695 | −0.142347 | − | 0.989817i | \(-0.545465\pi\) | ||||
−0.142347 | + | 0.989817i | \(0.545465\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −54185.5 | −1.90747 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −27653.8 | −0.967247 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38362.0 | −1.33749 | −0.668746 | − | 0.743491i | \(-0.733169\pi\) | ||||
−0.668746 | + | 0.743491i | \(0.733169\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25782.6 | 0.893188 | 0.446594 | − | 0.894737i | \(-0.352637\pi\) | ||||
0.446594 | + | 0.894737i | \(0.352637\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 27785.1 | 0.959498 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −48058.9 | −1.64911 | −0.824554 | − | 0.565783i | \(-0.808574\pi\) | ||||
−0.824554 | + | 0.565783i | \(0.808574\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17231.1 | 0.589405 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −49570.9 | −1.68495 | −0.842476 | − | 0.538733i | \(-0.818903\pi\) | ||||
−0.842476 | + | 0.538733i | \(0.818903\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 25952.3 | 0.879368 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 28330.4 | 0.953947 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24466.0 | −0.821254 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −45174.9 | −1.50698 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43179.2 | 1.43594 | 0.717968 | − | 0.696076i | \(-0.245072\pi\) | ||||
0.717968 | + | 0.696076i | \(0.245072\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23494.7 | 0.776498 | 0.388249 | − | 0.921554i | \(-0.373080\pi\) | ||||
0.388249 | + | 0.921554i | \(0.373080\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −63010.1 | −2.07606 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −20192.7 | −0.661231 | −0.330616 | − | 0.943765i | \(-0.607256\pi\) | ||||
−0.330616 | + | 0.943765i | \(0.607256\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 43401.3 | 1.41686 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 49221.9 | 1.59708 | 0.798542 | − | 0.601939i | \(-0.205605\pi\) | ||||
0.798542 | + | 0.601939i | \(0.205605\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 41815.8 | 1.35265 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5804.77 | −0.186634 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −38703.5 | −1.24062 | −0.620312 | − | 0.784355i | \(-0.712994\pi\) | ||||
−0.620312 | + | 0.784355i | \(0.712994\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4728.26 | −0.150649 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8342.78 | 0.265013 | 0.132507 | − | 0.991182i | \(-0.457697\pi\) | ||||
0.132507 | + | 0.991182i | \(0.457697\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1296.4.a.z.1.1 | 4 | ||
3.2 | odd | 2 | inner | 1296.4.a.z.1.4 | 4 | ||
4.3 | odd | 2 | 324.4.a.e.1.1 | ✓ | 4 | ||
12.11 | even | 2 | 324.4.a.e.1.4 | yes | 4 | ||
36.7 | odd | 6 | 324.4.e.i.109.4 | 8 | |||
36.11 | even | 6 | 324.4.e.i.109.1 | 8 | |||
36.23 | even | 6 | 324.4.e.i.217.1 | 8 | |||
36.31 | odd | 6 | 324.4.e.i.217.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
324.4.a.e.1.1 | ✓ | 4 | 4.3 | odd | 2 | ||
324.4.a.e.1.4 | yes | 4 | 12.11 | even | 2 | ||
324.4.e.i.109.1 | 8 | 36.11 | even | 6 | |||
324.4.e.i.109.4 | 8 | 36.7 | odd | 6 | |||
324.4.e.i.217.1 | 8 | 36.23 | even | 6 | |||
324.4.e.i.217.4 | 8 | 36.31 | odd | 6 | |||
1296.4.a.z.1.1 | 4 | 1.1 | even | 1 | trivial | ||
1296.4.a.z.1.4 | 4 | 3.2 | odd | 2 | inner |