Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1280,3,Mod(639,1280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1280.639");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1280 = 2^{8} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1280.e (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: | \(34.8774738381\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.1827904.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 9x^{4} + 14x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 160) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 639.1 | ||
Root | \(-2.65109i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1280.639 |
Dual form | 1280.3.e.f.639.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(261\) | \(511\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 5.30219i | − | 1.76740i | −0.468058 | − | 0.883698i | \(-0.655046\pi\) | ||
0.468058 | − | 0.883698i | \(-0.344954\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.75441 | − | 1.54778i | −0.950881 | − | 0.309556i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.206625 | 0.0295178 | 0.0147589 | − | 0.999891i | \(-0.495302\pi\) | ||||
0.0147589 | + | 0.999891i | \(0.495302\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −19.1132 | −2.12369 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −15.0176 | −1.36524 | −0.682619 | − | 0.730774i | \(-0.739159\pi\) | ||||
−0.682619 | + | 0.730774i | \(0.739159\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −11.6999 | −0.899995 | −0.449998 | − | 0.893030i | \(-0.648575\pi\) | ||||
−0.449998 | + | 0.893030i | \(0.648575\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −8.20662 | + | 25.2087i | −0.547108 | + | 1.68058i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 18.1911i | − | 1.07007i | −0.844831 | − | 0.535033i | \(-0.820299\pi\) | ||
0.844831 | − | 0.535033i | \(-0.179701\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −19.3999 | −1.02105 | −0.510523 | − | 0.859864i | \(-0.670548\pi\) | ||||
−0.510523 | + | 0.859864i | \(0.670548\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 1.09556i | − | 0.0521696i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 27.2242 | 1.18366 | 0.591831 | − | 0.806062i | \(-0.298405\pi\) | ||||
0.591831 | + | 0.806062i | \(0.298405\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 20.2087 | + | 14.7176i | 0.808350 | + | 0.588702i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 53.6220i | 1.98600i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 44.4175i | − | 1.53164i | −0.643056 | − | 0.765819i | \(-0.722334\pi\) | ||
0.643056 | − | 0.765819i | \(-0.277666\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 20.3822i | 0.657492i | 0.944418 | + | 0.328746i | \(0.106626\pi\) | ||||
−0.944418 | + | 0.328746i | \(0.893374\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 79.6262i | 2.41292i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.982377 | − | 0.319810i | −0.0280679 | − | 0.00913742i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 18.1089 | 0.489431 | 0.244715 | − | 0.969595i | \(-0.421305\pi\) | ||||
0.244715 | + | 0.969595i | \(0.421305\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 62.0352i | 1.59065i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 32.3043 | 0.787910 | 0.393955 | − | 0.919130i | \(-0.371107\pi\) | ||||
0.393955 | + | 0.919130i | \(0.371107\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 4.06244i | − | 0.0944753i | −0.998884 | − | 0.0472377i | \(-0.984958\pi\) | ||
0.998884 | − | 0.0472377i | \(-0.0150418\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 90.8718 | + | 29.5830i | 2.01937 | + | 0.657401i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.37588 | 0.114380 | 0.0571902 | − | 0.998363i | \(-0.481786\pi\) | ||||
0.0571902 | + | 0.998363i | \(0.481786\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −48.9573 | −0.999129 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −96.4527 | −1.89123 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 79.1703 | 1.49378 | 0.746890 | − | 0.664948i | \(-0.231546\pi\) | ||||
0.746890 | + | 0.664948i | \(0.231546\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 71.3999 | + | 23.2440i | 1.29818 | + | 0.422618i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 102.862i | 1.80459i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −83.3999 | −1.41356 | −0.706779 | − | 0.707435i | \(-0.749852\pi\) | ||||
−0.706779 | + | 0.707435i | \(0.749852\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 36.7486i | 0.602435i | 0.953555 | + | 0.301218i | \(0.0973931\pi\) | ||||
−0.953555 | + | 0.301218i | \(0.902607\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.94925 | −0.0626866 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 55.6262 | + | 18.1089i | 0.855788 | + | 0.278599i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.51518i | 0.0673907i | 0.999432 | + | 0.0336954i | \(0.0107276\pi\) | ||||
−0.999432 | + | 0.0336954i | \(0.989272\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 144.348i | − | 2.09200i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 41.6530i | − | 0.586662i | −0.956011 | − | 0.293331i | \(-0.905236\pi\) | ||
0.956011 | − | 0.293331i | \(-0.0947638\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 41.5910i | − | 0.569740i | −0.958566 | − | 0.284870i | \(-0.908050\pi\) | ||
0.958566 | − | 0.284870i | \(-0.0919504\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 78.0352 | − | 107.151i | 1.04047 | − | 1.42867i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.10301 | −0.0402988 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 15.5473i | − | 0.196801i | −0.995147 | − | 0.0984004i | \(-0.968627\pi\) | ||
0.995147 | − | 0.0984004i | \(-0.0313726\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 112.295 | 1.38636 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 50.9862i | 0.614291i | 0.951663 | + | 0.307146i | \(0.0993739\pi\) | ||||
−0.951663 | + | 0.307146i | \(0.900626\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −28.1559 | + | 86.4880i | −0.331246 | + | 1.01751i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −235.510 | −2.70701 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.8885 | −0.122343 | −0.0611713 | − | 0.998127i | \(-0.519484\pi\) | ||||
−0.0611713 | + | 0.998127i | \(0.519484\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.41749 | −0.0265659 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 108.070 | 1.16205 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 92.2349 | + | 30.0268i | 0.970893 | + | 0.316071i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 12.1559i | − | 0.125318i | −0.998035 | − | 0.0626592i | \(-0.980042\pi\) | ||
0.998035 | − | 0.0626592i | \(-0.0199581\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 287.035 | 2.89934 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 127.723i | 1.26459i | 0.774728 | + | 0.632294i | \(0.217887\pi\) | ||||
−0.774728 | + | 0.632294i | \(0.782113\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.77575 | −0.0463665 | −0.0231833 | − | 0.999731i | \(-0.507380\pi\) | ||||
−0.0231833 | + | 0.999731i | \(0.507380\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.69569 | + | 5.20875i | −0.0161494 | + | 0.0496071i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 107.213i | 1.00199i | 0.865449 | + | 0.500997i | \(0.167033\pi\) | ||||
−0.865449 | + | 0.500997i | \(0.832967\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 53.6689i | − | 0.492376i | −0.969222 | − | 0.246188i | \(-0.920822\pi\) | ||
0.969222 | − | 0.246188i | \(-0.0791780\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 96.0170i | − | 0.865018i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 20.5063i | 0.181471i | 0.995875 | + | 0.0907356i | \(0.0289218\pi\) | ||||
−0.995875 | + | 0.0907356i | \(0.971078\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −129.435 | − | 42.1372i | −1.12552 | − | 0.366410i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 223.623 | 1.91131 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 3.75873i | − | 0.0315860i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 104.529 | 0.863876 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 171.283i | − | 1.39255i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −73.3010 | − | 101.252i | −0.586408 | − | 0.810016i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −138.477 | −1.09037 | −0.545184 | − | 0.838316i | \(-0.683540\pi\) | ||||
−0.545184 | + | 0.838316i | \(0.683540\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −21.5398 | −0.166975 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 219.105 | 1.67256 | 0.836279 | − | 0.548304i | \(-0.184726\pi\) | ||||
0.836279 | + | 0.548304i | \(0.184726\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.00849 | −0.0301390 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 82.9951 | − | 254.941i | 0.614779 | − | 1.88845i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 59.7821i | 0.436366i | 0.975908 | + | 0.218183i | \(0.0700129\pi\) | ||||
−0.975908 | + | 0.218183i | \(0.929987\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 26.6524 | 0.191744 | 0.0958718 | − | 0.995394i | \(-0.469436\pi\) | ||||
0.0958718 | + | 0.995394i | \(0.469436\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 28.5039i | − | 0.202155i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 175.705 | 1.22871 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −68.7486 | + | 211.179i | −0.474128 | + | 1.45641i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 259.581i | 1.76586i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 143.463i | 0.962838i | 0.876490 | + | 0.481419i | \(0.159879\pi\) | ||||
−0.876490 | + | 0.481419i | \(0.840121\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 83.4937i | − | 0.552939i | −0.961023 | − | 0.276469i | \(-0.910836\pi\) | ||
0.961023 | − | 0.276469i | \(-0.0891644\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 347.690i | 2.27249i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 31.5473 | − | 96.9055i | 0.203531 | − | 0.625197i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 169.673 | 1.08072 | 0.540360 | − | 0.841434i | \(-0.318288\pi\) | ||||
0.540360 | + | 0.841434i | \(0.318288\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 419.776i | − | 2.64010i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.62520 | 0.0349391 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 275.478i | − | 1.69005i | −0.534726 | − | 0.845026i | \(-0.679585\pi\) | ||
0.534726 | − | 0.845026i | \(-0.320415\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 123.244 | − | 378.575i | 0.746933 | − | 2.29440i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −132.481 | −0.793299 | −0.396650 | − | 0.917970i | \(-0.629827\pi\) | ||||
−0.396650 | + | 0.917970i | \(0.629827\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −32.1115 | −0.190009 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 370.793 | 2.16838 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 272.614 | 1.57580 | 0.787901 | − | 0.615801i | \(-0.211168\pi\) | ||||
0.787901 | + | 0.615801i | \(0.211168\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.17562 | + | 3.04101i | 0.0238607 | + | 0.0173772i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 442.202i | 2.49831i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −157.523 | −0.880014 | −0.440007 | − | 0.897994i | \(-0.645024\pi\) | ||||
−0.440007 | + | 0.897994i | \(0.645024\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 335.063i | − | 1.85118i | −0.378529 | − | 0.925590i | \(-0.623570\pi\) | ||
0.378529 | − | 0.925590i | \(-0.376430\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 194.848 | 1.06474 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −86.0972 | − | 28.0287i | −0.465391 | − | 0.151506i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 273.187i | 1.46090i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 11.0796i | 0.0586223i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 298.575i | 1.56322i | 0.623766 | + | 0.781611i | \(0.285602\pi\) | ||||
−0.623766 | + | 0.781611i | \(0.714398\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 191.915i | − | 0.994376i | −0.867643 | − | 0.497188i | \(-0.834366\pi\) | ||
0.867643 | − | 0.497188i | \(-0.165634\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 96.0170 | − | 294.941i | 0.492395 | − | 1.51252i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −59.2472 | −0.300747 | −0.150374 | − | 0.988629i | \(-0.548048\pi\) | ||||
−0.150374 | + | 0.988629i | \(0.548048\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 309.100i | 1.55327i | 0.629953 | + | 0.776633i | \(0.283074\pi\) | ||||
−0.629953 | + | 0.776633i | \(0.716926\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 23.9403 | 0.119106 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 9.17775i | − | 0.0452106i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −153.588 | − | 50.0000i | −0.749209 | − | 0.243902i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −520.342 | −2.51373 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 291.340 | 1.39397 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −205.693 | −0.974850 | −0.487425 | − | 0.873165i | \(-0.662064\pi\) | ||||
−0.487425 | + | 0.873165i | \(0.662064\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −220.852 | −1.03686 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.28777 | + | 19.3145i | −0.0292454 | + | 0.0898348i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.21147i | 0.0194077i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −220.523 | −1.00696 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 212.835i | 0.963054i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −228.723 | −1.02567 | −0.512833 | − | 0.858488i | \(-0.671404\pi\) | ||||
−0.512833 | + | 0.858488i | \(0.671404\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −386.254 | − | 281.299i | −1.71668 | − | 1.25022i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 282.403i | 1.24407i | 0.782991 | + | 0.622033i | \(0.213693\pi\) | ||||
−0.782991 | + | 0.622033i | \(0.786307\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 49.2525i | 0.215076i | 0.994201 | + | 0.107538i | \(0.0342968\pi\) | ||||
−0.994201 | + | 0.107538i | \(0.965703\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 16.4527i | 0.0712240i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 124.273i | − | 0.533363i | −0.963785 | − | 0.266681i | \(-0.914073\pi\) | ||
0.963785 | − | 0.266681i | \(-0.0859271\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −25.5591 | − | 8.32069i | −0.108762 | − | 0.0354072i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −82.4345 | −0.347825 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 80.4527i | 0.336622i | 0.985734 | + | 0.168311i | \(0.0538313\pi\) | ||||
−0.985734 | + | 0.168311i | \(0.946169\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.20979 | −0.00501988 | −0.00250994 | − | 0.999997i | \(-0.500799\pi\) | ||||
−0.00250994 | + | 0.999997i | \(0.500799\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 112.812i | − | 0.464247i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 232.763 | + | 75.7752i | 0.950053 | + | 0.309287i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 226.977 | 0.918936 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 270.338 | 1.08570 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −211.853 | −0.844034 | −0.422017 | − | 0.906588i | \(-0.638678\pi\) | ||||
−0.422017 | + | 0.906588i | \(0.638678\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −408.843 | −1.61598 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 458.575 | + | 149.288i | 1.79834 | + | 0.585442i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 182.646i | − | 0.710685i | −0.934736 | − | 0.355342i | \(-0.884364\pi\) | ||
0.934736 | − | 0.355342i | \(-0.115636\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.74175 | 0.0144469 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 848.960i | 3.25272i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −74.6636 | −0.283892 | −0.141946 | − | 0.989874i | \(-0.545336\pi\) | ||||
−0.141946 | + | 0.989874i | \(0.545336\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −376.408 | − | 122.538i | −1.42041 | − | 0.462409i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 57.7329i | 0.216228i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 184.089i | 0.684344i | 0.939637 | + | 0.342172i | \(0.111163\pi\) | ||||
−0.939637 | + | 0.342172i | \(0.888837\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 234.746i | 0.866222i | 0.901341 | + | 0.433111i | \(0.142584\pi\) | ||||
−0.901341 | + | 0.433111i | \(0.857416\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 12.8180i | 0.0469524i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −303.487 | − | 221.023i | −1.10359 | − | 0.803719i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −452.208 | −1.63252 | −0.816260 | − | 0.577684i | \(-0.803957\pi\) | ||||
−0.816260 | + | 0.577684i | \(0.803957\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 389.570i | − | 1.39631i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 196.110 | 0.697900 | 0.348950 | − | 0.937141i | \(-0.386538\pi\) | ||||
0.348950 | + | 0.937141i | \(0.386538\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 418.449i | 1.47862i | 0.673366 | + | 0.739309i | \(0.264848\pi\) | ||||
−0.673366 | + | 0.739309i | \(0.735152\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 159.207 | − | 489.046i | 0.558623 | − | 1.71595i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.67486 | 0.0232574 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −41.9170 | −0.145042 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −64.4527 | −0.221487 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 286.666 | 0.978383 | 0.489191 | − | 0.872176i | \(-0.337292\pi\) | ||||
0.489191 | + | 0.872176i | \(0.337292\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 396.517 | + | 129.085i | 1.34412 | + | 0.437575i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 805.275i | − | 2.71136i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −318.522 | −1.06529 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 0.839400i | − | 0.00278870i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 677.214 | 2.23503 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 56.8787 | − | 174.718i | 0.186488 | − | 0.572844i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 261.715i | 0.852493i | 0.904607 | + | 0.426247i | \(0.140164\pi\) | ||||
−0.904607 | + | 0.426247i | \(0.859836\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 25.3219i | 0.0819480i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 578.904i | 1.86143i | 0.365747 | + | 0.930714i | \(0.380813\pi\) | ||||
−0.365747 | + | 0.930714i | \(0.619187\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 99.3124i | 0.317292i | 0.987336 | + | 0.158646i | \(0.0507129\pi\) | ||||
−0.987336 | + | 0.158646i | \(0.949287\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 18.7764 | + | 6.11258i | 0.0596075 | + | 0.0194050i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 191.623 | 0.604489 | 0.302245 | − | 0.953230i | \(-0.402264\pi\) | ||||
0.302245 | + | 0.953230i | \(0.402264\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 667.045i | 2.09105i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 568.466 | 1.77092 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 352.905i | 1.09259i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −236.441 | − | 172.194i | −0.727511 | − | 0.529829i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −284.563 | −0.870222 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.11079 | 0.00337626 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −530.187 | −1.60177 | −0.800886 | − | 0.598816i | \(-0.795638\pi\) | ||||
−0.800886 | + | 0.598816i | \(0.795638\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −346.120 | −1.03940 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.98851 | − | 21.4670i | 0.0208612 | − | 0.0640806i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 487.427i | − | 1.44637i | −0.690653 | − | 0.723186i | \(-0.742677\pi\) | ||
0.690653 | − | 0.723186i | \(-0.257323\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 108.728 | 0.320731 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 306.093i | − | 0.897633i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.2404 | −0.0590099 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −223.419 | + | 686.289i | −0.647592 | + | 1.98924i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 310.497i | − | 0.894804i | −0.894333 | − | 0.447402i | \(-0.852349\pi\) | ||
0.894333 | − | 0.447402i | \(-0.147651\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 253.004i | 0.724941i | 0.931995 | + | 0.362471i | \(0.118067\pi\) | ||||
−0.931995 | + | 0.362471i | \(0.881933\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 627.374i | − | 1.78739i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 322.639i | 0.913992i | 0.889469 | + | 0.456996i | \(0.151075\pi\) | ||||
−0.889469 | + | 0.456996i | \(0.848925\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −64.4697 | + | 198.035i | −0.181605 | + | 0.557846i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −19.9295 | −0.0558250 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 254.975i | 0.710236i | 0.934822 | + | 0.355118i | \(0.115559\pi\) | ||||
−0.934822 | + | 0.355118i | \(0.884441\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.3550 | 0.0425347 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 554.232i | − | 1.52681i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −64.3738 | + | 197.740i | −0.176366 | + | 0.541755i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −207.935 | −0.566581 | −0.283291 | − | 0.959034i | \(-0.591426\pi\) | ||||
−0.283291 | + | 0.959034i | \(0.591426\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −617.438 | −1.67327 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16.3585 | 0.0440931 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 203.826 | 0.546450 | 0.273225 | − | 0.961950i | \(-0.411910\pi\) | ||||
0.273225 | + | 0.961950i | \(0.411910\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −536.857 | + | 388.656i | −1.43162 | + | 1.03642i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 519.682i | 1.37847i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 454.099 | 1.19815 | 0.599076 | − | 0.800692i | \(-0.295535\pi\) | ||||
0.599076 | + | 0.800692i | \(0.295535\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 734.229i | 1.92711i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −541.569 | −1.41402 | −0.707009 | − | 0.707205i | \(-0.749956\pi\) | ||||
−0.707009 | + | 0.707205i | \(0.749956\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.7530 | + | 4.80278i | 0.0383194 | + | 0.0124748i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 77.6462i | 0.200636i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 423.431i | − | 1.08851i | −0.838919 | − | 0.544256i | \(-0.816812\pi\) | ||
0.838919 | − | 0.544256i | \(-0.183188\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 495.240i | − | 1.26660i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 1161.74i | − | 2.95607i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −24.0638 | + | 73.9180i | −0.0609209 | + | 0.187134i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.7772 | −0.0296654 | −0.0148327 | − | 0.999890i | \(-0.504722\pi\) | ||||
−0.0148327 | + | 0.999890i | \(0.504722\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 21.2538i | 0.0532676i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 127.442 | 0.317809 | 0.158905 | − | 0.987294i | \(-0.449204\pi\) | ||||
0.158905 | + | 0.987294i | \(0.449204\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 238.471i | − | 0.591739i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −533.897 | − | 173.808i | −1.31826 | − | 0.429156i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −271.953 | −0.668190 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −608.012 | −1.48658 | −0.743290 | − | 0.668969i | \(-0.766736\pi\) | ||||
−0.743290 | + | 0.668969i | \(0.766736\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 316.976 | 0.771231 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −17.2325 | −0.0417251 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 78.9155 | − | 242.409i | 0.190158 | − | 0.584118i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 141.316i | − | 0.338887i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −565.630 | −1.34995 | −0.674976 | − | 0.737840i | \(-0.735846\pi\) | ||||
−0.674976 | + | 0.737840i | \(0.735846\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 711.356i | 1.68968i | 0.535018 | + | 0.844841i | \(0.320305\pi\) | ||||
−0.535018 | + | 0.844841i | \(0.679695\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −102.750 | −0.242908 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 267.729 | − | 367.620i | 0.629950 | − | 0.864988i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.59316i | 0.0177826i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 931.622i | − | 2.17161i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 309.254i | − | 0.717526i | −0.933429 | − | 0.358763i | \(-0.883199\pi\) | ||
0.933429 | − | 0.358763i | \(-0.116801\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 187.374i | − | 0.432735i | −0.976312 | − | 0.216368i | \(-0.930579\pi\) | ||
0.976312 | − | 0.216368i | \(-0.0694210\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1119.71 | + | 364.518i | 2.57404 | + | 0.837972i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −528.147 | −1.20857 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 289.657i | 0.659811i | 0.944014 | + | 0.329906i | \(0.107017\pi\) | ||||
−0.944014 | + | 0.329906i | \(0.892983\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 935.730 | 2.12184 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 295.516i | − | 0.667079i | −0.942736 | − | 0.333539i | \(-0.891757\pi\) | ||
0.942736 | − | 0.333539i | \(-0.108243\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 51.7683 | + | 16.8530i | 0.116333 | + | 0.0378719i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 760.667 | 1.70172 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −604.409 | −1.34612 | −0.673061 | − | 0.739587i | \(-0.735021\pi\) | ||||
−0.673061 | + | 0.739587i | \(0.735021\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −485.134 | −1.07569 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −442.699 | −0.977262 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 11.4937 | + | 3.74175i | 0.0252610 | + | 0.00822363i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 392.507i | − | 0.858877i | −0.903096 | − | 0.429438i | \(-0.858712\pi\) | ||
0.903096 | − | 0.429438i | \(-0.141288\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 975.444 | 2.12515 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 400.277i | 0.868279i | 0.900846 | + | 0.434139i | \(0.142947\pi\) | ||||
−0.900846 | + | 0.434139i | \(0.857053\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 732.679 | 1.58246 | 0.791230 | − | 0.611518i | \(-0.209441\pi\) | ||||
0.791230 | + | 0.611518i | \(0.209441\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −513.811 | − | 167.269i | −1.10497 | − | 0.359719i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 592.126i | − | 1.26794i | −0.773360 | − | 0.633968i | \(-0.781425\pi\) | ||
0.773360 | − | 0.633968i | \(-0.218575\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.932947i | 0.00198923i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 899.639i | − | 1.91006i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 61.0082i | 0.128981i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −392.047 | − | 285.519i | −0.825362 | − | 0.601092i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1513.20 | −3.17232 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 309.151i | − | 0.645409i | −0.946500 | − | 0.322705i | \(-0.895408\pi\) | ||
0.946500 | − | 0.322705i | \(-0.104592\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −211.873 | −0.440485 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 29.8259i | − | 0.0617513i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −18.8146 | + | 57.7940i | −0.0387931 | + | 0.119163i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 570.769 | 1.17201 | 0.586005 | − | 0.810307i | \(-0.300700\pi\) | ||||
0.586005 | + | 0.810307i | \(0.300700\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1460.64 | −2.98699 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −301.659 | −0.614378 | −0.307189 | − | 0.951649i | \(-0.599388\pi\) | ||||
−0.307189 | + | 0.951649i | \(0.599388\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −808.004 | −1.63895 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1364.68 | − | 444.267i | −2.75693 | − | 0.897509i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 8.60653i | − | 0.0173170i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 517.758 | 1.03759 | 0.518795 | − | 0.854898i | \(-0.326381\pi\) | ||||
0.518795 | + | 0.854898i | \(0.326381\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 702.439i | 1.40207i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 406.671 | 0.808491 | 0.404246 | − | 0.914650i | \(-0.367534\pi\) | ||||
0.404246 | + | 0.914650i | \(0.367534\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 197.688 | − | 607.249i | 0.391461 | − | 1.20247i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 170.261i | 0.335821i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 627.097i | − | 1.23202i | −0.787739 | − | 0.616009i | \(-0.788748\pi\) | ||
0.787739 | − | 0.616009i | \(-0.211252\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 8.59372i | − | 0.0168175i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 1040.26i | − | 2.02780i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 22.7059 | + | 7.39182i | 0.0440891 | + | 0.0143530i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −80.7330 | −0.156157 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 1445.45i | − | 2.78507i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 111.743 | 0.214478 | 0.107239 | − | 0.994233i | \(-0.465799\pi\) | ||||
0.107239 | + | 0.994233i | \(0.465799\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 769.813i | 1.47192i | 0.677027 | + | 0.735959i | \(0.263268\pi\) | ||||
−0.677027 | + | 0.735959i | \(0.736732\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 16.1240 | − | 22.1399i | 0.0307124 | − | 0.0421713i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 370.776 | 0.703560 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 212.160 | 0.401058 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1594.04 | 3.00195 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −377.958 | −0.709115 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 165.943 | − | 509.736i | 0.310174 | − | 0.952778i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 835.214i | 1.55533i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 735.222 | 1.36405 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 225.558i | 0.416927i | 0.978030 | + | 0.208463i | \(0.0668462\pi\) | ||||
−0.978030 | + | 0.208463i | \(0.933154\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1776.57 | −3.27177 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −83.0678 | + | 255.164i | −0.152418 | + | 0.468191i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 882.346i | − | 1.61306i | −0.591190 | − | 0.806532i | \(-0.701342\pi\) | ||
0.591190 | − | 0.806532i | \(-0.298658\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 702.382i | − | 1.27938i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 861.694i | 1.56387i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 3.21245i | − | 0.00580913i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −148.613 | + | 456.504i | −0.267772 | + | 0.822529i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 303.119 | 0.544199 | 0.272100 | − | 0.962269i | \(-0.412282\pi\) | ||||
0.272100 | + | 0.962269i | \(0.412282\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 47.5303i | 0.0850273i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1448.49 | 2.58198 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 344.003i | 0.611017i | 0.952189 | + | 0.305508i | \(0.0988264\pi\) | ||||
−0.952189 | + | 0.305508i | \(0.901174\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 31.7392 | − | 97.4950i | 0.0561756 | − | 0.172558i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 23.2029 | 0.0409223 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 228.925 | 0.402329 | 0.201165 | − | 0.979557i | \(-0.435527\pi\) | ||||
0.201165 | + | 0.979557i | \(0.435527\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 371.169 | 0.650033 | 0.325017 | − | 0.945708i | \(-0.394630\pi\) | ||||
0.325017 | + | 0.945708i | \(0.394630\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1583.10 | 2.76283 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 550.168 | + | 400.674i | 0.956814 | + | 0.696825i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 580.289i | − | 1.00570i | −0.864374 | − | 0.502850i | \(-0.832285\pi\) | ||
0.864374 | − | 0.502850i | \(-0.167715\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1017.57 | −1.75746 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.5350i | 0.0181325i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1188.95 | −2.03936 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1063.19 | − | 346.120i | −1.81743 | − | 0.591657i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 65.0801i | 0.110869i | 0.998462 | + | 0.0554345i | \(0.0176544\pi\) | ||||
−0.998462 | + | 0.0554345i | \(0.982346\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 395.413i | − | 0.671329i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 314.140i | 0.531539i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1002.90i | 1.69124i | 0.533787 | + | 0.845619i | \(0.320768\pi\) | ||||
−0.533787 | + | 0.845619i | \(0.679232\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.81770 | + | 17.8705i | −0.00977764 | + | 0.0300345i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1638.91 | 2.74524 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 888.567i | − | 1.48342i | −0.670722 | − | 0.741709i | \(-0.734016\pi\) | ||
0.670722 | − | 0.741709i | \(-0.265984\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −132.065 | −0.219742 | −0.109871 | − | 0.993946i | \(-0.535044\pi\) | ||||
−0.109871 | + | 0.993946i | \(0.535044\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 86.2995i | − | 0.143117i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −496.973 | − | 161.788i | −0.821443 | − | 0.267418i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 700.090 | 1.15336 | 0.576680 | − | 0.816970i | \(-0.304348\pi\) | ||||
0.576680 | + | 0.816970i | \(0.304348\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −48.6621 | −0.0799050 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −62.8975 | −0.102942 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −727.420 | −1.18666 | −0.593328 | − | 0.804961i | \(-0.702186\pi\) | ||||
−0.593328 | + | 0.804961i | \(0.702186\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −265.109 | + | 814.351i | −0.431072 | + | 1.32415i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 99.7137i | − | 0.161611i | −0.996730 | − | 0.0808053i | \(-0.974251\pi\) | ||
0.996730 | − | 0.0808053i | \(-0.0257492\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −721.349 | −1.16535 | −0.582673 | − | 0.812707i | \(-0.697993\pi\) | ||||
−0.582673 | + | 0.812707i | \(0.697993\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1459.82i | 2.35075i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.24983 | −0.00361129 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 191.787 | + | 594.847i | 0.306859 | + | 0.951755i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 1544.74i | − | 2.46370i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 329.422i | − | 0.523723i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 796.856i | 1.26285i | 0.775438 | + | 0.631423i | \(0.217529\pi\) | ||||
−0.775438 | + | 0.631423i | \(0.782471\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1090.62i | 1.72295i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 658.375 | + | 214.332i | 1.03681 | + | 0.337530i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 572.797 | 0.899211 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 796.121i | 1.24589i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 205.013 | 0.319833 | 0.159917 | − | 0.987131i | \(-0.448877\pi\) | ||||
0.159917 | + | 0.987131i | \(0.448877\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 495.044i | 0.769897i | 0.922938 | + | 0.384949i | \(0.125781\pi\) | ||||
−0.922938 | + | 0.384949i | \(0.874219\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 102.409 | + | 33.3389i | 0.158774 | + | 0.0516882i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1121.84 | 1.73391 | 0.866953 | − | 0.498389i | \(-0.166075\pi\) | ||||
0.866953 | + | 0.498389i | \(0.166075\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1252.47 | 1.92984 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 22.3300 | 0.0343011 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 622.987 | 0.954038 | 0.477019 | − | 0.878893i | \(-0.341717\pi\) | ||||
0.477019 | + | 0.878893i | \(0.341717\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1041.71 | − | 339.127i | −1.59040 | − | 0.517751i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 794.936i | 1.20995i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −264.030 | −0.400653 | −0.200326 | − | 0.979729i | \(-0.564200\pi\) | ||||
−0.200326 | + | 0.979729i | \(0.564200\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1285.15i | 1.94425i | 0.234469 | + | 0.972124i | \(0.424665\pi\) | ||||
−0.234469 | + | 0.972124i | \(0.575335\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1128.49 | 1.70210 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 19.0580 | + | 6.20427i | 0.0286586 | + | 0.00932972i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 1209.23i | − | 1.81294i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1212.73i | 1.81276i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 551.876i | − | 0.822468i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 1244.16i | − | 1.84868i | −0.381565 | − | 0.924342i | \(-0.624615\pi\) | ||
0.381565 | − | 0.924342i | \(-0.375385\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −789.185 | + | 1083.63i | −1.16916 | + | 1.60538i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 963.335 | 1.42295 | 0.711473 | − | 0.702713i | \(-0.248028\pi\) | ||||
0.711473 | + | 0.702713i | \(0.248028\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 2.51170i | − | 0.00369912i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1497.35 | 2.19876 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 770.819i | 1.12858i | 0.825577 | + | 0.564289i | \(0.190850\pi\) | ||||
−0.825577 | + | 0.564289i | \(0.809150\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 92.5296 | − | 284.228i | 0.135080 | − | 0.414932i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 261.146 | 0.380125 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −926.287 | −1.34439 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −408.765 | −0.591555 | −0.295778 | − | 0.955257i | \(-0.595579\pi\) | ||||
−0.295778 | + | 0.955257i | \(0.595579\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 59.3084 | 0.0855821 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −126.716 | − | 41.2520i | −0.182325 | − | 0.0593554i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 587.652i | − | 0.843116i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −658.921 | −0.942663 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1335.62i | − | 1.90530i | −0.304068 | − | 0.952650i | \(-0.598345\pi\) | ||
0.304068 | − | 0.952650i | \(-0.401655\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −351.311 | −0.499731 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −44.1178 | + | 135.519i | −0.0625785 | + | 0.192226i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 26.3908i | 0.0373279i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 362.956i | 0.511927i | 0.966686 | + | 0.255964i | \(0.0823927\pi\) | ||||
−0.966686 | + | 0.255964i | \(0.917607\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 297.158i | 0.417943i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 554.891i | 0.778249i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −835.374 | − | 271.953i | −1.16836 | − | 0.380354i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 426.575 | 0.594945 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 648.098i | 0.901388i | 0.892679 | + | 0.450694i | \(0.148823\pi\) | ||||
−0.892679 | + | 0.450694i | \(0.851177\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.986788 | −0.00136864 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.41453i | 0.00887211i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 653.717 | − | 897.622i | 0.901679 | − | 1.23810i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −431.123 | −0.593017 | −0.296508 | − | 0.955030i | \(-0.595822\pi\) | ||||
−0.296508 | + | 0.955030i | \(0.595822\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 412.506 | 0.565852 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −73.9003 | −0.101095 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1464.87 | −1.99846 | −0.999231 | − | 0.0392126i | \(-0.987515\pi\) | ||||
−0.999231 | + | 0.0392126i | \(0.987515\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 401.774 | − | 1234.15i | 0.546632 | − | 1.67912i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 67.8073i | − | 0.0920044i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −99.1951 | −0.134229 | −0.0671144 | − | 0.997745i | \(-0.521379\pi\) | ||||
−0.0671144 | + | 0.997745i | \(0.521379\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 1203.48i | − | 1.62412i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −602.719 | −0.811196 | −0.405598 | − | 0.914052i | \(-0.632937\pi\) | ||||
−0.405598 | + | 0.914052i | \(0.632937\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 222.049 | − | 682.081i | 0.298053 | − | 0.915545i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 974.508i | − | 1.30456i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 22.1529i | 0.0295767i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 541.472i | 0.721001i | 0.932759 | + | 0.360501i | \(0.117394\pi\) | ||||
−0.932759 | + | 0.360501i | \(0.882606\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1123.28i | 1.49174i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −129.230 | + | 396.963i | −0.171166 | + | 0.525779i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1092.79 | −1.44358 | −0.721789 | − | 0.692113i | \(-0.756680\pi\) | ||||
−0.721789 | + | 0.692113i | \(0.756680\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2167.76i | 2.85608i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.7706 | 0.0246657 | 0.0123328 | − | 0.999924i | \(-0.496074\pi\) | ||||
0.0123328 | + | 0.999924i | \(0.496074\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 11.0893i | − | 0.0145338i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 538.149 | − | 1653.06i | 0.703462 | − | 2.16086i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 975.773 | 1.27219 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 39.0830 | 0.0508231 | 0.0254116 | − | 0.999677i | \(-0.491910\pi\) | ||||
0.0254116 | + | 0.999677i | \(0.491910\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −968.423 | −1.25606 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 31.2171 | 0.0403843 | 0.0201922 | − | 0.999796i | \(-0.493572\pi\) | ||||
0.0201922 | + | 0.999796i | \(0.493572\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −299.977 | + | 411.900i | −0.387067 | + | 0.531484i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 19.8395i | − | 0.0255334i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −626.699 | −0.804492 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 625.529i | 0.800933i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2381.75 | 3.04183 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −806.695 | − | 262.617i | −1.02764 | − | 0.334544i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 988.563i | 1.25612i | 0.778167 | + | 0.628058i | \(0.216150\pi\) | ||||
−0.778167 | + | 0.628058i | \(0.783850\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 395.880i | 0.501750i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.23710i | 0.00535663i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 429.956i | − | 0.542189i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −649.721 | + | 1995.78i | −0.817259 | + | 2.51042i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −118.920 | −0.149210 | −0.0746048 | − | 0.997213i | \(-0.523770\pi\) | ||||
−0.0746048 | + | 0.997213i | \(0.523770\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 97.7933i | − | 0.122395i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 208.114 | 0.259818 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 624.598i | 0.777831i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −26.7445 | − | 8.70658i | −0.0332230 | − | 0.0108156i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 976.072 | 1.20951 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1214.04 | −1.50067 | −0.750337 | − | 0.661056i | \(-0.770109\pi\) | ||||
−0.750337 | + | 0.661056i | \(0.770109\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 706.666 | 0.871351 | 0.435676 | − | 0.900104i | \(-0.356509\pi\) | ||||
0.435676 | + | 0.900104i | \(0.356509\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1244.67 | 1.53096 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −426.380 | + | 1309.74i | −0.523166 | + | 1.60704i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 78.8108i | 0.0964636i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 46.2060 | 0.0564176 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 991.775i | 1.20801i | 0.796981 | + | 0.604004i | \(0.206429\pi\) | ||||
−0.796981 | + | 0.604004i | \(0.793571\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −523.998 | −0.636693 | −0.318347 | − | 0.947974i | \(-0.603128\pi\) | ||||
−0.318347 | + | 0.947974i | \(0.603128\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1171.90 | + | 1609.15i | −1.42049 | + | 1.95048i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 318.794i | 0.385483i | 0.981250 | + | 0.192741i | \(0.0617379\pi\) | ||||
−0.981250 | + | 0.192741i | \(0.938262\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1034.11i | 1.24742i | 0.781655 | + | 0.623711i | \(0.214376\pi\) | ||||
−0.781655 | + | 0.623711i | \(0.785624\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2397.69i | 2.88531i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 890.588i | 1.06913i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 629.868 | + | 205.052i | 0.754333 | + | 0.245571i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1092.94 | −1.30578 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 445.284i | − | 0.530732i | −0.964148 | − | 0.265366i | \(-0.914507\pi\) | ||
0.964148 | − | 0.265366i | \(-0.0854928\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1131.91 | −1.34591 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 1039.81i | − | 1.23346i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 152.671 | + | 49.7016i | 0.180676 | + | 0.0588184i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 21.5983 | 0.0254997 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2218.69 | 2.61330 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 493.002 | 0.579321 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1200.49 | 1.40737 | 0.703684 | − | 0.710513i | \(-0.251537\pi\) | ||||
0.703684 | + | 0.710513i | \(0.251537\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1762.90 | − | 573.907i | −2.06187 | − | 0.671236i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1223.15i | 1.42724i | 0.700531 | + | 0.713622i | \(0.252946\pi\) | ||||
−0.700531 | + | 0.713622i | \(0.747054\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 210.033 | 0.244509 | 0.122254 | − | 0.992499i | \(-0.460988\pi\) | ||||
0.122254 | + | 0.992499i | \(0.460988\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 35.3914i | − | 0.0411050i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1560.47 | −1.80819 | −0.904095 | − | 0.427333i | \(-0.859453\pi\) | ||||
−0.904095 | + | 0.427333i | \(0.859453\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1296.12 | − | 421.947i | −1.49840 | − | 0.487800i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 222.252i | 0.256346i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 233.483i | 0.268680i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 52.8273i | − | 0.0606513i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 232.338i | 0.266137i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −15.1458 | − | 20.9211i | −0.0173095 | − | 0.0239099i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1011.66 | −1.15354 | −0.576771 | − | 0.816906i | \(-0.695687\pi\) | ||||
−0.576771 | + | 0.816906i | \(0.695687\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 1519.96i | − | 1.72919i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 266.455 | 0.302446 | 0.151223 | − | 0.988500i | \(-0.451679\pi\) | ||||
0.151223 | + | 0.988500i | \(0.451679\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 469.871i | 0.532130i | 0.963955 | + | 0.266065i | \(0.0857237\pi\) | ||||
−0.963955 | + | 0.266065i | \(0.914276\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 684.431 | − | 2102.41i | 0.773369 | − | 2.37560i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 764.559 | 0.861961 | 0.430980 | − | 0.902361i | \(-0.358168\pi\) | ||||
0.430980 | + | 0.902361i | \(0.358168\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −28.6127 | −0.0321853 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1686.41 | −1.89271 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −104.291 | −0.116788 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 748.926 | + | 243.810i | 0.836789 | + | 0.272414i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1688.86i | 1.88279i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 905.328 | 1.00704 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 1440.20i | − | 1.59844i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.45065 | −0.00492874 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −518.605 | + | 1593.03i | −0.573044 | + | 1.76025i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1333.20i | − | 1.46990i | −0.678123 | − | 0.734948i | \(-0.737206\pi\) | ||
0.678123 | − | 0.734948i | \(-0.262794\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 2441.20i | − | 2.68559i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1496.11i | − | 1.64227i | −0.570736 | − | 0.821134i | \(-0.693342\pi\) | ||
0.570736 | − | 0.821134i | \(-0.306658\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 765.691i | − | 0.838654i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −926.385 | − | 301.582i | −1.01244 | − | 0.329597i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 45.2725 | 0.0493702 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 564.228i | 0.613959i | 0.951716 | + | 0.306980i | \(0.0993183\pi\) | ||||
−0.951716 | + | 0.306980i | \(0.900682\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1387.66 | 1.50669 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 487.337i | 0.527993i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 365.959 | + | 266.519i | 0.395631 | + | 0.288129i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 91.2798 | 0.0984680 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1449.16 | 1.55991 | 0.779957 | − | 0.625833i | \(-0.215241\pi\) | ||||
0.779957 | + | 0.625833i | \(0.215241\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 949.765 | 1.02016 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3069.46 | 3.28988 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 422.834 | − | 1298.84i | 0.452229 | − | 1.38914i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 258.795i | 0.276196i | 0.990419 | + | 0.138098i | \(0.0440989\pi\) | ||||
−0.990419 | + | 0.138098i | \(0.955901\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 526.573 | 0.560781 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 20.3444i | − | 0.0216200i | −0.999942 | − | 0.0108100i | \(-0.996559\pi\) | ||
0.999942 | − | 0.0108100i | \(-0.00344100\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 879.461 | 0.932620 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 17.1488 | − | 52.6770i | 0.0181469 | − | 0.0557429i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 613.539i | − | 0.647876i | −0.946078 | − | 0.323938i | \(-0.894993\pi\) | ||
0.946078 | − | 0.323938i | \(-0.105007\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 486.612i | 0.512763i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 1016.02i | − | 1.06837i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 81.6126i | 0.0856376i | 0.999083 | + | 0.0428188i | \(0.0136338\pi\) | ||||
−0.999083 | + | 0.0428188i | \(0.986366\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 462.129 | − | 1419.55i | 0.483905 | − | 1.48644i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3536.80 | 3.69571 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12.3525i | 0.0128806i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 545.564 | 0.567704 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 2049.19i | − | 2.12792i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −297.042 | + | 912.440i | −0.307815 | + | 0.945534i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 127.482 | 0.131833 | 0.0659165 | − | 0.997825i | \(-0.479003\pi\) | ||||
0.0659165 | + | 0.997825i | \(0.479003\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1871.17 | 1.93103 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1122.62 | −1.15615 | −0.578076 | − | 0.815983i | \(-0.696196\pi\) | ||||
−0.578076 | + | 0.815983i | \(0.696196\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.50703 | 0.00565985 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −913.007 | + | 1253.65i | −0.936418 | + | 1.28580i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 424.837i | 0.434838i | 0.976078 | + | 0.217419i | \(0.0697639\pi\) | ||||
−0.976078 | + | 0.217419i | \(0.930236\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 163.519 | 0.167027 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1025.78i | 1.04565i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −663.324 | −0.674795 | −0.337398 | − | 0.941362i | \(-0.609547\pi\) | ||||
−0.337398 | + | 0.941362i | \(0.609547\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 281.685 | + | 91.7017i | 0.285975 | + | 0.0930982i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 5.88961i | − | 0.00596719i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 110.597i | − | 0.111827i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1771.36i | − | 1.78745i | −0.448616 | − | 0.893724i | \(-0.648083\pi\) | ||
0.448616 | − | 0.893724i | \(-0.351917\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2811.15i | 2.83097i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 478.419 | − | 1469.59i | 0.480823 | − | 1.47697i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −447.066 | −0.448411 | −0.224205 | − | 0.974542i | \(-0.571979\pi\) | ||||
−0.224205 | + | 0.974542i | \(0.571979\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 971.038i | 0.972010i |
(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 | 1280.3.e.f.639.1 | 6 | ||
4.3 | odd | 2 | 1280.3.e.g.639.6 | 6 | |||
5.4 | even | 2 | 1280.3.e.i.639.6 | 6 | |||
8.3 | odd | 2 | 1280.3.e.i.639.1 | 6 | |||
8.5 | even | 2 | 1280.3.e.h.639.6 | 6 | |||
16.3 | odd | 4 | 160.3.h.a.159.2 | yes | 6 | ||
16.5 | even | 4 | 320.3.h.f.319.1 | 6 | |||
16.11 | odd | 4 | 320.3.h.g.319.5 | 6 | |||
16.13 | even | 4 | 160.3.h.b.159.6 | yes | 6 | ||
20.19 | odd | 2 | 1280.3.e.h.639.1 | 6 | |||
40.19 | odd | 2 | inner | 1280.3.e.f.639.6 | 6 | ||
40.29 | even | 2 | 1280.3.e.g.639.1 | 6 | |||
48.29 | odd | 4 | 1440.3.j.b.1279.3 | 6 | |||
48.35 | even | 4 | 1440.3.j.a.1279.3 | 6 | |||
80.3 | even | 4 | 800.3.b.h.351.1 | 6 | |||
80.13 | odd | 4 | 800.3.b.h.351.6 | 6 | |||
80.19 | odd | 4 | 160.3.h.b.159.5 | yes | 6 | ||
80.27 | even | 4 | 1600.3.b.w.1151.1 | 6 | |||
80.29 | even | 4 | 160.3.h.a.159.1 | ✓ | 6 | ||
80.37 | odd | 4 | 1600.3.b.w.1151.6 | 6 | |||
80.43 | even | 4 | 1600.3.b.v.1151.6 | 6 | |||
80.53 | odd | 4 | 1600.3.b.v.1151.1 | 6 | |||
80.59 | odd | 4 | 320.3.h.f.319.2 | 6 | |||
80.67 | even | 4 | 800.3.b.i.351.6 | 6 | |||
80.69 | even | 4 | 320.3.h.g.319.6 | 6 | |||
80.77 | odd | 4 | 800.3.b.i.351.1 | 6 | |||
240.29 | odd | 4 | 1440.3.j.a.1279.4 | 6 | |||
240.179 | even | 4 | 1440.3.j.b.1279.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
160.3.h.a.159.1 | ✓ | 6 | 80.29 | even | 4 | ||
160.3.h.a.159.2 | yes | 6 | 16.3 | odd | 4 | ||
160.3.h.b.159.5 | yes | 6 | 80.19 | odd | 4 | ||
160.3.h.b.159.6 | yes | 6 | 16.13 | even | 4 | ||
320.3.h.f.319.1 | 6 | 16.5 | even | 4 | |||
320.3.h.f.319.2 | 6 | 80.59 | odd | 4 | |||
320.3.h.g.319.5 | 6 | 16.11 | odd | 4 | |||
320.3.h.g.319.6 | 6 | 80.69 | even | 4 | |||
800.3.b.h.351.1 | 6 | 80.3 | even | 4 | |||
800.3.b.h.351.6 | 6 | 80.13 | odd | 4 | |||
800.3.b.i.351.1 | 6 | 80.77 | odd | 4 | |||
800.3.b.i.351.6 | 6 | 80.67 | even | 4 | |||
1280.3.e.f.639.1 | 6 | 1.1 | even | 1 | trivial | ||
1280.3.e.f.639.6 | 6 | 40.19 | odd | 2 | inner | ||
1280.3.e.g.639.1 | 6 | 40.29 | even | 2 | |||
1280.3.e.g.639.6 | 6 | 4.3 | odd | 2 | |||
1280.3.e.h.639.1 | 6 | 20.19 | odd | 2 | |||
1280.3.e.h.639.6 | 6 | 8.5 | even | 2 | |||
1280.3.e.i.639.1 | 6 | 8.3 | odd | 2 | |||
1280.3.e.i.639.6 | 6 | 5.4 | even | 2 | |||
1440.3.j.a.1279.3 | 6 | 48.35 | even | 4 | |||
1440.3.j.a.1279.4 | 6 | 240.29 | odd | 4 | |||
1440.3.j.b.1279.3 | 6 | 48.29 | odd | 4 | |||
1440.3.j.b.1279.4 | 6 | 240.179 | even | 4 | |||
1600.3.b.v.1151.1 | 6 | 80.53 | odd | 4 | |||
1600.3.b.v.1151.6 | 6 | 80.43 | even | 4 | |||
1600.3.b.w.1151.1 | 6 | 80.27 | even | 4 | |||
1600.3.b.w.1151.6 | 6 | 80.37 | odd | 4 |