Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,3,Mod(1151,1600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1600, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.1151");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.b (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(43.5968422976\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 20) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1151.4 | ||
Root | \(-0.309017 + 0.951057i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.1151 |
Dual form | 1600.3.b.s.1151.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1151\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 3.80423i | 1.26808i | 0.773302 | + | 0.634038i | \(0.218604\pi\) | ||||
−0.773302 | + | 0.634038i | \(0.781396\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 8.50651i | 1.21522i | 0.794237 | + | 0.607608i | \(0.207871\pi\) | ||||
−0.794237 | + | 0.607608i | \(0.792129\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −5.47214 | −0.608015 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 1.79611i | − 0.163283i | −0.996662 | − | 0.0816415i | \(-0.973984\pi\) | ||||
0.996662 | − | 0.0816415i | \(-0.0260162\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.472136 | 0.0363182 | 0.0181591 | − | 0.999835i | \(-0.494219\pi\) | ||||
0.0181591 | + | 0.999835i | \(0.494219\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 23.8885 | 1.40521 | 0.702604 | − | 0.711581i | \(-0.252020\pi\) | ||||
0.702604 | + | 0.711581i | \(0.252020\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 9.40456i | 0.494977i | 0.968891 | + | 0.247489i | \(0.0796053\pi\) | ||||
−0.968891 | + | 0.247489i | \(0.920395\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −32.3607 | −1.54098 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 16.1150i | 0.700650i | 0.936628 | + | 0.350325i | \(0.113929\pi\) | ||||
−0.936628 | + | 0.350325i | \(0.886071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 13.4208i | 0.497066i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.94427 | −0.239458 | −0.119729 | − | 0.992807i | \(-0.538203\pi\) | ||||
−0.119729 | + | 0.992807i | \(0.538203\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 47.4468i | 1.53054i | 0.643708 | + | 0.765271i | \(0.277395\pi\) | ||||
−0.643708 | + | 0.765271i | \(0.722605\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.83282 | 0.207055 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 26.3607 | 0.712451 | 0.356225 | − | 0.934400i | \(-0.384064\pi\) | ||||
0.356225 | + | 0.934400i | \(0.384064\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.79611i | 0.0460542i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −41.4164 | −1.01016 | −0.505078 | − | 0.863074i | \(-0.668536\pi\) | ||||
−0.505078 | + | 0.863074i | \(0.668536\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 2.00811i | − 0.0467003i | −0.999727 | − | 0.0233502i | \(-0.992567\pi\) | ||||
0.999727 | − | 0.0233502i | \(-0.00743326\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 35.3481i | 0.752087i | 0.926602 | + | 0.376044i | \(0.122716\pi\) | ||||
−0.926602 | + | 0.376044i | \(0.877284\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −23.3607 | −0.476749 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 90.8774i | 1.78191i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −21.6393 | −0.408289 | −0.204145 | − | 0.978941i | \(-0.565441\pi\) | ||||
−0.204145 | + | 0.978941i | \(0.565441\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −35.7771 | −0.627668 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 73.8644i | − 1.25194i | −0.779848 | − | 0.625970i | \(-0.784703\pi\) | ||||
0.779848 | − | 0.625970i | \(-0.215297\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 26.1378 | 0.428488 | 0.214244 | − | 0.976780i | \(-0.431271\pi\) | ||||
0.214244 | + | 0.976780i | \(0.431271\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 46.5488i | − 0.738869i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 88.8693i | 1.32641i | 0.748439 | + | 0.663204i | \(0.230804\pi\) | ||||
−0.748439 | + | 0.663204i | \(0.769196\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −61.3050 | −0.888478 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 39.4144i | − 0.555132i | −0.960707 | − | 0.277566i | \(-0.910472\pi\) | ||||
0.960707 | − | 0.277566i | \(-0.0895277\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −137.554 | −1.88430 | −0.942152 | − | 0.335186i | \(-0.891201\pi\) | ||||
−0.942152 | + | 0.335186i | \(0.891201\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 15.2786 | 0.198424 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 113.703i | − 1.43928i | −0.694350 | − | 0.719638i | \(-0.744308\pi\) | ||||
0.694350 | − | 0.719638i | \(-0.255692\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −100.305 | −1.23833 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 21.2412i | 0.255919i | 0.991779 | + | 0.127959i | \(0.0408427\pi\) | ||||
−0.991779 | + | 0.127959i | \(0.959157\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 26.4176i | − 0.303650i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 67.4427 | 0.757783 | 0.378892 | − | 0.925441i | \(-0.376305\pi\) | ||||
0.378892 | + | 0.925441i | \(0.376305\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.01623i | 0.0441344i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −180.498 | −1.94084 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 39.1672 | 0.403785 | 0.201893 | − | 0.979408i | \(-0.435291\pi\) | ||||
0.201893 | + | 0.979408i | \(0.435291\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 9.82857i | 0.0992785i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −99.8885 | −0.988995 | −0.494498 | − | 0.869179i | \(-0.664648\pi\) | ||||
−0.494498 | + | 0.869179i | \(0.664648\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 35.7721i | 0.347302i | 0.984807 | + | 0.173651i | \(0.0555565\pi\) | ||||
−0.984807 | + | 0.173651i | \(0.944444\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 121.099i | − 1.13177i | −0.824485 | − | 0.565884i | \(-0.808535\pi\) | ||||
0.824485 | − | 0.565884i | \(-0.191465\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 197.469 | 1.81164 | 0.905821 | − | 0.423660i | \(-0.139255\pi\) | ||||
0.905821 | + | 0.423660i | \(0.139255\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 100.282i | 0.903441i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −81.2786 | −0.719280 | −0.359640 | − | 0.933091i | \(-0.617100\pi\) | ||||
−0.359640 | + | 0.933091i | \(0.617100\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.58359 | −0.0220820 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 203.208i | 1.70763i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 117.774 | 0.973339 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 157.557i | − 1.28095i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.84616i | 0.0145367i | 0.999974 | + | 0.00726834i | \(0.00231361\pi\) | ||||
−0.999974 | + | 0.00726834i | \(0.997686\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.63932 | 0.0592195 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 225.609i | − 1.72221i | −0.508428 | − | 0.861105i | \(-0.669773\pi\) | ||||
0.508428 | − | 0.861105i | \(-0.330227\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −80.0000 | −0.601504 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 52.8328 | 0.385641 | 0.192820 | − | 0.981234i | \(-0.438236\pi\) | ||||
0.192820 | + | 0.981234i | \(0.438236\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 125.852i | 0.905407i | 0.891661 | + | 0.452703i | \(0.149540\pi\) | ||||
−0.891661 | + | 0.452703i | \(0.850460\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −134.472 | −0.953703 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 0.848009i | − 0.00593013i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 88.8693i | − 0.604553i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −132.971 | −0.892420 | −0.446210 | − | 0.894928i | \(-0.647227\pi\) | ||||
−0.446210 | + | 0.894928i | \(0.647227\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 151.221i | − 1.00146i | −0.865603 | − | 0.500732i | \(-0.833064\pi\) | ||||
0.865603 | − | 0.500732i | \(-0.166936\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −130.721 | −0.854388 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −36.7477 | −0.234062 | −0.117031 | − | 0.993128i | \(-0.537338\pi\) | ||||
−0.117031 | + | 0.993128i | \(0.537338\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 82.3209i | − 0.517741i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −137.082 | −0.851441 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 302.854i | 1.85800i | 0.370079 | + | 0.929000i | \(0.379331\pi\) | ||||
−0.370079 | + | 0.929000i | \(0.620669\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 99.3839i | − 0.595113i | −0.954704 | − | 0.297557i | \(-0.903828\pi\) | ||||
0.954704 | − | 0.297557i | \(-0.0961717\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −168.777 | −0.998681 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 51.4631i | − 0.300954i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −181.639 | −1.04994 | −0.524969 | − | 0.851121i | \(-0.675923\pi\) | ||||
−0.524969 | + | 0.851121i | \(0.675923\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 280.997 | 1.58755 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 260.907i | 1.45758i | 0.684735 | + | 0.728792i | \(0.259918\pi\) | ||||
−0.684735 | + | 0.728792i | \(0.740082\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −157.777 | −0.871697 | −0.435848 | − | 0.900020i | \(-0.643552\pi\) | ||||
−0.435848 | + | 0.900020i | \(0.643552\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 99.4340i | 0.543355i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 42.9065i | − 0.229447i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −114.164 | −0.604043 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 324.095i | − 1.69683i | −0.529328 | − | 0.848417i | \(-0.677556\pi\) | ||||
0.529328 | − | 0.848417i | \(-0.322444\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −181.777 | −0.941850 | −0.470925 | − | 0.882173i | \(-0.656080\pi\) | ||||
−0.470925 | + | 0.882173i | \(0.656080\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 140.525 | 0.713324 | 0.356662 | − | 0.934234i | \(-0.383915\pi\) | ||||
0.356662 | + | 0.934234i | \(0.383915\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 168.234i | 0.845397i | 0.906270 | + | 0.422698i | \(0.138917\pi\) | ||||
−0.906270 | + | 0.422698i | \(0.861083\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −338.079 | −1.68198 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 59.0715i | − 0.290993i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 88.1833i | − 0.426006i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.8916 | 0.0808213 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 93.9455i | − 0.445240i | −0.974905 | − | 0.222620i | \(-0.928539\pi\) | ||||
0.974905 | − | 0.222620i | \(-0.0714608\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 149.941 | 0.703949 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −403.607 | −1.85994 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 523.287i | − 2.38944i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 11.2786 | 0.0510346 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 214.035i | − 0.959797i | −0.877324 | − | 0.479899i | \(-0.840673\pi\) | ||||
0.877324 | − | 0.479899i | \(-0.159327\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 41.4225i | − 0.182478i | −0.995829 | − | 0.0912389i | \(-0.970917\pi\) | ||||
0.995829 | − | 0.0912389i | \(-0.0290827\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −73.2786 | −0.319994 | −0.159997 | − | 0.987117i | \(-0.551148\pi\) | ||||
−0.159997 | + | 0.987117i | \(0.551148\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 58.1234i | 0.251616i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 307.050 | 1.31781 | 0.658905 | − | 0.752227i | \(-0.271020\pi\) | ||||
0.658905 | + | 0.752227i | \(0.271020\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 432.551 | 1.82511 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 42.9065i | − 0.179525i | −0.995963 | − | 0.0897625i | \(-0.971389\pi\) | ||||
0.995963 | − | 0.0897625i | \(-0.0286108\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −135.082 | −0.560506 | −0.280253 | − | 0.959926i | \(-0.590418\pi\) | ||||
−0.280253 | + | 0.959926i | \(0.590418\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 260.796i | − 1.07323i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.44023i | 0.0179767i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −80.8065 | −0.324524 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 221.169i | 0.881152i | 0.897715 | + | 0.440576i | \(0.145226\pi\) | ||||
−0.897715 | + | 0.440576i | \(0.854774\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 28.9443 | 0.114404 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 257.056 | 1.00022 | 0.500108 | − | 0.865963i | \(-0.333293\pi\) | ||||
0.500108 | + | 0.865963i | \(0.333293\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 224.237i | 0.865781i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 38.0000 | 0.145594 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 164.168i | 0.624212i | 0.950047 | + | 0.312106i | \(0.101034\pi\) | ||||
−0.950047 | + | 0.312106i | \(0.898966\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 256.567i | 0.960926i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 35.4752 | 0.131878 | 0.0659391 | − | 0.997824i | \(-0.478996\pi\) | ||||
0.0659391 | + | 0.997824i | \(0.478996\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 298.950i | 1.10314i | 0.834130 | + | 0.551568i | \(0.185970\pi\) | ||||
−0.834130 | + | 0.551568i | \(0.814030\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −15.2786 | −0.0559657 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −457.246 | −1.65071 | −0.825354 | − | 0.564616i | \(-0.809024\pi\) | ||||
−0.825354 | + | 0.564616i | \(0.809024\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 259.635i | − 0.930593i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.63932 | −0.0200688 | −0.0100344 | − | 0.999950i | \(-0.503194\pi\) | ||||
−0.0100344 | + | 0.999950i | \(0.503194\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 169.918i | − 0.600418i | −0.953874 | − | 0.300209i | \(-0.902944\pi\) | ||||
0.953874 | − | 0.300209i | \(-0.0970563\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 352.309i | − 1.22756i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 281.663 | 0.974611 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 149.001i | 0.512030i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −26.8591 | −0.0916694 | −0.0458347 | − | 0.998949i | \(-0.514595\pi\) | ||||
−0.0458347 | + | 0.998949i | \(0.514595\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 24.1052 | 0.0811624 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.60845i | 0.0254463i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 17.0820 | 0.0567510 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 379.999i | − 1.25412i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 118.031i | − 0.384466i | −0.981349 | − | 0.192233i | \(-0.938427\pi\) | ||||
0.981349 | − | 0.192233i | \(-0.0615730\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −136.085 | −0.440405 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 121.835i | 0.391753i | 0.980629 | + | 0.195877i | \(0.0627552\pi\) | ||||
−0.980629 | + | 0.195877i | \(0.937245\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −219.548 | −0.701431 | −0.350716 | − | 0.936482i | \(-0.614062\pi\) | ||||
−0.350716 | + | 0.936482i | \(0.614062\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 366.859 | 1.15728 | 0.578642 | − | 0.815582i | \(-0.303583\pi\) | ||||
0.578642 | + | 0.815582i | \(0.303583\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.4727i | 0.0390993i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 460.689 | 1.43517 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 224.661i | 0.695546i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 751.217i | 2.29730i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −300.689 | −0.913948 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 162.846i | 0.491981i | 0.969272 | + | 0.245990i | \(0.0791132\pi\) | ||||
−0.969272 | + | 0.245990i | \(0.920887\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −144.249 | −0.433181 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.1084 | −0.0507666 | −0.0253833 | − | 0.999678i | \(-0.508081\pi\) | ||||
−0.0253833 | + | 0.999678i | \(0.508081\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 309.202i | − 0.912101i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 85.2198 | 0.249911 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 218.101i | 0.635863i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 167.498i | 0.482703i | 0.970438 | + | 0.241351i | \(0.0775906\pi\) | ||||
−0.970438 | + | 0.241351i | \(0.922409\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 483.495 | 1.38537 | 0.692687 | − | 0.721239i | \(-0.256427\pi\) | ||||
0.692687 | + | 0.721239i | \(0.256427\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.33644i | 0.0180525i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −307.994 | −0.872504 | −0.436252 | − | 0.899825i | \(-0.643694\pi\) | ||||
−0.436252 | + | 0.899825i | \(0.643694\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −773.050 | −2.16540 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 23.2494i | − 0.0647615i | −0.999476 | − | 0.0323807i | \(-0.989691\pi\) | ||||
0.999476 | − | 0.0323807i | \(-0.0103089\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 272.554 | 0.754998 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 448.039i | 1.23427i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 517.325i | 1.40960i | 0.709404 | + | 0.704802i | \(0.248964\pi\) | ||||
−0.709404 | + | 0.704802i | \(0.751036\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 226.636 | 0.614190 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 184.075i | − 0.496159i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −88.3545 | −0.236875 | −0.118438 | − | 0.992961i | \(-0.537789\pi\) | ||||
−0.118438 | + | 0.992961i | \(0.537789\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.27864 | −0.00869666 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 19.3332i | − 0.0510112i | −0.999675 | − | 0.0255056i | \(-0.991880\pi\) | ||||
0.999675 | − | 0.0255056i | \(-0.00811956\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.02321 | −0.0184336 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 431.612i | 1.12692i | 0.826142 | + | 0.563462i | \(0.190531\pi\) | ||||
−0.826142 | + | 0.563462i | \(0.809469\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.9887i | 0.0283945i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 296.354 | 0.761837 | 0.380918 | − | 0.924609i | \(-0.375608\pi\) | ||||
0.380918 | + | 0.924609i | \(0.375608\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 384.963i | 0.984560i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 858.269 | 2.18389 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −86.1904 | −0.217104 | −0.108552 | − | 0.994091i | \(-0.534621\pi\) | ||||
−0.108552 | + | 0.994091i | \(0.534621\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − 304.338i | − 0.762752i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 442.997 | 1.10473 | 0.552365 | − | 0.833602i | \(-0.313725\pi\) | ||||
0.552365 | + | 0.833602i | \(0.313725\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 22.4014i | 0.0555865i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 47.3467i | − 0.116331i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 63.4102 | 0.155037 | 0.0775186 | − | 0.996991i | \(-0.475300\pi\) | ||||
0.0775186 | + | 0.996991i | \(0.475300\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 200.988i | 0.489022i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 628.328 | 1.52138 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −478.768 | −1.14812 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 435.678i | 1.03980i | 0.854226 | + | 0.519902i | \(0.174032\pi\) | ||||
−0.854226 | + | 0.519902i | \(0.825968\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 582.912 | 1.38459 | 0.692294 | − | 0.721615i | \(-0.256600\pi\) | ||||
0.692294 | + | 0.721615i | \(0.256600\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 193.430i | − 0.457280i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 222.341i | 0.520705i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.22602 | 0.00751986 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 375.882i | 0.872117i | 0.899918 | + | 0.436058i | \(0.143626\pi\) | ||||
−0.899918 | + | 0.436058i | \(0.856374\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 368.164 | 0.850263 | 0.425132 | − | 0.905131i | \(-0.360228\pi\) | ||||
0.425132 | + | 0.905131i | \(0.360228\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −151.554 | −0.346806 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 483.549i | 1.10148i | 0.834677 | + | 0.550739i | \(0.185654\pi\) | ||||
−0.834677 | + | 0.550739i | \(0.814346\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 127.833 | 0.289870 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 279.181i | − 0.630205i | −0.949058 | − | 0.315102i | \(-0.897961\pi\) | ||||
0.949058 | − | 0.315102i | \(-0.102039\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 505.850i | − 1.13166i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 756.079 | 1.68392 | 0.841959 | − | 0.539542i | \(-0.181403\pi\) | ||||
0.841959 | + | 0.539542i | \(0.181403\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 74.3885i | 0.164941i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 575.279 | 1.26993 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −285.672 | −0.625103 | −0.312551 | − | 0.949901i | \(-0.601184\pi\) | ||||
−0.312551 | + | 0.949901i | \(0.601184\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 320.603i | 0.698482i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 99.1146 | 0.214999 | 0.107500 | − | 0.994205i | \(-0.465716\pi\) | ||||
0.107500 | + | 0.994205i | \(0.465716\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 630.603i | 1.36199i | 0.732286 | + | 0.680997i | \(0.238453\pi\) | ||||
−0.732286 | + | 0.680997i | \(0.761547\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 496.010i | 1.06212i | 0.847334 | + | 0.531060i | \(0.178206\pi\) | ||||
−0.847334 | + | 0.531060i | \(0.821794\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −755.967 | −1.61187 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 139.796i | − 0.296808i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.60680 | −0.00762537 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 118.413 | 0.248246 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 579.090i | 1.20896i | 0.796621 | + | 0.604478i | \(0.206618\pi\) | ||||
−0.796621 | + | 0.604478i | \(0.793382\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.4458 | 0.0258749 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 521.491i | − 1.07969i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 626.363i | − 1.28617i | −0.765796 | − | 0.643084i | \(-0.777655\pi\) | ||||
0.765796 | − | 0.643084i | \(-0.222345\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1152.13 | −2.35608 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 22.3013i | − 0.0454201i | −0.999742 | − | 0.0227100i | \(-0.992771\pi\) | ||||
0.999742 | − | 0.0227100i | \(-0.00722945\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −165.889 | −0.336488 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 335.279 | 0.674605 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 627.362i | − 1.25724i | −0.777714 | − | 0.628619i | \(-0.783621\pi\) | ||||
0.777714 | − | 0.628619i | \(-0.216379\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 378.079 | 0.754649 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 780.853i | − 1.55239i | −0.630492 | − | 0.776196i | \(-0.717147\pi\) | ||||
0.630492 | − | 0.776196i | \(-0.282853\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 642.066i | − 1.26640i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 288.950 | 0.567683 | 0.283841 | − | 0.958871i | \(-0.408391\pi\) | ||||
0.283841 | + | 0.958871i | \(0.408391\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 1170.11i | − 2.28984i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −126.217 | −0.246036 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 63.4891 | 0.122803 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 690.997i | − 1.33140i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −602.984 | −1.15736 | −0.578680 | − | 0.815555i | \(-0.696432\pi\) | ||||
−0.578680 | + | 0.815555i | \(0.696432\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 367.962i | 0.703560i | 0.936083 | + | 0.351780i | \(0.114423\pi\) | ||||
−0.936083 | + | 0.351780i | \(0.885577\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1133.44i | 2.15073i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 269.308 | 0.509089 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 404.196i | 0.761198i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −19.5542 | −0.0366870 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −992.551 | −1.84833 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 41.9584i | 0.0778449i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 616.885 | 1.14027 | 0.570134 | − | 0.821551i | \(-0.306891\pi\) | ||||
0.570134 | + | 0.821551i | \(0.306891\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 600.220i | − 1.10538i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 97.8499i | − 0.178885i | −0.995992 | − | 0.0894423i | \(-0.971492\pi\) | ||||
0.995992 | − | 0.0894423i | \(-0.0285085\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −143.029 | −0.260527 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 65.3078i | − 0.118526i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 967.214 | 1.74903 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 896.302 | 1.60916 | 0.804580 | − | 0.593845i | \(-0.202391\pi\) | ||||
0.804580 | + | 0.593845i | \(0.202391\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 0.948103i | − 0.00169607i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 163.226 | 0.290955 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 771.186i | 1.36978i | 0.728647 | + | 0.684890i | \(0.240150\pi\) | ||||
−0.728647 | + | 0.684890i | \(0.759850\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 853.245i | − 1.50484i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.74767 | 0.0153738 | 0.00768688 | − | 0.999970i | \(-0.497553\pi\) | ||||
0.00768688 | + | 0.999970i | \(0.497553\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 511.138i | − 0.895164i | −0.894243 | − | 0.447582i | \(-0.852285\pi\) | ||||
0.894243 | − | 0.447582i | \(-0.147715\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1232.93 | 2.15171 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 713.712 | 1.23694 | 0.618468 | − | 0.785810i | \(-0.287754\pi\) | ||||
0.618468 | + | 0.785810i | \(0.287754\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 691.521i | − 1.19434i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −180.689 | −0.310996 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 38.8666i | 0.0666666i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 422.169i | − 0.719198i | −0.933107 | − | 0.359599i | \(-0.882914\pi\) | ||||
0.933107 | − | 0.359599i | \(-0.117086\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −446.217 | −0.757584 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 534.588i | 0.904548i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 308.663 | 0.520510 | 0.260255 | − | 0.965540i | \(-0.416193\pi\) | ||||
0.260255 | + | 0.965540i | \(0.416193\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −640.000 | −1.07203 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 462.196i | − 0.771612i | −0.922580 | − | 0.385806i | \(-0.873923\pi\) | ||||
0.922580 | − | 0.385806i | \(-0.126077\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 355.358 | 0.591277 | 0.295639 | − | 0.955300i | \(-0.404468\pi\) | ||||
0.295639 | + | 0.955300i | \(0.404468\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 486.305i | − 0.806476i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 630.403i | − 1.03856i | −0.854605 | − | 0.519278i | \(-0.826201\pi\) | ||||
0.854605 | − | 0.519278i | \(-0.173799\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 224.721 | 0.369001 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16.6891i | 0.0273144i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 812.525 | 1.32549 | 0.662745 | − | 0.748846i | \(-0.269392\pi\) | ||||
0.662745 | + | 0.748846i | \(0.269392\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 437.935 | 0.709781 | 0.354891 | − | 0.934908i | \(-0.384518\pi\) | ||||
0.354891 | + | 0.934908i | \(0.384518\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 770.250i | 1.24435i | 0.782880 | + | 0.622173i | \(0.213750\pi\) | ||||
−0.782880 | + | 0.622173i | \(0.786250\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −216.276 | −0.348270 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 573.702i | 0.920870i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 64.2597i | 0.102487i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 629.718 | 1.00114 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 875.496i | − 1.38747i | −0.720228 | − | 0.693737i | \(-0.755963\pi\) | ||||
0.720228 | − | 0.693737i | \(-0.244037\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 357.390 | 0.564597 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −11.0294 | −0.0173146 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 215.681i | 0.337529i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 842.571 | 1.31446 | 0.657232 | − | 0.753689i | \(-0.271727\pi\) | ||||
0.657232 | + | 0.753689i | \(0.271727\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 1153.20i | − 1.79348i | −0.442563 | − | 0.896738i | \(-0.645931\pi\) | ||||
0.442563 | − | 0.896738i | \(-0.354069\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 355.751i | 0.549847i | 0.961466 | + | 0.274924i | \(0.0886526\pi\) | ||||
−0.961466 | + | 0.274924i | \(0.911347\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −132.669 | −0.204420 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 1535.41i | − 2.35854i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −557.915 | −0.854387 | −0.427194 | − | 0.904160i | \(-0.640498\pi\) | ||||
−0.427194 | + | 0.904160i | \(0.640498\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 752.715 | 1.14569 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 284.157i | − 0.431194i | −0.976482 | − | 0.215597i | \(-0.930830\pi\) | ||||
0.976482 | − | 0.215597i | \(-0.0691697\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −716.735 | −1.08432 | −0.542160 | − | 0.840275i | \(-0.682393\pi\) | ||||
−0.542160 | + | 0.840275i | \(0.682393\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 42.9065i | 0.0647157i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 111.907i | − 0.167776i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 814.237 | 1.21710 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 46.9464i | − 0.0699648i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 695.378 | 1.03325 | 0.516625 | − | 0.856212i | \(-0.327188\pi\) | ||||
0.516625 | + | 0.856212i | \(0.327188\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −820.237 | −1.21158 | −0.605788 | − | 0.795626i | \(-0.707142\pi\) | ||||
−0.605788 | + | 0.795626i | \(0.707142\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 333.176i | 0.490686i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 157.580 | 0.231396 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 335.508i | 0.491227i | 0.969368 | + | 0.245613i | \(0.0789894\pi\) | ||||
−0.969368 | + | 0.245613i | \(0.921011\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 278.769i | − 0.405777i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.2167 | −0.0148283 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 336.568i | − 0.487074i | −0.969892 | − | 0.243537i | \(-0.921692\pi\) | ||||
0.969892 | − | 0.243537i | \(-0.0783077\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −83.6068 | −0.120645 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −989.378 | −1.41948 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1168.09i | 1.67108i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 429.364 | 0.612502 | 0.306251 | − | 0.951951i | \(-0.400925\pi\) | ||||
0.306251 | + | 0.951951i | \(0.400925\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 247.911i | 0.352647i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 849.703i | − 1.20184i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1224.60 | −1.72722 | −0.863609 | − | 0.504162i | \(-0.831801\pi\) | ||||
−0.863609 | + | 0.504162i | \(0.831801\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 622.197i | 0.875101i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −764.604 | −1.07238 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 163.226 | 0.227651 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 496.022i | 0.689877i | 0.938625 | + | 0.344939i | \(0.112100\pi\) | ||||
−0.938625 | + | 0.344939i | \(0.887900\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −304.296 | −0.422047 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 513.883i | − 0.710764i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 152.843i | 0.210238i | 0.994460 | + | 0.105119i | \(0.0335224\pi\) | ||||
−0.994460 | + | 0.105119i | \(0.966478\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 89.3808 | 0.122607 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 47.9709i | − 0.0656237i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −761.286 | −1.03859 | −0.519295 | − | 0.854595i | \(-0.673805\pi\) | ||||
−0.519295 | + | 0.854595i | \(0.673805\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 159.619 | 0.216580 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 183.975i | 0.248951i | 0.992223 | + | 0.124476i | \(0.0397249\pi\) | ||||
−0.992223 | + | 0.124476i | \(0.960275\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −16.8916 | −0.0227957 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 495.247i | − 0.666551i | −0.942830 | − | 0.333275i | \(-0.891846\pi\) | ||||
0.942830 | − | 0.333275i | \(-0.108154\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 116.235i | − 0.155602i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1030.13 | 1.37534 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 800.059i | 1.06533i | 0.846328 | + | 0.532663i | \(0.178809\pi\) | ||||
−0.846328 | + | 0.532663i | \(0.821191\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −841.378 | −1.11737 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −276.367 | −0.365082 | −0.182541 | − | 0.983198i | \(-0.558432\pi\) | ||||
−0.182541 | + | 0.983198i | \(0.558432\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 110.111i | 0.145073i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 891.207 | 1.17110 | 0.585550 | − | 0.810636i | \(-0.300879\pi\) | ||||
0.585550 | + | 0.810636i | \(0.300879\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1679.77i | 2.20154i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 34.8740i | − 0.0454681i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −835.430 | −1.08639 | −0.543193 | − | 0.839608i | \(-0.682785\pi\) | ||||
−0.543193 | + | 0.839608i | \(0.682785\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 977.898i | 1.26835i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 213.522 | 0.276225 | 0.138112 | − | 0.990417i | \(-0.455897\pi\) | ||||
0.138112 | + | 0.990417i | \(0.455897\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −853.050 | −1.09788 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 389.503i | − 0.500004i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −70.7926 | −0.0906436 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 93.1976i | − 0.119026i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 370.182i | − 0.470371i | −0.971951 | − | 0.235185i | \(-0.924430\pi\) | ||||
0.971951 | − | 0.235185i | \(-0.0755697\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −624.531 | −0.791547 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 691.397i | − 0.874080i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.3406 | 0.0155619 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 274.426 | 0.344323 | 0.172162 | − | 0.985069i | \(-0.444925\pi\) | ||||
0.172162 | + | 0.985069i | \(0.444925\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 844.414i | 1.05684i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −369.056 | −0.460744 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 247.063i | 0.307675i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 134.956i | 0.167232i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 665.214 | 0.822266 | 0.411133 | − | 0.911575i | \(-0.365133\pi\) | ||||
0.411133 | + | 0.911575i | \(0.365133\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 360.665i | 0.444717i | 0.974965 | + | 0.222358i | \(0.0713755\pi\) | ||||
−0.974965 | + | 0.222358i | \(0.928624\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1137.27 | −1.39886 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18.8854 | 0.0231156 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 21.9773i | − 0.0268344i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 666.899 | 0.812301 | 0.406151 | − | 0.913806i | \(-0.366871\pi\) | ||||
0.406151 | + | 0.913806i | \(0.366871\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 122.433i | 0.148764i | 0.997230 | + | 0.0743822i | \(0.0236985\pi\) | ||||
−0.997230 | + | 0.0743822i | \(0.976302\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1532.98i | 1.85366i | 0.375477 | + | 0.926832i | \(0.377479\pi\) | ||||
−0.375477 | + | 0.926832i | \(0.622521\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 195.475 | 0.235796 | 0.117898 | − | 0.993026i | \(-0.462384\pi\) | ||||
0.117898 | + | 0.993026i | \(0.462384\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 1739.47i | − 2.09322i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −558.053 | −0.669931 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −636.774 | −0.760781 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 1325.97i | − 1.58041i | −0.612840 | − | 0.790207i | \(-0.709973\pi\) | ||||
0.612840 | − | 0.790207i | \(-0.290027\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −792.777 | −0.942660 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 21.4532i | − 0.0254487i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1001.85i | 1.18282i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 646.407 | 0.761375 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 424.801i | 0.499179i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1055.28 | 1.23714 | 0.618570 | − | 0.785730i | \(-0.287712\pi\) | ||||
0.618570 | + | 0.785730i | \(0.287712\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −155.378 | −0.181304 | −0.0906521 | − | 0.995883i | \(-0.528895\pi\) | ||||
−0.0906521 | + | 0.995883i | \(0.528895\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 226.033i | − 0.263136i | −0.991307 | − | 0.131568i | \(-0.957999\pi\) | ||||
0.991307 | − | 0.131568i | \(-0.0420011\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1340.26 | 1.55664 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 930.702i | 1.07845i | 0.842162 | + | 0.539225i | \(0.181283\pi\) | ||||
−0.842162 | + | 0.539225i | \(0.818717\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1071.51i | 1.23588i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −204.223 | −0.235009 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 41.9584i | 0.0481727i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −214.328 | −0.245508 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −33.5217 | −0.0382231 | −0.0191115 | − | 0.999817i | \(-0.506084\pi\) | ||||
−0.0191115 | + | 0.999817i | \(0.506084\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 102.178i | − 0.116244i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −933.850 | −1.05999 | −0.529994 | − | 0.848001i | \(-0.677806\pi\) | ||||
−0.529994 | + | 0.848001i | \(0.677806\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 542.308i | − 0.614166i | −0.951683 | − | 0.307083i | \(-0.900647\pi\) | ||||
0.951683 | − | 0.307083i | \(-0.0993529\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 714.720i | − 0.805773i | −0.915250 | − | 0.402886i | \(-0.868007\pi\) | ||||
0.915250 | − | 0.402886i | \(-0.131993\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −15.7044 | −0.0176652 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 180.159i | 0.202199i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −332.433 | −0.372266 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −28.9443 | −0.0322679 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 329.484i | − 0.366500i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −516.932 | −0.573731 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 64.9839i | 0.0719645i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 347.233i | 0.382837i | 0.981509 | + | 0.191418i | \(0.0613087\pi\) | ||||
−0.981509 | + | 0.191418i | \(0.938691\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 546.604 | 0.601324 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1427.54i | 1.56701i | 0.621386 | + | 0.783504i | \(0.286570\pi\) | ||||
−0.621386 | + | 0.783504i | \(0.713430\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 38.1517 | 0.0417871 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1919.15 | 2.09286 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 569.162i | − 0.619327i | −0.950846 | − | 0.309664i | \(-0.899784\pi\) | ||||
0.950846 | − | 0.309664i | \(-0.100216\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 449.017 | 0.487532 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 18.6089i | − 0.0201614i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 195.750i | − 0.211165i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1535.96 | 1.65335 | 0.826675 | − | 0.562680i | \(-0.190230\pi\) | ||||
0.826675 | + | 0.562680i | \(0.190230\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 219.697i | − 0.235980i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −463.489 | −0.496773 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −338.721 | −0.361496 | −0.180748 | − | 0.983529i | \(-0.557852\pi\) | ||||
−0.180748 | + | 0.983529i | \(0.557852\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 835.210i | − 0.889468i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1439.77 | −1.53004 | −0.765022 | − | 0.644004i | \(-0.777272\pi\) | ||||
−0.765022 | + | 0.644004i | \(0.777272\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 667.424i | − 0.707766i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 656.135i | 0.692856i | 0.938077 | + | 0.346428i | \(0.112606\pi\) | ||||
−0.938077 | + | 0.346428i | \(0.887394\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −64.9443 | −0.0684344 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1395.62i | 1.46752i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −436.675 | −0.458211 | −0.229105 | − | 0.973402i | \(-0.573580\pi\) | ||||
−0.229105 | + | 0.973402i | \(0.573580\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −47.4489 | −0.0495809 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 449.423i | 0.468637i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1290.20 | −1.34256 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 662.671i | 0.688132i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 903.436i | 0.934267i | 0.884187 | + | 0.467133i | \(0.154713\pi\) | ||||
−0.884187 | + | 0.467133i | \(0.845287\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −854.663 | −0.882005 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1866.89i | 1.92265i | 0.275420 | + | 0.961324i | \(0.411183\pi\) | ||||
−0.275420 | + | 0.961324i | \(0.588817\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1070.56 | −1.10026 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1073.95 | 1.09923 | 0.549615 | − | 0.835418i | \(-0.314774\pi\) | ||||
0.549615 | + | 0.835418i | \(0.314774\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 121.135i | − 0.123733i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1080.58 | −1.10151 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 534.114i | − 0.543351i | −0.962389 | − | 0.271675i | \(-0.912422\pi\) | ||||
0.962389 | − | 0.271675i | \(-0.0875777\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 1143.89i | − 1.15895i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 32.3607 | 0.0327206 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 520.419i | 0.525146i | 0.964912 | + | 0.262573i | \(0.0845710\pi\) | ||||
−0.964912 | + | 0.262573i | \(0.915429\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −619.502 | −0.623869 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 457.680 | 0.459057 | 0.229528 | − | 0.973302i | \(-0.426282\pi\) | ||||
0.229528 | + | 0.973302i | \(0.426282\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 353.781i | 0.354135i |
(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 | 1600.3.b.s.1151.4 | 4 | ||
4.3 | odd | 2 | inner | 1600.3.b.s.1151.1 | 4 | ||
5.2 | odd | 4 | 1600.3.h.n.1599.7 | 8 | |||
5.3 | odd | 4 | 1600.3.h.n.1599.1 | 8 | |||
5.4 | even | 2 | 320.3.b.c.191.1 | 4 | |||
8.3 | odd | 2 | 100.3.b.f.51.4 | 4 | |||
8.5 | even | 2 | 100.3.b.f.51.3 | 4 | |||
15.14 | odd | 2 | 2880.3.e.e.2431.3 | 4 | |||
20.3 | even | 4 | 1600.3.h.n.1599.8 | 8 | |||
20.7 | even | 4 | 1600.3.h.n.1599.2 | 8 | |||
20.19 | odd | 2 | 320.3.b.c.191.4 | 4 | |||
24.5 | odd | 2 | 900.3.c.k.451.2 | 4 | |||
24.11 | even | 2 | 900.3.c.k.451.1 | 4 | |||
40.3 | even | 4 | 100.3.d.b.99.5 | 8 | |||
40.13 | odd | 4 | 100.3.d.b.99.3 | 8 | |||
40.19 | odd | 2 | 20.3.b.a.11.1 | ✓ | 4 | ||
40.27 | even | 4 | 100.3.d.b.99.4 | 8 | |||
40.29 | even | 2 | 20.3.b.a.11.2 | yes | 4 | ||
40.37 | odd | 4 | 100.3.d.b.99.6 | 8 | |||
60.59 | even | 2 | 2880.3.e.e.2431.4 | 4 | |||
80.19 | odd | 4 | 1280.3.g.e.1151.2 | 8 | |||
80.29 | even | 4 | 1280.3.g.e.1151.8 | 8 | |||
80.59 | odd | 4 | 1280.3.g.e.1151.7 | 8 | |||
80.69 | even | 4 | 1280.3.g.e.1151.1 | 8 | |||
120.29 | odd | 2 | 180.3.c.a.91.3 | 4 | |||
120.53 | even | 4 | 900.3.f.e.199.6 | 8 | |||
120.59 | even | 2 | 180.3.c.a.91.4 | 4 | |||
120.77 | even | 4 | 900.3.f.e.199.3 | 8 | |||
120.83 | odd | 4 | 900.3.f.e.199.4 | 8 | |||
120.107 | odd | 4 | 900.3.f.e.199.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
20.3.b.a.11.1 | ✓ | 4 | 40.19 | odd | 2 | ||
20.3.b.a.11.2 | yes | 4 | 40.29 | even | 2 | ||
100.3.b.f.51.3 | 4 | 8.5 | even | 2 | |||
100.3.b.f.51.4 | 4 | 8.3 | odd | 2 | |||
100.3.d.b.99.3 | 8 | 40.13 | odd | 4 | |||
100.3.d.b.99.4 | 8 | 40.27 | even | 4 | |||
100.3.d.b.99.5 | 8 | 40.3 | even | 4 | |||
100.3.d.b.99.6 | 8 | 40.37 | odd | 4 | |||
180.3.c.a.91.3 | 4 | 120.29 | odd | 2 | |||
180.3.c.a.91.4 | 4 | 120.59 | even | 2 | |||
320.3.b.c.191.1 | 4 | 5.4 | even | 2 | |||
320.3.b.c.191.4 | 4 | 20.19 | odd | 2 | |||
900.3.c.k.451.1 | 4 | 24.11 | even | 2 | |||
900.3.c.k.451.2 | 4 | 24.5 | odd | 2 | |||
900.3.f.e.199.3 | 8 | 120.77 | even | 4 | |||
900.3.f.e.199.4 | 8 | 120.83 | odd | 4 | |||
900.3.f.e.199.5 | 8 | 120.107 | odd | 4 | |||
900.3.f.e.199.6 | 8 | 120.53 | even | 4 | |||
1280.3.g.e.1151.1 | 8 | 80.69 | even | 4 | |||
1280.3.g.e.1151.2 | 8 | 80.19 | odd | 4 | |||
1280.3.g.e.1151.7 | 8 | 80.59 | odd | 4 | |||
1280.3.g.e.1151.8 | 8 | 80.29 | even | 4 | |||
1600.3.b.s.1151.1 | 4 | 4.3 | odd | 2 | inner | ||
1600.3.b.s.1151.4 | 4 | 1.1 | even | 1 | trivial | ||
1600.3.h.n.1599.1 | 8 | 5.3 | odd | 4 | |||
1600.3.h.n.1599.2 | 8 | 20.7 | even | 4 | |||
1600.3.h.n.1599.7 | 8 | 5.2 | odd | 4 | |||
1600.3.h.n.1599.8 | 8 | 20.3 | even | 4 | |||
2880.3.e.e.2431.3 | 4 | 15.14 | odd | 2 | |||
2880.3.e.e.2431.4 | 4 | 60.59 | even | 2 |