Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,5,Mod(53,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.53");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.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: | \(11.1639560131\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 53.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 108.53 |
Dual form | 108.5.c.c.53.2 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 9.00000i | − 0.360000i | −0.983667 | − | 0.180000i | \(-0.942390\pi\) | ||||
0.983667 | − | 0.180000i | \(-0.0576098\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.00000 | 0.102041 | 0.0510204 | − | 0.998698i | \(-0.483753\pi\) | ||||
0.0510204 | + | 0.998698i | \(0.483753\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 117.000i | − 0.966942i | −0.875360 | − | 0.483471i | \(-0.839376\pi\) | ||||
0.875360 | − | 0.483471i | \(-0.160624\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −34.0000 | −0.201183 | −0.100592 | − | 0.994928i | \(-0.532074\pi\) | ||||
−0.100592 | + | 0.994928i | \(0.532074\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 450.000i | − 1.55709i | −0.627587 | − | 0.778547i | \(-0.715957\pi\) | ||||
0.627587 | − | 0.778547i | \(-0.284043\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −64.0000 | −0.177285 | −0.0886427 | − | 0.996063i | \(-0.528253\pi\) | ||||
−0.0886427 | + | 0.996063i | \(0.528253\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 612.000i | − 1.15690i | −0.815718 | − | 0.578450i | \(-0.803658\pi\) | ||||
0.815718 | − | 0.578450i | \(-0.196342\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 544.000 | 0.870400 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 1062.00i | − 1.26278i | −0.775464 | − | 0.631391i | \(-0.782484\pi\) | ||||
0.775464 | − | 0.631391i | \(-0.217516\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −697.000 | −0.725286 | −0.362643 | − | 0.931928i | \(-0.618126\pi\) | ||||
−0.362643 | + | 0.931928i | \(0.618126\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 45.0000i | − 0.0367347i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −748.000 | −0.546384 | −0.273192 | − | 0.961959i | \(-0.588079\pi\) | ||||
−0.273192 | + | 0.961959i | \(0.588079\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 684.000i | − 0.406901i | −0.979085 | − | 0.203450i | \(-0.934784\pi\) | ||||
0.979085 | − | 0.203450i | \(-0.0652155\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2618.00 | 1.41590 | 0.707950 | − | 0.706262i | \(-0.249620\pi\) | ||||
0.707950 | + | 0.706262i | \(0.249620\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2646.00i | 1.19783i | 0.800814 | + | 0.598914i | \(0.204401\pi\) | ||||
−0.800814 | + | 0.598914i | \(0.795599\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2376.00 | −0.989588 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1071.00i | 0.381274i | 0.981661 | + | 0.190637i | \(0.0610554\pi\) | ||||
−0.981661 | + | 0.190637i | \(0.938945\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1053.00 | −0.348099 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5814.00i | 1.67021i | 0.550091 | + | 0.835105i | \(0.314593\pi\) | ||||
−0.550091 | + | 0.835105i | \(0.685407\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6404.00 | 1.72104 | 0.860521 | − | 0.509414i | \(-0.170138\pi\) | ||||
0.860521 | + | 0.509414i | \(0.170138\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 306.000i | 0.0724260i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5218.00 | −1.16240 | −0.581198 | − | 0.813762i | \(-0.697416\pi\) | ||||
−0.581198 | + | 0.813762i | \(0.697416\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6570.00i | 1.30331i | 0.758514 | + | 0.651656i | \(0.225926\pi\) | ||||
−0.758514 | + | 0.651656i | \(0.774074\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4519.00 | −0.848002 | −0.424001 | − | 0.905662i | \(-0.639375\pi\) | ||||
−0.424001 | + | 0.905662i | \(0.639375\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 585.000i | − 0.0986676i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7502.00 | 1.20205 | 0.601025 | − | 0.799230i | \(-0.294759\pi\) | ||||
0.601025 | + | 0.799230i | \(0.294759\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5481.00i | 0.795616i | 0.917469 | + | 0.397808i | \(0.130229\pi\) | ||||
−0.917469 | + | 0.397808i | \(0.869771\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4050.00 | −0.560554 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 8874.00i | − 1.12031i | −0.828387 | − | 0.560157i | \(-0.810741\pi\) | ||||
0.828387 | − | 0.560157i | \(-0.189259\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −170.000 | −0.0205289 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 576.000i | 0.0638227i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10571.0 | 1.12350 | 0.561749 | − | 0.827307i | \(-0.310129\pi\) | ||||
0.561749 | + | 0.827307i | \(0.310129\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 13113.0i | − 1.28546i | −0.766092 | − | 0.642731i | \(-0.777801\pi\) | ||||
0.766092 | − | 0.642731i | \(-0.222199\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5830.00 | −0.549533 | −0.274767 | − | 0.961511i | \(-0.588601\pi\) | ||||
−0.274767 | + | 0.961511i | \(0.588601\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 1089.00i | − 0.0951175i | −0.998868 | − | 0.0475587i | \(-0.984856\pi\) | ||||
0.998868 | − | 0.0475587i | \(-0.0151441\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5020.00 | −0.422523 | −0.211262 | − | 0.977430i | \(-0.567757\pi\) | ||||
−0.211262 | + | 0.977430i | \(0.567757\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 21384.0i | − 1.67468i | −0.546682 | − | 0.837340i | \(-0.684109\pi\) | ||||
0.546682 | − | 0.837340i | \(-0.315891\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5508.00 | −0.416484 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 2250.00i | − 0.158887i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 952.000 | 0.0650229 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 10521.0i | − 0.673344i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9227.00 | 0.572075 | 0.286038 | − | 0.958218i | \(-0.407662\pi\) | ||||
0.286038 | + | 0.958218i | \(0.407662\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 4275.00i | − 0.249111i | −0.992213 | − | 0.124556i | \(-0.960249\pi\) | ||||
0.992213 | − | 0.124556i | \(-0.0397505\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −320.000 | −0.0180903 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 11322.0i | − 0.603229i | −0.953430 | − | 0.301614i | \(-0.902474\pi\) | ||||
0.953430 | − | 0.301614i | \(-0.0975255\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9812.00 | 0.507841 | 0.253921 | − | 0.967225i | \(-0.418280\pi\) | ||||
0.253921 | + | 0.967225i | \(0.418280\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3978.00i | 0.194533i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9558.00 | −0.454602 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16479.0i | 0.742264i | 0.928580 | + | 0.371132i | \(0.121030\pi\) | ||||
−0.928580 | + | 0.371132i | \(0.878970\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −25555.0 | −1.12078 | −0.560392 | − | 0.828227i | \(-0.689350\pi\) | ||||
−0.560392 | + | 0.828227i | \(0.689350\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6273.00i | 0.261103i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21164.0 | 0.858615 | 0.429307 | − | 0.903158i | \(-0.358758\pi\) | ||||
0.429307 | + | 0.903158i | \(0.358758\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 3060.00i | − 0.118051i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 33830.0 | 1.27329 | 0.636644 | − | 0.771158i | \(-0.280322\pi\) | ||||
0.636644 | + | 0.771158i | \(0.280322\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 27378.0i | 0.981677i | 0.871250 | + | 0.490839i | \(0.163310\pi\) | ||||
−0.871250 | + | 0.490839i | \(0.836690\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −27405.0 | −0.959525 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 46197.0i | 1.54355i | 0.635894 | + | 0.771777i | \(0.280632\pi\) | ||||
−0.635894 | + | 0.771777i | \(0.719368\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2720.00 | 0.0888163 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20781.0i | 0.648575i | 0.945959 | + | 0.324288i | \(0.105125\pi\) | ||||
−0.945959 | + | 0.324288i | \(0.894875\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19504.0 | −0.595342 | −0.297671 | − | 0.954669i | \(-0.596210\pi\) | ||||
−0.297671 | + | 0.954669i | \(0.596210\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6732.00i | 0.196698i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −52650.0 | −1.50562 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 7038.00i | − 0.192922i | −0.995337 | − | 0.0964612i | \(-0.969248\pi\) | ||||
0.995337 | − | 0.0964612i | \(-0.0307524\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 51527.0 | 1.38331 | 0.691656 | − | 0.722227i | \(-0.256881\pi\) | ||||
0.691656 | + | 0.722227i | \(0.256881\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 60435.0i | 1.55724i | 0.627495 | + | 0.778621i | \(0.284080\pi\) | ||||
−0.627495 | + | 0.778621i | \(0.715920\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 45665.0 | 1.15313 | 0.576564 | − | 0.817052i | \(-0.304393\pi\) | ||||
0.576564 | + | 0.817052i | \(0.304393\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 5310.00i | − 0.128855i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6156.00 | −0.146484 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7488.00i | 0.171425i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13124.0 | 0.294782 | 0.147391 | − | 0.989078i | \(-0.452912\pi\) | ||||
0.147391 | + | 0.989078i | \(0.452912\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 23562.0i | − 0.509724i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3485.00 | −0.0740088 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 15300.0i | 0.313261i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −78850.0 | −1.58559 | −0.792797 | − | 0.609486i | \(-0.791376\pi\) | ||||
−0.792797 | + | 0.609486i | \(0.791376\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 22302.0i | − 0.432805i | −0.976304 | − | 0.216402i | \(-0.930568\pi\) | ||||
0.976304 | − | 0.216402i | \(-0.0694323\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8870.00 | 0.169142 | 0.0845712 | − | 0.996417i | \(-0.473048\pi\) | ||||
0.0845712 | + | 0.996417i | \(0.473048\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 26010.0i | − 0.479103i | −0.970884 | − | 0.239551i | \(-0.923000\pi\) | ||||
0.970884 | − | 0.239551i | \(-0.0770003\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 23814.0 | 0.431218 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 64152.0i | − 1.12309i | −0.827446 | − | 0.561545i | \(-0.810207\pi\) | ||||
0.827446 | − | 0.561545i | \(-0.189793\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 33422.0 | 0.575438 | 0.287719 | − | 0.957715i | \(-0.407103\pi\) | ||||
0.287719 | + | 0.957715i | \(0.407103\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 21384.0i | 0.356252i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2176.00 | 0.0356669 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 110466.i | − 1.75340i | −0.481037 | − | 0.876700i | \(-0.659740\pi\) | ||||
0.481037 | − | 0.876700i | \(-0.340260\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −71604.0 | −1.11866 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 15174.0i | − 0.229739i | −0.993381 | − | 0.114869i | \(-0.963355\pi\) | ||||
0.993381 | − | 0.114869i | \(-0.0366449\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3740.00 | −0.0557535 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 69948.0i | − 1.01126i | −0.862750 | − | 0.505631i | \(-0.831260\pi\) | ||||
0.862750 | − | 0.505631i | \(-0.168740\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9639.00 | 0.137259 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 50346.0i | 0.695762i | 0.937539 | + | 0.347881i | \(0.113099\pi\) | ||||
−0.937539 | + | 0.347881i | \(0.886901\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 108323. | 1.47497 | 0.737483 | − | 0.675366i | \(-0.236014\pi\) | ||||
0.737483 | + | 0.675366i | \(0.236014\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 63648.0i | − 0.841626i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 30716.0 | 0.400318 | 0.200159 | − | 0.979763i | \(-0.435854\pi\) | ||||
0.200159 | + | 0.979763i | \(0.435854\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 129258.i | − 1.63699i | −0.574517 | − | 0.818493i | \(-0.694810\pi\) | ||||
0.574517 | − | 0.818493i | \(-0.305190\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −63976.0 | −0.798811 | −0.399406 | − | 0.916774i | \(-0.630783\pi\) | ||||
−0.399406 | + | 0.916774i | \(0.630783\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 3420.00i | − 0.0415205i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −118979. | −1.42454 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 108630.i | 1.26536i | 0.774413 | + | 0.632681i | \(0.218045\pi\) | ||||
−0.774413 | + | 0.632681i | \(0.781955\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 52326.0 | 0.601275 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 20808.0i | 0.232749i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 13090.0 | 0.144480 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 57636.0i | − 0.619575i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6410.00 | 0.0680113 | 0.0340057 | − | 0.999422i | \(-0.489174\pi\) | ||||
0.0340057 | + | 0.999422i | \(0.489174\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 70992.0i | − 0.733987i | −0.930223 | − | 0.366994i | \(-0.880387\pi\) | ||||
0.930223 | − | 0.366994i | \(-0.119613\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 160961. | 1.64298 | 0.821489 | − | 0.570224i | \(-0.193143\pi\) | ||||
0.821489 | + | 0.570224i | \(0.193143\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 194733.i | 1.93785i | 0.247347 | + | 0.968927i | \(0.420441\pi\) | ||||
−0.247347 | + | 0.968927i | \(0.579559\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −124254. | −1.22104 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 28800.0i | 0.276050i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −18496.0 | −0.175110 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 13230.0i | 0.122227i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −33286.0 | −0.303812 | −0.151906 | − | 0.988395i | \(-0.548541\pi\) | ||||
−0.151906 | + | 0.988395i | \(0.548541\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 46962.0i | 0.418463i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −127690. | −1.12434 | −0.562169 | − | 0.827022i | \(-0.690033\pi\) | ||||
−0.562169 | + | 0.827022i | \(0.690033\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 81549.0i | 0.701310i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −23885.0 | −0.203019 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 138807.i | 1.15280i | 0.817169 | + | 0.576398i | \(0.195542\pi\) | ||||
−0.817169 | + | 0.576398i | \(0.804458\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 203792. | 1.67316 | 0.836578 | − | 0.547848i | \(-0.184553\pi\) | ||||
0.836578 | + | 0.547848i | \(0.184553\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 32328.0i | − 0.259436i | −0.991551 | − | 0.129718i | \(-0.958593\pi\) | ||||
0.991551 | − | 0.129718i | \(-0.0414071\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 59130.0 | 0.469193 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 185922.i | 1.44259i | 0.692630 | + | 0.721293i | \(0.256452\pi\) | ||||
−0.692630 | + | 0.721293i | \(0.743548\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −126225. | −0.968570 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 40671.0i | 0.305281i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 151079. | 1.12169 | 0.560844 | − | 0.827922i | \(-0.310477\pi\) | ||||
0.560844 | + | 0.827922i | \(0.310477\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5355.00i | 0.0389056i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6478.00 | −0.0465611 | −0.0232806 | − | 0.999729i | \(-0.507411\pi\) | ||||
−0.0232806 | + | 0.999729i | \(0.507411\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 36108.0i | 0.254051i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 99008.0 | 0.689274 | 0.344637 | − | 0.938736i | \(-0.388002\pi\) | ||||
0.344637 | + | 0.938736i | \(0.388002\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 91062.0i | 0.620783i | 0.950609 | + | 0.310391i | \(0.100460\pi\) | ||||
−0.950609 | + | 0.310391i | \(0.899540\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5265.00 | −0.0355203 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 95319.0i | 0.629913i | 0.949106 | + | 0.314956i | \(0.101990\pi\) | ||||
−0.949106 | + | 0.314956i | \(0.898010\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −275400. | −1.80140 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 67518.0i | − 0.432738i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −163438. | −1.03698 | −0.518492 | − | 0.855083i | \(-0.673506\pi\) | ||||
−0.518492 | + | 0.855083i | \(0.673506\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 284616.i | − 1.76999i | −0.465601 | − | 0.884994i | \(-0.654162\pi\) | ||||
0.465601 | − | 0.884994i | \(-0.345838\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 23698.0 | 0.145916 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 87516.0i | 0.528322i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 107525. | 0.642781 | 0.321390 | − | 0.946947i | \(-0.395850\pi\) | ||||
0.321390 | + | 0.946947i | \(0.395850\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 29070.0i | 0.170430i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 49329.0 | 0.286422 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 150282.i | 0.856010i | 0.903776 | + | 0.428005i | \(0.140783\pi\) | ||||
−0.903776 | + | 0.428005i | \(0.859217\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 134420. | 0.758402 | 0.379201 | − | 0.925314i | \(-0.376199\pi\) | ||||
0.379201 | + | 0.925314i | \(0.376199\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 244800.i | − 1.35529i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 32020.0 | 0.175617 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 237726.i | − 1.27974i | −0.768483 | − | 0.639871i | \(-0.778988\pi\) | ||||
0.768483 | − | 0.639871i | \(-0.221012\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 112187. | 0.598366 | 0.299183 | − | 0.954196i | \(-0.403286\pi\) | ||||
0.299183 | + | 0.954196i | \(0.403286\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 39168.0i | 0.205101i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −204643. | −1.06186 | −0.530931 | − | 0.847415i | \(-0.678158\pi\) | ||||
−0.530931 | + | 0.847415i | \(0.678158\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 50490.0i | − 0.257275i | −0.991692 | − | 0.128638i | \(-0.958940\pi\) | ||||
0.991692 | − | 0.128638i | \(-0.0410604\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −79866.0 | −0.403313 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 363528.i | − 1.80321i | −0.432565 | − | 0.901603i | \(-0.642391\pi\) | ||||
0.432565 | − | 0.901603i | \(-0.357609\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −80028.0 | −0.393449 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1530.00i | 0.00739041i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6677.00 | 0.0319705 | 0.0159852 | − | 0.999872i | \(-0.494912\pi\) | ||||
0.0159852 | + | 0.999872i | \(0.494912\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 229347.i | − 1.07917i | −0.841930 | − | 0.539587i | \(-0.818581\pi\) | ||||
0.841930 | − | 0.539587i | \(-0.181419\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 238799. | 1.11396 | 0.556981 | − | 0.830525i | \(-0.311960\pi\) | ||||
0.556981 | + | 0.830525i | \(0.311960\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 263133.i | 1.20654i | 0.797537 | + | 0.603270i | \(0.206136\pi\) | ||||
−0.797537 | + | 0.603270i | \(0.793864\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −26090.0 | −0.118612 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 306306.i | − 1.36909i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −34816.0 | −0.154309 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 9342.00i | − 0.0407163i | −0.999793 | − | 0.0203582i | \(-0.993519\pi\) | ||||
0.999793 | − | 0.0203582i | \(-0.00648066\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 25432.0 | 0.109923 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 95139.0i | − 0.404460i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 331262. | 1.39673 | 0.698367 | − | 0.715740i | \(-0.253910\pi\) | ||||
0.698367 | + | 0.715740i | \(0.253910\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 396297.i | − 1.64383i | −0.569608 | − | 0.821917i | \(-0.692905\pi\) | ||||
0.569608 | − | 0.821917i | \(-0.307095\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −477900. | −1.96627 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 32850.0i | 0.132991i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 45050.0 | 0.180923 | 0.0904615 | − | 0.995900i | \(-0.471166\pi\) | ||||
0.0904615 | + | 0.995900i | \(0.471166\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 233172.i | 0.921596i | 0.887505 | + | 0.460798i | \(0.152437\pi\) | ||||
−0.887505 | + | 0.460798i | \(0.847563\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −118017. | −0.462766 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 163449.i | 0.630880i | 0.948946 | + | 0.315440i | \(0.102152\pi\) | ||||
−0.948946 | + | 0.315440i | \(0.897848\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −22595.0 | −0.0865308 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 52470.0i | 0.197832i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 309582. | 1.15823 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 384606.i | − 1.41690i | −0.705759 | − | 0.708452i | \(-0.749394\pi\) | ||||
0.705759 | − | 0.708452i | \(-0.250606\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −214642. | −0.784714 | −0.392357 | − | 0.919813i | \(-0.628340\pi\) | ||||
−0.392357 | + | 0.919813i | \(0.628340\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 313650.i | 1.12934i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −94703.0 | −0.338417 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 23256.0i | 0.0818617i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9801.00 | −0.0342423 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 277992.i | 0.956874i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 545156. | 1.86263 | 0.931314 | − | 0.364217i | \(-0.118663\pi\) | ||||
0.931314 | + | 0.364217i | \(0.118663\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 45180.0i | 0.152108i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −491422. | −1.64240 | −0.821202 | − | 0.570638i | \(-0.806696\pi\) | ||||
−0.821202 | + | 0.570638i | \(0.806696\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 67968.0i | 0.223873i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 37510.0 | 0.122658 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 445077.i | 1.43458i | 0.696775 | + | 0.717290i | \(0.254618\pi\) | ||||
−0.696775 | + | 0.717290i | \(0.745382\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −89012.0 | −0.284856 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 153765.i | 0.485111i | 0.970138 | + | 0.242555i | \(0.0779856\pi\) | ||||
−0.970138 | + | 0.242555i | \(0.922014\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −192456. | −0.602885 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 269712.i | 0.833059i | 0.909122 | + | 0.416529i | \(0.136754\pi\) | ||||
−0.909122 | + | 0.416529i | \(0.863246\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 589718. | 1.80872 | 0.904362 | − | 0.426767i | \(-0.140347\pi\) | ||||
0.904362 | + | 0.426767i | \(0.140347\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 332928.i | − 1.00697i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 184094. | 0.552953 | 0.276476 | − | 0.961021i | \(-0.410833\pi\) | ||||
0.276476 | + | 0.961021i | \(0.410833\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 27405.0i | 0.0811853i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 125307. | 0.368670 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 411543.i | 1.19437i | 0.802103 | + | 0.597185i | \(0.203714\pi\) | ||||
−0.802103 | + | 0.597185i | \(0.796286\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 44608.0 | 0.128583 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 339966.i | 0.966777i | 0.875406 | + | 0.483388i | \(0.160594\pi\) | ||||
−0.875406 | + | 0.483388i | \(0.839406\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −20250.0 | −0.0571994 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 299574.i | 0.834931i | 0.908693 | + | 0.417465i | \(0.137082\pi\) | ||||
−0.908693 | + | 0.417465i | \(0.862918\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −516115. | −1.42889 | −0.714443 | − | 0.699694i | \(-0.753320\pi\) | ||||
−0.714443 | + | 0.699694i | \(0.753320\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 8568.00i | − 0.0234082i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −486574. | −1.32060 | −0.660300 | − | 0.751002i | \(-0.729571\pi\) | ||||
−0.660300 | + | 0.751002i | \(0.729571\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 89964.0i | − 0.240983i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −189550. | −0.504432 | −0.252216 | − | 0.967671i | \(-0.581159\pi\) | ||||
−0.252216 | + | 0.967671i | \(0.581159\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 148248.i | 0.389420i | 0.980861 | + | 0.194710i | \(0.0623766\pi\) | ||||
−0.980861 | + | 0.194710i | \(0.937623\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11390.0 | 0.0297264 | 0.0148632 | − | 0.999890i | \(-0.495269\pi\) | ||||
0.0148632 | + | 0.999890i | \(0.495269\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 44370.0i | − 0.114318i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 245311. | 0.627996 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 336600.i | 0.850771i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6715.00 | −0.0168650 | −0.00843252 | − | 0.999964i | \(-0.502684\pi\) | ||||
−0.00843252 | + | 0.999964i | \(0.502684\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 83043.0i | − 0.205947i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 80784.0 | 0.199089 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 441108.i | − 1.07357i | −0.843720 | − | 0.536783i | \(-0.819639\pi\) | ||||
0.843720 | − | 0.536783i | \(-0.180361\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 547448. | 1.32410 | 0.662050 | − | 0.749459i | \(-0.269687\pi\) | ||||
0.662050 | + | 0.749459i | \(0.269687\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 42228.0i | − 0.100877i | −0.998727 | − | 0.0504385i | \(-0.983938\pi\) | ||||
0.998727 | − | 0.0504385i | \(-0.0160619\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 680238. | 1.61500 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 258993.i | 0.607382i | 0.952771 | + | 0.303691i | \(0.0982190\pi\) | ||||
−0.952771 | + | 0.303691i | \(0.901781\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −38475.0 | −0.0896801 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 313083.i | − 0.720923i | −0.932774 | − | 0.360461i | \(-0.882619\pi\) | ||||
0.932774 | − | 0.360461i | \(-0.117381\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −686320. | −1.57081 | −0.785405 | − | 0.618982i | \(-0.787545\pi\) | ||||
−0.785405 | + | 0.618982i | \(0.787545\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2880.00i | 0.00651252i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −649944. | −1.46091 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 749268.i | − 1.66415i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 214727. | 0.474085 | 0.237043 | − | 0.971499i | \(-0.423822\pi\) | ||||
0.237043 | + | 0.971499i | \(0.423822\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 343638.i | 0.749763i | 0.927073 | + | 0.374881i | \(0.122317\pi\) | ||||
−0.927073 | + | 0.374881i | \(0.877683\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 52855.0 | 0.114643 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 626238.i | − 1.34245i | −0.741254 | − | 0.671225i | \(-0.765769\pi\) | ||||
0.741254 | − | 0.671225i | \(-0.234231\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −101898. | −0.217162 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 36414.0i | − 0.0767061i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 684476. | 1.43351 | 0.716757 | − | 0.697323i | \(-0.245626\pi\) | ||||
0.716757 | + | 0.697323i | \(0.245626\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 88308.0i | − 0.182823i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −307800. | −0.633582 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 809523.i | − 1.64738i | −0.567042 | − | 0.823689i | \(-0.691912\pi\) | ||||
0.567042 | − | 0.823689i | \(-0.308088\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 47872.0 | 0.0968659 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 65565.0i | − 0.131170i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −319648. | −0.635886 | −0.317943 | − | 0.948110i | \(-0.602992\pi\) | ||||
−0.317943 | + | 0.948110i | \(0.602992\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 426564.i | 0.839083i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 35802.0 | 0.0700318 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 55836.0i | − 0.108008i | −0.998541 | − | 0.0540041i | \(-0.982802\pi\) | ||||
0.998541 | − | 0.0540041i | \(-0.0171984\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −29150.0 | −0.0560748 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 577728.i | − 1.09913i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 863873. | 1.63449 | 0.817243 | − | 0.576294i | \(-0.195502\pi\) | ||||
0.817243 | + | 0.576294i | \(0.195502\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 1.17810e6i | − 2.20469i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 207608. | 0.386399 | 0.193200 | − | 0.981159i | \(-0.438114\pi\) | ||||
0.193200 | + | 0.981159i | \(0.438114\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 610506.i | 1.12397i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −803590. | −1.47145 | −0.735725 | − | 0.677280i | \(-0.763159\pi\) | ||||
−0.735725 | + | 0.677280i | \(0.763159\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 619650.i | − 1.12245i | −0.827662 | − | 0.561227i | \(-0.810329\pi\) | ||||
0.827662 | − | 0.561227i | \(-0.189671\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 148311. | 0.267215 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 5445.00i | − 0.00970587i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.06598e6 | −1.89004 | −0.945020 | − | 0.327011i | \(-0.893959\pi\) | ||||
−0.945020 | + | 0.327011i | \(0.893959\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 229995.i | 0.403482i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 750410. | 1.30950 | 0.654752 | − | 0.755844i | \(-0.272773\pi\) | ||||
0.654752 | + | 0.755844i | \(0.272773\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 413208.i | 0.713509i | 0.934198 | + | 0.356754i | \(0.116117\pi\) | ||||
−0.934198 | + | 0.356754i | \(0.883883\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −25100.0 | −0.0431146 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 197676.i | − 0.336019i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −733381. | −1.24016 | −0.620079 | − | 0.784539i | \(-0.712899\pi\) | ||||
−0.620079 | + | 0.784539i | \(0.712899\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 231822.i | − 0.387968i | −0.981005 | − | 0.193984i | \(-0.937859\pi\) | ||||
0.981005 | − | 0.193984i | \(-0.0621410\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −379168. | −0.631289 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 43776.0i | 0.0721375i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 768690. | 1.26023 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 190476.i | − 0.309101i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 502724. | 0.811671 | 0.405836 | − | 0.913946i | \(-0.366981\pi\) | ||||
0.405836 | + | 0.913946i | \(0.366981\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 106920.i | − 0.170886i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −217736. | −0.346245 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 596241.i | 0.938653i | 0.883025 | + | 0.469327i | \(0.155503\pi\) | ||||
−0.883025 | + | 0.469327i | \(0.844497\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.19070e6 | 1.86513 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 528723.i | 0.819968i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −27540.0 | −0.0424984 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 376038.i | 0.574559i | 0.957847 | + | 0.287280i | \(0.0927509\pi\) | ||||
−0.957847 | + | 0.287280i | \(0.907249\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −331072. | −0.503362 | −0.251681 | − | 0.967810i | \(-0.580983\pi\) | ||||
−0.251681 | + | 0.967810i | \(0.580983\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 304470.i | − 0.458384i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −167552. | −0.251018 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 274626.i | 0.407432i | 0.979030 | + | 0.203716i | \(0.0653019\pi\) | ||||
−0.979030 | + | 0.203716i | \(0.934698\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −541195. | −0.799013 | −0.399507 | − | 0.916730i | \(-0.630819\pi\) | ||||
−0.399507 | + | 0.916730i | \(0.630819\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 358362.i | − 0.523975i | −0.965071 | − | 0.261988i | \(-0.915622\pi\) | ||||
0.965071 | − | 0.261988i | \(-0.0843780\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 39626.0 | 0.0576595 | 0.0288298 | − | 0.999584i | \(-0.490822\pi\) | ||||
0.0288298 | + | 0.999584i | \(0.490822\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.06920e6i | 1.54088i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 246402. | 0.353404 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.05543e6i | 1.49936i | 0.661801 | + | 0.749679i | \(0.269792\pi\) | ||||
−0.661801 | + | 0.749679i | \(0.730208\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −420563. | −0.594619 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 246645.i | 0.345429i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4760.00 | 0.00663499 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 457776.i | 0.632112i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −33034.0 | −0.0454008 | −0.0227004 | − | 0.999742i | \(-0.507226\pi\) | ||||
−0.0227004 | + | 0.999742i | \(0.507226\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 456246.i | 0.621209i | 0.950539 | + | 0.310604i | \(0.100531\pi\) | ||||
−0.950539 | + | 0.310604i | \(0.899469\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 343604. | 0.465663 | 0.232832 | − | 0.972517i | \(-0.425201\pi\) | ||||
0.232832 | + | 0.972517i | \(0.425201\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 74556.0i | 0.100106i | 0.998747 | + | 0.0500531i | \(0.0159391\pi\) | ||||
−0.998747 | + | 0.0500531i | \(0.984061\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 415773. | 0.555679 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 877734.i | − 1.16231i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 177412. | 0.233855 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 52605.0i | − 0.0687086i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −696094. | −0.905042 | −0.452521 | − | 0.891754i | \(-0.649475\pi\) | ||||
−0.452521 | + | 0.891754i | \(0.649475\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 672426.i | 0.866349i | 0.901310 | + | 0.433174i | \(0.142607\pi\) | ||||
−0.901310 | + | 0.433174i | \(0.857393\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.44813e6 | −1.85731 | −0.928657 | − | 0.370938i | \(-0.879036\pi\) | ||||
−0.928657 | + | 0.370938i | \(0.879036\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.50964e6i | 1.91879i | 0.282071 | + | 0.959393i | \(0.408978\pi\) | ||||
−0.282071 | + | 0.959393i | \(0.591022\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 46135.0 | 0.0583750 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 169344.i | − 0.212357i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 187029. | 0.233487 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 740214.i | 0.915879i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 481950. | 0.593680 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 175536.i | 0.214323i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 374828. | 0.455635 | 0.227818 | − | 0.973704i | \(-0.426841\pi\) | ||||
0.227818 | + | 0.973704i | \(0.426841\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 1.21149e6i | − 1.45977i | −0.683572 | − | 0.729883i | \(-0.739575\pi\) | ||||
0.683572 | − | 0.729883i | \(-0.260425\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 641277. | 0.769315 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 21375.0i | − 0.0254195i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 656777. | 0.777655 | 0.388827 | − | 0.921311i | \(-0.372880\pi\) | ||||
0.388827 | + | 0.921311i | \(0.372880\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 223380.i | − 0.262205i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −406912. | −0.475573 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 578988.i | 0.670870i | 0.942063 | + | 0.335435i | \(0.108883\pi\) | ||||
−0.942063 | + | 0.335435i | \(0.891117\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 152064. | 0.175439 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 473850.i | 0.542023i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 195173. | 0.222301 | 0.111150 | − | 0.993804i | \(-0.464547\pi\) | ||||
0.111150 | + | 0.993804i | \(0.464547\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 1.31932e6i | − 1.48995i | −0.667095 | − | 0.744973i | \(-0.732462\pi\) | ||||
0.667095 | − | 0.744973i | \(-0.267538\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −418608. | −0.470743 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 972621.i | 1.08454i | 0.840206 | + | 0.542268i | \(0.182434\pi\) | ||||
−0.840206 | + | 0.542268i | \(0.817566\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 153646. | 0.170604 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 534384.i | − 0.588393i | −0.955745 | − | 0.294197i | \(-0.904948\pi\) | ||||
0.955745 | − | 0.294197i | \(-0.0950520\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −63342.0 | −0.0694520 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 56610.0i | − 0.0615540i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −437712. | −0.473960 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 463743.i | − 0.497992i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −783619. | −0.838015 | −0.419008 | − | 0.907983i | \(-0.637622\pi\) | ||||
−0.419008 | + | 0.907983i | \(0.637622\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 276777.i | − 0.293556i | −0.989169 | − | 0.146778i | \(-0.953110\pi\) | ||||
0.989169 | − | 0.146778i | \(-0.0468904\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 49060.0 | 0.0518205 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 648234.i | − 0.679114i | −0.940585 | − | 0.339557i | \(-0.889723\pi\) | ||||
0.940585 | − | 0.339557i | \(-0.110277\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.03826e6 | −1.08328 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 290862.i | − 0.301009i | −0.988609 | − | 0.150505i | \(-0.951910\pi\) | ||||
0.988609 | − | 0.150505i | \(-0.0480899\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 543915. | 0.560607 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 1.60222e6i | − 1.63806i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 881243. | 0.897322 | 0.448661 | − | 0.893702i | \(-0.351901\pi\) | ||||
0.448661 | + | 0.893702i | \(0.351901\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 410985.i | − 0.415126i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −690166. | −0.694326 | −0.347163 | − | 0.937805i | \(-0.612855\pi\) | ||||
−0.347163 | + | 0.937805i | \(0.612855\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 108.5.c.c.53.1 | ✓ | 2 | |
3.2 | odd | 2 | inner | 108.5.c.c.53.2 | yes | 2 | |
4.3 | odd | 2 | 432.5.e.d.161.1 | 2 | |||
9.2 | odd | 6 | 324.5.g.d.53.1 | 4 | |||
9.4 | even | 3 | 324.5.g.d.269.1 | 4 | |||
9.5 | odd | 6 | 324.5.g.d.269.2 | 4 | |||
9.7 | even | 3 | 324.5.g.d.53.2 | 4 | |||
12.11 | even | 2 | 432.5.e.d.161.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.5.c.c.53.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
108.5.c.c.53.2 | yes | 2 | 3.2 | odd | 2 | inner | |
324.5.g.d.53.1 | 4 | 9.2 | odd | 6 | |||
324.5.g.d.53.2 | 4 | 9.7 | even | 3 | |||
324.5.g.d.269.1 | 4 | 9.4 | even | 3 | |||
324.5.g.d.269.2 | 4 | 9.5 | odd | 6 | |||
432.5.e.d.161.1 | 2 | 4.3 | odd | 2 | |||
432.5.e.d.161.2 | 2 | 12.11 | even | 2 |