Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2160,4,Mod(1,2160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2160, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2160.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2160.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: | \(127.444125612\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{21}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 5 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2\cdot 3 \) |
Twist minimal: | no (minimal twist has level 540) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.79129\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2160.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −12.7477 | −0.688313 | −0.344156 | − | 0.938912i | \(-0.611835\pi\) | ||||
−0.344156 | + | 0.938912i | \(0.611835\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −34.7477 | −0.952439 | −0.476220 | − | 0.879326i | \(-0.657993\pi\) | ||||
−0.476220 | + | 0.879326i | \(0.657993\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −75.7386 | −1.61586 | −0.807928 | − | 0.589282i | \(-0.799411\pi\) | ||||
−0.807928 | + | 0.589282i | \(0.799411\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −84.2341 | −1.20175 | −0.600876 | − | 0.799343i | \(-0.705181\pi\) | ||||
−0.600876 | + | 0.799343i | \(0.705181\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 83.7477 | 1.01121 | 0.505606 | − | 0.862764i | \(-0.331269\pi\) | ||||
0.505606 | + | 0.862764i | \(0.331269\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −172.982 | −1.56823 | −0.784113 | − | 0.620618i | \(-0.786882\pi\) | ||||
−0.784113 | + | 0.620618i | \(0.786882\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 88.2250 | 0.564930 | 0.282465 | − | 0.959278i | \(-0.408848\pi\) | ||||
0.282465 | + | 0.959278i | \(0.408848\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −205.711 | −1.19183 | −0.595917 | − | 0.803046i | \(-0.703211\pi\) | ||||
−0.595917 | + | 0.803046i | \(0.703211\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 63.7386 | 0.307823 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −286.000 | −1.27076 | −0.635380 | − | 0.772200i | \(-0.719156\pi\) | ||||
−0.635380 | + | 0.772200i | \(0.719156\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −321.702 | −1.22540 | −0.612701 | − | 0.790315i | \(-0.709917\pi\) | ||||
−0.612701 | + | 0.790315i | \(0.709917\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 168.766 | 0.598525 | 0.299262 | − | 0.954171i | \(-0.403259\pi\) | ||||
0.299262 | + | 0.954171i | \(0.403259\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 390.468 | 1.21182 | 0.605911 | − | 0.795532i | \(-0.292809\pi\) | ||||
0.605911 | + | 0.795532i | \(0.292809\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −180.495 | −0.526226 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 91.6932 | 0.237642 | 0.118821 | − | 0.992916i | \(-0.462089\pi\) | ||||
0.118821 | + | 0.992916i | \(0.462089\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 173.739 | 0.425944 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −122.766 | −0.270894 | −0.135447 | − | 0.990785i | \(-0.543247\pi\) | ||||
−0.135447 | + | 0.990785i | \(0.543247\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −878.405 | −1.84374 | −0.921870 | − | 0.387499i | \(-0.873339\pi\) | ||||
−0.921870 | + | 0.387499i | \(0.873339\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 378.693 | 0.722632 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1037.40 | 1.89163 | 0.945814 | − | 0.324708i | \(-0.105266\pi\) | ||||
0.945814 | + | 0.324708i | \(0.105266\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −605.216 | −1.01163 | −0.505816 | − | 0.862641i | \(-0.668809\pi\) | ||||
−0.505816 | + | 0.862641i | \(0.668809\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.8114 | −0.0221438 | −0.0110719 | − | 0.999939i | \(-0.503524\pi\) | ||||
−0.0110719 | + | 0.999939i | \(0.503524\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 442.955 | 0.655576 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 573.298 | 0.816469 | 0.408234 | − | 0.912877i | \(-0.366145\pi\) | ||||
0.408234 | + | 0.912877i | \(0.366145\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 627.936 | 0.830421 | 0.415211 | − | 0.909725i | \(-0.363708\pi\) | ||||
0.415211 | + | 0.909725i | \(0.363708\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 421.170 | 0.537439 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1013.11 | −1.20662 | −0.603310 | − | 0.797507i | \(-0.706152\pi\) | ||||
−0.603310 | + | 0.797507i | \(0.706152\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 965.495 | 1.11221 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −418.739 | −0.452228 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1155.82 | 1.20985 | 0.604926 | − | 0.796282i | \(-0.293203\pi\) | ||||
0.604926 | + | 0.796282i | \(0.293203\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −853.873 | −0.841223 | −0.420611 | − | 0.907241i | \(-0.638184\pi\) | ||||
−0.420611 | + | 0.907241i | \(0.638184\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1029.95 | 0.985277 | 0.492639 | − | 0.870234i | \(-0.336032\pi\) | ||||
0.492639 | + | 0.870234i | \(0.336032\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −514.845 | −0.465159 | −0.232579 | − | 0.972577i | \(-0.574717\pi\) | ||||
−0.232579 | + | 0.972577i | \(0.574717\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −656.873 | −0.577220 | −0.288610 | − | 0.957447i | \(-0.593193\pi\) | ||||
−0.288610 | + | 0.957447i | \(0.593193\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1701.44 | 1.41644 | 0.708222 | − | 0.705990i | \(-0.249498\pi\) | ||||
0.708222 | + | 0.705990i | \(0.249498\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 864.909 | 0.701332 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1073.79 | 0.827180 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −123.595 | −0.0928591 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −345.405 | −0.241336 | −0.120668 | − | 0.992693i | \(-0.538504\pi\) | ||||
−0.120668 | + | 0.992693i | \(0.538504\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2827.87 | −1.88605 | −0.943024 | − | 0.332724i | \(-0.892032\pi\) | ||||
−0.943024 | + | 0.332724i | \(0.892032\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1067.59 | −0.696031 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1227.84 | −0.765703 | −0.382852 | − | 0.923810i | \(-0.625058\pi\) | ||||
−0.382852 | + | 0.923810i | \(0.625058\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 40.1091 | 0.0244749 | 0.0122374 | − | 0.999925i | \(-0.496105\pi\) | ||||
0.0122374 | + | 0.999925i | \(0.496105\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2631.75 | 1.53900 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −441.125 | −0.252644 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 480.730 | 0.264315 | 0.132157 | − | 0.991229i | \(-0.457810\pi\) | ||||
0.132157 | + | 0.991229i | \(0.457810\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 76.0000 | 0.0409589 | 0.0204794 | − | 0.999790i | \(-0.493481\pi\) | ||||
0.0204794 | + | 0.999790i | \(0.493481\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1028.56 | 0.533004 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −438.602 | −0.222957 | −0.111479 | − | 0.993767i | \(-0.535559\pi\) | ||||
−0.111479 | + | 0.993767i | \(0.535559\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2205.12 | 1.07943 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1755.87 | −0.843746 | −0.421873 | − | 0.906655i | \(-0.638627\pi\) | ||||
−0.421873 | + | 0.906655i | \(0.638627\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2787.55 | 1.29166 | 0.645831 | − | 0.763481i | \(-0.276511\pi\) | ||||
0.645831 | + | 0.763481i | \(0.276511\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3539.34 | 1.61099 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1216.36 | −0.534556 | −0.267278 | − | 0.963619i | \(-0.586124\pi\) | ||||
−0.267278 | + | 0.963619i | \(0.586124\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −318.693 | −0.137663 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2531.98 | −1.05726 | −0.528628 | − | 0.848854i | \(-0.677293\pi\) | ||||
−0.528628 | + | 0.848854i | \(0.677293\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3444.82 | 1.41465 | 0.707324 | − | 0.706889i | \(-0.249902\pi\) | ||||
0.707324 | + | 0.706889i | \(0.249902\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1430.00 | 0.568301 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2926.94 | 1.14460 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1702.57 | −0.644994 | −0.322497 | − | 0.946571i | \(-0.604522\pi\) | ||||
−0.322497 | + | 0.946571i | \(0.604522\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 685.489 | 0.255661 | 0.127830 | − | 0.991796i | \(-0.459199\pi\) | ||||
0.127830 | + | 0.991796i | \(0.459199\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4362.95 | −1.57791 | −0.788953 | − | 0.614454i | \(-0.789377\pi\) | ||||
−0.788953 | + | 0.614454i | \(0.789377\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2920.20 | 1.04024 | 0.520119 | − | 0.854094i | \(-0.325888\pi\) | ||||
0.520119 | + | 0.854094i | \(0.325888\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1124.67 | −0.388848 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1608.51 | 0.548016 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2910.04 | −0.963119 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 213.384 | 0.0696207 | 0.0348103 | − | 0.999394i | \(-0.488917\pi\) | ||||
0.0348103 | + | 0.999394i | \(0.488917\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −843.830 | −0.267668 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2622.35 | 0.820354 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6379.78 | 1.94186 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2091.55 | −0.628073 | −0.314036 | − | 0.949411i | \(-0.601681\pi\) | ||||
−0.314036 | + | 0.949411i | \(0.601681\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4483.60 | 1.31095 | 0.655477 | − | 0.755215i | \(-0.272468\pi\) | ||||
0.655477 | + | 0.755215i | \(0.272468\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4931.09 | 1.42295 | 0.711475 | − | 0.702712i | \(-0.248028\pi\) | ||||
0.711475 | + | 0.702712i | \(0.248028\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −773.782 | −0.217563 | −0.108781 | − | 0.994066i | \(-0.534695\pi\) | ||||
−0.108781 | + | 0.994066i | \(0.534695\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1952.34 | −0.541943 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4412.40 | −1.19420 | −0.597101 | − | 0.802166i | \(-0.703681\pi\) | ||||
−0.597101 | + | 0.802166i | \(0.703681\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6143.41 | 1.64204 | 0.821021 | − | 0.570898i | \(-0.193405\pi\) | ||||
0.821021 | + | 0.570898i | \(0.193405\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 902.477 | 0.235335 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6342.94 | −1.63397 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 746.895 | 0.187823 | 0.0939116 | − | 0.995581i | \(-0.470063\pi\) | ||||
0.0939116 | + | 0.995581i | \(0.470063\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6010.72 | 1.49364 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7546.62 | 1.83169 | 0.915847 | − | 0.401528i | \(-0.131521\pi\) | ||||
0.915847 | + | 0.401528i | \(0.131521\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3645.85 | 0.874680 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1383.99 | 0.324488 | 0.162244 | − | 0.986751i | \(-0.448127\pi\) | ||||
0.162244 | + | 0.986751i | \(0.448127\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −458.466 | −0.106277 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6987.28 | −1.58372 | −0.791862 | − | 0.610700i | \(-0.790888\pi\) | ||||
−0.791862 | + | 0.610700i | \(0.790888\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3600.27 | 0.807014 | 0.403507 | − | 0.914977i | \(-0.367791\pi\) | ||||
0.403507 | + | 0.914977i | \(0.367791\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −868.693 | −0.190488 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1803.74 | 0.391251 | 0.195625 | − | 0.980679i | \(-0.437326\pi\) | ||||
0.195625 | + | 0.980679i | \(0.437326\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3712.97 | 0.788245 | 0.394123 | − | 0.919058i | \(-0.371048\pi\) | ||||
0.394123 | + | 0.919058i | \(0.371048\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 828.961 | 0.174122 | 0.0870612 | − | 0.996203i | \(-0.472252\pi\) | ||||
0.0870612 | + | 0.996203i | \(0.472252\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4100.97 | 0.843459 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2182.38 | 0.444206 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1686.32 | −0.336232 | −0.168116 | − | 0.985767i | \(-0.553768\pi\) | ||||
−0.168116 | + | 0.985767i | \(0.553768\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 613.830 | 0.121148 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 13101.4 | 2.53403 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2151.38 | −0.411972 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4392.02 | 0.824546 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5760.81 | 1.07097 | 0.535483 | − | 0.844546i | \(-0.320129\pi\) | ||||
0.535483 | + | 0.844546i | \(0.320129\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6887.96 | −1.25588 | −0.627942 | − | 0.778260i | \(-0.716103\pi\) | ||||
−0.627942 | + | 0.778260i | \(0.716103\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3056.66 | −0.551989 | −0.275995 | − | 0.961159i | \(-0.589007\pi\) | ||||
−0.275995 | + | 0.961159i | \(0.589007\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9656.47 | −1.71092 | −0.855459 | − | 0.517870i | \(-0.826725\pi\) | ||||
−0.855459 | + | 0.517870i | \(0.826725\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3065.62 | −0.538062 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7054.41 | −1.21523 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1893.47 | −0.323171 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4977.58 | −0.834112 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8879.07 | −1.47443 | −0.737217 | − | 0.675656i | \(-0.763861\pi\) | ||||
−0.737217 | + | 0.675656i | \(0.763861\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5187.02 | −0.845962 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2610.17 | 0.421914 | 0.210957 | − | 0.977495i | \(-0.432342\pi\) | ||||
0.210957 | + | 0.977495i | \(0.432342\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7148.00 | 1.13515 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6673.38 | 1.05052 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3806.48 | 0.588884 | 0.294442 | − | 0.955669i | \(-0.404866\pi\) | ||||
0.294442 | + | 0.955669i | \(0.404866\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4080.99 | 0.625932 | 0.312966 | − | 0.949764i | \(-0.398677\pi\) | ||||
0.312966 | + | 0.949764i | \(0.398677\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5016.64 | −0.756399 | −0.378200 | − | 0.925724i | \(-0.623457\pi\) | ||||
−0.378200 | + | 0.925724i | \(0.623457\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3026.08 | 0.452416 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −515.859 | −0.0758384 | −0.0379192 | − | 0.999281i | \(-0.512073\pi\) | ||||
−0.0379192 | + | 0.999281i | \(0.512073\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 154.682 | 0.0225517 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 69.0568 | 0.00990301 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4562.29 | −0.648909 | −0.324455 | − | 0.945901i | \(-0.605181\pi\) | ||||
−0.324455 | + | 0.945901i | \(0.605181\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1168.88 | −0.163572 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10438.1 | 1.44897 | 0.724485 | − | 0.689290i | \(-0.242078\pi\) | ||||
0.724485 | + | 0.689290i | \(0.242078\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6682.04 | −0.912845 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7375.64 | −0.999634 | −0.499817 | − | 0.866131i | \(-0.666599\pi\) | ||||
−0.499817 | + | 0.866131i | \(0.666599\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7277.13 | −0.970872 | −0.485436 | − | 0.874272i | \(-0.661339\pi\) | ||||
−0.485436 | + | 0.874272i | \(0.661339\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2214.77 | −0.293183 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11099.4 | 1.44669 | 0.723344 | − | 0.690488i | \(-0.242604\pi\) | ||||
0.723344 | + | 0.690488i | \(0.242604\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14571.0 | 1.88462 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2866.49 | −0.365136 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.73405 | 0.000724896 0 | 0.000362448 | − | 1.00000i | \(-0.499885\pi\) | ||||
0.000362448 | 1.00000i | \(0.499885\pi\) | ||||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6078.65 | 0.756991 | 0.378496 | − | 0.925603i | \(-0.376441\pi\) | ||||
0.378496 | + | 0.925603i | \(0.376441\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15580.3 | 1.92583 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9937.85 | 1.21032 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11154.5 | −1.34855 | −0.674273 | − | 0.738482i | \(-0.735543\pi\) | ||||
−0.674273 | + | 0.738482i | \(0.735543\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1564.99 | 0.186460 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3139.68 | −0.371376 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6718.81 | −0.783378 | −0.391689 | − | 0.920098i | \(-0.628109\pi\) | ||||
−0.391689 | + | 0.920098i | \(0.628109\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9299.47 | −1.07655 | −0.538276 | − | 0.842768i | \(-0.680924\pi\) | ||||
−0.538276 | + | 0.842768i | \(0.680924\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2105.85 | −0.240350 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11197.7 | 1.26907 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2338.96 | −0.261400 | −0.130700 | − | 0.991422i | \(-0.541723\pi\) | ||||
−0.130700 | + | 0.991422i | \(0.541723\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11685.4 | 1.29691 | 0.648457 | − | 0.761251i | \(-0.275414\pi\) | ||||
0.648457 | + | 0.761251i | \(0.275414\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −14486.8 | −1.58581 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16103.8 | 1.75078 | 0.875388 | − | 0.483421i | \(-0.160606\pi\) | ||||
0.875388 | + | 0.483421i | \(0.160606\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11263.9 | 1.20804 | 0.604021 | − | 0.796968i | \(-0.293564\pi\) | ||||
0.604021 | + | 0.796968i | \(0.293564\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5065.53 | 0.539617 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10612.8 | −1.11548 | −0.557739 | − | 0.830016i | \(-0.688331\pi\) | ||||
−0.557739 | + | 0.830016i | \(0.688331\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11178.4 | 1.16712 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4827.48 | −0.497397 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2493.02 | 0.255183 | 0.127592 | − | 0.991827i | \(-0.459275\pi\) | ||||
0.127592 | + | 0.991827i | \(0.459275\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15411.4 | 1.55701 | 0.778506 | − | 0.627637i | \(-0.215978\pi\) | ||||
0.778506 | + | 0.627637i | \(0.215978\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8831.79 | 0.886497 | 0.443248 | − | 0.896399i | \(-0.353826\pi\) | ||||
0.443248 | + | 0.896399i | \(0.353826\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8430.83 | 0.835401 | 0.417701 | − | 0.908585i | \(-0.362836\pi\) | ||||
0.417701 | + | 0.908585i | \(0.362836\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13224.5 | −1.30203 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5864.23 | −0.570058 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2093.69 | 0.202243 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8626.05 | −0.822827 | −0.411414 | − | 0.911449i | \(-0.634965\pi\) | ||||
−0.411414 | + | 0.911449i | \(0.634965\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21661.2 | 2.05336 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5779.09 | −0.541062 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12182.8 | 1.13358 | 0.566792 | − | 0.823861i | \(-0.308184\pi\) | ||||
0.566792 | + | 0.823861i | \(0.308184\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −21020.9 | −1.93210 | −0.966049 | − | 0.258357i | \(-0.916819\pi\) | ||||
−0.966049 | + | 0.258357i | \(0.916819\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7431.55 | −0.678905 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7715.13 | 0.696319 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8890.70 | 0.797600 | 0.398800 | − | 0.917038i | \(-0.369427\pi\) | ||||
0.398800 | + | 0.917038i | \(0.369427\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2433.17 | 0.215686 | 0.107843 | − | 0.994168i | \(-0.465606\pi\) | ||||
0.107843 | + | 0.994168i | \(0.465606\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4269.36 | 0.376206 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15257.6 | −1.32865 | −0.664324 | − | 0.747445i | \(-0.731281\pi\) | ||||
−0.664324 | + | 0.747445i | \(0.731281\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 176.064 | 0.0152419 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5149.73 | −0.440629 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13567.9 | −1.15419 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12991.2 | 1.09242 | 0.546212 | − | 0.837647i | \(-0.316069\pi\) | ||||
0.546212 | + | 0.837647i | \(0.316069\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1501.60 | −0.125545 | −0.0627727 | − | 0.998028i | \(-0.519994\pi\) | ||||
−0.0627727 | + | 0.998028i | \(0.519994\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 17327.9 | 1.43229 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17755.7 | 1.45933 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 24365.3 | 1.98007 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2574.23 | 0.208025 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6271.81 | 0.501198 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18683.1 | −1.48475 | −0.742375 | − | 0.669985i | \(-0.766301\pi\) | ||||
−0.742375 | + | 0.669985i | \(0.766301\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3284.36 | 0.258141 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2830.89 | 0.221280 | 0.110640 | − | 0.993861i | \(-0.464710\pi\) | ||||
0.110640 | + | 0.993861i | \(0.464710\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7388.64 | 0.571265 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7308.24 | −0.561986 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2065.19 | −0.157100 | −0.0785500 | − | 0.996910i | \(-0.525029\pi\) | ||||
−0.0785500 | + | 0.996910i | \(0.525029\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12782.1 | −0.967129 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20528.0 | 1.53668 | 0.768341 | − | 0.640040i | \(-0.221082\pi\) | ||||
0.768341 | + | 0.640040i | \(0.221082\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8507.20 | −0.633453 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −17758.5 | −1.30839 | −0.654195 | − | 0.756326i | \(-0.726992\pi\) | ||||
−0.654195 | + | 0.756326i | \(0.726992\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12609.1 | −0.924126 | −0.462063 | − | 0.886847i | \(-0.652891\pi\) | ||||
−0.462063 | + | 0.886847i | \(0.652891\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4324.55 | −0.313645 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1266.62 | 0.0913863 | 0.0456932 | − | 0.998956i | \(-0.485450\pi\) | ||||
0.0456932 | + | 0.998956i | \(0.485450\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8004.76 | −0.571589 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3186.13 | −0.226340 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8943.52 | −0.628856 | −0.314428 | − | 0.949281i | \(-0.601813\pi\) | ||||
−0.314428 | + | 0.949281i | \(0.601813\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17227.9 | −1.20520 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −16200.0 | −1.12185 | −0.560924 | − | 0.827868i | \(-0.689554\pi\) | ||||
−0.560924 | + | 0.827868i | \(0.689554\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5368.97 | −0.369926 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19630.1 | 1.33900 | 0.669501 | − | 0.742811i | \(-0.266508\pi\) | ||||
0.669501 | + | 0.742811i | \(0.266508\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11537.5 | 0.783066 | 0.391533 | − | 0.920164i | \(-0.371945\pi\) | ||||
0.391533 | + | 0.920164i | \(0.371945\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 617.977 | 0.0415279 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6346.35 | 0.424366 | 0.212183 | − | 0.977230i | \(-0.431943\pi\) | ||||
0.212183 | + | 0.977230i | \(0.431943\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −29573.5 | −1.95813 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12007.3 | −0.791144 | −0.395572 | − | 0.918435i | \(-0.629454\pi\) | ||||
−0.395572 | + | 0.918435i | \(0.629454\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8650.85 | 0.564457 | 0.282229 | − | 0.959347i | \(-0.408926\pi\) | ||||
0.282229 | + | 0.959347i | \(0.408926\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11528.8 | −0.748597 | −0.374299 | − | 0.927308i | \(-0.622117\pi\) | ||||
−0.374299 | + | 0.927308i | \(0.622117\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12914.8 | 0.830531 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 24090.9 | 1.52714 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4739.76 | 0.299028 | 0.149514 | − | 0.988760i | \(-0.452229\pi\) | ||||
0.149514 | + | 0.988760i | \(0.452229\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1727.02 | 0.107929 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13670.5 | 0.850305 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 29213.8 | 1.80012 | 0.900060 | − | 0.435766i | \(-0.143522\pi\) | ||||
0.900060 | + | 0.435766i | \(0.143522\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23444.5 | −1.43789 | −0.718943 | − | 0.695069i | \(-0.755374\pi\) | ||||
−0.718943 | + | 0.695069i | \(0.755374\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −27783.6 | −1.68823 | −0.844116 | − | 0.536160i | \(-0.819874\pi\) | ||||
−0.844116 | + | 0.536160i | \(0.819874\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4265.84 | 0.258010 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8533.05 | 0.511369 | 0.255684 | − | 0.966760i | \(-0.417699\pi\) | ||||
0.255684 | + | 0.966760i | \(0.417699\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14139.4 | 0.843467 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1085.28 | −0.0641522 | −0.0320761 | − | 0.999485i | \(-0.510212\pi\) | ||||
−0.0320761 | + | 0.999485i | \(0.510212\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −403.736 | −0.0237572 | −0.0118786 | − | 0.999929i | \(-0.503781\pi\) | ||||
−0.0118786 | + | 0.999929i | \(0.503781\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5337.97 | 0.311274 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15261.3 | −0.885938 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 30522.6 | 1.75605 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25125.0 | −1.43907 | −0.719537 | − | 0.694454i | \(-0.755646\pi\) | ||||
−0.719537 | + | 0.694454i | \(0.755646\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4361.67 | −0.247611 | −0.123805 | − | 0.992307i | \(-0.539510\pi\) | ||||
−0.123805 | + | 0.992307i | \(0.539510\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14734.1 | −0.832756 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14945.1 | 0.837275 | 0.418637 | − | 0.908153i | \(-0.362508\pi\) | ||||
0.418637 | + | 0.908153i | \(0.362508\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6139.19 | 0.342433 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6944.72 | −0.383995 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21499.1 | −1.18359 | −0.591797 | − | 0.806087i | \(-0.701581\pi\) | ||||
−0.591797 | + | 0.806087i | \(0.701581\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −200.545 | −0.0109455 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 27098.3 | 1.47263 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28878.4 | −1.55595 | −0.777977 | − | 0.628293i | \(-0.783754\pi\) | ||||
−0.777977 | + | 0.628293i | \(0.783754\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −23951.8 | −1.28501 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10884.9 | 0.579024 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19945.5 | −1.05651 | −0.528257 | − | 0.849084i | \(-0.677154\pi\) | ||||
−0.528257 | + | 0.849084i | \(0.677154\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 35584.3 | 1.86907 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13158.7 | −0.688264 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −18280.0 | −0.948160 | −0.474080 | − | 0.880482i | \(-0.657219\pi\) | ||||
−0.474080 | + | 0.880482i | \(0.657219\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13129.5 | −0.678179 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2205.62 | 0.112986 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17999.1 | −0.918225 | −0.459112 | − | 0.888378i | \(-0.651833\pi\) | ||||
−0.459112 | + | 0.888378i | \(0.651833\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −14215.8 | −0.719278 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9899.87 | 0.498854 | 0.249427 | − | 0.968394i | \(-0.419758\pi\) | ||||
0.249427 | + | 0.968394i | \(0.419758\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −36047.4 | −1.80166 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16358.7 | 0.814294 | 0.407147 | − | 0.913363i | \(-0.366524\pi\) | ||||
0.407147 | + | 0.913363i | \(0.366524\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 756.028 | 0.0373297 | 0.0186648 | − | 0.999826i | \(-0.494058\pi\) | ||||
0.0186648 | + | 0.999826i | \(0.494058\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2403.65 | −0.118205 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6563.11 | 0.320175 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31368.4 | 1.52417 | 0.762083 | − | 0.647480i | \(-0.224177\pi\) | ||||
0.762083 | + | 0.647480i | \(0.224177\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −380.000 | −0.0183174 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17559.4 | −0.843072 | −0.421536 | − | 0.906812i | \(-0.638509\pi\) | ||||
−0.421536 | + | 0.906812i | \(0.638509\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23502.4 | −1.11953 | −0.559765 | − | 0.828651i | \(-0.689109\pi\) | ||||
−0.559765 | + | 0.828651i | \(0.689109\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8373.63 | 0.397308 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9298.12 | 0.437726 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32276.0 | 1.51352 | 0.756762 | − | 0.653690i | \(-0.226780\pi\) | ||||
0.756762 | + | 0.653690i | \(0.226780\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8693.38 | 0.404501 | 0.202251 | − | 0.979334i | \(-0.435174\pi\) | ||||
0.202251 | + | 0.979334i | \(0.435174\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5142.78 | −0.238367 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −26941.8 | −1.23914 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 21029.9 | 0.963519 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2193.01 | 0.0997095 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20817.0 | −0.942881 | −0.471440 | − | 0.881898i | \(-0.656266\pi\) | ||||
−0.471440 | + | 0.881898i | \(0.656266\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −21689.5 | −0.974956 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 66529.2 | 2.97922 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −42466.0 | −1.88736 | −0.943678 | − | 0.330865i | \(-0.892659\pi\) | ||||
−0.943678 | + | 0.330865i | \(0.892659\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −32890.7 | −1.45631 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 479.914 | 0.0210906 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11025.6 | −0.482736 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −32955.4 | −1.43220 | −0.716101 | − | 0.697997i | \(-0.754075\pi\) | ||||
−0.716101 | + | 0.697997i | \(0.754075\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3396.82 | 0.147076 | 0.0735379 | − | 0.997292i | \(-0.476571\pi\) | ||||
0.0735379 | + | 0.997292i | \(0.476571\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8779.36 | 0.377335 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14133.8 | 0.605236 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13138.9 | 0.558529 | 0.279265 | − | 0.960214i | \(-0.409909\pi\) | ||||
0.279265 | + | 0.960214i | \(0.409909\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24645.2 | −1.04384 | −0.521918 | − | 0.852996i | \(-0.674783\pi\) | ||||
−0.521918 | + | 0.852996i | \(0.674783\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14508.9 | −0.610064 | −0.305032 | − | 0.952342i | \(-0.598667\pi\) | ||||
−0.305032 | + | 0.952342i | \(0.598667\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28408.6 | 1.19019 | 0.595097 | − | 0.803654i | \(-0.297113\pi\) | ||||
0.595097 | + | 0.803654i | \(0.297113\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 15203.9 | 0.632392 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13937.8 | −0.577649 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14950.0 | −0.615173 | −0.307587 | − | 0.951520i | \(-0.599521\pi\) | ||||
−0.307587 | + | 0.951520i | \(0.599521\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16605.3 | −0.680854 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −17696.7 | −0.720456 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1575.56 | 0.0639161 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 49472.8 | 1.99284 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −47855.4 | −1.92091 | −0.960456 | − | 0.278432i | \(-0.910185\pi\) | ||||
−0.960456 | + | 0.278432i | \(0.910185\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 25938.2 | 1.03388 | 0.516939 | − | 0.856022i | \(-0.327071\pi\) | ||||
0.516939 | + | 0.856022i | \(0.327071\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7594.80 | 0.301666 | 0.150833 | − | 0.988559i | \(-0.451804\pi\) | ||||
0.150833 | + | 0.988559i | \(0.451804\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −20686.0 | −0.815943 | −0.407972 | − | 0.912995i | \(-0.633764\pi\) | ||||
−0.407972 | + | 0.912995i | \(0.633764\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6081.81 | 0.239061 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −19920.8 | −0.777637 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −78571.6 | −3.05660 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1593.47 | 0.0615645 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −40023.1 | −1.54103 | −0.770515 | − | 0.637422i | \(-0.780001\pi\) | ||||
−0.770515 | + | 0.637422i | \(0.780001\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −21863.6 | −0.836100 | −0.418050 | − | 0.908424i | \(-0.637286\pi\) | ||||
−0.418050 | + | 0.908424i | \(0.637286\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25239.1 | −0.961906 | −0.480953 | − | 0.876746i | \(-0.659709\pi\) | ||||
−0.480953 | + | 0.876746i | \(0.659709\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −42160.4 | −1.59595 | −0.797974 | − | 0.602691i | \(-0.794095\pi\) | ||||
−0.797974 | + | 0.602691i | \(0.794095\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4403.12 | 0.166115 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 32700.8 | 1.22541 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12659.9 | 0.472819 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −18148.9 | −0.673303 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7723.69 | −0.285587 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −17224.1 | −0.632650 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9290.99 | 0.340135 | 0.170067 | − | 0.985432i | \(-0.445601\pi\) | ||||
0.170067 | + | 0.985432i | \(0.445601\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 48448.8 | 1.76200 | 0.881000 | − | 0.473116i | \(-0.156871\pi\) | ||||
0.881000 | + | 0.473116i | \(0.156871\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21819.4 | −0.790926 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 36048.9 | 1.29819 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 39905.6 | 1.43239 | 0.716193 | − | 0.697902i | \(-0.245883\pi\) | ||||
0.716193 | + | 0.697902i | \(0.245883\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 45838.2 | 1.63465 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7150.00 | −0.254152 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 34488.4 | 1.21800 | 0.609002 | − | 0.793169i | \(-0.291570\pi\) | ||||
0.609002 | + | 0.793169i | \(0.291570\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15116.1 | −0.532126 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −14634.7 | −0.511878 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −57056.3 | −1.98927 | −0.994635 | − | 0.103443i | \(-0.967014\pi\) | ||||
−0.994635 | + | 0.103443i | \(0.967014\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 52473.4 | 1.81784 | 0.908919 | − | 0.416974i | \(-0.136909\pi\) | ||||
0.908919 | + | 0.416974i | \(0.136909\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 55648.6 | 1.92171 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −19062.2 | −0.654107 | −0.327053 | − | 0.945006i | \(-0.606056\pi\) | ||||
−0.327053 | + | 0.945006i | \(0.606056\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1046.05 | 0.0357812 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36107.0 | 1.22730 | 0.613652 | − | 0.789577i | \(-0.289700\pi\) | ||||
0.613652 | + | 0.789577i | \(0.289700\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8512.86 | 0.288450 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 15652.2 | 0.527043 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12526.2 | 0.420468 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3427.44 | −0.114335 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −42749.6 | −1.42165 | −0.710824 | − | 0.703369i | \(-0.751678\pi\) | ||||
−0.710824 | + | 0.703369i | \(0.751678\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 42208.9 | 1.39500 | 0.697501 | − | 0.716583i | \(-0.254295\pi\) | ||||
0.697501 | + | 0.716583i | \(0.254295\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −511.300 | −0.0168464 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6217.51 | −0.203599 | −0.101799 | − | 0.994805i | \(-0.532460\pi\) | ||||
−0.101799 | + | 0.994805i | \(0.532460\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 35203.2 | 1.14923 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 40932.0 | 1.32811 | 0.664053 | − | 0.747686i | \(-0.268835\pi\) | ||||
0.664053 | + | 0.747686i | \(0.268835\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 21814.8 | 0.705661 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −29193.4 | −0.938622 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13878.5 | −0.444870 | −0.222435 | − | 0.974947i | \(-0.571401\pi\) | ||||
−0.222435 | + | 0.974947i | \(0.571401\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14601.0 | −0.465208 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6733.80 | 0.213903 | 0.106952 | − | 0.994264i | \(-0.465891\pi\) | ||||
0.106952 | + | 0.994264i | \(0.465891\pi\) | |||||||
\(998\) | 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 | 2160.4.a.x.1.1 | 2 | ||
3.2 | odd | 2 | 2160.4.a.bc.1.1 | 2 | |||
4.3 | odd | 2 | 540.4.a.e.1.2 | ✓ | 2 | ||
12.11 | even | 2 | 540.4.a.h.1.2 | yes | 2 | ||
36.7 | odd | 6 | 1620.4.i.r.1081.1 | 4 | |||
36.11 | even | 6 | 1620.4.i.o.1081.1 | 4 | |||
36.23 | even | 6 | 1620.4.i.o.541.1 | 4 | |||
36.31 | odd | 6 | 1620.4.i.r.541.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
540.4.a.e.1.2 | ✓ | 2 | 4.3 | odd | 2 | ||
540.4.a.h.1.2 | yes | 2 | 12.11 | even | 2 | ||
1620.4.i.o.541.1 | 4 | 36.23 | even | 6 | |||
1620.4.i.o.1081.1 | 4 | 36.11 | even | 6 | |||
1620.4.i.r.541.1 | 4 | 36.31 | odd | 6 | |||
1620.4.i.r.1081.1 | 4 | 36.7 | odd | 6 | |||
2160.4.a.x.1.1 | 2 | 1.1 | even | 1 | trivial | ||
2160.4.a.bc.1.1 | 2 | 3.2 | odd | 2 |