Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2240,2,Mod(449,2240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2240.449");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2240 = 2^{6} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2240.g (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: | \(17.8864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 13x^{8} + 56x^{6} + 97x^{4} + 61x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 1120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.3 | ||
Root | \(2.52064i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2240.449 |
Dual form | 2240.2.g.o.449.8 |
$q$-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 \(\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times\).
\(n\) | \(897\) | \(1471\) | \(1541\) | \(1921\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | − | 1.83297i | − | 1.05827i | −0.848539 | − | 0.529133i | \(-0.822517\pi\) | ||
0.848539 | − | 0.529133i | \(-0.177483\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.86302 | − | 1.23660i | −0.833166 | − | 0.553023i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.359777 | −0.119926 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.40105 | 1.32697 | 0.663483 | − | 0.748191i | \(-0.269077\pi\) | ||||
0.663483 | + | 0.748191i | \(0.269077\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3.20830i | − | 0.889823i | −0.895575 | − | 0.444911i | \(-0.853235\pi\) | ||
0.895575 | − | 0.444911i | \(-0.146765\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.26664 | + | 3.41485i | −0.585245 | + | 0.881711i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.14821i | 0.278482i | 0.990259 | + | 0.139241i | \(0.0444662\pi\) | ||||
−0.990259 | + | 0.139241i | \(0.955534\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.72603 | 0.395979 | 0.197990 | − | 0.980204i | \(-0.436559\pi\) | ||||
0.197990 | + | 0.980204i | \(0.436559\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.83297 | 0.399987 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 3.25284i | − | 0.678264i | −0.940739 | − | 0.339132i | \(-0.889867\pi\) | ||
0.940739 | − | 0.339132i | \(-0.110133\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.94166 | + | 4.60760i | 0.388332 | + | 0.921520i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 4.83945i | − | 0.931352i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.18948 | 0.777967 | 0.388983 | − | 0.921245i | \(-0.372826\pi\) | ||||
0.388983 | + | 0.921245i | \(0.372826\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.36952 | −0.245973 | −0.122987 | − | 0.992408i | \(-0.539247\pi\) | ||||
−0.122987 | + | 0.992408i | \(0.539247\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 8.06699i | − | 1.40428i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.23660 | − | 1.86302i | 0.209023 | − | 0.314907i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 4.19923i | − | 0.690348i | −0.938539 | − | 0.345174i | \(-0.887820\pi\) | ||
0.938539 | − | 0.345174i | \(-0.112180\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.88072 | −0.941669 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.7485 | 1.83480 | 0.917402 | − | 0.397961i | \(-0.130282\pi\) | ||||
0.917402 | + | 0.397961i | \(0.130282\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2.64997i | − | 0.404116i | −0.979374 | − | 0.202058i | \(-0.935237\pi\) | ||
0.979374 | − | 0.202058i | \(-0.0647630\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.670270 | + | 0.444899i | 0.0999180 | + | 0.0663216i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.106937i | 0.0155983i | 0.999970 | + | 0.00779917i | \(0.00248258\pi\) | ||||
−0.999970 | + | 0.00779917i | \(0.997517\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.10463 | 0.294707 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.86516i | 1.08036i | 0.841548 | + | 0.540182i | \(0.181644\pi\) | ||||
−0.841548 | + | 0.540182i | \(0.818356\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.19923 | − | 5.44232i | −1.10558 | − | 0.733842i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 3.16376i | − | 0.419051i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13.3029 | −1.73189 | −0.865945 | − | 0.500140i | \(-0.833282\pi\) | ||||
−0.865945 | + | 0.500140i | \(0.833282\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.0224 | 1.28324 | 0.641622 | − | 0.767021i | \(-0.278262\pi\) | ||||
0.641622 | + | 0.767021i | \(0.278262\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 0.359777i | − | 0.0453276i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.96737 | + | 5.97712i | −0.492092 | + | 0.741370i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 1.28045i | − | 0.156431i | −0.996936 | − | 0.0782157i | \(-0.975078\pi\) | ||
0.996936 | − | 0.0782157i | \(-0.0249223\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.96236 | −0.717783 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.1616 | −1.68067 | −0.840335 | − | 0.542067i | \(-0.817642\pi\) | ||||
−0.840335 | + | 0.542067i | \(0.817642\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 11.8652i | − | 1.38871i | −0.719631 | − | 0.694356i | \(-0.755689\pi\) | ||
0.719631 | − | 0.694356i | \(-0.244311\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.44559 | − | 3.55900i | 0.975212 | − | 0.410958i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.40105i | 0.501546i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.48227 | 0.616804 | 0.308402 | − | 0.951256i | \(-0.400206\pi\) | ||||
0.308402 | + | 0.951256i | \(0.400206\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.94989 | −1.10554 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 17.1586i | − | 1.88340i | −0.336451 | − | 0.941701i | \(-0.609227\pi\) | ||
0.336451 | − | 0.941701i | \(-0.390773\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.41987 | − | 2.13913i | 0.154007 | − | 0.232021i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 7.67919i | − | 0.823296i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.31591 | −0.457485 | −0.228743 | − | 0.973487i | \(-0.573461\pi\) | ||||
−0.228743 | + | 0.973487i | \(0.573461\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.20830 | 0.336321 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.51029i | 0.260305i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.21563 | − | 2.13441i | −0.329916 | − | 0.218985i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.65389i | 0.777135i | 0.921420 | + | 0.388567i | \(0.127030\pi\) | ||||
−0.921420 | + | 0.388567i | \(0.872970\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.58340 | −0.159137 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.25581 | 0.224462 | 0.112231 | − | 0.993682i | \(-0.464200\pi\) | ||||
0.112231 | + | 0.993682i | \(0.464200\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 6.61262i | − | 0.651560i | −0.945446 | − | 0.325780i | \(-0.894373\pi\) | ||
0.945446 | − | 0.325780i | \(-0.105627\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.41485 | − | 2.26664i | −0.333255 | − | 0.221202i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 5.83756i | − | 0.564338i | −0.959365 | − | 0.282169i | \(-0.908946\pi\) | ||
0.959365 | − | 0.282169i | \(-0.0910539\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.6952 | −1.02441 | −0.512205 | − | 0.858863i | \(-0.671171\pi\) | ||||
−0.512205 | + | 0.858863i | \(0.671171\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.69705 | −0.730572 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.867348i | 0.0815932i | 0.999167 | + | 0.0407966i | \(0.0129896\pi\) | ||||
−0.999167 | + | 0.0407966i | \(0.987010\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.02245 | + | 6.06009i | −0.375095 | + | 0.565107i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.15427i | 0.106713i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.14821 | −0.105256 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.36923 | 0.760839 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 21.5346i | − | 1.94171i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.08040 | − | 10.9851i | 0.186076 | − | 0.982535i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.6158i | 1.29695i | 0.761238 | + | 0.648473i | \(0.224592\pi\) | ||||
−0.761238 | + | 0.648473i | \(0.775408\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.85731 | −0.427662 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.8600 | −1.56044 | −0.780218 | − | 0.625508i | \(-0.784892\pi\) | ||||
−0.780218 | + | 0.625508i | \(0.784892\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.72603i | 0.149666i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.98444 | + | 9.01597i | −0.515059 | + | 0.775971i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 5.22523i | − | 0.446422i | −0.974770 | − | 0.223211i | \(-0.928346\pi\) | ||
0.974770 | − | 0.223211i | \(-0.0716539\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.25800 | −0.445977 | −0.222989 | − | 0.974821i | \(-0.571581\pi\) | ||||
−0.222989 | + | 0.974821i | \(0.571581\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.196012 | 0.0165072 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 14.1199i | − | 1.18076i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.80507 | − | 5.18070i | −0.648176 | − | 0.430233i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.83297i | 0.151181i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.8928 | −0.974294 | −0.487147 | − | 0.873320i | \(-0.661962\pi\) | ||||
−0.487147 | + | 0.873320i | \(0.661962\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.54534 | −0.695410 | −0.347705 | − | 0.937604i | \(-0.613039\pi\) | ||||
−0.347705 | + | 0.937604i | \(0.613039\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 0.413099i | − | 0.0333971i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.55144 | + | 1.69355i | 0.204937 | + | 0.136029i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.36436i | 0.268506i | 0.990947 | + | 0.134253i | \(0.0428634\pi\) | ||||
−0.990947 | + | 0.134253i | \(0.957137\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 14.4166 | 1.14331 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.25284 | 0.256360 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.8310i | 1.23998i | 0.784609 | + | 0.619991i | \(0.212864\pi\) | ||||
−0.784609 | + | 0.619991i | \(0.787136\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −9.97561 | + | 15.0289i | −0.776600 | + | 1.17000i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 20.8843i | − | 1.61608i | −0.589128 | − | 0.808040i | \(-0.700529\pi\) | ||
0.589128 | − | 0.808040i | \(-0.299471\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.70680 | 0.208215 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.620986 | −0.0474880 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.94735i | 0.452168i | 0.974108 | + | 0.226084i | \(0.0725924\pi\) | ||||
−0.974108 | + | 0.226084i | \(0.927408\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.60760 | + | 1.94166i | −0.348302 | + | 0.146776i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 24.3838i | 1.83280i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −22.9041 | −1.71194 | −0.855968 | − | 0.517030i | \(-0.827038\pi\) | ||||
−0.855968 | + | 0.517030i | \(0.827038\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.77746 | 0.132118 | 0.0660589 | − | 0.997816i | \(-0.478957\pi\) | ||||
0.0660589 | + | 0.997816i | \(0.478957\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 18.3708i | − | 1.35801i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.19275 | + | 7.82322i | −0.381778 | + | 0.575175i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.05332i | 0.369536i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.83945 | 0.352018 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.7183 | 1.42676 | 0.713382 | − | 0.700775i | \(-0.247162\pi\) | ||||
0.713382 | + | 0.700775i | \(0.247162\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.4956i | 1.33135i | 0.746244 | + | 0.665673i | \(0.231855\pi\) | ||||
−0.746244 | + | 0.665673i | \(0.768145\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 10.9559 | + | 7.27208i | 0.784567 | + | 0.520764i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 19.4179i | − | 1.38347i | −0.722151 | − | 0.691735i | \(-0.756847\pi\) | ||
0.722151 | − | 0.691735i | \(-0.243153\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.7485 | 1.54171 | 0.770855 | − | 0.637011i | \(-0.219830\pi\) | ||||
0.770855 | + | 0.637011i | \(0.219830\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.34702 | −0.165546 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.18948i | 0.294044i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −21.8876 | − | 14.5281i | −1.52870 | − | 1.01469i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.17030i | 0.0813412i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.59635 | 0.525451 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.2091 | 1.59778 | 0.798890 | − | 0.601477i | \(-0.205421\pi\) | ||||
0.798890 | + | 0.601477i | \(0.205421\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 25.9577i | 1.77860i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.27694 | + | 4.93693i | −0.223485 | + | 0.336696i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 1.36952i | − | 0.0929692i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −21.7485 | −1.46963 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.68380 | 0.247799 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.784235i | 0.0525163i | 0.999655 | + | 0.0262581i | \(0.00835919\pi\) | ||||
−0.999655 | + | 0.0262581i | \(0.991641\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.698564 | − | 1.65771i | −0.0465709 | − | 0.110514i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.7257i | 0.778265i | 0.921182 | + | 0.389132i | \(0.127225\pi\) | ||||
−0.921182 | + | 0.389132i | \(0.872775\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.09555 | −0.0723962 | −0.0361981 | − | 0.999345i | \(-0.511525\pi\) | ||||
−0.0361981 | + | 0.999345i | \(0.511525\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.06699 | 0.530769 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 25.3345i | 1.65972i | 0.557972 | + | 0.829860i | \(0.311580\pi\) | ||||
−0.557972 | + | 0.829860i | \(0.688420\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.132238 | − | 0.199225i | 0.00862624 | − | 0.0129960i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 10.0488i | − | 0.652742i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 28.8886 | 1.86865 | 0.934323 | − | 0.356427i | \(-0.116005\pi\) | ||||
0.934323 | + | 0.356427i | \(0.116005\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.2542 | 0.660529 | 0.330264 | − | 0.943888i | \(-0.392862\pi\) | ||||
0.330264 | + | 0.943888i | \(0.392862\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.71950i | 0.238606i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.86302 | + | 1.23660i | 0.119024 | + | 0.0790032i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 5.53763i | − | 0.352351i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −31.4512 | −1.99314 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −27.5389 | −1.73824 | −0.869120 | − | 0.494601i | \(-0.835314\pi\) | ||||
−0.869120 | + | 0.494601i | \(0.835314\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 14.3159i | − | 0.900033i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.92096 | − | 2.60258i | −0.245540 | − | 0.162980i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 12.2636i | − | 0.764983i | −0.923959 | − | 0.382492i | \(-0.875066\pi\) | ||
0.923959 | − | 0.382492i | \(-0.124934\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.19923 | 0.260927 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.50728 | −0.0932982 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 17.8928i | − | 1.10332i | −0.834071 | − | 0.551658i | \(-0.813995\pi\) | ||
0.834071 | − | 0.551658i | \(-0.186005\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.72603 | − | 14.6529i | 0.597465 | − | 0.900122i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.91092i | 0.484141i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 25.2295 | 1.53827 | 0.769136 | − | 0.639085i | \(-0.220687\pi\) | ||||
0.769136 | + | 0.639085i | \(0.220687\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.65999 | −0.586803 | −0.293401 | − | 0.955989i | \(-0.594787\pi\) | ||||
−0.293401 | + | 0.955989i | \(0.594787\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 5.88072i | − | 0.355917i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.54534 | + | 20.2783i | 0.515303 | + | 1.22283i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.1970i | 1.39378i | 0.717180 | + | 0.696888i | \(0.245432\pi\) | ||||
−0.717180 | + | 0.696888i | \(0.754568\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.492722 | 0.0294985 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.9734 | 1.60910 | 0.804550 | − | 0.593885i | \(-0.202407\pi\) | ||||
0.804550 | + | 0.593885i | \(0.202407\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 22.2119i | − | 1.32036i | −0.751106 | − | 0.660181i | \(-0.770480\pi\) | ||
0.751106 | − | 0.660181i | \(-0.229520\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.91230 | + | 5.89415i | −0.231745 | + | 0.349139i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.7485i | 0.693491i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.6816 | 0.922448 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.0293 | 0.822415 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 20.8756i | − | 1.21956i | −0.792569 | − | 0.609782i | \(-0.791257\pi\) | ||
0.792569 | − | 0.609782i | \(-0.208743\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 24.7835 | + | 16.4503i | 1.44295 | + | 0.957774i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 21.2986i | − | 1.23587i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.4361 | −0.603535 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.64997 | 0.152742 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 4.13484i | − | 0.237540i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −18.6720 | − | 12.3937i | −1.06915 | − | 0.709663i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 2.97374i | − | 0.169720i | −0.996393 | − | 0.0848601i | \(-0.972956\pi\) | ||
0.996393 | − | 0.0848601i | \(-0.0270443\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.1207 | −0.689524 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.04007 | −0.0589770 | −0.0294885 | − | 0.999565i | \(-0.509388\pi\) | ||||
−0.0294885 | + | 0.999565i | \(0.509388\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 9.12411i | − | 0.515725i | −0.966182 | − | 0.257863i | \(-0.916982\pi\) | ||
0.966182 | − | 0.257863i | \(-0.0830182\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.444899 | + | 0.670270i | −0.0250672 | + | 0.0377654i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 4.74255i | − | 0.266368i | −0.991091 | − | 0.133184i | \(-0.957480\pi\) | ||
0.991091 | − | 0.133184i | \(-0.0425201\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.4381 | 1.03234 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.7001 | −0.597219 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.98185i | 0.110273i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 14.7826 | − | 6.22943i | 0.819989 | − | 0.345547i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 19.6039i | 1.08410i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.106937 | −0.00589562 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.38114 | 0.515634 | 0.257817 | − | 0.966194i | \(-0.416997\pi\) | ||||
0.257817 | + | 0.966194i | \(0.416997\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.51078i | 0.0827904i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.58340 | + | 2.38549i | −0.0865101 | + | 0.130333i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 17.4797i | − | 0.952178i | −0.879397 | − | 0.476089i | \(-0.842054\pi\) | ||
0.879397 | − | 0.476089i | \(-0.157946\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.58982 | 0.0863472 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.02733 | −0.326398 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 11.1080 | + | 7.37303i | 0.598033 | + | 0.396950i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 19.2623i | 1.03405i | 0.855969 | + | 0.517027i | \(0.172961\pi\) | ||||
−0.855969 | + | 0.517027i | \(0.827039\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.5730 | 1.52948 | 0.764740 | − | 0.644339i | \(-0.222868\pi\) | ||||
0.764740 | + | 0.644339i | \(0.222868\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.5264 | −0.828739 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 23.8293i | − | 1.26831i | −0.773208 | − | 0.634153i | \(-0.781349\pi\) | ||
0.773208 | − | 0.634153i | \(-0.218651\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 26.3833 | + | 17.5122i | 1.40028 | + | 0.929449i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.10463i | 0.111389i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.03194 | −0.107242 | −0.0536209 | − | 0.998561i | \(-0.517076\pi\) | ||||
−0.0536209 | + | 0.998561i | \(0.517076\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.0208 | −0.843201 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 15.3405i | − | 0.805170i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −14.6724 | + | 22.1050i | −0.767989 | + | 1.15703i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.6965i | 1.18475i | 0.805663 | + | 0.592374i | \(0.201809\pi\) | ||||
−0.805663 | + | 0.592374i | \(0.798191\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.22683 | −0.220040 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.86516 | −0.408339 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 30.2909i | − | 1.56841i | −0.620505 | − | 0.784203i | \(-0.713072\pi\) | ||
0.620505 | − | 0.784203i | \(-0.286928\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −20.1353 | − | 3.81330i | −1.03978 | − | 0.196918i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 13.4411i | − | 0.692253i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.9783 | −0.769385 | −0.384692 | − | 0.923045i | \(-0.625693\pi\) | ||||
−0.384692 | + | 0.923045i | \(0.625693\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 26.7904 | 1.37251 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 5.37413i | − | 0.274605i | −0.990529 | − | 0.137303i | \(-0.956157\pi\) | ||
0.990529 | − | 0.137303i | \(-0.0438433\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.44232 | − | 8.19923i | 0.277366 | − | 0.417871i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.953397i | 0.0484639i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.87331 | −0.145683 | −0.0728413 | − | 0.997344i | \(-0.523207\pi\) | ||||
−0.0728413 | + | 0.997344i | \(0.523207\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.73494 | 0.188884 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 32.7368i | 1.65136i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.2136 | − | 6.77935i | −0.513900 | − | 0.341106i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.2887i | 1.21901i | 0.792781 | + | 0.609507i | \(0.208632\pi\) | ||||
−0.792781 | + | 0.609507i | \(0.791368\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.16376 | 0.158386 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.7274 | 0.635575 | 0.317787 | − | 0.948162i | \(-0.397060\pi\) | ||||
0.317787 | + | 0.948162i | \(0.397060\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.39384i | 0.218873i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 18.5368 | + | 12.3040i | 0.921101 | + | 0.611391i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 18.4810i | − | 0.916069i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.0455 | 0.496717 | 0.248359 | − | 0.968668i | \(-0.420109\pi\) | ||||
0.248359 | + | 0.968668i | \(0.420109\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.57769 | −0.472433 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 13.3029i | − | 0.654593i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −21.2183 | + | 31.9668i | −1.04156 | + | 1.56919i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.63775i | 0.471962i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.2433 | −0.793539 | −0.396769 | − | 0.917918i | \(-0.629869\pi\) | ||||
−0.396769 | + | 0.917918i | \(0.629869\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.8066 | 1.55016 | 0.775080 | − | 0.631863i | \(-0.217709\pi\) | ||||
0.775080 | + | 0.631863i | \(0.217709\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 0.0384734i | − | 0.00187064i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.29048 | + | 2.22943i | −0.256626 | + | 0.108143i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.0224i | 0.485020i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −25.8813 | −1.24956 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.8177 | 0.906414 | 0.453207 | − | 0.891405i | \(-0.350280\pi\) | ||||
0.453207 | + | 0.891405i | \(0.350280\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.5825i | 1.03719i | 0.855020 | + | 0.518595i | \(0.173545\pi\) | ||||
−0.855020 | + | 0.518595i | \(0.826455\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9.49606 | + | 14.3065i | −0.455301 | + | 0.685942i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 5.61451i | − | 0.268578i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.69487 | −0.128619 | −0.0643095 | − | 0.997930i | \(-0.520484\pi\) | ||||
−0.0643095 | + | 0.997930i | \(0.520484\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.359777 | 0.0171322 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 18.5368i | − | 0.880710i | −0.897824 | − | 0.440355i | \(-0.854853\pi\) | ||
0.897824 | − | 0.440355i | \(-0.145147\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.04060 | + | 5.33703i | 0.381161 | + | 0.253000i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 21.7991i | 1.03106i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.6816 | 0.598483 | 0.299241 | − | 0.954177i | \(-0.403266\pi\) | ||||
0.299241 | + | 0.954177i | \(0.403266\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 51.7056 | 2.43472 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 15.6633i | 0.735928i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.97712 | − | 3.96737i | −0.280212 | − | 0.185993i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.5381i | 0.913954i | 0.889478 | + | 0.456977i | \(0.151068\pi\) | ||||
−0.889478 | + | 0.456977i | \(0.848932\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.55670 | 0.259364 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.9929 | −0.698291 | −0.349145 | − | 0.937069i | \(-0.613528\pi\) | ||||
−0.349145 | + | 0.937069i | \(0.613528\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.9309i | 1.15864i | 0.815102 | + | 0.579318i | \(0.196681\pi\) | ||||
−0.815102 | + | 0.579318i | \(0.803319\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.10422 | − | 4.67671i | 0.143955 | − | 0.216877i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 30.4350i | 1.40836i | 0.710020 | + | 0.704181i | \(0.248686\pi\) | ||||
−0.710020 | + | 0.704181i | \(0.751314\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.28045 | 0.0591255 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.16678 | 0.284150 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 11.6626i | − | 0.536249i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.35137 | + | 7.95286i | 0.153771 | + | 0.364902i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 2.82970i | − | 0.129563i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.9694 | −0.821041 | −0.410521 | − | 0.911851i | \(-0.634653\pi\) | ||||
−0.410521 | + | 0.911851i | \(0.634653\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.4724 | −0.614288 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 5.96236i | − | 0.271297i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.46477 | − | 14.2593i | 0.429773 | − | 0.647482i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.51295i | 0.431073i | 0.976496 | + | 0.215536i | \(0.0691500\pi\) | ||||
−0.976496 | + | 0.215536i | \(0.930850\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 29.0178 | 1.31223 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.0466 | 0.949822 | 0.474911 | − | 0.880034i | \(-0.342480\pi\) | ||||
0.474911 | + | 0.880034i | \(0.342480\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.81040i | 0.216649i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.94989 | + | 1.95802i | 0.132588 | + | 0.0880065i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 14.1616i | − | 0.635234i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 36.4408 | 1.63131 | 0.815656 | − | 0.578537i | \(-0.196376\pi\) | ||||
0.815656 | + | 0.578537i | \(0.196376\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −38.2804 | −1.71024 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 32.1783i | − | 1.43476i | −0.696681 | − | 0.717381i | \(-0.745341\pi\) | ||
0.696681 | − | 0.717381i | \(-0.254659\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.20262 | − | 2.78953i | −0.187014 | − | 0.124132i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 4.96147i | − | 0.220347i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.06604 | 0.0915756 | 0.0457878 | − | 0.998951i | \(-0.485420\pi\) | ||||
0.0457878 | + | 0.998951i | \(0.485420\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.8652 | 0.524884 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 8.35305i | − | 0.368796i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.17714 | + | 12.3194i | −0.360328 | + | 0.542858i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.470634i | 0.0206985i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.9013 | 0.478514 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.0609 | −1.01032 | −0.505158 | − | 0.863027i | \(-0.668566\pi\) | ||||
−0.505158 | + | 0.863027i | \(0.668566\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 26.1602i | − | 1.14391i | −0.820286 | − | 0.571953i | \(-0.806186\pi\) | ||
0.820286 | − | 0.571953i | \(-0.193814\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.55900 | + | 8.44559i | 0.155328 | + | 0.368596i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 1.57250i | − | 0.0684990i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.4190 | 0.539958 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.78607 | 0.207698 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 37.6927i | − | 1.63265i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.21870 | + | 10.8755i | −0.312092 | + | 0.470187i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 41.9826i | 1.81168i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.40105 | −0.189567 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −41.2094 | −1.77173 | −0.885866 | − | 0.463941i | \(-0.846435\pi\) | ||||
−0.885866 | + | 0.463941i | \(0.846435\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 3.25804i | − | 0.139816i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 19.9253 | + | 13.2256i | 0.853504 | + | 0.566522i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 7.67055i | − | 0.327969i | −0.986463 | − | 0.163985i | \(-0.947565\pi\) | ||
0.986463 | − | 0.163985i | \(-0.0524347\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.60585 | −0.153894 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.23118 | 0.308059 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.48227i | 0.233130i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 14.3397 | + | 9.51814i | 0.608688 | + | 0.404023i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 31.8600i | 1.34995i | 0.737841 | + | 0.674975i | \(0.235846\pi\) | ||||
−0.737841 | + | 0.674975i | \(0.764154\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.50190 | −0.359592 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.26258 | 0.391067 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.20351i | 0.387882i | 0.981013 | + | 0.193941i | \(0.0621270\pi\) | ||||
−0.981013 | + | 0.193941i | \(0.937873\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.07256 | − | 1.61588i | 0.0451229 | − | 0.0679807i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 9.94989i | − | 0.417856i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.47615 | −0.355339 | −0.177669 | − | 0.984090i | \(-0.556856\pi\) | ||||
−0.177669 | + | 0.984090i | \(0.556856\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.1245 | 0.549245 | 0.274622 | − | 0.961552i | \(-0.411447\pi\) | ||||
0.274622 | + | 0.961552i | \(0.411447\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 36.1430i | − | 1.50990i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 14.9878 | − | 6.31591i | 0.625034 | − | 0.263392i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 16.5640i | − | 0.689567i | −0.938682 | − | 0.344783i | \(-0.887952\pi\) | ||
0.938682 | − | 0.344783i | \(-0.112048\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 33.9019 | 1.40892 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.1586 | 0.711859 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 34.6150i | 1.43361i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.42737 | − | 2.15043i | 0.0590145 | − | 0.0889093i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.890659i | 0.0367614i | 0.999831 | + | 0.0183807i | \(0.00585109\pi\) | ||||
−0.999831 | + | 0.0183807i | \(0.994149\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.36384 | −0.0974003 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −35.5925 | −1.46408 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.12654i | 0.333717i | 0.985981 | + | 0.166858i | \(0.0533623\pi\) | ||||
−0.985981 | + | 0.166858i | \(0.946638\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.13913 | + | 1.41987i | 0.0876958 | + | 0.0582090i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 39.8643i | − | 1.63154i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.38288 | 0.383374 | 0.191687 | − | 0.981456i | \(-0.438604\pi\) | ||||
0.191687 | + | 0.981456i | \(0.438604\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.44289 | −0.222020 | −0.111010 | − | 0.993819i | \(-0.535409\pi\) | ||||
−0.111010 | + | 0.993819i | \(0.535409\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.460675i | 0.0187601i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −15.5920 | − | 10.3494i | −0.633905 | − | 0.420761i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 36.7479i | 1.49155i | 0.666197 | + | 0.745776i | \(0.267921\pi\) | ||||
−0.666197 | + | 0.745776i | \(0.732079\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.67919 | 0.311176 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.343086 | 0.0138798 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 16.8238i | − | 0.679505i | −0.940515 | − | 0.339753i | \(-0.889657\pi\) | ||
0.940515 | − | 0.339753i | \(-0.110343\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −26.6296 | + | 40.1193i | −1.07381 | + | 1.61777i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 5.67406i | − | 0.228429i | −0.993456 | − | 0.114214i | \(-0.963565\pi\) | ||
0.993456 | − | 0.114214i | \(-0.0364351\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.33702 | 0.174320 | 0.0871598 | − | 0.996194i | \(-0.472221\pi\) | ||||
0.0871598 | + | 0.996194i | \(0.472221\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −15.7420 | −0.631703 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 4.31591i | − | 0.172913i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.4599 | + | 17.8928i | −0.698397 | + | 0.715711i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 13.9239i | − | 0.556066i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.82159 | 0.192249 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −41.9784 | −1.67113 | −0.835567 | − | 0.549389i | \(-0.814860\pi\) | ||||
−0.835567 | + | 0.549389i | \(0.814860\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 42.5416i | − | 1.69088i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 18.0739 | − | 27.2295i | 0.717240 | − | 1.08057i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.20830i | 0.127118i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.09501 | 0.201555 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −40.4035 | −1.59584 | −0.797922 | − | 0.602761i | \(-0.794067\pi\) | ||||
−0.797922 | + | 0.602761i | \(0.794067\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.7826i | 1.13507i | 0.823348 | + | 0.567537i | \(0.192104\pi\) | ||||
−0.823348 | + | 0.567537i | \(0.807896\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.04925 | + | 6.00653i | 0.356314 | + | 0.236507i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 50.0475i | 1.96757i | 0.179346 | + | 0.983786i | \(0.442602\pi\) | ||||
−0.179346 | + | 0.983786i | \(0.557398\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −58.5467 | −2.29816 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.51029 | −0.0983861 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 39.5622i | 1.54819i | 0.633070 | + | 0.774095i | \(0.281795\pi\) | ||||
−0.633070 | + | 0.774095i | \(0.718205\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 33.2735 | + | 22.0856i | 1.30010 | + | 0.862957i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.26881i | 0.166542i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.0994 | −0.393418 | −0.196709 | − | 0.980462i | \(-0.563025\pi\) | ||||
−0.196709 | + | 0.980462i | \(0.563025\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.51434 | 0.175588 | 0.0877938 | − | 0.996139i | \(-0.472018\pi\) | ||||
0.0877938 | + | 0.996139i | \(0.472018\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 6.75229i | − | 0.262237i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.13441 | − | 3.21563i | 0.0827687 | − | 0.124697i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 13.6277i | − | 0.527667i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.43748 | 0.0555762 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 44.1093 | 1.70282 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.62104i | 0.139581i | 0.997562 | + | 0.0697904i | \(0.0222330\pi\) | ||||
−0.997562 | + | 0.0697904i | \(0.977767\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 22.2982 | − | 9.39656i | 0.858259 | − | 0.361674i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 35.1617i | 1.35137i | 0.737189 | + | 0.675687i | \(0.236153\pi\) | ||||
−0.737189 | + | 0.675687i | \(0.763847\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.65389 | −0.293729 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 21.4929 | 0.823611 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.39058i | 0.168001i | 0.996466 | + | 0.0840005i | \(0.0267697\pi\) | ||||
−0.996466 | + | 0.0840005i | \(0.973230\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.46150 | + | 9.73470i | −0.246881 | + | 0.371944i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.00812i | 0.0766144i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 25.2338 | 0.961332 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.28314 | −0.239022 | −0.119511 | − | 0.992833i | \(-0.538133\pi\) | ||||
−0.119511 | + | 0.992833i | \(0.538133\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 1.58340i | − | 0.0601482i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.79573 | + | 6.50202i | 0.371573 | + | 0.246636i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.4897i | 0.510959i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 46.4374 | 1.75642 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.41413 | −0.204489 | −0.102244 | − | 0.994759i | \(-0.532602\pi\) | ||||
−0.102244 | + | 0.994759i | \(0.532602\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 7.24800i | − | 0.273363i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.365174 | − | 0.242388i | −0.0137532 | − | 0.00912885i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.25581i | 0.0848386i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.5284 | 0.583180 | 0.291590 | − | 0.956543i | \(-0.405816\pi\) | ||||
0.291590 | + | 0.956543i | \(0.405816\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.97239 | −0.0739705 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.45483i | 0.166835i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −17.4606 | + | 26.3056i | −0.652990 | + | 0.983773i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 52.9519i | − | 1.97752i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19.9304 | −0.743279 | −0.371640 | − | 0.928377i | \(-0.621204\pi\) | ||||
−0.371640 | + | 0.928377i | \(0.621204\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.61262 | 0.246267 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 18.7956i | − | 0.699015i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.13454 | + | 19.3034i | 0.302109 | + | 0.716912i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 24.0839i | − | 0.893222i | −0.894728 | − | 0.446611i | \(-0.852631\pi\) | ||
0.894728 | − | 0.446611i | \(-0.147369\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.0319 | −0.853035 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.04272 | 0.112539 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.8771i | 1.32515i | 0.748994 | + | 0.662576i | \(0.230537\pi\) | ||||
−0.748994 | + | 0.662576i | \(0.769463\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.26664 | − | 3.41485i | 0.0836064 | − | 0.125959i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 5.63531i | − | 0.207579i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.29734 | 0.0477233 | 0.0238617 | − | 0.999715i | \(-0.492404\pi\) | ||||
0.0238617 | + | 0.999715i | \(0.492404\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.1503 | −0.372881 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 8.53790i | − | 0.313225i | −0.987660 | − | 0.156613i | \(-0.949943\pi\) | ||
0.987660 | − | 0.156613i | \(-0.0500574\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 22.1564 | + | 14.7066i | 0.811749 | + | 0.538807i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.17327i | 0.225868i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.83756 | 0.213300 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.5930 | −0.641978 | −0.320989 | − | 0.947083i | \(-0.604015\pi\) | ||||
−0.320989 | + | 0.947083i | \(0.604015\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 50.4780i | 1.83952i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15.9201 | + | 10.5671i | 0.579392 | + | 0.384577i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.5195i | 1.21829i | 0.793061 | + | 0.609143i | \(0.208486\pi\) | ||||
−0.793061 | + | 0.609143i | \(0.791514\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −26.2406 | −0.952474 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.8063 | −0.935479 | −0.467740 | − | 0.883866i | \(-0.654931\pi\) | ||||
−0.467740 | + | 0.883866i | \(0.654931\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 10.6952i | − | 0.387191i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.510837 | + | 0.769610i | −0.0184693 | + | 0.0278253i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 42.6797i | 1.54108i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.6616 | 0.997502 | 0.498751 | − | 0.866745i | \(-0.333792\pi\) | ||||
0.498751 | + | 0.866745i | \(0.333792\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −22.4788 | −0.809555 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 49.4294i | 1.77785i | 0.458050 | + | 0.888927i | \(0.348548\pi\) | ||||
−0.458050 | + | 0.888927i | \(0.651452\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.65914 | − | 6.31020i | −0.0955193 | − | 0.226669i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 7.69705i | − | 0.276130i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 20.2783 | 0.726544 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −62.3258 | −2.23019 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 20.2748i | − | 0.724561i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.16036 | − | 6.26787i | 0.148490 | − | 0.223710i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 44.2790i | 1.57837i | 0.614153 | + | 0.789187i | \(0.289498\pi\) | ||||
−0.614153 | + | 0.789187i | \(0.710502\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −32.7969 | −1.16760 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.867348 | −0.0308393 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 32.1550i | − | 1.14186i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −26.8584 | − | 17.8275i | −0.952568 | − | 0.632277i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 17.7589i | − | 0.629052i | −0.949249 | − | 0.314526i | \(-0.898154\pi\) | ||
0.949249 | − | 0.314526i | \(-0.101846\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.122786 | −0.00434385 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.55276 | 0.0548642 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 52.2192i | − | 1.84277i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.06009 | − | 4.02245i | −0.213590 | − | 0.141773i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 46.2450i | − | 1.62790i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −31.2427 | −1.09844 | −0.549218 | − | 0.835679i | \(-0.685074\pi\) | ||||
−0.549218 | + | 0.835679i | \(0.685074\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.66672 | −0.234100 | −0.117050 | − | 0.993126i | \(-0.537344\pi\) | ||||
−0.117050 | + | 0.993126i | \(0.537344\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 17.7065i | 0.620993i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 19.5766 | − | 29.4935i | 0.685738 | − | 1.03311i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 4.57393i | − | 0.160022i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.15427 | −0.0403336 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 43.2138 | 1.50817 | 0.754086 | − | 0.656776i | \(-0.228080\pi\) | ||||
0.754086 | + | 0.656776i | \(0.228080\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 17.8129i | − | 0.620918i | −0.950587 | − | 0.310459i | \(-0.899517\pi\) | ||
0.950587 | − | 0.310459i | \(-0.100483\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 37.1694 | − | 15.6633i | 1.29407 | − | 0.545328i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.9139i | 0.657702i | 0.944382 | + | 0.328851i | \(0.106661\pi\) | ||||
−0.944382 | + | 0.328851i | \(0.893339\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.5969 | 1.30579 | 0.652897 | − | 0.757447i | \(-0.273554\pi\) | ||||
0.652897 | + | 0.757447i | \(0.273554\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 42.5195 | 1.47498 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 1.14821i | − | 0.0397831i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −25.8255 | + | 38.9079i | −0.893729 | + | 1.34646i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.62773i | 0.229088i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 32.2054 | 1.11185 | 0.555927 | − | 0.831231i | \(-0.312364\pi\) | ||||
0.555927 | + | 0.831231i | \(0.312364\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.4483 | −0.394767 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 49.4415i | − | 1.70285i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.04280 | − | 3.34721i | −0.173478 | − | 0.115148i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.36923i | 0.287570i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −40.7138 | −1.39729 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.6594 | −0.468238 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.6540i | 0.707179i | 0.935401 | + | 0.353590i | \(0.115039\pi\) | ||||
−0.935401 | + | 0.353590i | \(0.884961\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.15691 | + | 0.767910i | 0.0395654 | + | 0.0262620i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 42.6561i | 1.45711i | 0.684990 | + | 0.728553i | \(0.259807\pi\) | ||||
−0.684990 | + | 0.728553i | \(0.740193\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.95286 | 0.271348 | 0.135674 | − | 0.990754i | \(-0.456680\pi\) | ||||
0.135674 | + | 0.990754i | \(0.456680\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 21.5346 | 0.733897 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 29.0419i | − | 0.988597i | −0.869292 | − | 0.494299i | \(-0.835425\pi\) | ||
0.869292 | − | 0.494299i | \(-0.164575\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.35447 | − | 11.0800i | 0.250059 | − | 0.376731i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 28.7439i | − | 0.976195i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24.1277 | 0.818477 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.10806 | −0.139196 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 2.75369i | − | 0.0931983i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.9851 | + | 2.08040i | 0.371363 | + | 0.0703302i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.1827i | 0.512682i | 0.966586 | + | 0.256341i | \(0.0825170\pi\) | ||||
−0.966586 | + | 0.256341i | \(0.917483\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −38.2643 | −1.29062 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −17.3877 | −0.585806 | −0.292903 | − | 0.956142i | \(-0.594621\pi\) | ||||
−0.292903 | + | 0.956142i | \(0.594621\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 8.46587i | − | 0.284899i | −0.989802 | − | 0.142450i | \(-0.954502\pi\) | ||
0.989802 | − | 0.142450i | \(-0.0454979\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 30.1529 | − | 45.4274i | 1.01358 | − | 1.52703i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 32.8229i | − | 1.10208i | −0.834477 | − | 0.551042i | \(-0.814230\pi\) | ||
0.834477 | − | 0.551042i | \(-0.185770\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14.6158 | −0.490199 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −43.7900 | −1.46702 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.184577i | 0.00617662i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 42.6708 | + | 28.3232i | 1.42633 | + | 0.946739i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 19.1290i | 0.638700i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.73758 | −0.191359 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.03085 | −0.300861 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 4.85731i | − | 0.161641i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.31144 | − | 2.19801i | −0.110076 | − | 0.0730642i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 54.6260i | 1.81383i | 0.421317 | + | 0.906913i | \(0.361568\pi\) | ||||
−0.421317 | + | 0.906913i | \(0.638432\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.811589 | −0.0269187 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.21329 | −0.139592 | −0.0697962 | − | 0.997561i | \(-0.522235\pi\) | ||||
−0.0697962 | + | 0.997561i | \(0.522235\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 75.5159i | − | 2.49921i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −22.7173 | + | 34.2252i | −0.751011 | + | 1.13145i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 17.8600i | − | 0.589789i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.0033 | −0.824784 | −0.412392 | − | 0.911007i | \(-0.635307\pi\) | ||||
−0.412392 | + | 0.911007i | \(0.635307\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.45077 | −0.179609 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 45.4346i | 1.49550i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 19.3483 | − | 8.15346i | 0.636170 | − | 0.268084i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.37907i | 0.0781388i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 34.5462 | 1.13342 | 0.566712 | − | 0.823916i | \(-0.308215\pi\) | ||||
0.566712 | + | 0.823916i | \(0.308215\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.72603 | −0.0565684 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.90642i | 0.0624134i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.24892 | − | 9.41442i | 0.204362 | − | 0.307884i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 19.7689i | − | 0.645821i | −0.946429 | − | 0.322911i | \(-0.895339\pi\) | ||
0.946429 | − | 0.322911i | \(-0.104661\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16.7242 | −0.545774 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −23.0820 | −0.752452 | −0.376226 | − | 0.926528i | \(-0.622778\pi\) | ||||
−0.376226 | + | 0.926528i | \(0.622778\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 38.2159i | − | 1.24448i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −9.01597 | − | 5.98444i | −0.293290 | − | 0.194674i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 60.0386i | − | 1.95099i | −0.220019 | − | 0.975496i | \(-0.570612\pi\) | ||
0.220019 | − | 0.975496i | \(-0.429388\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −38.0670 | −1.23571 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.69295 | −0.281888 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.4188i | 0.369891i | 0.982749 | + | 0.184945i | \(0.0592108\pi\) | ||||
−0.982749 | + | 0.184945i | \(0.940789\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −36.7355 | − | 24.3835i | −1.18873 | − | 0.789033i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 33.7965i | − | 1.09249i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.22523 | 0.168732 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.1244 | −0.939497 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.10022i | 0.0676786i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 22.8716 | − | 34.4577i | 0.736264 | − | 1.10923i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 28.9169i | − | 0.929903i | −0.885336 | − | 0.464952i | \(-0.846072\pi\) | ||
0.885336 | − | 0.464952i | \(-0.153928\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.63266 | 0.116698 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −43.1410 | −1.38446 | −0.692230 | − | 0.721677i | \(-0.743371\pi\) | ||||
−0.692230 | + | 0.721677i | \(0.743371\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 5.25800i | − | 0.168564i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −11.4184 | − | 27.0960i | −0.365680 | − | 0.867766i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 38.0221i | − | 1.21644i | −0.793770 | − | 0.608218i | \(-0.791885\pi\) | ||
0.793770 | − | 0.608218i | \(-0.208115\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −18.9945 | −0.607067 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.84787 | 0.122853 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 12.7030i | − | 0.405164i | −0.979265 | − | 0.202582i | \(-0.935067\pi\) | ||
0.979265 | − | 0.202582i | \(-0.0649332\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −24.0121 | + | 36.1759i | −0.765090 | + | 1.15266i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.196012i | 0.00623913i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.61992 | −0.274098 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.4382 | −0.808073 | −0.404036 | − | 0.914743i | \(-0.632393\pi\) | ||||
−0.404036 | + | 0.914743i | \(0.632393\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 17.1954i | − | 0.545678i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −40.5178 | − | 26.8941i | −1.28450 | − | 0.852600i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 13.5489i | − | 0.429098i | −0.976713 | − | 0.214549i | \(-0.931172\pi\) | ||
0.976713 | − | 0.214549i | \(-0.0688281\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −20.3219 | −0.642958 |
(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 | 2240.2.g.o.449.3 | 10 | ||
4.3 | odd | 2 | 2240.2.g.n.449.8 | 10 | |||
5.4 | even | 2 | inner | 2240.2.g.o.449.8 | 10 | ||
8.3 | odd | 2 | 1120.2.g.c.449.3 | yes | 10 | ||
8.5 | even | 2 | 1120.2.g.b.449.8 | yes | 10 | ||
20.19 | odd | 2 | 2240.2.g.n.449.3 | 10 | |||
40.3 | even | 4 | 5600.2.a.bx.1.4 | 5 | |||
40.13 | odd | 4 | 5600.2.a.bu.1.2 | 5 | |||
40.19 | odd | 2 | 1120.2.g.c.449.8 | yes | 10 | ||
40.27 | even | 4 | 5600.2.a.bv.1.2 | 5 | |||
40.29 | even | 2 | 1120.2.g.b.449.3 | ✓ | 10 | ||
40.37 | odd | 4 | 5600.2.a.bw.1.4 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1120.2.g.b.449.3 | ✓ | 10 | 40.29 | even | 2 | ||
1120.2.g.b.449.8 | yes | 10 | 8.5 | even | 2 | ||
1120.2.g.c.449.3 | yes | 10 | 8.3 | odd | 2 | ||
1120.2.g.c.449.8 | yes | 10 | 40.19 | odd | 2 | ||
2240.2.g.n.449.3 | 10 | 20.19 | odd | 2 | |||
2240.2.g.n.449.8 | 10 | 4.3 | odd | 2 | |||
2240.2.g.o.449.3 | 10 | 1.1 | even | 1 | trivial | ||
2240.2.g.o.449.8 | 10 | 5.4 | even | 2 | inner | ||
5600.2.a.bu.1.2 | 5 | 40.13 | odd | 4 | |||
5600.2.a.bv.1.2 | 5 | 40.27 | even | 4 | |||
5600.2.a.bw.1.4 | 5 | 40.37 | odd | 4 | |||
5600.2.a.bx.1.4 | 5 | 40.3 | even | 4 |