Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4560,2,Mod(2431,4560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4560, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 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("4560.2431");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4560 = 2^{4} \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4560.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: | \(36.4117833217\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 35x^{10} + 202x^{8} + 362x^{6} + 245x^{4} + 63x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{11}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2431.4 | ||
Root | \(2.03924i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4560.2431 |
Dual form | 4560.2.d.l.2431.9 |
$q$-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 \(\left(\mathbb{Z}/4560\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(1711\) | \(1921\) | \(2737\) | \(3041\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.79053i | − | 1.05472i | −0.849642 | − | 0.527360i | \(-0.823182\pi\) | ||
0.849642 | − | 0.527360i | \(-0.176818\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 5.01148i | − | 1.51102i | −0.655139 | − | 0.755508i | \(-0.727390\pi\) | ||
0.655139 | − | 0.755508i | \(-0.272610\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3.47756i | − | 0.964503i | −0.876033 | − | 0.482251i | \(-0.839819\pi\) | ||
0.876033 | − | 0.482251i | \(-0.160181\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.25824 | 0.547703 | 0.273852 | − | 0.961772i | \(-0.411702\pi\) | ||||
0.273852 | + | 0.961772i | \(0.411702\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.19273 | − | 1.19207i | 0.961878 | − | 0.273479i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 2.79053i | − | 0.608943i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 0.453944i | − | 0.0946539i | −0.998879 | − | 0.0473269i | \(-0.984930\pi\) | ||
0.998879 | − | 0.0473269i | \(-0.0150703\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.54737i | 0.287340i | 0.989626 | + | 0.143670i | \(0.0458904\pi\) | ||||
−0.989626 | + | 0.143670i | \(0.954110\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.12801 | −0.921018 | −0.460509 | − | 0.887655i | \(-0.652333\pi\) | ||||
−0.460509 | + | 0.887655i | \(0.652333\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 5.01148i | − | 0.872386i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 2.79053i | − | 0.471685i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.77172i | 0.784466i | 0.919866 | + | 0.392233i | \(0.128297\pi\) | ||||
−0.919866 | + | 0.392233i | \(0.871703\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 3.47756i | − | 0.556856i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.33658i | 0.364913i | 0.983214 | + | 0.182457i | \(0.0584049\pi\) | ||||
−0.983214 | + | 0.182457i | \(0.941595\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.78713i | 0.272534i | 0.990672 | + | 0.136267i | \(0.0435106\pi\) | ||||
−0.990672 | + | 0.136267i | \(0.956489\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 8.48904i | − | 1.23825i | −0.785291 | − | 0.619127i | \(-0.787487\pi\) | ||
0.785291 | − | 0.619127i | \(-0.212513\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.787044 | −0.112435 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.25824 | 0.316217 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.01016i | 0.413477i | 0.978396 | + | 0.206738i | \(0.0662849\pi\) | ||||
−0.978396 | + | 0.206738i | \(0.933715\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 5.01148i | − | 0.675747i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.19273 | − | 1.19207i | 0.555341 | − | 0.157893i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.34096 | −0.174579 | −0.0872894 | − | 0.996183i | \(-0.527820\pi\) | ||||
−0.0872894 | + | 0.996183i | \(0.527820\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.21296 | −0.795488 | −0.397744 | − | 0.917497i | \(-0.630207\pi\) | ||||
−0.397744 | + | 0.917497i | \(0.630207\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 2.79053i | − | 0.351573i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 3.47756i | − | 0.431339i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.58856 | −0.438412 | −0.219206 | − | 0.975679i | \(-0.570347\pi\) | ||||
−0.219206 | + | 0.975679i | \(0.570347\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 0.453944i | − | 0.0546484i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.38625 | −0.639230 | −0.319615 | − | 0.947547i | \(-0.603554\pi\) | ||||
−0.319615 | + | 0.947547i | \(0.603554\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.7717 | −1.37777 | −0.688887 | − | 0.724869i | \(-0.741900\pi\) | ||||
−0.688887 | + | 0.724869i | \(0.741900\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −13.9847 | −1.59370 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.18919 | 0.246303 | 0.123152 | − | 0.992388i | \(-0.460700\pi\) | ||||
0.123152 | + | 0.992388i | \(0.460700\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.49244i | 1.04193i | 0.853578 | + | 0.520965i | \(0.174428\pi\) | ||||
−0.853578 | + | 0.520965i | \(0.825572\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.25824 | 0.244940 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.54737i | 0.165896i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 3.89792i | − | 0.413179i | −0.978428 | − | 0.206589i | \(-0.933764\pi\) | ||
0.978428 | − | 0.206589i | \(-0.0662364\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.70424 | −1.01728 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.12801 | −0.531750 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.19273 | − | 1.19207i | 0.430165 | − | 0.122303i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.67697i | 0.170271i | 0.996369 | + | 0.0851354i | \(0.0271323\pi\) | ||||
−0.996369 | + | 0.0851354i | \(0.972868\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 5.01148i | − | 0.503672i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.10425 | −0.507891 | −0.253946 | − | 0.967218i | \(-0.581728\pi\) | ||||
−0.253946 | + | 0.967218i | \(0.581728\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.58856 | 0.353591 | 0.176796 | − | 0.984248i | \(-0.443427\pi\) | ||||
0.176796 | + | 0.984248i | \(0.443427\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 2.79053i | − | 0.272328i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.79769 | 0.947179 | 0.473589 | − | 0.880746i | \(-0.342958\pi\) | ||||
0.473589 | + | 0.880746i | \(0.342958\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.0765684i | 0.00733392i | 0.999993 | + | 0.00366696i | \(0.00116723\pi\) | ||||
−0.999993 | + | 0.00366696i | \(0.998833\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.77172i | 0.452912i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 17.2670i | − | 1.62434i | −0.583418 | − | 0.812172i | \(-0.698285\pi\) | ||
0.583418 | − | 0.812172i | \(-0.301715\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 0.453944i | − | 0.0423305i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 3.47756i | − | 0.321501i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 6.30168i | − | 0.577674i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −14.1149 | −1.28317 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.33658i | 0.210683i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.1831 | −0.903608 | −0.451804 | − | 0.892117i | \(-0.649219\pi\) | ||||
−0.451804 | + | 0.892117i | \(0.649219\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.78713i | 0.157348i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 16.8540i | − | 1.47254i | −0.676689 | − | 0.736269i | \(-0.736586\pi\) | ||
0.676689 | − | 0.736269i | \(-0.263414\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.32650 | − | 11.6999i | −0.288444 | − | 1.01451i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.58172 | 0.733186 | 0.366593 | − | 0.930381i | \(-0.380524\pi\) | ||||
0.366593 | + | 0.930381i | \(0.380524\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 12.1130i | − | 1.02741i | −0.857967 | − | 0.513705i | \(-0.828273\pi\) | ||
0.857967 | − | 0.513705i | \(-0.171727\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 8.48904i | − | 0.714906i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −17.4277 | −1.45738 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.54737i | 0.128502i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.787044 | −0.0649143 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.6423 | −1.44531 | −0.722655 | − | 0.691209i | \(-0.757079\pi\) | ||||
−0.722655 | + | 0.691209i | \(0.757079\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.4559 | 1.82743 | 0.913716 | − | 0.406354i | \(-0.133200\pi\) | ||||
0.913716 | + | 0.406354i | \(0.133200\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.25824 | 0.182568 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.12801 | −0.411892 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.75320 | 0.379346 | 0.189673 | − | 0.981847i | \(-0.439257\pi\) | ||||
0.189673 | + | 0.981847i | \(0.439257\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.01016i | 0.238721i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.26674 | −0.0998334 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.33369i | 0.104462i | 0.998635 | + | 0.0522312i | \(0.0166333\pi\) | ||||
−0.998635 | + | 0.0522312i | \(0.983367\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 5.01148i | − | 0.390143i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.1717 | 0.864493 | 0.432247 | − | 0.901755i | \(-0.357721\pi\) | ||||
0.432247 | + | 0.901755i | \(0.357721\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.906548 | 0.0697344 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.19273 | − | 1.19207i | 0.320626 | − | 0.0911596i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.69811i | 0.737333i | 0.929562 | + | 0.368667i | \(0.120186\pi\) | ||||
−0.929562 | + | 0.368667i | \(0.879814\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 2.79053i | − | 0.210944i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.34096 | −0.100793 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.67272 | 0.125025 | 0.0625123 | − | 0.998044i | \(-0.480089\pi\) | ||||
0.0625123 | + | 0.998044i | \(0.480089\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.1587i | 0.755091i | 0.925991 | + | 0.377546i | \(0.123232\pi\) | ||||
−0.925991 | + | 0.377546i | \(0.876768\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.21296 | −0.459275 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.77172i | 0.350824i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 11.3171i | − | 0.827589i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 2.79053i | − | 0.202981i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.2959i | 1.54091i | 0.637492 | + | 0.770457i | \(0.279972\pi\) | ||||
−0.637492 | + | 0.770457i | \(0.720028\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.7269i | 0.844117i | 0.906569 | + | 0.422059i | \(0.138692\pi\) | ||||
−0.906569 | + | 0.422059i | \(0.861308\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 3.47756i | − | 0.249034i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.1885 | 0.868398 | 0.434199 | − | 0.900817i | \(-0.357031\pi\) | ||||
0.434199 | + | 0.900817i | \(0.357031\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 15.7331i | − | 1.11529i | −0.830079 | − | 0.557645i | \(-0.811705\pi\) | ||
0.830079 | − | 0.557645i | \(-0.188295\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.58856 | −0.253117 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.31799 | 0.303064 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.33658i | 0.163194i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 0.453944i | − | 0.0315513i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.97401 | − | 21.0118i | −0.413231 | − | 1.45341i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.9810 | 1.71976 | 0.859881 | − | 0.510495i | \(-0.170538\pi\) | ||||
0.859881 | + | 0.510495i | \(0.170538\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.38625 | −0.369060 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.78713i | 0.121881i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.3098i | 0.971416i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −11.7717 | −0.795458 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 7.85317i | − | 0.528261i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.0781 | 0.674880 | 0.337440 | − | 0.941347i | \(-0.390439\pi\) | ||||
0.337440 | + | 0.941347i | \(0.390439\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 21.9442 | 1.45649 | 0.728244 | − | 0.685318i | \(-0.240337\pi\) | ||||
0.728244 | + | 0.685318i | \(0.240337\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.91648 | −0.258809 | −0.129404 | − | 0.991592i | \(-0.541307\pi\) | ||||
−0.129404 | + | 0.991592i | \(0.541307\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −13.9847 | −0.920123 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.98688 | 0.654262 | 0.327131 | − | 0.944979i | \(-0.393918\pi\) | ||||
0.327131 | + | 0.944979i | \(0.393918\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 8.48904i | − | 0.553764i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.18919 | 0.142203 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 8.43260i | − | 0.545459i | −0.962091 | − | 0.272730i | \(-0.912074\pi\) | ||
0.962091 | − | 0.272730i | \(-0.0879264\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 30.1280i | 1.94072i | 0.241668 | + | 0.970359i | \(0.422306\pi\) | ||||
−0.241668 | + | 0.970359i | \(0.577694\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.787044 | −0.0502824 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.14549 | − | 14.5805i | −0.263771 | − | 0.927734i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.49244i | 0.601559i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 19.8949i | − | 1.25575i | −0.778313 | − | 0.627876i | \(-0.783924\pi\) | ||
0.778313 | − | 0.627876i | \(-0.216076\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.27493 | −0.143024 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.25824 | 0.141416 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 1.93019i | − | 0.120402i | −0.998186 | − | 0.0602010i | \(-0.980826\pi\) | ||
0.998186 | − | 0.0602010i | \(-0.0191742\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.3156 | 0.827393 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.54737i | 0.0957801i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 5.66147i | − | 0.349101i | −0.984648 | − | 0.174551i | \(-0.944153\pi\) | ||
0.984648 | − | 0.174551i | \(-0.0558473\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.01016i | 0.184913i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 3.89792i | − | 0.238549i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.92150i | 0.239098i | 0.992828 | + | 0.119549i | \(0.0381449\pi\) | ||||
−0.992828 | + | 0.119549i | \(0.961855\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.6114i | 0.766090i | 0.923730 | + | 0.383045i | \(0.125125\pi\) | ||||
−0.923730 | + | 0.383045i | \(0.874875\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −9.70424 | −0.587327 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 5.01148i | − | 0.302203i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.39936 | 0.204248 | 0.102124 | − | 0.994772i | \(-0.467436\pi\) | ||||
0.102124 | + | 0.994772i | \(0.467436\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.12801 | −0.307006 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.44525i | 0.444147i | 0.975030 | + | 0.222073i | \(0.0712824\pi\) | ||||
−0.975030 | + | 0.222073i | \(0.928718\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.08809i | 0.302455i | 0.988499 | + | 0.151228i | \(0.0483226\pi\) | ||||
−0.988499 | + | 0.151228i | \(0.951677\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.19273 | − | 1.19207i | 0.248356 | − | 0.0706119i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.52030 | 0.384881 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.9004 | −0.700021 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.67697i | 0.0983059i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 22.8707i | − | 1.33612i | −0.744108 | − | 0.668059i | \(-0.767125\pi\) | ||
0.744108 | − | 0.668059i | \(-0.232875\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.34096 | −0.0780740 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 5.01148i | − | 0.290795i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.57862 | −0.0912939 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.98703 | 0.287448 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.10425 | −0.293231 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.21296 | −0.355753 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −33.7089 | −1.92387 | −0.961933 | − | 0.273285i | \(-0.911890\pi\) | ||||
−0.961933 | + | 0.273285i | \(0.911890\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.58856 | 0.204146 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 4.53197i | − | 0.256984i | −0.991711 | − | 0.128492i | \(-0.958986\pi\) | ||
0.991711 | − | 0.128492i | \(-0.0410137\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.9549 | 1.24096 | 0.620481 | − | 0.784222i | \(-0.286937\pi\) | ||||
0.620481 | + | 0.784222i | \(0.286937\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − | 2.79053i | − | 0.157228i | ||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 9.73402i | − | 0.546717i | −0.961912 | − | 0.273358i | \(-0.911866\pi\) | ||
0.961912 | − | 0.273358i | \(-0.0881345\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.75463 | 0.434176 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.79769 | 0.546854 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.46818 | − | 2.69197i | 0.526824 | − | 0.149785i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 3.47756i | − | 0.192901i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.0765684i | 0.00423424i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −23.6889 | −1.30601 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.7097 | 1.08334 | 0.541672 | − | 0.840590i | \(-0.317791\pi\) | ||||
0.541672 | + | 0.840590i | \(0.317791\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.77172i | 0.261489i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.58856 | −0.196064 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.9177i | 1.46630i | 0.680068 | + | 0.733149i | \(0.261950\pi\) | ||||
−0.680068 | + | 0.733149i | \(0.738050\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 17.2670i | − | 0.937816i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 25.6989i | 1.39167i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 17.3374i | − | 0.936133i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 0.453944i | − | 0.0244395i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.345111i | 0.0185265i | 0.999957 | + | 0.00926325i | \(0.00294863\pi\) | ||||
−0.999957 | + | 0.00926325i | \(0.997051\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −33.9623 | −1.81796 | −0.908979 | − | 0.416842i | \(-0.863137\pi\) | ||||
−0.908979 | + | 0.416842i | \(0.863137\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 3.47756i | − | 0.185619i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25.5090 | 1.35771 | 0.678854 | − | 0.734274i | \(-0.262477\pi\) | ||||
0.678854 | + | 0.734274i | \(0.262477\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.38625 | −0.285872 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 6.30168i | − | 0.333520i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 7.48070i | − | 0.394816i | −0.980321 | − | 0.197408i | \(-0.936748\pi\) | ||
0.980321 | − | 0.197408i | \(-0.0632524\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.1580 | − | 9.99603i | 0.850419 | − | 0.526107i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −14.1149 | −0.740840 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11.7717 | −0.616159 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.36401i | 0.123400i | 0.998095 | + | 0.0617002i | \(0.0196523\pi\) | ||||
−0.998095 | + | 0.0617002i | \(0.980348\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.33658i | 0.121638i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.39993 | 0.436102 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 2.58300i | − | 0.133743i | −0.997762 | − | 0.0668713i | \(-0.978698\pi\) | ||
0.997762 | − | 0.0668713i | \(-0.0213017\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.38109 | 0.277140 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.3961 | 1.35588 | 0.677938 | − | 0.735119i | \(-0.262874\pi\) | ||||
0.677938 | + | 0.735119i | \(0.262874\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.1831 | −0.521699 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −23.9156 | −1.22203 | −0.611015 | − | 0.791619i | \(-0.709239\pi\) | ||||
−0.611015 | + | 0.791619i | \(0.709239\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.9847 | −0.712724 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.78713i | 0.0908448i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.2544 | −0.519921 | −0.259960 | − | 0.965619i | \(-0.583709\pi\) | ||||
−0.259960 | + | 0.965619i | \(0.583709\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 1.02511i | − | 0.0518423i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 16.8540i | − | 0.850170i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.18919 | 0.110150 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.5809 | −0.581230 | −0.290615 | − | 0.956840i | \(-0.593860\pi\) | ||||
−0.290615 | + | 0.956840i | \(0.593860\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.32650 | − | 11.6999i | −0.166533 | − | 0.585729i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 13.4206i | − | 0.670191i | −0.942184 | − | 0.335095i | \(-0.891231\pi\) | ||
0.942184 | − | 0.335095i | \(-0.108769\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 17.8330i | 0.888324i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 23.9134 | 1.18534 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.4595i | 0.912764i | 0.889784 | + | 0.456382i | \(0.150855\pi\) | ||||
−0.889784 | + | 0.456382i | \(0.849145\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.58172 | 0.423305 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.74200i | 0.184132i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.49244i | 0.465966i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 12.1130i | − | 0.593175i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 22.8974i | − | 1.11861i | −0.828961 | − | 0.559307i | \(-0.811067\pi\) | ||
0.828961 | − | 0.559307i | \(-0.188933\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 3.89670i | − | 0.189914i | −0.995481 | − | 0.0949568i | \(-0.969729\pi\) | ||
0.995481 | − | 0.0949568i | \(-0.0302713\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 8.48904i | − | 0.412751i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.25824 | 0.109541 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 17.3374i | 0.839017i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −17.4277 | −0.841419 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −41.2101 | −1.98502 | −0.992510 | − | 0.122164i | \(-0.961017\pi\) | ||||
−0.992510 | + | 0.122164i | \(0.961017\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 27.3990i | 1.31671i | 0.752706 | + | 0.658357i | \(0.228748\pi\) | ||||
−0.752706 | + | 0.658357i | \(0.771252\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.54737i | 0.0741909i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.541132 | − | 1.90326i | −0.0258858 | − | 0.0910455i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 27.6076 | 1.31764 | 0.658820 | − | 0.752301i | \(-0.271056\pi\) | ||||
0.658820 | + | 0.752301i | \(0.271056\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.787044 | −0.0374783 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.94502i | 0.472502i | 0.971692 | + | 0.236251i | \(0.0759188\pi\) | ||||
−0.971692 | + | 0.236251i | \(0.924081\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 3.89792i | − | 0.184779i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −17.6423 | −0.834450 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 25.5454i | − | 1.20556i | −0.797906 | − | 0.602781i | \(-0.794059\pi\) | ||
0.797906 | − | 0.602781i | \(-0.205941\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.7097 | 0.551390 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 22.4559 | 1.05507 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.70424 | −0.454942 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.3655 | −0.578433 | −0.289217 | − | 0.957264i | \(-0.593395\pi\) | ||||
−0.289217 | + | 0.957264i | \(0.593395\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.25824 | 0.105406 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.94867 | −0.463356 | −0.231678 | − | 0.972793i | \(-0.574422\pi\) | ||||
−0.231678 | + | 0.972793i | \(0.574422\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.4744i | 0.858580i | 0.903167 | + | 0.429290i | \(0.141236\pi\) | ||||
−0.903167 | + | 0.429290i | \(0.858764\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.12801 | −0.237806 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.09632i | 0.420928i | 0.977602 | + | 0.210464i | \(0.0674974\pi\) | ||||
−0.977602 | + | 0.210464i | \(0.932503\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.0140i | 0.462402i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.75320 | 0.219016 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.95615 | 0.411804 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.19273 | − | 1.19207i | 0.192376 | − | 0.0546958i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.01016i | 0.137826i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 20.5135i | − | 0.937284i | −0.883388 | − | 0.468642i | \(-0.844743\pi\) | ||
0.883388 | − | 0.468642i | \(-0.155257\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.5940 | 0.756620 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.26674 | −0.0576388 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.67697i | 0.0761474i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.2253 | 1.18838 | 0.594192 | − | 0.804323i | \(-0.297472\pi\) | ||||
0.594192 | + | 0.804323i | \(0.297472\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.33369i | 0.0603114i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.1642i | 0.458702i | 0.973344 | + | 0.229351i | \(0.0736603\pi\) | ||||
−0.973344 | + | 0.229351i | \(0.926340\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.49434i | 0.157377i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 5.01148i | − | 0.225249i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 15.0305i | 0.674209i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 4.94452i | − | 0.221347i | −0.993857 | − | 0.110674i | \(-0.964699\pi\) | ||
0.993857 | − | 0.110674i | \(-0.0353008\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.1717 | 0.499115 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 20.1453i | − | 0.898233i | −0.893473 | − | 0.449116i | \(-0.851739\pi\) | ||
0.893473 | − | 0.449116i | \(-0.148261\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.10425 | −0.227136 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.906548 | 0.0402612 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 10.7845i | − | 0.478013i | −0.971018 | − | 0.239006i | \(-0.923178\pi\) | ||
0.971018 | − | 0.239006i | \(-0.0768217\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 32.8493i | 1.45317i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.19273 | − | 1.19207i | 0.185114 | − | 0.0526310i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.58856 | 0.158131 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −42.5426 | −1.87102 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.69811i | 0.425700i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.2501i | 0.974794i | 0.873181 | + | 0.487397i | \(0.162053\pi\) | ||||
−0.873181 | + | 0.487397i | \(0.837947\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.5616 | −0.767917 | −0.383958 | − | 0.923350i | \(-0.625439\pi\) | ||||
−0.383958 | + | 0.923350i | \(0.625439\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 2.79053i | − | 0.121789i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −11.5803 | −0.504444 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.7939 | 0.991041 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.34096 | −0.0581929 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.12562 | 0.351960 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.79769 | 0.423591 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.67272 | 0.0721830 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.94425i | 0.169891i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.4645 | −0.793851 | −0.396926 | − | 0.917851i | \(-0.629923\pi\) | ||||
−0.396926 | + | 0.917851i | \(0.629923\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.1587i | 0.435952i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.0765684i | 0.00327983i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.3273 | 0.698105 | 0.349053 | − | 0.937103i | \(-0.386503\pi\) | ||||
0.349053 | + | 0.937103i | \(0.386503\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.21296 | −0.265163 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.84457 | + | 6.48772i | 0.0785815 | + | 0.276386i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 6.10900i | − | 0.259781i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.77172i | 0.202548i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −34.3987 | −1.45752 | −0.728760 | − | 0.684769i | \(-0.759903\pi\) | ||||
−0.728760 | + | 0.684769i | \(0.759903\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.21485 | 0.262860 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 11.3171i | − | 0.477809i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21.1471 | −0.891242 | −0.445621 | − | 0.895222i | \(-0.647017\pi\) | ||||
−0.445621 | + | 0.895222i | \(0.647017\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 17.2670i | − | 0.726429i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 2.79053i | − | 0.117191i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 26.5895i | − | 1.11469i | −0.830281 | − | 0.557344i | \(-0.811820\pi\) | ||
0.830281 | − | 0.557344i | \(-0.188180\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 27.6017i | − | 1.15509i | −0.816358 | − | 0.577547i | \(-0.804010\pi\) | ||
0.816358 | − | 0.577547i | \(-0.195990\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 21.2959i | 0.889647i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 0.453944i | − | 0.0189308i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.2290 | 0.967036 | 0.483518 | − | 0.875334i | \(-0.339359\pi\) | ||||
0.483518 | + | 0.875334i | \(0.339359\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.7269i | 0.487351i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 26.4889 | 1.09895 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.0853 | 0.624771 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 3.47756i | − | 0.143780i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 24.5441i | 1.01305i | 0.862227 | + | 0.506523i | \(0.169069\pi\) | ||||
−0.862227 | + | 0.506523i | \(0.830931\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −21.5004 | + | 6.11293i | −0.885906 | + | 0.251879i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12.1885 | 0.501370 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 30.1832 | 1.23947 | 0.619737 | − | 0.784809i | \(-0.287239\pi\) | ||||
0.619737 | + | 0.784809i | \(0.287239\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 6.30168i | − | 0.258344i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 15.7331i | − | 0.643913i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −26.6559 | −1.08913 | −0.544566 | − | 0.838718i | \(-0.683306\pi\) | ||||
−0.544566 | + | 0.838718i | \(0.683306\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 6.28750i | − | 0.256472i | −0.991744 | − | 0.128236i | \(-0.959068\pi\) | ||
0.991744 | − | 0.128236i | \(-0.0409315\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.58856 | −0.146137 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −14.1149 | −0.573852 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.4629 | 0.749387 | 0.374694 | − | 0.927149i | \(-0.377748\pi\) | ||||
0.374694 | + | 0.927149i | \(0.377748\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.31799 | 0.174974 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −29.5212 | −1.19430 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.2890 | 0.940634 | 0.470317 | − | 0.882498i | \(-0.344140\pi\) | ||||
0.470317 | + | 0.882498i | \(0.344140\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.33658i | 0.0942201i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 30.2276 | 1.21692 | 0.608458 | − | 0.793586i | \(-0.291788\pi\) | ||||
0.608458 | + | 0.793586i | \(0.291788\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.9782i | 0.441249i | 0.975359 | + | 0.220625i | \(0.0708096\pi\) | ||||
−0.975359 | + | 0.220625i | \(0.929190\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 0.453944i | − | 0.0182161i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −10.8773 | −0.435788 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.97401 | − | 21.0118i | −0.238579 | − | 0.839129i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.7757i | 0.429655i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.188288i | 0.00749561i | 0.999993 | + | 0.00374780i | \(0.00119297\pi\) | ||||
−0.999993 | + | 0.00374780i | \(0.998807\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 24.9810 | 0.992905 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10.1831 | −0.404106 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.73700i | 0.108444i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.38625 | −0.213077 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 19.5155i | − | 0.770817i | −0.922746 | − | 0.385409i | \(-0.874061\pi\) | ||
0.922746 | − | 0.385409i | \(-0.125939\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.6799i | 0.854972i | 0.904022 | + | 0.427486i | \(0.140601\pi\) | ||||
−0.904022 | + | 0.427486i | \(0.859399\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.78713i | 0.0703681i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.19675i | 0.282933i | 0.989943 | + | 0.141467i | \(0.0451818\pi\) | ||||
−0.989943 | + | 0.141467i | \(0.954818\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.72021i | 0.263791i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 14.3098i | 0.560847i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.95947 | −0.350611 | −0.175305 | − | 0.984514i | \(-0.556091\pi\) | ||||
−0.175305 | + | 0.984514i | \(0.556091\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 16.8540i | − | 0.658539i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11.7717 | −0.459258 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.61309 | 0.179700 | 0.0898502 | − | 0.995955i | \(-0.471361\pi\) | ||||
0.0898502 | + | 0.995955i | \(0.471361\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.6833i | 0.998964i | 0.866324 | + | 0.499482i | \(0.166476\pi\) | ||||
−0.866324 | + | 0.499482i | \(0.833524\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 7.85317i | − | 0.304992i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.32650 | − | 11.6999i | −0.128996 | − | 0.453704i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.702422 | 0.0271979 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10.0781 | 0.389642 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 31.1361i | 1.20200i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.0542i | 0.927221i | 0.886039 | + | 0.463610i | \(0.153446\pi\) | ||||
−0.886039 | + | 0.463610i | \(0.846554\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 16.5914i | − | 0.637659i | −0.947812 | − | 0.318830i | \(-0.896710\pi\) | ||
0.947812 | − | 0.318830i | \(-0.103290\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.67964 | 0.179588 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 21.9442 | 0.840904 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.79325 | 0.221672 | 0.110836 | − | 0.993839i | \(-0.464647\pi\) | ||||
0.110836 | + | 0.993839i | \(0.464647\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.58172 | 0.327891 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.91648 | −0.149423 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10.4680 | 0.398800 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 38.9878i | 1.48317i | 0.670861 | + | 0.741583i | \(0.265925\pi\) | ||||
−0.670861 | + | 0.741583i | \(0.734075\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −13.9847 | −0.531233 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 12.1130i | − | 0.459472i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.27656i | 0.199864i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.98688 | 0.377739 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.3226 | 1.14527 | 0.572635 | − | 0.819811i | \(-0.305921\pi\) | ||||
0.572635 | + | 0.819811i | \(0.305921\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.68821 | + | 20.0065i | 0.214535 | + | 0.754561i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 8.48904i | − | 0.319716i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14.2435i | 0.535683i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.21138 | −0.158162 | −0.0790808 | − | 0.996868i | \(-0.525199\pi\) | ||||
−0.0790808 | + | 0.996868i | \(0.525199\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.18919 | 0.0821011 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.32783i | 0.0871779i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −17.4277 | −0.651760 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 8.43260i | − | 0.314921i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 45.7427i | − | 1.70591i | −0.521980 | − | 0.852957i | \(-0.674807\pi\) | ||
0.521980 | − | 0.852957i | \(-0.325193\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 10.0140i | − | 0.372940i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 30.1280i | 1.12047i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.54737i | 0.0574680i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 13.6129i | − | 0.504876i | −0.967613 | − | 0.252438i | \(-0.918768\pi\) | ||
0.967613 | − | 0.252438i | \(-0.0812324\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.03576i | 0.149268i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.680329 | 0.0251285 | 0.0125643 | − | 0.999921i | \(-0.496001\pi\) | ||||
0.0125643 | + | 0.999921i | \(0.496001\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.787044 | −0.0290305 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 17.9840i | 0.662448i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 30.8656i | − | 1.13541i | −0.823232 | − | 0.567704i | \(-0.807832\pi\) | ||
0.823232 | − | 0.567704i | \(-0.192168\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.14549 | − | 14.5805i | −0.152288 | − | 0.535627i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −30.9470 | −1.13534 | −0.567668 | − | 0.823258i | \(-0.692154\pi\) | ||||
−0.567668 | + | 0.823258i | \(0.692154\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −17.6423 | −0.646363 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9.49244i | 0.347310i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 27.3407i | − | 0.999008i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34.0255 | 1.24161 | 0.620804 | − | 0.783966i | \(-0.286806\pi\) | ||||
0.620804 | + | 0.783966i | \(0.286806\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 19.8949i | − | 0.725009i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 22.4559 | 0.817252 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34.9975 | −1.27200 | −0.636002 | − | 0.771687i | \(-0.719413\pi\) | ||||
−0.636002 | + | 0.771687i | \(0.719413\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.27493 | −0.0825747 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.12865 | 0.113414 | 0.0567068 | − | 0.998391i | \(-0.481940\pi\) | ||||
0.0567068 | + | 0.998391i | \(0.481940\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.213666 | 0.00773524 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.25824 | 0.0816468 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.66329i | 0.168382i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.4129 | −0.483682 | −0.241841 | − | 0.970316i | \(-0.577751\pi\) | ||||
−0.241841 | + | 0.970316i | \(0.577751\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 1.93019i | − | 0.0695141i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 16.3402i | − | 0.587716i | −0.955849 | − | 0.293858i | \(-0.905061\pi\) | ||
0.955849 | − | 0.293858i | \(-0.0949392\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.12801 | −0.184204 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 13.3156 | 0.477695 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.78536 | + | 9.79666i | 0.0997960 | + | 0.351002i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 26.9931i | 0.965887i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.54737i | 0.0552987i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.75320 | 0.169649 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −38.2407 | −1.36313 | −0.681566 | − | 0.731757i | \(-0.738701\pi\) | ||||
−0.681566 | + | 0.731757i | \(0.738701\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 5.66147i | − | 0.201554i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −48.1841 | −1.71323 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 21.6060i | 0.767250i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.01016i | 0.106759i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 9.62113i | − | 0.340798i | −0.985375 | − | 0.170399i | \(-0.945494\pi\) | ||
0.985375 | − | 0.170399i | \(-0.0545056\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 19.1703i | − | 0.678196i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 3.89792i | − | 0.137726i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 58.9936i | 2.08184i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.26674 | −0.0446468 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.92150i | 0.138043i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 27.3647 | 0.962092 | 0.481046 | − | 0.876695i | \(-0.340257\pi\) | ||||
0.481046 | + | 0.876695i | \(0.340257\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −52.6092 | −1.84736 | −0.923680 | − | 0.383165i | \(-0.874834\pi\) | ||||
−0.923680 | + | 0.383165i | \(0.874834\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.6114i | 0.442302i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.33369i | 0.0467170i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.13038 | + | 7.49294i | 0.0745324 | + | 0.262145i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −9.70424 | −0.339094 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.27371 | 0.149154 | 0.0745768 | − | 0.997215i | \(-0.476239\pi\) | ||||
0.0745768 | + | 0.997215i | \(0.476239\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 30.5714i | 1.06565i | 0.846225 | + | 0.532826i | \(0.178870\pi\) | ||||
−0.846225 | + | 0.532826i | \(0.821130\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 5.01148i | − | 0.174477i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −56.4650 | −1.96348 | −0.981740 | − | 0.190229i | \(-0.939077\pi\) | ||||
−0.981740 | + | 0.190229i | \(0.939077\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 18.7202i | − | 0.650179i | −0.945683 | − | 0.325089i | \(-0.894606\pi\) | ||
0.945683 | − | 0.325089i | \(-0.105394\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.39936 | 0.117923 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.77733 | −0.0615809 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11.1717 | 0.386613 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.12801 | −0.177250 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −17.5811 | −0.606966 | −0.303483 | − | 0.952837i | \(-0.598150\pi\) | ||||
−0.303483 | + | 0.952837i | \(0.598150\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.6056 | 0.917436 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.44525i | 0.256428i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.906548 | 0.0311862 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 39.3880i | 1.35339i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.08809i | 0.174623i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.16610 | 0.0742528 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.39936 | 0.116392 | 0.0581960 | − | 0.998305i | \(-0.481465\pi\) | ||||
0.0581960 | + | 0.998305i | \(0.481465\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.19273 | − | 1.19207i | 0.143388 | − | 0.0407678i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 35.9868i | 1.22929i | 0.788806 | + | 0.614643i | \(0.210700\pi\) | ||||
−0.788806 | + | 0.614643i | \(0.789300\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 19.7234i | − | 0.672954i | −0.941692 | − | 0.336477i | \(-0.890764\pi\) | ||
0.941692 | − | 0.336477i | \(-0.109236\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.52030 | 0.222211 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.30483 | −0.0784573 | −0.0392287 | − | 0.999230i | \(-0.512490\pi\) | ||||
−0.0392287 | + | 0.999230i | \(0.512490\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.69811i | 0.329745i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −11.9004 | −0.404157 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 10.9711i | − | 0.372169i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.4794i | 0.422850i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.67697i | 0.0567570i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 2.79053i | − | 0.0943370i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.248047i | 0.00837594i | 0.999991 | + | 0.00418797i | \(0.00133308\pi\) | ||||
−0.999991 | + | 0.00418797i | \(0.998667\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 22.8707i | − | 0.771408i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.9135 | 0.367684 | 0.183842 | − | 0.982956i | \(-0.441147\pi\) | ||||
0.183842 | + | 0.982956i | \(0.441147\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 45.6930i | 1.53769i | 0.639434 | + | 0.768846i | \(0.279169\pi\) | ||||
−0.639434 | + | 0.768846i | \(0.720831\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.34096 | −0.0450760 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 26.4723 | 0.888852 | 0.444426 | − | 0.895816i | \(-0.353408\pi\) | ||||
0.444426 | + | 0.895816i | \(0.353408\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 28.4164i | 0.953054i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 5.01148i | − | 0.167891i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −10.1195 | − | 35.5922i | −0.338636 | − | 1.19105i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.67272 | 0.0559127 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.57862 | −0.0527086 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 7.93495i | − | 0.264645i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.79765i | 0.226463i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.98703 | 0.165958 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.1587i | 0.337687i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.42828 | 0.113834 | 0.0569171 | − | 0.998379i | \(-0.481873\pi\) | ||||
0.0569171 | + | 0.998379i | \(0.481873\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.10425 | −0.169297 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.27414 | −0.0422142 | −0.0211071 | − | 0.999777i | \(-0.506719\pi\) | ||||
−0.0211071 | + | 0.999777i | \(0.506719\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 47.5711 | 1.57437 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6.21296 | −0.205394 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −47.0314 | −1.55312 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 4.73219i | − | 0.156101i | −0.996949 | − | 0.0780504i | \(-0.975131\pi\) | ||
0.996949 | − | 0.0780504i | \(-0.0248695\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −33.7089 | −1.11074 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 18.7310i | 0.616539i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.77172i | 0.156893i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.58856 | 0.117864 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 17.7772 | 0.583251 | 0.291625 | − | 0.956533i | \(-0.405804\pi\) | ||||
0.291625 | + | 0.956533i | \(0.405804\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.29986 | + | 0.938209i | −0.108149 | + | 0.0307486i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 4.53197i | − | 0.148370i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 11.3171i | − | 0.370109i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 48.1049 | 1.57152 | 0.785760 | − | 0.618531i | \(-0.212272\pi\) | ||||
0.785760 | + | 0.618531i | \(0.212272\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 21.9549 | 0.716470 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 49.1215i | − | 1.60132i | −0.599121 | − | 0.800658i | \(-0.704483\pi\) | ||
0.599121 | − | 0.800658i | \(-0.295517\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.06068 | 0.0345404 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 2.79053i | − | 0.0907759i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 32.8252i | 1.06668i | 0.845902 | + | 0.533338i | \(0.179062\pi\) | ||||
−0.845902 | + | 0.533338i | \(0.820938\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 40.9369i | 1.32887i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 9.73402i | − | 0.315647i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 61.1052i | − | 1.97939i | −0.143190 | − | 0.989695i | \(-0.545736\pi\) | ||
0.143190 | − | 0.989695i | \(-0.454264\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.2959i | 0.689118i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.75463 | 0.250672 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 23.9475i | − | 0.773306i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.70353 | −0.151727 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.79769 | 0.315726 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.7269i | 0.377501i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 48.6878i | 1.56569i | 0.622215 | + | 0.782846i | \(0.286233\pi\) | ||||
−0.622215 | + | 0.782846i | \(0.713767\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.46818 | − | 2.69197i | 0.304162 | − | 0.0864786i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.64648 | −0.309570 | −0.154785 | − | 0.987948i | \(-0.549469\pi\) | ||||
−0.154785 | + | 0.987948i | \(0.549469\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −33.8016 | −1.08363 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 3.47756i | − | 0.111371i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 10.3497i | − | 0.331116i | −0.986200 | − | 0.165558i | \(-0.947057\pi\) | ||
0.986200 | − | 0.165558i | \(-0.0529425\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −19.5343 | −0.624320 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.0765684i | 0.00244464i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 55.7912 | 1.77946 | 0.889731 | − | 0.456485i | \(-0.150892\pi\) | ||||
0.889731 | + | 0.456485i | \(0.150892\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.1885 | 0.388359 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −23.6889 | −0.754026 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.811256 | 0.0257964 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.0505 | −0.700458 | −0.350229 | − | 0.936664i | \(-0.613896\pi\) | ||||
−0.350229 | + | 0.936664i | \(0.613896\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 19.7097 | 0.625469 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 15.7331i | − | 0.498773i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 49.3087 | 1.56162 | 0.780811 | − | 0.624767i | \(-0.214806\pi\) | ||||
0.780811 | + | 0.624767i | \(0.214806\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.77172i | 0.150971i |
(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 | 4560.2.d.l.2431.4 | yes | 12 | |
4.3 | odd | 2 | 4560.2.d.j.2431.9 | yes | 12 | ||
19.18 | odd | 2 | 4560.2.d.j.2431.4 | ✓ | 12 | ||
76.75 | even | 2 | inner | 4560.2.d.l.2431.9 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4560.2.d.j.2431.4 | ✓ | 12 | 19.18 | odd | 2 | ||
4560.2.d.j.2431.9 | yes | 12 | 4.3 | odd | 2 | ||
4560.2.d.l.2431.4 | yes | 12 | 1.1 | even | 1 | trivial | |
4560.2.d.l.2431.9 | yes | 12 | 76.75 | even | 2 | inner |