Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [720,4,Mod(1,720)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(720, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("720.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 720.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: | \(42.4813752041\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 15) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 720.1 |
$q$-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 | ||||||||
\(7\) | 24.0000 | 1.29588 | 0.647939 | − | 0.761692i | \(-0.275631\pi\) | ||||
0.647939 | + | 0.761692i | \(0.275631\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 52.0000 | 1.42533 | 0.712663 | − | 0.701506i | \(-0.247489\pi\) | ||||
0.712663 | + | 0.701506i | \(0.247489\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 22.0000 | 0.469362 | 0.234681 | − | 0.972072i | \(-0.424595\pi\) | ||||
0.234681 | + | 0.972072i | \(0.424595\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 14.0000 | 0.199735 | 0.0998676 | − | 0.995001i | \(-0.468158\pi\) | ||||
0.0998676 | + | 0.995001i | \(0.468158\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 20.0000 | 0.241490 | 0.120745 | − | 0.992684i | \(-0.461472\pi\) | ||||
0.120745 | + | 0.992684i | \(0.461472\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −168.000 | −1.52306 | −0.761531 | − | 0.648129i | \(-0.775552\pi\) | ||||
−0.761531 | + | 0.648129i | \(0.775552\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −230.000 | −1.47276 | −0.736378 | − | 0.676570i | \(-0.763465\pi\) | ||||
−0.736378 | + | 0.676570i | \(0.763465\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 288.000 | 1.66859 | 0.834296 | − | 0.551317i | \(-0.185875\pi\) | ||||
0.834296 | + | 0.551317i | \(0.185875\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −120.000 | −0.579534 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −34.0000 | −0.151069 | −0.0755347 | − | 0.997143i | \(-0.524066\pi\) | ||||
−0.0755347 | + | 0.997143i | \(0.524066\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −122.000 | −0.464712 | −0.232356 | − | 0.972631i | \(-0.574643\pi\) | ||||
−0.232356 | + | 0.972631i | \(0.574643\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 188.000 | 0.666738 | 0.333369 | − | 0.942796i | \(-0.391815\pi\) | ||||
0.333369 | + | 0.942796i | \(0.391815\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 256.000 | 0.794499 | 0.397249 | − | 0.917711i | \(-0.369965\pi\) | ||||
0.397249 | + | 0.917711i | \(0.369965\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 233.000 | 0.679300 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 338.000 | 0.875998 | 0.437999 | − | 0.898976i | \(-0.355687\pi\) | ||||
0.437999 | + | 0.898976i | \(0.355687\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −260.000 | −0.637425 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 100.000 | 0.220659 | 0.110330 | − | 0.993895i | \(-0.464809\pi\) | ||||
0.110330 | + | 0.993895i | \(0.464809\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 742.000 | 1.55743 | 0.778716 | − | 0.627376i | \(-0.215871\pi\) | ||||
0.778716 | + | 0.627376i | \(0.215871\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −110.000 | −0.209905 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 84.0000 | 0.153168 | 0.0765838 | − | 0.997063i | \(-0.475599\pi\) | ||||
0.0765838 | + | 0.997063i | \(0.475599\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −328.000 | −0.548260 | −0.274130 | − | 0.961693i | \(-0.588390\pi\) | ||||
−0.274130 | + | 0.961693i | \(0.588390\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −38.0000 | −0.0609255 | −0.0304628 | − | 0.999536i | \(-0.509698\pi\) | ||||
−0.0304628 | + | 0.999536i | \(0.509698\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1248.00 | 1.84705 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 240.000 | 0.341799 | 0.170899 | − | 0.985288i | \(-0.445333\pi\) | ||||
0.170899 | + | 0.985288i | \(0.445333\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1212.00 | 1.60282 | 0.801411 | − | 0.598114i | \(-0.204083\pi\) | ||||
0.801411 | + | 0.598114i | \(0.204083\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −70.0000 | −0.0893243 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −330.000 | −0.393033 | −0.196516 | − | 0.980501i | \(-0.562963\pi\) | ||||
−0.196516 | + | 0.980501i | \(0.562963\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 528.000 | 0.608236 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −100.000 | −0.107998 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 866.000 | 0.906484 | 0.453242 | − | 0.891387i | \(-0.350267\pi\) | ||||
0.453242 | + | 0.891387i | \(0.350267\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1218.00 | 1.19996 | 0.599978 | − | 0.800017i | \(-0.295176\pi\) | ||||
0.599978 | + | 0.800017i | \(0.295176\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 88.0000 | 0.0841835 | 0.0420917 | − | 0.999114i | \(-0.486598\pi\) | ||||
0.0420917 | + | 0.999114i | \(0.486598\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 36.0000 | 0.0325257 | 0.0162629 | − | 0.999868i | \(-0.494823\pi\) | ||||
0.0162629 | + | 0.999868i | \(0.494823\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −970.000 | −0.852378 | −0.426189 | − | 0.904634i | \(-0.640144\pi\) | ||||
−0.426189 | + | 0.904634i | \(0.640144\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1042.00 | −0.867461 | −0.433731 | − | 0.901043i | \(-0.642803\pi\) | ||||
−0.433731 | + | 0.901043i | \(0.642803\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 840.000 | 0.681134 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 336.000 | 0.258833 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1373.00 | 1.03156 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1936.00 | −1.35269 | −0.676347 | − | 0.736583i | \(-0.736438\pi\) | ||||
−0.676347 | + | 0.736583i | \(0.736438\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 732.000 | 0.488207 | 0.244104 | − | 0.969749i | \(-0.421506\pi\) | ||||
0.244104 | + | 0.969749i | \(0.421506\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 480.000 | 0.312942 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2214.00 | 1.38069 | 0.690346 | − | 0.723479i | \(-0.257458\pi\) | ||||
0.690346 | + | 0.723479i | \(0.257458\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −20.0000 | −0.0122042 | −0.00610208 | − | 0.999981i | \(-0.501942\pi\) | ||||
−0.00610208 | + | 0.999981i | \(0.501942\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1144.00 | 0.668994 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1150.00 | 0.658637 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1330.00 | 0.731261 | 0.365630 | − | 0.930760i | \(-0.380853\pi\) | ||||
0.365630 | + | 0.930760i | \(0.380853\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1208.00 | 0.651031 | 0.325515 | − | 0.945537i | \(-0.394462\pi\) | ||||
0.325515 | + | 0.945537i | \(0.394462\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1440.00 | −0.746217 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3514.00 | −1.78629 | −0.893146 | − | 0.449768i | \(-0.851507\pi\) | ||||
−0.893146 | + | 0.449768i | \(0.851507\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4032.00 | −1.97370 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2068.00 | 0.993732 | 0.496866 | − | 0.867827i | \(-0.334484\pi\) | ||||
0.496866 | + | 0.867827i | \(0.334484\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −24.0000 | −0.0111208 | −0.00556041 | − | 0.999985i | \(-0.501770\pi\) | ||||
−0.00556041 | + | 0.999985i | \(0.501770\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1713.00 | −0.779700 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 618.000 | 0.271593 | 0.135797 | − | 0.990737i | \(-0.456641\pi\) | ||||
0.135797 | + | 0.990737i | \(0.456641\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 600.000 | 0.259176 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3340.00 | 1.39466 | 0.697328 | − | 0.716752i | \(-0.254372\pi\) | ||||
0.697328 | + | 0.716752i | \(0.254372\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −178.000 | −0.0730974 | −0.0365487 | − | 0.999332i | \(-0.511636\pi\) | ||||
−0.0365487 | + | 0.999332i | \(0.511636\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 170.000 | 0.0675603 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 728.000 | 0.284688 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1888.00 | −0.715240 | −0.357620 | − | 0.933867i | \(-0.616412\pi\) | ||||
−0.357620 | + | 0.933867i | \(0.616412\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1922.00 | 0.716832 | 0.358416 | − | 0.933562i | \(-0.383317\pi\) | ||||
0.358416 | + | 0.933562i | \(0.383317\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2526.00 | −0.913554 | −0.456777 | − | 0.889581i | \(-0.650996\pi\) | ||||
−0.456777 | + | 0.889581i | \(0.650996\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1160.00 | 0.413217 | 0.206609 | − | 0.978424i | \(-0.433757\pi\) | ||||
0.206609 | + | 0.978424i | \(0.433757\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5520.00 | −1.90851 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 610.000 | 0.207826 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1040.00 | 0.344202 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4468.00 | 1.45777 | 0.728886 | − | 0.684635i | \(-0.240039\pi\) | ||||
0.728886 | + | 0.684635i | \(0.240039\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −940.000 | −0.298174 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6912.00 | 2.16229 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 308.000 | 0.0937481 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6032.00 | −1.81136 | −0.905678 | − | 0.423965i | \(-0.860638\pi\) | ||||
−0.905678 | + | 0.423965i | \(0.860638\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2636.00 | 0.770738 | 0.385369 | − | 0.922763i | \(-0.374074\pi\) | ||||
0.385369 | + | 0.922763i | \(0.374074\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4830.00 | 1.39378 | 0.696889 | − | 0.717179i | \(-0.254567\pi\) | ||||
0.696889 | + | 0.717179i | \(0.254567\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2682.00 | −0.754093 | −0.377046 | − | 0.926194i | \(-0.623060\pi\) | ||||
−0.377046 | + | 0.926194i | \(0.623060\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1280.00 | −0.355311 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2320.00 | 0.627901 | 0.313950 | − | 0.949439i | \(-0.398347\pi\) | ||||
0.313950 | + | 0.949439i | \(0.398347\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2002.00 | 0.535104 | 0.267552 | − | 0.963543i | \(-0.413785\pi\) | ||||
0.267552 | + | 0.963543i | \(0.413785\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1165.00 | −0.303792 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 440.000 | 0.113346 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 132.000 | 0.0331943 | 0.0165971 | − | 0.999862i | \(-0.494717\pi\) | ||||
0.0165971 | + | 0.999862i | \(0.494717\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8736.00 | −2.17086 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7614.00 | 1.84805 | 0.924024 | − | 0.382335i | \(-0.124880\pi\) | ||||
0.924024 | + | 0.382335i | \(0.124880\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −816.000 | −0.195767 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4888.00 | −1.14603 | −0.573017 | − | 0.819543i | \(-0.694227\pi\) | ||||
−0.573017 | + | 0.819543i | \(0.694227\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1690.00 | −0.391758 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1270.00 | −0.287856 | −0.143928 | − | 0.989588i | \(-0.545973\pi\) | ||||
−0.143928 | + | 0.989588i | \(0.545973\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1072.00 | −0.240293 | −0.120146 | − | 0.992756i | \(-0.538336\pi\) | ||||
−0.120146 | + | 0.992756i | \(0.538336\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1300.00 | 0.285065 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5394.00 | −1.17001 | −0.585007 | − | 0.811028i | \(-0.698908\pi\) | ||||
−0.585007 | + | 0.811028i | \(0.698908\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2442.00 | −0.518425 | −0.259213 | − | 0.965820i | \(-0.583463\pi\) | ||||
−0.259213 | + | 0.965820i | \(0.583463\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2772.00 | −0.582255 | −0.291128 | − | 0.956684i | \(-0.594030\pi\) | ||||
−0.291128 | + | 0.956684i | \(0.594030\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2928.00 | −0.602210 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4717.00 | −0.960106 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4542.00 | −0.905619 | −0.452810 | − | 0.891607i | \(-0.649578\pi\) | ||||
−0.452810 | + | 0.891607i | \(0.649578\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −500.000 | −0.0986818 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3696.00 | −0.714867 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4512.00 | 0.864011 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3710.00 | −0.696505 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5116.00 | −0.951093 | −0.475546 | − | 0.879691i | \(-0.657750\pi\) | ||||
−0.475546 | + | 0.879691i | \(0.657750\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2808.00 | −0.511984 | −0.255992 | − | 0.966679i | \(-0.582402\pi\) | ||||
−0.255992 | + | 0.966679i | \(0.582402\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7318.00 | −1.32153 | −0.660763 | − | 0.750594i | \(-0.729767\pi\) | ||||
−0.660763 | + | 0.750594i | \(0.729767\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2246.00 | −0.397943 | −0.198971 | − | 0.980005i | \(-0.563760\pi\) | ||||
−0.198971 | + | 0.980005i | \(0.563760\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11960.0 | −2.09916 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 280.000 | 0.0482341 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 550.000 | 0.0938723 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6144.00 | 1.02957 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1332.00 | −0.221188 | −0.110594 | − | 0.993866i | \(-0.535275\pi\) | ||||
−0.110594 | + | 0.993866i | \(0.535275\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −420.000 | −0.0684987 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11534.0 | −1.86438 | −0.932191 | − | 0.361966i | \(-0.882106\pi\) | ||||
−0.932191 | + | 0.361966i | \(0.882106\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14976.0 | 2.37829 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2640.00 | −0.415588 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11956.0 | 1.84966 | 0.924830 | − | 0.380382i | \(-0.124207\pi\) | ||||
0.924830 | + | 0.380382i | \(0.124207\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4870.00 | 0.746949 | 0.373474 | − | 0.927640i | \(-0.378166\pi\) | ||||
0.373474 | + | 0.927640i | \(0.378166\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10722.0 | −1.61664 | −0.808321 | − | 0.588742i | \(-0.799623\pi\) | ||||
−0.808321 | + | 0.588742i | \(0.799623\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1640.00 | 0.245189 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 120.000 | 0.0176417 | 0.00882083 | − | 0.999961i | \(-0.497192\pi\) | ||||
0.00882083 | + | 0.999961i | \(0.497192\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6459.00 | −0.941682 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 190.000 | 0.0272467 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3936.00 | −0.559830 | −0.279915 | − | 0.960025i | \(-0.590306\pi\) | ||||
−0.279915 | + | 0.960025i | \(0.590306\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8112.00 | 1.13519 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3022.00 | 0.419499 | 0.209750 | − | 0.977755i | \(-0.432735\pi\) | ||||
0.209750 | + | 0.977755i | \(0.432735\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5060.00 | −0.691255 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13340.0 | 1.80799 | 0.903997 | − | 0.427539i | \(-0.140619\pi\) | ||||
0.903997 | + | 0.427539i | \(0.140619\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1008.00 | −0.134481 | −0.0672407 | − | 0.997737i | \(-0.521420\pi\) | ||||
−0.0672407 | + | 0.997737i | \(0.521420\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6240.00 | −0.826026 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9630.00 | −1.25517 | −0.627584 | − | 0.778549i | \(-0.715956\pi\) | ||||
−0.627584 | + | 0.778549i | \(0.715956\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2352.00 | −0.304209 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1200.00 | −0.152857 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7126.00 | 0.900866 | 0.450433 | − | 0.892810i | \(-0.351270\pi\) | ||||
0.450433 | + | 0.892810i | \(0.351270\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8718.00 | 1.08568 | 0.542838 | − | 0.839837i | \(-0.317350\pi\) | ||||
0.542838 | + | 0.839837i | \(0.317350\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6336.00 | 0.783173 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1768.00 | −0.215323 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10870.0 | −1.31415 | −0.657074 | − | 0.753826i | \(-0.728206\pi\) | ||||
−0.657074 | + | 0.753826i | \(0.728206\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2400.00 | 0.285947 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6060.00 | −0.716804 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9700.00 | −1.13097 | −0.565484 | − | 0.824759i | \(-0.691311\pi\) | ||||
−0.565484 | + | 0.824759i | \(0.691311\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 862.000 | 0.0997893 | 0.0498947 | − | 0.998754i | \(-0.484111\pi\) | ||||
0.0498947 | + | 0.998754i | \(0.484111\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 350.000 | 0.0399470 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 17808.0 | 2.01824 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15792.0 | 1.76490 | 0.882452 | − | 0.470402i | \(-0.155891\pi\) | ||||
0.882452 | + | 0.470402i | \(0.155891\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11602.0 | 1.28766 | 0.643830 | − | 0.765169i | \(-0.277345\pi\) | ||||
0.643830 | + | 0.765169i | \(0.277345\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3360.00 | −0.367805 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 440.000 | 0.0478361 | 0.0239181 | − | 0.999714i | \(-0.492386\pi\) | ||||
0.0239181 | + | 0.999714i | \(0.492386\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10188.0 | −1.09266 | −0.546328 | − | 0.837571i | \(-0.683975\pi\) | ||||
−0.546328 | + | 0.837571i | \(0.683975\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1650.00 | 0.175770 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13310.0 | 1.39897 | 0.699485 | − | 0.714647i | \(-0.253413\pi\) | ||||
0.699485 | + | 0.714647i | \(0.253413\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6344.00 | −0.662367 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2640.00 | −0.272011 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3226.00 | 0.330210 | 0.165105 | − | 0.986276i | \(-0.447204\pi\) | ||||
0.165105 | + | 0.986276i | \(0.447204\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6582.00 | −0.664977 | −0.332488 | − | 0.943107i | \(-0.607888\pi\) | ||||
−0.332488 | + | 0.943107i | \(0.607888\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15072.0 | −1.51286 | −0.756431 | − | 0.654073i | \(-0.773059\pi\) | ||||
−0.756431 | + | 0.654073i | \(0.773059\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 476.000 | 0.0471663 | 0.0235831 | − | 0.999722i | \(-0.492493\pi\) | ||||
0.0235831 | + | 0.999722i | \(0.492493\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2016.00 | 0.198487 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9776.00 | 0.950319 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 500.000 | 0.0482980 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19680.0 | −1.87725 | −0.938624 | − | 0.344941i | \(-0.887899\pi\) | ||||
−0.938624 | + | 0.344941i | \(0.887899\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −748.000 | −0.0709062 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4330.00 | −0.405392 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5944.00 | 0.553077 | 0.276538 | − | 0.961003i | \(-0.410813\pi\) | ||||
0.276538 | + | 0.961003i | \(0.410813\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10772.0 | 0.990089 | 0.495044 | − | 0.868868i | \(-0.335152\pi\) | ||||
0.495044 | + | 0.868868i | \(0.335152\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3220.00 | −0.294161 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7872.00 | −0.710478 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8140.00 | −0.730253 | −0.365127 | − | 0.930958i | \(-0.618974\pi\) | ||||
−0.365127 | + | 0.930958i | \(0.618974\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13768.0 | −1.22045 | −0.610223 | − | 0.792229i | \(-0.708920\pi\) | ||||
−0.610223 | + | 0.792229i | \(0.708920\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6090.00 | −0.536637 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −22150.0 | −1.92884 | −0.964422 | − | 0.264368i | \(-0.914837\pi\) | ||||
−0.964422 | + | 0.264368i | \(0.914837\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −912.000 | −0.0789521 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −440.000 | −0.0376480 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13312.0 | 1.13242 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1562.00 | −0.131348 | −0.0656741 | − | 0.997841i | \(-0.520920\pi\) | ||||
−0.0656741 | + | 0.997841i | \(0.520920\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 668.000 | 0.0558501 | 0.0279250 | − | 0.999610i | \(-0.491110\pi\) | ||||
0.0279250 | + | 0.999610i | \(0.491110\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4032.00 | 0.333276 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16057.0 | 1.31972 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2684.00 | −0.218118 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −180.000 | −0.0145459 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12116.0 | 0.968225 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6138.00 | −0.487788 | −0.243894 | − | 0.969802i | \(-0.578425\pi\) | ||||
−0.243894 | + | 0.969802i | \(0.578425\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4850.00 | 0.381195 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10484.0 | 0.819494 | 0.409747 | − | 0.912199i | \(-0.365617\pi\) | ||||
0.409747 | + | 0.912199i | \(0.365617\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4600.00 | −0.355656 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5760.00 | 0.442930 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3606.00 | −0.274311 | −0.137155 | − | 0.990550i | \(-0.543796\pi\) | ||||
−0.137155 | + | 0.990550i | \(0.543796\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4136.00 | 0.312941 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12252.0 | 0.917159 | 0.458579 | − | 0.888654i | \(-0.348359\pi\) | ||||
0.458579 | + | 0.888654i | \(0.348359\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5210.00 | 0.387940 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14550.0 | 1.07200 | 0.536000 | − | 0.844218i | \(-0.319935\pi\) | ||||
0.536000 | + | 0.844218i | \(0.319935\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25468.0 | 1.86655 | 0.933277 | − | 0.359157i | \(-0.116936\pi\) | ||||
0.933277 | + | 0.359157i | \(0.116936\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4200.00 | −0.304612 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12866.0 | 0.928282 | 0.464141 | − | 0.885761i | \(-0.346363\pi\) | ||||
0.464141 | + | 0.885761i | \(0.346363\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 29088.0 | 2.07706 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17576.0 | 1.24858 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14844.0 | −1.04374 | −0.521872 | − | 0.853024i | \(-0.674766\pi\) | ||||
−0.521872 | + | 0.853024i | \(0.674766\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5760.00 | 0.402948 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −20402.0 | −1.41283 | −0.706416 | − | 0.707797i | \(-0.749689\pi\) | ||||
−0.706416 | + | 0.707797i | \(0.749689\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1680.00 | −0.115753 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10760.0 | 0.733959 | 0.366980 | − | 0.930229i | \(-0.380392\pi\) | ||||
0.366980 | + | 0.930229i | \(0.380392\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14282.0 | 0.969343 | 0.484671 | − | 0.874696i | \(-0.338939\pi\) | ||||
0.484671 | + | 0.874696i | \(0.338939\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6865.00 | −0.461326 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11056.0 | −0.739290 | −0.369645 | − | 0.929173i | \(-0.620521\pi\) | ||||
−0.369645 | + | 0.929173i | \(0.620521\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5632.00 | 0.372907 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16418.0 | −1.08176 | −0.540878 | − | 0.841101i | \(-0.681908\pi\) | ||||
−0.540878 | + | 0.841101i | \(0.681908\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10374.0 | 0.676891 | 0.338445 | − | 0.940986i | \(-0.390099\pi\) | ||||
0.338445 | + | 0.940986i | \(0.390099\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5260.00 | 0.341546 | 0.170773 | − | 0.985310i | \(-0.445373\pi\) | ||||
0.170773 | + | 0.985310i | \(0.445373\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7920.00 | −0.509323 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −476.000 | −0.0301739 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21352.0 | −1.34708 | −0.673542 | − | 0.739149i | \(-0.735228\pi\) | ||||
−0.673542 | + | 0.739149i | \(0.735228\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9680.00 | 0.604943 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5126.00 | 0.318838 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 29118.0 | 1.79422 | 0.897108 | − | 0.441812i | \(-0.145664\pi\) | ||||
0.897108 | + | 0.441812i | \(0.145664\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5772.00 | −0.354005 | −0.177003 | − | 0.984210i | \(-0.556640\pi\) | ||||
−0.177003 | + | 0.984210i | \(0.556640\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −14264.0 | −0.866732 | −0.433366 | − | 0.901218i | \(-0.642674\pi\) | ||||
−0.433366 | + | 0.901218i | \(0.642674\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5200.00 | 0.314511 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6902.00 | −0.413623 | −0.206812 | − | 0.978381i | \(-0.566309\pi\) | ||||
−0.206812 | + | 0.978381i | \(0.566309\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3660.00 | −0.218333 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20140.0 | 1.19051 | 0.595253 | − | 0.803539i | \(-0.297052\pi\) | ||||
0.595253 | + | 0.803539i | \(0.297052\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3218.00 | −0.189358 | −0.0946790 | − | 0.995508i | \(-0.530182\pi\) | ||||
−0.0946790 | + | 0.995508i | \(0.530182\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2400.00 | −0.139952 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 38640.0 | 2.24310 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 38584.0 | 2.21985 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7518.00 | −0.430606 | −0.215303 | − | 0.976547i | \(-0.569074\pi\) | ||||
−0.215303 | + | 0.976547i | \(0.569074\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18114.0 | 1.02833 | 0.514164 | − | 0.857692i | \(-0.328102\pi\) | ||||
0.514164 | + | 0.857692i | \(0.328102\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20784.0 | 1.17469 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −23868.0 | −1.33716 | −0.668582 | − | 0.743638i | \(-0.733099\pi\) | ||||
−0.668582 | + | 0.743638i | \(0.733099\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11070.0 | −0.617464 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7436.00 | 0.411160 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −172.000 | −0.00946916 | −0.00473458 | − | 0.999989i | \(-0.501507\pi\) | ||||
−0.00473458 | + | 0.999989i | \(0.501507\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 100.000 | 0.00545787 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1708.00 | −0.0928194 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22138.0 | 1.19278 | 0.596391 | − | 0.802694i | \(-0.296601\pi\) | ||||
0.596391 | + | 0.802694i | \(0.296601\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −680.000 | −0.0364818 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 29232.0 | 1.55500 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3070.00 | 0.162618 | 0.0813091 | − | 0.996689i | \(-0.474090\pi\) | ||||
0.0813091 | + | 0.996689i | \(0.474090\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −48384.0 | −2.54137 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5720.00 | −0.299183 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15600.0 | 0.809154 | 0.404577 | − | 0.914504i | \(-0.367419\pi\) | ||||
0.404577 | + | 0.914504i | \(0.367419\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2112.00 | 0.109092 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5750.00 | −0.294551 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20696.0 | −1.05581 | −0.527904 | − | 0.849304i | \(-0.677022\pi\) | ||||
−0.527904 | + | 0.849304i | \(0.677022\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2632.00 | 0.133171 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −30778.0 | −1.55090 | −0.775451 | − | 0.631408i | \(-0.782478\pi\) | ||||
−0.775451 | + | 0.631408i | \(0.782478\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4368.00 | 0.218314 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11740.0 | −0.584388 | −0.292194 | − | 0.956359i | \(-0.594385\pi\) | ||||
−0.292194 | + | 0.956359i | \(0.594385\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2632.00 | 0.129958 | 0.0649789 | − | 0.997887i | \(-0.479302\pi\) | ||||
0.0649789 | + | 0.997887i | \(0.479302\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6650.00 | −0.327030 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 864.000 | 0.0421494 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20528.0 | 0.997440 | 0.498720 | − | 0.866763i | \(-0.333804\pi\) | ||||
0.498720 | + | 0.866763i | \(0.333804\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6040.00 | −0.291150 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21646.0 | 1.03928 | 0.519642 | − | 0.854384i | \(-0.326066\pi\) | ||||
0.519642 | + | 0.854384i | \(0.326066\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18282.0 | −0.870857 | −0.435428 | − | 0.900223i | \(-0.643403\pi\) | ||||
−0.435428 | + | 0.900223i | \(0.643403\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −23280.0 | −1.10458 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2200.00 | 0.103569 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24190.0 | −1.13435 | −0.567174 | − | 0.823598i | \(-0.691963\pi\) | ||||
−0.567174 | + | 0.823598i | \(0.691963\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 25698.0 | 1.19572 | 0.597861 | − | 0.801600i | \(-0.296018\pi\) | ||||
0.597861 | + | 0.801600i | \(0.296018\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7200.00 | 0.333718 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2440.00 | −0.112223 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17056.0 | −0.781449 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 17570.0 | 0.798854 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −33436.0 | −1.51444 | −0.757220 | − | 0.653160i | \(-0.773443\pi\) | ||||
−0.757220 | + | 0.653160i | \(0.773443\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −25008.0 | −1.12412 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16324.0 | 0.730999 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 37594.0 | 1.67083 | 0.835413 | − | 0.549623i | \(-0.185229\pi\) | ||||
0.835413 | + | 0.549623i | \(0.185229\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3584.00 | 0.158689 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1976.00 | −0.0868388 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 20160.0 | 0.882667 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4730.00 | −0.205560 | −0.102780 | − | 0.994704i | \(-0.532774\pi\) | ||||
−0.102780 | + | 0.994704i | \(0.532774\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8748.00 | 0.378772 | 0.189386 | − | 0.981903i | \(-0.439350\pi\) | ||||
0.189386 | + | 0.981903i | \(0.439350\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10340.0 | −0.444410 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3760.00 | 0.161011 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −44142.0 | −1.87645 | −0.938226 | − | 0.346024i | \(-0.887532\pi\) | ||||
−0.938226 | + | 0.346024i | \(0.887532\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3992.00 | −0.169079 | −0.0845397 | − | 0.996420i | \(-0.526942\pi\) | ||||
−0.0845397 | + | 0.996420i | \(0.526942\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14444.0 | −0.607336 | −0.303668 | − | 0.952778i | \(-0.598211\pi\) | ||||
−0.303668 | + | 0.952778i | \(0.598211\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 42150.0 | 1.76590 | 0.882949 | − | 0.469468i | \(-0.155554\pi\) | ||||
0.882949 | + | 0.469468i | \(0.155554\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3262.00 | 0.135680 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 120.000 | 0.00497338 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13400.0 | 0.551394 | 0.275697 | − | 0.961245i | \(-0.411091\pi\) | ||||
0.275697 | + | 0.961245i | \(0.411091\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28511.0 | 1.16901 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8565.00 | 0.348692 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 32952.0 | 1.33677 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5712.00 | 0.230088 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8658.00 | −0.347531 | −0.173766 | − | 0.984787i | \(-0.555594\pi\) | ||||
−0.173766 | + | 0.984787i | \(0.555594\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −42826.0 | −1.70701 | −0.853505 | − | 0.521084i | \(-0.825528\pi\) | ||||
−0.853505 | + | 0.521084i | \(0.825528\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 35900.0 | 1.42595 | 0.712976 | − | 0.701189i | \(-0.247347\pi\) | ||||
0.712976 | + | 0.701189i | \(0.247347\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3088.00 | −0.121804 | −0.0609019 | − | 0.998144i | \(-0.519398\pi\) | ||||
−0.0609019 | + | 0.998144i | \(0.519398\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3090.00 | −0.121460 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12480.0 | 0.487175 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1848.00 | 0.0718910 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3000.00 | −0.115907 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −35274.0 | −1.35817 | −0.679087 | − | 0.734058i | \(-0.737624\pi\) | ||||
−0.679087 | + | 0.734058i | \(0.737624\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25042.0 | −0.957646 | −0.478823 | − | 0.877911i | \(-0.658936\pi\) | ||||
−0.478823 | + | 0.877911i | \(0.658936\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12572.0 | −0.479141 | −0.239570 | − | 0.970879i | \(-0.577007\pi\) | ||||
−0.239570 | + | 0.970879i | \(0.577007\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −21864.0 | −0.827645 | −0.413823 | − | 0.910358i | \(-0.635807\pi\) | ||||
−0.413823 | + | 0.910358i | \(0.635807\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −46464.0 | −1.75293 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5120.00 | 0.191864 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16700.0 | −0.623709 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −66240.0 | −2.45743 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4732.00 | 0.174968 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 890.000 | 0.0326902 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −31236.0 | −1.14352 | −0.571761 | − | 0.820420i | \(-0.693740\pi\) | ||||
−0.571761 | + | 0.820420i | \(0.693740\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8272.00 | 0.300838 | 0.150419 | − | 0.988622i | \(-0.451938\pi\) | ||||
0.150419 | + | 0.988622i | \(0.451938\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 63024.0 | 2.28455 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 17568.0 | 0.632657 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −20200.0 | −0.725067 | −0.362533 | − | 0.931971i | \(-0.618088\pi\) | ||||
−0.362533 | + | 0.931971i | \(0.618088\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7216.00 | −0.257332 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −850.000 | −0.0302139 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −31010.0 | −1.09516 | −0.547581 | − | 0.836753i | \(-0.684451\pi\) | ||||
−0.547581 | + | 0.836753i | \(0.684451\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4660.00 | 0.164044 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3640.00 | −0.127316 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −39174.0 | −1.36580 | −0.682902 | − | 0.730510i | \(-0.739283\pi\) | ||||
−0.682902 | + | 0.730510i | \(0.739283\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4138.00 | 0.143353 | 0.0716764 | − | 0.997428i | \(-0.477165\pi\) | ||||
0.0716764 | + | 0.997428i | \(0.477165\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 20496.0 | 0.707785 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23676.0 | 0.812425 | 0.406213 | − | 0.913779i | \(-0.366849\pi\) | ||||
0.406213 | + | 0.913779i | \(0.366849\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −836.000 | −0.0285961 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −18922.0 | −0.643173 | −0.321586 | − | 0.946880i | \(-0.604216\pi\) | ||||
−0.321586 | + | 0.946880i | \(0.604216\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9440.00 | 0.319865 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 53136.0 | 1.78921 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 53153.0 | 1.78420 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9610.00 | −0.320577 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −39656.0 | −1.31877 | −0.659385 | − | 0.751805i | \(-0.729183\pi\) | ||||
−0.659385 | + | 0.751805i | \(0.729183\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −33228.0 | −1.09818 | −0.549092 | − | 0.835762i | \(-0.685026\pi\) | ||||
−0.549092 | + | 0.835762i | \(0.685026\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −480.000 | −0.0158151 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 974.000 | 0.0318946 | 0.0159473 | − | 0.999873i | \(-0.494924\pi\) | ||||
0.0159473 | + | 0.999873i | \(0.494924\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −17160.0 | −0.560200 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −13608.0 | −0.441534 | −0.220767 | − | 0.975327i | \(-0.570856\pi\) | ||||
−0.220767 | + | 0.975327i | \(0.570856\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12630.0 | 0.408554 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −31584.0 | −1.01548 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13472.0 | −0.431839 | −0.215919 | − | 0.976411i | \(-0.569275\pi\) | ||||
−0.215919 | + | 0.976411i | \(0.569275\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5800.00 | −0.184796 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3234.00 | −0.102730 | −0.0513650 | − | 0.998680i | \(-0.516357\pi\) | ||||
−0.0513650 | + | 0.998680i | \(0.516357\pi\) | |||||||
\(998\) | 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 | 720.4.a.n.1.1 | 1 | ||
3.2 | odd | 2 | 240.4.a.e.1.1 | 1 | |||
4.3 | odd | 2 | 45.4.a.c.1.1 | 1 | |||
12.11 | even | 2 | 15.4.a.a.1.1 | ✓ | 1 | ||
15.2 | even | 4 | 1200.4.f.b.49.2 | 2 | |||
15.8 | even | 4 | 1200.4.f.b.49.1 | 2 | |||
15.14 | odd | 2 | 1200.4.a.t.1.1 | 1 | |||
20.3 | even | 4 | 225.4.b.e.199.2 | 2 | |||
20.7 | even | 4 | 225.4.b.e.199.1 | 2 | |||
20.19 | odd | 2 | 225.4.a.f.1.1 | 1 | |||
24.5 | odd | 2 | 960.4.a.ba.1.1 | 1 | |||
24.11 | even | 2 | 960.4.a.b.1.1 | 1 | |||
28.27 | even | 2 | 2205.4.a.l.1.1 | 1 | |||
36.7 | odd | 6 | 405.4.e.i.271.1 | 2 | |||
36.11 | even | 6 | 405.4.e.g.271.1 | 2 | |||
36.23 | even | 6 | 405.4.e.g.136.1 | 2 | |||
36.31 | odd | 6 | 405.4.e.i.136.1 | 2 | |||
60.23 | odd | 4 | 75.4.b.b.49.1 | 2 | |||
60.47 | odd | 4 | 75.4.b.b.49.2 | 2 | |||
60.59 | even | 2 | 75.4.a.b.1.1 | 1 | |||
84.83 | odd | 2 | 735.4.a.e.1.1 | 1 | |||
132.131 | odd | 2 | 1815.4.a.e.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.4.a.a.1.1 | ✓ | 1 | 12.11 | even | 2 | ||
45.4.a.c.1.1 | 1 | 4.3 | odd | 2 | |||
75.4.a.b.1.1 | 1 | 60.59 | even | 2 | |||
75.4.b.b.49.1 | 2 | 60.23 | odd | 4 | |||
75.4.b.b.49.2 | 2 | 60.47 | odd | 4 | |||
225.4.a.f.1.1 | 1 | 20.19 | odd | 2 | |||
225.4.b.e.199.1 | 2 | 20.7 | even | 4 | |||
225.4.b.e.199.2 | 2 | 20.3 | even | 4 | |||
240.4.a.e.1.1 | 1 | 3.2 | odd | 2 | |||
405.4.e.g.136.1 | 2 | 36.23 | even | 6 | |||
405.4.e.g.271.1 | 2 | 36.11 | even | 6 | |||
405.4.e.i.136.1 | 2 | 36.31 | odd | 6 | |||
405.4.e.i.271.1 | 2 | 36.7 | odd | 6 | |||
720.4.a.n.1.1 | 1 | 1.1 | even | 1 | trivial | ||
735.4.a.e.1.1 | 1 | 84.83 | odd | 2 | |||
960.4.a.b.1.1 | 1 | 24.11 | even | 2 | |||
960.4.a.ba.1.1 | 1 | 24.5 | odd | 2 | |||
1200.4.a.t.1.1 | 1 | 15.14 | odd | 2 | |||
1200.4.f.b.49.1 | 2 | 15.8 | even | 4 | |||
1200.4.f.b.49.2 | 2 | 15.2 | even | 4 | |||
1815.4.a.e.1.1 | 1 | 132.131 | odd | 2 | |||
2205.4.a.l.1.1 | 1 | 28.27 | even | 2 |