Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [20,4,Mod(9,20)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(20, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("20.9");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 20 = 2^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 20.c (of order \(2\), degree \(1\), 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: | \(1.18003820011\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-19}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 5 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 9.1 | ||
Root | \(0.500000 + 2.17945i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 20.9 |
Dual form | 20.4.c.a.9.2 |
$q$-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 \(\left(\mathbb{Z}/20\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(17\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − | 8.71780i | − | 1.67774i | −0.544331 | − | 0.838870i | \(-0.683216\pi\) | ||
0.544331 | − | 0.838870i | \(-0.316784\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 7.00000 | + | 8.71780i | 0.626099 | + | 0.779744i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 8.71780i | 0.470717i | 0.971909 | + | 0.235358i | \(0.0756264\pi\) | ||||
−0.971909 | + | 0.235358i | \(0.924374\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −49.0000 | −1.81481 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 20.0000 | 0.548202 | 0.274101 | − | 0.961701i | \(-0.411620\pi\) | ||||
0.274101 | + | 0.961701i | \(0.411620\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 52.3068i | 1.11595i | 0.829859 | + | 0.557973i | \(0.188421\pi\) | ||||
−0.829859 | + | 0.557973i | \(0.811579\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 76.0000 | − | 61.0246i | 1.30821 | − | 1.05043i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 69.7424i | − | 0.995001i | −0.867464 | − | 0.497500i | \(-0.834251\pi\) | ||
0.867464 | − | 0.497500i | \(-0.165749\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −84.0000 | −1.01426 | −0.507130 | − | 0.861870i | \(-0.669293\pi\) | ||||
−0.507130 | + | 0.861870i | \(0.669293\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 76.0000 | 0.789741 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 61.0246i | − | 0.553239i | −0.960979 | − | 0.276620i | \(-0.910786\pi\) | ||
0.960979 | − | 0.276620i | \(-0.0892142\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −27.0000 | + | 122.049i | −0.216000 | + | 0.976393i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 191.792i | 1.36705i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.00000 | 0.0384197 | 0.0192099 | − | 0.999815i | \(-0.493885\pi\) | ||||
0.0192099 | + | 0.999815i | \(0.493885\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −224.000 | −1.29779 | −0.648897 | − | 0.760877i | \(-0.724769\pi\) | ||||
−0.648897 | + | 0.760877i | \(0.724769\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 174.356i | − | 0.919742i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −76.0000 | + | 61.0246i | −0.367038 | + | 0.294715i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 122.049i | − | 0.542291i | −0.962538 | − | 0.271145i | \(-0.912598\pi\) | ||
0.962538 | − | 0.271145i | \(-0.0874024\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 456.000 | 1.87227 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 266.000 | 1.01322 | 0.506612 | − | 0.862174i | \(-0.330898\pi\) | ||||
0.506612 | + | 0.862174i | \(0.330898\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 305.123i | 1.08211i | 0.840987 | + | 0.541056i | \(0.181975\pi\) | ||||
−0.840987 | + | 0.541056i | \(0.818025\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −343.000 | − | 427.172i | −1.13625 | − | 1.41509i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 374.865i | − | 1.16340i | −0.813404 | − | 0.581699i | \(-0.802388\pi\) | ||
0.813404 | − | 0.581699i | \(-0.197612\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 267.000 | 0.778426 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −608.000 | −1.66935 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 366.148i | 0.948948i | 0.880270 | + | 0.474474i | \(0.157362\pi\) | ||||
−0.880270 | + | 0.474474i | \(0.842638\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 140.000 | + | 174.356i | 0.343229 | + | 0.427457i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 732.295i | 1.70166i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −28.0000 | −0.0617846 | −0.0308923 | − | 0.999523i | \(-0.509835\pi\) | ||||
−0.0308923 | + | 0.999523i | \(0.509835\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 182.000 | 0.382012 | 0.191006 | − | 0.981589i | \(-0.438825\pi\) | ||||
0.191006 | + | 0.981589i | \(0.438825\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 427.172i | − | 0.854264i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −456.000 | + | 366.148i | −0.870151 | + | 0.698692i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 427.172i | − | 0.778916i | −0.921044 | − | 0.389458i | \(-0.872662\pi\) | ||
0.921044 | − | 0.389458i | \(-0.127338\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −532.000 | −0.928192 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 408.000 | 0.681982 | 0.340991 | − | 0.940067i | \(-0.389238\pi\) | ||||
0.340991 | + | 0.940067i | \(0.389238\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 1081.01i | − | 1.73318i | −0.499019 | − | 0.866591i | \(-0.666306\pi\) | ||
0.499019 | − | 0.866591i | \(-0.333694\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1064.00 | + | 235.381i | 1.63814 | + | 0.362392i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 174.356i | 0.258048i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 48.0000 | 0.0683598 | 0.0341799 | − | 0.999416i | \(-0.489118\pi\) | ||||
0.0341799 | + | 0.999416i | \(0.489118\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 349.000 | 0.478738 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 200.509i | 0.265166i | 0.991172 | + | 0.132583i | \(0.0423271\pi\) | ||||
−0.991172 | + | 0.132583i | \(0.957673\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 608.000 | − | 488.197i | 0.775845 | − | 0.622969i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 52.3068i | − | 0.0644583i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1526.00 | −1.81748 | −0.908740 | − | 0.417363i | \(-0.862954\pi\) | ||||
−0.908740 | + | 0.417363i | \(0.862954\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −456.000 | −0.525294 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1952.79i | 2.17736i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −588.000 | − | 732.295i | −0.635027 | − | 0.790862i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 557.939i | − | 0.584022i | −0.956415 | − | 0.292011i | \(-0.905676\pi\) | ||
0.956415 | − | 0.292011i | \(-0.0943244\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −980.000 | −0.994886 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1246.00 | 1.22754 | 0.613770 | − | 0.789485i | \(-0.289652\pi\) | ||||
0.613770 | + | 0.789485i | \(0.289652\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 845.626i | 0.808952i | 0.914549 | + | 0.404476i | \(0.132546\pi\) | ||||
−0.914549 | + | 0.404476i | \(0.867454\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 532.000 | + | 662.553i | 0.494456 | + | 0.615795i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1281.52i | 1.15784i | 0.815384 | + | 0.578920i | \(0.196526\pi\) | ||||
−0.815384 | + | 0.578920i | \(0.803474\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 902.000 | 0.792623 | 0.396312 | − | 0.918116i | \(-0.370290\pi\) | ||||
0.396312 | + | 0.918116i | \(0.370290\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1064.00 | −0.909824 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1464.59i | − | 1.21927i | −0.792684 | − | 0.609633i | \(-0.791317\pi\) | ||
0.792684 | − | 0.609633i | \(-0.208683\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 532.000 | − | 427.172i | 0.431385 | − | 0.346383i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 2563.03i | − | 2.02523i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 608.000 | 0.468364 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −931.000 | −0.699474 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 2318.93i | − | 1.69993i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1253.00 | + | 618.964i | −0.896574 | + | 0.442894i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2624.06i | 1.83344i | 0.399525 | + | 0.916722i | \(0.369175\pi\) | ||||
−0.399525 | + | 0.916722i | \(0.630825\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2660.00 | 1.81550 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2940.00 | 1.96083 | 0.980416 | − | 0.196938i | \(-0.0630997\pi\) | ||||
0.980416 | + | 0.196938i | \(0.0630997\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 732.295i | − | 0.477429i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1672.00 | + | 1342.54i | −1.06595 | + | 0.855908i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 732.295i | 0.456673i | 0.973582 | + | 0.228336i | \(0.0733286\pi\) | ||||
−0.973582 | + | 0.228336i | \(0.926671\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −364.000 | −0.222116 | −0.111058 | − | 0.993814i | \(-0.535424\pi\) | ||||
−0.111058 | + | 0.993814i | \(0.535424\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3268.00 | −1.95188 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1046.14i | 0.611764i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 42.0000 | + | 52.3068i | 0.0240546 | + | 0.0299575i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 2327.65i | − | 1.30600i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 254.000 | 0.139654 | 0.0698272 | − | 0.997559i | \(-0.477755\pi\) | ||||
0.0698272 | + | 0.997559i | \(0.477755\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2360.00 | −1.27188 | −0.635941 | − | 0.771738i | \(-0.719388\pi\) | ||||
−0.635941 | + | 0.771738i | \(0.719388\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3417.38i | 1.80574i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1568.00 | − | 1952.79i | −0.812547 | − | 1.01195i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2214.32i | 1.12562i | 0.826587 | + | 0.562809i | \(0.190279\pi\) | ||||
−0.826587 | + | 0.562809i | \(0.809721\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3192.00 | 1.59209 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 532.000 | 0.260419 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1525.61i | 0.733100i | 0.930398 | + | 0.366550i | \(0.119461\pi\) | ||||
−0.930398 | + | 0.366550i | \(0.880539\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1520.00 | − | 1220.49i | 0.717163 | − | 0.575849i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 3059.95i | − | 1.41788i | −0.705269 | − | 0.708940i | \(-0.749174\pi\) | ||
0.705269 | − | 0.708940i | \(-0.250826\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −539.000 | −0.245335 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4116.00 | 1.84069 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 1900.48i | − | 0.835207i | −0.908629 | − | 0.417604i | \(-0.862870\pi\) | ||
0.908629 | − | 0.417604i | \(-0.137130\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1064.00 | − | 235.381i | −0.459605 | − | 0.101675i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 244.098i | 0.103659i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1972.00 | −0.823431 | −0.411716 | − | 0.911312i | \(-0.635070\pi\) | ||||
−0.411716 | + | 0.911312i | \(0.635070\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1330.00 | −0.546177 | −0.273089 | − | 0.961989i | \(-0.588045\pi\) | ||||
−0.273089 | + | 0.961989i | \(0.588045\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 1586.64i | − | 0.640917i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1064.00 | − | 854.344i | 0.422848 | − | 0.339528i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 1394.85i | − | 0.545462i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1672.00 | −0.643493 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1728.00 | 0.654627 | 0.327313 | − | 0.944916i | \(-0.393857\pi\) | ||||
0.327313 | + | 0.944916i | \(0.393857\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 976.393i | − | 0.364157i | −0.983284 | − | 0.182079i | \(-0.941717\pi\) | ||
0.983284 | − | 0.182079i | \(-0.0582825\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3192.00 | + | 3975.32i | 1.17222 | + | 1.45989i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3783.52i | 1.36835i | 0.729318 | + | 0.684175i | \(0.239838\pi\) | ||||
−0.729318 | + | 0.684175i | \(0.760162\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1512.00 | −0.538607 | −0.269304 | − | 0.963055i | \(-0.586794\pi\) | ||||
−0.269304 | + | 0.963055i | \(0.586794\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3724.00 | −1.30682 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 52.3068i | 0.0180848i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1862.00 | + | 2318.93i | 0.634379 | + | 0.790056i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2990.20i | 1.00403i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1680.00 | −0.556019 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1644.00 | 0.536387 | 0.268193 | − | 0.963365i | \(-0.413573\pi\) | ||||
0.268193 | + | 0.963365i | \(0.413573\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 3556.86i | − | 1.14419i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2660.00 | + | 2135.86i | −0.843770 | + | 0.677509i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 1952.79i | − | 0.610893i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9424.00 | −2.90783 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3648.00 | 1.11037 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1089.72i | 0.327235i | 0.986524 | + | 0.163617i | \(0.0523163\pi\) | ||||
−0.986524 | + | 0.163617i | \(0.947684\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1323.00 | − | 5980.41i | 0.392000 | − | 1.77197i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 985.111i | − | 0.288036i | −0.989575 | − | 0.144018i | \(-0.953998\pi\) | ||
0.989575 | − | 0.144018i | \(-0.0460023\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3934.00 | 1.13522 | 0.567611 | − | 0.823297i | \(-0.307868\pi\) | ||||
0.567611 | + | 0.823297i | \(0.307868\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1520.00 | 0.432938 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4637.87i | 1.30402i | 0.758210 | + | 0.652010i | \(0.226074\pi\) | ||||
−0.758210 | + | 0.652010i | \(0.773926\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3268.00 | − | 2624.06i | 0.907152 | − | 0.728403i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 418.454i | − | 0.114690i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3856.00 | 1.04361 | 0.521807 | − | 0.853063i | \(-0.325258\pi\) | ||||
0.521807 | + | 0.853063i | \(0.325258\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 994.000 | 0.265681 | 0.132841 | − | 0.991137i | \(-0.457590\pi\) | ||||
0.132841 | + | 0.991137i | \(0.457590\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2135.86i | 0.563850i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1869.00 | + | 2327.65i | 0.487372 | + | 0.606972i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 4393.77i | − | 1.13186i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1748.00 | 0.444880 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6300.00 | −1.58427 | −0.792136 | − | 0.610344i | \(-0.791031\pi\) | ||||
−0.792136 | + | 0.610344i | \(0.791031\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 1220.49i | − | 0.303287i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4256.00 | − | 5300.42i | −1.04518 | − | 1.30167i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 6695.27i | − | 1.62506i | −0.582922 | − | 0.812528i | \(-0.698091\pi\) | ||
0.582922 | − | 0.812528i | \(-0.301909\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1064.00 | 0.255265 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −294.000 | −0.0697247 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1403.57i | 0.329078i | 0.986371 | + | 0.164539i | \(0.0526137\pi\) | ||||
−0.986371 | + | 0.164539i | \(0.947386\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3192.00 | + | 2563.03i | −0.739936 | + | 0.594135i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 13303.4i | 3.04926i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5082.00 | −1.15188 | −0.575939 | − | 0.817493i | \(-0.695363\pi\) | ||||
−0.575939 | + | 0.817493i | \(0.695363\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2800.00 | 0.627631 | 0.313815 | − | 0.949484i | \(-0.398393\pi\) | ||||
0.313815 | + | 0.949484i | \(0.398393\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3975.32i | 0.881308i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −540.000 | + | 2440.98i | −0.118412 | + | 0.535261i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 1586.64i | − | 0.344159i | −0.985083 | − | 0.172079i | \(-0.944951\pi\) | ||
0.985083 | − | 0.172079i | \(-0.0550485\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 10976.0 | 2.35525 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1254.00 | −0.266218 | −0.133109 | − | 0.991101i | \(-0.542496\pi\) | ||||
−0.133109 | + | 0.991101i | \(0.542496\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 4646.59i | − | 0.976010i | −0.872841 | − | 0.488005i | \(-0.837725\pi\) | ||
0.872841 | − | 0.488005i | \(-0.162275\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6384.00 | + | 5126.07i | −1.32686 | + | 1.06541i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2318.93i | 0.476942i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 49.0000 | 0.00997354 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4864.00 | −0.979838 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 6538.35i | − | 1.30367i | −0.758362 | − | 0.651833i | \(-0.774000\pi\) | ||
0.758362 | − | 0.651833i | \(-0.226000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −196.000 | − | 244.098i | −0.0386833 | − | 0.0481761i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3835.83i | 0.749419i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3192.00 | 0.617385 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2660.00 | −0.509368 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 10862.4i | − | 2.05950i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1274.00 | + | 1586.64i | 0.239177 | + | 0.297871i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 6355.27i | − | 1.18148i | −0.806862 | − | 0.590741i | \(-0.798836\pi\) | ||
0.806862 | − | 0.590741i | \(-0.201164\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7372.00 | 1.35721 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5208.00 | −0.949577 | −0.474789 | − | 0.880100i | \(-0.657476\pi\) | ||||
−0.474789 | + | 0.880100i | \(0.657476\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4568.13i | 0.824939i | 0.910972 | + | 0.412469i | \(0.135334\pi\) | ||||
−0.910972 | + | 0.412469i | \(0.864666\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3724.00 | − | 2990.20i | 0.666107 | − | 0.534854i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 854.344i | − | 0.151371i | −0.997132 | − | 0.0756857i | \(-0.975885\pi\) | ||
0.997132 | − | 0.0756857i | \(-0.0241146\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 120.000 | 0.0210618 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11172.0 | 1.94256 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5858.36i | 1.00919i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6384.00 | − | 1412.28i | −1.08960 | − | 0.241044i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 7863.45i | − | 1.32982i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3268.00 | 0.547631 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7828.00 | 1.29990 | 0.649948 | − | 0.759978i | \(-0.274791\pi\) | ||||
0.649948 | + | 0.759978i | \(0.274791\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5980.41i | 0.984157i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3724.00 | − | 2990.20i | 0.607355 | − | 0.487679i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5370.16i | 0.868046i | 0.900902 | + | 0.434023i | \(0.142906\pi\) | ||||
−0.900902 | + | 0.434023i | \(0.857094\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12768.0 | −2.04561 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4480.00 | −0.711453 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5317.86i | 0.837135i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3724.00 | − | 4637.87i | −0.581140 | − | 0.723752i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2746.11i | 0.424838i | 0.977179 | + | 0.212419i | \(0.0681341\pi\) | ||||
−0.977179 | + | 0.212419i | \(0.931866\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8890.00 | −1.36353 | −0.681763 | − | 0.731573i | \(-0.738787\pi\) | ||||
−0.681763 | + | 0.731573i | \(0.738787\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10032.0 | −1.52555 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 1534.33i | − | 0.231344i | −0.993287 | − | 0.115672i | \(-0.963098\pi\) | ||
0.993287 | − | 0.115672i | \(-0.0369021\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2856.00 | + | 3556.86i | 0.426988 | + | 0.531771i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 5300.42i | − | 0.785793i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9144.00 | 1.34429 | 0.672147 | − | 0.740417i | \(-0.265372\pi\) | ||||
0.672147 | + | 0.740417i | \(0.265372\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 197.000 | 0.0287214 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8116.27i | 1.17354i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9424.00 | − | 7567.05i | 1.35144 | − | 1.08514i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10365.5i | 1.47431i | 0.675722 | + | 0.737156i | \(0.263832\pi\) | ||||
−0.675722 | + | 0.737156i | \(0.736168\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −13034.0 | −1.83882 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3192.00 | −0.446686 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3295.33i | 0.457441i | 0.973492 | + | 0.228721i | \(0.0734542\pi\) | ||||
−0.973492 | + | 0.228721i | \(0.926546\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5396.00 | + | 10923.4i | 0.743062 | + | 1.50422i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 313.841i | 0.0428743i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2588.00 | −0.350756 | −0.175378 | − | 0.984501i | \(-0.556115\pi\) | ||||
−0.175378 | + | 0.984501i | \(0.556115\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 22876.0 | 3.07604 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 4071.21i | − | 0.543157i | −0.962416 | − | 0.271579i | \(-0.912454\pi\) | ||
0.962416 | − | 0.271579i | \(-0.0875457\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1520.00 | + | 1220.49i | −0.201211 | + | 0.161564i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 14951.0i | − | 1.96383i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5426.00 | −0.707221 | −0.353611 | − | 0.935393i | \(-0.615046\pi\) | ||||
−0.353611 | + | 0.935393i | \(0.615046\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4256.00 | −0.550474 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 25630.3i | − | 3.28977i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 336.000 | + | 418.454i | 0.0428000 | + | 0.0533031i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9816.24i | 1.24096i | 0.784220 | + | 0.620482i | \(0.213063\pi\) | ||||
−0.784220 | + | 0.620482i | \(0.786937\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6384.00 | −0.801002 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 370.000 | 0.0460771 | 0.0230386 | − | 0.999735i | \(-0.492666\pi\) | ||||
0.0230386 | + | 0.999735i | \(0.492666\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 11716.7i | − | 1.44827i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2443.00 | + | 3042.51i | 0.299737 | + | 0.373293i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 2440.98i | − | 0.297285i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4186.00 | 0.506074 | 0.253037 | − | 0.967457i | \(-0.418571\pi\) | ||||
0.253037 | + | 0.967457i | \(0.418571\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6384.00 | 0.766179 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 244.098i | − | 0.0290830i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1748.00 | + | 1403.57i | −0.206761 | + | 0.166020i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3173.28i | 0.372653i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2716.00 | 0.316671 | 0.158336 | − | 0.987385i | \(-0.449387\pi\) | ||||
0.158336 | + | 0.987385i | \(0.449387\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1966.00 | 0.227594 | 0.113797 | − | 0.993504i | \(-0.463699\pi\) | ||||
0.113797 | + | 0.993504i | \(0.463699\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 18368.4i | 2.11135i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8512.00 | + | 1883.04i | 0.971512 | + | 0.214920i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1586.64i | 0.179819i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9120.00 | 1.02638 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11824.0 | −1.32144 | −0.660722 | − | 0.750631i | \(-0.729750\pi\) | ||||
−0.660722 | + | 0.750631i | \(0.729750\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2580.47i | 0.286396i | 0.989694 | + | 0.143198i | \(0.0457385\pi\) | ||||
−0.989694 | + | 0.143198i | \(0.954261\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 456.000 | − | 366.148i | 0.0502610 | − | 0.0403573i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5126.07i | 0.561128i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13272.0 | −1.44291 | −0.721456 | − | 0.692461i | \(-0.756527\pi\) | ||||
−0.721456 | + | 0.692461i | \(0.756527\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −13083.0 | −1.41270 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 3112.25i | − | 0.333787i | −0.985975 | − | 0.166894i | \(-0.946626\pi\) | ||
0.985975 | − | 0.166894i | \(-0.0533736\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10682.0 | − | 13303.4i | −1.13792 | − | 1.41717i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 2214.32i | − | 0.234304i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2094.00 | −0.220093 | −0.110047 | − | 0.993926i | \(-0.535100\pi\) | ||||
−0.110047 | + | 0.993926i | \(0.535100\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5320.00 | 0.555452 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 20574.0i | 2.13389i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3192.00 | − | 3975.32i | −0.328886 | − | 0.409595i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 7078.85i | − | 0.724584i | −0.932065 | − | 0.362292i | \(-0.881994\pi\) | ||
0.932065 | − | 0.362292i | \(-0.118006\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 13376.0 | 1.36021 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9450.00 | −0.954730 | −0.477365 | − | 0.878705i | \(-0.658408\pi\) | ||||
−0.477365 | + | 0.878705i | \(0.658408\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3112.25i | 0.312395i | 0.987726 | + | 0.156197i | \(0.0499236\pi\) | ||||
−0.987726 | + | 0.156197i | \(0.950076\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −17024.0 | + | 13669.5i | −1.69778 | + | 1.36324i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5361.45i | 0.531259i | 0.964075 | + | 0.265630i | \(0.0855798\pi\) | ||||
−0.964075 | + | 0.265630i | \(0.914420\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3724.00 | 0.366649 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 19304.0 | 1.88850 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6102.46i | 0.593216i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2268.00 | − | 10252.1i | 0.219080 | − | 0.990316i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 17941.2i | − | 1.72216i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13216.0 | 1.26066 | 0.630328 | − | 0.776329i | \(-0.282920\pi\) | ||||
0.630328 | + | 0.776329i | \(0.282920\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6384.00 | 0.605167 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 4637.87i | − | 0.436916i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4864.00 | − | 3905.57i | 0.455387 | − | 0.365656i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2379.96i | 0.221450i | 0.993851 | + | 0.110725i | \(0.0353173\pi\) | ||||
−0.993851 | + | 0.110725i | \(0.964683\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 13300.0 | 1.22995 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12300.0 | −1.13053 | −0.565266 | − | 0.824909i | \(-0.691226\pi\) | ||||
−0.565266 | + | 0.824909i | \(0.691226\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 418.454i | − | 0.0382277i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6860.00 | − | 8543.44i | −0.622897 | − | 0.775756i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3556.86i | 0.321020i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15756.0 | 1.41350 | 0.706749 | − | 0.707464i | \(-0.250161\pi\) | ||||
0.706749 | + | 0.707464i | \(0.250161\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −26676.0 | −2.37883 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 19170.4i | − | 1.69934i | −0.527316 | − | 0.849670i | \(-0.676801\pi\) | ||
0.527316 | − | 0.849670i | \(-0.323199\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8722.00 | + | 10862.4i | 0.768562 | + | 0.957167i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4698.89i | 0.411608i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2394.00 | −0.208472 | −0.104236 | − | 0.994553i | \(-0.533240\pi\) | ||||
−0.104236 | + | 0.994553i | \(0.533240\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9424.00 | 0.815838 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 16110.5i | − | 1.38654i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7372.00 | + | 5919.38i | −0.630775 | + | 0.506484i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 7497.31i | − | 0.637778i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16568.0 | −1.40126 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6874.00 | 0.578033 | 0.289017 | − | 0.957324i | \(-0.406672\pi\) | ||||
0.289017 | + | 0.957324i | \(0.406672\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 16154.1i | − | 1.35061i | −0.737539 | − | 0.675305i | \(-0.764012\pi\) | ||
0.737539 | − | 0.675305i | \(-0.235988\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2052.00 | + | 9275.74i | −0.170584 | + | 0.771098i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 15622.3i | 1.29131i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8443.00 | 0.693926 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1372.00 | 0.112128 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13913.6i | 1.13070i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11172.0 | + | 8970.61i | −0.902818 | + | 0.724922i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 17191.5i | 1.38150i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5340.00 | 0.426735 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7174.00 | 0.570119 | 0.285059 | − | 0.958510i | \(-0.407987\pi\) | ||||
0.285059 | + | 0.958510i | \(0.407987\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11594.7i | 0.916344i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6314.00 | + | 7863.45i | 0.496261 | + | 0.618043i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 4332.75i | − | 0.338674i | −0.985558 | − | 0.169337i | \(-0.945837\pi\) | ||
0.985558 | − | 0.169337i | \(-0.0541627\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8918.00 | −0.693280 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −504.000 | −0.0389676 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 418.454i | 0.0321781i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7448.00 | − | 9275.74i | −0.569640 | − | 0.709429i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 9153.69i | − | 0.696327i | −0.937434 | − | 0.348164i | \(-0.886805\pi\) | ||
0.937434 | − | 0.348164i | \(-0.113195\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15960.0 | −1.20758 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12160.0 | −0.915144 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13870.0i | 1.03828i | 0.854689 | + | 0.519140i | \(0.173748\pi\) | ||||
−0.854689 | + | 0.519140i | \(0.826252\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12768.0 | − | 10252.1i | 0.950715 | − | 0.763381i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3042.51i | 0.225350i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16070.0 | −1.18399 | −0.591994 | − | 0.805942i | \(-0.701659\pi\) | ||||
−0.591994 | + | 0.805942i | \(0.701659\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3932.00 | −0.288177 | −0.144089 | − | 0.989565i | \(-0.546025\pi\) | ||||
−0.144089 | + | 0.989565i | \(0.546025\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 15064.4i | − | 1.09829i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7448.00 | + | 1647.66i | 0.540179 | + | 0.119500i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 16180.2i | − | 1.16740i | −0.811968 | − | 0.583702i | \(-0.801604\pi\) | ||
0.811968 | − | 0.583702i | \(-0.198396\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8512.00 | −0.610961 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1748.00 | −0.124818 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7322.95i | 0.520215i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 22344.0 | − | 17941.2i | 1.57916 | − | 1.26800i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 11272.1i | − | 0.792589i | −0.918123 | − | 0.396295i | \(-0.870296\pi\) | ||
0.918123 | − | 0.396295i | \(-0.129704\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18816.0 | 1.31630 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 32984.0 | 2.29574 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10670.6i | 0.738935i | 0.929244 | + | 0.369467i | \(0.120460\pi\) | ||||
−0.929244 | + | 0.369467i | \(0.879540\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4256.00 | + | 5300.42i | 0.293242 | + | 0.365203i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13181.3i | 0.903643i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6840.00 | −0.466569 | −0.233284 | − | 0.972409i | \(-0.574947\pi\) | ||||
−0.233284 | + | 0.972409i | \(0.574947\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10150.0 | −0.688897 | −0.344449 | − | 0.938805i | \(-0.611934\pi\) | ||||
−0.344449 | + | 0.938805i | \(0.611934\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 20931.4i | 1.41359i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6517.00 | − | 8116.27i | −0.437940 | − | 0.545410i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 1839.46i | − | 0.123000i | −0.998107 | − | 0.0615002i | \(-0.980412\pi\) | ||
0.998107 | − | 0.0615002i | \(-0.0195885\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 456.000 | 0.0303416 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 19608.0 | 1.29829 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 5004.02i | − | 0.329707i | −0.986318 | − | 0.164853i | \(-0.947285\pi\) | ||
0.986318 | − | 0.164853i | \(-0.0527151\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 20216.0 | − | 16232.5i | 1.32551 | − | 1.06432i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 24653.9i | − | 1.60864i | −0.594197 | − | 0.804319i | \(-0.702530\pi\) | ||
0.594197 | − | 0.804319i | \(-0.297470\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −27020.0 | −1.75448 | −0.877242 | − | 0.480049i | \(-0.840619\pi\) | ||||
−0.877242 | + | 0.480049i | \(0.840619\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11704.0 | 0.756305 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 13303.4i | − | 0.855518i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14167.0 | − | 6590.66i | −0.906688 | − | 0.421802i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 14645.9i | 0.932856i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8512.00 | −0.539580 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10648.0 | −0.671775 | −0.335888 | − | 0.941902i | \(-0.609036\pi\) | ||||
−0.335888 | + | 0.941902i | \(0.609036\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 14332.1i | − | 0.899918i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −22876.0 | + | 18368.4i | −1.42962 | + | 1.14792i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13965.9i | 0.868681i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −19992.0 | −1.23767 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1682.00 | 0.103643 | 0.0518214 | − | 0.998656i | \(-0.483497\pi\) | ||||
0.0518214 | + | 0.998656i | \(0.483497\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18542.8i | 1.13725i | 0.822595 | + | 0.568627i | \(0.192525\pi\) | ||||
−0.822595 | + | 0.568627i | \(0.807475\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 18620.0 | + | 23189.3i | 1.13668 | + | 1.41563i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 30677.9i | − | 1.86410i | −0.362327 | − | 0.932051i | \(-0.618018\pi\) | ||
0.362327 | − | 0.932051i | \(-0.381982\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −560.000 | −0.0338705 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −17024.0 | −1.02492 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 1342.54i | − | 0.0804559i | −0.999191 | − | 0.0402279i | \(-0.987192\pi\) | ||
0.999191 | − | 0.0402279i | \(-0.0128084\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20580.0 | + | 25630.3i | 1.22768 | + | 1.52895i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 52969.3i | 3.14540i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21356.0 | 1.26238 | 0.631192 | − | 0.775626i | \(-0.282566\pi\) | ||||
0.631192 | + | 0.775626i | \(0.282566\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13762.0 | −0.809803 | −0.404901 | − | 0.914360i | \(-0.632694\pi\) | ||||
−0.404901 | + | 0.914360i | \(0.632694\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 31802.5i | − | 1.86291i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6384.00 | − | 5126.07i | 0.372272 | − | 0.298918i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 366.148i | − | 0.0212553i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9500.00 | 0.549015 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3640.00 | 0.209420 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5858.36i | 0.335547i | 0.985826 | + | 0.167774i | \(0.0536577\pi\) | ||||
−0.985826 | + | 0.167774i | \(0.946342\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −23408.0 | − | 5178.37i | −1.33478 | − | 0.295282i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 29588.2i | 1.67972i | 0.542807 | + | 0.839858i | \(0.317362\pi\) | ||||
−0.542807 | + | 0.839858i | \(0.682638\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4864.00 | 0.274909 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8588.00 | −0.483249 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 17270.0i | − | 0.967521i | −0.875201 | − | 0.483760i | \(-0.839271\pi\) | ||
0.875201 | − | 0.483760i | \(-0.160729\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6384.00 | + | 5126.07i | −0.356088 | + | 0.285922i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 34295.8i | − | 1.90461i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −19152.0 | −1.05897 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1652.00 | −0.0909480 | −0.0454740 | − | 0.998966i | \(-0.514480\pi\) | ||||
−0.0454740 | + | 0.998966i | \(0.514480\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 8543.44i | − | 0.468310i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2548.00 | − | 3173.28i | −0.139066 | − | 0.173193i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 18551.5i | − | 1.00816i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 40432.0 | 2.18781 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28790.0 | 1.55119 | 0.775594 | − | 0.631232i | \(-0.217450\pi\) | ||||
0.775594 | + | 0.631232i | \(0.217450\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10252.1i | 0.550023i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −22876.0 | − | 28489.8i | −1.22207 | − | 1.52197i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10862.4i | 0.577824i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7554.00 | −0.400136 | −0.200068 | − | 0.979782i | \(-0.564116\pi\) | ||||
−0.200068 | + | 0.979782i | \(0.564116\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2352.00 | −0.124060 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13669.5i | 0.717990i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9120.00 | + | 7322.95i | −0.477019 | + | 0.383025i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 33615.8i | − | 1.75092i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 28336.0 | 1.46976 | 0.734878 | − | 0.678199i | \(-0.237239\pi\) | ||||
0.734878 | + | 0.678199i | \(0.237239\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7372.00 | −0.380787 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 8665.49i | − | 0.445744i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −162.000 | + | 732.295i | −0.00829866 | + | 0.0375128i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23511.9i | 1.19946i | 0.800202 | + | 0.599730i | \(0.204726\pi\) | ||||
−0.800202 | + | 0.599730i | \(0.795274\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 28043.0 | 1.42473 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 21280.0 | 1.07670 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 3365.07i | − | 0.169566i | −0.996399 | − | 0.0847829i | \(-0.972980\pi\) | ||
0.996399 | − | 0.0847829i | \(-0.0270197\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 20292.0 | − | 16293.6i | 1.01834 | − | 0.817683i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 8543.44i | − | 0.427004i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14300.0 | 0.711819 | 0.355909 | − | 0.934520i | \(-0.384171\pi\) | ||||
0.355909 | + | 0.934520i | \(0.384171\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −38304.0 | −1.89896 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31671.8i | 1.56383i | 0.623386 | + | 0.781914i | \(0.285756\pi\) | ||||
−0.623386 | + | 0.781914i | \(0.714244\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1778.00 | + | 2214.32i | 0.0874374 | + | 0.108895i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 9824.96i | − | 0.481227i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11172.0 | −0.545015 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11824.0 | −0.574519 | −0.287260 | − | 0.957853i | \(-0.592744\pi\) | ||||
−0.287260 | + | 0.957853i | \(0.592744\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 54922.1i | 2.65800i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16520.0 | − | 20574.0i | −0.796324 | − | 0.991741i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1342.54i | 0.0644590i | 0.999480 | + | 0.0322295i | \(0.0102607\pi\) | ||||
−0.999480 | + | 0.0322295i | \(0.989739\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10640.0 | −0.508837 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6762.00 | 0.322106 | 0.161053 | − | 0.986946i | \(-0.448511\pi\) | ||||
0.161053 | + | 0.986946i | \(0.448511\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7863.45i | 0.373101i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −29792.0 | + | 23921.6i | −1.40802 | + | 1.13057i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 1464.59i | − | 0.0689482i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29442.0 | 1.38063 | 0.690316 | − | 0.723508i | \(-0.257472\pi\) | ||||
0.690316 | + | 0.723508i | \(0.257472\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −58368.0 | −2.72642 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 35830.1i | − | 1.66717i | −0.552393 | − | 0.833584i | \(-0.686285\pi\) | ||
0.552393 | − | 0.833584i | \(-0.313715\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6048.00 | − | 27339.0i | 0.280323 | − | 1.26716i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 9275.74i | − | 0.428269i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −22344.0 | −1.02767 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8160.00 | 0.373864 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1150.75i | 0.0525216i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −19304.0 | + | 15500.2i | −0.877693 | + | 0.704748i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23912.9i | 1.08310i | 0.840667 | + | 0.541552i | \(0.182163\pi\) | ||||
−0.840667 | + | 0.541552i | \(0.817837\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12236.0 | 0.552108 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12768.0 | 0.573929 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9519.84i | 0.426304i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 22344.0 | + | 27827.2i | 0.996805 | + | 1.24142i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17139.2i | 0.761733i | 0.924630 | + | 0.380867i | \(0.124374\pi\) | ||||
−0.924630 | + | 0.380867i | \(0.875626\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −26144.0 | −1.15758 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 74774.0 | 3.29839 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 21620.1i | − | 0.950135i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3724.00 | + | 4637.87i | 0.163048 | + | 0.203060i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 44303.8i | 1.93255i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8646.00 | −0.375744 | −0.187872 | − | 0.982193i | \(-0.560159\pi\) | ||||
−0.187872 | + | 0.982193i | \(0.560159\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18956.0 | −0.820759 | −0.410379 | − | 0.911915i | \(-0.634604\pi\) | ||||
−0.410379 | + | 0.911915i | \(0.634604\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 24409.8i | − | 1.05300i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −13300.0 | + | 10679.3i | −0.571630 | + | 0.458993i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 25630.3i | − | 1.09754i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 22344.0 | 0.953312 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13726.0 | 0.583484 | 0.291742 | − | 0.956497i | \(-0.405765\pi\) | ||||
0.291742 | + | 0.956497i | \(0.405765\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 45951.5i | − | 1.94626i | −0.230264 | − | 0.973128i | \(-0.573959\pi\) | ||
0.230264 | − | 0.973128i | \(-0.426041\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 21280.0 | + | 4707.61i | 0.898030 | + | 0.198664i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 2135.86i | − | 0.0898079i | −0.998991 | − | 0.0449040i | \(-0.985702\pi\) | ||
0.998991 | − | 0.0449040i | \(-0.0142982\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8778.00 | −0.367759 | −0.183880 | − | 0.982949i | \(-0.558866\pi\) | ||||
−0.183880 | + | 0.982949i | \(0.558866\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13832.0 | −0.577409 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 18621.2i | − | 0.774534i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 26676.0 | − | 21419.6i | 1.10558 | − | 0.887733i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 42961.3i | − | 1.77415i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18088.0 | −0.744299 | −0.372150 | − | 0.928173i | \(-0.621379\pi\) | ||||
−0.372150 | + | 0.928173i | \(0.621379\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24353.0 | −0.998524 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10932.1i | 0.446646i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3773.00 | − | 4698.89i | −0.153604 | − | 0.191298i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 8116.27i | − | 0.329254i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −40508.0 | −1.63749 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7448.00 | −0.300017 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 22927.8i | − | 0.920320i | −0.887836 | − | 0.460160i | \(-0.847792\pi\) | ||
0.887836 | − | 0.460160i | \(-0.152208\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 28812.0 | + | 35882.5i | 1.15246 | + | 1.43527i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 4498.38i | − | 0.179302i | −0.995973 | − | 0.0896510i | \(-0.971425\pi\) | ||
0.995973 | − | 0.0896510i | \(-0.0285752\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40516.0 | 1.60930 | 0.804650 | − | 0.593750i | \(-0.202353\pi\) | ||||
0.804650 | + | 0.593750i | \(0.202353\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 20216.0 | 0.800185 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 28010.3i | 1.10484i | 0.833564 | + | 0.552422i | \(0.186296\pi\) | ||||
−0.833564 | + | 0.552422i | \(0.813704\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16568.0 | − | 13303.4i | 0.651247 | − | 0.522922i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 427.172i | − | 0.0167330i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 960.000 | 0.0374750 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 22344.0 | 0.869228 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 27339.0i | 1.05989i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5396.00 | − | 10923.4i | −0.208478 | − | 0.422032i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33807.6i | 1.30171i | 0.759201 | + | 0.650856i | \(0.225590\pi\) | ||||
−0.759201 | + | 0.650856i | \(0.774410\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −57000.0 | −2.18722 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19362.0 | 0.740434 | 0.370217 | − | 0.928945i | \(-0.379283\pi\) | ||||
0.370217 | + | 0.928945i | \(0.379283\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4942.99i | 0.188386i | 0.995554 | + | 0.0941930i | \(0.0300271\pi\) | ||||
−0.995554 | + | 0.0941930i | \(0.969973\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2128.00 | + | 1708.69i | −0.0808270 | + | 0.0649005i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 44016.2i | 1.66620i | 0.553124 | + | 0.833099i | \(0.313436\pi\) | ||||
−0.553124 | + | 0.833099i | \(0.686564\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −22876.0 | −0.863033 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6980.00 | 0.262445 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 31488.7i | 1.17999i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −13804.0 | − | 17191.5i | −0.515550 | − | 0.642065i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 27827.2i | − | 1.03581i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1344.00 | −0.0498609 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 25536.0 | 0.944204 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 23189.3i | 0.854588i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9310.00 | − | 11594.7i | −0.341961 | − | 0.425878i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 42656.2i | − | 1.56160i | −0.624778 | − | 0.780802i | \(-0.714811\pi\) | ||
0.624778 | − | 0.780802i | \(-0.285189\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −61054.0 | −2.22776 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15888.0 | −0.577819 | −0.288909 | − | 0.957356i | \(-0.593293\pi\) | ||||
−0.288909 | + | 0.957356i | \(0.593293\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4010.19i | 0.145365i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 13832.0 | − | 11106.5i | 0.499751 | − | 0.401277i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 25630.3i | 0.922997i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7944.00 | 0.285145 | 0.142573 | − | 0.989784i | \(-0.454463\pi\) | ||||
0.142573 | + | 0.989784i | \(0.454463\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −55404.0 | −1.98222 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 21341.2i | 0.761054i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14896.0 | + | 3295.33i | 0.529489 | + | 0.117135i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 41435.7i | − | 1.46810i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −20622.0 | −0.728295 | −0.364147 | − | 0.931341i | \(-0.618640\pi\) | ||||
−0.364147 | + | 0.931341i | \(0.618640\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −22428.0 | −0.789525 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 45402.3i | 1.59315i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12160.0 | − | 9763.93i | 0.425320 | − | 0.341513i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 41182.9i | 1.43584i | 0.696123 | + | 0.717922i | \(0.254907\pi\) | ||||
−0.696123 | + | 0.717922i | \(0.745093\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 39824.0 | 1.38403 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 40502.0 | 1.40311 | 0.701556 | − | 0.712615i | \(-0.252489\pi\) | ||||
0.701556 | + | 0.712615i | \(0.252489\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 16232.5i | − | 0.560556i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −11704.0 | − | 14576.2i | −0.402890 | − | 0.501759i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 3844.55i | − | 0.131923i | −0.997822 | − | 0.0659615i | \(-0.978989\pi\) | ||
0.997822 | − | 0.0659615i | \(-0.0210114\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 56544.0 | 1.93414 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7448.00 | −0.253962 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 31976.9i | − | 1.08692i | −0.839436 | − | 0.543459i | \(-0.817114\pi\) | ||
0.839436 | − | 0.543459i | \(-0.182886\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12096.0 | + | 15064.4i | 0.409861 | + | 0.510441i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 1046.14i | − | 0.0353362i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6384.00 | −0.214964 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20385.0 | 0.684267 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 62794.3i | − | 2.10126i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8512.00 | − | 6834.75i | 0.283949 | − | 0.227998i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 19100.7i | − | 0.635198i | −0.948225 | − | 0.317599i | \(-0.897123\pi\) | ||
0.948225 | − | 0.317599i | \(-0.102877\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 51072.0 | 1.69316 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 17556.0 | 0.580225 | 0.290113 | − | 0.956992i | \(-0.406307\pi\) | ||||
0.290113 | + | 0.956992i | \(0.406307\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 3173.28i | − | 0.104554i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −12312.0 | + | 55654.4i | −0.404410 | + | 1.82807i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4393.77i | 0.143878i | 0.997409 | + | 0.0719392i | \(0.0229188\pi\) | ||||
−0.997409 | + | 0.0719392i | \(0.977081\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −30520.0 | −0.996347 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −44198.0 | −1.43846 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 9406.50i | − | 0.305209i | −0.988287 | − | 0.152605i | \(-0.951234\pi\) | ||
0.988287 | − | 0.152605i | \(-0.0487661\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −32984.0 | + | 26484.7i | −1.06696 | + | 0.856723i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 28489.8i | − | 0.918783i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 18620.0 | 0.598667 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28576.0 | 0.915990 | 0.457995 | − | 0.888955i | \(-0.348568\pi\) | ||||
0.457995 | + | 0.888955i | \(0.348568\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 68242.9i | − | 2.18089i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10584.0 | − | 13181.3i | −0.337221 | − | 0.419976i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 31541.0i | 1.00192i | 0.865471 | + | 0.500960i | \(0.167019\pi\) | ||||
−0.865471 | + | 0.500960i | \(0.832981\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 23408.0 | 0.741338 |
(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 | 20.4.c.a.9.1 | ✓ | 2 | |
3.2 | odd | 2 | 180.4.d.a.109.1 | 2 | |||
4.3 | odd | 2 | 80.4.c.b.49.2 | 2 | |||
5.2 | odd | 4 | 100.4.a.d.1.1 | 2 | |||
5.3 | odd | 4 | 100.4.a.d.1.2 | 2 | |||
5.4 | even | 2 | inner | 20.4.c.a.9.2 | yes | 2 | |
7.6 | odd | 2 | 980.4.e.a.589.2 | 2 | |||
8.3 | odd | 2 | 320.4.c.b.129.1 | 2 | |||
8.5 | even | 2 | 320.4.c.a.129.2 | 2 | |||
12.11 | even | 2 | 720.4.f.a.289.1 | 2 | |||
15.2 | even | 4 | 900.4.a.s.1.1 | 2 | |||
15.8 | even | 4 | 900.4.a.s.1.2 | 2 | |||
15.14 | odd | 2 | 180.4.d.a.109.2 | 2 | |||
20.3 | even | 4 | 400.4.a.w.1.1 | 2 | |||
20.7 | even | 4 | 400.4.a.w.1.2 | 2 | |||
20.19 | odd | 2 | 80.4.c.b.49.1 | 2 | |||
35.34 | odd | 2 | 980.4.e.a.589.1 | 2 | |||
40.3 | even | 4 | 1600.4.a.ck.1.2 | 2 | |||
40.13 | odd | 4 | 1600.4.a.cj.1.1 | 2 | |||
40.19 | odd | 2 | 320.4.c.b.129.2 | 2 | |||
40.27 | even | 4 | 1600.4.a.ck.1.1 | 2 | |||
40.29 | even | 2 | 320.4.c.a.129.1 | 2 | |||
40.37 | odd | 4 | 1600.4.a.cj.1.2 | 2 | |||
60.59 | even | 2 | 720.4.f.a.289.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
20.4.c.a.9.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
20.4.c.a.9.2 | yes | 2 | 5.4 | even | 2 | inner | |
80.4.c.b.49.1 | 2 | 20.19 | odd | 2 | |||
80.4.c.b.49.2 | 2 | 4.3 | odd | 2 | |||
100.4.a.d.1.1 | 2 | 5.2 | odd | 4 | |||
100.4.a.d.1.2 | 2 | 5.3 | odd | 4 | |||
180.4.d.a.109.1 | 2 | 3.2 | odd | 2 | |||
180.4.d.a.109.2 | 2 | 15.14 | odd | 2 | |||
320.4.c.a.129.1 | 2 | 40.29 | even | 2 | |||
320.4.c.a.129.2 | 2 | 8.5 | even | 2 | |||
320.4.c.b.129.1 | 2 | 8.3 | odd | 2 | |||
320.4.c.b.129.2 | 2 | 40.19 | odd | 2 | |||
400.4.a.w.1.1 | 2 | 20.3 | even | 4 | |||
400.4.a.w.1.2 | 2 | 20.7 | even | 4 | |||
720.4.f.a.289.1 | 2 | 12.11 | even | 2 | |||
720.4.f.a.289.2 | 2 | 60.59 | even | 2 | |||
900.4.a.s.1.1 | 2 | 15.2 | even | 4 | |||
900.4.a.s.1.2 | 2 | 15.8 | even | 4 | |||
980.4.e.a.589.1 | 2 | 35.34 | odd | 2 | |||
980.4.e.a.589.2 | 2 | 7.6 | odd | 2 | |||
1600.4.a.cj.1.1 | 2 | 40.13 | odd | 4 | |||
1600.4.a.cj.1.2 | 2 | 40.37 | odd | 4 | |||
1600.4.a.ck.1.1 | 2 | 40.27 | even | 4 | |||
1600.4.a.ck.1.2 | 2 | 40.3 | even | 4 |