Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,5,Mod(257,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("384.257");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.e (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: | \(39.6940658242\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} - 32 x^{14} + 356 x^{13} + 1348 x^{12} - 8992 x^{11} + 22064 x^{10} + \cdots + 21479188203 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{54}\cdot 3^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 257.1 | ||
Root | \(-5.66644 - 2.02063i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.257 |
Dual form | 384.5.e.b.257.2 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | −8.99926 | − | 0.115244i | −0.999918 | − | 0.0128049i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 25.0292i | 1.00117i | 0.865688 | + | 0.500584i | \(0.166881\pi\) | ||||
−0.865688 | + | 0.500584i | \(0.833119\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −59.0069 | −1.20422 | −0.602111 | − | 0.798412i | \(-0.705674\pi\) | ||||
−0.602111 | + | 0.798412i | \(0.705674\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 80.9734 | + | 2.07423i | 0.999672 | + | 0.0256077i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 219.418i | − | 1.81337i | −0.421805 | − | 0.906687i | \(-0.638603\pi\) | ||
0.421805 | − | 0.906687i | \(-0.361397\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.112775 | 0.000667306 | 0.000333653 | − | 1.00000i | \(-0.499894\pi\) | ||||
0.000333653 | 1.00000i | \(0.499894\pi\) | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.88447 | − | 225.244i | 0.0128199 | − | 1.00109i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 160.826i | 0.556491i | 0.960510 | + | 0.278245i | \(0.0897528\pi\) | ||||
−0.960510 | + | 0.278245i | \(0.910247\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 592.455 | 1.64115 | 0.820575 | − | 0.571539i | \(-0.193653\pi\) | ||||
0.820575 | + | 0.571539i | \(0.193653\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 531.019 | + | 6.80020i | 1.20412 | + | 0.0154200i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 11.6137i | − | 0.0219540i | −0.999940 | − | 0.0109770i | \(-0.996506\pi\) | ||
0.999940 | − | 0.0109770i | \(-0.00349416\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.46145 | −0.00233833 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −728.462 | − | 27.9982i | −0.999262 | − | 0.0384063i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 1261.19i | − | 1.49963i | −0.661648 | − | 0.749815i | \(-0.730143\pi\) | ||
0.661648 | − | 0.749815i | \(-0.269857\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −217.007 | −0.225813 | −0.112907 | − | 0.993606i | \(-0.536016\pi\) | ||||
−0.112907 | + | 0.993606i | \(0.536016\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −25.2867 | + | 1974.60i | −0.0232201 | + | 1.81322i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 1476.90i | − | 1.20563i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1940.21 | −1.41725 | −0.708624 | − | 0.705586i | \(-0.750684\pi\) | ||||
−0.708624 | + | 0.705586i | \(0.750684\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.01489 | − | 0.0129966i | −0.000667252 | − | 8.54480e-6i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1163.10i | 0.691912i | 0.938251 | + | 0.345956i | \(0.112445\pi\) | ||||
−0.938251 | + | 0.345956i | \(0.887555\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1084.69 | −0.586634 | −0.293317 | − | 0.956015i | \(-0.594759\pi\) | ||||
−0.293317 | + | 0.956015i | \(0.594759\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −51.9162 | + | 2026.70i | −0.0256376 | + | 1.00084i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3114.40i | 1.40987i | 0.709272 | + | 0.704935i | \(0.249024\pi\) | ||||
−0.709272 | + | 0.704935i | \(0.750976\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1080.81 | 0.450152 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 18.5342 | − | 1447.31i | 0.00712581 | − | 0.556445i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4799.21i | 1.70851i | 0.519852 | + | 0.854256i | \(0.325987\pi\) | ||||
−0.519852 | + | 0.854256i | \(0.674013\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5491.86 | 1.81549 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5331.66 | − | 68.2770i | −1.64102 | − | 0.0210148i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 4250.36i | − | 1.22102i | −0.792009 | − | 0.610509i | \(-0.790965\pi\) | ||
0.792009 | − | 0.610509i | \(-0.209035\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3336.81 | 0.896752 | 0.448376 | − | 0.893845i | \(-0.352003\pi\) | ||||
0.448376 | + | 0.893845i | \(0.352003\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4777.99 | − | 122.394i | −1.20383 | − | 0.0308374i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.82266i | 0.000668086i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2642.37 | 0.588632 | 0.294316 | − | 0.955708i | \(-0.404908\pi\) | ||||
0.294316 | + | 0.955708i | \(0.404908\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.33841 | + | 104.514i | −0.000281119 | + | 0.0219522i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6539.46i | 1.29725i | 0.761106 | + | 0.648627i | \(0.224657\pi\) | ||||
−0.761106 | + | 0.648627i | \(0.775343\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4384.38 | 0.822740 | 0.411370 | − | 0.911468i | \(-0.365050\pi\) | ||||
0.411370 | + | 0.911468i | \(0.365050\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 13.1520 | + | 0.168424i | 0.00233813 | + | 2.99421e-5i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12947.2i | 2.18370i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4151.19 | −0.665148 | −0.332574 | − | 0.943077i | \(-0.607917\pi\) | ||||
−0.332574 | + | 0.943077i | \(0.607917\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6552.40 | + | 335.914i | 0.998688 | + | 0.0511986i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6495.95i | 0.942945i | 0.881881 | + | 0.471473i | \(0.156277\pi\) | ||||
−0.881881 | + | 0.471473i | \(0.843723\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4025.34 | −0.557141 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −145.345 | + | 11349.8i | −0.0192026 | + | 1.49951i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8685.42i | 1.09651i | 0.836313 | + | 0.548253i | \(0.184707\pi\) | ||||
−0.836313 | + | 0.548253i | \(0.815293\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.65449 | −0.000803585 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1952.90 | + | 25.0088i | 0.225795 | + | 0.00289152i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 14828.7i | 1.64307i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 274.827 | 0.0292090 | 0.0146045 | − | 0.999893i | \(-0.495351\pi\) | ||||
0.0146045 | + | 0.999893i | \(0.495351\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 455.123 | − | 17767.0i | 0.0464363 | − | 1.81278i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5692.09i | 0.557993i | 0.960292 | + | 0.278997i | \(0.0900018\pi\) | ||||
−0.960292 | + | 0.278997i | \(0.909998\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8524.52 | −0.803518 | −0.401759 | − | 0.915746i | \(-0.631601\pi\) | ||||
−0.401759 | + | 0.915746i | \(0.631601\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −170.204 | + | 13291.0i | −0.0154380 | + | 1.20553i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 3118.98i | − | 0.272423i | −0.990680 | − | 0.136212i | \(-0.956507\pi\) | ||
0.990680 | − | 0.136212i | \(-0.0434927\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11890.3 | 1.00078 | 0.500390 | − | 0.865800i | \(-0.333190\pi\) | ||||
0.500390 | + | 0.865800i | \(0.333190\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 17460.5 | + | 223.598i | 1.41713 | + | 0.0181477i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10893.3i | 0.853105i | 0.904463 | + | 0.426553i | \(0.140272\pi\) | ||||
−0.904463 | + | 0.426553i | \(0.859728\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 290.681 | 0.0219796 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.13176 | + | 0.233920i | 0.000667087 | + | 1.70882e-5i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 9489.83i | − | 0.670139i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −33503.3 | −2.28832 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 134.041 | − | 10467.1i | 0.00885988 | − | 0.691856i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 15606.7i | 0.998827i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7804.26 | 0.483865 | 0.241932 | − | 0.970293i | \(-0.422219\pi\) | ||||
0.241932 | + | 0.970293i | \(0.422219\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9761.37 | + | 125.004i | 0.586586 | + | 0.00751179i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 12622.7i | − | 0.735544i | −0.929916 | − | 0.367772i | \(-0.880121\pi\) | ||
0.929916 | − | 0.367772i | \(-0.119879\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −34958.9 | −1.97631 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 700.773 | − | 18232.8i | 0.0384512 | − | 1.00043i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 16861.5i | − | 0.898367i | −0.893439 | − | 0.449184i | \(-0.851715\pi\) | ||
0.893439 | − | 0.449184i | \(-0.148285\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9216.37 | −0.477013 | −0.238507 | − | 0.971141i | \(-0.576658\pi\) | ||||
−0.238507 | + | 0.971141i | \(0.576658\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 358.917 | − | 28027.3i | 0.0180532 | − | 1.40975i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 24.7448i | − | 0.00121008i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 31566.6 | 1.50138 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −9726.53 | − | 124.558i | −0.450115 | − | 0.00576415i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 3916.55i | − | 0.176413i | −0.996102 | − | 0.0882066i | \(-0.971886\pi\) | ||
0.996102 | − | 0.0882066i | \(-0.0281136\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15731.8 | −0.689960 | −0.344980 | − | 0.938610i | \(-0.612114\pi\) | ||||
−0.344980 | + | 0.938610i | \(0.612114\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −333.589 | + | 13022.6i | −0.0142505 | + | 0.556308i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 5431.51i | − | 0.226077i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 41175.4 | 1.67047 | 0.835234 | − | 0.549895i | \(-0.185332\pi\) | ||||
0.835234 | + | 0.549895i | \(0.185332\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 553.081 | − | 43189.4i | 0.0218774 | − | 1.70837i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 685.286i | 0.0264375i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −30022.1 | −1.12997 | −0.564984 | − | 0.825102i | \(-0.691118\pi\) | ||||
−0.564984 | + | 0.825102i | \(0.691118\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −49422.7 | − | 632.905i | −1.81534 | − | 0.0232472i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 32800.4i | 1.17610i | 0.808823 | + | 0.588052i | \(0.200105\pi\) | ||||
−0.808823 | + | 0.588052i | \(0.799895\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −28561.0 | −1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 47973.1 | + | 1228.89i | 1.64061 | + | 0.0420261i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 33725.5i | − | 1.12685i | −0.826168 | − | 0.563424i | \(-0.809484\pi\) | ||
0.826168 | − | 0.563424i | \(-0.190516\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 86.2359 | 0.00281587 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −489.830 | + | 38250.1i | −0.0156350 | + | 1.22092i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 54831.5i | 1.71129i | 0.517563 | + | 0.855645i | \(0.326839\pi\) | ||||
−0.517563 | + | 0.855645i | \(0.673161\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 45688.3 | 1.39459 | 0.697297 | − | 0.716782i | \(-0.254386\pi\) | ||||
0.697297 | + | 0.716782i | \(0.254386\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −30028.9 | − | 384.548i | −0.896678 | − | 0.0114828i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 48562.0i | − | 1.41890i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 35288.1 | 1.00913 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 42984.3 | + | 1652.09i | 1.20333 | + | 0.0462498i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 23834.3i | 0.653336i | 0.945139 | + | 0.326668i | \(0.105926\pi\) | ||||
−0.945139 | + | 0.326668i | \(0.894074\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 47703.4 | 1.28066 | 0.640331 | − | 0.768099i | \(-0.278797\pi\) | ||||
0.640331 | + | 0.768099i | \(0.278797\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.325295 | − | 25.4019i | 8.55478e−6 | − | 0.000668031i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23866.2i | 0.614965i | 0.951554 | + | 0.307482i | \(0.0994865\pi\) | ||||
−0.951554 | + | 0.307482i | \(0.900513\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 52663.7 | 1.32986 | 0.664929 | − | 0.746907i | \(-0.268462\pi\) | ||||
0.664929 | + | 0.746907i | \(0.268462\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −23779.4 | − | 304.517i | −0.588583 | − | 0.00753737i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 74418.8i | 1.80589i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −29111.6 | −0.692721 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 24.0893 | − | 940.398i | 0.000562192 | − | 0.0219468i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 129995.i | − | 2.97602i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 34108.9 | 0.766130 | 0.383065 | − | 0.923721i | \(-0.374869\pi\) | ||||
0.383065 | + | 0.923721i | \(0.374869\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 753.635 | − | 58850.3i | 0.0166112 | − | 1.29715i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 27148.8i | − | 0.587319i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12804.9 | 0.271930 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −39456.2 | − | 505.275i | −0.822673 | − | 0.0105351i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.1371i | 0.000371350i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −58821.7 | −1.18284 | −0.591422 | − | 0.806362i | \(-0.701433\pi\) | ||||
−0.591422 | + | 0.806362i | \(0.701433\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −118.339 | − | 3.03138i | −0.00233756 | − | 5.98792e-5i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 42343.8i | 0.821748i | 0.911692 | + | 0.410874i | \(0.134776\pi\) | ||||
−0.911692 | + | 0.410874i | \(0.865224\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −91545.0 | −1.74568 | −0.872838 | − | 0.488010i | \(-0.837723\pi\) | ||||
−0.872838 | + | 0.488010i | \(0.837723\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1492.09 | − | 116515.i | 0.0279621 | − | 2.18353i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 49016.4i | − | 0.902880i | −0.892302 | − | 0.451440i | \(-0.850911\pi\) | ||
0.892302 | − | 0.451440i | \(-0.149089\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −77951.0 | −1.41152 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 37357.7 | + | 478.401i | 0.665094 | + | 0.00851716i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 35317.4i | − | 0.618291i | −0.951015 | − | 0.309145i | \(-0.899957\pi\) | ||
0.951015 | − | 0.309145i | \(-0.100043\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5583.38 | −0.0961309 | −0.0480655 | − | 0.998844i | \(-0.515306\pi\) | ||||
−0.0480655 | + | 0.998844i | \(0.515306\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −58928.0 | − | 3778.11i | −0.997951 | − | 0.0639826i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 27051.9i | 0.450678i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 66.8140 | 0.00109515 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 748.620 | − | 58458.8i | 0.0120743 | − | 0.942868i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 116699.i | 1.85234i | 0.377105 | + | 0.926171i | \(0.376920\pi\) | ||||
−0.377105 | + | 0.926171i | \(0.623080\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2548.25 | −0.0398108 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 36225.1 | + | 463.897i | 0.557095 | + | 0.00713414i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 61721.4i | − | 0.934479i | −0.884131 | − | 0.467240i | \(-0.845249\pi\) | ||
0.884131 | − | 0.467240i | \(-0.154751\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 114486. | 1.70668 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2615.99 | − | 102123.i | 0.0384021 | − | 1.49914i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 77838.7i | 1.12534i | 0.826681 | + | 0.562671i | \(0.190226\pi\) | ||||
−0.826681 | + | 0.562671i | \(0.809774\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −120121. | −1.71051 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1000.94 | − | 78162.4i | 0.0140406 | − | 1.09642i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 79264.6i | 1.09541i | 0.836673 | + | 0.547703i | \(0.184497\pi\) | ||||
−0.836673 | + | 0.547703i | \(0.815503\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 69505.5 | 0.946413 | 0.473207 | − | 0.880952i | \(-0.343096\pi\) | ||||
0.473207 | + | 0.880952i | \(0.343096\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 59.8855 | + | 0.766891i | 0.000803519 | + | 1.02898e-5i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 320.670i | 0.00424026i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −28221.2 | −0.367804 | −0.183902 | − | 0.982945i | \(-0.558873\pi\) | ||||
−0.183902 | + | 0.982945i | \(0.558873\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −17571.8 | − | 450.121i | −0.225739 | − | 0.00578257i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 96283.0i | 1.21937i | 0.792642 | + | 0.609687i | \(0.208705\pi\) | ||||
−0.792642 | + | 0.609687i | \(0.791295\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −37534.3 | −0.468658 | −0.234329 | − | 0.972157i | \(-0.575289\pi\) | ||||
−0.234329 | + | 0.972157i | \(0.575289\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1708.92 | − | 133447.i | 0.0210393 | − | 1.64293i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 68631.2i | − | 0.833216i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 57656.1 | 0.690318 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2473.24 | − | 31.6723i | −0.0292066 | − | 0.000374018i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 55043.1i | − | 0.641161i | −0.947221 | − | 0.320581i | \(-0.896122\pi\) | ||
0.947221 | − | 0.320581i | \(-0.103878\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 106383. | 1.22245 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −6143.32 | + | 159838.i | −0.0696450 | + | 1.81204i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 1.30973i | − | 1.46500e-5i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 64003.9 | 0.706437 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 655.980 | − | 51224.6i | 0.00714505 | − | 0.557948i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 83517.8i | 0.897800i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 105346. | 1.11774 | 0.558872 | − | 0.829254i | \(-0.311234\pi\) | ||||
0.558872 | + | 0.829254i | \(0.311234\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 76714.4 | + | 982.401i | 0.803452 | + | 0.0102890i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 4905.52i | − | 0.0507183i | −0.999678 | − | 0.0253591i | \(-0.991927\pi\) | ||
0.999678 | − | 0.0253591i | \(-0.00807293\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 132759. | 1.35512 | 0.677558 | − | 0.735470i | \(-0.263038\pi\) | ||||
0.677558 | + | 0.735470i | \(0.263038\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3063.42 | − | 119589.i | 0.0308734 | − | 1.20523i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 35271.0i | − | 0.350993i | −0.984480 | − | 0.175497i | \(-0.943847\pi\) | ||
0.984480 | − | 0.175497i | \(-0.0561531\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −276728. | −2.71939 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −359.444 | + | 28068.5i | −0.00348836 | + | 0.272401i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 95282.1i | 0.913285i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.164815 | −1.56038e−6 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −107004. | − | 1370.28i | −1.00070 | − | 0.0128149i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 183771.i | − | 1.69780i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −106590. | −0.972884 | −0.486442 | − | 0.873713i | \(-0.661705\pi\) | ||||
−0.486442 | + | 0.873713i | \(0.661705\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −157106. | − | 4024.44i | −1.41678 | − | 0.0362925i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 66136.4i | 0.589319i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −66337.7 | −0.584118 | −0.292059 | − | 0.956400i | \(-0.594340\pi\) | ||||
−0.292059 | + | 0.956400i | \(0.594340\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1255.39 | − | 98031.6i | 0.0109239 | − | 0.853035i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 47615.2i | 0.409484i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 77900.1 | 0.662140 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2615.91 | − | 33.4993i | −0.0219778 | − | 0.000281447i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 9211.86i | − | 0.0765047i | −0.999268 | − | 0.0382524i | \(-0.987821\pi\) | ||
0.999268 | − | 0.0382524i | \(-0.0121791\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 39622.4 | 0.325304 | 0.162652 | − | 0.986683i | \(-0.447995\pi\) | ||||
0.162652 | + | 0.986683i | \(0.447995\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −82.1521 | − | 3.15749i | −0.000666814 | − | 2.56288e-5i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 43436.9i | 0.348586i | 0.984694 | + | 0.174293i | \(0.0557639\pi\) | ||||
−0.984694 | + | 0.174293i | \(0.944236\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −163678. | −1.29877 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1093.65 | + | 85401.5i | −0.00858106 | + | 0.670084i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 38920.2i | − | 0.301986i | −0.988535 | − | 0.150993i | \(-0.951753\pi\) | ||
0.988535 | − | 0.150993i | \(-0.0482470\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 220682. | 1.69337 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 301505. | + | 3861.06i | 2.28813 | + | 0.0293018i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 109738.i | 0.823702i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 118239. | 0.877866 | 0.438933 | − | 0.898520i | \(-0.355357\pi\) | ||||
0.438933 | + | 0.898520i | \(0.355357\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2412.54 | + | 94180.6i | −0.0177183 | + | 0.691686i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 283187.i | − | 2.05743i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 263000. | 1.89033 | 0.945167 | − | 0.326586i | \(-0.105898\pi\) | ||||
0.945167 | + | 0.326586i | \(0.105898\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1798.58 | − | 140449.i | 0.0127899 | − | 0.998746i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 142.230i | − | 0.00100071i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 63440.1 | 0.441657 | 0.220829 | − | 0.975313i | \(-0.429124\pi\) | ||||
0.220829 | + | 0.975313i | \(0.429124\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −70232.5 | − | 899.395i | −0.483825 | − | 0.00619585i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 251370.i | 1.71363i | 0.515627 | + | 0.856813i | \(0.327559\pi\) | ||||
−0.515627 | + | 0.856813i | \(0.672441\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −324058. | −2.18626 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −87830.7 | − | 2249.88i | −0.586441 | − | 0.0150223i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 215823.i | 1.42626i | 0.701032 | + | 0.713130i | \(0.252723\pi\) | ||||
−0.701032 | + | 0.713130i | \(0.747277\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1867.78 | 0.0122172 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1454.69 | + | 113595.i | −0.00941857 | + | 0.735483i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 103901.i | − | 0.665926i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −204653. | −1.29848 | −0.649242 | − | 0.760582i | \(-0.724914\pi\) | ||||
−0.649242 | + | 0.760582i | \(0.724914\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 314605. | + | 4028.82i | 1.97615 | + | 0.0253065i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 73107.8i | 0.454648i | 0.973819 | + | 0.227324i | \(0.0729976\pi\) | ||||
−0.973819 | + | 0.227324i | \(0.927002\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −24.4729 | −0.000150687 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −8407.67 | + | 164001.i | −0.0512585 | + | 0.999855i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 425718.i | 2.57000i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −104755. | −0.626221 | −0.313110 | − | 0.949717i | \(-0.601371\pi\) | ||||
−0.313110 | + | 0.949717i | \(0.601371\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1943.18 | + | 151741.i | −0.0115035 | + | 0.898293i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 250801.i | 1.47038i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −162589. | −0.944047 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 82940.5 | + | 1062.13i | 0.476974 | + | 0.00610811i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 57233.8i | 0.326005i | 0.986626 | + | 0.163003i | \(0.0521179\pi\) | ||||
−0.986626 | + | 0.163003i | \(0.947882\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26782.1 | 0.151106 | 0.0755528 | − | 0.997142i | \(-0.475928\pi\) | ||||
0.0755528 | + | 0.997142i | \(0.475928\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6459.97 | + | 252184.i | −0.0361035 | + | 1.40941i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 235.040i | − | 0.00130126i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −196895. | −1.07989 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.85170 | + | 222.685i | −1.54949e−5 | + | 0.00120998i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 202264.i | 1.08884i | 0.838812 | + | 0.544421i | \(0.183251\pi\) | ||||
−0.838812 | + | 0.544421i | \(0.816749\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −150338. | −0.801850 | −0.400925 | − | 0.916111i | \(-0.631311\pi\) | ||||
−0.400925 | + | 0.916111i | \(0.631311\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −284076. | − | 3637.86i | −1.50126 | − | 0.0192251i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 6880.57i | − | 0.0360298i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −115380. | −0.598690 | −0.299345 | − | 0.954145i | \(-0.596768\pi\) | ||||
−0.299345 | + | 0.954145i | \(0.596768\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 87517.2 | + | 2241.85i | 0.450004 | + | 0.0115274i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 76763.3i | − | 0.391152i | −0.980689 | − | 0.195576i | \(-0.937342\pi\) | ||
0.980689 | − | 0.195576i | \(-0.0626577\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −217389. | −1.09779 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −451.359 | + | 35246.0i | −0.00225895 | + | 0.176399i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 102877.i | 0.510302i | 0.966901 | + | 0.255151i | \(0.0821252\pi\) | ||||
−0.966901 | + | 0.255151i | \(0.917875\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 255206. | 1.25470 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 141574. | + | 1813.00i | 0.689903 | + | 0.00883487i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 166.557i | − | 0.000804524i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 238938. | 1.14407 | 0.572035 | − | 0.820229i | \(-0.306154\pi\) | ||||
0.572035 | + | 0.820229i | \(0.306154\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4502.84 | − | 117156.i | 0.0213728 | − | 0.556080i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 238281.i | − | 1.12121i | −0.828082 | − | 0.560607i | \(-0.810568\pi\) | ||
0.828082 | − | 0.560607i | \(-0.189432\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 133548. | 0.622980 | 0.311490 | − | 0.950249i | \(-0.399172\pi\) | ||||
0.311490 | + | 0.950249i | \(0.399172\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −625.949 | + | 48879.5i | −0.00289490 | + | 0.226059i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 258049.i | 1.18323i | 0.806221 | + | 0.591614i | \(0.201509\pi\) | ||||
−0.806221 | + | 0.591614i | \(0.798491\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −155918. | −0.708843 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −370548. | − | 4745.22i | −1.67033 | − | 0.0213902i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 238000.i | 1.06379i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −865.846 | −0.00383755 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9954.65 | + | 388609.i | −0.0437511 | + | 1.70795i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 230624.i | − | 1.00515i | −0.864532 | − | 0.502577i | \(-0.832385\pi\) | ||
0.864532 | − | 0.502577i | \(-0.167615\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −218.807 | −0.000945738 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 78.9752 | − | 6167.07i | 0.000338530 | − | 0.0264353i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6878.71i | 0.0292431i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 79003.8 | 0.333112 | 0.166556 | − | 0.986032i | \(-0.446735\pi\) | ||||
0.166556 | + | 0.986032i | \(0.446735\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 270177. | + | 3459.87i | 1.12988 | + | 0.0144691i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 225320.i | − | 0.934625i | −0.884092 | − | 0.467313i | \(-0.845222\pi\) | ||
0.884092 | − | 0.467313i | \(-0.154778\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 202832. | 0.834530 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 444695. | + | 11391.4i | 1.81490 | + | 0.0464906i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 385873.i | − | 1.56218i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 127276. | 0.511146 | 0.255573 | − | 0.966790i | \(-0.417736\pi\) | ||||
0.255573 | + | 0.966790i | \(0.417736\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3780.05 | − | 295179.i | 0.0150599 | − | 1.17601i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 308204.i | − | 1.21815i | −0.793111 | − | 0.609077i | \(-0.791540\pi\) | ||
0.793111 | − | 0.609077i | \(-0.208460\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −142469. | −0.558645 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 257028. | + | 3291.49i | 0.999918 | + | 0.0128049i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 114499.i | 0.441944i | 0.975280 | + | 0.220972i | \(0.0709229\pi\) | ||||
−0.975280 | + | 0.220972i | \(0.929077\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −258709. | −0.990762 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −431581. | − | 16587.7i | −1.63994 | − | 0.0630306i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 213362.i | − | 0.804457i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 683356. | 2.55662 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3886.66 | + | 303504.i | −0.0144292 | + | 1.12676i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 321111.i | 1.18299i | 0.806310 | + | 0.591494i | \(0.201462\pi\) | ||||
−0.806310 | + | 0.591494i | \(0.798538\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 132528. | 0.484511 | 0.242255 | − | 0.970213i | \(-0.422113\pi\) | ||||
0.242255 | + | 0.970213i | \(0.422113\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −776.059 | − | 9.93818i | −0.00281563 | − | 3.60569e-5i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 34900.3i | − | 0.125663i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 279706. | 0.999518 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8816.21 | − | 344167.i | 0.0312675 | − | 1.22062i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 131.169i | 0.000461717i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 78065.5 | 0.272742 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6319.01 | − | 493443.i | 0.0219129 | − | 1.71115i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 237150.i | − | 0.816293i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −526786. | −1.79986 | −0.899932 | − | 0.436030i | \(-0.856384\pi\) | ||||
−0.899932 | + | 0.436030i | \(0.856384\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −411161. | − | 5265.31i | −1.39448 | − | 0.0178577i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 297604.i | 1.00195i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 79324.7 | 0.265115 | 0.132557 | − | 0.991175i | \(-0.457681\pi\) | ||||
0.132557 | + | 0.991175i | \(0.457681\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 270193. | + | 6921.30i | 0.896458 | + | 0.0229638i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 747198.i | − | 2.46112i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 244949. | 0.800987 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5596.49 | + | 437022.i | −0.0181689 | + | 1.41879i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 104134.i | − | 0.335648i | −0.985817 | − | 0.167824i | \(-0.946326\pi\) | ||
0.985817 | − | 0.167824i | \(-0.0536741\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −122.325 | −0.000391464 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −317567. | − | 4066.75i | −1.00904 | − | 0.0129218i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 112937.i | − | 0.356304i | −0.984003 | − | 0.178152i | \(-0.942988\pi\) | ||
0.984003 | − | 0.178152i | \(-0.0570119\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −272651. | −0.854102 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −386637. | − | 19821.3i | −1.20264 | − | 0.0616546i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 449057.i | 1.38700i | 0.720455 | + | 0.693501i | \(0.243933\pi\) | ||||
−0.720455 | + | 0.693501i | \(0.756067\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −605841. | −1.85818 | −0.929088 | − | 0.369860i | \(-0.879406\pi\) | ||||
−0.929088 | + | 0.369860i | \(0.879406\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2746.77 | − | 214491.i | 0.00836590 | − | 0.653282i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16.9728i | 5.13356e-5i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 94919.8 | 0.285105 | 0.142553 | − | 0.989787i | \(-0.454469\pi\) | ||||
0.142553 | + | 0.989787i | \(0.454469\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −429295. | − | 5497.53i | −1.28056 | − | 0.0163988i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 383306.i | − | 1.13552i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.05303e6 | 3.09817 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.85484 | + | 228.561i | −1.71082e−5 | + | 0.000667867i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 416501.i | 1.20876i | 0.796697 | + | 0.604379i | \(0.206579\pi\) | ||||
−0.796697 | + | 0.604379i | \(0.793421\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −128567. | −0.370594 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2750.44 | − | 214778.i | 0.00787457 | − | 0.614914i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 212187.i | 0.603405i | 0.953402 | + | 0.301702i | \(0.0975549\pi\) | ||||
−0.953402 | + | 0.301702i | \(0.902445\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 237523. | 0.670922 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −473934. | − | 6069.18i | −1.32975 | − | 0.0170287i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 98563.1i | 0.274701i | 0.990522 | + | 0.137351i | \(0.0438587\pi\) | ||||
−0.990522 | + | 0.137351i | \(0.956141\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 456630. | 1.26420 | 0.632100 | − | 0.774887i | \(-0.282193\pi\) | ||||
0.632100 | + | 0.774887i | \(0.282193\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 213962. | + | 5480.86i | 0.588438 | + | 0.0150735i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 838562.i | − | 2.29100i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −588973. | −1.59852 | −0.799260 | − | 0.600986i | \(-0.794775\pi\) | ||||
−0.799260 | + | 0.600986i | \(0.794775\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8576.34 | − | 669715.i | 0.0231242 | − | 1.80574i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 351.226i | 0.000940814i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 97484.6 | 0.259427 | 0.129713 | − | 0.991552i | \(-0.458594\pi\) | ||||
0.129713 | + | 0.991552i | \(0.458594\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 261983. | + | 3354.94i | 0.692664 | + | 0.00887023i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 664979.i | − | 1.74678i | −0.487022 | − | 0.873389i | \(-0.661917\pi\) | ||
0.487022 | − | 0.873389i | \(-0.338083\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −157113. | −0.410046 | −0.205023 | − | 0.978757i | \(-0.565727\pi\) | ||||
−0.205023 | + | 0.978757i | \(0.565727\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −325.162 | + | 8460.11i | −0.000843172 | + | 0.0219378i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 512500.i | − | 1.32044i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −391536. | −1.00233 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −14981.2 | + | 1.16986e6i | −0.0381076 | + | 2.97577i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 312036.i | − | 0.788685i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 37893.3 | 0.0951707 | 0.0475853 | − | 0.998867i | \(-0.484847\pi\) | ||||
0.0475853 | + | 0.998867i | \(0.484847\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −306955. | − | 3930.85i | −0.766067 | − | 0.00981022i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 195334.i | 0.484430i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 121.889 | 0.000300389 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −13564.3 | + | 529523.i | −0.0332197 | + | 1.29683i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 20542.7i | − | 0.0499967i | −0.999687 | − | 0.0249984i | \(-0.992042\pi\) | ||
0.999687 | − | 0.0249984i | \(-0.00795806\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 318711. | 0.770858 | 0.385429 | − | 0.922737i | \(-0.374053\pi\) | ||||
0.385429 | + | 0.922737i | \(0.374053\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3128.74 | + | 244319.i | −0.00752057 | + | 0.587271i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 55597.0i | − | 0.132814i | −0.997793 | − | 0.0664068i | \(-0.978846\pi\) | ||
0.997793 | − | 0.0664068i | \(-0.0211535\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −932607. | −2.21416 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −115235. | − | 1475.69i | −0.271907 | − | 0.00348203i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 141166.i | 0.331058i | 0.986205 | + | 0.165529i | \(0.0529331\pi\) | ||||
−0.986205 | + | 0.165529i | \(0.947067\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 315935. | 0.736403 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 355019. | + | 9094.20i | 0.822470 | + | 0.0210685i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 536334.i | 1.23499i | 0.786574 | + | 0.617496i | \(0.211853\pi\) | ||||
−0.786574 | + | 0.617496i | \(0.788147\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 36981.2 | 0.0846404 | 0.0423202 | − | 0.999104i | \(-0.486525\pi\) | ||||
0.0423202 | + | 0.999104i | \(0.486525\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.09019 | − | 163.220i | 4.75510e−6 | − | 0.000371319i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 874995.i | − | 1.97862i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14647.0 | −0.0329229 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 529352. | + | 6778.86i | 1.18275 | + | 0.0151462i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 732157.i | − | 1.62615i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 114011. | 0.251720 | 0.125860 | − | 0.992048i | \(-0.459831\pi\) | ||||
0.125860 | + | 0.992048i | \(0.459831\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1064.61 | + | 40.9181i | 0.00233660 | + | 8.98065e-5i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 425402.i | − | 0.928158i | −0.885794 | − | 0.464079i | \(-0.846385\pi\) | ||
0.885794 | − | 0.464079i | \(-0.153615\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −16216.7 | −0.0351741 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4879.88 | − | 381063.i | 0.0105224 | − | 0.821680i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 333970.i | − | 0.715923i | −0.933736 | − | 0.357962i | \(-0.883472\pi\) | ||
0.933736 | − | 0.357962i | \(-0.116528\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 422029. | 0.899417 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 823837. | + | 10550.0i | 1.74553 | + | 0.0223532i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 541.230i | 0.00114010i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 180196. | 0.377388 | 0.188694 | − | 0.982036i | \(-0.439575\pi\) | ||||
0.188694 | + | 0.982036i | \(0.439575\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −26855.4 | + | 1.04838e6i | −0.0559197 | + | 2.18299i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 230678.i | − | 0.477570i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −187057. | −0.385043 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5648.86 | + | 441112.i | −0.0115613 | + | 0.902806i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 406441.i | − | 0.827107i | −0.910480 | − | 0.413554i | \(-0.864287\pi\) | ||
0.910480 | − | 0.413554i | \(-0.135713\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.14949e6 | −2.32592 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 701502. | + | 8983.40i | 1.41140 | + | 0.0180743i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 335873.i | − | 0.671948i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −544669. | −1.08353 | −0.541764 | − | 0.840531i | \(-0.682243\pi\) | ||||
−0.541764 | + | 0.840531i | \(0.682243\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −336136. | − | 8610.50i | −0.664930 | − | 0.0170329i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2520.24i | 0.00495751i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 619.344 | 0.00121149 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4070.12 | + | 317831.i | −0.00791716 | + | 0.618240i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 345757.i | 0.668825i | 0.942427 | + | 0.334413i | \(0.108538\pi\) | ||||
−0.942427 | + | 0.334413i | \(0.891462\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 503005. | 0.967614 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 50246.3 | + | 643.452i | 0.0961231 | + | 0.00123095i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1843.17i | 0.00350662i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −732496. | −1.38591 | −0.692957 | − | 0.720978i | \(-0.743693\pi\) | ||||
−0.692957 | + | 0.720978i | \(0.743693\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 529873. | + | 40791.3i | 0.997050 | + | 0.0767560i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 174445.i | − | 0.326456i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 111923. | 0.208311 | 0.104155 | − | 0.994561i | \(-0.466786\pi\) | ||||
0.104155 | + | 0.994561i | \(0.466786\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3117.58 | − | 243447.i | 0.00577089 | − | 0.450641i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 579783.i | − | 1.06741i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 450315. | 0.824570 | 0.412285 | − | 0.911055i | \(-0.364731\pi\) | ||||
0.412285 | + | 0.911055i | \(0.364731\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −601.277 | − | 7.69992i | −0.00109506 | − | 1.40233e-5i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 448643.i | 0.812687i | 0.913720 | + | 0.406344i | \(0.133196\pi\) | ||||
−0.913720 | + | 0.406344i | \(0.866804\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 98028.1 | 0.176619 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −13474.1 | + | 525999.i | −0.0241467 | + | 0.942636i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 184041.i | 0.328058i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 752993. | 1.33509 | 0.667546 | − | 0.744569i | \(-0.267345\pi\) | ||||
0.667546 | + | 0.744569i | \(0.267345\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 13448.9 | − | 1.05021e6i | 0.0237191 | − | 1.85219i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 393754.i | − | 0.690766i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −524087. | −0.914560 | −0.457280 | − | 0.889323i | \(-0.651176\pi\) | ||||
−0.457280 | + | 0.889323i | \(0.651176\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 22932.3 | + | 293.671i | 0.0398075 | + | 0.000509773i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 408763.i | 0.705833i | 0.935655 | + | 0.352916i | \(0.114810\pi\) | ||||
−0.935655 | + | 0.352916i | \(0.885190\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −701608. | −1.20516 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −325946. | − | 8349.47i | −0.556958 | − | 0.0142671i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 479.334i | − | 0.000814793i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 181813. | 0.307449 | 0.153725 | − | 0.988114i | \(-0.450873\pi\) | ||||
0.153725 | + | 0.988114i | \(0.450873\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7113.03 | + | 555447.i | −0.0119659 | + | 0.934403i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 332218.i | − | 0.555986i | −0.960583 | − | 0.277993i | \(-0.910331\pi\) | ||
0.960583 | − | 0.277993i | \(-0.0896693\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 317.145 | 0.000528025 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.03029e6 | − | 13193.8i | −1.70654 | − | 0.0218539i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 689088.i | 1.13553i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.43488e6 | 2.35241 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −35311.0 | + | 918728.i | −0.0575953 | + | 1.49852i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.03059e6i | 1.67242i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −421772. | −0.680970 | −0.340485 | − | 0.940250i | \(-0.610591\pi\) | ||||
−0.340485 | + | 0.940250i | \(0.610591\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8970.46 | − | 700491.i | 0.0144099 | − | 1.12525i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 642780.i | − | 1.02733i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 376.308 | 0.000598408 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.08100e6 | + | 13843.2i | 1.71037 | + | 0.0219029i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 49979.5i | − | 0.0786820i | −0.999226 | − | 0.0393410i | \(-0.987474\pi\) | ||
0.999226 | − | 0.0393410i | \(-0.0125259\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −500876. | −0.784579 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −18015.5 | + | 703288.i | −0.0280790 | + | 1.09615i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 962013.i | − | 1.49194i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −17152.2 | −0.0264684 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9134.79 | − | 713323.i | 0.0140266 | − | 1.09532i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 891165.i | 1.36164i | 0.732453 | + | 0.680818i | \(0.238376\pi\) | ||||
−0.732453 | + | 0.680818i | \(0.761624\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 267631. | 0.406906 | 0.203453 | − | 0.979085i | \(-0.434784\pi\) | ||||
0.203453 | + | 0.979085i | \(0.434784\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −625498. | − | 8010.11i | −0.946335 | − | 0.0121187i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 751430.i | − | 1.13129i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −642628. | −0.962754 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −538.837 | − | 13.8029i | −0.000803322 | − | 2.05780e-5i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 657856.i | − | 0.975988i | −0.872847 | − | 0.487994i | \(-0.837729\pi\) | ||
0.872847 | − | 0.487994i | \(-0.162271\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 214191. | 0.316229 | 0.158115 | − | 0.987421i | \(-0.449458\pi\) | ||||
0.158115 | + | 0.987421i | \(0.449458\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 36.9553 | − | 2885.79i | 5.42961e−5 | − | 0.00423991i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 409128.i | − | 0.598202i | −0.954221 | − | 0.299101i | \(-0.903313\pi\) | ||
0.954221 | − | 0.299101i | \(-0.0966867\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 435720. | 0.634013 | 0.317007 | − | 0.948423i | \(-0.397322\pi\) | ||||
0.317007 | + | 0.948423i | \(0.397322\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 253970. | + | 3252.33i | 0.367774 | + | 0.00470970i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 173823.i | 0.250505i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −820967. | −1.17748 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 158081. | + | 6075.80i | 0.225647 | + | 0.00867266i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 317366.i | 0.450855i | 0.974260 | + | 0.225427i | \(0.0723779\pi\) | ||||
−0.974260 | + | 0.225427i | \(0.927622\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −883316. | −1.24889 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 11096.1 | − | 866476.i | 0.0156140 | − | 1.21927i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 714859.i | − | 1.00117i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.97693e6 | 2.75565 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 337781. | + | 4325.61i | 0.468619 | + | 0.00600112i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 22533.0i | 0.0311142i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −531190. | −0.730049 | −0.365025 | − | 0.930998i | \(-0.618939\pi\) | ||||
−0.365025 | + | 0.930998i | \(0.618939\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −30758.0 | + | 1.20073e6i | −0.0420752 | + | 1.64253i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 919137.i | 1.25147i | 0.780038 | + | 0.625733i | \(0.215200\pi\) | ||||
−0.780038 | + | 0.625733i | \(0.784800\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 397727. | 0.539013 | 0.269506 | − | 0.962999i | \(-0.413139\pi\) | ||||
0.269506 | + | 0.962999i | \(0.413139\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7909.35 | + | 617630.i | −0.0106693 | + | 0.833148i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 592105.i | 0.795019i | 0.917598 | + | 0.397509i | \(0.130125\pi\) | ||||
−0.917598 | + | 0.397509i | \(0.869875\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 844122. | 1.12817 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −518862. | − | 6644.52i | −0.690261 | − | 0.00883946i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 910847.i | 1.20616i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 297.992 | 0.000392797 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 22253.7 | + | 570.054i | 0.0291994 | + | 0.000747976i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 920902.i | − | 1.20281i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −47500.1 | −0.0617583 | −0.0308792 | − | 0.999523i | \(-0.509831\pi\) | ||||
−0.0308792 | + | 0.999523i | \(0.509831\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6343.39 | + | 495347.i | −0.00821001 | + | 0.641109i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 404360.i | − | 0.520975i | −0.965477 | − | 0.260488i | \(-0.916117\pi\) | ||
0.965477 | − | 0.260488i | \(-0.0838833\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.36248e6 | −1.74747 | −0.873733 | − | 0.486406i | \(-0.838308\pi\) | ||||
−0.873733 | + | 0.486406i | \(0.838308\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −957371. | − | 12260.1i | −1.22234 | − | 0.0156533i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 112.901i | − | 0.000143500i | −1.00000 | 7.17499e-5i | \(-0.999977\pi\) | |||
1.00000 | 7.17499e-5i | \(-2.28387e-5\pi\) | ||||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −460505. | −0.582681 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 73705.7 | − | 1.43771e6i | 0.0928422 | − | 1.81099i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.84514e6i | 2.31381i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.37239e6 | −1.71329 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.150938 | + | 11.7866i | −1.87592e−7 | + | 1.46488e-5i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 273686.i | 0.338636i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −771837. | −0.950772 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −575988. | − | 7376.08i | −0.706379 | − | 0.00904587i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.14354e6i | 1.39622i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.14759e6 | 1.39499 | 0.697496 | − | 0.716589i | \(-0.254298\pi\) | ||||
0.697496 | + | 0.716589i | \(0.254298\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −11806.7 | + | 460908.i | −0.0142889 | + | 0.557810i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1.43436e6i | − | 1.72831i | −0.503223 | − | 0.864156i | \(-0.667853\pi\) | ||
0.503223 | − | 0.864156i | \(-0.332147\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.42533e6 | 1.70991 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9624.94 | − | 751599.i | 0.0114962 | − | 0.897726i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 744824.i | 0.885758i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 245973. | 0.291243 | 0.145622 | − | 0.989340i | \(-0.453482\pi\) | ||||
0.145622 | + | 0.989340i | \(0.453482\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −948039. | − | 12140.5i | −1.11765 | − | 0.0143126i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 737.486i | 0.000865666i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2835.53 | 0.00331399 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −690260. | − | 17681.8i | −0.803254 | − | 0.0205763i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.15123e6i | 1.33392i | 0.745092 | + | 0.666962i | \(0.232406\pi\) | ||||
−0.745092 | + | 0.666962i | \(0.767594\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 640334. | 0.738767 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −565.333 | + | 44146.1i | −0.000649443 | + | 0.0507141i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 883233.i | 1.01030i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 959065. | 1.09237 | 0.546184 | − | 0.837665i | \(-0.316080\pi\) | ||||
0.546184 | + | 0.837665i | \(0.316080\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.19474e6 | − | 15299.7i | −1.35500 | − | 0.0173521i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 706010.i | − | 0.797318i | −0.917099 | − | 0.398659i | \(-0.869476\pi\) | ||
0.917099 | − | 0.398659i | \(-0.130524\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13507.9 | 0.0151902 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −41350.5 | + | 1.07586e6i | −0.0463038 | + | 1.20474i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 1.51964e6i | − | 1.69450i | −0.531195 | − | 0.847250i | \(-0.678257\pi\) | ||
0.531195 | − | 0.847250i | \(-0.321743\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 494.448 | 0.000549020 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4064.77 | + | 317413.i | −0.00449444 | + | 0.350964i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 672925.i | − | 0.740937i | −0.928845 | − | 0.370468i | \(-0.879197\pi\) | ||
0.928845 | − | 0.370468i | \(-0.120803\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −596555. | −0.654099 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.49034e6 | + | 31891.3i | 2.71917 | + | 0.0348215i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 994942.i | 1.08183i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −876429. | −0.949008 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6469.46 | − | 252554.i | 0.00697614 | − | 0.272334i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.19398e6i | 1.28216i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 280845. | 0.300341 | 0.150170 | − | 0.988660i | \(-0.452018\pi\) | ||||
0.150170 | + | 0.988660i | \(0.452018\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 10980.7 | − | 857469.i | 0.0116945 | − | 0.913210i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 430675.i | − | 0.456784i | −0.973569 | − | 0.228392i | \(-0.926653\pi\) | ||
0.973569 | − | 0.228392i | \(-0.0733468\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 543829. | 0.574430 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.48321 | + | 0.0189940i | 1.56025e−6 | + | 1.99805e-8i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1.01475e6i | − | 1.06309i | −0.847029 | − | 0.531547i | \(-0.821611\pi\) | ||
0.847029 | − | 0.531547i | \(-0.178389\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.90574e6 | 1.98837 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 962796. | + | 24663.1i | 1.00045 | + | 0.0256277i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 77690.9i | 0.0804013i | 0.999192 | + | 0.0402006i | \(0.0127997\pi\) | ||||
−0.999192 | + | 0.0402006i | \(0.987200\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −597352. | −0.615683 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −21178.6 | + | 1.65380e6i | −0.0217401 | + | 1.69766i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12597.2i | 0.0128789i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 500260. | 0.509388 | 0.254694 | − | 0.967022i | \(-0.418025\pi\) | ||||
0.254694 | + | 0.967022i | \(0.418025\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 959232. | + | 12283.9i | 0.972804 | + | 0.0124577i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.31813e6i | 1.33141i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −975422. | −0.981301 | −0.490651 | − | 0.871356i | \(-0.663241\pi\) | ||||
−0.490651 | + | 0.871356i | \(0.663241\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.41337e6 | + | 54322.5i | 1.41620 | + | 0.0544313i |
(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 | 384.5.e.b.257.1 | yes | 16 | |
3.2 | odd | 2 | inner | 384.5.e.b.257.2 | yes | 16 | |
4.3 | odd | 2 | 384.5.e.c.257.16 | yes | 16 | ||
8.3 | odd | 2 | 384.5.e.a.257.1 | ✓ | 16 | ||
8.5 | even | 2 | 384.5.e.d.257.16 | yes | 16 | ||
12.11 | even | 2 | 384.5.e.c.257.15 | yes | 16 | ||
24.5 | odd | 2 | 384.5.e.d.257.15 | yes | 16 | ||
24.11 | even | 2 | 384.5.e.a.257.2 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.5.e.a.257.1 | ✓ | 16 | 8.3 | odd | 2 | ||
384.5.e.a.257.2 | yes | 16 | 24.11 | even | 2 | ||
384.5.e.b.257.1 | yes | 16 | 1.1 | even | 1 | trivial | |
384.5.e.b.257.2 | yes | 16 | 3.2 | odd | 2 | inner | |
384.5.e.c.257.15 | yes | 16 | 12.11 | even | 2 | ||
384.5.e.c.257.16 | yes | 16 | 4.3 | odd | 2 | ||
384.5.e.d.257.15 | yes | 16 | 24.5 | odd | 2 | ||
384.5.e.d.257.16 | yes | 16 | 8.5 | even | 2 |