Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,3,Mod(101,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.101");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.p (of order \(6\), degree \(2\), 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: | \(24.5232237924\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 180) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 401.1 | ||
Character | \(\chi\) | \(=\) | 900.401 |
Dual form | 900.3.p.f.101.1 |
$q$-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 \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −2.88925 | − | 0.807601i | −0.963084 | − | 0.269200i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −6.19003 | − | 10.7214i | −0.884290 | − | 1.53164i | −0.846525 | − | 0.532349i | \(-0.821309\pi\) |
−0.0377652 | − | 0.999287i | \(-0.512024\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.69556 | + | 4.66673i | 0.855062 | + | 0.518525i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.00882 | + | 2.31449i | −0.364438 | + | 0.210408i | −0.671026 | − | 0.741434i | \(-0.734146\pi\) |
0.306588 | + | 0.951842i | \(0.400813\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.631764 | + | 1.09425i | −0.0485972 | + | 0.0841728i | −0.889301 | − | 0.457323i | \(-0.848808\pi\) |
0.840704 | + | 0.541496i | \(0.182142\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 22.9122i | − | 1.34778i | −0.738833 | − | 0.673889i | \(-0.764623\pi\) | ||
0.738833 | − | 0.673889i | \(-0.235377\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −32.8729 | −1.73015 | −0.865075 | − | 0.501642i | \(-0.832730\pi\) | ||||
−0.865075 | + | 0.501642i | \(0.832730\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 9.22592 | + | 35.9760i | 0.439329 | + | 1.71315i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.690324 | − | 0.398559i | −0.0300141 | − | 0.0173286i | 0.484918 | − | 0.874560i | \(-0.338849\pi\) |
−0.514932 | + | 0.857231i | \(0.672183\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −18.4656 | − | 19.6983i | −0.683910 | − | 0.729566i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 34.3302 | − | 19.8206i | 1.18380 | − | 0.683468i | 0.226910 | − | 0.973916i | \(-0.427138\pi\) |
0.956891 | + | 0.290448i | \(0.0938042\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.730215 | + | 1.26477i | −0.0235553 | + | 0.0407990i | −0.877563 | − | 0.479462i | \(-0.840832\pi\) |
0.854007 | + | 0.520261i | \(0.174165\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 13.4517 | − | 3.44963i | 0.407627 | − | 0.104534i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 44.9884 | 1.21590 | 0.607952 | − | 0.793974i | \(-0.291991\pi\) | ||||
0.607952 | + | 0.793974i | \(0.291991\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.70904 | − | 2.65134i | 0.0694626 | − | 0.0679831i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −33.8915 | − | 19.5673i | −0.826623 | − | 0.477251i | 0.0260720 | − | 0.999660i | \(-0.491700\pi\) |
−0.852695 | + | 0.522409i | \(0.825033\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 18.1908 | + | 31.5074i | 0.423043 | + | 0.732731i | 0.996235 | − | 0.0866892i | \(-0.0276287\pi\) |
−0.573193 | + | 0.819421i | \(0.694295\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −52.8629 | + | 30.5204i | −1.12474 | + | 0.649370i | −0.942607 | − | 0.333904i | \(-0.891634\pi\) |
−0.182134 | + | 0.983274i | \(0.558301\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −52.1330 | + | 90.2970i | −1.06394 | + | 1.84280i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −18.5039 | + | 66.1992i | −0.362822 | + | 1.29802i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 13.9872i | − | 0.263909i | −0.991256 | − | 0.131954i | \(-0.957875\pi\) | ||
0.991256 | − | 0.131954i | \(-0.0421252\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 94.9780 | + | 26.5482i | 1.66628 | + | 0.465757i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 50.2415 | + | 29.0069i | 0.851550 | + | 0.491643i | 0.861174 | − | 0.508311i | \(-0.169730\pi\) |
−0.00962347 | + | 0.999954i | \(0.503063\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 27.5253 | + | 47.6752i | 0.451234 | + | 0.781561i | 0.998463 | − | 0.0554222i | \(-0.0176505\pi\) |
−0.547229 | + | 0.836983i | \(0.684317\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.39828 | − | 111.395i | 0.0380680 | − | 1.76817i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −33.4960 | + | 58.0167i | −0.499940 | + | 0.865921i | −1.00000 | 6.94337e-5i | \(-0.999978\pi\) | |
0.500060 | + | 0.865991i | \(0.333311\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.67264 | + | 1.70904i | 0.0242412 | + | 0.0247687i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 70.6560i | 0.995156i | 0.867419 | + | 0.497578i | \(0.165777\pi\) | ||||
−0.867419 | + | 0.497578i | \(0.834223\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −23.1498 | −0.317121 | −0.158561 | − | 0.987349i | \(-0.550685\pi\) | ||||
−0.158561 | + | 0.987349i | \(0.550685\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 49.6294 | + | 28.6536i | 0.644538 | + | 0.372124i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.5725 | − | 25.2404i | −0.184462 | − | 0.319498i | 0.758933 | − | 0.651169i | \(-0.225721\pi\) |
−0.943395 | + | 0.331671i | \(0.892388\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 37.4434 | + | 71.8261i | 0.462264 | + | 0.886743i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −112.958 | + | 65.2165i | −1.36094 | + | 0.785741i | −0.989749 | − | 0.142815i | \(-0.954385\pi\) |
−0.371193 | + | 0.928556i | \(0.621051\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −115.196 | + | 29.5415i | −1.32409 | + | 0.339558i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 48.0873i | 0.540307i | 0.962817 | + | 0.270153i | \(0.0870744\pi\) | ||||
−0.962817 | + | 0.270153i | \(0.912926\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 15.6425 | 0.171896 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.13120 | − | 3.06452i | 0.0336689 | − | 0.0329518i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.68803 | − | 16.7802i | −0.0998766 | − | 0.172991i | 0.811757 | − | 0.583996i | \(-0.198511\pi\) |
−0.911633 | + | 0.411004i | \(0.865178\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −41.6512 | − | 0.896733i | −0.420719 | − | 0.00905791i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −112.152 | + | 64.7508i | −1.11041 | + | 0.641097i | −0.938936 | − | 0.344092i | \(-0.888187\pi\) |
−0.171476 | + | 0.985188i | \(0.554854\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.20123 | − | 7.27674i | 0.0407886 | − | 0.0706480i | −0.844910 | − | 0.534908i | \(-0.820346\pi\) |
0.885699 | + | 0.464260i | \(0.153680\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 61.1389i | − | 0.571391i | −0.958320 | − | 0.285696i | \(-0.907775\pi\) | ||
0.958320 | − | 0.285696i | \(-0.0922246\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 161.771 | 1.48414 | 0.742068 | − | 0.670324i | \(-0.233845\pi\) | ||||
0.742068 | + | 0.670324i | \(0.233845\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −129.983 | − | 36.3327i | −1.17102 | − | 0.327322i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −29.6592 | − | 17.1238i | −0.262471 | − | 0.151538i | 0.362990 | − | 0.931793i | \(-0.381756\pi\) |
−0.625461 | + | 0.780255i | \(0.715089\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −9.96833 | + | 5.47258i | −0.0851994 | + | 0.0467742i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −245.652 | + | 141.827i | −2.06430 | + | 1.19183i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −49.7862 | + | 86.2323i | −0.411457 | + | 0.712664i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 82.1187 | + | 83.9057i | 0.667632 | + | 0.682160i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 104.320 | 0.821421 | 0.410710 | − | 0.911766i | \(-0.365281\pi\) | ||||
0.410710 | + | 0.911766i | \(0.365281\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −27.1125 | − | 105.724i | −0.210174 | − | 0.819565i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 190.209 | + | 109.817i | 1.45198 | + | 0.838299i | 0.998594 | − | 0.0530175i | \(-0.0168839\pi\) |
0.453382 | + | 0.891316i | \(0.350217\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 203.484 | + | 352.445i | 1.52996 | + | 2.64996i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −164.090 | + | 94.7374i | −1.19774 | + | 0.691514i | −0.960050 | − | 0.279828i | \(-0.909722\pi\) |
−0.237687 | + | 0.971342i | \(0.576389\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 110.020 | − | 190.560i | 0.791511 | − | 1.37094i | −0.133520 | − | 0.991046i | \(-0.542628\pi\) |
0.925031 | − | 0.379892i | \(-0.124039\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 177.382 | − | 45.4890i | 1.25803 | − | 0.322617i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 5.84885i | − | 0.0409010i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 223.549 | − | 218.788i | 1.52074 | − | 1.48835i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.00402 | + | 5.19847i | 0.0604297 | + | 0.0348891i | 0.529910 | − | 0.848054i | \(-0.322226\pi\) |
−0.469481 | + | 0.882943i | \(0.655559\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 40.8811 | + | 70.8081i | 0.270736 | + | 0.468928i | 0.969050 | − | 0.246863i | \(-0.0793998\pi\) |
−0.698315 | + | 0.715791i | \(0.746066\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 106.925 | − | 176.322i | 0.698856 | − | 1.15243i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −66.1558 | + | 114.585i | −0.421375 | + | 0.729842i | −0.996074 | − | 0.0885222i | \(-0.971786\pi\) |
0.574700 | + | 0.818364i | \(0.305119\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −11.2960 | + | 40.4124i | −0.0710443 | + | 0.254166i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.86836i | 0.0612942i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 81.7721 | 0.501669 | 0.250835 | − | 0.968030i | \(-0.419295\pi\) | ||||
0.250835 | + | 0.968030i | \(0.419295\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 23.9909 | + | 13.8512i | 0.143658 | + | 0.0829411i | 0.570106 | − | 0.821571i | \(-0.306902\pi\) |
−0.426448 | + | 0.904512i | \(0.640235\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 83.7017 | + | 144.976i | 0.495277 | + | 0.857844i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −252.975 | − | 153.409i | −1.47939 | − | 0.897127i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −241.288 | + | 139.308i | −1.39473 | + | 0.805246i | −0.993834 | − | 0.110878i | \(-0.964634\pi\) |
−0.400894 | + | 0.916125i | \(0.631300\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −121.734 | − | 124.383i | −0.687764 | − | 0.702731i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 175.928i | − | 0.982839i | −0.870923 | − | 0.491419i | \(-0.836478\pi\) | ||
0.870923 | − | 0.491419i | \(-0.163522\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −180.887 | −0.999377 | −0.499689 | − | 0.866205i | \(-0.666552\pi\) | ||||
−0.499689 | + | 0.866205i | \(0.666552\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −41.0250 | − | 159.975i | −0.224180 | − | 0.874181i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 53.0302 | + | 91.8509i | 0.283584 | + | 0.491181i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −96.8917 | + | 319.911i | −0.512655 | + | 1.69265i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 120.178 | − | 69.3846i | 0.629202 | − | 0.363270i | −0.151241 | − | 0.988497i | \(-0.548327\pi\) |
0.780443 | + | 0.625227i | \(0.214994\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 89.4876 | − | 154.997i | 0.463666 | − | 0.803093i | −0.535474 | − | 0.844552i | \(-0.679867\pi\) |
0.999140 | + | 0.0414582i | \(0.0132004\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 136.877i | − | 0.694809i | −0.937715 | − | 0.347405i | \(-0.887063\pi\) | ||
0.937715 | − | 0.347405i | \(-0.112937\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.4634 | −0.0576050 | −0.0288025 | − | 0.999585i | \(-0.509169\pi\) | ||||
−0.0288025 | + | 0.999585i | \(0.509169\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 143.633 | − | 140.574i | 0.714590 | − | 0.699371i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −425.010 | − | 245.380i | −2.09365 | − | 1.20877i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.45247 | − | 6.28869i | −0.0166786 | − | 0.0303801i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 131.781 | − | 76.0840i | 0.630533 | − | 0.364038i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 38.7228 | − | 67.0698i | 0.183520 | − | 0.317867i | −0.759557 | − | 0.650441i | \(-0.774584\pi\) |
0.943077 | + | 0.332575i | \(0.107917\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 57.0619 | − | 204.143i | 0.267896 | − | 0.958419i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.0802 | 0.0833190 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 66.8857 | + | 18.6958i | 0.305414 | + | 0.0853691i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 25.0716 | + | 14.4751i | 0.113446 | + | 0.0654982i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 72.1175 | + | 124.911i | 0.323397 | + | 0.560140i | 0.981187 | − | 0.193062i | \(-0.0618417\pi\) |
−0.657790 | + | 0.753202i | \(0.728508\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 42.5248 | − | 24.5517i | 0.187334 | − | 0.108157i | −0.403400 | − | 0.915024i | \(-0.632172\pi\) |
0.590734 | + | 0.806867i | \(0.298838\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −50.4902 | + | 87.4515i | −0.220481 | + | 0.381884i | −0.954954 | − | 0.296753i | \(-0.904096\pi\) |
0.734473 | + | 0.678638i | \(0.237429\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −120.251 | − | 122.868i | −0.520568 | − | 0.531897i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 120.466i | − | 0.517021i | −0.966009 | − | 0.258510i | \(-0.916768\pi\) | ||
0.966009 | − | 0.258510i | \(-0.0832316\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 21.7196 | + | 84.6946i | 0.0916438 | + | 0.357361i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −157.093 | − | 90.6979i | −0.657294 | − | 0.379489i | 0.133951 | − | 0.990988i | \(-0.457234\pi\) |
−0.791245 | + | 0.611499i | \(0.790567\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −81.1538 | − | 140.562i | −0.336738 | − | 0.583247i | 0.647079 | − | 0.762423i | \(-0.275990\pi\) |
−0.983817 | + | 0.179176i | \(0.942657\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −50.1765 | − | 237.763i | −0.206488 | − | 0.978449i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 20.7679 | − | 35.9710i | 0.0840805 | − | 0.145632i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 379.034 | − | 97.2017i | 1.52222 | − | 0.390368i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 445.457i | − | 1.77473i | −0.461069 | − | 0.887364i | \(-0.652534\pi\) | ||
0.461069 | − | 0.887364i | \(-0.347466\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.68984 | 0.0145844 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −214.270 | − | 123.709i | −0.833734 | − | 0.481357i | 0.0213954 | − | 0.999771i | \(-0.493189\pi\) |
−0.855129 | + | 0.518414i | \(0.826522\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −278.480 | − | 482.341i | −1.07521 | − | 1.86232i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 356.688 | + | 7.67933i | 1.36662 | + | 0.0294227i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −74.4992 | + | 43.0121i | −0.283267 | + | 0.163544i | −0.634901 | − | 0.772593i | \(-0.718959\pi\) |
0.351635 | + | 0.936137i | \(0.385626\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 38.8353 | − | 138.936i | 0.145451 | − | 0.520361i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 368.618i | − | 1.37033i | −0.728389 | − | 0.685164i | \(-0.759731\pi\) | ||
0.728389 | − | 0.685164i | \(-0.240269\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −130.740 | −0.482434 | −0.241217 | − | 0.970471i | \(-0.577546\pi\) | ||||
−0.241217 | + | 0.970471i | \(0.577546\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −45.1953 | − | 12.6329i | −0.165550 | − | 0.0462745i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −108.635 | − | 188.162i | −0.392185 | − | 0.679284i | 0.600553 | − | 0.799585i | \(-0.294947\pi\) |
−0.992737 | + | 0.120301i | \(0.961614\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −11.5217 | + | 6.32540i | −0.0412966 | + | 0.0226717i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 149.240 | − | 86.1636i | 0.531102 | − | 0.306632i | −0.210363 | − | 0.977623i | \(-0.567465\pi\) |
0.741465 | + | 0.670991i | \(0.234131\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −218.079 | + | 377.723i | −0.770596 | + | 1.33471i | 0.166640 | + | 0.986018i | \(0.446708\pi\) |
−0.937237 | + | 0.348694i | \(0.886625\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 484.489i | 1.68811i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −235.970 | −0.816504 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.4395 | + | 56.3062i | 0.0496203 | + | 0.193492i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 25.1499 | + | 14.5203i | 0.0858359 | + | 0.0495574i | 0.542304 | − | 0.840183i | \(-0.317552\pi\) |
−0.456468 | + | 0.889740i | \(0.650886\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 119.617 | + | 36.2284i | 0.402750 | + | 0.121981i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.872243 | − | 0.503590i | 0.00291720 | − | 0.00168425i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 225.204 | − | 390.064i | 0.748185 | − | 1.29589i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 376.327 | − | 96.5076i | 1.24200 | − | 0.318507i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 306.163 | 0.997273 | 0.498637 | − | 0.866811i | \(-0.333834\pi\) | ||||
0.498637 | + | 0.866811i | \(0.333834\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −18.0151 | + | 17.6314i | −0.0583013 | + | 0.0570596i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −344.003 | − | 198.610i | −1.10612 | − | 0.638618i | −0.168298 | − | 0.985736i | \(-0.553827\pi\) |
−0.937821 | + | 0.347118i | \(0.887160\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 195.881 | + | 339.276i | 0.625818 | + | 1.08395i | 0.988382 | + | 0.151990i | \(0.0485681\pi\) |
−0.362564 | + | 0.931959i | \(0.618099\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 140.112 | − | 80.8940i | 0.441995 | − | 0.255186i | −0.262448 | − | 0.964946i | \(-0.584530\pi\) |
0.704444 | + | 0.709760i | \(0.251197\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −91.7491 | + | 158.914i | −0.287615 | + | 0.498164i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −49.3758 | + | 176.646i | −0.153819 | + | 0.550298i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 753.190i | 2.33186i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −467.397 | − | 130.646i | −1.42935 | − | 0.399530i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 654.446 | + | 377.844i | 1.98920 | + | 1.14846i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −118.594 | − | 205.411i | −0.358291 | − | 0.620578i | 0.629385 | − | 0.777094i | \(-0.283307\pi\) |
−0.987675 | + | 0.156516i | \(0.949974\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 346.211 | + | 209.949i | 1.03967 | + | 0.630476i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −211.024 | + | 365.505i | −0.626185 | + | 1.08458i | 0.362125 | + | 0.932129i | \(0.382051\pi\) |
−0.988310 | + | 0.152455i | \(0.951282\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 71.8638 | + | 73.4276i | 0.211988 | + | 0.216601i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 6.76031i | − | 0.0198250i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 684.196 | 1.99474 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −478.474 | − | 276.247i | −1.37889 | − | 0.796102i | −0.386863 | − | 0.922137i | \(-0.626441\pi\) |
−0.992026 | + | 0.126036i | \(0.959775\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 198.589 | + | 343.966i | 0.569022 | + | 0.985575i | 0.996663 | + | 0.0816263i | \(0.0260114\pi\) |
−0.427641 | + | 0.903949i | \(0.640655\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 33.2207 | − | 7.76123i | 0.0946458 | − | 0.0221118i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −267.320 | + | 154.337i | −0.757281 | + | 0.437216i | −0.828319 | − | 0.560257i | \(-0.810702\pi\) |
0.0710376 | + | 0.997474i | \(0.477369\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 824.291 | − | 211.386i | 2.30894 | − | 0.592118i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 278.225i | − | 0.775000i | −0.921870 | − | 0.387500i | \(-0.873339\pi\) | ||
0.921870 | − | 0.387500i | \(-0.126661\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 719.626 | 1.99342 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 213.486 | − | 208.940i | 0.588117 | − | 0.575591i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 304.122 | + | 526.754i | 0.828669 | + | 1.43530i | 0.899082 | + | 0.437780i | \(0.144235\pi\) |
−0.0704128 | + | 0.997518i | \(0.522432\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −169.499 | − | 308.744i | −0.459348 | − | 0.836704i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −149.963 | + | 86.5810i | −0.404212 | + | 0.233372i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −179.439 | + | 310.798i | −0.481070 | + | 0.833238i | −0.999764 | − | 0.0217222i | \(-0.993085\pi\) |
0.518694 | + | 0.854960i | \(0.326418\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 50.0877i | 0.132859i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −353.208 | −0.931948 | −0.465974 | − | 0.884798i | \(-0.654296\pi\) | ||||
−0.465974 | + | 0.884798i | \(0.654296\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −301.408 | − | 84.2493i | −0.791097 | − | 0.221127i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −235.029 | − | 135.694i | −0.613653 | − | 0.354293i | 0.160741 | − | 0.986997i | \(-0.448612\pi\) |
−0.774394 | + | 0.632704i | \(0.781945\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.04790 | + | 327.359i | −0.0182116 | + | 0.845889i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −227.502 | + | 131.349i | −0.584839 | + | 0.337657i | −0.763054 | − | 0.646334i | \(-0.776301\pi\) |
0.178215 | + | 0.983992i | \(0.442968\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.13186 | + | 15.8169i | −0.0233552 | + | 0.0404523i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −460.873 | − | 470.902i | −1.17270 | − | 1.19822i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −53.4516 | −0.134639 | −0.0673194 | − | 0.997731i | \(-0.521445\pi\) | ||||
−0.0673194 | + | 0.997731i | \(0.521445\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −303.282 | − | 1182.64i | −0.760106 | − | 2.96400i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −160.143 | − | 92.4584i | −0.399358 | − | 0.230570i | 0.286849 | − | 0.957976i | \(-0.407392\pi\) |
−0.686207 | + | 0.727406i | \(0.740726\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.922647 | − | 1.59807i | −0.00228945 | − | 0.00396544i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −180.350 | + | 104.125i | −0.443122 | + | 0.255836i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 116.052 | − | 201.008i | 0.283746 | − | 0.491463i | −0.688558 | − | 0.725181i | \(-0.741756\pi\) |
0.972304 | + | 0.233718i | \(0.0750893\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 550.607 | − | 141.201i | 1.33968 | − | 0.343555i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 718.215i | − | 1.73902i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −471.772 | + | 461.725i | −1.13135 | + | 1.10725i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 336.098 | + | 194.046i | 0.802143 | + | 0.463117i | 0.844220 | − | 0.535997i | \(-0.180064\pi\) |
−0.0420770 | + | 0.999114i | \(0.513397\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −77.0016 | − | 133.371i | −0.182902 | − | 0.316795i | 0.759966 | − | 0.649963i | \(-0.225216\pi\) |
−0.942867 | + | 0.333168i | \(0.891882\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −549.240 | − | 11.8249i | −1.29844 | − | 0.0279548i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 340.765 | − | 590.222i | 0.798044 | − | 1.38225i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.72354 | + | 16.8988i | −0.0110106 | + | 0.0393912i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 238.147i | − | 0.552544i | −0.961079 | − | 0.276272i | \(-0.910901\pi\) | ||
0.961079 | − | 0.276272i | \(-0.0890991\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −523.956 | −1.21006 | −0.605030 | − | 0.796203i | \(-0.706839\pi\) | ||||
−0.605030 | + | 0.796203i | \(0.706839\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 22.6929 | + | 13.1018i | 0.0519289 | + | 0.0299812i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 228.172 | + | 395.206i | 0.519755 | + | 0.900242i | 0.999736 | + | 0.0229630i | \(0.00730999\pi\) |
−0.479982 | + | 0.877279i | \(0.659357\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −822.584 | + | 451.596i | −1.86527 | + | 1.02403i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 235.368 | − | 135.890i | 0.531305 | − | 0.306749i | −0.210242 | − | 0.977649i | \(-0.567425\pi\) |
0.741548 | + | 0.670900i | \(0.234092\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −21.8166 | − | 22.2914i | −0.0488067 | − | 0.0498688i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 386.192i | 0.860116i | 0.902801 | + | 0.430058i | \(0.141507\pi\) | ||||
−0.902801 | + | 0.430058i | \(0.858493\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 181.153 | 0.401671 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −60.9311 | − | 237.598i | −0.134506 | − | 0.524499i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.24416 | + | 3.88700i | 0.00491063 | + | 0.00850546i | 0.868470 | − | 0.495741i | \(-0.165104\pi\) |
−0.863560 | + | 0.504247i | \(0.831770\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −451.331 | + | 423.087i | −0.983293 | + | 0.921759i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −283.502 | + | 163.680i | −0.614972 | + | 0.355054i | −0.774909 | − | 0.632073i | \(-0.782204\pi\) |
0.159937 | + | 0.987127i | \(0.448871\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 106.071 | − | 183.720i | 0.229094 | − | 0.396803i | −0.728446 | − | 0.685103i | \(-0.759757\pi\) |
0.957540 | + | 0.288301i | \(0.0930903\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 471.246i | 1.00909i | 0.863385 | + | 0.504546i | \(0.168340\pi\) | ||||
−0.863385 | + | 0.504546i | \(0.831660\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 829.364 | 1.76837 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 283.680 | − | 277.638i | 0.602293 | − | 0.589465i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −145.847 | − | 84.2051i | −0.308346 | − | 0.178023i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 65.2742 | − | 107.639i | 0.136843 | − | 0.225658i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −762.164 | + | 440.035i | −1.59116 | + | 0.918654i | −0.598047 | + | 0.801461i | \(0.704056\pi\) |
−0.993109 | + | 0.117193i | \(0.962610\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −28.4221 | + | 49.2285i | −0.0590895 | + | 0.102346i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7.96970 | − | 28.5122i | 0.0165004 | − | 0.0590315i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −606.421 | −1.24522 | −0.622609 | − | 0.782533i | \(-0.713927\pi\) | ||||
−0.622609 | + | 0.782533i | \(0.713927\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −236.260 | − | 66.0392i | −0.483150 | − | 0.135050i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 488.016 | + | 281.756i | 0.993922 | + | 0.573841i | 0.906444 | − | 0.422325i | \(-0.138786\pi\) |
0.0874776 | + | 0.996166i | \(0.472119\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −454.133 | − | 786.582i | −0.921163 | − | 1.59550i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 757.535 | − | 437.363i | 1.52422 | − | 0.880006i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 35.9407 | − | 62.2511i | 0.0720254 | − | 0.124752i | −0.827763 | − | 0.561077i | \(-0.810387\pi\) |
0.899789 | + | 0.436326i | \(0.143720\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −58.1296 | − | 59.3946i | −0.116027 | − | 0.118552i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 124.538i | 0.247591i | 0.992308 | + | 0.123795i | \(0.0395067\pi\) | ||||
−0.992308 | + | 0.123795i | \(0.960493\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −124.753 | − | 486.469i | −0.246061 | − | 0.959505i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 466.058 | + | 269.079i | 0.915634 | + | 0.528642i | 0.882240 | − | 0.470801i | \(-0.156035\pi\) |
0.0333945 | + | 0.999442i | \(0.489368\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 143.298 | + | 248.200i | 0.280427 | + | 0.485714i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 607.016 | + | 647.539i | 1.18327 | + | 1.26226i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 141.278 | − | 244.701i | 0.273266 | − | 0.473310i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 809.647 | − | 207.631i | 1.56001 | − | 0.400059i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 147.767i | 0.283622i | 0.989894 | + | 0.141811i | \(0.0452925\pi\) | ||||
−0.989894 | + | 0.141811i | \(0.954707\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 701.166 | 1.34066 | 0.670331 | − | 0.742063i | \(-0.266152\pi\) | ||||
0.670331 | + | 0.742063i | \(0.266152\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 28.9787 | + | 16.7308i | 0.0549880 | + | 0.0317473i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −264.182 | − | 457.577i | −0.499399 | − | 0.864985i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 251.269 | + | 457.688i | 0.473200 | + | 0.861935i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 42.8229 | − | 24.7238i | 0.0803431 | − | 0.0463861i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −142.080 | + | 508.301i | −0.264580 | + | 0.946556i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 482.646i | − | 0.895446i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −573.411 | −1.05991 | −0.529955 | − | 0.848026i | \(-0.677791\pi\) | ||||
−0.529955 | + | 0.848026i | \(0.677791\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 522.629 | + | 146.085i | 0.962484 | + | 0.269033i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 152.510 | + | 264.155i | 0.278812 | + | 0.482916i | 0.971090 | − | 0.238715i | \(-0.0767261\pi\) |
−0.692278 | + | 0.721631i | \(0.743393\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −10.6645 | + | 495.341i | −0.0194253 | + | 0.902260i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1128.53 | + | 651.559i | −2.04815 | + | 1.18250i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −180.409 | + | 312.477i | −0.326237 | + | 0.565058i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 686.875i | − | 1.23317i | −0.787288 | − | 0.616585i | \(-0.788516\pi\) | ||
0.787288 | − | 0.616585i | \(-0.211484\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −45.9692 | −0.0822348 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −79.0386 | − | 308.208i | −0.140889 | − | 0.549390i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 402.756 | + | 232.531i | 0.715374 | + | 0.413021i | 0.813048 | − | 0.582197i | \(-0.197807\pi\) |
−0.0976736 | + | 0.995219i | \(0.531140\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 538.305 | − | 846.053i | 0.949391 | − | 1.49216i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −954.086 | + | 550.842i | −1.67678 | + | 0.968088i | −0.713084 | + | 0.701079i | \(0.752702\pi\) |
−0.963694 | + | 0.267009i | \(0.913965\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −381.027 | + | 659.958i | −0.667298 | + | 1.15579i | 0.311359 | + | 0.950292i | \(0.399216\pi\) |
−0.978657 | + | 0.205501i | \(0.934118\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −403.259 | + | 103.414i | −0.703767 | + | 0.180478i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −673.918 | −1.16797 | −0.583985 | − | 0.811765i | \(-0.698507\pi\) | ||||
−0.583985 | + | 0.811765i | \(0.698507\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −383.728 | + | 375.555i | −0.662743 | + | 0.648628i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1398.43 | + | 807.384i | 2.40694 | + | 1.38965i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 32.3732 | + | 56.0720i | 0.0555286 | + | 0.0961784i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −337.196 | + | 194.680i | −0.574439 | + | 0.331653i | −0.758920 | − | 0.651183i | \(-0.774273\pi\) |
0.184481 | + | 0.982836i | \(0.440939\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 24.0043 | − | 41.5766i | 0.0407543 | − | 0.0705885i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −110.542 | + | 395.473i | −0.187043 | + | 0.669160i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 640.797i | 1.08060i | 0.841472 | + | 0.540301i | \(0.181690\pi\) | ||||
−0.841472 | + | 0.540301i | \(0.818310\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 33.1206 | + | 9.25784i | 0.0554785 | + | 0.0155073i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −403.936 | − | 233.212i | −0.674350 | − | 0.389336i | 0.123373 | − | 0.992360i | \(-0.460629\pi\) |
−0.797723 | + | 0.603024i | \(0.793962\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 493.215 | + | 854.273i | 0.820657 | + | 1.42142i | 0.905194 | + | 0.425000i | \(0.139726\pi\) |
−0.0845364 | + | 0.996420i | \(0.526941\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −528.518 | + | 290.155i | −0.876482 | + | 0.481185i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 434.982 | − | 753.411i | 0.716610 | − | 1.24120i | −0.245725 | − | 0.969339i | \(-0.579026\pi\) |
0.962335 | − | 0.271865i | \(-0.0876405\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1029.79 | + | 1052.20i | 1.69096 | + | 1.72776i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 77.1267i | − | 0.126230i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 376.400 | 0.614029 | 0.307014 | − | 0.951705i | \(-0.400670\pi\) | ||||
0.307014 | + | 0.951705i | \(0.400670\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −100.567 | − | 58.0623i | −0.162993 | − | 0.0941041i | 0.416285 | − | 0.909234i | \(-0.363332\pi\) |
−0.579278 | + | 0.815130i | \(0.696665\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 119.765 | + | 207.439i | 0.193482 | + | 0.335120i | 0.946402 | − | 0.322992i | \(-0.104689\pi\) |
−0.752920 | + | 0.658112i | \(0.771355\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.89630 | + | 20.9578i | 0.00788455 | + | 0.0337485i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 515.566 | − | 297.662i | 0.827553 | − | 0.477788i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −442.195 | + | 113.399i | −0.705255 | + | 0.180860i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1030.78i | − | 1.63877i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −590.863 | −0.936392 | −0.468196 | − | 0.883625i | \(-0.655096\pi\) | ||||
−0.468196 | + | 0.883625i | \(0.655096\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −166.046 | + | 162.509i | −0.262315 | + | 0.256729i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −65.8715 | − | 114.093i | −0.103409 | − | 0.179109i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −329.732 | + | 543.738i | −0.516013 | + | 0.850920i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 663.399 | − | 383.014i | 1.03494 | − | 0.597525i | 0.116547 | − | 0.993185i | \(-0.462817\pi\) |
0.918397 | + | 0.395660i | \(0.129484\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −38.0263 | + | 65.8635i | −0.0591389 | + | 0.102432i | −0.894079 | − | 0.447909i | \(-0.852169\pi\) |
0.834940 | + | 0.550341i | \(0.185502\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 287.130i | − | 0.443786i | −0.975071 | − | 0.221893i | \(-0.928776\pi\) | ||
0.975071 | − | 0.221893i | \(-0.0712236\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −268.545 | −0.413783 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −52.2383 | − | 14.6016i | −0.0802432 | − | 0.0224295i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 194.364 | + | 112.216i | 0.297647 | + | 0.171847i | 0.641386 | − | 0.767219i | \(-0.278360\pi\) |
−0.343738 | + | 0.939066i | \(0.611693\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −178.151 | − | 108.034i | −0.271158 | − | 0.164435i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 942.931 | − | 544.401i | 1.43085 | − | 0.826102i | 0.433665 | − | 0.901074i | \(-0.357220\pi\) |
0.997186 | + | 0.0749720i | \(0.0238867\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −439.376 | + | 761.021i | −0.664714 | + | 1.15132i | 0.314649 | + | 0.949208i | \(0.398113\pi\) |
−0.979363 | + | 0.202110i | \(0.935220\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −60.7481 | − | 62.0701i | −0.0916262 | − | 0.0936201i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −31.5986 | −0.0473743 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −107.487 | − | 419.142i | −0.160669 | − | 0.626521i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −220.688 | − | 127.414i | −0.328894 | − | 0.189887i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −278.142 | − | 481.757i | −0.413287 | − | 0.715835i | 0.581960 | − | 0.813218i | \(-0.302286\pi\) |
−0.995247 | + | 0.0973831i | \(0.968953\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −486.720 | + | 281.008i | −0.718937 | + | 0.415078i | −0.814361 | − | 0.580358i | \(-0.802913\pi\) |
0.0954244 | + | 0.995437i | \(0.469579\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −119.938 | + | 207.739i | −0.176640 | + | 0.305949i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −142.693 | + | 36.5930i | −0.209534 | + | 0.0537342i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 500.931i | − | 0.733427i | −0.930334 | − | 0.366714i | \(-0.880483\pi\) | ||
0.930334 | − | 0.366714i | \(-0.119517\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 216.505 | − | 211.894i | 0.315145 | − | 0.308433i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 15.3054 | + | 8.83658i | 0.0222139 | + | 0.0128252i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −361.250 | − | 625.703i | −0.522793 | − | 0.905504i | −0.999648 | − | 0.0265221i | \(-0.991557\pi\) |
0.476855 | − | 0.878982i | \(-0.341777\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 248.208 | + | 452.112i | 0.358165 | + | 0.652399i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −448.330 | + | 776.530i | −0.643228 | + | 1.11410i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −97.2883 | + | 348.056i | −0.139182 | + | 0.497934i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 788.759i | 1.12519i | 0.826732 | + | 0.562595i | \(0.190197\pi\) | ||||
−0.826732 | + | 0.562595i | \(0.809803\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1478.90 | −2.10370 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1388.44 | + | 801.618i | 1.96385 | + | 1.13383i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −199.643 | − | 345.792i | −0.281584 | − | 0.487718i | 0.690191 | − | 0.723627i | \(-0.257526\pi\) |
−0.971775 | + | 0.235910i | \(0.924193\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.64602 | − | 262.245i | 0.00794095 | − | 0.368839i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.00817 | − | 0.582067i | 0.00141398 | − | 0.000816364i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 380.635 | + | 388.918i | 0.530871 | + | 0.542424i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 844.389i | − | 1.17439i | −0.809444 | − | 0.587197i | \(-0.800232\pi\) | ||
0.809444 | − | 0.587197i | \(-0.199768\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −104.023 | −0.144276 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 120.955 | + | 471.660i | 0.167297 | + | 0.652365i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 202.857 | + | 351.359i | 0.279033 | + | 0.483300i | 0.971145 | − | 0.238491i | \(-0.0766526\pi\) |
−0.692111 | + | 0.721791i | \(0.743319\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −47.0452 | + | 727.480i | −0.0645339 | + | 0.997916i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 721.905 | − | 416.792i | 0.987559 | − | 0.570167i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 602.495 | − | 1043.55i | 0.821958 | − | 1.42367i | −0.0822636 | − | 0.996611i | \(-0.526215\pi\) |
0.904222 | − | 0.427063i | \(-0.140452\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 310.105i | − | 0.420766i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −539.145 | −0.729561 | −0.364780 | − | 0.931094i | \(-0.618856\pi\) | ||||
−0.364780 | + | 0.931094i | \(0.618856\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −89.0539 | + | 87.1572i | −0.120181 | + | 0.117621i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 269.337 | + | 155.502i | 0.362500 | + | 0.209289i | 0.670177 | − | 0.742202i | \(-0.266218\pi\) |
−0.307677 | + | 0.951491i | \(0.599552\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1173.62 | − | 25.2676i | −1.57112 | − | 0.0338255i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −655.497 | + | 378.452i | −0.875163 | + | 0.505276i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −463.288 | + | 802.439i | −0.616895 | + | 1.06849i | 0.373153 | + | 0.927770i | \(0.378276\pi\) |
−0.990049 | + | 0.140724i | \(0.955057\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −359.751 | + | 1287.04i | −0.477757 | + | 1.70921i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −450.364 | −0.594933 | −0.297467 | − | 0.954732i | \(-0.596142\pi\) | ||||
−0.297467 | + | 0.954732i | \(0.596142\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10.6609 | − | 2.97992i | −0.0140460 | − | 0.00392612i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −581.319 | − | 335.624i | −0.763888 | − | 0.441031i | 0.0668021 | − | 0.997766i | \(-0.478720\pi\) |
−0.830690 | + | 0.556735i | \(0.812054\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1001.37 | − | 1734.42i | −1.31241 | − | 2.27316i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −63.4815 | + | 36.6510i | −0.0827659 | + | 0.0477849i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −37.3520 | + | 64.6955i | −0.0485721 | + | 0.0841294i | −0.889289 | − | 0.457345i | \(-0.848800\pi\) |
0.840717 | + | 0.541475i | \(0.182134\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 519.172 | + | 530.470i | 0.673375 | + | 0.688028i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 1226.34i | − | 1.58647i | −0.608917 | − | 0.793234i | \(-0.708396\pi\) | ||
0.608917 | − | 0.793234i | \(-0.291604\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 415.060 | + | 1618.51i | 0.534182 | + | 2.08302i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1114.11 | + | 643.233i | 1.43018 | + | 0.825716i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −163.533 | − | 283.247i | −0.209389 | − | 0.362673i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1024.36 | − | 310.249i | −1.30825 | − | 0.396231i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 129.596 | − | 224.466i | 0.164670 | − | 0.285218i | −0.771868 | − | 0.635783i | \(-0.780677\pi\) |
0.936538 | + | 0.350566i | \(0.114011\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 249.984 | − | 64.1073i | 0.316836 | − | 0.0812513i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 423.986i | 0.536013i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −69.5579 | −0.0877149 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1286.14 | + | 742.554i | 1.61373 | + | 0.931686i | 0.988496 | + | 0.151247i | \(0.0483287\pi\) |
0.625231 | + | 0.780439i | \(0.285005\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 699.290 | + | 1211.21i | 0.875206 | + | 1.51590i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −224.410 | + | 370.059i | −0.280163 | + | 0.461996i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 92.8035 | − | 53.5801i | 0.115571 | − | 0.0667249i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −297.696 | + | 1065.03i | −0.368893 | + | 1.31974i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 10.2026i | − | 0.0126114i | −0.999980 | − | 0.00630569i | \(-0.997993\pi\) | ||
0.999980 | − | 0.00630569i | \(-0.00200718\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1113.80 | 1.37337 | 0.686685 | − | 0.726955i | \(-0.259065\pi\) | ||||
0.686685 | + | 0.726955i | \(0.259065\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 377.739 | + | 105.585i | 0.464624 | + | 0.129871i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −597.985 | − | 1035.74i | −0.731928 | − | 1.26774i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 120.378 | + | 72.9995i | 0.146982 | + | 0.0891324i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −266.290 | + | 153.742i | −0.324348 | + | 0.187262i | −0.653329 | − | 0.757074i | \(-0.726628\pi\) |
0.328981 | + | 0.944337i | \(0.393295\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −297.749 | + | 515.717i | −0.361785 | + | 0.626630i | −0.988255 | − | 0.152816i | \(-0.951166\pi\) |
0.626469 | + | 0.779446i | \(0.284499\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1110.81i | 1.34318i | 0.740921 | + | 0.671592i | \(0.234389\pi\) | ||||
−0.740921 | + | 0.671592i | \(0.765611\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −390.454 | −0.470994 | −0.235497 | − | 0.971875i | \(-0.575672\pi\) | ||||
−0.235497 | + | 0.971875i | \(0.575672\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 161.915 | + | 631.381i | 0.194844 | + | 0.759784i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2068.90 | + | 1194.48i | 2.48368 | + | 1.43395i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 38.3976 | − | 8.97071i | 0.0458753 | − | 0.0107177i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −928.946 | + | 536.327i | −1.10721 | + | 0.639246i | −0.938104 | − | 0.346353i | \(-0.887420\pi\) |
−0.169102 | + | 0.985599i | \(0.554087\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 365.210 | − | 632.562i | 0.434257 | − | 0.752155i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −500.777 | + | 128.422i | −0.594041 | + | 0.152340i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1232.71 | 1.45539 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 935.134 | − | 915.218i | 1.10145 | − | 1.07800i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −31.0566 | − | 17.9305i | −0.0364942 | − | 0.0210700i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 454.724 | + | 787.604i | 0.533087 | + | 0.923334i | 0.999253 | + | 0.0386371i | \(0.0123016\pi\) |
−0.466166 | + | 0.884697i | \(0.654365\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 564.185 | − | 325.732i | 0.658325 | − | 0.380084i | −0.133313 | − | 0.991074i | \(-0.542562\pi\) |
0.791639 | + | 0.610990i | \(0.209228\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 230.239 | − | 398.786i | 0.268032 | − | 0.464244i | −0.700322 | − | 0.713827i | \(-0.746960\pi\) |
0.968353 | + | 0.249583i | \(0.0802935\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 391.273 | − | 1399.81i | 0.454441 | − | 1.62580i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 359.492i | 0.416560i | 0.978069 | + | 0.208280i | \(0.0667866\pi\) | ||||
−0.978069 | + | 0.208280i | \(0.933213\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 681.776 | + | 190.569i | 0.786362 | + | 0.219803i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 116.837 | + | 67.4560i | 0.134450 | + | 0.0776249i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −42.3231 | − | 73.3057i | −0.0485914 | − | 0.0841627i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.75356 | − | 174.344i | 0.00429960 | − | 0.199707i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −569.520 | + | 986.437i | −0.649395 | + | 1.12479i | 0.333872 | + | 0.942618i | \(0.391645\pi\) |
−0.983268 | + | 0.182167i | \(0.941689\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −60.9379 | − | 62.2639i | −0.0693263 | − | 0.0708350i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1612.41i | − | 1.83020i | −0.403227 | − | 0.915100i | \(-0.632112\pi\) | ||
0.403227 | − | 0.915100i | \(-0.367888\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 688.542 | 0.779775 | 0.389888 | − | 0.920862i | \(-0.372514\pi\) | ||||
0.389888 | + | 0.920862i | \(0.372514\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −974.792 | − | 562.797i | −1.09898 | − | 0.634494i | −0.163025 | − | 0.986622i | \(-0.552125\pi\) |
−0.935952 | + | 0.352128i | \(0.885458\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −645.747 | − | 1118.47i | −0.726374 | − | 1.25812i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −316.345 | − | 201.276i | −0.355045 | − | 0.225899i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1737.75 | − | 1003.29i | 1.94597 | − | 1.12351i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.92683 | + | 0.750574i | −0.00326291 | + | 0.000836761i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 57.8931i | 0.0643972i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −320.477 | −0.355690 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −965.686 | + | 945.119i | −1.06942 | + | 1.04664i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −311.993 | − | 540.388i | −0.343984 | − | 0.595798i | 0.641185 | − | 0.767387i | \(-0.278443\pi\) |
−0.985169 | + | 0.171589i | \(0.945110\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1165.24 | − | 25.0872i | −1.28190 | − | 0.0275987i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1321.03 | + | 762.700i | −1.45009 | + | 0.837212i | −0.998486 | − | 0.0550052i | \(-0.982482\pi\) |
−0.451607 | + | 0.892217i | \(0.649149\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 301.886 | − | 522.882i | 0.330653 | − | 0.572708i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 2719.09i | − | 2.96520i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 875.498 | 0.952663 | 0.476332 | − | 0.879266i | \(-0.341966\pi\) | ||||
0.476332 | + | 0.879266i | \(0.341966\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −884.582 | − | 247.257i | −0.960458 | − | 0.268466i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −77.3152 | − | 44.6379i | −0.0837651 | − | 0.0483618i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 66.2894 | − | 36.3926i | 0.0715096 | − | 0.0392585i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −341.363 | + | 197.086i | −0.367452 | + | 0.212148i | −0.672345 | − | 0.740238i | \(-0.734713\pi\) |
0.304893 | + | 0.952387i | \(0.401379\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1713.76 | − | 2968.32i | 1.84077 | − | 3.18831i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 833.514 | + | 851.652i | 0.893370 | + | 0.912811i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 600.533 | 0.640911 | 0.320455 | − | 0.947264i | \(-0.396164\pi\) | ||||
0.320455 | + | 0.947264i | \(0.396164\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −291.950 | − | 1138.45i | −0.310916 | − | 1.21240i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −572.208 | − | 330.364i | −0.608085 | − | 0.351078i | 0.164131 | − | 0.986439i | \(-0.447518\pi\) |
−0.772216 | + | 0.635361i | \(0.780851\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15.5974 | + | 27.0155i | 0.0165402 | + | 0.0286485i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1096.03 | + | 632.795i | −1.15737 | + | 0.668210i | −0.950673 | − | 0.310194i | \(-0.899606\pi\) |
−0.206701 | + | 0.978404i | \(0.566273\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.6252 | − | 25.3316i | 0.0154112 | − | 0.0266930i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −470.150 | + | 120.568i | −0.494375 | + | 0.126780i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 428.958i | 0.450113i | 0.974346 | + | 0.225057i | \(0.0722567\pi\) | ||||
−0.974346 | + | 0.225057i | \(0.927743\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 393.426 | − | 385.046i | 0.411103 | − | 0.402347i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2031.44 | + | 1172.85i | 2.11829 | + | 1.22300i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 479.434 | + | 830.403i | 0.498890 | + | 0.864103i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 285.318 | − | 470.498i | 0.296281 | − | 0.488575i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 221.642 | − | 383.896i | 0.229206 | − | 0.396996i | −0.728367 | − | 0.685187i | \(-0.759720\pi\) |
0.957573 | + | 0.288191i | \(0.0930537\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 608.277 | − | 2176.16i | 0.627737 | − | 2.24578i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 444.042i | − | 0.457304i | −0.973508 | − | 0.228652i | \(-0.926568\pi\) | ||
0.973508 | − | 0.228652i | \(-0.0734317\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2724.11 | −2.79970 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −200.009 | − | 115.475i | −0.204717 | − | 0.118194i | 0.394137 | − | 0.919052i | \(-0.371044\pi\) |
−0.598854 | + | 0.800858i | \(0.704377\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −111.298 | − | 192.773i | −0.113685 | − | 0.196908i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1244.92 | + | 754.940i | 1.26903 | + | 0.769562i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −971.023 | + | 560.620i | −0.987816 | + | 0.570316i | −0.904621 | − | 0.426218i | \(-0.859846\pi\) |
−0.0831949 | + | 0.996533i | \(0.526512\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1585.71 | − | 1620.22i | −1.60660 | − | 1.64156i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 29.0005i | − | 0.0293230i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 182.717 | 0.184377 | 0.0921884 | − | 0.995742i | \(-0.470614\pi\) | ||||
0.0921884 | + | 0.995742i | \(0.470614\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 176.758 | + | 689.262i | 0.178005 | + | 0.694121i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −616.618 | − | 1068.01i | −0.618473 | − | 1.07123i | −0.989764 | − | 0.142711i | \(-0.954418\pi\) |
0.371291 | − | 0.928517i | \(-0.378915\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −830.737 | − | 886.195i | −0.831569 | − | 0.887082i |
(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 | 900.3.p.f.401.1 | 24 | ||
3.2 | odd | 2 | 2700.3.p.f.2501.1 | 24 | |||
5.2 | odd | 4 | 180.3.t.a.149.6 | yes | 24 | ||
5.3 | odd | 4 | 180.3.t.a.149.7 | yes | 24 | ||
5.4 | even | 2 | inner | 900.3.p.f.401.12 | 24 | ||
9.2 | odd | 6 | inner | 900.3.p.f.101.1 | 24 | ||
9.7 | even | 3 | 2700.3.p.f.1601.1 | 24 | |||
15.2 | even | 4 | 540.3.t.a.449.5 | 24 | |||
15.8 | even | 4 | 540.3.t.a.449.10 | 24 | |||
15.14 | odd | 2 | 2700.3.p.f.2501.12 | 24 | |||
45.2 | even | 12 | 180.3.t.a.29.7 | yes | 24 | ||
45.7 | odd | 12 | 540.3.t.a.89.10 | 24 | |||
45.13 | odd | 12 | 1620.3.b.b.809.22 | 24 | |||
45.22 | odd | 12 | 1620.3.b.b.809.4 | 24 | |||
45.23 | even | 12 | 1620.3.b.b.809.3 | 24 | |||
45.29 | odd | 6 | inner | 900.3.p.f.101.12 | 24 | ||
45.32 | even | 12 | 1620.3.b.b.809.21 | 24 | |||
45.34 | even | 6 | 2700.3.p.f.1601.12 | 24 | |||
45.38 | even | 12 | 180.3.t.a.29.6 | ✓ | 24 | ||
45.43 | odd | 12 | 540.3.t.a.89.5 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
180.3.t.a.29.6 | ✓ | 24 | 45.38 | even | 12 | ||
180.3.t.a.29.7 | yes | 24 | 45.2 | even | 12 | ||
180.3.t.a.149.6 | yes | 24 | 5.2 | odd | 4 | ||
180.3.t.a.149.7 | yes | 24 | 5.3 | odd | 4 | ||
540.3.t.a.89.5 | 24 | 45.43 | odd | 12 | |||
540.3.t.a.89.10 | 24 | 45.7 | odd | 12 | |||
540.3.t.a.449.5 | 24 | 15.2 | even | 4 | |||
540.3.t.a.449.10 | 24 | 15.8 | even | 4 | |||
900.3.p.f.101.1 | 24 | 9.2 | odd | 6 | inner | ||
900.3.p.f.101.12 | 24 | 45.29 | odd | 6 | inner | ||
900.3.p.f.401.1 | 24 | 1.1 | even | 1 | trivial | ||
900.3.p.f.401.12 | 24 | 5.4 | even | 2 | inner | ||
1620.3.b.b.809.3 | 24 | 45.23 | even | 12 | |||
1620.3.b.b.809.4 | 24 | 45.22 | odd | 12 | |||
1620.3.b.b.809.21 | 24 | 45.32 | even | 12 | |||
1620.3.b.b.809.22 | 24 | 45.13 | odd | 12 | |||
2700.3.p.f.1601.1 | 24 | 9.7 | even | 3 | |||
2700.3.p.f.1601.12 | 24 | 45.34 | even | 6 | |||
2700.3.p.f.2501.1 | 24 | 3.2 | odd | 2 | |||
2700.3.p.f.2501.12 | 24 | 15.14 | odd | 2 |