Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8100,2,Mod(649,8100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8100, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8100.649");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8100 = 2^{2} \cdot 3^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8100.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(64.6788256372\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 1620) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 649.4 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8100.649 |
Dual form | 8100.2.d.l.649.1 |
$q$-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 \(\left(\mathbb{Z}/8100\mathbb{Z}\right)^\times\).
\(n\) | \(4051\) | \(6401\) | \(7777\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.73205i | 1.03262i | 0.856402 | + | 0.516309i | \(0.172694\pi\) | ||||
−0.856402 | + | 0.516309i | \(0.827306\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.73205 | −0.522233 | −0.261116 | − | 0.965307i | \(-0.584091\pi\) | ||||
−0.261116 | + | 0.965307i | \(0.584091\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.46410i | 1.51547i | 0.652563 | + | 0.757735i | \(0.273694\pi\) | ||||
−0.652563 | + | 0.757735i | \(0.726306\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 4.73205i | − 1.14769i | −0.818964 | − | 0.573845i | \(-0.805451\pi\) | ||||
0.818964 | − | 0.573845i | \(-0.194549\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.46410 | 1.02414 | 0.512068 | − | 0.858945i | \(-0.328880\pi\) | ||||
0.512068 | + | 0.858945i | \(0.328880\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 3.46410i | − 0.722315i | −0.932505 | − | 0.361158i | \(-0.882382\pi\) | ||||
0.932505 | − | 0.361158i | \(-0.117618\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.73205 | −1.43581 | −0.717903 | − | 0.696143i | \(-0.754898\pi\) | ||||
−0.717903 | + | 0.696143i | \(0.754898\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.92820 | 1.06474 | 0.532368 | − | 0.846513i | \(-0.321302\pi\) | ||||
0.532368 | + | 0.846513i | \(0.321302\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.19615i | 1.01864i | 0.860577 | + | 0.509321i | \(0.170103\pi\) | ||||
−0.860577 | + | 0.509321i | \(0.829897\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.1962 | 1.74855 | 0.874273 | − | 0.485435i | \(-0.161339\pi\) | ||||
0.874273 | + | 0.485435i | \(0.161339\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.26795i | 0.498358i | 0.968458 | + | 0.249179i | \(0.0801607\pi\) | ||||
−0.968458 | + | 0.249179i | \(0.919839\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 1.26795i | − 0.184949i | −0.995715 | − | 0.0924747i | \(-0.970522\pi\) | ||||
0.995715 | − | 0.0924747i | \(-0.0294777\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.464102 | −0.0663002 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.26795i | 0.998330i | 0.866507 | + | 0.499165i | \(0.166360\pi\) | ||||
−0.866507 | + | 0.499165i | \(0.833640\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.73205 | −1.00663 | −0.503314 | − | 0.864104i | \(-0.667886\pi\) | ||||
−0.503314 | + | 0.864104i | \(0.667886\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.00000 | −0.512148 | −0.256074 | − | 0.966657i | \(-0.582429\pi\) | ||||
−0.256074 | + | 0.966657i | \(0.582429\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 6.39230i | − 0.780944i | −0.920615 | − | 0.390472i | \(-0.872312\pi\) | ||||
0.920615 | − | 0.390472i | \(-0.127688\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.1962 | 1.32874 | 0.664369 | − | 0.747404i | \(-0.268700\pi\) | ||||
0.664369 | + | 0.747404i | \(0.268700\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 0.196152i | − 0.0229579i | −0.999934 | − | 0.0114790i | \(-0.996346\pi\) | ||||
0.999934 | − | 0.0114790i | \(-0.00365394\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 4.73205i | − 0.539267i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.3923 | 1.61926 | 0.809630 | − | 0.586940i | \(-0.199668\pi\) | ||||
0.809630 | + | 0.586940i | \(0.199668\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 15.1244i | 1.66011i | 0.557679 | + | 0.830057i | \(0.311692\pi\) | ||||
−0.557679 | + | 0.830057i | \(0.688308\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.19615 | 0.550791 | 0.275396 | − | 0.961331i | \(-0.411191\pi\) | ||||
0.275396 | + | 0.961331i | \(0.411191\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.9282 | −1.56490 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 0.732051i | − 0.0743285i | −0.999309 | − | 0.0371642i | \(-0.988168\pi\) | ||||
0.999309 | − | 0.0371642i | \(-0.0118325\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.12436 | −0.609396 | −0.304698 | − | 0.952449i | \(-0.598556\pi\) | ||||
−0.304698 | + | 0.952449i | \(0.598556\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.3923i | 1.81225i | 0.423013 | + | 0.906124i | \(0.360973\pi\) | ||||
−0.423013 | + | 0.906124i | \(0.639027\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.46410i | 0.334887i | 0.985882 | + | 0.167444i | \(0.0535512\pi\) | ||||
−0.985882 | + | 0.167444i | \(0.946449\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.92820 | 0.759384 | 0.379692 | − | 0.925113i | \(-0.376030\pi\) | ||||
0.379692 | + | 0.925113i | \(0.376030\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.339746i | 0.0319606i | 0.999872 | + | 0.0159803i | \(0.00508691\pi\) | ||||
−0.999872 | + | 0.0159803i | \(0.994913\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 12.9282 | 1.18513 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.00000 | −0.727273 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 4.19615i | − 0.372348i | −0.982517 | − | 0.186174i | \(-0.940391\pi\) | ||||
0.982517 | − | 0.186174i | \(-0.0596089\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.2679 | −0.897115 | −0.448557 | − | 0.893754i | \(-0.648062\pi\) | ||||
−0.448557 | + | 0.893754i | \(0.648062\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.1962i | 1.05754i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.39230i | 0.375260i | 0.982240 | + | 0.187630i | \(0.0600806\pi\) | ||||
−0.982240 | + | 0.187630i | \(0.939919\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.3923 | −1.30556 | −0.652779 | − | 0.757548i | \(-0.726397\pi\) | ||||
−0.652779 | + | 0.757548i | \(0.726397\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 9.46410i | − 0.791428i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.3923 | −1.41537 | −0.707683 | − | 0.706530i | \(-0.750259\pi\) | ||||
−0.707683 | + | 0.706530i | \(0.750259\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 3.26795i | − 0.260811i | −0.991461 | − | 0.130405i | \(-0.958372\pi\) | ||||
0.991461 | − | 0.130405i | \(-0.0416279\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.46410 | 0.745876 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.7321i | 1.46721i | 0.679577 | + | 0.733604i | \(0.262163\pi\) | ||||
−0.679577 | + | 0.733604i | \(0.737837\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 21.1244i | − 1.63465i | −0.576176 | − | 0.817326i | \(-0.695456\pi\) | ||||
0.576176 | − | 0.817326i | \(-0.304544\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −16.8564 | −1.29665 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 24.2487i | 1.84360i | 0.387671 | + | 0.921798i | \(0.373280\pi\) | ||||
−0.387671 | + | 0.921798i | \(0.626720\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.1244 | −0.906217 | −0.453108 | − | 0.891455i | \(-0.649685\pi\) | ||||
−0.453108 | + | 0.891455i | \(0.649685\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.4641 | −1.22377 | −0.611884 | − | 0.790948i | \(-0.709588\pi\) | ||||
−0.611884 | + | 0.790948i | \(0.709588\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.19615i | 0.599362i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.0526 | −1.37859 | −0.689297 | − | 0.724479i | \(-0.742081\pi\) | ||||
−0.689297 | + | 0.724479i | \(0.742081\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 10.5885i | − 0.762174i | −0.924539 | − | 0.381087i | \(-0.875550\pi\) | ||||
0.924539 | − | 0.381087i | \(-0.124450\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 13.8564i | − 0.987228i | −0.869681 | − | 0.493614i | \(-0.835676\pi\) | ||||
0.869681 | − | 0.493614i | \(-0.164324\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.8564 | −1.12403 | −0.562015 | − | 0.827127i | \(-0.689974\pi\) | ||||
−0.562015 | + | 0.827127i | \(0.689974\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 21.1244i | − 1.48264i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.73205 | −0.534837 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.9282 | −1.37191 | −0.685957 | − | 0.727642i | \(-0.740616\pi\) | ||||
−0.685957 | + | 0.727642i | \(0.740616\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 16.1962i | 1.09947i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 25.8564 | 1.73929 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 5.85641i | − 0.392174i | −0.980587 | − | 0.196087i | \(-0.937177\pi\) | ||||
0.980587 | − | 0.196087i | \(-0.0628235\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 26.1962i | 1.73870i | 0.494197 | + | 0.869350i | \(0.335462\pi\) | ||||
−0.494197 | + | 0.869350i | \(0.664538\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.8564 | 1.17998 | 0.589992 | − | 0.807409i | \(-0.299131\pi\) | ||||
0.589992 | + | 0.807409i | \(0.299131\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 24.5885i | − 1.61084i | −0.592702 | − | 0.805422i | \(-0.701939\pi\) | ||||
0.592702 | − | 0.805422i | \(-0.298061\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.53590 | 0.552141 | 0.276071 | − | 0.961137i | \(-0.410968\pi\) | ||||
0.276071 | + | 0.961137i | \(0.410968\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.3205 | 0.664802 | 0.332401 | − | 0.943138i | \(-0.392141\pi\) | ||||
0.332401 | + | 0.943138i | \(0.392141\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 24.3923i | 1.55205i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −20.5359 | −1.29621 | −0.648107 | − | 0.761549i | \(-0.724439\pi\) | ||||
−0.648107 | + | 0.761549i | \(0.724439\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.00000i | 0.377217i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.4641i | 0.964624i | 0.875999 | + | 0.482312i | \(0.160203\pi\) | ||||
−0.875999 | + | 0.482312i | \(0.839797\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −16.9282 | −1.05187 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 24.2487i | 1.49524i | 0.664127 | + | 0.747620i | \(0.268803\pi\) | ||||
−0.664127 | + | 0.747620i | \(0.731197\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −16.2679 | −0.991874 | −0.495937 | − | 0.868358i | \(-0.665175\pi\) | ||||
−0.495937 | + | 0.868358i | \(0.665175\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.7846 | 1.01959 | 0.509796 | − | 0.860295i | \(-0.329721\pi\) | ||||
0.509796 | + | 0.860295i | \(0.329721\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 5.12436i | − 0.307893i | −0.988079 | − | 0.153946i | \(-0.950802\pi\) | ||||
0.988079 | − | 0.153946i | \(-0.0491983\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −29.3205 | −1.74911 | −0.874557 | − | 0.484922i | \(-0.838848\pi\) | ||||
−0.874557 | + | 0.484922i | \(0.838848\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.5359i | 0.982957i | 0.870890 | + | 0.491479i | \(0.163543\pi\) | ||||
−0.870890 | + | 0.491479i | \(0.836457\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 30.5885i | 1.80558i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.39230 | −0.317194 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 24.5885i | − 1.43647i | −0.695799 | − | 0.718237i | \(-0.744950\pi\) | ||||
0.695799 | − | 0.718237i | \(-0.255050\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 18.9282 | 1.09465 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.92820 | −0.514613 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.80385i | 0.102951i | 0.998674 | + | 0.0514755i | \(0.0163924\pi\) | ||||
−0.998674 | + | 0.0514755i | \(0.983608\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.5167 | 0.936574 | 0.468287 | − | 0.883576i | \(-0.344871\pi\) | ||||
0.468287 | + | 0.883576i | \(0.344871\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.9282i | 0.843792i | 0.906644 | + | 0.421896i | \(0.138635\pi\) | ||||
−0.906644 | + | 0.421896i | \(0.861365\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.12436i | 0.175481i | 0.996143 | + | 0.0877406i | \(0.0279647\pi\) | ||||
−0.996143 | + | 0.0877406i | \(0.972035\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.3923 | 0.749825 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 21.1244i | − 1.17539i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.46410 | 0.190982 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −29.3923 | −1.61555 | −0.807774 | − | 0.589493i | \(-0.799328\pi\) | ||||
−0.807774 | + | 0.589493i | \(0.799328\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 34.2487i | 1.86565i | 0.360335 | + | 0.932823i | \(0.382662\pi\) | ||||
−0.360335 | + | 0.932823i | \(0.617338\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.2679 | −0.556041 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.8564i | 0.964155i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 21.8038i | 1.17049i | 0.810856 | + | 0.585246i | \(0.199002\pi\) | ||||
−0.810856 | + | 0.585246i | \(0.800998\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.0000 | 1.33822 | 0.669110 | − | 0.743164i | \(-0.266676\pi\) | ||||
0.669110 | + | 0.743164i | \(0.266676\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 28.9808i | 1.54249i | 0.636538 | + | 0.771245i | \(0.280366\pi\) | ||||
−0.636538 | + | 0.771245i | \(0.719634\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.33975 | 0.492933 | 0.246466 | − | 0.969151i | \(-0.420730\pi\) | ||||
0.246466 | + | 0.969151i | \(0.420730\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.928203 | 0.0488528 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 26.3923i | 1.37767i | 0.724920 | + | 0.688834i | \(0.241877\pi\) | ||||
−0.724920 | + | 0.688834i | \(0.758123\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −19.8564 | −1.03089 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 14.0526i | − 0.727614i | −0.931474 | − | 0.363807i | \(-0.881477\pi\) | ||||
0.931474 | − | 0.363807i | \(-0.118523\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 42.2487i | − 2.17592i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.53590 | −0.232993 | −0.116497 | − | 0.993191i | \(-0.537166\pi\) | ||||
−0.116497 | + | 0.993191i | \(0.537166\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 18.2487i | − 0.932466i | −0.884662 | − | 0.466233i | \(-0.845611\pi\) | ||||
0.884662 | − | 0.466233i | \(-0.154389\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 27.4641 | 1.39249 | 0.696243 | − | 0.717807i | \(-0.254854\pi\) | ||||
0.696243 | + | 0.717807i | \(0.254854\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.3923 | −0.828994 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 37.3205i | − 1.87306i | −0.350584 | − | 0.936531i | \(-0.614017\pi\) | ||||
0.350584 | − | 0.936531i | \(-0.385983\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.7846 | 0.738308 | 0.369154 | − | 0.929368i | \(-0.379647\pi\) | ||||
0.369154 | + | 0.929368i | \(0.379647\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 32.3923i | 1.61358i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 10.7321i | − 0.531968i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.8564 | 0.882942 | 0.441471 | − | 0.897275i | \(-0.354457\pi\) | ||||
0.441471 | + | 0.897275i | \(0.354457\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 21.1244i | − 1.03946i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 21.4641 | 1.04859 | 0.524295 | − | 0.851537i | \(-0.324329\pi\) | ||||
0.524295 | + | 0.851537i | \(0.324329\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.7846 | 0.671821 | 0.335910 | − | 0.941894i | \(-0.390956\pi\) | ||||
0.335910 | + | 0.941894i | \(0.390956\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 10.9282i | − 0.528853i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 33.5885 | 1.61790 | 0.808950 | − | 0.587878i | \(-0.200037\pi\) | ||||
0.808950 | + | 0.587878i | \(0.200037\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.4641i | 0.550930i | 0.961311 | + | 0.275465i | \(0.0888317\pi\) | ||||
−0.961311 | + | 0.275465i | \(0.911168\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 15.4641i | − 0.739748i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.60770 | −0.315368 | −0.157684 | − | 0.987490i | \(-0.550403\pi\) | ||||
−0.157684 | + | 0.987490i | \(0.550403\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 37.2679i | − 1.77065i | −0.464969 | − | 0.885327i | \(-0.653935\pi\) | ||||
0.464969 | − | 0.885327i | \(-0.346065\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.1244 | 1.13850 | 0.569249 | − | 0.822165i | \(-0.307234\pi\) | ||||
0.569249 | + | 0.822165i | \(0.307234\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −19.3923 | −0.913148 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 22.1962i | − 1.03829i | −0.854686 | − | 0.519146i | \(-0.826250\pi\) | ||||
0.854686 | − | 0.519146i | \(-0.173750\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.58846 | −0.446579 | −0.223289 | − | 0.974752i | \(-0.571680\pi\) | ||||
−0.223289 | + | 0.974752i | \(0.571680\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 2.39230i | − 0.111180i | −0.998454 | − | 0.0555899i | \(-0.982296\pi\) | ||||
0.998454 | − | 0.0555899i | \(-0.0177039\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 26.1962i | 1.21221i | 0.795383 | + | 0.606107i | \(0.207270\pi\) | ||||
−0.795383 | + | 0.606107i | \(0.792730\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 17.4641 | 0.806417 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 5.66025i | − 0.260259i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.33975 | −0.152597 | −0.0762984 | − | 0.997085i | \(-0.524310\pi\) | ||||
−0.0762984 | + | 0.997085i | \(0.524310\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −33.8564 | −1.54372 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 30.5359i | 1.38371i | 0.722035 | + | 0.691857i | \(0.243207\pi\) | ||||
−0.722035 | + | 0.691857i | \(0.756793\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.26795 | 0.192610 | 0.0963049 | − | 0.995352i | \(-0.469298\pi\) | ||||
0.0963049 | + | 0.995352i | \(0.469298\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 36.5885i | 1.64786i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 30.5885i | 1.37208i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −27.3923 | −1.22625 | −0.613124 | − | 0.789987i | \(-0.710087\pi\) | ||||
−0.613124 | + | 0.789987i | \(0.710087\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 35.3205i | 1.57486i | 0.616402 | + | 0.787432i | \(0.288590\pi\) | ||||
−0.616402 | + | 0.787432i | \(0.711410\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −26.7846 | −1.18721 | −0.593603 | − | 0.804758i | \(-0.702295\pi\) | ||||
−0.593603 | + | 0.804758i | \(0.702295\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.535898 | 0.0237067 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.19615i | 0.0965867i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.3923 | 0.455295 | 0.227648 | − | 0.973744i | \(-0.426897\pi\) | ||||
0.227648 | + | 0.973744i | \(0.426897\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.60770i | 0.157753i | 0.996884 | + | 0.0788767i | \(0.0251334\pi\) | ||||
−0.996884 | + | 0.0788767i | \(0.974867\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 28.0526i | − 1.22199i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.0000 | 0.478261 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 61.1769i | 2.64987i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.803848 | 0.0346242 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.46410 | 0.105940 | 0.0529700 | − | 0.998596i | \(-0.483131\pi\) | ||||
0.0529700 | + | 0.998596i | \(0.483131\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 4.78461i | − 0.204575i | −0.994755 | − | 0.102288i | \(-0.967384\pi\) | ||||
0.994755 | − | 0.102288i | \(-0.0326162\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −34.5167 | −1.47046 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 39.3205i | 1.67208i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 4.39230i | − 0.186108i | −0.995661 | − | 0.0930540i | \(-0.970337\pi\) | ||||
0.995661 | − | 0.0930540i | \(-0.0296629\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −17.8564 | −0.755246 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 22.7321i | − 0.958042i | −0.877804 | − | 0.479021i | \(-0.840992\pi\) | ||||
0.877804 | − | 0.479021i | \(-0.159008\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −43.0526 | −1.80486 | −0.902429 | − | 0.430839i | \(-0.858218\pi\) | ||||
−0.902429 | + | 0.430839i | \(0.858218\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.856406 | 0.0358395 | 0.0179197 | − | 0.999839i | \(-0.494296\pi\) | ||||
0.0179197 | + | 0.999839i | \(0.494296\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 11.8038i | − 0.491401i | −0.969346 | − | 0.245700i | \(-0.920982\pi\) | ||||
0.969346 | − | 0.245700i | \(-0.0790179\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −41.3205 | −1.71426 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 12.5885i | − 0.521361i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.80385i | 0.157002i | 0.996914 | + | 0.0785008i | \(0.0250133\pi\) | ||||
−0.996914 | + | 0.0785008i | \(0.974987\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 26.4641 | 1.09043 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 23.0718i | 0.947445i | 0.880674 | + | 0.473723i | \(0.157090\pi\) | ||||
−0.880674 | + | 0.473723i | \(0.842910\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14.4115 | −0.588840 | −0.294420 | − | 0.955676i | \(-0.595126\pi\) | ||||
−0.294420 | + | 0.955676i | \(0.595126\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24.3205 | −0.992054 | −0.496027 | − | 0.868307i | \(-0.665208\pi\) | ||||
−0.496027 | + | 0.868307i | \(0.665208\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 2.58846i | − 0.105062i | −0.998619 | − | 0.0525311i | \(-0.983271\pi\) | ||||
0.998619 | − | 0.0525311i | \(-0.0167289\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.92820 | 0.280285 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.3923i | 0.985196i | 0.870257 | + | 0.492598i | \(0.163953\pi\) | ||||
−0.870257 | + | 0.492598i | \(0.836047\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 12.0000i | − 0.483102i | −0.970388 | − | 0.241551i | \(-0.922344\pi\) | ||||
0.970388 | − | 0.241551i | \(-0.0776561\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.0000 | 0.401934 | 0.200967 | − | 0.979598i | \(-0.435592\pi\) | ||||
0.200967 | + | 0.979598i | \(0.435592\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 14.1962i | 0.568757i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 29.3205 | 1.16909 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.0717968 | −0.00285818 | −0.00142909 | − | 0.999999i | \(-0.500455\pi\) | ||||
−0.00142909 | + | 0.999999i | \(0.500455\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 2.53590i | − 0.100476i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.8038 | 0.505722 | 0.252861 | − | 0.967503i | \(-0.418629\pi\) | ||||
0.252861 | + | 0.967503i | \(0.418629\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.5885i | 0.575313i | 0.957734 | + | 0.287656i | \(0.0928761\pi\) | ||||
−0.957734 | + | 0.287656i | \(0.907124\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.248711i | 0.00977785i | 0.999988 | + | 0.00488893i | \(0.00155620\pi\) | ||||
−0.999988 | + | 0.00488893i | \(0.998444\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.3923 | 0.525694 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.53590i | 0.0992374i | 0.998768 | + | 0.0496187i | \(0.0158006\pi\) | ||||
−0.998768 | + | 0.0496187i | \(0.984199\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.53590 | −0.0987846 | −0.0493923 | − | 0.998779i | \(-0.515728\pi\) | ||||
−0.0493923 | + | 0.998779i | \(0.515728\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.3923 | 0.598691 | 0.299346 | − | 0.954145i | \(-0.403232\pi\) | ||||
0.299346 | + | 0.954145i | \(0.403232\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 26.7846i | 1.03710i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.92820 | 0.267460 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 38.3923i | − 1.47991i | −0.672654 | − | 0.739957i | \(-0.734846\pi\) | ||||
0.672654 | − | 0.739957i | \(-0.265154\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 40.6410i | 1.56196i | 0.624555 | + | 0.780981i | \(0.285280\pi\) | ||||
−0.624555 | + | 0.780981i | \(0.714720\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.00000 | 0.0767530 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 21.4641i | − 0.821301i | −0.911793 | − | 0.410651i | \(-0.865302\pi\) | ||||
0.911793 | − | 0.410651i | \(-0.134698\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −39.7128 | −1.51294 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.0000 | −0.380418 | −0.190209 | − | 0.981744i | \(-0.560917\pi\) | ||||
−0.190209 | + | 0.981744i | \(0.560917\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 52.9808i | − 2.00679i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.8756 | 0.675154 | 0.337577 | − | 0.941298i | \(-0.390393\pi\) | ||||
0.337577 | + | 0.941298i | \(0.390393\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 27.6603i | 1.04323i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 16.7321i | − 0.629274i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.5359 | −0.395684 | −0.197842 | − | 0.980234i | \(-0.563393\pi\) | ||||
−0.197842 | + | 0.980234i | \(0.563393\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 20.5359i | − 0.769075i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17.1962 | −0.641308 | −0.320654 | − | 0.947196i | \(-0.603903\pi\) | ||||
−0.320654 | + | 0.947196i | \(0.603903\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −50.2487 | −1.87136 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 29.1769i | 1.08211i | 0.840987 | + | 0.541056i | \(0.181975\pi\) | ||||
−0.840987 | + | 0.541056i | \(0.818025\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.4641 | 0.571960 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 43.5692i | 1.60927i | 0.593773 | + | 0.804633i | \(0.297638\pi\) | ||||
−0.593773 | + | 0.804633i | \(0.702362\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.0718i | 0.407835i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26.1769 | 0.962933 | 0.481467 | − | 0.876464i | \(-0.340104\pi\) | ||||
0.481467 | + | 0.876464i | \(0.340104\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.41154i | 0.198530i | 0.995061 | + | 0.0992651i | \(0.0316492\pi\) | ||||
−0.995061 | + | 0.0992651i | \(0.968351\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.46410 | −0.345811 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40.7846 | 1.48825 | 0.744126 | − | 0.668040i | \(-0.232866\pi\) | ||||
0.744126 | + | 0.668040i | \(0.232866\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.3923i | 0.741171i | 0.928798 | + | 0.370585i | \(0.120843\pi\) | ||||
−0.928798 | + | 0.370585i | \(0.879157\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 30.1244 | 1.09201 | 0.546004 | − | 0.837783i | \(-0.316149\pi\) | ||||
0.546004 | + | 0.837783i | \(0.316149\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 21.6603i | 0.784154i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 42.2487i | − 1.52551i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −35.2487 | −1.27110 | −0.635551 | − | 0.772059i | \(-0.719227\pi\) | ||||
−0.635551 | + | 0.772059i | \(0.719227\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 17.6603i | − 0.635195i | −0.948226 | − | 0.317598i | \(-0.897124\pi\) | ||||
0.948226 | − | 0.317598i | \(-0.102876\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 49.9808 | 1.79075 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.3923 | −0.693911 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 36.1962i | 1.29025i | 0.764076 | + | 0.645127i | \(0.223195\pi\) | ||||
−0.764076 | + | 0.645127i | \(0.776805\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.928203 | −0.0330031 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 21.8564i | − 0.776144i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 23.3205i | 0.826055i | 0.910719 | + | 0.413027i | \(0.135529\pi\) | ||||
−0.910719 | + | 0.413027i | \(0.864471\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.00000 | −0.212265 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.339746i | 0.0119894i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8.41154 | −0.295734 | −0.147867 | − | 0.989007i | \(-0.547241\pi\) | ||||
−0.147867 | + | 0.989007i | \(0.547241\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −25.2487 | −0.886602 | −0.443301 | − | 0.896373i | \(-0.646193\pi\) | ||||
−0.443301 | + | 0.896373i | \(0.646193\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14.5885i | 0.510386i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.33975 | −0.116558 | −0.0582790 | − | 0.998300i | \(-0.518561\pi\) | ||||
−0.0582790 | + | 0.998300i | \(0.518561\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 16.9282i | − 0.590080i | −0.955485 | − | 0.295040i | \(-0.904667\pi\) | ||||
0.955485 | − | 0.295040i | \(-0.0953330\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 45.4641i | − 1.58094i | −0.612500 | − | 0.790471i | \(-0.709836\pi\) | ||||
0.612500 | − | 0.790471i | \(-0.290164\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 51.7846 | 1.79855 | 0.899277 | − | 0.437380i | \(-0.144093\pi\) | ||||
0.899277 | + | 0.437380i | \(0.144093\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.19615i | 0.0760922i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8.41154 | −0.290399 | −0.145199 | − | 0.989402i | \(-0.546382\pi\) | ||||
−0.145199 | + | 0.989402i | \(0.546382\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 30.7846 | 1.06154 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 21.8564i | − 0.750995i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 21.4641 | 0.735780 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 0.196152i | − 0.00671613i | −0.999994 | − | 0.00335807i | \(-0.998931\pi\) | ||||
0.999994 | − | 0.00335807i | \(-0.00106891\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 29.0718i | − 0.993074i | −0.868016 | − | 0.496537i | \(-0.834605\pi\) | ||||
0.868016 | − | 0.496537i | \(-0.165395\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.78461 | −0.265607 | −0.132804 | − | 0.991142i | \(-0.542398\pi\) | ||||
−0.132804 | + | 0.991142i | \(0.542398\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 49.5167i | 1.68557i | 0.538253 | + | 0.842783i | \(0.319085\pi\) | ||||
−0.538253 | + | 0.842783i | \(0.680915\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −24.9282 | −0.845631 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 34.9282 | 1.18350 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 14.2487i | − 0.481145i | −0.970631 | − | 0.240572i | \(-0.922665\pi\) | ||||
0.970631 | − | 0.240572i | \(-0.0773351\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.80385 | −0.229227 | −0.114614 | − | 0.993410i | \(-0.536563\pi\) | ||||
−0.114614 | + | 0.993410i | \(0.536563\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 46.8372i | − 1.57620i | −0.615550 | − | 0.788098i | \(-0.711066\pi\) | ||||
0.615550 | − | 0.788098i | \(-0.288934\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13.2679i | 0.445494i | 0.974876 | + | 0.222747i | \(0.0715024\pi\) | ||||
−0.974876 | + | 0.222747i | \(0.928498\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.4641 | 0.384494 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 5.66025i | − 0.189413i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −45.8372 | −1.52876 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 34.3923 | 1.14577 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.21539i | 0.0403564i | 0.999796 | + | 0.0201782i | \(0.00642335\pi\) | ||||
−0.999796 | + | 0.0201782i | \(0.993577\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.80385 | 0.225422 | 0.112711 | − | 0.993628i | \(-0.464047\pi\) | ||||
0.112711 | + | 0.993628i | \(0.464047\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 26.1962i | − 0.866966i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 28.0526i | − 0.926377i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −51.3923 | −1.69528 | −0.847638 | − | 0.530575i | \(-0.821976\pi\) | ||||
−0.847638 | + | 0.530575i | \(0.821976\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 61.1769i | 2.01366i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.48334 | 0.0486668 | 0.0243334 | − | 0.999704i | \(-0.492254\pi\) | ||||
0.0243334 | + | 0.999704i | \(0.492254\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.07180 | −0.0679004 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 19.0718i | − 0.623048i | −0.950238 | − | 0.311524i | \(-0.899160\pi\) | ||||
0.950238 | − | 0.311524i | \(-0.100840\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.53590 | 0.278262 | 0.139131 | − | 0.990274i | \(-0.455569\pi\) | ||||
0.139131 | + | 0.990274i | \(0.455569\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 38.7846i | − 1.26300i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 52.6410i | − 1.71060i | −0.518130 | − | 0.855302i | \(-0.673372\pi\) | ||||
0.518130 | − | 0.855302i | \(-0.326628\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.07180 | 0.0347920 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.53590i | 0.0821458i | 0.999156 | + | 0.0410729i | \(0.0130776\pi\) | ||||
−0.999156 | + | 0.0410729i | \(0.986922\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −12.0000 | −0.387500 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.14359 | 0.133664 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 7.41154i | − 0.238339i | −0.992874 | − | 0.119170i | \(-0.961977\pi\) | ||||
0.992874 | − | 0.119170i | \(-0.0380232\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22.2679 | −0.714612 | −0.357306 | − | 0.933987i | \(-0.616305\pi\) | ||||
−0.357306 | + | 0.933987i | \(0.616305\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 42.0526i | − 1.34814i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.39230i | 0.140522i | 0.997529 | + | 0.0702611i | \(0.0223833\pi\) | ||||
−0.997529 | + | 0.0702611i | \(0.977617\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.00000 | −0.287641 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 52.7321i | 1.68189i | 0.541120 | + | 0.840946i | \(0.318001\pi\) | ||||
−0.541120 | + | 0.840946i | \(0.681999\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.3205 | 0.359971 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 55.7846 | 1.77206 | 0.886028 | − | 0.463631i | \(-0.153454\pi\) | ||||
0.886028 | + | 0.463631i | \(0.153454\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 52.1962i | − 1.65307i | −0.562886 | − | 0.826534i | \(-0.690309\pi\) | ||||
0.562886 | − | 0.826534i | \(-0.309691\pi\) | |||||||
\(998\) | 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 | 8100.2.d.l.649.4 | 4 | ||
3.2 | odd | 2 | 8100.2.d.m.649.4 | 4 | |||
5.2 | odd | 4 | 1620.2.a.h.1.1 | yes | 2 | ||
5.3 | odd | 4 | 8100.2.a.s.1.2 | 2 | |||
5.4 | even | 2 | inner | 8100.2.d.l.649.1 | 4 | ||
15.2 | even | 4 | 1620.2.a.g.1.1 | ✓ | 2 | ||
15.8 | even | 4 | 8100.2.a.t.1.2 | 2 | |||
15.14 | odd | 2 | 8100.2.d.m.649.1 | 4 | |||
20.7 | even | 4 | 6480.2.a.bp.1.2 | 2 | |||
45.2 | even | 12 | 1620.2.i.n.1081.2 | 4 | |||
45.7 | odd | 12 | 1620.2.i.m.1081.2 | 4 | |||
45.22 | odd | 12 | 1620.2.i.m.541.2 | 4 | |||
45.32 | even | 12 | 1620.2.i.n.541.2 | 4 | |||
60.47 | odd | 4 | 6480.2.a.bh.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1620.2.a.g.1.1 | ✓ | 2 | 15.2 | even | 4 | ||
1620.2.a.h.1.1 | yes | 2 | 5.2 | odd | 4 | ||
1620.2.i.m.541.2 | 4 | 45.22 | odd | 12 | |||
1620.2.i.m.1081.2 | 4 | 45.7 | odd | 12 | |||
1620.2.i.n.541.2 | 4 | 45.32 | even | 12 | |||
1620.2.i.n.1081.2 | 4 | 45.2 | even | 12 | |||
6480.2.a.bh.1.2 | 2 | 60.47 | odd | 4 | |||
6480.2.a.bp.1.2 | 2 | 20.7 | even | 4 | |||
8100.2.a.s.1.2 | 2 | 5.3 | odd | 4 | |||
8100.2.a.t.1.2 | 2 | 15.8 | even | 4 | |||
8100.2.d.l.649.1 | 4 | 5.4 | even | 2 | inner | ||
8100.2.d.l.649.4 | 4 | 1.1 | even | 1 | trivial | ||
8100.2.d.m.649.1 | 4 | 15.14 | odd | 2 | |||
8100.2.d.m.649.4 | 4 | 3.2 | odd | 2 |