Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [300,4,Mod(49,300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(300, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("300.49");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(17.7005730017\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 300.49 |
Dual form | 300.4.d.a.49.2 |
$q$-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 \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(277\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 3.00000i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 7.00000i | − 0.377964i | −0.981981 | − | 0.188982i | \(-0.939481\pi\) | ||||
0.981981 | − | 0.188982i | \(-0.0605189\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −54.0000 | −1.48015 | −0.740073 | − | 0.672526i | \(-0.765209\pi\) | ||||
−0.740073 | + | 0.672526i | \(0.765209\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 55.0000i | 1.17340i | 0.809803 | + | 0.586702i | \(0.199574\pi\) | ||||
−0.809803 | + | 0.586702i | \(0.800426\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 18.0000i | 0.256802i | 0.991722 | + | 0.128401i | \(0.0409845\pi\) | ||||
−0.991722 | + | 0.128401i | \(0.959015\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 25.0000 | 0.301863 | 0.150931 | − | 0.988544i | \(-0.451773\pi\) | ||||
0.150931 | + | 0.988544i | \(0.451773\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −21.0000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 18.0000i | 0.163185i | 0.996666 | + | 0.0815926i | \(0.0260006\pi\) | ||||
−0.996666 | + | 0.0815926i | \(0.973999\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 54.0000 | 0.345778 | 0.172889 | − | 0.984941i | \(-0.444690\pi\) | ||||
0.172889 | + | 0.984941i | \(0.444690\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −271.000 | −1.57010 | −0.785049 | − | 0.619434i | \(-0.787362\pi\) | ||||
−0.785049 | + | 0.619434i | \(0.787362\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 162.000i | 0.854563i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 314.000i | 1.39517i | 0.716502 | + | 0.697585i | \(0.245742\pi\) | ||||
−0.716502 | + | 0.697585i | \(0.754258\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 165.000 | 0.677465 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −360.000 | −1.37128 | −0.685641 | − | 0.727940i | \(-0.740478\pi\) | ||||
−0.685641 | + | 0.727940i | \(0.740478\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 163.000i | 0.578076i | 0.957318 | + | 0.289038i | \(0.0933354\pi\) | ||||
−0.957318 | + | 0.289038i | \(0.906665\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 522.000i | 1.62003i | 0.586407 | + | 0.810016i | \(0.300542\pi\) | ||||
−0.586407 | + | 0.810016i | \(0.699458\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 294.000 | 0.857143 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 54.0000 | 0.148265 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 36.0000i | 0.0933015i | 0.998911 | + | 0.0466508i | \(0.0148548\pi\) | ||||
−0.998911 | + | 0.0466508i | \(0.985145\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 75.0000i | − 0.174281i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −126.000 | −0.278031 | −0.139015 | − | 0.990290i | \(-0.544394\pi\) | ||||
−0.139015 | + | 0.990290i | \(0.544394\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 47.0000 | 0.0986514 | 0.0493257 | − | 0.998783i | \(-0.484293\pi\) | ||||
0.0493257 | + | 0.998783i | \(0.484293\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 63.0000i | 0.125988i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 343.000i | − 0.625435i | −0.949846 | − | 0.312717i | \(-0.898761\pi\) | ||||
0.949846 | − | 0.312717i | \(-0.101239\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 54.0000 | 0.0942150 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1080.00 | −1.80525 | −0.902623 | − | 0.430433i | \(-0.858361\pi\) | ||||
−0.902623 | + | 0.430433i | \(0.858361\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1054.00i | 1.68988i | 0.534860 | + | 0.844941i | \(0.320364\pi\) | ||||
−0.534860 | + | 0.844941i | \(0.679636\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 378.000i | 0.559443i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 568.000 | 0.808924 | 0.404462 | − | 0.914555i | \(-0.367459\pi\) | ||||
0.404462 | + | 0.914555i | \(0.367459\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 1422.00i | − 1.88054i | −0.340430 | − | 0.940270i | \(-0.610573\pi\) | ||||
0.340430 | − | 0.940270i | \(-0.389427\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 162.000i | − 0.199635i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1440.00 | −1.71505 | −0.857526 | − | 0.514440i | \(-0.828000\pi\) | ||||
−0.857526 | + | 0.514440i | \(0.828000\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 385.000 | 0.443505 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 813.000i | 0.906496i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 439.000i | − 0.459523i | −0.973247 | − | 0.229761i | \(-0.926205\pi\) | ||||
0.973247 | − | 0.229761i | \(-0.0737946\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 486.000 | 0.493382 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 828.000 | 0.815733 | 0.407867 | − | 0.913041i | \(-0.366273\pi\) | ||||
0.407867 | + | 0.913041i | \(0.366273\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 548.000i | − 0.524233i | −0.965036 | − | 0.262117i | \(-0.915579\pi\) | ||||
0.965036 | − | 0.262117i | \(-0.0844205\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 1476.00i | − 1.33355i | −0.745257 | − | 0.666777i | \(-0.767673\pi\) | ||||
0.745257 | − | 0.666777i | \(-0.232327\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1277.00 | −1.12215 | −0.561075 | − | 0.827765i | \(-0.689612\pi\) | ||||
−0.561075 | + | 0.827765i | \(0.689612\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 942.000 | 0.805502 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 1836.00i | − 1.52846i | −0.644942 | − | 0.764232i | \(-0.723118\pi\) | ||||
0.644942 | − | 0.764232i | \(-0.276882\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 495.000i | − 0.391135i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 126.000 | 0.0970622 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1585.00 | 1.19083 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1080.00i | 0.791710i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 592.000i | − 0.413634i | −0.978380 | − | 0.206817i | \(-0.933690\pi\) | ||||
0.978380 | − | 0.206817i | \(-0.0663105\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 489.000 | 0.333752 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −468.000 | −0.312132 | −0.156066 | − | 0.987747i | \(-0.549881\pi\) | ||||
−0.156066 | + | 0.987747i | \(0.549881\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 175.000i | − 0.114093i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2574.00i | 1.60519i | 0.596521 | + | 0.802597i | \(0.296549\pi\) | ||||
−0.596521 | + | 0.802597i | \(0.703451\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1756.00 | 1.07153 | 0.535763 | − | 0.844369i | \(-0.320024\pi\) | ||||
0.535763 | + | 0.844369i | \(0.320024\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1566.00 | 0.935326 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 2970.00i | − 1.73681i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 882.000i | − 0.494872i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2682.00 | −1.47462 | −0.737309 | − | 0.675556i | \(-0.763904\pi\) | ||||
−0.737309 | + | 0.675556i | \(0.763904\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3395.00 | 1.82968 | 0.914838 | − | 0.403820i | \(-0.132318\pi\) | ||||
0.914838 | + | 0.403820i | \(0.132318\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 162.000i | − 0.0856008i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 1549.00i | − 0.787412i | −0.919236 | − | 0.393706i | \(-0.871193\pi\) | ||||
0.919236 | − | 0.393706i | \(-0.128807\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 108.000 | 0.0538677 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 126.000 | 0.0616782 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 505.000i | 0.242667i | 0.992612 | + | 0.121333i | \(0.0387170\pi\) | ||||
−0.992612 | + | 0.121333i | \(0.961283\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 1476.00i | − 0.683930i | −0.939713 | − | 0.341965i | \(-0.888908\pi\) | ||||
0.939713 | − | 0.341965i | \(-0.111092\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −828.000 | −0.376878 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −225.000 | −0.100621 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 2358.00i | − 1.03627i | −0.855298 | − | 0.518137i | \(-0.826626\pi\) | ||||
0.855298 | − | 0.518137i | \(-0.173374\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 378.000i | 0.160521i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1566.00 | −0.653901 | −0.326951 | − | 0.945041i | \(-0.606021\pi\) | ||||
−0.326951 | + | 0.945041i | \(0.606021\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 305.000 | 0.125251 | 0.0626256 | − | 0.998037i | \(-0.480053\pi\) | ||||
0.0626256 | + | 0.998037i | \(0.480053\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 141.000i | − 0.0569564i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 972.000i | − 0.380105i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 189.000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1746.00 | −0.661446 | −0.330723 | − | 0.943728i | \(-0.607293\pi\) | ||||
−0.330723 | + | 0.943728i | \(0.607293\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3877.00i | 1.44597i | 0.690863 | + | 0.722986i | \(0.257231\pi\) | ||||
−0.690863 | + | 0.722986i | \(0.742769\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2142.00i | 0.774676i | 0.921938 | + | 0.387338i | \(0.126605\pi\) | ||||
−0.921938 | + | 0.387338i | \(0.873395\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4033.00 | 1.43664 | 0.718321 | − | 0.695712i | \(-0.244911\pi\) | ||||
0.718321 | + | 0.695712i | \(0.244911\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1029.00 | −0.361095 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 378.000i | − 0.130692i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 162.000i | − 0.0543951i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1350.00 | −0.446801 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4105.00 | −1.33934 | −0.669668 | − | 0.742661i | \(-0.733564\pi\) | ||||
−0.669668 | + | 0.742661i | \(0.733564\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3240.00i | 1.04226i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1897.00i | 0.593441i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3162.00 | 0.975654 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −990.000 | −0.301333 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 1385.00i | − 0.415903i | −0.978139 | − | 0.207952i | \(-0.933320\pi\) | ||||
0.978139 | − | 0.207952i | \(-0.0666797\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 2520.00i | − 0.736821i | −0.929663 | − | 0.368410i | \(-0.879902\pi\) | ||||
0.929663 | − | 0.368410i | \(-0.120098\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5129.00 | −1.48006 | −0.740030 | − | 0.672574i | \(-0.765189\pi\) | ||||
−0.740030 | + | 0.672574i | \(0.765189\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1134.00 | 0.322994 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3240.00i | 0.910985i | 0.890240 | + | 0.455492i | \(0.150537\pi\) | ||||
−0.890240 | + | 0.455492i | \(0.849463\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 1704.00i | − 0.467032i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2988.00 | 0.808693 | 0.404347 | − | 0.914606i | \(-0.367499\pi\) | ||||
0.404347 | + | 0.914606i | \(0.367499\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2647.00 | −0.707503 | −0.353752 | − | 0.935339i | \(-0.615094\pi\) | ||||
−0.353752 | + | 0.935339i | \(0.615094\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 243.000i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1375.00i | 0.354207i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4266.00 | −1.08573 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4212.00 | −1.05920 | −0.529600 | − | 0.848248i | \(-0.677658\pi\) | ||||
−0.529600 | + | 0.848248i | \(0.677658\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 972.000i | − 0.241538i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5724.00i | 1.38931i | 0.719342 | + | 0.694656i | \(0.244444\pi\) | ||||
−0.719342 | + | 0.694656i | \(0.755556\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2198.00 | 0.527325 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −486.000 | −0.115259 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4608.00i | 1.08039i | 0.841541 | + | 0.540193i | \(0.181649\pi\) | ||||
−0.841541 | + | 0.540193i | \(0.818351\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4320.00i | 0.990186i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6426.00 | 1.45651 | 0.728253 | − | 0.685308i | \(-0.240333\pi\) | ||||
0.728253 | + | 0.685308i | \(0.240333\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3376.00 | −0.756743 | −0.378372 | − | 0.925654i | \(-0.623516\pi\) | ||||
−0.378372 | + | 0.925654i | \(0.623516\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 1155.00i | − 0.256058i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5381.00i | 1.16719i | 0.812043 | + | 0.583597i | \(0.198355\pi\) | ||||
−0.812043 | + | 0.583597i | \(0.801645\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2439.00 | 0.523366 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3474.00 | −0.737514 | −0.368757 | − | 0.929526i | \(-0.620217\pi\) | ||||
−0.368757 | + | 0.929526i | \(0.620217\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2269.00i | 0.476601i | 0.971191 | + | 0.238300i | \(0.0765903\pi\) | ||||
−0.971191 | + | 0.238300i | \(0.923410\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2520.00i | 0.518296i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4589.00 | 0.934053 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1317.00 | −0.265306 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1674.00i | 0.333775i | 0.985976 | + | 0.166888i | \(0.0533717\pi\) | ||||
−0.985976 | + | 0.166888i | \(0.946628\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 1458.00i | − 0.284854i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −990.000 | −0.191482 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1141.00 | 0.218492 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 2484.00i | − 0.470964i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 539.000i | 0.100203i | 0.998744 | + | 0.0501016i | \(0.0159545\pi\) | ||||
−0.998744 | + | 0.0501016i | \(0.984046\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1644.00 | −0.302666 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1494.00 | 0.272402 | 0.136201 | − | 0.990681i | \(-0.456511\pi\) | ||||
0.136201 | + | 0.990681i | \(0.456511\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3997.00i | 0.721801i | 0.932604 | + | 0.360901i | \(0.117531\pi\) | ||||
−0.932604 | + | 0.360901i | \(0.882469\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 3672.00i | − 0.650600i | −0.945611 | − | 0.325300i | \(-0.894535\pi\) | ||||
0.945611 | − | 0.325300i | \(-0.105465\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2916.00 | −0.511801 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4428.00 | −0.769928 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 450.000i | 0.0775191i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3831.00i | 0.647874i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3654.00 | 0.612315 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1052.00 | 0.174692 | 0.0873461 | − | 0.996178i | \(-0.472161\pi\) | ||||
0.0873461 | + | 0.996178i | \(0.472161\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 2826.00i | − 0.465057i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 3871.00i | − 0.625718i | −0.949800 | − | 0.312859i | \(-0.898713\pi\) | ||||
0.949800 | − | 0.312859i | \(-0.101287\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5508.00 | −0.882459 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14634.0 | 2.32398 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 4459.00i | − 0.701934i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 7686.00i | − 1.18907i | −0.804071 | − | 0.594533i | \(-0.797337\pi\) | ||||
0.804071 | − | 0.594533i | \(-0.202663\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 46.0000 | 0.00705537 | 0.00352768 | − | 0.999994i | \(-0.498877\pi\) | ||||
0.00352768 | + | 0.999994i | \(0.498877\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1485.00 | −0.225822 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6714.00i | 1.01232i | 0.862439 | + | 0.506162i | \(0.168936\pi\) | ||||
−0.862439 | + | 0.506162i | \(0.831064\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 378.000i | − 0.0560389i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1296.00 | −0.190530 | −0.0952650 | − | 0.995452i | \(-0.530370\pi\) | ||||
−0.0952650 | + | 0.995452i | \(0.530370\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6234.00 | −0.908879 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 4755.00i | − 0.687528i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5903.00i | 0.839602i | 0.907616 | + | 0.419801i | \(0.137900\pi\) | ||||
−0.907616 | + | 0.419801i | \(0.862100\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3240.00 | 0.457094 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 252.000 | 0.0352647 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 8867.00i | − 1.23087i | −0.788186 | − | 0.615437i | \(-0.788980\pi\) | ||||
0.788186 | − | 0.615437i | \(-0.211020\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2970.00i | 0.405737i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8837.00 | −1.19769 | −0.598847 | − | 0.800863i | \(-0.704374\pi\) | ||||
−0.598847 | + | 0.800863i | \(0.704374\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1776.00 | −0.238812 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10044.0i | 1.34001i | 0.742356 | + | 0.670006i | \(0.233708\pi\) | ||||
−0.742356 | + | 0.670006i | \(0.766292\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 1467.00i | − 0.192692i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2736.00 | 0.356609 | 0.178304 | − | 0.983975i | \(-0.442939\pi\) | ||||
0.178304 | + | 0.983975i | \(0.442939\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −324.000 | −0.0419064 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1404.00i | 0.180210i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 12241.0i | − 1.54750i | −0.633490 | − | 0.773751i | \(-0.718378\pi\) | ||||
0.633490 | − | 0.773751i | \(-0.281622\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −525.000 | −0.0658719 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9036.00 | 1.12528 | 0.562639 | − | 0.826703i | \(-0.309786\pi\) | ||||
0.562639 | + | 0.826703i | \(0.309786\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 14905.0i | − 1.84236i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 16956.0i | − 2.06506i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8549.00 | −1.03355 | −0.516774 | − | 0.856122i | \(-0.672867\pi\) | ||||
−0.516774 | + | 0.856122i | \(0.672867\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7722.00 | 0.926760 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 882.000i | 0.105086i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 5268.00i | − 0.618645i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1548.00 | −0.180489 | −0.0902443 | − | 0.995920i | \(-0.528765\pi\) | ||||
−0.0902443 | + | 0.995920i | \(0.528765\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6110.00 | 0.707323 | 0.353662 | − | 0.935373i | \(-0.384936\pi\) | ||||
0.353662 | + | 0.935373i | \(0.384936\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 4698.00i | − 0.540011i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 329.000i | − 0.0372867i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8910.00 | −1.00275 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5958.00 | 0.665863 | 0.332931 | − | 0.942951i | \(-0.391962\pi\) | ||||
0.332931 | + | 0.942951i | \(0.391962\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 7163.00i | − 0.794993i | −0.917604 | − | 0.397496i | \(-0.869879\pi\) | ||||
0.917604 | − | 0.397496i | \(-0.130121\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 450.000i | 0.0492595i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.0000 | −0.00184821 | −0.000924107 | − | 1.00000i | \(-0.500294\pi\) | ||||
−0.000924107 | 1.00000i | \(0.500294\pi\) | ||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2646.00 | −0.285714 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9432.00i | 1.01158i | 0.862658 | + | 0.505788i | \(0.168798\pi\) | ||||
−0.862658 | + | 0.505788i | \(0.831202\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8046.00i | 0.851371i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15228.0 | 1.60057 | 0.800283 | − | 0.599623i | \(-0.204683\pi\) | ||||
0.800283 | + | 0.599623i | \(0.204683\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19440.0 | 2.02970 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 10185.0i | − 1.05636i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 250.000i | − 0.0255897i | −0.999918 | − | 0.0127949i | \(-0.995927\pi\) | ||||
0.999918 | − | 0.0127949i | \(-0.00407284\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −486.000 | −0.0494217 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16956.0 | 1.71306 | 0.856529 | − | 0.516099i | \(-0.172616\pi\) | ||||
0.856529 | + | 0.516099i | \(0.172616\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4384.00i | 0.440047i | 0.975495 | + | 0.220023i | \(0.0706134\pi\) | ||||
−0.975495 | + | 0.220023i | \(0.929387\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 5166.00i | − 0.511893i | −0.966691 | − | 0.255946i | \(-0.917613\pi\) | ||||
0.966691 | − | 0.255946i | \(-0.0823871\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2401.00 | −0.236392 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4647.00 | −0.454612 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 8802.00i | − 0.855637i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 324.000i | − 0.0311005i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6966.00 | −0.664477 | −0.332239 | − | 0.943195i | \(-0.607804\pi\) | ||||
−0.332239 | + | 0.943195i | \(0.607804\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17270.0 | −1.63710 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 378.000i | − 0.0356099i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18431.0i | 1.71497i | 0.514512 | + | 0.857483i | \(0.327973\pi\) | ||||
−0.514512 | + | 0.857483i | \(0.672027\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1515.00 | 0.140104 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1224.00 | 0.112502 | 0.0562509 | − | 0.998417i | \(-0.482085\pi\) | ||||
0.0562509 | + | 0.998417i | \(0.482085\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 972.000i | 0.0887965i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7560.00i | 0.682319i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2449.00 | 0.219704 | 0.109852 | − | 0.993948i | \(-0.464962\pi\) | ||||
0.109852 | + | 0.993948i | \(0.464962\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4428.00 | −0.394867 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3312.00i | 0.293588i | 0.989167 | + | 0.146794i | \(0.0468954\pi\) | ||||
−0.989167 | + | 0.146794i | \(0.953105\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2484.00i | 0.217590i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9162.00 | 0.797836 | 0.398918 | − | 0.916987i | \(-0.369386\pi\) | ||||
0.398918 | + | 0.916987i | \(0.369386\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7378.00 | 0.638715 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 675.000i | 0.0580935i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 28188.0i | − 2.39789i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7074.00 | −0.598293 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5418.00 | −0.455599 | −0.227799 | − | 0.973708i | \(-0.573153\pi\) | ||||
−0.227799 | + | 0.973708i | \(0.573153\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6829.00i | 0.570959i | 0.958385 | + | 0.285479i | \(0.0921528\pi\) | ||||
−0.958385 | + | 0.285479i | \(0.907847\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 4878.00i | − 0.403205i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11843.0 | 0.973371 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1134.00 | 0.0926769 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 19800.0i | − 1.60907i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4698.00i | 0.377530i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −15876.0 | −1.26870 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3053.00 | 0.242622 | 0.121311 | − | 0.992615i | \(-0.461290\pi\) | ||||
0.121311 | + | 0.992615i | \(0.461290\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 915.000i | − 0.0723138i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20456.0i | 1.59897i | 0.600687 | + | 0.799484i | \(0.294894\pi\) | ||||
−0.600687 | + | 0.799484i | \(0.705106\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −423.000 | −0.0328838 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1350.00 | 0.104377 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 3976.00i | − 0.305745i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 10854.0i | − 0.825671i | −0.910806 | − | 0.412835i | \(-0.864538\pi\) | ||||
0.910806 | − | 0.412835i | \(-0.135462\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8965.00 | −0.678317 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2916.00 | −0.219454 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 24930.0i | 1.86621i | 0.359609 | + | 0.933103i | \(0.382910\pi\) | ||||
−0.359609 | + | 0.933103i | \(0.617090\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 567.000i | − 0.0419961i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24786.0 | 1.82616 | 0.913078 | − | 0.407784i | \(-0.133698\pi\) | ||||
0.913078 | + | 0.407784i | \(0.133698\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14785.0 | −1.08360 | −0.541798 | − | 0.840509i | \(-0.682256\pi\) | ||||
−0.541798 | + | 0.840509i | \(0.682256\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5238.00i | 0.381886i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15851.0i | 1.14365i | 0.820376 | + | 0.571825i | \(0.193764\pi\) | ||||
−0.820376 | + | 0.571825i | \(0.806236\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11631.0 | 0.834832 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9954.00 | −0.710777 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 1944.00i | − 0.138100i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23148.0i | 1.62763i | 0.581122 | + | 0.813816i | \(0.302614\pi\) | ||||
−0.581122 | + | 0.813816i | \(0.697386\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6775.00 | −0.473954 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6426.00 | 0.447259 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 21888.0i | 1.51574i | 0.652407 | + | 0.757869i | \(0.273759\pi\) | ||||
−0.652407 | + | 0.757869i | \(0.726241\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 12099.0i | − 0.829446i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10764.0 | −0.734232 | −0.367116 | − | 0.930175i | \(-0.619655\pi\) | ||||
−0.367116 | + | 0.930175i | \(0.619655\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25597.0 | −1.73731 | −0.868655 | − | 0.495417i | \(-0.835015\pi\) | ||||
−0.868655 | + | 0.495417i | \(0.835015\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3087.00i | 0.208478i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 24976.0i | − 1.67009i | −0.550182 | − | 0.835045i | \(-0.685442\pi\) | ||||
0.550182 | − | 0.835045i | \(-0.314558\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1134.00 | −0.0754548 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −28710.0 | −1.90095 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2134.00i | 0.140606i | 0.997526 | + | 0.0703030i | \(0.0223966\pi\) | ||||
−0.997526 | + | 0.0703030i | \(0.977603\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13932.0i | 0.909046i | 0.890735 | + | 0.454523i | \(0.150190\pi\) | ||||
−0.890735 | + | 0.454523i | \(0.849810\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10429.0 | 0.677184 | 0.338592 | − | 0.940933i | \(-0.390049\pi\) | ||||
0.338592 | + | 0.940933i | \(0.390049\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −486.000 | −0.0314050 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10080.0i | 0.648229i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4050.00i | 0.257961i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5652.00 | −0.358283 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6283.00 | −0.396390 | −0.198195 | − | 0.980163i | \(-0.563508\pi\) | ||||
−0.198195 | + | 0.980163i | \(0.563508\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12315.0i | 0.773266i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 16170.0i | 1.00578i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9720.00 | 0.601748 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20916.0 | −1.28882 | −0.644409 | − | 0.764681i | \(-0.722897\pi\) | ||||
−0.644409 | + | 0.764681i | \(0.722897\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23452.0i | 1.43835i | 0.694831 | + | 0.719173i | \(0.255479\pi\) | ||||
−0.694831 | + | 0.719173i | \(0.744521\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 11916.0i | − 0.724059i | −0.932167 | − | 0.362030i | \(-0.882084\pi\) | ||||
0.932167 | − | 0.362030i | \(-0.117916\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6804.00 | 0.411526 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5691.00 | 0.342623 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 31842.0i | − 1.90823i | −0.299441 | − | 0.954115i | \(-0.596800\pi\) | ||||
0.299441 | − | 0.954115i | \(-0.403200\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 9486.00i | − 0.563294i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3672.00 | −0.217057 | −0.108529 | − | 0.994093i | \(-0.534614\pi\) | ||||
−0.108529 | + | 0.994093i | \(0.534614\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5138.00 | 0.302337 | 0.151169 | − | 0.988508i | \(-0.451696\pi\) | ||||
0.151169 | + | 0.988508i | \(0.451696\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2970.00i | 0.173975i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 972.000i | 0.0564258i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4155.00 | −0.240122 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2538.00 | −0.146018 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5050.00i | 0.289247i | 0.989487 | + | 0.144623i | \(0.0461971\pi\) | ||||
−0.989487 | + | 0.144623i | \(0.953803\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28458.0i | 1.61555i | 0.589488 | + | 0.807777i | \(0.299329\pi\) | ||||
−0.589488 | + | 0.807777i | \(0.700671\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3073.00 | −0.173683 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7560.00 | −0.425404 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 24408.0i | − 1.36742i | −0.729755 | − | 0.683709i | \(-0.760366\pi\) | ||||
0.729755 | − | 0.683709i | \(-0.239634\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 15387.0i | 0.854513i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1980.00 | −0.109480 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16328.0 | 0.898909 | 0.449455 | − | 0.893303i | \(-0.351618\pi\) | ||||
0.449455 | + | 0.893303i | \(0.351618\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 3402.00i | − 0.186481i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 6480.00i | − 0.352148i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9720.00 | 0.525957 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6246.00 | 0.336531 | 0.168265 | − | 0.985742i | \(-0.446183\pi\) | ||||
0.168265 | + | 0.985742i | \(0.446183\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7850.00i | 0.421150i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 5796.00i | − 0.308318i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 30679.0 | 1.62507 | 0.812535 | − | 0.582913i | \(-0.198087\pi\) | ||||
0.812535 | + | 0.582913i | \(0.198087\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5112.00 | −0.269641 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 4878.00i | − 0.256217i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 8964.00i | − 0.466899i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15462.0 | −0.801996 | −0.400998 | − | 0.916079i | \(-0.631337\pi\) | ||||
−0.400998 | + | 0.916079i | \(0.631337\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3836.00 | −0.198142 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7941.00i | 0.408477i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26801.0i | 1.36725i | 0.729831 | + | 0.683627i | \(0.239599\pi\) | ||||
−0.729831 | + | 0.683627i | \(0.760401\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2934.00 | −0.148451 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22858.0i | 1.15181i | 0.817515 | + | 0.575907i | \(0.195351\pi\) | ||||
−0.817515 | + | 0.575907i | \(0.804649\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 18522.0i | 0.925735i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16900.0 | 0.841240 | 0.420620 | − | 0.907237i | \(-0.361813\pi\) | ||||
0.420620 | + | 0.907237i | \(0.361813\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4125.00 | 0.204502 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 8028.00i | − 0.396391i | −0.980162 | − | 0.198196i | \(-0.936492\pi\) | ||||
0.980162 | − | 0.198196i | \(-0.0635081\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12798.0i | 0.626846i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10332.0 | −0.504036 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12448.0 | −0.604839 | −0.302419 | − | 0.953175i | \(-0.597794\pi\) | ||||
−0.302419 | + | 0.953175i | \(0.597794\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12636.0i | 0.611529i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 30103.0i | − 1.44533i | −0.691200 | − | 0.722663i | \(-0.742918\pi\) | ||||
0.691200 | − | 0.722663i | \(-0.257082\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2916.00 | −0.139452 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17748.0 | −0.845420 | −0.422710 | − | 0.906265i | \(-0.638921\pi\) | ||||
−0.422710 | + | 0.906265i | \(0.638921\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8939.00i | 0.424133i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 6930.00i | − 0.326242i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13283.0 | −0.622883 | −0.311442 | − | 0.950265i | \(-0.600812\pi\) | ||||
−0.311442 | + | 0.950265i | \(0.600812\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17172.0 | 0.802120 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 26424.0i | − 1.22950i | −0.788721 | − | 0.614751i | \(-0.789256\pi\) | ||||
0.788721 | − | 0.614751i | \(-0.210744\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 6594.00i | − 0.304451i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9000.00 | −0.413939 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 58320.0 | 2.67203 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1458.00i | 0.0665449i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 9709.00i | − 0.439757i | −0.975527 | − | 0.219878i | \(-0.929434\pi\) | ||||
0.975527 | − | 0.219878i | \(-0.0705660\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 13824.0 | 0.623761 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12852.0 | −0.577705 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2585.00i | 0.115758i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 7884.00i | − 0.350396i | −0.984533 | − | 0.175198i | \(-0.943943\pi\) | ||||
0.984533 | − | 0.175198i | \(-0.0560566\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9396.00 | −0.416028 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12960.0 | 0.571684 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 56916.0i | − 2.50127i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 19278.0i | − 0.840914i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1476.00 | 0.0641451 | 0.0320726 | − | 0.999486i | \(-0.489789\pi\) | ||||
0.0320726 | + | 0.999486i | \(0.489789\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21455.0 | 0.928960 | 0.464480 | − | 0.885583i | \(-0.346241\pi\) | ||||
0.464480 | + | 0.885583i | \(0.346241\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10128.0i | 0.436906i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4075.00i | 0.174500i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3465.00 | −0.147835 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31086.0 | 1.32145 | 0.660724 | − | 0.750629i | \(-0.270249\pi\) | ||||
0.660724 | + | 0.750629i | \(0.270249\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 23381.0i | − 0.990292i | −0.868810 | − | 0.495146i | \(-0.835115\pi\) | ||||
0.868810 | − | 0.495146i | \(-0.164885\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3636.00i | 0.152885i | 0.997074 | + | 0.0764426i | \(0.0243562\pi\) | ||||
−0.997074 | + | 0.0764426i | \(0.975644\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4058.00 | −0.170012 | −0.0850061 | − | 0.996380i | \(-0.527091\pi\) | ||||
−0.0850061 | + | 0.996380i | \(0.527091\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 16143.0 | 0.673880 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5292.00i | 0.220116i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 7317.00i | − 0.302165i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −306.000 | −0.0125915 | −0.00629576 | − | 0.999980i | \(-0.502004\pi\) | ||||
−0.00629576 | + | 0.999980i | \(0.502004\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21473.0 | −0.880438 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10422.0i | 0.425804i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 11095.0i | − 0.450093i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6807.00 | 0.275166 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5652.00 | −0.227671 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 42299.0i | − 1.69788i | −0.528491 | − | 0.848939i | \(-0.677242\pi\) | ||||
0.528491 | − | 0.848939i | \(-0.322758\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 11484.0i | − 0.457743i | −0.973457 | − | 0.228872i | \(-0.926496\pi\) | ||||
0.973457 | − | 0.228872i | \(-0.0735036\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33560.0 | −1.33301 | −0.666503 | − | 0.745502i | \(-0.732210\pi\) | ||||
−0.666503 | + | 0.745502i | \(0.732210\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7560.00 | 0.299238 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14976.0i | 0.590717i | 0.955386 | + | 0.295359i | \(0.0954391\pi\) | ||||
−0.955386 | + | 0.295359i | \(0.904561\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 13767.0i | − 0.539275i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −30672.0 | −1.19733 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18865.0 | 0.733888 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3951.00i | 0.153174i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 41893.0i | − 1.61303i | −0.591215 | − | 0.806514i | \(-0.701351\pi\) | ||||
0.591215 | − | 0.806514i | \(-0.298649\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5022.00 | 0.192705 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −720.000 | −0.0275340 | −0.0137670 | − | 0.999905i | \(-0.504382\pi\) | ||||
−0.0137670 | + | 0.999905i | \(0.504382\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 17309.0i | − 0.659676i | −0.944037 | − | 0.329838i | \(-0.893006\pi\) | ||||
0.944037 | − | 0.329838i | \(-0.106994\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 7002.00i | − 0.265055i | −0.991179 | − | 0.132528i | \(-0.957691\pi\) | ||||
0.991179 | − | 0.132528i | \(-0.0423094\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4144.00 | −0.156339 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4374.00 | −0.164461 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13050.0i | 0.489028i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2970.00i | 0.110552i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −14634.0 | −0.542905 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −648.000 | −0.0239601 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 3423.00i | − 0.126147i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1484.00i | 0.0543279i | 0.999631 | + | 0.0271640i | \(0.00864762\pi\) | ||||
−0.999631 | + | 0.0271640i | \(0.991352\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7452.00 | −0.271911 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18882.0 | −0.686705 | −0.343353 | − | 0.939207i | \(-0.611563\pi\) | ||||
−0.343353 | + | 0.939207i | \(0.611563\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 76788.0i | 2.78347i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3276.00i | 0.117975i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 50653.0 | 1.81816 | 0.909080 | − | 0.416622i | \(-0.136786\pi\) | ||||
0.909080 | + | 0.416622i | \(0.136786\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1617.00 | 0.0578523 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 59400.0i | − 2.11828i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4932.00i | 0.174744i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −35262.0 | −1.24533 | −0.622663 | − | 0.782490i | \(-0.713949\pi\) | ||||
−0.622663 | + | 0.782490i | \(0.713949\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7350.00 | 0.258740 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 4482.00i | − 0.157271i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20279.0i | 0.707029i | 0.935429 | + | 0.353514i | \(0.115013\pi\) | ||||
−0.935429 | + | 0.353514i | \(0.884987\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11991.0 | 0.416732 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 42390.0 | 1.46852 | 0.734259 | − | 0.678870i | \(-0.237530\pi\) | ||||
0.734259 | + | 0.678870i | \(0.237530\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 6480.00i | − 0.223773i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 42426.0i | − 1.45582i | −0.685674 | − | 0.727909i | \(-0.740492\pi\) | ||||
0.685674 | − | 0.727909i | \(-0.259508\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −57970.0 | −1.98291 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11016.0 | −0.375624 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 48168.0i | − 1.63727i | −0.574317 | − | 0.818633i | \(-0.694732\pi\) | ||||
0.574317 | − | 0.818633i | \(-0.305268\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8748.00i | 0.295489i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 18018.0 | 0.606707 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 43650.0 | 1.46521 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 13284.0i | 0.444518i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 51400.0i | − 1.70932i | −0.519188 | − | 0.854660i | \(-0.673766\pi\) | ||||
0.519188 | − | 0.854660i | \(-0.326234\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1350.00 | 0.0447557 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 33858.0 | 1.11901 | 0.559503 | − | 0.828828i | \(-0.310992\pi\) | ||||
0.559503 | + | 0.828828i | \(0.310992\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 12292.0i | − 0.404998i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 47106.0i | 1.54253i | 0.636513 | + | 0.771266i | \(0.280376\pi\) | ||||
−0.636513 | + | 0.771266i | \(0.719624\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 77760.0 | 2.53853 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11493.0 | 0.374050 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 20844.0i | 0.676318i | 0.941089 | + | 0.338159i | \(0.109804\pi\) | ||||
−0.941089 | + | 0.338159i | \(0.890196\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 10962.0i | − 0.353520i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2934.00 | −0.0943334 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4133.00 | 0.132481 | 0.0662407 | − | 0.997804i | \(-0.478899\pi\) | ||||
0.0662407 | + | 0.997804i | \(0.478899\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 3156.00i | − 0.100859i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33122.0i | 1.05214i | 0.850441 | + | 0.526070i | \(0.176335\pi\) | ||||
−0.850441 | + | 0.526070i | \(0.823665\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8478.00 | −0.268501 |
(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 | 300.4.d.a.49.1 | 2 | ||
3.2 | odd | 2 | 900.4.d.j.649.1 | 2 | |||
4.3 | odd | 2 | 1200.4.f.s.49.2 | 2 | |||
5.2 | odd | 4 | 300.4.a.c.1.1 | ✓ | 1 | ||
5.3 | odd | 4 | 300.4.a.g.1.1 | yes | 1 | ||
5.4 | even | 2 | inner | 300.4.d.a.49.2 | 2 | ||
15.2 | even | 4 | 900.4.a.k.1.1 | 1 | |||
15.8 | even | 4 | 900.4.a.h.1.1 | 1 | |||
15.14 | odd | 2 | 900.4.d.j.649.2 | 2 | |||
20.3 | even | 4 | 1200.4.a.m.1.1 | 1 | |||
20.7 | even | 4 | 1200.4.a.y.1.1 | 1 | |||
20.19 | odd | 2 | 1200.4.f.s.49.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.4.a.c.1.1 | ✓ | 1 | 5.2 | odd | 4 | ||
300.4.a.g.1.1 | yes | 1 | 5.3 | odd | 4 | ||
300.4.d.a.49.1 | 2 | 1.1 | even | 1 | trivial | ||
300.4.d.a.49.2 | 2 | 5.4 | even | 2 | inner | ||
900.4.a.h.1.1 | 1 | 15.8 | even | 4 | |||
900.4.a.k.1.1 | 1 | 15.2 | even | 4 | |||
900.4.d.j.649.1 | 2 | 3.2 | odd | 2 | |||
900.4.d.j.649.2 | 2 | 15.14 | odd | 2 | |||
1200.4.a.m.1.1 | 1 | 20.3 | even | 4 | |||
1200.4.a.y.1.1 | 1 | 20.7 | even | 4 | |||
1200.4.f.s.49.1 | 2 | 20.19 | odd | 2 | |||
1200.4.f.s.49.2 | 2 | 4.3 | odd | 2 |