Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,3,Mod(685,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.685");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.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: | \(48.0655186332\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.0.2048.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 4x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 7^{2} \) |
Twist minimal: | no (minimal twist has level 196) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 685.4 | ||
Root | \(-0.765367i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.685 |
Dual form | 1764.3.d.e.685.1 |
$q$-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 \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | 8.47343i | 1.69469i | 0.531046 | + | 0.847343i | \(0.321799\pi\) | ||||
−0.531046 | + | 0.847343i | \(0.678201\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.89949 | −0.354500 | −0.177250 | − | 0.984166i | \(-0.556720\pi\) | ||||
−0.177250 | + | 0.984166i | \(0.556720\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 19.1886i | 1.47604i | 0.674777 | + | 0.738022i | \(0.264240\pi\) | ||||
−0.674777 | + | 0.738022i | \(0.735760\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 13.3827i | 0.787215i | 0.919279 | + | 0.393607i | \(0.128773\pi\) | ||||
−0.919279 | + | 0.393607i | \(0.871227\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.70259i | 0.352768i | 0.984321 | + | 0.176384i | \(0.0564401\pi\) | ||||
−0.984321 | + | 0.176384i | \(0.943560\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −26.0000 | −1.13043 | −0.565217 | − | 0.824942i | \(-0.691208\pi\) | ||||
−0.565217 | + | 0.824942i | \(0.691208\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −46.7990 | −1.87196 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 11.7990 | 0.406862 | 0.203431 | − | 0.979089i | \(-0.434791\pi\) | ||||
0.203431 | + | 0.979089i | \(0.434791\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 36.5838i | − 1.18012i | −0.807359 | − | 0.590061i | \(-0.799104\pi\) | ||||
0.807359 | − | 0.590061i | \(-0.200896\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −32.0000 | −0.864865 | −0.432432 | − | 0.901666i | \(-0.642345\pi\) | ||||
−0.432432 | + | 0.901666i | \(0.642345\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 20.9594i | 0.511205i | 0.966782 | + | 0.255602i | \(0.0822738\pi\) | ||||
−0.966782 | + | 0.255602i | \(0.917726\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 79.2965 | 1.84410 | 0.922052 | − | 0.387066i | \(-0.126512\pi\) | ||||
0.922052 | + | 0.387066i | \(0.126512\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 14.3019i | 0.304295i | 0.988358 | + | 0.152148i | \(0.0486189\pi\) | ||||
−0.988358 | + | 0.152148i | \(0.951381\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.7990 | 0.260358 | 0.130179 | − | 0.991490i | \(-0.458445\pi\) | ||||
0.130179 | + | 0.991490i | \(0.458445\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 33.0421i | − 0.600765i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 8.45090i | − 0.143236i | −0.997432 | − | 0.0716178i | \(-0.977184\pi\) | ||||
0.997432 | − | 0.0716178i | \(-0.0228162\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 31.6520i | 0.518885i | 0.965759 | + | 0.259443i | \(0.0835389\pi\) | ||||
−0.965759 | + | 0.259443i | \(0.916461\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −162.593 | −2.50143 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −31.3970 | −0.468611 | −0.234306 | − | 0.972163i | \(-0.575282\pi\) | ||||
−0.234306 | + | 0.972163i | \(0.575282\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −95.5980 | −1.34645 | −0.673225 | − | 0.739438i | \(-0.735092\pi\) | ||||
−0.673225 | + | 0.739438i | \(0.735092\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 18.3144i | 0.250882i | 0.992101 | + | 0.125441i | \(0.0400346\pi\) | ||||
−0.992101 | + | 0.125441i | \(0.959965\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 79.7990 | 1.01011 | 0.505057 | − | 0.863086i | \(-0.331472\pi\) | ||||
0.505057 | + | 0.863086i | \(0.331472\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 141.381i | − 1.70338i | −0.524044 | − | 0.851691i | \(-0.675577\pi\) | ||||
0.524044 | − | 0.851691i | \(-0.324423\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −113.397 | −1.33408 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 116.454i | 1.30847i | 0.756291 | + | 0.654235i | \(0.227009\pi\) | ||||
−0.756291 | + | 0.654235i | \(0.772991\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −56.7939 | −0.597831 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 137.346i | − 1.41593i | −0.706245 | − | 0.707967i | \(-0.749612\pi\) | ||||
0.706245 | − | 0.707967i | \(-0.250388\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 90.5177i | − 0.896214i | −0.893980 | − | 0.448107i | \(-0.852098\pi\) | ||||
0.893980 | − | 0.448107i | \(-0.147902\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 14.2568i | − 0.138416i | −0.997602 | − | 0.0692078i | \(-0.977953\pi\) | ||||
0.997602 | − | 0.0692078i | \(-0.0220472\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 49.5980 | 0.463533 | 0.231766 | − | 0.972772i | \(-0.425550\pi\) | ||||
0.231766 | + | 0.972772i | \(0.425550\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 147.196 | 1.35042 | 0.675211 | − | 0.737625i | \(-0.264053\pi\) | ||||
0.675211 | + | 0.737625i | \(0.264053\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −74.3015 | −0.657536 | −0.328768 | − | 0.944411i | \(-0.606633\pi\) | ||||
−0.328768 | + | 0.944411i | \(0.606633\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 220.309i | − 1.91573i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −105.794 | −0.874330 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 184.712i | − 1.47770i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −76.9949 | −0.606259 | −0.303130 | − | 0.952949i | \(-0.598032\pi\) | ||||
−0.303130 | + | 0.952949i | \(0.598032\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 155.189i | 1.18465i | 0.805699 | + | 0.592325i | \(0.201790\pi\) | ||||
−0.805699 | + | 0.592325i | \(0.798210\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 130.101 | 0.949639 | 0.474819 | − | 0.880083i | \(-0.342513\pi\) | ||||
0.474819 | + | 0.880083i | \(0.342513\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 200.740i | − 1.44417i | −0.691804 | − | 0.722086i | \(-0.743184\pi\) | ||||
0.691804 | − | 0.722086i | \(-0.256816\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 74.8257i | − 0.523257i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 99.9779i | 0.689503i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −169.397 | −1.13689 | −0.568446 | − | 0.822720i | \(-0.692455\pi\) | ||||
−0.568446 | + | 0.822720i | \(0.692455\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.20101 | −0.0145762 | −0.00728811 | − | 0.999973i | \(-0.502320\pi\) | ||||
−0.00728811 | + | 0.999973i | \(0.502320\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 309.990 | 1.99993 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 161.085i | 1.02602i | 0.858382 | + | 0.513010i | \(0.171470\pi\) | ||||
−0.858382 | + | 0.513010i | \(0.828530\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −222.291 | −1.36375 | −0.681876 | − | 0.731468i | \(-0.738835\pi\) | ||||
−0.681876 | + | 0.731468i | \(0.738835\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 207.084i | − 1.24003i | −0.784592 | − | 0.620013i | \(-0.787127\pi\) | ||||
0.784592 | − | 0.620013i | \(-0.212873\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −199.201 | −1.17870 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 277.830i | − 1.60595i | −0.596011 | − | 0.802976i | \(-0.703249\pi\) | ||||
0.596011 | − | 0.802976i | \(-0.296751\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −340.392 | −1.90163 | −0.950815 | − | 0.309758i | \(-0.899752\pi\) | ||||
−0.950815 | + | 0.309758i | \(0.899752\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 184.174i | 1.01753i | 0.860904 | + | 0.508767i | \(0.169899\pi\) | ||||
−0.860904 | + | 0.508767i | \(0.830101\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 271.150i | − 1.46567i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 52.1856i | − 0.279067i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −229.588 | −1.20203 | −0.601015 | − | 0.799237i | \(-0.705237\pi\) | ||||
−0.601015 | + | 0.799237i | \(0.705237\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −41.4975 | −0.215013 | −0.107506 | − | 0.994204i | \(-0.534287\pi\) | ||||
−0.107506 | + | 0.994204i | \(0.534287\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −253.598 | −1.28730 | −0.643650 | − | 0.765320i | \(-0.722581\pi\) | ||||
−0.643650 | + | 0.765320i | \(0.722581\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 112.351i | 0.564579i | 0.959329 | + | 0.282289i | \(0.0910939\pi\) | ||||
−0.959329 | + | 0.282289i | \(0.908906\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −177.598 | −0.866332 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 26.1367i | − 0.125056i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 353.789 | 1.67672 | 0.838362 | − | 0.545113i | \(-0.183513\pi\) | ||||
0.838362 | + | 0.545113i | \(0.183513\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 671.913i | 3.12518i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −256.794 | −1.16196 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 126.653i | 0.567951i | 0.958832 | + | 0.283976i | \(0.0916534\pi\) | ||||
−0.958832 | + | 0.283976i | \(0.908347\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 225.847i | − 0.994920i | −0.867487 | − | 0.497460i | \(-0.834266\pi\) | ||||
0.867487 | − | 0.497460i | \(-0.165734\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 258.283i | 1.12787i | 0.825818 | + | 0.563937i | \(0.190714\pi\) | ||||
−0.825818 | + | 0.563937i | \(0.809286\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −57.6985 | −0.247633 | −0.123816 | − | 0.992305i | \(-0.539513\pi\) | ||||
−0.123816 | + | 0.992305i | \(0.539513\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −121.186 | −0.515685 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −82.6030 | −0.345619 | −0.172810 | − | 0.984955i | \(-0.555285\pi\) | ||||
−0.172810 | + | 0.984955i | \(0.555285\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 130.666i | 0.542181i | 0.962554 | + | 0.271091i | \(0.0873843\pi\) | ||||
−0.962554 | + | 0.271091i | \(0.912616\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −128.613 | −0.520701 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 149.854i | 0.597029i | 0.954405 | + | 0.298514i | \(0.0964911\pi\) | ||||
−0.954405 | + | 0.298514i | \(0.903509\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 101.387 | 0.400739 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 5.22239i | − 0.0203206i | −0.999948 | − | 0.0101603i | \(-0.996766\pi\) | ||||
0.999948 | − | 0.0101603i | \(-0.00323417\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 133.407 | 0.507251 | 0.253626 | − | 0.967302i | \(-0.418377\pi\) | ||||
0.253626 | + | 0.967302i | \(0.418377\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 116.925i | 0.441225i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.12519i | 0.0153353i | 0.999971 | + | 0.00766765i | \(0.00244071\pi\) | ||||
−0.999971 | + | 0.00766765i | \(0.997559\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 315.759i | 1.16516i | 0.812773 | + | 0.582580i | \(0.197957\pi\) | ||||
−0.812773 | + | 0.582580i | \(0.802043\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 182.492 | 0.663609 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −260.191 | −0.939317 | −0.469659 | − | 0.882848i | \(-0.655623\pi\) | ||||
−0.469659 | + | 0.882848i | \(0.655623\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 372.894 | 1.32703 | 0.663513 | − | 0.748165i | \(-0.269065\pi\) | ||||
0.663513 | + | 0.748165i | \(0.269065\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 79.9602i | 0.282545i | 0.989971 | + | 0.141273i | \(0.0451194\pi\) | ||||
−0.989971 | + | 0.141273i | \(0.954881\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 109.905 | 0.380293 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 112.038i | 0.382382i | 0.981553 | + | 0.191191i | \(0.0612351\pi\) | ||||
−0.981553 | + | 0.191191i | \(0.938765\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 71.6081 | 0.242739 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 498.903i | − 1.66857i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −268.201 | −0.879348 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 146.177i | − 0.476148i | −0.971247 | − | 0.238074i | \(-0.923484\pi\) | ||||
0.971247 | − | 0.238074i | \(-0.0765160\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 422.955i | 1.35998i | 0.733220 | + | 0.679992i | \(0.238017\pi\) | ||||
−0.733220 | + | 0.679992i | \(0.761983\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 87.7150i | − 0.280239i | −0.990135 | − | 0.140120i | \(-0.955251\pi\) | ||||
0.990135 | − | 0.140120i | \(-0.0447488\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −431.387 | −1.36084 | −0.680421 | − | 0.732822i | \(-0.738203\pi\) | ||||
−0.680421 | + | 0.732822i | \(0.738203\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −46.0101 | −0.144232 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −89.6985 | −0.277704 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 898.005i | − 2.76309i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −341.487 | −1.03168 | −0.515842 | − | 0.856684i | \(-0.672521\pi\) | ||||
−0.515842 | + | 0.856684i | \(0.672521\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 266.040i | − 0.794149i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −391.377 | −1.16136 | −0.580678 | − | 0.814134i | \(-0.697212\pi\) | ||||
−0.580678 | + | 0.814134i | \(0.697212\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 142.658i | 0.418352i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 608.482 | 1.75355 | 0.876776 | − | 0.480900i | \(-0.159690\pi\) | ||||
0.876776 | + | 0.480900i | \(0.159690\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 93.1627i | 0.266942i | 0.991053 | + | 0.133471i | \(0.0426123\pi\) | ||||
−0.991053 | + | 0.133471i | \(0.957388\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 92.3786i | − 0.261696i | −0.991402 | − | 0.130848i | \(-0.958230\pi\) | ||||
0.991402 | − | 0.130848i | \(-0.0417700\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 810.043i | − 2.28181i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 289.176 | 0.805504 | 0.402752 | − | 0.915309i | \(-0.368054\pi\) | ||||
0.402752 | + | 0.915309i | \(0.368054\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 316.075 | 0.875555 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −155.186 | −0.425167 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 529.971i | 1.44406i | 0.691860 | + | 0.722032i | \(0.256791\pi\) | ||||
−0.691860 | + | 0.722032i | \(0.743209\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 465.799 | 1.24879 | 0.624395 | − | 0.781108i | \(-0.285345\pi\) | ||||
0.624395 | + | 0.781108i | \(0.285345\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 226.406i | 0.600546i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 91.8793 | 0.242426 | 0.121213 | − | 0.992627i | \(-0.461322\pi\) | ||||
0.121213 | + | 0.992627i | \(0.461322\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 311.275i | 0.812729i | 0.913711 | + | 0.406364i | \(0.133204\pi\) | ||||
−0.913711 | + | 0.406364i | \(0.866796\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 542.593 | 1.39484 | 0.697420 | − | 0.716662i | \(-0.254331\pi\) | ||||
0.697420 | + | 0.716662i | \(0.254331\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 347.949i | − 0.889895i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 676.171i | 1.71183i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 163.775i | − 0.412532i | −0.978496 | − | 0.206266i | \(-0.933869\pi\) | ||||
0.978496 | − | 0.206266i | \(-0.0661313\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 143.407 | 0.357624 | 0.178812 | − | 0.983883i | \(-0.442775\pi\) | ||||
0.178812 | + | 0.983883i | \(0.442775\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 701.990 | 1.74191 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 124.784 | 0.306594 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 290.003i | − 0.709053i | −0.935046 | − | 0.354526i | \(-0.884642\pi\) | ||||
0.935046 | − | 0.354526i | \(-0.115358\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1197.98 | 2.88670 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 340.170i | − 0.811860i | −0.913904 | − | 0.405930i | \(-0.866948\pi\) | ||||
0.913904 | − | 0.405930i | \(-0.133052\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.18081 | −0.0146813 | −0.00734063 | − | 0.999973i | \(-0.502337\pi\) | ||||
−0.00734063 | + | 0.999973i | \(0.502337\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 626.295i | − 1.47363i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 28.5929 | 0.0663409 | 0.0331705 | − | 0.999450i | \(-0.489440\pi\) | ||||
0.0331705 | + | 0.999450i | \(0.489440\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 243.736i | − 0.562900i | −0.959576 | − | 0.281450i | \(-0.909185\pi\) | ||||
0.959576 | − | 0.281450i | \(-0.0908153\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 174.267i | − 0.398781i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 494.910i | 1.12736i | 0.825994 | + | 0.563679i | \(0.190615\pi\) | ||||
−0.825994 | + | 0.563679i | \(0.809385\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −79.3970 | −0.179226 | −0.0896128 | − | 0.995977i | \(-0.528563\pi\) | ||||
−0.0896128 | + | 0.995977i | \(0.528563\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −986.764 | −2.21745 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −804.362 | −1.79145 | −0.895726 | − | 0.444607i | \(-0.853343\pi\) | ||||
−0.895726 | + | 0.444607i | \(0.853343\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 81.7311i | − 0.181222i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 537.477 | 1.17610 | 0.588050 | − | 0.808825i | \(-0.299896\pi\) | ||||
0.588050 | + | 0.808825i | \(0.299896\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 524.278i | 1.13726i | 0.822593 | + | 0.568631i | \(0.192527\pi\) | ||||
−0.822593 | + | 0.568631i | \(0.807473\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −506.995 | −1.09502 | −0.547511 | − | 0.836799i | \(-0.684424\pi\) | ||||
−0.547511 | + | 0.836799i | \(0.684424\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 205.807i | − 0.440700i | −0.975421 | − | 0.220350i | \(-0.929280\pi\) | ||||
0.975421 | − | 0.220350i | \(-0.0707199\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −309.216 | −0.653734 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 313.675i | − 0.660368i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 496.032i | 1.03556i | 0.855514 | + | 0.517779i | \(0.173241\pi\) | ||||
−0.855514 | + | 0.517779i | \(0.826759\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − 614.034i | − 1.27658i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1163.79 | 2.39956 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 473.377 | 0.972026 | 0.486013 | − | 0.873952i | \(-0.338451\pi\) | ||||
0.486013 | + | 0.873952i | \(0.338451\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 143.417 | 0.292092 | 0.146046 | − | 0.989278i | \(-0.453345\pi\) | ||||
0.146046 | + | 0.989278i | \(0.453345\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 157.902i | 0.320288i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −446.995 | −0.895781 | −0.447891 | − | 0.894088i | \(-0.647825\pi\) | ||||
−0.447891 | + | 0.894088i | \(0.647825\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 660.346i | 1.31282i | 0.754406 | + | 0.656408i | \(0.227925\pi\) | ||||
−0.754406 | + | 0.656408i | \(0.772075\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 766.995 | 1.51880 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 486.392i | − 0.955583i | −0.878473 | − | 0.477792i | \(-0.841437\pi\) | ||||
0.878473 | − | 0.477792i | \(-0.158563\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 120.804 | 0.234571 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 55.7701i | − 0.107872i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 102.781i | − 0.197276i | −0.995123 | − | 0.0986378i | \(-0.968551\pi\) | ||||
0.995123 | − | 0.0986378i | \(-0.0314485\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 517.260i | 0.989025i | 0.869171 | + | 0.494512i | \(0.164653\pi\) | ||||
−0.869171 | + | 0.494512i | \(0.835347\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 489.588 | 0.929009 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 147.000 | 0.277883 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −402.181 | −0.754561 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 420.265i | 0.785542i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −450.402 | −0.832536 | −0.416268 | − | 0.909242i | \(-0.636662\pi\) | ||||
−0.416268 | + | 0.909242i | \(0.636662\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1247.25i | 2.28854i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 195.095 | 0.356664 | 0.178332 | − | 0.983970i | \(-0.442930\pi\) | ||||
0.178332 | + | 0.983970i | \(0.442930\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 79.0838i | 0.143528i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 689.960 | 1.23871 | 0.619353 | − | 0.785112i | \(-0.287395\pi\) | ||||
0.619353 | + | 0.785112i | \(0.287395\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1521.59i | 2.72198i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 836.876i | 1.48646i | 0.669037 | + | 0.743229i | \(0.266707\pi\) | ||||
−0.669037 | + | 0.743229i | \(0.733293\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 629.589i | − 1.11432i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.81919 | −0.0137420 | −0.00687100 | − | 0.999976i | \(-0.502187\pi\) | ||||
−0.00687100 | + | 0.999976i | \(0.502187\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.70859 | 0.00299227 | 0.00149613 | − | 0.999999i | \(-0.499524\pi\) | ||||
0.00149613 | + | 0.999999i | \(0.499524\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1216.77 | 2.11613 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 216.880i | − 0.375875i | −0.982181 | − | 0.187938i | \(-0.939820\pi\) | ||||
0.982181 | − | 0.187938i | \(-0.0601803\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −53.8091 | −0.0922969 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 50.9983i | − 0.0868795i | −0.999056 | − | 0.0434398i | \(-0.986168\pi\) | ||||
0.999056 | − | 0.0434398i | \(-0.0138317\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 245.206 | 0.416309 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 650.773i | − 1.09743i | −0.836011 | − | 0.548713i | \(-0.815118\pi\) | ||||
0.836011 | − | 0.548713i | \(-0.184882\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 33.7889 | 0.0564088 | 0.0282044 | − | 0.999602i | \(-0.491021\pi\) | ||||
0.0282044 | + | 0.999602i | \(0.491021\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 415.133i | 0.690737i | 0.938467 | + | 0.345368i | \(0.112246\pi\) | ||||
−0.938467 | + | 0.345368i | \(0.887754\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 896.437i | − 1.48171i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 435.418i | 0.717329i | 0.933467 | + | 0.358664i | \(0.116768\pi\) | ||||
−0.933467 | + | 0.358664i | \(0.883232\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −274.432 | −0.449153 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 424.764 | 0.692926 | 0.346463 | − | 0.938064i | \(-0.387383\pi\) | ||||
0.346463 | + | 0.938064i | \(0.387383\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 726.563 | 1.17757 | 0.588787 | − | 0.808289i | \(-0.299606\pi\) | ||||
0.588787 | + | 0.808289i | \(0.299606\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 708.920i | 1.14527i | 0.819812 | + | 0.572633i | \(0.194078\pi\) | ||||
−0.819812 | + | 0.572633i | \(0.805922\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 395.171 | 0.632273 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 428.245i | − 0.680835i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 207.176 | 0.328329 | 0.164165 | − | 0.986433i | \(-0.447507\pi\) | ||||
0.164165 | + | 0.986433i | \(0.447507\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 652.411i | − 1.02742i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −912.583 | −1.42369 | −0.711843 | − | 0.702339i | \(-0.752139\pi\) | ||||
−0.711843 | + | 0.702339i | \(0.752139\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 656.917i | 1.02164i | 0.859686 | + | 0.510822i | \(0.170659\pi\) | ||||
−0.859686 | + | 0.510822i | \(0.829341\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 38.1068i | 0.0588976i | 0.999566 | + | 0.0294488i | \(0.00937520\pi\) | ||||
−0.999566 | + | 0.0294488i | \(0.990625\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 32.9542i | 0.0507769i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 376.583 | 0.576697 | 0.288348 | − | 0.957526i | \(-0.406894\pi\) | ||||
0.288348 | + | 0.957526i | \(0.406894\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1314.98 | −2.00761 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 954.291 | 1.44809 | 0.724045 | − | 0.689753i | \(-0.242281\pi\) | ||||
0.724045 | + | 0.689753i | \(0.242281\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1166.37i | 1.76456i | 0.470724 | + | 0.882281i | \(0.343993\pi\) | ||||
−0.470724 | + | 0.882281i | \(0.656007\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −306.774 | −0.459931 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 123.427i | − 0.183945i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −774.101 | −1.15022 | −0.575112 | − | 0.818075i | \(-0.695041\pi\) | ||||
−0.575112 | + | 0.818075i | \(0.695041\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 561.488i | 0.829377i | 0.909964 | + | 0.414688i | \(0.136109\pi\) | ||||
−0.909964 | + | 0.414688i | \(0.863891\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −352.161 | −0.515608 | −0.257804 | − | 0.966197i | \(-0.582999\pi\) | ||||
−0.257804 | + | 0.966197i | \(0.582999\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1102.40i | 1.60934i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 264.783i | 0.384300i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 1047.50i | − 1.51592i | −0.652300 | − | 0.757961i | \(-0.726196\pi\) | ||||
0.652300 | − | 0.757961i | \(-0.273804\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1700.95 | 2.44742 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −280.492 | −0.402428 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −809.990 | −1.15548 | −0.577739 | − | 0.816222i | \(-0.696065\pi\) | ||||
−0.577739 | + | 0.816222i | \(0.696065\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 214.483i | − 0.305097i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −459.960 | −0.648744 | −0.324372 | − | 0.945930i | \(-0.605153\pi\) | ||||
−0.324372 | + | 0.945930i | \(0.605153\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 951.178i | 1.33405i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 634.030 | 0.886756 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 86.0365i | − 0.119661i | −0.998209 | − | 0.0598307i | \(-0.980944\pi\) | ||||
0.998209 | − | 0.0598307i | \(-0.0190561\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −552.181 | −0.761629 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 78.4124i | − 0.107858i | −0.998545 | − | 0.0539288i | \(-0.982826\pi\) | ||||
0.998545 | − | 0.0539288i | \(-0.0171744\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1061.20i | 1.45171i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 519.569i | − 0.708826i | −0.935089 | − | 0.354413i | \(-0.884681\pi\) | ||||
0.935089 | − | 0.354413i | \(-0.115319\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 122.432 | 0.166123 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1163.48 | 1.57439 | 0.787197 | − | 0.616702i | \(-0.211531\pi\) | ||||
0.787197 | + | 0.616702i | \(0.211531\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 66.8040 | 0.0899112 | 0.0449556 | − | 0.998989i | \(-0.485685\pi\) | ||||
0.0449556 | + | 0.998989i | \(0.485685\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 1435.37i | − 1.92668i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.38687 | 0.00450981 | 0.00225491 | − | 0.999997i | \(-0.499282\pi\) | ||||
0.00225491 | + | 0.999997i | \(0.499282\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 18.6501i | − 0.0247021i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −700.402 | −0.925234 | −0.462617 | − | 0.886558i | \(-0.653089\pi\) | ||||
−0.462617 | + | 0.886558i | \(0.653089\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 611.948i | 0.804136i | 0.915610 | + | 0.402068i | \(0.131709\pi\) | ||||
−0.915610 | + | 0.402068i | \(0.868291\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 162.161 | 0.211422 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 638.310i | − 0.830052i | −0.909810 | − | 0.415026i | \(-0.863773\pi\) | ||||
0.909810 | − | 0.415026i | \(-0.136227\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 475.005i | − 0.614496i | −0.951629 | − | 0.307248i | \(-0.900592\pi\) | ||||
0.951629 | − | 0.307248i | \(-0.0994081\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1712.08i | 2.20914i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −140.482 | −0.180337 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 372.784 | 0.477316 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1364.94 | −1.73878 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1475.43i | 1.87476i | 0.348313 | + | 0.937378i | \(0.386755\pi\) | ||||
−0.348313 | + | 0.937378i | \(0.613245\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −607.357 | −0.765897 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 330.869i | 0.415143i | 0.978220 | + | 0.207572i | \(0.0665560\pi\) | ||||
−0.978220 | + | 0.207572i | \(0.933444\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −191.397 | −0.239546 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 71.4170i | − 0.0889377i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 735.889 | 0.909628 | 0.454814 | − | 0.890586i | \(-0.349706\pi\) | ||||
0.454814 | + | 0.890586i | \(0.349706\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 1129.32i | − 1.39251i | −0.717796 | − | 0.696253i | \(-0.754849\pi\) | ||||
0.717796 | − | 0.696253i | \(-0.245151\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 1883.57i | − 2.31113i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 531.492i | 0.650541i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1453.96 | 1.77096 | 0.885481 | − | 0.464676i | \(-0.153829\pi\) | ||||
0.885481 | + | 0.464676i | \(0.153829\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −584.965 | −0.710771 | −0.355386 | − | 0.934720i | \(-0.615650\pi\) | ||||
−0.355386 | + | 0.934720i | \(0.615650\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1453.16 | 1.75714 | 0.878570 | − | 0.477613i | \(-0.158498\pi\) | ||||
0.878570 | + | 0.477613i | \(0.158498\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 403.586i | 0.486835i | 0.969922 | + | 0.243417i | \(0.0782685\pi\) | ||||
−0.969922 | + | 0.243417i | \(0.921731\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1754.71 | 2.10145 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 191.525i | 0.228278i | 0.993465 | + | 0.114139i | \(0.0364109\pi\) | ||||
−0.993465 | + | 0.114139i | \(0.963589\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −701.784 | −0.834464 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 1687.92i | − 1.99753i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 832.000 | 0.977673 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 220.893i | 0.258960i | 0.991582 | + | 0.129480i | \(0.0413308\pi\) | ||||
−0.991582 | + | 0.129480i | \(0.958669\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 939.501i | 1.09627i | 0.836391 | + | 0.548133i | \(0.184661\pi\) | ||||
−0.836391 | + | 0.548133i | \(0.815339\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 930.534i | − 1.08328i | −0.840612 | − | 0.541638i | \(-0.817804\pi\) | ||||
0.840612 | − | 0.541638i | \(-0.182196\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1172.16 | −1.35824 | −0.679120 | − | 0.734028i | \(-0.737638\pi\) | ||||
−0.679120 | + | 0.734028i | \(0.737638\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2354.17 | 2.72158 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −311.176 | −0.358085 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 602.463i | − 0.691691i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −501.407 | −0.571730 | −0.285865 | − | 0.958270i | \(-0.592281\pi\) | ||||
−0.285865 | + | 0.958270i | \(0.592281\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 1037.14i | − 1.17723i | −0.808412 | − | 0.588616i | \(-0.799673\pi\) | ||||
0.808412 | − | 0.588616i | \(-0.200327\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 103.226 | 0.116904 | 0.0584520 | − | 0.998290i | \(-0.481384\pi\) | ||||
0.0584520 | + | 0.998290i | \(0.481384\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 540.015i | − 0.608811i | −0.952543 | − | 0.304405i | \(-0.901542\pi\) | ||||
0.952543 | − | 0.304405i | \(-0.0984577\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −95.8596 | −0.107346 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 2884.29i | − 3.22267i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 431.651i | − 0.480146i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 184.667i | 0.204958i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1560.58 | −1.72440 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −722.382 | −0.796452 | −0.398226 | − | 0.917287i | \(-0.630374\pi\) | ||||
−0.398226 | + | 0.917287i | \(0.630374\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1292.59 | −1.41887 | −0.709436 | − | 0.704770i | \(-0.751050\pi\) | ||||
−0.709436 | + | 0.704770i | \(0.751050\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 551.314i | 0.603848i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1076.98 | 1.17191 | 0.585955 | − | 0.810344i | \(-0.300720\pi\) | ||||
0.585955 | + | 0.810344i | \(0.300720\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 1834.39i | − 1.98742i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1497.57 | 1.61899 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1252.03i | 1.34772i | 0.738860 | + | 0.673859i | \(0.235365\pi\) | ||||
−0.738860 | + | 0.673859i | \(0.764635\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 442.191 | 0.472931 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 857.272i | 0.914911i | 0.889232 | + | 0.457456i | \(0.151239\pi\) | ||||
−0.889232 | + | 0.457456i | \(0.848761\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 708.319i | 0.752730i | 0.926472 | + | 0.376365i | \(0.122826\pi\) | ||||
−0.926472 | + | 0.376365i | \(0.877174\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 544.944i | − 0.577884i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −483.095 | −0.510132 | −0.255066 | − | 0.966924i | \(-0.582097\pi\) | ||||
−0.255066 | + | 0.966924i | \(0.582097\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −351.427 | −0.370313 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −67.5778 | −0.0709106 | −0.0354553 | − | 0.999371i | \(-0.511288\pi\) | ||||
−0.0354553 | + | 0.999371i | \(0.511288\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 1945.40i | − 2.03706i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −377.372 | −0.392686 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 351.626i | − 0.364379i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −806.382 | −0.833901 | −0.416950 | − | 0.908929i | \(-0.636901\pi\) | ||||
−0.416950 | + | 0.908929i | \(0.636901\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 691.124i | 0.711765i | 0.934531 | + | 0.355883i | \(0.115820\pi\) | ||||
−0.934531 | + | 0.355883i | \(0.884180\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −359.648 | −0.368115 | −0.184057 | − | 0.982916i | \(-0.558923\pi\) | ||||
−0.184057 | + | 0.982916i | \(0.558923\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 454.111i | − 0.463852i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 391.751i | − 0.398526i | −0.979946 | − | 0.199263i | \(-0.936145\pi\) | ||||
0.979946 | − | 0.199263i | \(-0.0638548\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − 2148.84i | − 2.18157i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2061.71 | −2.08464 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1409.39 | 1.42219 | 0.711093 | − | 0.703098i | \(-0.248200\pi\) | ||||
0.711093 | + | 0.703098i | \(0.248200\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −952.000 | −0.956784 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 460.568i | − 0.461954i | −0.972959 | − | 0.230977i | \(-0.925808\pi\) | ||||
0.972959 | − | 0.230977i | \(-0.0741922\pi\) | |||||||
\(998\) | 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 | 1764.3.d.e.685.4 | 4 | ||
3.2 | odd | 2 | 196.3.b.b.97.1 | ✓ | 4 | ||
7.2 | even | 3 | 1764.3.z.k.325.4 | 8 | |||
7.3 | odd | 6 | 1764.3.z.k.901.4 | 8 | |||
7.4 | even | 3 | 1764.3.z.k.901.1 | 8 | |||
7.5 | odd | 6 | 1764.3.z.k.325.1 | 8 | |||
7.6 | odd | 2 | inner | 1764.3.d.e.685.1 | 4 | ||
12.11 | even | 2 | 784.3.c.d.97.4 | 4 | |||
21.2 | odd | 6 | 196.3.h.c.129.4 | 8 | |||
21.5 | even | 6 | 196.3.h.c.129.1 | 8 | |||
21.11 | odd | 6 | 196.3.h.c.117.1 | 8 | |||
21.17 | even | 6 | 196.3.h.c.117.4 | 8 | |||
21.20 | even | 2 | 196.3.b.b.97.4 | yes | 4 | ||
84.11 | even | 6 | 784.3.s.g.705.4 | 8 | |||
84.23 | even | 6 | 784.3.s.g.129.1 | 8 | |||
84.47 | odd | 6 | 784.3.s.g.129.4 | 8 | |||
84.59 | odd | 6 | 784.3.s.g.705.1 | 8 | |||
84.83 | odd | 2 | 784.3.c.d.97.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
196.3.b.b.97.1 | ✓ | 4 | 3.2 | odd | 2 | ||
196.3.b.b.97.4 | yes | 4 | 21.20 | even | 2 | ||
196.3.h.c.117.1 | 8 | 21.11 | odd | 6 | |||
196.3.h.c.117.4 | 8 | 21.17 | even | 6 | |||
196.3.h.c.129.1 | 8 | 21.5 | even | 6 | |||
196.3.h.c.129.4 | 8 | 21.2 | odd | 6 | |||
784.3.c.d.97.1 | 4 | 84.83 | odd | 2 | |||
784.3.c.d.97.4 | 4 | 12.11 | even | 2 | |||
784.3.s.g.129.1 | 8 | 84.23 | even | 6 | |||
784.3.s.g.129.4 | 8 | 84.47 | odd | 6 | |||
784.3.s.g.705.1 | 8 | 84.59 | odd | 6 | |||
784.3.s.g.705.4 | 8 | 84.11 | even | 6 | |||
1764.3.d.e.685.1 | 4 | 7.6 | odd | 2 | inner | ||
1764.3.d.e.685.4 | 4 | 1.1 | even | 1 | trivial | ||
1764.3.z.k.325.1 | 8 | 7.5 | odd | 6 | |||
1764.3.z.k.325.4 | 8 | 7.2 | even | 3 | |||
1764.3.z.k.901.1 | 8 | 7.4 | even | 3 | |||
1764.3.z.k.901.4 | 8 | 7.3 | odd | 6 |