Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [180,4,Mod(1,180)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(180, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("180.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 180 = 2^{2} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 180.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: | \(10.6203438010\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 20) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 180.1 |
$q$-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 | ||||||||
\(7\) | −16.0000 | −0.863919 | −0.431959 | − | 0.901893i | \(-0.642178\pi\) | ||||
−0.431959 | + | 0.901893i | \(0.642178\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 60.0000 | 1.64461 | 0.822304 | − | 0.569049i | \(-0.192689\pi\) | ||||
0.822304 | + | 0.569049i | \(0.192689\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 86.0000 | 1.83478 | 0.917389 | − | 0.397992i | \(-0.130293\pi\) | ||||
0.917389 | + | 0.397992i | \(0.130293\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −18.0000 | −0.256802 | −0.128401 | − | 0.991722i | \(-0.540985\pi\) | ||||
−0.128401 | + | 0.991722i | \(0.540985\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 44.0000 | 0.531279 | 0.265639 | − | 0.964072i | \(-0.414417\pi\) | ||||
0.265639 | + | 0.964072i | \(0.414417\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −48.0000 | −0.435161 | −0.217580 | − | 0.976042i | \(-0.569816\pi\) | ||||
−0.217580 | + | 0.976042i | \(0.569816\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 186.000 | 1.19101 | 0.595506 | − | 0.803351i | \(-0.296952\pi\) | ||||
0.595506 | + | 0.803351i | \(0.296952\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 176.000 | 1.01969 | 0.509847 | − | 0.860265i | \(-0.329702\pi\) | ||||
0.509847 | + | 0.860265i | \(0.329702\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 80.0000 | 0.386356 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 254.000 | 1.12858 | 0.564288 | − | 0.825578i | \(-0.309151\pi\) | ||||
0.564288 | + | 0.825578i | \(0.309151\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −186.000 | −0.708496 | −0.354248 | − | 0.935152i | \(-0.615263\pi\) | ||||
−0.354248 | + | 0.935152i | \(0.615263\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −100.000 | −0.354648 | −0.177324 | − | 0.984153i | \(-0.556744\pi\) | ||||
−0.177324 | + | 0.984153i | \(0.556744\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −168.000 | −0.521390 | −0.260695 | − | 0.965421i | \(-0.583952\pi\) | ||||
−0.260695 | + | 0.965421i | \(0.583952\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −87.0000 | −0.253644 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 498.000 | 1.29067 | 0.645335 | − | 0.763899i | \(-0.276718\pi\) | ||||
0.645335 | + | 0.763899i | \(0.276718\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −300.000 | −0.735491 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 252.000 | 0.556061 | 0.278031 | − | 0.960572i | \(-0.410318\pi\) | ||||
0.278031 | + | 0.960572i | \(0.410318\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −58.0000 | −0.121740 | −0.0608700 | − | 0.998146i | \(-0.519388\pi\) | ||||
−0.0608700 | + | 0.998146i | \(0.519388\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −430.000 | −0.820537 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1036.00 | −1.88907 | −0.944534 | − | 0.328414i | \(-0.893486\pi\) | ||||
−0.944534 | + | 0.328414i | \(0.893486\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −168.000 | −0.280816 | −0.140408 | − | 0.990094i | \(-0.544841\pi\) | ||||
−0.140408 | + | 0.990094i | \(0.544841\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 506.000 | 0.811272 | 0.405636 | − | 0.914035i | \(-0.367050\pi\) | ||||
0.405636 | + | 0.914035i | \(0.367050\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −960.000 | −1.42081 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 272.000 | 0.387372 | 0.193686 | − | 0.981064i | \(-0.437956\pi\) | ||||
0.193686 | + | 0.981064i | \(0.437956\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −948.000 | −1.25369 | −0.626846 | − | 0.779143i | \(-0.715655\pi\) | ||||
−0.626846 | + | 0.779143i | \(0.715655\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 90.0000 | 0.114846 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1014.00 | 1.20768 | 0.603841 | − | 0.797104i | \(-0.293636\pi\) | ||||
0.603841 | + | 0.797104i | \(0.293636\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1376.00 | −1.58510 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −220.000 | −0.237595 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −766.000 | −0.801809 | −0.400905 | − | 0.916120i | \(-0.631304\pi\) | ||||
−0.400905 | + | 0.916120i | \(0.631304\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1314.00 | 1.29453 | 0.647267 | − | 0.762264i | \(-0.275912\pi\) | ||||
0.647267 | + | 0.762264i | \(0.275912\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −448.000 | −0.428570 | −0.214285 | − | 0.976771i | \(-0.568742\pi\) | ||||
−0.214285 | + | 0.976771i | \(0.568742\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1548.00 | −1.39861 | −0.699303 | − | 0.714826i | \(-0.746506\pi\) | ||||
−0.699303 | + | 0.714826i | \(0.746506\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 278.000 | 0.244290 | 0.122145 | − | 0.992512i | \(-0.461023\pi\) | ||||
0.122145 | + | 0.992512i | \(0.461023\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 558.000 | 0.464533 | 0.232266 | − | 0.972652i | \(-0.425386\pi\) | ||||
0.232266 | + | 0.972652i | \(0.425386\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 240.000 | 0.194610 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 288.000 | 0.221856 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2269.00 | 1.70473 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 344.000 | 0.240355 | 0.120177 | − | 0.992752i | \(-0.461654\pi\) | ||||
0.120177 | + | 0.992752i | \(0.461654\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −780.000 | −0.520221 | −0.260110 | − | 0.965579i | \(-0.583759\pi\) | ||||
−0.260110 | + | 0.965579i | \(0.583759\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −704.000 | −0.458982 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −666.000 | −0.415330 | −0.207665 | − | 0.978200i | \(-0.566586\pi\) | ||||
−0.207665 | + | 0.978200i | \(0.566586\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 884.000 | 0.539424 | 0.269712 | − | 0.962941i | \(-0.413072\pi\) | ||||
0.269712 | + | 0.962941i | \(0.413072\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5160.00 | 3.01749 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −930.000 | −0.532637 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 114.000 | 0.0626795 | 0.0313397 | − | 0.999509i | \(-0.490023\pi\) | ||||
0.0313397 | + | 0.999509i | \(0.490023\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −40.0000 | −0.0215573 | −0.0107787 | − | 0.999942i | \(-0.503431\pi\) | ||||
−0.0107787 | + | 0.999942i | \(0.503431\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −880.000 | −0.456021 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −154.000 | −0.0782837 | −0.0391418 | − | 0.999234i | \(-0.512462\pi\) | ||||
−0.0391418 | + | 0.999234i | \(0.512462\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 768.000 | 0.375943 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2180.00 | 1.04755 | 0.523775 | − | 0.851856i | \(-0.324523\pi\) | ||||
0.523775 | + | 0.851856i | \(0.324523\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3696.00 | −1.71261 | −0.856303 | − | 0.516474i | \(-0.827244\pi\) | ||||
−0.856303 | + | 0.516474i | \(0.827244\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5199.00 | 2.36641 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1302.00 | −0.572192 | −0.286096 | − | 0.958201i | \(-0.592358\pi\) | ||||
−0.286096 | + | 0.958201i | \(0.592358\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −400.000 | −0.172784 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4308.00 | 1.79885 | 0.899427 | − | 0.437070i | \(-0.143984\pi\) | ||||
0.899427 | + | 0.437070i | \(0.143984\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1550.00 | 0.636523 | 0.318261 | − | 0.948003i | \(-0.396901\pi\) | ||||
0.318261 | + | 0.948003i | \(0.396901\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1270.00 | −0.504715 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1080.00 | −0.422339 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −48.0000 | −0.0181841 | −0.00909204 | − | 0.999959i | \(-0.502894\pi\) | ||||
−0.00909204 | + | 0.999959i | \(0.502894\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1058.00 | 0.394593 | 0.197297 | − | 0.980344i | \(-0.436784\pi\) | ||||
0.197297 | + | 0.980344i | \(0.436784\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3714.00 | 1.34321 | 0.671603 | − | 0.740911i | \(-0.265606\pi\) | ||||
0.671603 | + | 0.740911i | \(0.265606\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1768.00 | −0.629800 | −0.314900 | − | 0.949125i | \(-0.601971\pi\) | ||||
−0.314900 | + | 0.949125i | \(0.601971\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2976.00 | −1.02894 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 930.000 | 0.316849 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2640.00 | 0.873745 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4036.00 | −1.31682 | −0.658412 | − | 0.752658i | \(-0.728771\pi\) | ||||
−0.658412 | + | 0.752658i | \(0.728771\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 500.000 | 0.158603 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2816.00 | −0.880933 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1548.00 | −0.471175 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 680.000 | 0.204198 | 0.102099 | − | 0.994774i | \(-0.467444\pi\) | ||||
0.102099 | + | 0.994774i | \(0.467444\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2388.00 | −0.698225 | −0.349113 | − | 0.937081i | \(-0.613517\pi\) | ||||
−0.349113 | + | 0.937081i | \(0.613517\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3874.00 | −1.11791 | −0.558954 | − | 0.829198i | \(-0.688797\pi\) | ||||
−0.558954 | + | 0.829198i | \(0.688797\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3162.00 | −0.889054 | −0.444527 | − | 0.895766i | \(-0.646628\pi\) | ||||
−0.444527 | + | 0.895766i | \(0.646628\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 840.000 | 0.233173 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5424.00 | −1.46799 | −0.733995 | − | 0.679155i | \(-0.762346\pi\) | ||||
−0.733995 | + | 0.679155i | \(0.762346\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3886.00 | −1.03867 | −0.519335 | − | 0.854571i | \(-0.673820\pi\) | ||||
−0.519335 | + | 0.854571i | \(0.673820\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 435.000 | 0.113433 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3784.00 | 0.974778 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5100.00 | 1.28251 | 0.641253 | − | 0.767329i | \(-0.278415\pi\) | ||||
0.641253 | + | 0.767329i | \(0.278415\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2880.00 | −0.715668 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2178.00 | −0.528638 | −0.264319 | − | 0.964435i | \(-0.585147\pi\) | ||||
−0.264319 | + | 0.964435i | \(0.585147\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4064.00 | −0.974999 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6144.00 | 1.44051 | 0.720257 | − | 0.693707i | \(-0.244024\pi\) | ||||
0.720257 | + | 0.693707i | \(0.244024\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2490.00 | −0.577206 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −822.000 | −0.186313 | −0.0931566 | − | 0.995651i | \(-0.529696\pi\) | ||||
−0.0931566 | + | 0.995651i | \(0.529696\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8480.00 | 1.90082 | 0.950412 | − | 0.310994i | \(-0.100662\pi\) | ||||
0.950412 | + | 0.310994i | \(0.100662\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1500.00 | 0.328921 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1138.00 | −0.246844 | −0.123422 | − | 0.992354i | \(-0.539387\pi\) | ||||
−0.123422 | + | 0.992354i | \(0.539387\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5706.00 | −1.21136 | −0.605679 | − | 0.795709i | \(-0.707098\pi\) | ||||
−0.605679 | + | 0.795709i | \(0.707098\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3028.00 | −0.636028 | −0.318014 | − | 0.948086i | \(-0.603016\pi\) | ||||
−0.318014 | + | 0.948086i | \(0.603016\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2976.00 | 0.612083 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4589.00 | −0.934053 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3390.00 | −0.675925 | −0.337962 | − | 0.941160i | \(-0.609738\pi\) | ||||
−0.337962 | + | 0.941160i | \(0.609738\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1260.00 | −0.248678 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4128.00 | −0.798423 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1600.00 | 0.306387 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 290.000 | 0.0544438 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4156.00 | −0.772624 | −0.386312 | − | 0.922368i | \(-0.626251\pi\) | ||||
−0.386312 | + | 0.922368i | \(0.626251\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6552.00 | −1.19463 | −0.597315 | − | 0.802007i | \(-0.703766\pi\) | ||||
−0.597315 | + | 0.802007i | \(0.703766\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1366.00 | −0.246680 | −0.123340 | − | 0.992364i | \(-0.539361\pi\) | ||||
−0.123340 | + | 0.992364i | \(0.539361\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2598.00 | −0.460310 | −0.230155 | − | 0.973154i | \(-0.573923\pi\) | ||||
−0.230155 | + | 0.973154i | \(0.573923\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11160.0 | 1.95875 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −792.000 | −0.136434 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2150.00 | 0.366956 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2688.00 | 0.450438 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3292.00 | −0.546661 | −0.273330 | − | 0.961920i | \(-0.588125\pi\) | ||||
−0.273330 | + | 0.961920i | \(0.588125\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5180.00 | 0.844817 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6194.00 | 1.00121 | 0.500606 | − | 0.865675i | \(-0.333110\pi\) | ||||
0.500606 | + | 0.865675i | \(0.333110\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10560.0 | 1.67700 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6880.00 | 1.08305 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10020.0 | 1.55015 | 0.775075 | − | 0.631870i | \(-0.217712\pi\) | ||||
0.775075 | + | 0.631870i | \(0.217712\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3130.00 | −0.480072 | −0.240036 | − | 0.970764i | \(-0.577159\pi\) | ||||
−0.240036 | + | 0.970764i | \(0.577159\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4194.00 | −0.632363 | −0.316181 | − | 0.948699i | \(-0.602401\pi\) | ||||
−0.316181 | + | 0.948699i | \(0.602401\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 840.000 | 0.125585 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4104.00 | 0.603345 | 0.301672 | − | 0.953412i | \(-0.402455\pi\) | ||||
0.301672 | + | 0.953412i | \(0.402455\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4923.00 | −0.717743 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2530.00 | −0.362812 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7496.00 | 1.06618 | 0.533090 | − | 0.846059i | \(-0.321031\pi\) | ||||
0.533090 | + | 0.846059i | \(0.321031\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7968.00 | −1.11503 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5842.00 | −0.810958 | −0.405479 | − | 0.914104i | \(-0.632895\pi\) | ||||
−0.405479 | + | 0.914104i | \(0.632895\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 15996.0 | 2.18524 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −412.000 | −0.0558391 | −0.0279195 | − | 0.999610i | \(-0.508888\pi\) | ||||
−0.0279195 | + | 0.999610i | \(0.508888\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2568.00 | −0.342607 | −0.171304 | − | 0.985218i | \(-0.554798\pi\) | ||||
−0.171304 | + | 0.985218i | \(0.554798\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4800.00 | 0.635404 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −13086.0 | −1.70562 | −0.852810 | − | 0.522221i | \(-0.825104\pi\) | ||||
−0.852810 | + | 0.522221i | \(0.825104\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 864.000 | 0.111750 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1360.00 | −0.173238 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10454.0 | 1.32159 | 0.660795 | − | 0.750566i | \(-0.270219\pi\) | ||||
0.660795 | + | 0.750566i | \(0.270219\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10830.0 | 1.34869 | 0.674345 | − | 0.738417i | \(-0.264426\pi\) | ||||
0.674345 | + | 0.738417i | \(0.264426\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15136.0 | 1.87091 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 15240.0 | 1.85607 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8566.00 | −1.03560 | −0.517801 | − | 0.855501i | \(-0.673249\pi\) | ||||
−0.517801 | + | 0.855501i | \(0.673249\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4032.00 | −0.480392 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4740.00 | 0.560669 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13884.0 | −1.61880 | −0.809401 | − | 0.587257i | \(-0.800208\pi\) | ||||
−0.809401 | + | 0.587257i | \(0.800208\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4286.00 | 0.496168 | 0.248084 | − | 0.968738i | \(-0.420199\pi\) | ||||
0.248084 | + | 0.968738i | \(0.420199\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −450.000 | −0.0513605 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 928.000 | 0.105173 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6336.00 | −0.708108 | −0.354054 | − | 0.935225i | \(-0.615197\pi\) | ||||
−0.354054 | + | 0.935225i | \(0.615197\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8974.00 | −0.995988 | −0.497994 | − | 0.867180i | \(-0.665930\pi\) | ||||
−0.497994 | + | 0.867180i | \(0.665930\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2112.00 | −0.231191 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2968.00 | −0.322676 | −0.161338 | − | 0.986899i | \(-0.551581\pi\) | ||||
−0.161338 | + | 0.986899i | \(0.551581\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12372.0 | 1.32689 | 0.663444 | − | 0.748226i | \(-0.269094\pi\) | ||||
0.663444 | + | 0.748226i | \(0.269094\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5070.00 | −0.540092 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11394.0 | −1.19759 | −0.598793 | − | 0.800904i | \(-0.704353\pi\) | ||||
−0.598793 | + | 0.800904i | \(0.704353\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11160.0 | −1.16520 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6880.00 | 0.708878 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −358.000 | −0.0366445 | −0.0183222 | − | 0.999832i | \(-0.505832\pi\) | ||||
−0.0183222 | + | 0.999832i | \(0.505832\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7530.00 | 0.760753 | 0.380376 | − | 0.924832i | \(-0.375794\pi\) | ||||
0.380376 | + | 0.924832i | \(0.375794\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13768.0 | −1.38197 | −0.690986 | − | 0.722868i | \(-0.742823\pi\) | ||||
−0.690986 | + | 0.722868i | \(0.742823\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −13380.0 | −1.32581 | −0.662904 | − | 0.748704i | \(-0.730676\pi\) | ||||
−0.662904 | + | 0.748704i | \(0.730676\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16576.0 | 1.63200 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6000.00 | −0.583256 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1100.00 | 0.106256 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6336.00 | 0.604383 | 0.302191 | − | 0.953247i | \(-0.402282\pi\) | ||||
0.302191 | + | 0.953247i | \(0.402282\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21844.0 | 2.07069 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3830.00 | 0.358580 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5008.00 | −0.465984 | −0.232992 | − | 0.972479i | \(-0.574852\pi\) | ||||
−0.232992 | + | 0.972479i | \(0.574852\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12900.0 | −1.18568 | −0.592840 | − | 0.805320i | \(-0.701993\pi\) | ||||
−0.592840 | + | 0.805320i | \(0.701993\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3348.00 | −0.305855 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2688.00 | 0.242602 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8116.00 | −0.728100 | −0.364050 | − | 0.931379i | \(-0.618606\pi\) | ||||
−0.364050 | + | 0.931379i | \(0.618606\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4944.00 | 0.438255 | 0.219127 | − | 0.975696i | \(-0.429679\pi\) | ||||
0.219127 | + | 0.975696i | \(0.429679\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6570.00 | −0.578933 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5466.00 | 0.475985 | 0.237992 | − | 0.971267i | \(-0.423511\pi\) | ||||
0.237992 | + | 0.971267i | \(0.423511\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8096.00 | −0.700873 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2240.00 | 0.191663 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10080.0 | −0.857481 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10074.0 | −0.847121 | −0.423560 | − | 0.905868i | \(-0.639220\pi\) | ||||
−0.423560 | + | 0.905868i | \(0.639220\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13828.0 | −1.15613 | −0.578065 | − | 0.815991i | \(-0.696192\pi\) | ||||
−0.578065 | + | 0.815991i | \(0.696192\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3168.00 | −0.261860 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9863.00 | −0.810635 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −15996.0 | −1.29993 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7740.00 | 0.625475 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5220.00 | −0.417145 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15226.0 | −1.21001 | −0.605006 | − | 0.796221i | \(-0.706829\pi\) | ||||
−0.605006 | + | 0.796221i | \(0.706829\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1390.00 | −0.109250 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13228.0 | −1.03398 | −0.516991 | − | 0.855991i | \(-0.672948\pi\) | ||||
−0.516991 | + | 0.855991i | \(0.672948\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8184.00 | 0.632759 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4352.00 | −0.334658 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8490.00 | 0.645840 | 0.322920 | − | 0.946426i | \(-0.395336\pi\) | ||||
0.322920 | + | 0.946426i | \(0.395336\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8600.00 | −0.650700 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10284.0 | 0.769838 | 0.384919 | − | 0.922950i | \(-0.374229\pi\) | ||||
0.384919 | + | 0.922950i | \(0.374229\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2790.00 | −0.207745 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1770.00 | −0.130408 | −0.0652041 | − | 0.997872i | \(-0.520770\pi\) | ||||
−0.0652041 | + | 0.997872i | \(0.520770\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6068.00 | 0.444725 | 0.222362 | − | 0.974964i | \(-0.428623\pi\) | ||||
0.222362 | + | 0.974964i | \(0.428623\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1200.00 | −0.0870321 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21506.0 | 1.55166 | 0.775829 | − | 0.630943i | \(-0.217332\pi\) | ||||
0.775829 | + | 0.630943i | \(0.217332\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15168.0 | 1.08309 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 29880.0 | 2.12265 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12108.0 | −0.851364 | −0.425682 | − | 0.904873i | \(-0.639966\pi\) | ||||
−0.425682 | + | 0.904873i | \(0.639966\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7744.00 | 0.541742 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −15474.0 | −1.07157 | −0.535785 | − | 0.844354i | \(-0.679984\pi\) | ||||
−0.535785 | + | 0.844354i | \(0.679984\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1440.00 | −0.0992172 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2520.00 | 0.171894 | 0.0859469 | − | 0.996300i | \(-0.472608\pi\) | ||||
0.0859469 | + | 0.996300i | \(0.472608\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12790.0 | −0.868078 | −0.434039 | − | 0.900894i | \(-0.642912\pi\) | ||||
−0.434039 | + | 0.900894i | \(0.642912\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −11345.0 | −0.762380 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11576.0 | 0.774062 | 0.387031 | − | 0.922067i | \(-0.373501\pi\) | ||||
0.387031 | + | 0.922067i | \(0.373501\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −14448.0 | −0.956634 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20126.0 | 1.32607 | 0.663035 | − | 0.748588i | \(-0.269268\pi\) | ||||
0.663035 | + | 0.748588i | \(0.269268\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 27942.0 | 1.82318 | 0.911590 | − | 0.411100i | \(-0.134855\pi\) | ||||
0.911590 | + | 0.411100i | \(0.134855\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22540.0 | −1.46358 | −0.731792 | − | 0.681528i | \(-0.761316\pi\) | ||||
−0.731792 | + | 0.681528i | \(0.761316\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −16224.0 | −1.04334 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4572.00 | −0.289821 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5128.00 | −0.323522 | −0.161761 | − | 0.986830i | \(-0.551717\pi\) | ||||
−0.161761 | + | 0.986830i | \(0.551717\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1720.00 | −0.107490 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7482.00 | −0.465381 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12798.0 | 0.788597 | 0.394298 | − | 0.918982i | \(-0.370988\pi\) | ||||
0.394298 | + | 0.918982i | \(0.370988\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21148.0 | −1.29704 | −0.648519 | − | 0.761198i | \(-0.724611\pi\) | ||||
−0.648519 | + | 0.761198i | \(0.724611\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16464.0 | −1.00041 | −0.500206 | − | 0.865906i | \(-0.666742\pi\) | ||||
−0.500206 | + | 0.865906i | \(0.666742\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15120.0 | 0.914502 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 24234.0 | 1.45230 | 0.726148 | − | 0.687538i | \(-0.241309\pi\) | ||||
0.726148 | + | 0.687538i | \(0.241309\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3900.00 | 0.232650 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22836.0 | 1.34987 | 0.674935 | − | 0.737877i | \(-0.264172\pi\) | ||||
0.674935 | + | 0.737877i | \(0.264172\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26318.0 | 1.54864 | 0.774320 | − | 0.632794i | \(-0.218092\pi\) | ||||
0.774320 | + | 0.632794i | \(0.218092\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3520.00 | 0.205263 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8928.00 | −0.518281 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3480.00 | −0.200214 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28802.0 | 1.64968 | 0.824841 | − | 0.565365i | \(-0.191265\pi\) | ||||
0.824841 | + | 0.565365i | \(0.191265\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2526.00 | −0.143400 | −0.0717002 | − | 0.997426i | \(-0.522842\pi\) | ||||
−0.0717002 | + | 0.997426i | \(0.522842\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12256.0 | 0.692698 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23076.0 | 1.29279 | 0.646397 | − | 0.763001i | \(-0.276275\pi\) | ||||
0.646397 | + | 0.763001i | \(0.276275\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3330.00 | 0.185741 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 42828.0 | 2.36809 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7868.00 | 0.433159 | 0.216579 | − | 0.976265i | \(-0.430510\pi\) | ||||
0.216579 | + | 0.976265i | \(0.430510\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4420.00 | −0.241238 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3348.00 | 0.181943 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21510.0 | −1.15895 | −0.579473 | − | 0.814991i | \(-0.696742\pi\) | ||||
−0.579473 | + | 0.814991i | \(0.696742\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11176.0 | 0.599589 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −21024.0 | −1.11837 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 30014.0 | 1.58984 | 0.794922 | − | 0.606712i | \(-0.207512\pi\) | ||||
0.794922 | + | 0.606712i | \(0.207512\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8448.00 | −0.443731 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −25800.0 | −1.34946 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 816.000 | 0.0423250 | 0.0211625 | − | 0.999776i | \(-0.493263\pi\) | ||||
0.0211625 | + | 0.999776i | \(0.493263\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7168.00 | 0.370250 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4650.00 | 0.238202 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9952.00 | −0.507702 | −0.253851 | − | 0.967243i | \(-0.581697\pi\) | ||||
−0.253851 | + | 0.967243i | \(0.581697\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1800.00 | 0.0910744 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −33946.0 | −1.71054 | −0.855269 | − | 0.518185i | \(-0.826608\pi\) | ||||
−0.855269 | + | 0.518185i | \(0.826608\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −62160.0 | −3.10677 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23420.0 | 1.16579 | 0.582895 | − | 0.812548i | \(-0.301920\pi\) | ||||
0.582895 | + | 0.812548i | \(0.301920\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14592.0 | 0.720496 | 0.360248 | − | 0.932857i | \(-0.382692\pi\) | ||||
0.360248 | + | 0.932857i | \(0.382692\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −570.000 | −0.0280311 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 24768.0 | 1.20828 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9056.00 | 0.440024 | 0.220012 | − | 0.975497i | \(-0.429390\pi\) | ||||
0.220012 | + | 0.975497i | \(0.429390\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 200.000 | 0.00964072 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17554.0 | −0.842815 | −0.421408 | − | 0.906871i | \(-0.638464\pi\) | ||||
−0.421408 | + | 0.906871i | \(0.638464\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 36438.0 | 1.73571 | 0.867856 | − | 0.496816i | \(-0.165498\pi\) | ||||
0.867856 | + | 0.496816i | \(0.165498\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4448.00 | −0.211046 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 21672.0 | 1.02025 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9022.00 | −0.423071 | −0.211536 | − | 0.977370i | \(-0.567846\pi\) | ||||
−0.211536 | + | 0.977370i | \(0.567846\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1470.00 | −0.0683987 | −0.0341994 | − | 0.999415i | \(-0.510888\pi\) | ||||
−0.0341994 | + | 0.999415i | \(0.510888\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4400.00 | 0.203939 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8184.00 | −0.376409 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10080.0 | −0.461832 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 770.000 | 0.0350095 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5252.00 | 0.237883 | 0.118941 | − | 0.992901i | \(-0.462050\pi\) | ||||
0.118941 | + | 0.992901i | \(0.462050\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8928.00 | −0.401319 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4988.00 | −0.223366 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12294.0 | −0.546394 | −0.273197 | − | 0.961958i | \(-0.588081\pi\) | ||||
−0.273197 | + | 0.961958i | \(0.588081\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3024.00 | 0.133894 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 30360.0 | 1.33422 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3840.00 | −0.168127 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15546.0 | −0.675610 | −0.337805 | − | 0.941216i | \(-0.609684\pi\) | ||||
−0.337805 | + | 0.941216i | \(0.609684\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19364.0 | 0.838424 | 0.419212 | − | 0.907888i | \(-0.362306\pi\) | ||||
0.419212 | + | 0.907888i | \(0.362306\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10900.0 | −0.468479 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4400.00 | −0.188417 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7314.00 | 0.310914 | 0.155457 | − | 0.987843i | \(-0.450315\pi\) | ||||
0.155457 | + | 0.987843i | \(0.450315\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11984.0 | 0.507577 | 0.253789 | − | 0.967260i | \(-0.418323\pi\) | ||||
0.253789 | + | 0.967260i | \(0.418323\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −13500.0 | −0.567643 | −0.283822 | − | 0.958877i | \(-0.591602\pi\) | ||||
−0.283822 | + | 0.958877i | \(0.591602\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −44602.0 | −1.86863 | −0.934313 | − | 0.356453i | \(-0.883986\pi\) | ||||
−0.934313 | + | 0.356453i | \(0.883986\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1566.00 | 0.0651365 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18480.0 | 0.765900 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −35448.0 | −1.45864 | −0.729321 | − | 0.684172i | \(-0.760164\pi\) | ||||
−0.729321 | + | 0.684172i | \(0.760164\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10207.0 | 0.418508 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −25995.0 | −1.05829 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −36304.0 | −1.47275 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12192.0 | −0.491112 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12590.0 | 0.505362 | 0.252681 | − | 0.967550i | \(-0.418688\pi\) | ||||
0.252681 | + | 0.967550i | \(0.418688\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −24906.0 | −0.992734 | −0.496367 | − | 0.868113i | \(-0.665333\pi\) | ||||
−0.496367 | + | 0.868113i | \(0.665333\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23204.0 | 0.921665 | 0.460833 | − | 0.887487i | \(-0.347551\pi\) | ||||
0.460833 | + | 0.887487i | \(0.347551\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19848.0 | −0.782890 | −0.391445 | − | 0.920202i | \(-0.628025\pi\) | ||||
−0.391445 | + | 0.920202i | \(0.628025\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6510.00 | 0.255892 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 16320.0 | 0.637075 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −89096.0 | −3.46602 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2000.00 | 0.0772712 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27542.0 | 1.06046 | 0.530232 | − | 0.847852i | \(-0.322105\pi\) | ||||
0.530232 | + | 0.847852i | \(0.322105\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20718.0 | 0.792290 | 0.396145 | − | 0.918188i | \(-0.370348\pi\) | ||||
0.396145 | + | 0.918188i | \(0.370348\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25172.0 | 0.959349 | 0.479675 | − | 0.877446i | \(-0.340755\pi\) | ||||
0.479675 | + | 0.877446i | \(0.340755\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12864.0 | 0.486957 | 0.243478 | − | 0.969906i | \(-0.421711\pi\) | ||||
0.243478 | + | 0.969906i | \(0.421711\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5504.00 | −0.207647 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7392.00 | −0.277003 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −21540.0 | −0.804472 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 32736.0 | 1.21447 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8964.00 | −0.331447 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7750.00 | −0.284662 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −23092.0 | −0.845377 | −0.422689 | − | 0.906275i | \(-0.638914\pi\) | ||||
−0.422689 | + | 0.906275i | \(0.638914\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14208.0 | 0.516720 | 0.258360 | − | 0.966049i | \(-0.416818\pi\) | ||||
0.258360 | + | 0.966049i | \(0.416818\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −56880.0 | −2.06183 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 12480.0 | 0.449428 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26584.0 | −0.954217 | −0.477108 | − | 0.878844i | \(-0.658315\pi\) | ||||
−0.477108 | + | 0.878844i | \(0.658315\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −14448.0 | −0.515235 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6350.00 | 0.225715 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −162.000 | −0.00572126 | −0.00286063 | − | 0.999996i | \(-0.500911\pi\) | ||||
−0.00286063 | + | 0.999996i | \(0.500911\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3828.00 | −0.134756 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5400.00 | 0.188876 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −29734.0 | −1.03668 | −0.518339 | − | 0.855175i | \(-0.673449\pi\) | ||||
−0.518339 | + | 0.855175i | \(0.673449\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −17142.0 | −0.593850 | −0.296925 | − | 0.954901i | \(-0.595961\pi\) | ||||
−0.296925 | + | 0.954901i | \(0.595961\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8928.00 | 0.308309 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −26436.0 | −0.907133 | −0.453566 | − | 0.891223i | \(-0.649848\pi\) | ||||
−0.453566 | + | 0.891223i | \(0.649848\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 43516.0 | 1.48850 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −27882.0 | −0.947730 | −0.473865 | − | 0.880598i | \(-0.657142\pi\) | ||||
−0.473865 | + | 0.880598i | \(0.657142\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 240.000 | 0.00813217 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10656.0 | 0.358811 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1185.00 | 0.0397771 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5290.00 | −0.176467 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12656.0 | 0.420879 | 0.210439 | − | 0.977607i | \(-0.432511\pi\) | ||||
0.210439 | + | 0.977607i | \(0.432511\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2916.00 | −0.0963737 | −0.0481869 | − | 0.998838i | \(-0.515344\pi\) | ||||
−0.0481869 | + | 0.998838i | \(0.515344\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14144.0 | −0.466018 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6894.00 | 0.225751 | 0.112875 | − | 0.993609i | \(-0.463994\pi\) | ||||
0.112875 | + | 0.993609i | \(0.463994\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 60840.0 | 1.98616 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 45264.0 | 1.46866 | 0.734332 | − | 0.678790i | \(-0.237495\pi\) | ||||
0.734332 | + | 0.678790i | \(0.237495\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18570.0 | −0.600700 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4800.00 | 0.154329 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 52016.0 | 1.66735 | 0.833674 | − | 0.552256i | \(-0.186233\pi\) | ||||
0.833674 | + | 0.552256i | \(0.186233\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8840.00 | 0.281655 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13858.0 | −0.440208 | −0.220104 | − | 0.975476i | \(-0.570640\pi\) | ||||
−0.220104 | + | 0.975476i | \(0.570640\pi\) | |||||||
\(998\) | 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 | 180.4.a.a.1.1 | 1 | ||
3.2 | odd | 2 | 20.4.a.a.1.1 | ✓ | 1 | ||
4.3 | odd | 2 | 720.4.a.k.1.1 | 1 | |||
5.2 | odd | 4 | 900.4.d.k.649.1 | 2 | |||
5.3 | odd | 4 | 900.4.d.k.649.2 | 2 | |||
5.4 | even | 2 | 900.4.a.m.1.1 | 1 | |||
9.2 | odd | 6 | 1620.4.i.d.1081.1 | 2 | |||
9.4 | even | 3 | 1620.4.i.j.541.1 | 2 | |||
9.5 | odd | 6 | 1620.4.i.d.541.1 | 2 | |||
9.7 | even | 3 | 1620.4.i.j.1081.1 | 2 | |||
12.11 | even | 2 | 80.4.a.c.1.1 | 1 | |||
15.2 | even | 4 | 100.4.c.a.49.1 | 2 | |||
15.8 | even | 4 | 100.4.c.a.49.2 | 2 | |||
15.14 | odd | 2 | 100.4.a.a.1.1 | 1 | |||
21.2 | odd | 6 | 980.4.i.e.361.1 | 2 | |||
21.5 | even | 6 | 980.4.i.n.361.1 | 2 | |||
21.11 | odd | 6 | 980.4.i.e.961.1 | 2 | |||
21.17 | even | 6 | 980.4.i.n.961.1 | 2 | |||
21.20 | even | 2 | 980.4.a.c.1.1 | 1 | |||
24.5 | odd | 2 | 320.4.a.d.1.1 | 1 | |||
24.11 | even | 2 | 320.4.a.k.1.1 | 1 | |||
33.32 | even | 2 | 2420.4.a.d.1.1 | 1 | |||
48.5 | odd | 4 | 1280.4.d.n.641.1 | 2 | |||
48.11 | even | 4 | 1280.4.d.c.641.2 | 2 | |||
48.29 | odd | 4 | 1280.4.d.n.641.2 | 2 | |||
48.35 | even | 4 | 1280.4.d.c.641.1 | 2 | |||
60.23 | odd | 4 | 400.4.c.j.49.1 | 2 | |||
60.47 | odd | 4 | 400.4.c.j.49.2 | 2 | |||
60.59 | even | 2 | 400.4.a.o.1.1 | 1 | |||
120.29 | odd | 2 | 1600.4.a.bl.1.1 | 1 | |||
120.59 | even | 2 | 1600.4.a.p.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
20.4.a.a.1.1 | ✓ | 1 | 3.2 | odd | 2 | ||
80.4.a.c.1.1 | 1 | 12.11 | even | 2 | |||
100.4.a.a.1.1 | 1 | 15.14 | odd | 2 | |||
100.4.c.a.49.1 | 2 | 15.2 | even | 4 | |||
100.4.c.a.49.2 | 2 | 15.8 | even | 4 | |||
180.4.a.a.1.1 | 1 | 1.1 | even | 1 | trivial | ||
320.4.a.d.1.1 | 1 | 24.5 | odd | 2 | |||
320.4.a.k.1.1 | 1 | 24.11 | even | 2 | |||
400.4.a.o.1.1 | 1 | 60.59 | even | 2 | |||
400.4.c.j.49.1 | 2 | 60.23 | odd | 4 | |||
400.4.c.j.49.2 | 2 | 60.47 | odd | 4 | |||
720.4.a.k.1.1 | 1 | 4.3 | odd | 2 | |||
900.4.a.m.1.1 | 1 | 5.4 | even | 2 | |||
900.4.d.k.649.1 | 2 | 5.2 | odd | 4 | |||
900.4.d.k.649.2 | 2 | 5.3 | odd | 4 | |||
980.4.a.c.1.1 | 1 | 21.20 | even | 2 | |||
980.4.i.e.361.1 | 2 | 21.2 | odd | 6 | |||
980.4.i.e.961.1 | 2 | 21.11 | odd | 6 | |||
980.4.i.n.361.1 | 2 | 21.5 | even | 6 | |||
980.4.i.n.961.1 | 2 | 21.17 | even | 6 | |||
1280.4.d.c.641.1 | 2 | 48.35 | even | 4 | |||
1280.4.d.c.641.2 | 2 | 48.11 | even | 4 | |||
1280.4.d.n.641.1 | 2 | 48.5 | odd | 4 | |||
1280.4.d.n.641.2 | 2 | 48.29 | odd | 4 | |||
1600.4.a.p.1.1 | 1 | 120.59 | even | 2 | |||
1600.4.a.bl.1.1 | 1 | 120.29 | odd | 2 | |||
1620.4.i.d.541.1 | 2 | 9.5 | odd | 6 | |||
1620.4.i.d.1081.1 | 2 | 9.2 | odd | 6 | |||
1620.4.i.j.541.1 | 2 | 9.4 | even | 3 | |||
1620.4.i.j.1081.1 | 2 | 9.7 | even | 3 | |||
2420.4.a.d.1.1 | 1 | 33.32 | even | 2 |