Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1840,4,Mod(1,1840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1840, 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("1840.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1840 = 2^{4} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1840.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: | \(108.563514411\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 230) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1840.1 |
$q$-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 | ||||||||
\(3\) | −4.00000 | −0.769800 | −0.384900 | − | 0.922958i | \(-0.625764\pi\) | ||||
−0.384900 | + | 0.922958i | \(0.625764\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.00000 | −0.161985 | −0.0809924 | − | 0.996715i | \(-0.525809\pi\) | ||||
−0.0809924 | + | 0.996715i | \(0.525809\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −11.0000 | −0.407407 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000 | 0.0548202 | 0.0274101 | − | 0.999624i | \(-0.491274\pi\) | ||||
0.0274101 | + | 0.999624i | \(0.491274\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −38.0000 | −0.810716 | −0.405358 | − | 0.914158i | \(-0.632853\pi\) | ||||
−0.405358 | + | 0.914158i | \(0.632853\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 20.0000 | 0.344265 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −45.0000 | −0.642006 | −0.321003 | − | 0.947078i | \(-0.604020\pi\) | ||||
−0.321003 | + | 0.947078i | \(0.604020\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 74.0000 | 0.893514 | 0.446757 | − | 0.894655i | \(-0.352579\pi\) | ||||
0.446757 | + | 0.894655i | \(0.352579\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 12.0000 | 0.124696 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −23.0000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 152.000 | 1.08342 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 283.000 | 1.81213 | 0.906065 | − | 0.423138i | \(-0.139072\pi\) | ||||
0.906065 | + | 0.423138i | \(0.139072\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 303.000 | 1.75550 | 0.877748 | − | 0.479122i | \(-0.159045\pi\) | ||||
0.877748 | + | 0.479122i | \(0.159045\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −8.00000 | −0.0422006 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 15.0000 | 0.0724418 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 79.0000 | 0.351014 | 0.175507 | − | 0.984478i | \(-0.443844\pi\) | ||||
0.175507 | + | 0.984478i | \(0.443844\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 152.000 | 0.624089 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −407.000 | −1.55031 | −0.775155 | − | 0.631771i | \(-0.782328\pi\) | ||||
−0.775155 | + | 0.631771i | \(0.782328\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 328.000 | 1.16324 | 0.581622 | − | 0.813459i | \(-0.302418\pi\) | ||||
0.581622 | + | 0.813459i | \(0.302418\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 55.0000 | 0.182198 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −360.000 | −1.11726 | −0.558632 | − | 0.829416i | \(-0.688674\pi\) | ||||
−0.558632 | + | 0.829416i | \(0.688674\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −334.000 | −0.973761 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 180.000 | 0.494217 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −561.000 | −1.45395 | −0.726974 | − | 0.686665i | \(-0.759074\pi\) | ||||
−0.726974 | + | 0.686665i | \(0.759074\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.0000 | −0.0245164 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −296.000 | −0.687827 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −101.000 | −0.222866 | −0.111433 | − | 0.993772i | \(-0.535544\pi\) | ||||
−0.111433 | + | 0.993772i | \(0.535544\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −268.000 | −0.562523 | −0.281261 | − | 0.959631i | \(-0.590753\pi\) | ||||
−0.281261 | + | 0.959631i | \(0.590753\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 33.0000 | 0.0659938 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 190.000 | 0.362563 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 69.0000 | 0.125816 | 0.0629081 | − | 0.998019i | \(-0.479962\pi\) | ||||
0.0629081 | + | 0.998019i | \(0.479962\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 92.0000 | 0.160514 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 641.000 | 1.07145 | 0.535723 | − | 0.844394i | \(-0.320039\pi\) | ||||
0.535723 | + | 0.844394i | \(0.320039\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 994.000 | 1.59368 | 0.796842 | − | 0.604188i | \(-0.206502\pi\) | ||||
0.796842 | + | 0.604188i | \(0.206502\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −100.000 | −0.153960 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.00000 | −0.00888004 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 884.000 | 1.25896 | 0.629480 | − | 0.777017i | \(-0.283268\pi\) | ||||
0.629480 | + | 0.777017i | \(0.283268\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −311.000 | −0.426612 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −503.000 | −0.665198 | −0.332599 | − | 0.943068i | \(-0.607926\pi\) | ||||
−0.332599 | + | 0.943068i | \(0.607926\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 225.000 | 0.287114 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1132.00 | −1.39498 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1608.00 | 1.91514 | 0.957571 | − | 0.288197i | \(-0.0930558\pi\) | ||||
0.957571 | + | 0.288197i | \(0.0930558\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 114.000 | 0.131324 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1212.00 | −1.35138 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −370.000 | −0.399592 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1082.00 | 1.13258 | 0.566291 | − | 0.824205i | \(-0.308378\pi\) | ||||
0.566291 | + | 0.824205i | \(0.308378\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −22.0000 | −0.0223342 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 879.000 | 0.865978 | 0.432989 | − | 0.901399i | \(-0.357459\pi\) | ||||
0.432989 | + | 0.901399i | \(0.357459\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −360.000 | −0.344387 | −0.172193 | − | 0.985063i | \(-0.555085\pi\) | ||||
−0.172193 | + | 0.985063i | \(0.555085\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −60.0000 | −0.0557657 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1815.00 | −1.63984 | −0.819919 | − | 0.572480i | \(-0.805982\pi\) | ||||
−0.819919 | + | 0.572480i | \(0.805982\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −430.000 | −0.377858 | −0.188929 | − | 0.981991i | \(-0.560502\pi\) | ||||
−0.188929 | + | 0.981991i | \(0.560502\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −316.000 | −0.270211 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 255.000 | 0.212287 | 0.106143 | − | 0.994351i | \(-0.466150\pi\) | ||||
0.106143 | + | 0.994351i | \(0.466150\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 115.000 | 0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 418.000 | 0.330292 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 135.000 | 0.103995 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1327.00 | −0.996995 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1628.00 | 1.19343 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −344.000 | −0.240355 | −0.120177 | − | 0.992752i | \(-0.538346\pi\) | ||||
−0.120177 | + | 0.992752i | \(0.538346\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1312.00 | −0.895466 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1348.00 | 0.899048 | 0.449524 | − | 0.893268i | \(-0.351594\pi\) | ||||
0.449524 | + | 0.893268i | \(0.351594\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −222.000 | −0.144736 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −760.000 | −0.484521 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 734.000 | 0.457736 | 0.228868 | − | 0.973457i | \(-0.426498\pi\) | ||||
0.228868 | + | 0.973457i | \(0.426498\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2659.00 | −1.62254 | −0.811271 | − | 0.584670i | \(-0.801224\pi\) | ||||
−0.811271 | + | 0.584670i | \(0.801224\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1440.00 | 0.860070 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −76.0000 | −0.0444436 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1415.00 | −0.810409 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1336.00 | 0.749602 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3196.00 | −1.75722 | −0.878612 | − | 0.477535i | \(-0.841530\pi\) | ||||
−0.878612 | + | 0.477535i | \(0.841530\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 100.000 | 0.0538933 | 0.0269466 | − | 0.999637i | \(-0.491422\pi\) | ||||
0.0269466 | + | 0.999637i | \(0.491422\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 495.000 | 0.261558 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1515.00 | −0.785082 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −787.000 | −0.400060 | −0.200030 | − | 0.979790i | \(-0.564104\pi\) | ||||
−0.200030 | + | 0.979790i | \(0.564104\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2244.00 | 1.11925 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 69.0000 | 0.0337762 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 70.0000 | 0.0336370 | 0.0168185 | − | 0.999859i | \(-0.494646\pi\) | ||||
0.0168185 | + | 0.999859i | \(0.494646\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 40.0000 | 0.0188727 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1784.00 | −0.826647 | −0.413324 | − | 0.910584i | \(-0.635632\pi\) | ||||
−0.413324 | + | 0.910584i | \(0.635632\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −753.000 | −0.342740 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −814.000 | −0.364024 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −28.0000 | −0.0123052 | −0.00615260 | − | 0.999981i | \(-0.501958\pi\) | ||||
−0.00615260 | + | 0.999981i | \(0.501958\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −75.0000 | −0.0323970 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 404.000 | 0.171562 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 32.0000 | 0.0133620 | 0.00668098 | − | 0.999978i | \(-0.497873\pi\) | ||||
0.00668098 | + | 0.999978i | \(0.497873\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1172.00 | −0.481293 | −0.240647 | − | 0.970613i | \(-0.577359\pi\) | ||||
−0.240647 | + | 0.970613i | \(0.577359\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1072.00 | 0.433030 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −395.000 | −0.156978 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −90.0000 | −0.0351949 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −456.000 | −0.175498 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 648.000 | 0.245485 | 0.122742 | − | 0.992439i | \(-0.460831\pi\) | ||||
0.122742 | + | 0.992439i | \(0.460831\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −772.000 | −0.287926 | −0.143963 | − | 0.989583i | \(-0.545985\pi\) | ||||
−0.143963 | + | 0.989583i | \(0.545985\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −760.000 | −0.279101 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −66.0000 | −0.0238696 | −0.0119348 | − | 0.999929i | \(-0.503799\pi\) | ||||
−0.0119348 | + | 0.999929i | \(0.503799\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3358.00 | 1.19619 | 0.598096 | − | 0.801424i | \(-0.295924\pi\) | ||||
0.598096 | + | 0.801424i | \(0.295924\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −276.000 | −0.0968534 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −849.000 | −0.293538 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2035.00 | 0.693320 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 253.000 | 0.0849503 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 148.000 | 0.0489827 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4489.00 | −1.46462 | −0.732312 | − | 0.680970i | \(-0.761559\pi\) | ||||
−0.732312 | + | 0.680970i | \(0.761559\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2564.00 | −0.824800 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1640.00 | −0.520219 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −909.000 | −0.284364 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3976.00 | −1.22682 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1710.00 | 0.520484 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1990.00 | −0.597580 | −0.298790 | − | 0.954319i | \(-0.596583\pi\) | ||||
−0.298790 | + | 0.954319i | \(0.596583\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −275.000 | −0.0814815 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5524.00 | −1.61516 | −0.807579 | − | 0.589760i | \(-0.799222\pi\) | ||||
−0.807579 | + | 0.589760i | \(0.799222\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1300.00 | −0.375137 | −0.187569 | − | 0.982252i | \(-0.560061\pi\) | ||||
−0.187569 | + | 0.982252i | \(0.560061\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 24.0000 | 0.00683586 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1212.00 | −0.340776 | −0.170388 | − | 0.985377i | \(-0.554502\pi\) | ||||
−0.170388 | + | 0.985377i | \(0.554502\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1800.00 | 0.499656 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3536.00 | −0.969147 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2761.00 | −0.747256 | −0.373628 | − | 0.927579i | \(-0.621886\pi\) | ||||
−0.373628 | + | 0.927579i | \(0.621886\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5742.00 | −1.53475 | −0.767375 | − | 0.641199i | \(-0.778437\pi\) | ||||
−0.767375 | + | 0.641199i | \(0.778437\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2860.00 | −0.755017 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1670.00 | 0.435479 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2812.00 | −0.724386 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2012.00 | 0.512070 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4162.00 | 1.04663 | 0.523313 | − | 0.852141i | \(-0.324696\pi\) | ||||
0.523313 | + | 0.852141i | \(0.324696\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −46.0000 | −0.0114308 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −900.000 | −0.221020 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2464.00 | 0.598055 | 0.299027 | − | 0.954245i | \(-0.403338\pi\) | ||||
0.299027 | + | 0.954245i | \(0.403338\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −237.000 | −0.0568589 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3113.00 | −0.738275 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4167.00 | 0.976989 | 0.488495 | − | 0.872567i | \(-0.337546\pi\) | ||||
0.488495 | + | 0.872567i | \(0.337546\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2805.00 | 0.650226 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6432.00 | −1.47428 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1639.00 | −0.371493 | −0.185746 | − | 0.982598i | \(-0.559470\pi\) | ||||
−0.185746 | + | 0.982598i | \(0.559470\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2655.00 | −0.595128 | −0.297564 | − | 0.954702i | \(-0.596174\pi\) | ||||
−0.297564 | + | 0.954702i | \(0.596174\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −456.000 | −0.101093 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 50.0000 | 0.0109640 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −826.000 | −0.179168 | −0.0895840 | − | 0.995979i | \(-0.528554\pi\) | ||||
−0.0895840 | + | 0.995979i | \(0.528554\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3333.00 | −0.715202 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3930.00 | 0.834321 | 0.417160 | − | 0.908833i | \(-0.363025\pi\) | ||||
0.417160 | + | 0.908833i | \(0.363025\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7339.00 | 1.54155 | 0.770774 | − | 0.637108i | \(-0.219870\pi\) | ||||
0.770774 | + | 0.637108i | \(0.219870\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1480.00 | 0.307606 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1221.00 | 0.251127 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2888.00 | −0.587828 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4328.00 | −0.871862 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4763.00 | −0.949684 | −0.474842 | − | 0.880071i | \(-0.657495\pi\) | ||||
−0.474842 | + | 0.880071i | \(0.657495\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 505.000 | 0.0996686 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 304.000 | 0.0593935 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 874.000 | 0.169046 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −984.000 | −0.188428 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3516.00 | −0.666630 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1340.00 | 0.251568 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4238.00 | 0.787868 | 0.393934 | − | 0.919139i | \(-0.371114\pi\) | ||||
0.393934 | + | 0.919139i | \(0.371114\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1440.00 | 0.265109 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4352.00 | −0.793503 | −0.396751 | − | 0.917926i | \(-0.629862\pi\) | ||||
−0.396751 | + | 0.917926i | \(0.629862\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −515.000 | −0.0930017 | −0.0465008 | − | 0.998918i | \(-0.514807\pi\) | ||||
−0.0465008 | + | 0.998918i | \(0.514807\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −165.000 | −0.0295133 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6816.00 | −1.20765 | −0.603824 | − | 0.797117i | \(-0.706357\pi\) | ||||
−0.603824 | + | 0.797117i | \(0.706357\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 566.000 | 0.0993414 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7260.00 | 1.26235 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3330.00 | −0.573641 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −950.000 | −0.162143 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1720.00 | 0.290875 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1080.00 | 0.180980 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8795.00 | 1.46047 | 0.730237 | − | 0.683194i | \(-0.239410\pi\) | ||||
0.730237 | + | 0.683194i | \(0.239410\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −869.000 | −0.143006 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −345.000 | −0.0562668 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10654.0 | −1.72214 | −0.861069 | − | 0.508488i | \(-0.830204\pi\) | ||||
−0.861069 | + | 0.508488i | \(0.830204\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1020.00 | −0.163418 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 606.000 | 0.0962368 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2031.00 | 0.319719 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −460.000 | −0.0717843 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6624.00 | −1.02477 | −0.512385 | − | 0.858756i | \(-0.671238\pi\) | ||||
−0.512385 | + | 0.858756i | \(0.671238\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9719.00 | 1.49068 | 0.745338 | − | 0.666686i | \(-0.232288\pi\) | ||||
0.745338 | + | 0.666686i | \(0.232288\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5776.00 | −0.878348 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 664.000 | 0.100117 | 0.0500583 | − | 0.998746i | \(-0.484059\pi\) | ||||
0.0500583 | + | 0.998746i | \(0.484059\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3205.00 | −0.479165 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −540.000 | −0.0800555 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5600.00 | −0.823278 | −0.411639 | − | 0.911347i | \(-0.635043\pi\) | ||||
−0.411639 | + | 0.911347i | \(0.635043\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1383.00 | −0.201633 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5308.00 | 0.767487 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4970.00 | −0.712717 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5689.00 | −0.809165 | −0.404582 | − | 0.914502i | \(-0.632583\pi\) | ||||
−0.404582 | + | 0.914502i | \(0.632583\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4477.00 | 0.631608 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1683.00 | 0.235518 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10626.0 | −1.47505 | −0.737525 | − | 0.675320i | \(-0.764005\pi\) | ||||
−0.737525 | + | 0.675320i | \(0.764005\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 500.000 | 0.0688530 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10754.0 | −1.46912 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5160.00 | −0.699344 | −0.349672 | − | 0.936872i | \(-0.613707\pi\) | ||||
−0.349672 | + | 0.936872i | \(0.613707\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1376.00 | 0.185025 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11063.0 | 1.47596 | 0.737980 | − | 0.674822i | \(-0.235780\pi\) | ||||
0.737980 | + | 0.674822i | \(0.235780\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 30.0000 | 0.00397128 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3608.00 | −0.473915 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5374.00 | −0.700444 | −0.350222 | − | 0.936667i | \(-0.613894\pi\) | ||||
−0.350222 | + | 0.936667i | \(0.613894\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1035.00 | 0.133868 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5392.00 | −0.692088 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4420.00 | −0.563024 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 376.000 | 0.0475338 | 0.0237669 | − | 0.999718i | \(-0.492434\pi\) | ||||
0.0237669 | + | 0.999718i | \(0.492434\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 888.000 | 0.111418 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7790.00 | −0.970110 | −0.485055 | − | 0.874484i | \(-0.661200\pi\) | ||||
−0.485055 | + | 0.874484i | \(0.661200\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11514.0 | −1.42321 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1555.00 | 0.190787 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 158.000 | 0.0192427 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11909.0 | 1.43976 | 0.719880 | − | 0.694098i | \(-0.244197\pi\) | ||||
0.719880 | + | 0.694098i | \(0.244197\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2936.00 | −0.352365 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 303.000 | 0.0361009 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2515.00 | 0.297486 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10636.0 | 1.24903 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9162.00 | −1.06824 | −0.534121 | − | 0.845408i | \(-0.679357\pi\) | ||||
−0.534121 | + | 0.845408i | \(0.679357\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2086.00 | 0.241486 | 0.120743 | − | 0.992684i | \(-0.461472\pi\) | ||||
0.120743 | + | 0.992684i | \(0.461472\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3960.00 | 0.455182 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1125.00 | −0.128401 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 804.000 | 0.0911201 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 304.000 | 0.0342127 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9824.00 | 1.09792 | 0.548962 | − | 0.835847i | \(-0.315023\pi\) | ||||
0.548962 | + | 0.835847i | \(0.315023\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1793.00 | −0.198998 | −0.0994989 | − | 0.995038i | \(-0.531724\pi\) | ||||
−0.0994989 | + | 0.995038i | \(0.531724\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5660.00 | 0.623853 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1702.00 | −0.186311 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7544.00 | 0.820172 | 0.410086 | − | 0.912047i | \(-0.365499\pi\) | ||||
0.410086 | + | 0.912047i | \(0.365499\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3674.00 | 0.396717 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6548.00 | −0.702268 | −0.351134 | − | 0.936325i | \(-0.614204\pi\) | ||||
−0.351134 | + | 0.936325i | \(0.614204\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8040.00 | −0.856478 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12784.0 | 1.35271 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14235.0 | 1.49619 | 0.748097 | − | 0.663589i | \(-0.230968\pi\) | ||||
0.748097 | + | 0.663589i | \(0.230968\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −814.000 | −0.0849884 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −400.000 | −0.0414871 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −570.000 | −0.0587297 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8039.00 | −0.822863 | −0.411432 | − | 0.911441i | \(-0.634971\pi\) | ||||
−0.411432 | + | 0.911441i | \(0.634971\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6840.00 | −0.695564 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9354.00 | −0.945031 | −0.472515 | − | 0.881322i | \(-0.656654\pi\) | ||||
−0.472515 | + | 0.881322i | \(0.656654\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2402.00 | 0.241102 | 0.120551 | − | 0.992707i | \(-0.461534\pi\) | ||||
0.120551 | + | 0.992707i | \(0.461534\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6060.00 | 0.604356 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14529.0 | 1.43966 | 0.719831 | − | 0.694150i | \(-0.244219\pi\) | ||||
0.719831 | + | 0.694150i | \(0.244219\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −207.000 | −0.0203803 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3148.00 | 0.307966 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 656.000 | 0.0637694 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1850.00 | 0.178703 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6171.00 | 0.592349 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1724.00 | −0.164450 | −0.0822250 | − | 0.996614i | \(-0.526203\pi\) | ||||
−0.0822250 | + | 0.996614i | \(0.526203\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3002.00 | −0.284573 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −276.000 | −0.0260009 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5410.00 | −0.506506 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9920.00 | 0.923035 | 0.461518 | − | 0.887131i | \(-0.347305\pi\) | ||||
0.461518 | + | 0.887131i | \(0.347305\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −280.000 | −0.0258937 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8665.00 | 0.796428 | 0.398214 | − | 0.917293i | \(-0.369630\pi\) | ||||
0.398214 | + | 0.917293i | \(0.369630\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12735.0 | −1.16340 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 110.000 | 0.00998815 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1923.00 | −0.173558 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12673.0 | 1.13692 | 0.568458 | − | 0.822712i | \(-0.307540\pi\) | ||||
0.568458 | + | 0.822712i | \(0.307540\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7136.00 | 0.636353 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3667.00 | 0.325057 | 0.162528 | − | 0.986704i | \(-0.448035\pi\) | ||||
0.162528 | + | 0.986704i | \(0.448035\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4395.00 | −0.387277 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3012.00 | 0.263841 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13246.0 | −1.15347 | −0.576737 | − | 0.816930i | \(-0.695674\pi\) | ||||
−0.576737 | + | 0.816930i | \(0.695674\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2982.00 | −0.258152 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 11248.0 | 0.968053 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1800.00 | 0.154015 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −720.000 | −0.0612487 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 112.000 | 0.00947255 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4934.00 | −0.414899 | −0.207450 | − | 0.978246i | \(-0.566516\pi\) | ||||
−0.207450 | + | 0.978246i | \(0.566516\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17436.0 | −1.45779 | −0.728894 | − | 0.684627i | \(-0.759965\pi\) | ||||
−0.728894 | + | 0.684627i | \(0.759965\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 300.000 | 0.0249392 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −13635.0 | −1.12704 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1111.00 | 0.0907972 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15466.0 | 1.25686 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9075.00 | 0.733358 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −128.000 | −0.0102860 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −668.000 | −0.0533818 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1714.00 | −0.136212 | −0.0681059 | − | 0.997678i | \(-0.521696\pi\) | ||||
−0.0681059 | + | 0.997678i | \(0.521696\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4688.00 | 0.370500 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2150.00 | 0.168983 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9616.00 | −0.751646 | −0.375823 | − | 0.926691i | \(-0.622640\pi\) | ||||
−0.375823 | + | 0.926691i | \(0.622640\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2948.00 | 0.229176 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 20942.0 | 1.61916 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2652.00 | −0.203932 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1580.00 | 0.120842 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −21385.0 | −1.62677 | −0.813386 | − | 0.581725i | \(-0.802378\pi\) | ||||
−0.813386 | + | 0.581725i | \(0.802378\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12464.0 | −0.943061 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 360.000 | 0.0270931 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5967.00 | 0.446677 | 0.223338 | − | 0.974741i | \(-0.428304\pi\) | ||||
0.223338 | + | 0.974741i | \(0.428304\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1275.00 | −0.0949374 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 933.000 | 0.0691046 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9714.00 | 0.715698 | 0.357849 | − | 0.933779i | \(-0.383510\pi\) | ||||
0.357849 | + | 0.933779i | \(0.383510\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4244.00 | −0.311044 | −0.155522 | − | 0.987832i | \(-0.549706\pi\) | ||||
−0.155522 | + | 0.987832i | \(0.549706\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2592.00 | −0.188974 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −575.000 | −0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15136.0 | −1.09206 | −0.546031 | − | 0.837765i | \(-0.683862\pi\) | ||||
−0.546031 | + | 0.837765i | \(0.683862\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3088.00 | 0.221646 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1509.00 | 0.107752 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1122.00 | −0.0797058 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2090.00 | −0.147711 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −22414.0 | −1.57602 | −0.788011 | − | 0.615661i | \(-0.788889\pi\) | ||||
−0.788011 | + | 0.615661i | \(0.788889\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22422.0 | 1.56856 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 264.000 | 0.0183748 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22560.0 | 1.56227 | 0.781137 | − | 0.624360i | \(-0.214640\pi\) | ||||
0.781137 | + | 0.624360i | \(0.214640\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −675.000 | −0.0465081 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −13432.0 | −0.920829 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1240.00 | 0.0845827 | 0.0422913 | − | 0.999105i | \(-0.486534\pi\) | ||||
0.0422913 | + | 0.999105i | \(0.486534\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27931.0 | 1.89572 | 0.947861 | − | 0.318683i | \(-0.103241\pi\) | ||||
0.947861 | + | 0.318683i | \(0.103241\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −759.000 | −0.0512585 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6635.00 | 0.445870 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8660.00 | −0.579075 | −0.289538 | − | 0.957167i | \(-0.593502\pi\) | ||||
−0.289538 | + | 0.957167i | \(0.593502\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3396.00 | 0.225965 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13680.0 | 0.905783 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22326.0 | 1.47103 | 0.735513 | − | 0.677511i | \(-0.236941\pi\) | ||||
0.735513 | + | 0.677511i | \(0.236941\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8140.00 | −0.533718 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7035.00 | −0.459025 | −0.229513 | − | 0.973306i | \(-0.573713\pi\) | ||||
−0.229513 | + | 0.973306i | \(0.573713\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15808.0 | 1.02646 | 0.513229 | − | 0.858252i | \(-0.328449\pi\) | ||||
0.513229 | + | 0.858252i | \(0.328449\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3496.00 | −0.225909 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4824.00 | −0.310224 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −592.000 | −0.0377069 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3555.00 | −0.225353 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9740.00 | 0.614490 | 0.307245 | − | 0.951630i | \(-0.400593\pi\) | ||||
0.307245 | + | 0.951630i | \(0.400593\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 17956.0 | 1.12747 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1720.00 | 0.107490 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12692.0 | 0.789443 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7051.00 | −0.436515 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18730.0 | −1.15412 | −0.577060 | − | 0.816702i | \(-0.695800\pi\) | ||||
−0.577060 | + | 0.816702i | \(0.695800\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18191.0 | −1.11568 | −0.557841 | − | 0.829948i | \(-0.688370\pi\) | ||||
−0.557841 | + | 0.829948i | \(0.688370\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6560.00 | 0.400465 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2126.00 | −0.129183 | −0.0645917 | − | 0.997912i | \(-0.520575\pi\) | ||||
−0.0645917 | + | 0.997912i | \(0.520575\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −202.000 | −0.0122176 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3636.00 | 0.218903 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −27478.0 | −1.64670 | −0.823352 | − | 0.567532i | \(-0.807898\pi\) | ||||
−0.823352 | + | 0.567532i | \(0.807898\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6740.00 | −0.402067 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −10934.0 | −0.649278 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25430.0 | 1.50321 | 0.751603 | − | 0.659616i | \(-0.229281\pi\) | ||||
0.751603 | + | 0.659616i | \(0.229281\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 33610.0 | 1.97773 | 0.988863 | − | 0.148826i | \(-0.0475493\pi\) | ||||
0.988863 | + | 0.148826i | \(0.0475493\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6840.00 | −0.400669 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1110.00 | 0.0647278 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6509.00 | −0.377855 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7960.00 | 0.460017 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −536.000 | −0.0308376 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20732.0 | 1.18746 | 0.593729 | − | 0.804665i | \(-0.297655\pi\) | ||||
0.593729 | + | 0.804665i | \(0.297655\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3800.00 | 0.216685 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −24271.0 | −1.37786 | −0.688929 | − | 0.724829i | \(-0.741919\pi\) | ||||
−0.688929 | + | 0.724829i | \(0.741919\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3246.00 | −0.183461 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 22096.0 | 1.24335 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14280.0 | 0.800013 | 0.400007 | − | 0.916512i | \(-0.369008\pi\) | ||||
0.400007 | + | 0.916512i | \(0.369008\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3670.00 | −0.204706 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5200.00 | 0.288781 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 21318.0 | 1.17874 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4756.00 | 0.261833 | 0.130917 | − | 0.991393i | \(-0.458208\pi\) | ||||
0.130917 | + | 0.991393i | \(0.458208\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 66.0000 | 0.00361780 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13295.0 | 0.725623 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18315.0 | 0.995309 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4848.00 | 0.262329 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5632.00 | 0.303449 | 0.151724 | − | 0.988423i | \(-0.451517\pi\) | ||||
0.151724 | + | 0.988423i | \(0.451517\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5846.00 | 0.313636 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7200.00 | −0.384635 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2637.00 | −0.140275 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8536.00 | −0.452153 | −0.226076 | − | 0.974110i | \(-0.572590\pi\) | ||||
−0.226076 | + | 0.974110i | \(0.572590\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9724.00 | −0.512909 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6969.00 | −0.366046 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 380.000 | 0.0198758 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 11044.0 | 0.575238 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −32137.0 | −1.66691 | −0.833455 | − | 0.552588i | \(-0.813640\pi\) | ||||
−0.833455 | + | 0.552588i | \(0.813640\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1080.00 | 0.0557854 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 22968.0 | 1.18145 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7075.00 | 0.362426 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20329.0 | −1.03709 | −0.518543 | − | 0.855052i | \(-0.673525\pi\) | ||||
−0.518543 | + | 0.855052i | \(0.673525\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19837.0 | 1.00782 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −14760.0 | −0.746810 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12879.0 | 0.648972 | 0.324486 | − | 0.945890i | \(-0.394809\pi\) | ||||
0.324486 | + | 0.945890i | \(0.394809\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6680.00 | −0.335232 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 138.000 | 0.00689728 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16689.0 | −0.830737 | −0.415369 | − | 0.909653i | \(-0.636347\pi\) | ||||
−0.415369 | + | 0.909653i | \(0.636347\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11248.0 | 0.557632 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −32328.0 | −1.59623 | −0.798115 | − | 0.602505i | \(-0.794169\pi\) | ||||
−0.798115 | + | 0.602505i | \(0.794169\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15980.0 | 0.785855 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5533.00 | 0.271007 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5445.00 | 0.265629 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13966.0 | 0.678597 | 0.339299 | − | 0.940679i | \(-0.389810\pi\) | ||||
0.339299 | + | 0.940679i | \(0.389810\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −16648.0 | −0.805693 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −500.000 | −0.0241018 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14103.0 | −0.677123 | −0.338562 | − | 0.940944i | \(-0.609940\pi\) | ||||
−0.338562 | + | 0.940944i | \(0.609940\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 184.000 | 0.00879944 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28805.0 | 1.37212 | 0.686058 | − | 0.727547i | \(-0.259340\pi\) | ||||
0.686058 | + | 0.727547i | \(0.259340\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1290.00 | 0.0612073 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2475.00 | −0.116972 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3838.00 | 0.180681 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −26264.0 | −1.23160 | −0.615802 | − | 0.787901i | \(-0.711168\pi\) | ||||
−0.615802 | + | 0.787901i | \(0.711168\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9856.00 | −0.460383 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 29622.0 | 1.37830 | 0.689152 | − | 0.724617i | \(-0.257983\pi\) | ||||
0.689152 | + | 0.724617i | \(0.257983\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7575.00 | 0.351099 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 948.000 | 0.0437700 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −30118.0 | −1.38522 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1282.00 | 0.0587370 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 43016.0 | 1.96330 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3935.00 | 0.178912 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8129.00 | 0.368193 | 0.184096 | − | 0.982908i | \(-0.441064\pi\) | ||||
0.184096 | + | 0.982908i | \(0.441064\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −16668.0 | −0.752087 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −765.000 | −0.0343872 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10184.0 | 0.456046 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −11220.0 | −0.500544 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −35431.0 | −1.57469 | −0.787347 | − | 0.616511i | \(-0.788546\pi\) | ||||
−0.787347 | + | 0.616511i | \(0.788546\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16200.0 | 0.717290 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −17688.0 | −0.780243 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1988.00 | 0.0873661 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −345.000 | −0.0151052 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6556.00 | 0.285975 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −36025.0 | −1.56560 | −0.782801 | − | 0.622272i | \(-0.786210\pi\) | ||||
−0.782801 | + | 0.622272i | \(0.786210\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 35351.0 | 1.53063 | 0.765315 | − | 0.643656i | \(-0.222583\pi\) | ||||
0.765315 | + | 0.643656i | \(0.222583\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10620.0 | 0.458130 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −350.000 | −0.0150429 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24272.0 | 1.03938 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1254.00 | −0.0535022 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −33534.0 | −1.42551 | −0.712756 | − | 0.701412i | \(-0.752553\pi\) | ||||
−0.712756 | + | 0.701412i | \(0.752553\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −452.000 | −0.0191443 | −0.00957213 | − | 0.999954i | \(-0.503047\pi\) | ||||
−0.00957213 | + | 0.999954i | \(0.503047\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −200.000 | −0.00844013 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2379.00 | 0.100031 | 0.0500157 | − | 0.998748i | \(-0.484073\pi\) | ||||
0.0500157 | + | 0.998748i | \(0.484073\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −599.000 | −0.0250955 | −0.0125477 | − | 0.999921i | \(-0.503994\pi\) | ||||
−0.0125477 | + | 0.999921i | \(0.503994\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3304.00 | 0.137924 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 15030.0 | 0.625160 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8920.00 | 0.369688 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 46056.0 | 1.90195 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16746.0 | 0.689078 | 0.344539 | − | 0.938772i | \(-0.388035\pi\) | ||||
0.344539 | + | 0.938772i | \(0.388035\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 55700.0 | 2.28382 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −15720.0 | −0.642260 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3765.00 | 0.153278 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3981.00 | 0.161498 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −29356.0 | −1.18668 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1817.00 | −0.0731915 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −41754.0 | −1.67600 | −0.838001 | − | 0.545669i | \(-0.816276\pi\) | ||||
−0.838001 | + | 0.545669i | \(0.816276\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4070.00 | 0.162797 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8802.00 | −0.350841 | −0.175420 | − | 0.984494i | \(-0.556128\pi\) | ||||
−0.175420 | + | 0.984494i | \(0.556128\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7901.00 | −0.313828 | −0.156914 | − | 0.987612i | \(-0.550155\pi\) | ||||
−0.156914 | + | 0.987612i | \(0.550155\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4884.00 | −0.193317 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 43358.0 | 1.71022 | 0.855112 | − | 0.518443i | \(-0.173488\pi\) | ||||
0.855112 | + | 0.518443i | \(0.173488\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 140.000 | 0.00550306 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 11552.0 | 0.452510 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1768.00 | 0.0690164 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2622.00 | −0.102001 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −11902.0 | −0.461422 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 375.000 | 0.0144884 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5834.00 | −0.224630 | −0.112315 | − | 0.993673i | \(-0.535827\pi\) | ||||
−0.112315 | + | 0.993673i | \(0.535827\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 19052.0 | 0.731067 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −40940.0 | −1.56561 | −0.782806 | − | 0.622266i | \(-0.786212\pi\) | ||||
−0.782806 | + | 0.622266i | \(0.786212\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22756.0 | 0.867271 | 0.433636 | − | 0.901088i | \(-0.357231\pi\) | ||||
0.433636 | + | 0.901088i | \(0.357231\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2020.00 | −0.0767249 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −20814.0 | −0.787898 | −0.393949 | − | 0.919132i | \(-0.628891\pi\) | ||||
−0.393949 | + | 0.919132i | \(0.628891\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1032.00 | 0.0389338 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −622.000 | −0.0233870 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −26640.0 | −0.998291 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −160.000 | −0.00597565 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3496.00 | −0.130132 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 85749.0 | 3.18119 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 25245.0 | 0.933444 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3936.00 | 0.145052 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5860.00 | 0.215241 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 36661.0 | 1.34213 | 0.671063 | − | 0.741400i | \(-0.265838\pi\) | ||||
0.671063 | + | 0.741400i | \(0.265838\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9669.00 | −0.352806 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22340.0 | −0.812467 | −0.406233 | − | 0.913769i | \(-0.633158\pi\) | ||||
−0.406233 | + | 0.913769i | \(0.633158\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1006.00 | −0.0364663 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5360.00 | −0.193657 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4044.00 | −0.145632 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34112.0 | 1.22443 | 0.612215 | − | 0.790691i | \(-0.290279\pi\) | ||||
0.612215 | + | 0.790691i | \(0.290279\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −16952.0 | −0.606501 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −24358.0 | −0.868639 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1975.00 | 0.0702028 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3960.00 | 0.140306 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14133.0 | −0.499127 | −0.249563 | − | 0.968358i | \(-0.580287\pi\) | ||||
−0.249563 | + | 0.968358i | \(0.580287\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −24716.0 | −0.870069 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 17408.0 | 0.610839 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 450.000 | 0.0157397 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22442.0 | 0.782442 | 0.391221 | − | 0.920297i | \(-0.372053\pi\) | ||||
0.391221 | + | 0.920297i | \(0.372053\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2060.00 | 0.0715927 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −36076.0 | −1.24978 | −0.624891 | − | 0.780712i | \(-0.714856\pi\) | ||||
−0.624891 | + | 0.780712i | \(0.714856\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9361.00 | 0.323262 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2280.00 | 0.0784851 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 43316.0 | 1.48636 | 0.743179 | − | 0.669093i | \(-0.233317\pi\) | ||||
0.743179 | + | 0.669093i | \(0.233317\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −37772.0 | −1.29202 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 27264.0 | 0.929649 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8326.00 | −0.283007 | −0.141503 | − | 0.989938i | \(-0.545194\pi\) | ||||
−0.141503 | + | 0.989938i | \(0.545194\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3240.00 | −0.109784 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2264.00 | −0.0764731 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2202.00 | −0.0741463 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 62018.0 | 2.08177 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 19965.0 | 0.668082 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3860.00 | 0.128765 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −47244.0 | −1.57111 | −0.785556 | − | 0.618791i | \(-0.787623\pi\) | ||||
−0.785556 | + | 0.618791i | \(0.787623\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 13320.0 | 0.441589 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 40460.0 | 1.33720 | 0.668601 | − | 0.743621i | \(-0.266893\pi\) | ||||
0.668601 | + | 0.743621i | \(0.266893\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7977.00 | 0.262827 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3800.00 | 0.124818 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 42369.0 | 1.38741 | 0.693707 | − | 0.720257i | \(-0.255976\pi\) | ||||
0.693707 | + | 0.720257i | \(0.255976\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3216.00 | 0.104989 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4730.00 | 0.153942 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −56331.0 | −1.82775 | −0.913876 | − | 0.405994i | \(-0.866925\pi\) | ||||
−0.913876 | + | 0.405994i | \(0.866925\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 330.000 | 0.0106748 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4320.00 | −0.139318 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7544.00 | −0.242553 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −237.000 | −0.00759693 | −0.00379846 | − | 0.999993i | \(-0.501209\pi\) | ||||
−0.00379846 | + | 0.999993i | \(0.501209\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −35180.0 | −1.12427 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −16790.0 | −0.534954 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −36856.0 | −1.17075 | −0.585377 | − | 0.810761i | \(-0.699053\pi\) | ||||
−0.585377 | + | 0.810761i | \(0.699053\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 12008.0 | 0.380297 |
(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 | 1840.4.a.b.1.1 | 1 | ||
4.3 | odd | 2 | 230.4.a.b.1.1 | ✓ | 1 | ||
12.11 | even | 2 | 2070.4.a.n.1.1 | 1 | |||
20.3 | even | 4 | 1150.4.b.c.599.2 | 2 | |||
20.7 | even | 4 | 1150.4.b.c.599.1 | 2 | |||
20.19 | odd | 2 | 1150.4.a.f.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.4.a.b.1.1 | ✓ | 1 | 4.3 | odd | 2 | ||
1150.4.a.f.1.1 | 1 | 20.19 | odd | 2 | |||
1150.4.b.c.599.1 | 2 | 20.7 | even | 4 | |||
1150.4.b.c.599.2 | 2 | 20.3 | even | 4 | |||
1840.4.a.b.1.1 | 1 | 1.1 | even | 1 | trivial | ||
2070.4.a.n.1.1 | 1 | 12.11 | even | 2 |