Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,4,Mod(1,320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(320, 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("320.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.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: | \(18.8806112018\) |
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 | \(\chi\) | \(=\) | 320.1 |
$q$-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 | ||||||||
\(7\) | −16.0000 | −0.863919 | −0.431959 | − | 0.901893i | \(-0.642178\pi\) | ||||
−0.431959 | + | 0.901893i | \(0.642178\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −11.0000 | −0.407407 | ||||||||
\(10\) | 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 | \(-0.869707\pi\) | ||||
−0.917389 | + | 0.397992i | \(0.869707\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 20.0000 | 0.344265 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 18.0000 | 0.256802 | 0.128401 | − | 0.991722i | \(-0.459015\pi\) | ||||
0.128401 | + | 0.991722i | \(0.459015\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −44.0000 | −0.531279 | −0.265639 | − | 0.964072i | \(-0.585583\pi\) | ||||
−0.265639 | + | 0.964072i | \(0.585583\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 64.0000 | 0.665045 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 48.0000 | 0.435161 | 0.217580 | − | 0.976042i | \(-0.430184\pi\) | ||||
0.217580 | + | 0.976042i | \(0.430184\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 152.000 | 1.08342 | ||||||||
\(28\) | 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 | ||||||||
\(33\) | −240.000 | −1.26602 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 80.0000 | 0.386356 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −254.000 | −1.12858 | −0.564288 | − | 0.825578i | \(-0.690849\pi\) | ||||
−0.564288 | + | 0.825578i | \(0.690849\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 344.000 | 1.41241 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 186.000 | 0.708496 | 0.354248 | − | 0.935152i | \(-0.384737\pi\) | ||||
0.354248 | + | 0.935152i | \(0.384737\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 100.000 | 0.354648 | 0.177324 | − | 0.984153i | \(-0.443256\pi\) | ||||
0.177324 | + | 0.984153i | \(0.443256\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 55.0000 | 0.182198 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 168.000 | 0.521390 | 0.260695 | − | 0.965421i | \(-0.416048\pi\) | ||||
0.260695 | + | 0.965421i | \(0.416048\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −87.0000 | −0.253644 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −72.0000 | −0.197687 | ||||||||
\(52\) | 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 | ||||||||
\(57\) | 176.000 | 0.408978 | ||||||||
\(58\) | 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 | \(-0.480612\pi\) | ||||
0.0608700 | + | 0.998146i | \(0.480612\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 176.000 | 0.351967 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 430.000 | 0.820537 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1036.00 | 1.88907 | 0.944534 | − | 0.328414i | \(-0.106514\pi\) | ||||
0.944534 | + | 0.328414i | \(0.106514\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −192.000 | −0.334987 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 168.000 | 0.280816 | 0.140408 | − | 0.990094i | \(-0.455159\pi\) | ||||
0.140408 | + | 0.990094i | \(0.455159\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 506.000 | 0.811272 | 0.405636 | − | 0.914035i | \(-0.367050\pi\) | ||||
0.405636 | + | 0.914035i | \(0.367050\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −100.000 | −0.153960 | ||||||||
\(76\) | 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 | ||||||||
\(81\) | −311.000 | −0.426612 | ||||||||
\(82\) | 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 | ||||||||
\(87\) | −744.000 | −0.916841 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1014.00 | −1.20768 | −0.603841 | − | 0.797104i | \(-0.706364\pi\) | ||||
−0.603841 | + | 0.797104i | \(0.706364\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1376.00 | 1.58510 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −704.000 | −0.784961 | ||||||||
\(94\) | 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 | ||||||||
\(99\) | −660.000 | −0.670025 | ||||||||
\(100\) | 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 | ||||||||
\(105\) | −320.000 | −0.297417 | ||||||||
\(106\) | 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 | \(-0.538977\pi\) | ||||
−0.122145 | + | 0.992512i | \(0.538977\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1016.00 | 0.868779 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −558.000 | −0.464533 | −0.232266 | − | 0.972652i | \(-0.574614\pi\) | ||||
−0.232266 | + | 0.972652i | \(0.574614\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −240.000 | −0.194610 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 946.000 | 0.747502 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −288.000 | −0.221856 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2269.00 | 1.70473 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −744.000 | −0.545400 | ||||||||
\(124\) | 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 | ||||||||
\(129\) | −400.000 | −0.273008 | ||||||||
\(130\) | 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 | ||||||||
\(135\) | −760.000 | −0.484521 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 666.000 | 0.415330 | 0.207665 | − | 0.978200i | \(-0.433414\pi\) | ||||
0.207665 | + | 0.978200i | \(0.433414\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −884.000 | −0.539424 | −0.269712 | − | 0.962941i | \(-0.586928\pi\) | ||||
−0.269712 | + | 0.962941i | \(0.586928\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −672.000 | −0.401366 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5160.00 | −3.01749 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −930.000 | −0.532637 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 348.000 | 0.195255 | ||||||||
\(148\) | 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 | ||||||||
\(153\) | −198.000 | −0.104623 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −880.000 | −0.456021 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 154.000 | 0.0782837 | 0.0391418 | − | 0.999234i | \(-0.487538\pi\) | ||||
0.0391418 | + | 0.999234i | \(0.487538\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1992.00 | −0.993559 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −768.000 | −0.375943 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2180.00 | −1.04755 | −0.523775 | − | 0.851856i | \(-0.675477\pi\) | ||||
−0.523775 | + | 0.851856i | \(0.675477\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1200.00 | 0.566181 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3696.00 | 1.71261 | 0.856303 | − | 0.516474i | \(-0.172756\pi\) | ||||
0.856303 | + | 0.516474i | \(0.172756\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5199.00 | 2.36641 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 484.000 | 0.216447 | ||||||||
\(172\) | 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 | ||||||||
\(177\) | −1008.00 | −0.428056 | ||||||||
\(178\) | 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 | \(-0.603099\pi\) | ||||
−0.318261 | + | 0.948003i | \(0.603099\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −232.000 | −0.0937155 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1270.00 | 0.504715 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1080.00 | 0.422339 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2432.00 | −0.935989 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 48.0000 | 0.0181841 | 0.00909204 | − | 0.999959i | \(-0.497106\pi\) | ||||
0.00909204 | + | 0.999959i | \(0.497106\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1058.00 | 0.394593 | 0.197297 | − | 0.980344i | \(-0.436784\pi\) | ||||
0.197297 | + | 0.980344i | \(0.436784\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1720.00 | −0.631650 | ||||||||
\(196\) | 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 | ||||||||
\(201\) | −4144.00 | −1.45421 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2976.00 | −1.02894 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −930.000 | −0.316849 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −528.000 | −0.177288 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2640.00 | −0.873745 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4036.00 | 1.31682 | 0.658412 | − | 0.752658i | \(-0.271229\pi\) | ||||
0.658412 | + | 0.752658i | \(0.271229\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −672.000 | −0.216172 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −500.000 | −0.158603 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2816.00 | −0.880933 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2024.00 | −0.624517 | ||||||||
\(220\) | 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 | ||||||||
\(225\) | −275.000 | −0.0814815 | ||||||||
\(226\) | 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 | \(-0.311203\pi\) | ||||
0.558954 | + | 0.829198i | \(0.311203\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3840.00 | 1.09374 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3162.00 | 0.889054 | 0.444527 | − | 0.895766i | \(-0.353372\pi\) | ||||
0.444527 | + | 0.895766i | \(0.353372\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −840.000 | −0.233173 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1088.00 | −0.298199 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5424.00 | 1.46799 | 0.733995 | − | 0.679155i | \(-0.237654\pi\) | ||||
0.733995 | + | 0.679155i | \(0.237654\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3886.00 | −1.03867 | −0.519335 | − | 0.854571i | \(-0.673820\pi\) | ||||
−0.519335 | + | 0.854571i | \(0.673820\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2860.00 | −0.755017 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 435.000 | 0.113433 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3784.00 | 0.974778 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3792.00 | 0.965093 | ||||||||
\(250\) | 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 | ||||||||
\(255\) | 360.000 | 0.0884081 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2178.00 | 0.528638 | 0.264319 | − | 0.964435i | \(-0.414853\pi\) | ||||
0.264319 | + | 0.964435i | \(0.414853\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4064.00 | 0.974999 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2046.00 | −0.485227 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6144.00 | −1.44051 | −0.720257 | − | 0.693707i | \(-0.755976\pi\) | ||||
−0.720257 | + | 0.693707i | \(0.755976\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2490.00 | −0.577206 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4056.00 | 0.929675 | ||||||||
\(268\) | 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 | ||||||||
\(273\) | −5504.00 | −1.22021 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1500.00 | 0.328921 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1138.00 | 0.246844 | 0.123422 | − | 0.992354i | \(-0.460613\pi\) | ||||
0.123422 | + | 0.992354i | \(0.460613\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1936.00 | −0.415431 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5706.00 | 1.21136 | 0.605679 | − | 0.795709i | \(-0.292902\pi\) | ||||
0.605679 | + | 0.795709i | \(0.292902\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3028.00 | 0.636028 | 0.318014 | − | 0.948086i | \(-0.396984\pi\) | ||||
0.318014 | + | 0.948086i | \(0.396984\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −880.000 | −0.182901 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2976.00 | −0.612083 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4589.00 | −0.934053 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3064.00 | 0.617233 | ||||||||
\(292\) | 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 | ||||||||
\(297\) | 9120.00 | 1.78180 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4128.00 | −0.798423 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1600.00 | −0.306387 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5256.00 | −0.996532 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −290.000 | −0.0544438 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4156.00 | 0.772624 | 0.386312 | − | 0.922368i | \(-0.373749\pi\) | ||||
0.386312 | + | 0.922368i | \(0.373749\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1792.00 | 0.329914 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6552.00 | 1.19463 | 0.597315 | − | 0.802007i | \(-0.296234\pi\) | ||||
0.597315 | + | 0.802007i | \(0.296234\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1366.00 | −0.246680 | −0.123340 | − | 0.992364i | \(-0.539361\pi\) | ||||
−0.123340 | + | 0.992364i | \(0.539361\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −880.000 | −0.157404 | ||||||||
\(316\) | 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 | ||||||||
\(321\) | 6192.00 | 1.07665 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −792.000 | −0.136434 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2150.00 | −0.366956 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1112.00 | 0.188054 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2688.00 | −0.450438 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3292.00 | 0.546661 | 0.273330 | − | 0.961920i | \(-0.411875\pi\) | ||||
0.273330 | + | 0.961920i | \(0.411875\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2794.00 | 0.459791 | ||||||||
\(334\) | 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 | ||||||||
\(339\) | 2232.00 | 0.357598 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10560.0 | 1.67700 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6880.00 | 1.08305 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 960.000 | 0.149811 | ||||||||
\(346\) | 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 | \(-0.422841\pi\) | ||||
0.240036 | + | 0.970764i | \(0.422841\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −13072.0 | −1.98784 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4194.00 | 0.632363 | 0.316181 | − | 0.948699i | \(-0.397599\pi\) | ||||
0.316181 | + | 0.948699i | \(0.397599\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −840.000 | −0.125585 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1152.00 | 0.170785 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4104.00 | −0.603345 | −0.301672 | − | 0.953412i | \(-0.597545\pi\) | ||||
−0.301672 | + | 0.953412i | \(0.597545\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4923.00 | −0.717743 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9076.00 | −1.31230 | ||||||||
\(364\) | 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 | ||||||||
\(369\) | −2046.00 | −0.288646 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7968.00 | −1.11503 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5842.00 | 0.810958 | 0.405479 | − | 0.914104i | \(-0.367105\pi\) | ||||
0.405479 | + | 0.914104i | \(0.367105\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 500.000 | 0.0688530 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −15996.0 | −2.18524 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 412.000 | 0.0558391 | 0.0279195 | − | 0.999610i | \(-0.491112\pi\) | ||||
0.0279195 | + | 0.999610i | \(0.491112\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1376.00 | −0.185025 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2568.00 | 0.342607 | 0.171304 | − | 0.985218i | \(-0.445202\pi\) | ||||
0.171304 | + | 0.985218i | \(0.445202\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4800.00 | 0.635404 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1100.00 | −0.144486 | ||||||||
\(388\) | 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 | ||||||||
\(393\) | 3120.00 | 0.400466 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1360.00 | −0.173238 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10454.0 | −1.32159 | −0.660795 | − | 0.750566i | \(-0.729781\pi\) | ||||
−0.660795 | + | 0.750566i | \(0.729781\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2816.00 | −0.353324 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10830.0 | −1.34869 | −0.674345 | − | 0.738417i | \(-0.735574\pi\) | ||||
−0.674345 | + | 0.738417i | \(0.735574\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15136.0 | −1.87091 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1555.00 | 0.190787 | ||||||||
\(406\) | 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 | ||||||||
\(411\) | −2664.00 | −0.319721 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4032.00 | −0.480392 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4740.00 | 0.560669 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3536.00 | 0.415249 | ||||||||
\(418\) | 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 | \(-0.579801\pi\) | ||||
−0.248084 | + | 0.968738i | \(0.579801\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1848.00 | −0.212418 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 450.000 | 0.0513605 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −928.000 | −0.105173 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 20640.0 | 2.32286 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6336.00 | 0.708108 | 0.354054 | − | 0.935225i | \(-0.384803\pi\) | ||||
0.354054 | + | 0.935225i | \(0.384803\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8974.00 | −0.995988 | −0.497994 | − | 0.867180i | \(-0.665930\pi\) | ||||
−0.497994 | + | 0.867180i | \(0.665930\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3720.00 | 0.410024 | ||||||||
\(436\) | 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 | ||||||||
\(441\) | 957.000 | 0.103337 | ||||||||
\(442\) | 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 | ||||||||
\(447\) | −456.000 | −0.0482507 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11394.0 | 1.19759 | 0.598793 | − | 0.800904i | \(-0.295647\pi\) | ||||
0.598793 | + | 0.800904i | \(0.295647\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11160.0 | 1.16520 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 160.000 | 0.0165948 | ||||||||
\(454\) | 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 | ||||||||
\(459\) | 2736.00 | 0.278226 | ||||||||
\(460\) | 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 | ||||||||
\(465\) | 3520.00 | 0.351045 | ||||||||
\(466\) | 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 | ||||||||
\(471\) | −616.000 | −0.0602628 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6000.00 | 0.583256 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1100.00 | −0.106256 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5478.00 | −0.525829 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6336.00 | −0.604383 | −0.302191 | − | 0.953247i | \(-0.597718\pi\) | ||||
−0.302191 | + | 0.953247i | \(0.597718\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21844.0 | 2.07069 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3072.00 | 0.289401 | ||||||||
\(484\) | 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 | ||||||||
\(489\) | 8720.00 | 0.806405 | ||||||||
\(490\) | 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 | ||||||||
\(495\) | 3300.00 | 0.299644 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2688.00 | −0.242602 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8116.00 | 0.728100 | 0.364050 | − | 0.931379i | \(-0.381394\pi\) | ||||
0.364050 | + | 0.931379i | \(0.381394\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −14784.0 | −1.31836 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4944.00 | −0.438255 | −0.219127 | − | 0.975696i | \(-0.570321\pi\) | ||||
−0.219127 | + | 0.975696i | \(0.570321\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6570.00 | −0.578933 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −20796.0 | −1.82166 | ||||||||
\(508\) | 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 | ||||||||
\(513\) | −6688.00 | −0.575599 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2240.00 | 0.191663 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10080.0 | 0.857481 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5208.00 | 0.440474 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10074.0 | 0.847121 | 0.423560 | − | 0.905868i | \(-0.360780\pi\) | ||||
0.423560 | + | 0.905868i | \(0.360780\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13828.0 | 1.15613 | 0.578065 | − | 0.815991i | \(-0.303808\pi\) | ||||
0.578065 | + | 0.815991i | \(0.303808\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1600.00 | 0.133009 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3168.00 | 0.261860 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9863.00 | −0.810635 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2772.00 | −0.226543 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −15996.0 | −1.29993 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7740.00 | 0.625475 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −17232.0 | −1.38476 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5220.00 | −0.417145 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15226.0 | 1.21001 | 0.605006 | − | 0.796221i | \(-0.293171\pi\) | ||||
0.605006 | + | 0.796221i | \(0.293171\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6200.00 | 0.489995 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1390.00 | 0.109250 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13228.0 | 1.03398 | 0.516991 | − | 0.855991i | \(-0.327052\pi\) | ||||
0.516991 | + | 0.855991i | \(0.327052\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −638.000 | −0.0495978 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8184.00 | −0.632759 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4352.00 | −0.334658 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5080.00 | −0.388530 | ||||||||
\(556\) | 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 | ||||||||
\(561\) | −4320.00 | −0.325117 | ||||||||
\(562\) | 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 | ||||||||
\(567\) | 4976.00 | 0.368558 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1770.00 | 0.130408 | 0.0652041 | − | 0.997872i | \(-0.479230\pi\) | ||||
0.0652041 | + | 0.997872i | \(0.479230\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6068.00 | −0.444725 | −0.222362 | − | 0.974964i | \(-0.571377\pi\) | ||||
−0.222362 | + | 0.974964i | \(0.571377\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −192.000 | −0.0139981 | ||||||||
\(574\) | 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 | ||||||||
\(579\) | −4232.00 | −0.303758 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15168.0 | 1.08309 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 29880.0 | 2.12265 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4730.00 | −0.334293 | ||||||||
\(586\) | 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 | ||||||||
\(591\) | −14856.0 | −1.03400 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15474.0 | 1.07157 | 0.535785 | − | 0.844354i | \(-0.320016\pi\) | ||||
0.535785 | + | 0.844354i | \(0.320016\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1440.00 | 0.0992172 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7072.00 | 0.484820 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2520.00 | −0.171894 | −0.0859469 | − | 0.996300i | \(-0.527392\pi\) | ||||
−0.0859469 | + | 0.996300i | \(0.527392\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12790.0 | −0.868078 | −0.434039 | − | 0.900894i | \(-0.642912\pi\) | ||||
−0.434039 | + | 0.900894i | \(0.642912\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −11396.0 | −0.769620 | ||||||||
\(604\) | 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 | ||||||||
\(609\) | 11904.0 | 0.792076 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −14448.0 | −0.956634 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20126.0 | −1.32607 | −0.663035 | − | 0.748588i | \(-0.730732\pi\) | ||||
−0.663035 | + | 0.748588i | \(0.730732\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3720.00 | 0.243910 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −27942.0 | −1.82318 | −0.911590 | − | 0.411100i | \(-0.865145\pi\) | ||||
−0.911590 | + | 0.411100i | \(0.865145\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22540.0 | 1.46358 | 0.731792 | − | 0.681528i | \(-0.238684\pi\) | ||||
0.731792 | + | 0.681528i | \(0.238684\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7296.00 | 0.471463 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16224.0 | 1.04334 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10560.0 | 0.672609 | ||||||||
\(628\) | 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 | ||||||||
\(633\) | −16144.0 | −1.01369 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1720.00 | −0.107490 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7482.00 | 0.465381 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1848.00 | −0.114406 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12798.0 | −0.788597 | −0.394298 | − | 0.918982i | \(-0.629012\pi\) | ||||
−0.394298 | + | 0.918982i | \(0.629012\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21148.0 | 1.29704 | 0.648519 | − | 0.761198i | \(-0.275389\pi\) | ||||
0.648519 | + | 0.761198i | \(0.275389\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2000.00 | 0.122093 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16464.0 | 1.00041 | 0.500206 | − | 0.865906i | \(-0.333258\pi\) | ||||
0.500206 | + | 0.865906i | \(0.333258\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15120.0 | 0.914502 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11264.0 | 0.678143 | ||||||||
\(652\) | 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 | ||||||||
\(657\) | −5566.00 | −0.330518 | ||||||||
\(658\) | 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 | \(-0.781908\pi\) | ||||
−0.774320 | + | 0.632794i | \(0.781908\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6192.00 | 0.362711 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3520.00 | −0.205263 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8928.00 | 0.518281 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2720.00 | −0.157192 | ||||||||
\(670\) | 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 | ||||||||
\(675\) | 3800.00 | 0.216685 | ||||||||
\(676\) | 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 | ||||||||
\(681\) | 9552.00 | 0.537494 | ||||||||
\(682\) | 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 | ||||||||
\(687\) | −15496.0 | −0.860567 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −42828.0 | −2.36809 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7868.00 | −0.433159 | −0.216579 | − | 0.976265i | \(-0.569490\pi\) | ||||
−0.216579 | + | 0.976265i | \(0.569490\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10560.0 | 0.578847 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4420.00 | 0.241238 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3348.00 | 0.181943 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −12648.0 | −0.684394 | ||||||||
\(700\) | 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 | ||||||||
\(705\) | 3360.00 | 0.179496 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −21024.0 | −1.11837 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −30014.0 | −1.58984 | −0.794922 | − | 0.606712i | \(-0.792488\pi\) | ||||
−0.794922 | + | 0.606712i | \(0.792488\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2992.00 | −0.157818 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8448.00 | 0.443731 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 25800.0 | 1.34946 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −21696.0 | −1.13006 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −816.000 | −0.0423250 | −0.0211625 | − | 0.999776i | \(-0.506737\pi\) | ||||
−0.0211625 | + | 0.999776i | \(0.506737\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7168.00 | 0.370250 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 15544.0 | 0.799568 | ||||||||
\(724\) | 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 | ||||||||
\(729\) | 19837.0 | 1.00782 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1800.00 | 0.0910744 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33946.0 | 1.71054 | 0.855269 | − | 0.518185i | \(-0.173392\pi\) | ||||
0.855269 | + | 0.518185i | \(0.173392\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1740.00 | −0.0873209 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 62160.0 | 3.10677 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23420.0 | −1.16579 | −0.582895 | − | 0.812548i | \(-0.698080\pi\) | ||||
−0.582895 | + | 0.812548i | \(0.698080\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −15136.0 | −0.750384 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14592.0 | −0.720496 | −0.360248 | − | 0.932857i | \(-0.617308\pi\) | ||||
−0.360248 | + | 0.932857i | \(0.617308\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −570.000 | −0.0280311 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10428.0 | 0.510764 | ||||||||
\(748\) | 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 | ||||||||
\(753\) | −20400.0 | −0.987274 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 200.000 | 0.00964072 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17554.0 | 0.842815 | 0.421408 | − | 0.906871i | \(-0.361536\pi\) | ||||
0.421408 | + | 0.906871i | \(0.361536\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −11520.0 | −0.550922 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −36438.0 | −1.73571 | −0.867856 | − | 0.496816i | \(-0.834502\pi\) | ||||
−0.867856 | + | 0.496816i | \(0.834502\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4448.00 | 0.211046 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 990.000 | 0.0467889 | ||||||||
\(766\) | 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 | ||||||||
\(771\) | −8712.00 | −0.406946 | ||||||||
\(772\) | 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 | ||||||||
\(777\) | −16256.0 | −0.750554 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8184.00 | −0.376409 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10080.0 | 0.461832 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 28272.0 | 1.29037 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −770.000 | −0.0350095 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5252.00 | −0.237883 | −0.118941 | − | 0.992901i | \(-0.537950\pi\) | ||||
−0.118941 | + | 0.992901i | \(0.537950\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 24576.0 | 1.10891 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8928.00 | 0.401319 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4988.00 | −0.223366 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 9960.00 | 0.444333 | ||||||||
\(796\) | 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 | ||||||||
\(801\) | 11154.0 | 0.492019 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 30360.0 | 1.33422 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3840.00 | 0.168127 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3288.00 | 0.143424 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 15546.0 | 0.675610 | 0.337805 | − | 0.941216i | \(-0.390316\pi\) | ||||
0.337805 | + | 0.941216i | \(0.390316\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19364.0 | −0.838424 | −0.419212 | − | 0.907888i | \(-0.637694\pi\) | ||||
−0.419212 | + | 0.907888i | \(0.637694\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −33920.0 | −1.46326 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10900.0 | 0.468479 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4400.00 | −0.188417 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −15136.0 | −0.645781 | ||||||||
\(820\) | 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 | ||||||||
\(825\) | −6000.00 | −0.253204 | ||||||||
\(826\) | 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 | \(-0.116014\pi\) | ||||
0.934313 | + | 0.356453i | \(0.116014\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4552.00 | −0.190021 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1566.00 | −0.0651365 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18480.0 | −0.765900 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 26752.0 | 1.10476 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 35448.0 | 1.45864 | 0.729321 | − | 0.684172i | \(-0.239836\pi\) | ||||
0.729321 | + | 0.684172i | \(0.239836\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10207.0 | 0.418508 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −22824.0 | −0.932503 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −25995.0 | −1.05829 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −36304.0 | −1.47275 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −12112.0 | −0.489615 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12192.0 | −0.491112 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12590.0 | −0.505362 | −0.252681 | − | 0.967550i | \(-0.581312\pi\) | ||||
−0.252681 | + | 0.967550i | \(0.581312\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2420.00 | −0.0967980 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24906.0 | 0.992734 | 0.496367 | − | 0.868113i | \(-0.334667\pi\) | ||||
0.496367 | + | 0.868113i | \(0.334667\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −23204.0 | −0.921665 | −0.460833 | − | 0.887487i | \(-0.652449\pi\) | ||||
−0.460833 | + | 0.887487i | \(0.652449\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11904.0 | 0.471181 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 19848.0 | 0.782890 | 0.391445 | − | 0.920202i | \(-0.371975\pi\) | ||||
0.391445 | + | 0.920202i | \(0.371975\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6510.00 | 0.255892 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 18356.0 | 0.719034 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 16320.0 | 0.637075 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −89096.0 | −3.46602 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8426.00 | 0.326663 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2000.00 | 0.0772712 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −27542.0 | −1.06046 | −0.530232 | − | 0.847852i | \(-0.677895\pi\) | ||||
−0.530232 | + | 0.847852i | \(0.677895\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 13560.0 | 0.520327 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20718.0 | −0.792290 | −0.396145 | − | 0.918188i | \(-0.629652\pi\) | ||||
−0.396145 | + | 0.918188i | \(0.629652\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25172.0 | −0.959349 | −0.479675 | − | 0.877446i | \(-0.659245\pi\) | ||||
−0.479675 | + | 0.877446i | \(0.659245\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5040.00 | 0.191432 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12864.0 | −0.486957 | −0.243478 | − | 0.969906i | \(-0.578289\pi\) | ||||
−0.243478 | + | 0.969906i | \(0.578289\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5504.00 | −0.207647 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −18660.0 | −0.701609 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7392.00 | −0.277003 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −21540.0 | −0.804472 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 16512.0 | 0.614626 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 32736.0 | 1.21447 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8964.00 | 0.331447 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6400.00 | 0.235857 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7750.00 | 0.284662 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23092.0 | 0.845377 | 0.422689 | − | 0.906275i | \(-0.361086\pi\) | ||||
0.422689 | + | 0.906275i | \(0.361086\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −14454.0 | −0.527403 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14208.0 | −0.516720 | −0.258360 | − | 0.966049i | \(-0.583182\pi\) | ||||
−0.258360 | + | 0.966049i | \(0.583182\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −56880.0 | −2.06183 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1160.00 | 0.0419108 | ||||||||
\(916\) | 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 | ||||||||
\(921\) | −16624.0 | −0.594766 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −14448.0 | −0.515235 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6350.00 | −0.225715 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4928.00 | 0.174603 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 162.000 | 0.00572126 | 0.00286063 | − | 0.999996i | \(-0.499089\pi\) | ||||
0.00286063 | + | 0.999996i | \(0.499089\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3828.00 | 0.134756 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −26208.0 | −0.919626 | ||||||||
\(934\) | 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 | ||||||||
\(939\) | 5464.00 | 0.189894 | ||||||||
\(940\) | 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 | ||||||||
\(945\) | 12160.0 | 0.418587 | ||||||||
\(946\) | 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 | ||||||||
\(951\) | 10392.0 | 0.354347 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27882.0 | 0.947730 | 0.473865 | − | 0.880598i | \(-0.342858\pi\) | ||||
0.473865 | + | 0.880598i | \(0.342858\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −240.000 | −0.00813217 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −44640.0 | −1.50784 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10656.0 | −0.358811 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1185.00 | 0.0397771 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 17028.0 | 0.569802 | ||||||||
\(964\) | 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 | ||||||||
\(969\) | 3168.00 | 0.105027 | ||||||||
\(970\) | 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 | ||||||||
\(975\) | 8600.00 | 0.282482 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6894.00 | −0.225751 | −0.112875 | − | 0.993609i | \(-0.536006\pi\) | ||||
−0.112875 | + | 0.993609i | \(0.536006\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −60840.0 | −1.98616 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3058.00 | 0.0995254 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −45264.0 | −1.46866 | −0.734332 | − | 0.678790i | \(-0.762505\pi\) | ||||
−0.734332 | + | 0.678790i | \(0.762505\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18570.0 | −0.600700 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10752.0 | 0.346748 | ||||||||
\(988\) | 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 | ||||||||
\(993\) | −13168.0 | −0.420820 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8840.00 | 0.281655 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13858.0 | 0.440208 | 0.220104 | − | 0.975476i | \(-0.429360\pi\) | ||||
0.220104 | + | 0.975476i | \(0.429360\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −38608.0 | −1.22273 |
(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 | 320.4.a.d.1.1 | 1 | ||
4.3 | odd | 2 | 320.4.a.k.1.1 | 1 | |||
5.4 | even | 2 | 1600.4.a.bl.1.1 | 1 | |||
8.3 | odd | 2 | 80.4.a.c.1.1 | 1 | |||
8.5 | even | 2 | 20.4.a.a.1.1 | ✓ | 1 | ||
16.3 | odd | 4 | 1280.4.d.c.641.2 | 2 | |||
16.5 | even | 4 | 1280.4.d.n.641.2 | 2 | |||
16.11 | odd | 4 | 1280.4.d.c.641.1 | 2 | |||
16.13 | even | 4 | 1280.4.d.n.641.1 | 2 | |||
20.19 | odd | 2 | 1600.4.a.p.1.1 | 1 | |||
24.5 | odd | 2 | 180.4.a.a.1.1 | 1 | |||
24.11 | even | 2 | 720.4.a.k.1.1 | 1 | |||
40.3 | even | 4 | 400.4.c.j.49.1 | 2 | |||
40.13 | odd | 4 | 100.4.c.a.49.2 | 2 | |||
40.19 | odd | 2 | 400.4.a.o.1.1 | 1 | |||
40.27 | even | 4 | 400.4.c.j.49.2 | 2 | |||
40.29 | even | 2 | 100.4.a.a.1.1 | 1 | |||
40.37 | odd | 4 | 100.4.c.a.49.1 | 2 | |||
56.5 | odd | 6 | 980.4.i.n.361.1 | 2 | |||
56.13 | odd | 2 | 980.4.a.c.1.1 | 1 | |||
56.37 | even | 6 | 980.4.i.e.361.1 | 2 | |||
56.45 | odd | 6 | 980.4.i.n.961.1 | 2 | |||
56.53 | even | 6 | 980.4.i.e.961.1 | 2 | |||
72.5 | odd | 6 | 1620.4.i.j.541.1 | 2 | |||
72.13 | even | 6 | 1620.4.i.d.541.1 | 2 | |||
72.29 | odd | 6 | 1620.4.i.j.1081.1 | 2 | |||
72.61 | even | 6 | 1620.4.i.d.1081.1 | 2 | |||
88.21 | odd | 2 | 2420.4.a.d.1.1 | 1 | |||
120.29 | odd | 2 | 900.4.a.m.1.1 | 1 | |||
120.53 | even | 4 | 900.4.d.k.649.2 | 2 | |||
120.77 | even | 4 | 900.4.d.k.649.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
20.4.a.a.1.1 | ✓ | 1 | 8.5 | even | 2 | ||
80.4.a.c.1.1 | 1 | 8.3 | odd | 2 | |||
100.4.a.a.1.1 | 1 | 40.29 | even | 2 | |||
100.4.c.a.49.1 | 2 | 40.37 | odd | 4 | |||
100.4.c.a.49.2 | 2 | 40.13 | odd | 4 | |||
180.4.a.a.1.1 | 1 | 24.5 | odd | 2 | |||
320.4.a.d.1.1 | 1 | 1.1 | even | 1 | trivial | ||
320.4.a.k.1.1 | 1 | 4.3 | odd | 2 | |||
400.4.a.o.1.1 | 1 | 40.19 | odd | 2 | |||
400.4.c.j.49.1 | 2 | 40.3 | even | 4 | |||
400.4.c.j.49.2 | 2 | 40.27 | even | 4 | |||
720.4.a.k.1.1 | 1 | 24.11 | even | 2 | |||
900.4.a.m.1.1 | 1 | 120.29 | odd | 2 | |||
900.4.d.k.649.1 | 2 | 120.77 | even | 4 | |||
900.4.d.k.649.2 | 2 | 120.53 | even | 4 | |||
980.4.a.c.1.1 | 1 | 56.13 | odd | 2 | |||
980.4.i.e.361.1 | 2 | 56.37 | even | 6 | |||
980.4.i.e.961.1 | 2 | 56.53 | even | 6 | |||
980.4.i.n.361.1 | 2 | 56.5 | odd | 6 | |||
980.4.i.n.961.1 | 2 | 56.45 | odd | 6 | |||
1280.4.d.c.641.1 | 2 | 16.11 | odd | 4 | |||
1280.4.d.c.641.2 | 2 | 16.3 | odd | 4 | |||
1280.4.d.n.641.1 | 2 | 16.13 | even | 4 | |||
1280.4.d.n.641.2 | 2 | 16.5 | even | 4 | |||
1600.4.a.p.1.1 | 1 | 20.19 | odd | 2 | |||
1600.4.a.bl.1.1 | 1 | 5.4 | even | 2 | |||
1620.4.i.d.541.1 | 2 | 72.13 | even | 6 | |||
1620.4.i.d.1081.1 | 2 | 72.61 | even | 6 | |||
1620.4.i.j.541.1 | 2 | 72.5 | odd | 6 | |||
1620.4.i.j.1081.1 | 2 | 72.29 | odd | 6 | |||
2420.4.a.d.1.1 | 1 | 88.21 | odd | 2 |