Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,4,Mod(865,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.865");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.d (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: | \(101.955300490\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.2261390379264.6 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 8x^{6} + 38x^{5} - 38x^{4} + 8x^{3} + 325x^{2} - 322x + 2122 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 865.4 | ||
Root | \(1.29746 + 1.88096i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.865 |
Dual form | 1728.4.d.e.865.6 |
$q$-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 \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 6.50098i | − 0.581466i | −0.956804 | − | 0.290733i | \(-0.906101\pi\) | ||||
0.956804 | − | 0.290733i | \(-0.0938991\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 16.0706 | 0.867728 | 0.433864 | − | 0.900978i | \(-0.357150\pi\) | ||||
0.433864 | + | 0.900978i | \(0.357150\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 27.9124i | 0.765082i | 0.923938 | + | 0.382541i | \(0.124951\pi\) | ||||
−0.923938 | + | 0.382541i | \(0.875049\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 35.5735i | − 0.758947i | −0.925203 | − | 0.379474i | \(-0.876105\pi\) | ||||
0.925203 | − | 0.379474i | \(-0.123895\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 18.9124 | 0.269820 | 0.134910 | − | 0.990858i | \(-0.456926\pi\) | ||||
0.134910 | + | 0.990858i | \(0.456926\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 76.7372i | 0.926564i | 0.886211 | + | 0.463282i | \(0.153328\pi\) | ||||
−0.886211 | + | 0.463282i | \(0.846672\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −190.142 | −1.72380 | −0.861898 | − | 0.507081i | \(-0.830724\pi\) | ||||
−0.861898 | + | 0.507081i | \(0.830724\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 82.7372 | 0.661898 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 138.134i | 0.884512i | 0.896889 | + | 0.442256i | \(0.145822\pi\) | ||||
−0.896889 | + | 0.442256i | \(0.854178\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −265.085 | −1.53583 | −0.767914 | − | 0.640553i | \(-0.778705\pi\) | ||||
−0.767914 | + | 0.640553i | \(0.778705\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 104.474i | − 0.504554i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 14.9791i | 0.0665556i | 0.999446 | + | 0.0332778i | \(0.0105946\pi\) | ||||
−0.999446 | + | 0.0332778i | \(0.989405\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −202.562 | −0.771582 | −0.385791 | − | 0.922586i | \(-0.626071\pi\) | ||||
−0.385791 | + | 0.922586i | \(0.626071\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 133.474i | − 0.473364i | −0.971587 | − | 0.236682i | \(-0.923940\pi\) | ||||
0.971587 | − | 0.236682i | \(-0.0760600\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 130.020 | 0.403517 | 0.201759 | − | 0.979435i | \(-0.435334\pi\) | ||||
0.201759 | + | 0.979435i | \(0.435334\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −84.7372 | −0.247047 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 131.633i | 0.341155i | 0.985344 | + | 0.170577i | \(0.0545632\pi\) | ||||
−0.985344 | + | 0.170577i | \(0.945437\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 181.458 | 0.444869 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 477.124i | 1.05282i | 0.850231 | + | 0.526409i | \(0.176462\pi\) | ||||
−0.850231 | + | 0.526409i | \(0.823538\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 582.906i | − 1.22350i | −0.791052 | − | 0.611749i | \(-0.790466\pi\) | ||||
0.791052 | − | 0.611749i | \(-0.209534\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −231.263 | −0.441302 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 20.0000i | − 0.0364685i | −0.999834 | − | 0.0182342i | \(-0.994196\pi\) | ||||
0.999834 | − | 0.0182342i | \(-0.00580446\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −60.1222 | −0.100496 | −0.0502479 | − | 0.998737i | \(-0.516001\pi\) | ||||
−0.0502479 | + | 0.998737i | \(0.516001\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −321.212 | −0.515000 | −0.257500 | − | 0.966278i | \(-0.582899\pi\) | ||||
−0.257500 | + | 0.966278i | \(0.582899\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 448.568i | 0.663884i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −210.009 | −0.299086 | −0.149543 | − | 0.988755i | \(-0.547780\pi\) | ||||
−0.149543 | + | 0.988755i | \(0.547780\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 587.737i | 0.777260i | 0.921394 | + | 0.388630i | \(0.127051\pi\) | ||||
−0.921394 | + | 0.388630i | \(0.872949\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 122.949i | − 0.156891i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −55.5767 | −0.0661924 | −0.0330962 | − | 0.999452i | \(-0.510537\pi\) | ||||
−0.0330962 | + | 0.999452i | \(0.510537\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 571.686i | − 0.658560i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 498.867 | 0.538765 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −75.9488 | −0.0794994 | −0.0397497 | − | 0.999210i | \(-0.512656\pi\) | ||||
−0.0397497 | + | 0.999210i | \(0.512656\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 1805.57i | − 1.77882i | −0.457114 | − | 0.889408i | \(-0.651117\pi\) | ||||
0.457114 | − | 0.889408i | \(-0.348883\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −896.519 | −0.857637 | −0.428819 | − | 0.903391i | \(-0.641070\pi\) | ||||
−0.428819 | + | 0.903391i | \(0.641070\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 554.226i | 0.500739i | 0.968150 | + | 0.250370i | \(0.0805521\pi\) | ||||
−0.968150 | + | 0.250370i | \(0.919448\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1256.94i | 1.10452i | 0.833672 | + | 0.552260i | \(0.186234\pi\) | ||||
−0.833672 | + | 0.552260i | \(0.813766\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1615.69 | −1.34505 | −0.672526 | − | 0.740073i | \(-0.734791\pi\) | ||||
−0.672526 | + | 0.740073i | \(0.734791\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1236.11i | 1.00233i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 303.933 | 0.234130 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 551.898 | 0.414649 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 1350.50i | − 0.966336i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1861.53 | 1.30066 | 0.650330 | − | 0.759652i | \(-0.274631\pi\) | ||||
0.650330 | + | 0.759652i | \(0.274631\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1335.53i | 0.890728i | 0.895350 | + | 0.445364i | \(0.146926\pi\) | ||||
−0.895350 | + | 0.445364i | \(0.853074\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1233.21i | 0.804006i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2153.20 | −1.34277 | −0.671387 | − | 0.741107i | \(-0.734301\pi\) | ||||
−0.671387 | + | 0.741107i | \(0.734301\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 97.4744i | 0.0594797i | 0.999558 | + | 0.0297398i | \(0.00946788\pi\) | ||||
−0.999558 | + | 0.0297398i | \(0.990532\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 992.942 | 0.580657 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 898.007 | 0.514313 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1392.82i | 0.765803i | 0.923789 | + | 0.382901i | \(0.125075\pi\) | ||||
−0.923789 | + | 0.382901i | \(0.874925\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 838.627 | 0.451963 | 0.225982 | − | 0.974132i | \(-0.427441\pi\) | ||||
0.225982 | + | 0.974132i | \(0.427441\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1723.31i | 0.893032i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 2738.54i | − 1.39210i | −0.717994 | − | 0.696049i | \(-0.754939\pi\) | ||||
0.717994 | − | 0.696049i | \(-0.245061\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3055.69 | −1.49579 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 421.788i | − 0.202681i | −0.994852 | − | 0.101341i | \(-0.967687\pi\) | ||||
0.994852 | − | 0.101341i | \(-0.0323132\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3364.09 | −1.55881 | −0.779405 | − | 0.626520i | \(-0.784479\pi\) | ||||
−0.779405 | + | 0.626520i | \(0.784479\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 931.526 | 0.423999 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1550.32i | 0.681321i | 0.940186 | + | 0.340660i | \(0.110651\pi\) | ||||
−0.940186 | + | 0.340660i | \(0.889349\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1329.63 | 0.574347 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4634.17i | 1.93505i | 0.252775 | + | 0.967525i | \(0.418657\pi\) | ||||
−0.252775 | + | 0.967525i | \(0.581343\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1688.80i | 0.693522i | 0.937953 | + | 0.346761i | \(0.112719\pi\) | ||||
−0.937953 | + | 0.346761i | \(0.887281\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 97.3792 | 0.0386998 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 527.891i | 0.206434i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3125.26 | 1.18396 | 0.591980 | − | 0.805953i | \(-0.298347\pi\) | ||||
0.591980 | + | 0.805953i | \(0.298347\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2085.96 | −0.777981 | −0.388991 | − | 0.921242i | \(-0.627176\pi\) | ||||
−0.388991 | + | 0.921242i | \(0.627176\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2356.44i | 0.852231i | 0.904669 | + | 0.426115i | \(0.140118\pi\) | ||||
−0.904669 | + | 0.426115i | \(0.859882\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −970.940 | −0.345870 | −0.172935 | − | 0.984933i | \(-0.555325\pi\) | ||||
−0.172935 | + | 0.984933i | \(0.555325\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2219.89i | 0.767516i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1316.85i | 0.448649i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2141.92 | −0.708898 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 1621.58i | − 0.529073i | −0.964376 | − | 0.264537i | \(-0.914781\pi\) | ||||
0.964376 | − | 0.264537i | \(-0.0852190\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −867.715 | −0.275245 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4260.07 | −1.33268 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 672.781i | − 0.204779i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3391.03 | −1.01830 | −0.509148 | − | 0.860679i | \(-0.670040\pi\) | ||||
−0.509148 | + | 0.860679i | \(0.670040\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3111.93i | 0.909894i | 0.890519 | + | 0.454947i | \(0.150342\pi\) | ||||
−0.890519 | + | 0.454947i | \(0.849658\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4512.85i | 1.30226i | 0.758966 | + | 0.651130i | \(0.225705\pi\) | ||||
−0.758966 | + | 0.651130i | \(0.774295\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6022.61 | −1.69337 | −0.846683 | − | 0.532097i | \(-0.821404\pi\) | ||||
−0.846683 | + | 0.532097i | \(0.821404\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 845.256i | − 0.234632i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2371.15 | −0.641745 | −0.320872 | − | 0.947122i | \(-0.603976\pi\) | ||||
−0.320872 | + | 0.947122i | \(0.603976\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4124.74 | 1.10248 | 0.551241 | − | 0.834346i | \(-0.314155\pi\) | ||||
0.551241 | + | 0.834346i | \(0.314155\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 550.875i | 0.143649i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2729.81 | 0.703214 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4354.18i | 1.09495i | 0.836821 | + | 0.547476i | \(0.184411\pi\) | ||||
−0.836821 | + | 0.547476i | \(0.815589\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 5307.32i | − 1.31885i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7727.55 | −1.87561 | −0.937805 | − | 0.347163i | \(-0.887145\pi\) | ||||
−0.937805 | + | 0.347163i | \(0.887145\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 240.723i | 0.0577522i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3944.29 | −0.924774 | −0.462387 | − | 0.886678i | \(-0.653007\pi\) | ||||
−0.462387 | + | 0.886678i | \(0.653007\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 855.744 | 0.198370 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 290.836i | 0.0659204i | 0.999457 | + | 0.0329602i | \(0.0104935\pi\) | ||||
−0.999457 | + | 0.0329602i | \(0.989507\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2842.92 | −0.637252 | −0.318626 | − | 0.947881i | \(-0.603221\pi\) | ||||
−0.318626 | + | 0.947881i | \(0.603221\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2309.39i | 0.506406i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 6030.03i | − 1.30798i | −0.756505 | − | 0.653988i | \(-0.773094\pi\) | ||||
0.756505 | − | 0.653988i | \(-0.226906\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3545.58 | −0.752711 | −0.376356 | − | 0.926475i | \(-0.622823\pi\) | ||||
−0.376356 | + | 0.926475i | \(0.622823\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1499.48i | 0.314964i | 0.987522 | + | 0.157482i | \(0.0503377\pi\) | ||||
−0.987522 | + | 0.157482i | \(0.949662\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3255.28 | −0.669524 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4555.32 | −0.927197 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1174.97i | 0.234275i | 0.993116 | + | 0.117137i | \(0.0373718\pi\) | ||||
−0.993116 | + | 0.117137i | \(0.962628\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3101.78 | 0.612177 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6764.01i | 1.30827i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 2145.01i | − 0.410752i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3789.46 | −0.711423 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 5403.90i | − 1.00462i | −0.864689 | − | 0.502308i | \(-0.832484\pi\) | ||||
0.864689 | − | 0.502308i | \(-0.167516\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9941.05 | 1.81256 | 0.906278 | − | 0.422682i | \(-0.138911\pi\) | ||||
0.906278 | + | 0.422682i | \(0.138911\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5905.11 | 1.06638 | 0.533189 | − | 0.845996i | \(-0.320993\pi\) | ||||
0.533189 | + | 0.845996i | \(0.320993\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 7828.23i | − 1.38699i | −0.720460 | − | 0.693497i | \(-0.756069\pi\) | ||||
0.720460 | − | 0.693497i | \(-0.243931\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3855.65 | −0.676724 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1451.29i | 0.250005i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 2943.25i | − 0.502346i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2089.49 | 0.350144 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11665.1i | 1.93707i | 0.248874 | + | 0.968536i | \(0.419939\pi\) | ||||
−0.248874 | + | 0.968536i | \(0.580061\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −130.020 | −0.0212052 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1705.59 | 0.275696 | 0.137848 | − | 0.990453i | \(-0.455982\pi\) | ||||
0.137848 | + | 0.990453i | \(0.455982\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 7399.16i | − 1.17504i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6873.98 | −1.08210 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7701.30i | 1.19143i | 0.803195 | + | 0.595717i | \(0.203132\pi\) | ||||
−0.803195 | + | 0.595717i | \(0.796868\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6875.08i | 1.05448i | 0.849715 | + | 0.527242i | \(0.176774\pi\) | ||||
−0.849715 | + | 0.527242i | \(0.823226\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7008.39 | −1.05671 | −0.528355 | − | 0.849023i | \(-0.677191\pi\) | ||||
−0.528355 | + | 0.849023i | \(0.677191\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 390.854i | 0.0584348i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8996.79 | 1.32265 | 0.661327 | − | 0.750098i | \(-0.269994\pi\) | ||||
0.661327 | + | 0.750098i | \(0.269994\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 970.400 | 0.141478 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2088.19i | 0.299455i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4690.25 | 0.667109 | 0.333554 | − | 0.942731i | \(-0.391752\pi\) | ||||
0.333554 | + | 0.942731i | \(0.391752\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2115.42i | 0.296029i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8072.72i | 1.12062i | 0.828285 | + | 0.560308i | \(0.189317\pi\) | ||||
−0.828285 | + | 0.560308i | \(0.810683\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4913.91 | 0.671298 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 8379.80i | − 1.13573i | −0.823122 | − | 0.567864i | \(-0.807770\pi\) | ||||
0.823122 | − | 0.567864i | \(-0.192230\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 869.756 | 0.116038 | 0.0580189 | − | 0.998315i | \(-0.481522\pi\) | ||||
0.0580189 | + | 0.998315i | \(0.481522\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2916.13 | 0.386026 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8524.17i | 1.11103i | 0.831505 | + | 0.555517i | \(0.187480\pi\) | ||||
−0.831505 | + | 0.555517i | \(0.812520\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3596.04 | −0.465114 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1365.26i | 0.173908i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 3385.75i | − 0.428025i | −0.976831 | − | 0.214012i | \(-0.931347\pi\) | ||||
0.976831 | − | 0.214012i | \(-0.0686533\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13391.3 | −1.66766 | −0.833829 | − | 0.552023i | \(-0.813856\pi\) | ||||
−0.833829 | + | 0.552023i | \(0.813856\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9430.01i | 1.16561i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −418.104 | −0.0509205 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7965.98 | −0.963062 | −0.481531 | − | 0.876429i | \(-0.659919\pi\) | ||||
−0.481531 | + | 0.876429i | \(0.659919\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7667.65i | 0.913560i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3820.87 | 0.451950 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6356.23i | 0.741103i | 0.928812 | + | 0.370552i | \(0.120831\pi\) | ||||
−0.928812 | + | 0.370552i | \(0.879169\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 6365.81i | − 0.736937i | −0.929640 | − | 0.368468i | \(-0.879882\pi\) | ||||
0.929640 | − | 0.368468i | \(-0.120118\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1564.76 | 0.178593 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 9367.62i | − 1.06166i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4612.28 | −0.515466 | −0.257733 | − | 0.966216i | \(-0.582975\pi\) | ||||
−0.257733 | + | 0.966216i | \(0.582975\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10400.1 | −1.15426 | −0.577131 | − | 0.816652i | \(-0.695828\pi\) | ||||
−0.577131 | + | 0.816652i | \(0.695828\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 14591.0i | − 1.59721i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1480.23 | −0.160928 | −0.0804642 | − | 0.996757i | \(-0.525640\pi\) | ||||
−0.0804642 | + | 0.996757i | \(0.525640\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 5799.47i | − 0.621989i | −0.950412 | − | 0.310995i | \(-0.899338\pi\) | ||||
0.950412 | − | 0.310995i | \(-0.100662\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 361.303i | 0.0384886i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6011.34 | −0.631832 | −0.315916 | − | 0.948787i | \(-0.602312\pi\) | ||||
−0.315916 | + | 0.948787i | \(0.602312\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 5653.99i | − 0.590324i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3716.52 | −0.382930 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7891.93 | 0.807810 | 0.403905 | − | 0.914801i | \(-0.367653\pi\) | ||||
0.403905 | + | 0.914801i | \(0.367653\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8338.72i | 0.842458i | 0.906954 | + | 0.421229i | \(0.138401\pi\) | ||||
−0.906954 | + | 0.421229i | \(0.861599\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16445.4 | 1.65072 | 0.825360 | − | 0.564607i | \(-0.190972\pi\) | ||||
0.825360 | + | 0.564607i | \(0.190972\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 4975.50i | − 0.493017i | −0.969141 | − | 0.246508i | \(-0.920717\pi\) | ||||
0.969141 | − | 0.246508i | \(-0.0792833\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 321.411i | − 0.0316447i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3725.59 | 0.362163 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6349.02i | 0.613291i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −617.261 | −0.0588797 | −0.0294398 | − | 0.999567i | \(-0.509372\pi\) | ||||
−0.0294398 | + | 0.999567i | \(0.509372\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 532.861 | 0.0505122 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 493.742i | 0.0462261i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4775.91 | 0.444389 | 0.222194 | − | 0.975002i | \(-0.428678\pi\) | ||||
0.222194 | + | 0.975002i | \(0.428678\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 8682.25i | − 0.798014i | −0.916948 | − | 0.399007i | \(-0.869355\pi\) | ||||
0.916948 | − | 0.399007i | \(-0.130645\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2612.45i | 0.238659i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −966.198 | −0.0872030 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 3011.15i | − 0.270136i | −0.990836 | − | 0.135068i | \(-0.956875\pi\) | ||||
0.990836 | − | 0.135068i | \(-0.0431252\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4948.29 | −0.438635 | −0.219318 | − | 0.975654i | \(-0.570383\pi\) | ||||
−0.219318 | + | 0.975654i | \(0.570383\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11737.9 | −1.03432 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 8060.89i | − 0.701950i | −0.936385 | − | 0.350975i | \(-0.885850\pi\) | ||||
0.936385 | − | 0.350975i | \(-0.114150\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5162.05 | −0.446880 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5828.25i | 0.498687i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3629.16i | 0.308724i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18392.8 | 1.54665 | 0.773325 | − | 0.634010i | \(-0.218592\pi\) | ||||
0.773325 | + | 0.634010i | \(0.218592\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 15531.7i | − 1.29857i | −0.760544 | − | 0.649286i | \(-0.775068\pi\) | ||||
0.760544 | − | 0.649286i | \(-0.224932\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5013.40 | −0.414397 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23986.9 | 1.97148 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7205.84i | 0.585590i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3603.02 | 0.291163 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 2365.22i | − 0.189012i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24594.4i | 1.95452i | 0.212035 | + | 0.977262i | \(0.431991\pi\) | ||||
−0.212035 | + | 0.977262i | \(0.568009\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8171.32 | 0.642240 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15437.8i | 1.20671i | 0.797471 | + | 0.603357i | \(0.206170\pi\) | ||||
−0.797471 | + | 0.603357i | \(0.793830\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10600.0 | −0.819557 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3374.96 | −0.259526 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7720.89i | 0.587333i | 0.955908 | + | 0.293667i | \(0.0948756\pi\) | ||||
−0.955908 | + | 0.293667i | \(0.905124\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4748.15 | −0.359258 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 4965.48i | − 0.371705i | −0.982578 | − | 0.185852i | \(-0.940495\pi\) | ||||
0.982578 | − | 0.185852i | \(-0.0595046\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10503.5i | 0.782102i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14638.2 | 1.07850 | 0.539250 | − | 0.842146i | \(-0.318708\pi\) | ||||
0.539250 | + | 0.842146i | \(0.318708\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10966.5i | 0.803735i | 0.915698 | + | 0.401867i | \(0.131639\pi\) | ||||
−0.915698 | + | 0.401867i | \(0.868361\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −15731.8 | −1.14098 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21576.8 | −1.55676 | −0.778382 | − | 0.627791i | \(-0.783959\pi\) | ||||
−0.778382 | + | 0.627791i | \(0.783959\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9445.26i | 0.674450i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3674.19 | −0.261011 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 7747.02i | − 0.544725i | −0.962195 | − | 0.272362i | \(-0.912195\pi\) | ||||
0.962195 | − | 0.272362i | \(-0.0878050\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 20341.9i | − 1.42304i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9423.20 | −0.652554 | −0.326277 | − | 0.945274i | \(-0.605794\pi\) | ||||
−0.326277 | + | 0.945274i | \(0.605794\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 1975.86i | − 0.136139i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16746.0 | 1.14227 | 0.571137 | − | 0.820855i | \(-0.306503\pi\) | ||||
0.571137 | + | 0.820855i | \(0.306503\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24440.4 | 1.65881 | 0.829405 | − | 0.558648i | \(-0.188680\pi\) | ||||
0.829405 | + | 0.558648i | \(0.188680\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 3587.88i | − 0.241104i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24645.3 | −1.64798 | −0.823988 | − | 0.566607i | \(-0.808256\pi\) | ||||
−0.823988 | + | 0.566607i | \(0.808256\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 4625.26i | − 0.306248i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 13945.4i | − 0.918842i | −0.888219 | − | 0.459421i | \(-0.848057\pi\) | ||||
0.888219 | − | 0.459421i | \(-0.151943\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20120.0 | 1.31281 | 0.656403 | − | 0.754410i | \(-0.272077\pi\) | ||||
0.656403 | + | 0.754410i | \(0.272077\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15834.6i | 1.02819i | 0.857734 | + | 0.514093i | \(0.171871\pi\) | ||||
−0.857734 | + | 0.514093i | \(0.828129\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −893.149 | −0.0574370 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1562.60 | 0.100006 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 283.292i | 0.0179580i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25542.9 | 1.61149 | 0.805744 | − | 0.592264i | \(-0.201766\pi\) | ||||
0.805744 | + | 0.592264i | \(0.201766\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 12101.8i | − 0.756289i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3014.40i | 0.187496i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4368.61 | −0.269188 | −0.134594 | − | 0.990901i | \(-0.542973\pi\) | ||||
−0.134594 | + | 0.990901i | \(0.542973\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 6253.46i | − 0.383534i | −0.981440 | − | 0.191767i | \(-0.938578\pi\) | ||||
0.981440 | − | 0.191767i | \(-0.0614218\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 27111.2 | 1.64737 | 0.823687 | − | 0.567045i | \(-0.191913\pi\) | ||||
0.823687 | + | 0.567045i | \(0.191913\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13317.7 | −0.805492 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11206.8i | 0.671601i | 0.941933 | + | 0.335801i | \(0.109007\pi\) | ||||
−0.941933 | + | 0.335801i | \(0.890993\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8682.23 | 0.517928 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 28324.2i | − 1.67429i | −0.546983 | − | 0.837143i | \(-0.684224\pi\) | ||||
0.546983 | − | 0.837143i | \(-0.315776\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 27069.6i | − 1.59287i | −0.604727 | − | 0.796433i | \(-0.706718\pi\) | ||||
0.604727 | − | 0.796433i | \(-0.293282\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8017.08 | 0.467502 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 26265.1i | − 1.52472i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 16270.3 | 0.936077 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18620.6 | 1.06652 | 0.533262 | − | 0.845950i | \(-0.320966\pi\) | ||||
0.533262 | + | 0.845950i | \(0.320966\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 25175.3i | − 1.42919i | −0.699536 | − | 0.714597i | \(-0.746610\pi\) | ||||
0.699536 | − | 0.714597i | \(-0.253390\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1220.54 | −0.0689839 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 13438.8i | − 0.752886i | −0.926440 | − | 0.376443i | \(-0.877147\pi\) | ||||
0.926440 | − | 0.376443i | \(-0.122853\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13997.9i | 0.780777i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4682.65 | 0.258918 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28254.8i | 1.55552i | 0.628563 | + | 0.777758i | \(0.283643\pi\) | ||||
−0.628563 | + | 0.777758i | \(0.716357\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 633.680 | 0.0345854 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3830.93 | −0.208188 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 32350.0i | − 1.74300i | −0.490397 | − | 0.871499i | \(-0.663148\pi\) | ||||
0.490397 | − | 0.871499i | \(-0.336852\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1149.46 | −0.0616680 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 29016.4i | − 1.54353i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 20041.0i | − 1.06157i | −0.847505 | − | 0.530787i | \(-0.821897\pi\) | ||||
0.847505 | − | 0.530787i | \(-0.178103\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 50403.8 | 2.64746 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 6455.10i | − 0.337632i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11518.4 | 0.597447 | 0.298723 | − | 0.954340i | \(-0.403439\pi\) | ||||
0.298723 | + | 0.954340i | \(0.403439\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14407.6 | −0.744196 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 11428.8i | 0.585456i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16989.3 | −0.866710 | −0.433355 | − | 0.901223i | \(-0.642670\pi\) | ||||
−0.433355 | + | 0.901223i | \(0.642670\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 2524.32i | − 0.127723i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11934.0i | 0.601355i | 0.953726 | + | 0.300677i | \(0.0972127\pi\) | ||||
−0.953726 | + | 0.300677i | \(0.902787\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 558.248 | 0.0279014 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 19610.5i | − 0.976160i | −0.872799 | − | 0.488080i | \(-0.837697\pi\) | ||||
0.872799 | − | 0.488080i | \(-0.162303\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25308.6 | −1.24964 | −0.624820 | − | 0.780769i | \(-0.714828\pi\) | ||||
−0.624820 | + | 0.780769i | \(0.714828\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9054.73 | 0.445288 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8906.73i | 0.434506i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11835.9 | −0.575097 | −0.287548 | − | 0.957766i | \(-0.592840\pi\) | ||||
−0.287548 | + | 0.957766i | \(0.592840\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 5451.90i | − 0.262801i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13648.5i | 0.655299i | 0.944799 | + | 0.327650i | \(0.106257\pi\) | ||||
−0.944799 | + | 0.327650i | \(0.893743\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 33364.9 | 1.58932 | 0.794662 | − | 0.607052i | \(-0.207648\pi\) | ||||
0.794662 | + | 0.607052i | \(0.207648\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 20199.7i | 0.958423i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 16973.0 | 0.799033 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17035.1 | −0.798830 | −0.399415 | − | 0.916770i | \(-0.630787\pi\) | ||||
−0.399415 | + | 0.916770i | \(0.630787\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18934.3i | 0.881010i | 0.897750 | + | 0.440505i | \(0.145201\pi\) | ||||
−0.897750 | + | 0.440505i | \(0.854799\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −21932.4 | −1.01656 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 15544.0i | − 0.714921i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 1678.16i | − 0.0768875i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −17803.2 | −0.809458 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 31964.7i | − 1.44780i | −0.689904 | − | 0.723901i | \(-0.742347\pi\) | ||||
0.689904 | − | 0.723901i | \(-0.257653\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −25965.0 | −1.16714 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20736.0 | −0.928571 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 27500.2i | − 1.22222i | −0.791546 | − | 0.611110i | \(-0.790723\pi\) | ||||
0.791546 | − | 0.611110i | \(-0.209277\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2458.98 | 0.108877 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 8965.79i | − 0.394017i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 19865.0i | 0.869749i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 41290.0 | 1.79441 | 0.897206 | − | 0.441613i | \(-0.145593\pi\) | ||||
0.897206 | + | 0.441613i | \(0.145593\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 25905.2i | − 1.12164i | −0.827936 | − | 0.560822i | \(-0.810485\pi\) | ||||
0.827936 | − | 0.560822i | \(-0.189515\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2742.04 | −0.117852 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10242.5 | 0.438602 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 9011.17i | − 0.383060i | −0.981487 | − | 0.191530i | \(-0.938655\pi\) | ||||
0.981487 | − | 0.191530i | \(-0.0613449\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7843.81 | −0.332221 | −0.166111 | − | 0.986107i | \(-0.553121\pi\) | ||||
−0.166111 | + | 0.986107i | \(0.553121\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 3843.55i | − 0.161612i | −0.996730 | − | 0.0808061i | \(-0.974251\pi\) | ||||
0.996730 | − | 0.0808061i | \(-0.0257495\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 36286.9i | − 1.52026i | −0.649770 | − | 0.760131i | \(-0.725135\pi\) | ||||
0.649770 | − | 0.760131i | \(-0.274865\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1602.58 | −0.0666582 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21869.9i | 0.906395i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 434.523 | 0.0178801 | 0.00894004 | − | 0.999960i | \(-0.497154\pi\) | ||||
0.00894004 | + | 0.999960i | \(0.497154\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5307.99 | 0.217639 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 6055.83i | − 0.246541i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8869.30 | 0.359803 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 2848.16i | − 0.114728i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 20871.7i | − 0.837787i | −0.908035 | − | 0.418893i | \(-0.862418\pi\) | ||||
0.908035 | − | 0.418893i | \(-0.137582\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 34692.7 | 1.38282 | 0.691412 | − | 0.722460i | \(-0.256989\pi\) | ||||
0.691412 | + | 0.722460i | \(0.256989\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22844.9i | 0.907403i | 0.891154 | + | 0.453702i | \(0.149897\pi\) | ||||
−0.891154 | + | 0.453702i | \(0.850103\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3998.34 | 0.157712 | 0.0788558 | − | 0.996886i | \(-0.474873\pi\) | ||||
0.0788558 | + | 0.996886i | \(0.474873\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10078.6 | 0.396165 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 5861.85i | − 0.228826i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −711.470 | −0.0276777 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 21703.2i | − 0.838518i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16596.6i | 0.639028i | 0.947581 | + | 0.319514i | \(0.103520\pi\) | ||||
−0.947581 | + | 0.319514i | \(0.896480\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 342.063 | 0.0130811 | 0.00654053 | − | 0.999979i | \(-0.497918\pi\) | ||||
0.00654053 | + | 0.999979i | \(0.497918\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 14529.0i | − 0.553725i | −0.960910 | − | 0.276862i | \(-0.910705\pi\) | ||||
0.960910 | − | 0.276862i | \(-0.0892946\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −33035.3 | −1.25053 | −0.625263 | − | 0.780414i | \(-0.715008\pi\) | ||||
−0.625263 | + | 0.780414i | \(0.715008\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 29915.8 | 1.12862 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9977.35i | 0.373885i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 30126.6 | 1.12517 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 36617.3i | − 1.35846i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2489.50i | 0.0920501i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10978.9 | 0.403259 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 52453.7i | 1.92028i | 0.279515 | + | 0.960141i | \(0.409826\pi\) | ||||
−0.279515 | + | 0.960141i | \(0.590174\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 48342.7 | 1.75814 | 0.879070 | − | 0.476692i | \(-0.158164\pi\) | ||||
0.879070 | + | 0.476692i | \(0.158164\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16405.2 | −0.594668 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 21462.6i | 0.772910i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21911.9 | 0.786514 | 0.393257 | − | 0.919429i | \(-0.371348\pi\) | ||||
0.393257 | + | 0.919429i | \(0.371348\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2138.76i | 0.0762710i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1239.33i | 0.0440530i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −25184.7 | −0.889433 | −0.444717 | − | 0.895671i | \(-0.646696\pi\) | ||||
−0.444717 | + | 0.895671i | \(0.646696\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 6502.50i | − 0.228905i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3431.81 | 0.120034 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −37948.3 | −1.32307 | −0.661536 | − | 0.749914i | \(-0.730095\pi\) | ||||
−0.661536 | + | 0.749914i | \(0.730095\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37907.9i | 1.31325i | 0.754219 | + | 0.656623i | \(0.228016\pi\) | ||||
−0.754219 | + | 0.656623i | \(0.771984\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 38515.5 | 1.33005 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 20062.2i | − 0.688419i | −0.938893 | − | 0.344209i | \(-0.888147\pi\) | ||||
0.938893 | − | 0.344209i | \(-0.111853\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11426.6i | 0.390858i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 43232.8 | 1.46952 | 0.734758 | − | 0.678329i | \(-0.237296\pi\) | ||||
0.734758 | + | 0.678329i | \(0.237296\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 20317.3i | − 0.688432i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −34603.1 | −1.16516 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 40479.1 | 1.35877 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 13560.8i | 0.452369i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9292.66 | −0.309030 | −0.154515 | − | 0.987990i | \(-0.549381\pi\) | ||||
−0.154515 | + | 0.987990i | \(0.549381\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 38499.0i | − 1.27239i | −0.771528 | − | 0.636196i | \(-0.780507\pi\) | ||||
0.771528 | − | 0.636196i | \(-0.219493\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1566.47i | 0.0516122i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9843.93 | −0.322349 | −0.161175 | − | 0.986926i | \(-0.551528\pi\) | ||||
−0.161175 | + | 0.986926i | \(0.551528\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 1551.28i | − 0.0506426i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −43241.9 | −1.40305 | −0.701527 | − | 0.712643i | \(-0.747498\pi\) | ||||
−0.701527 | + | 0.712643i | \(0.747498\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15319.2 | 0.495543 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 25379.1i | 0.815984i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −34891.3 | −1.11842 | −0.559212 | − | 0.829025i | \(-0.688896\pi\) | ||||
−0.559212 | + | 0.829025i | \(0.688896\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6312.07i | 0.201111i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 50166.9i | 1.59358i | 0.604256 | + | 0.796790i | \(0.293471\pi\) | ||||
−0.604256 | + | 0.796790i | \(0.706529\pi\) | |||||||
\(998\) | 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 | 1728.4.d.e.865.4 | yes | 8 | |
3.2 | odd | 2 | 1728.4.d.h.865.6 | yes | 8 | ||
4.3 | odd | 2 | inner | 1728.4.d.e.865.3 | ✓ | 8 | |
8.3 | odd | 2 | inner | 1728.4.d.e.865.5 | yes | 8 | |
8.5 | even | 2 | inner | 1728.4.d.e.865.6 | yes | 8 | |
12.11 | even | 2 | 1728.4.d.h.865.5 | yes | 8 | ||
24.5 | odd | 2 | 1728.4.d.h.865.4 | yes | 8 | ||
24.11 | even | 2 | 1728.4.d.h.865.3 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1728.4.d.e.865.3 | ✓ | 8 | 4.3 | odd | 2 | inner | |
1728.4.d.e.865.4 | yes | 8 | 1.1 | even | 1 | trivial | |
1728.4.d.e.865.5 | yes | 8 | 8.3 | odd | 2 | inner | |
1728.4.d.e.865.6 | yes | 8 | 8.5 | even | 2 | inner | |
1728.4.d.h.865.3 | yes | 8 | 24.11 | even | 2 | ||
1728.4.d.h.865.4 | yes | 8 | 24.5 | odd | 2 | ||
1728.4.d.h.865.5 | yes | 8 | 12.11 | even | 2 | ||
1728.4.d.h.865.6 | yes | 8 | 3.2 | odd | 2 |