Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [175,4,Mod(99,175)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(175, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("175.99");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 175 = 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 175.b (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: | \(10.3253342510\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 35) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 99.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 175.99 |
Dual form | 175.4.b.a.99.2 |
$q$-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 \(\left(\mathbb{Z}/175\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.00000i | − 0.353553i | −0.984251 | − | 0.176777i | \(-0.943433\pi\) | ||||
0.984251 | − | 0.176777i | \(-0.0565670\pi\) | |||||||
\(3\) | − 8.00000i | − 1.53960i | −0.638285 | − | 0.769800i | \(-0.720356\pi\) | ||||
0.638285 | − | 0.769800i | \(-0.279644\pi\) | |||||||
\(4\) | 7.00000 | 0.875000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −8.00000 | −0.544331 | ||||||||
\(7\) | − 7.00000i | − 0.377964i | ||||||||
\(8\) | − 15.0000i | − 0.662913i | ||||||||
\(9\) | −37.0000 | −1.37037 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 12.0000 | 0.328921 | 0.164461 | − | 0.986384i | \(-0.447412\pi\) | ||||
0.164461 | + | 0.986384i | \(0.447412\pi\) | |||||||
\(12\) | − 56.0000i | − 1.34715i | ||||||||
\(13\) | − 78.0000i | − 1.66410i | −0.554700 | − | 0.832050i | \(-0.687167\pi\) | ||||
0.554700 | − | 0.832050i | \(-0.312833\pi\) | |||||||
\(14\) | −7.00000 | −0.133631 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 41.0000 | 0.640625 | ||||||||
\(17\) | 94.0000i | 1.34108i | 0.741874 | + | 0.670540i | \(0.233937\pi\) | ||||
−0.741874 | + | 0.670540i | \(0.766063\pi\) | |||||||
\(18\) | 37.0000i | 0.484499i | ||||||||
\(19\) | −40.0000 | −0.482980 | −0.241490 | − | 0.970403i | \(-0.577636\pi\) | ||||
−0.241490 | + | 0.970403i | \(0.577636\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −56.0000 | −0.581914 | ||||||||
\(22\) | − 12.0000i | − 0.116291i | ||||||||
\(23\) | 32.0000i | 0.290107i | 0.989424 | + | 0.145054i | \(0.0463354\pi\) | ||||
−0.989424 | + | 0.145054i | \(0.953665\pi\) | |||||||
\(24\) | −120.000 | −1.02062 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −78.0000 | −0.588348 | ||||||||
\(27\) | 80.0000i | 0.570222i | ||||||||
\(28\) | − 49.0000i | − 0.330719i | ||||||||
\(29\) | 50.0000 | 0.320164 | 0.160082 | − | 0.987104i | \(-0.448824\pi\) | ||||
0.160082 | + | 0.987104i | \(0.448824\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −248.000 | −1.43684 | −0.718421 | − | 0.695608i | \(-0.755135\pi\) | ||||
−0.718421 | + | 0.695608i | \(0.755135\pi\) | |||||||
\(32\) | − 161.000i | − 0.889408i | ||||||||
\(33\) | − 96.0000i | − 0.506408i | ||||||||
\(34\) | 94.0000 | 0.474143 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −259.000 | −1.19907 | ||||||||
\(37\) | 434.000i | 1.92836i | 0.265257 | + | 0.964178i | \(0.414543\pi\) | ||||
−0.265257 | + | 0.964178i | \(0.585457\pi\) | |||||||
\(38\) | 40.0000i | 0.170759i | ||||||||
\(39\) | −624.000 | −2.56205 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 402.000 | 1.53126 | 0.765632 | − | 0.643278i | \(-0.222426\pi\) | ||||
0.765632 | + | 0.643278i | \(0.222426\pi\) | |||||||
\(42\) | 56.0000i | 0.205738i | ||||||||
\(43\) | − 68.0000i | − 0.241161i | −0.992704 | − | 0.120580i | \(-0.961524\pi\) | ||||
0.992704 | − | 0.120580i | \(-0.0384755\pi\) | |||||||
\(44\) | 84.0000 | 0.287806 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 32.0000 | 0.102568 | ||||||||
\(47\) | − 536.000i | − 1.66348i | −0.555164 | − | 0.831741i | \(-0.687345\pi\) | ||||
0.555164 | − | 0.831741i | \(-0.312655\pi\) | |||||||
\(48\) | − 328.000i | − 0.986307i | ||||||||
\(49\) | −49.0000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 752.000 | 2.06473 | ||||||||
\(52\) | − 546.000i | − 1.45609i | ||||||||
\(53\) | 22.0000i | 0.0570176i | 0.999594 | + | 0.0285088i | \(0.00907586\pi\) | ||||
−0.999594 | + | 0.0285088i | \(0.990924\pi\) | |||||||
\(54\) | 80.0000 | 0.201604 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −105.000 | −0.250557 | ||||||||
\(57\) | 320.000i | 0.743597i | ||||||||
\(58\) | − 50.0000i | − 0.113195i | ||||||||
\(59\) | 560.000 | 1.23569 | 0.617846 | − | 0.786299i | \(-0.288006\pi\) | ||||
0.617846 | + | 0.786299i | \(0.288006\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −278.000 | −0.583512 | −0.291756 | − | 0.956493i | \(-0.594240\pi\) | ||||
−0.291756 | + | 0.956493i | \(0.594240\pi\) | |||||||
\(62\) | 248.000i | 0.508001i | ||||||||
\(63\) | 259.000i | 0.517951i | ||||||||
\(64\) | 167.000 | 0.326172 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −96.0000 | −0.179042 | ||||||||
\(67\) | 164.000i | 0.299042i | 0.988759 | + | 0.149521i | \(0.0477731\pi\) | ||||
−0.988759 | + | 0.149521i | \(0.952227\pi\) | |||||||
\(68\) | 658.000i | 1.17344i | ||||||||
\(69\) | 256.000 | 0.446649 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 672.000 | 1.12326 | 0.561632 | − | 0.827387i | \(-0.310174\pi\) | ||||
0.561632 | + | 0.827387i | \(0.310174\pi\) | |||||||
\(72\) | 555.000i | 0.908436i | ||||||||
\(73\) | 82.0000i | 0.131471i | 0.997837 | + | 0.0657354i | \(0.0209393\pi\) | ||||
−0.997837 | + | 0.0657354i | \(0.979061\pi\) | |||||||
\(74\) | 434.000 | 0.681777 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −280.000 | −0.422608 | ||||||||
\(77\) | − 84.0000i | − 0.124321i | ||||||||
\(78\) | 624.000i | 0.905822i | ||||||||
\(79\) | 1000.00 | 1.42416 | 0.712081 | − | 0.702097i | \(-0.247753\pi\) | ||||
0.712081 | + | 0.702097i | \(0.247753\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −359.000 | −0.492455 | ||||||||
\(82\) | − 402.000i | − 0.541384i | ||||||||
\(83\) | − 448.000i | − 0.592463i | −0.955116 | − | 0.296231i | \(-0.904270\pi\) | ||||
0.955116 | − | 0.296231i | \(-0.0957299\pi\) | |||||||
\(84\) | −392.000 | −0.509175 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −68.0000 | −0.0852631 | ||||||||
\(87\) | − 400.000i | − 0.492925i | ||||||||
\(88\) | − 180.000i | − 0.218046i | ||||||||
\(89\) | 870.000 | 1.03618 | 0.518089 | − | 0.855327i | \(-0.326644\pi\) | ||||
0.518089 | + | 0.855327i | \(0.326644\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −546.000 | −0.628971 | ||||||||
\(92\) | 224.000i | 0.253844i | ||||||||
\(93\) | 1984.00i | 2.21216i | ||||||||
\(94\) | −536.000 | −0.588130 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1288.00 | −1.36933 | ||||||||
\(97\) | − 1026.00i | − 1.07396i | −0.843594 | − | 0.536982i | \(-0.819564\pi\) | ||||
0.843594 | − | 0.536982i | \(-0.180436\pi\) | |||||||
\(98\) | 49.0000i | 0.0505076i | ||||||||
\(99\) | −444.000 | −0.450744 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 482.000 | 0.474859 | 0.237430 | − | 0.971405i | \(-0.423695\pi\) | ||||
0.237430 | + | 0.971405i | \(0.423695\pi\) | |||||||
\(102\) | − 752.000i | − 0.729991i | ||||||||
\(103\) | 272.000i | 0.260203i | 0.991501 | + | 0.130102i | \(0.0415304\pi\) | ||||
−0.991501 | + | 0.130102i | \(0.958470\pi\) | |||||||
\(104\) | −1170.00 | −1.10315 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 22.0000 | 0.0201588 | ||||||||
\(107\) | 444.000i | 0.401150i | 0.979678 | + | 0.200575i | \(0.0642811\pi\) | ||||
−0.979678 | + | 0.200575i | \(0.935719\pi\) | |||||||
\(108\) | 560.000i | 0.498945i | ||||||||
\(109\) | 1170.00 | 1.02813 | 0.514063 | − | 0.857753i | \(-0.328140\pi\) | ||||
0.514063 | + | 0.857753i | \(0.328140\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3472.00 | 2.96890 | ||||||||
\(112\) | − 287.000i | − 0.242133i | ||||||||
\(113\) | − 798.000i | − 0.664332i | −0.943221 | − | 0.332166i | \(-0.892221\pi\) | ||||
0.943221 | − | 0.332166i | \(-0.107779\pi\) | |||||||
\(114\) | 320.000 | 0.262901 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 350.000 | 0.280144 | ||||||||
\(117\) | 2886.00i | 2.28043i | ||||||||
\(118\) | − 560.000i | − 0.436883i | ||||||||
\(119\) | 658.000 | 0.506880 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1187.00 | −0.891811 | ||||||||
\(122\) | 278.000i | 0.206303i | ||||||||
\(123\) | − 3216.00i | − 2.35754i | ||||||||
\(124\) | −1736.00 | −1.25724 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 259.000 | 0.183123 | ||||||||
\(127\) | − 776.000i | − 0.542196i | −0.962552 | − | 0.271098i | \(-0.912613\pi\) | ||||
0.962552 | − | 0.271098i | \(-0.0873867\pi\) | |||||||
\(128\) | − 1455.00i | − 1.00473i | ||||||||
\(129\) | −544.000 | −0.371291 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1112.00 | 0.741648 | 0.370824 | − | 0.928703i | \(-0.379075\pi\) | ||||
0.370824 | + | 0.928703i | \(0.379075\pi\) | |||||||
\(132\) | − 672.000i | − 0.443107i | ||||||||
\(133\) | 280.000i | 0.182549i | ||||||||
\(134\) | 164.000 | 0.105727 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1410.00 | 0.889018 | ||||||||
\(137\) | 694.000i | 0.432791i | 0.976306 | + | 0.216396i | \(0.0694301\pi\) | ||||
−0.976306 | + | 0.216396i | \(0.930570\pi\) | |||||||
\(138\) | − 256.000i | − 0.157914i | ||||||||
\(139\) | −360.000 | −0.219675 | −0.109837 | − | 0.993950i | \(-0.535033\pi\) | ||||
−0.109837 | + | 0.993950i | \(0.535033\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4288.00 | −2.56110 | ||||||||
\(142\) | − 672.000i | − 0.397134i | ||||||||
\(143\) | − 936.000i | − 0.547358i | ||||||||
\(144\) | −1517.00 | −0.877894 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 82.0000 | 0.0464820 | ||||||||
\(147\) | 392.000i | 0.219943i | ||||||||
\(148\) | 3038.00i | 1.68731i | ||||||||
\(149\) | −2270.00 | −1.24809 | −0.624046 | − | 0.781388i | \(-0.714512\pi\) | ||||
−0.624046 | + | 0.781388i | \(0.714512\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 632.000 | 0.340606 | 0.170303 | − | 0.985392i | \(-0.445525\pi\) | ||||
0.170303 | + | 0.985392i | \(0.445525\pi\) | |||||||
\(152\) | 600.000i | 0.320174i | ||||||||
\(153\) | − 3478.00i | − 1.83778i | ||||||||
\(154\) | −84.0000 | −0.0439540 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −4368.00 | −2.24179 | ||||||||
\(157\) | 734.000i | 0.373118i | 0.982444 | + | 0.186559i | \(0.0597336\pi\) | ||||
−0.982444 | + | 0.186559i | \(0.940266\pi\) | |||||||
\(158\) | − 1000.00i | − 0.503517i | ||||||||
\(159\) | 176.000 | 0.0877843 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 224.000 | 0.109650 | ||||||||
\(162\) | 359.000i | 0.174109i | ||||||||
\(163\) | 2532.00i | 1.21670i | 0.793670 | + | 0.608348i | \(0.208168\pi\) | ||||
−0.793670 | + | 0.608348i | \(0.791832\pi\) | |||||||
\(164\) | 2814.00 | 1.33986 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −448.000 | −0.209467 | ||||||||
\(167\) | − 416.000i | − 0.192761i | −0.995345 | − | 0.0963804i | \(-0.969273\pi\) | ||||
0.995345 | − | 0.0963804i | \(-0.0307265\pi\) | |||||||
\(168\) | 840.000i | 0.385758i | ||||||||
\(169\) | −3887.00 | −1.76923 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1480.00 | 0.661862 | ||||||||
\(172\) | − 476.000i | − 0.211015i | ||||||||
\(173\) | 3042.00i | 1.33687i | 0.743769 | + | 0.668436i | \(0.233036\pi\) | ||||
−0.743769 | + | 0.668436i | \(0.766964\pi\) | |||||||
\(174\) | −400.000 | −0.174275 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 492.000 | 0.210715 | ||||||||
\(177\) | − 4480.00i | − 1.90247i | ||||||||
\(178\) | − 870.000i | − 0.366344i | ||||||||
\(179\) | 180.000 | 0.0751611 | 0.0375805 | − | 0.999294i | \(-0.488035\pi\) | ||||
0.0375805 | + | 0.999294i | \(0.488035\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1958.00 | −0.804072 | −0.402036 | − | 0.915624i | \(-0.631697\pi\) | ||||
−0.402036 | + | 0.915624i | \(0.631697\pi\) | |||||||
\(182\) | 546.000i | 0.222375i | ||||||||
\(183\) | 2224.00i | 0.898376i | ||||||||
\(184\) | 480.000 | 0.192316 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1984.00 | 0.782118 | ||||||||
\(187\) | 1128.00i | 0.441110i | ||||||||
\(188\) | − 3752.00i | − 1.45555i | ||||||||
\(189\) | 560.000 | 0.215524 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2888.00 | −1.09408 | −0.547038 | − | 0.837108i | \(-0.684245\pi\) | ||||
−0.547038 | + | 0.837108i | \(0.684245\pi\) | |||||||
\(192\) | − 1336.00i | − 0.502174i | ||||||||
\(193\) | 1602.00i | 0.597484i | 0.954334 | + | 0.298742i | \(0.0965671\pi\) | ||||
−0.954334 | + | 0.298742i | \(0.903433\pi\) | |||||||
\(194\) | −1026.00 | −0.379704 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −343.000 | −0.125000 | ||||||||
\(197\) | 4794.00i | 1.73380i | 0.498483 | + | 0.866899i | \(0.333891\pi\) | ||||
−0.498483 | + | 0.866899i | \(0.666109\pi\) | |||||||
\(198\) | 444.000i | 0.159362i | ||||||||
\(199\) | −1280.00 | −0.455964 | −0.227982 | − | 0.973665i | \(-0.573213\pi\) | ||||
−0.227982 | + | 0.973665i | \(0.573213\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1312.00 | 0.460405 | ||||||||
\(202\) | − 482.000i | − 0.167888i | ||||||||
\(203\) | − 350.000i | − 0.121011i | ||||||||
\(204\) | 5264.00 | 1.80664 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 272.000 | 0.0919958 | ||||||||
\(207\) | − 1184.00i | − 0.397554i | ||||||||
\(208\) | − 3198.00i | − 1.06606i | ||||||||
\(209\) | −480.000 | −0.158863 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −68.0000 | −0.0221863 | −0.0110932 | − | 0.999938i | \(-0.503531\pi\) | ||||
−0.0110932 | + | 0.999938i | \(0.503531\pi\) | |||||||
\(212\) | 154.000i | 0.0498904i | ||||||||
\(213\) | − 5376.00i | − 1.72938i | ||||||||
\(214\) | 444.000 | 0.141828 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1200.00 | 0.378008 | ||||||||
\(217\) | 1736.00i | 0.543075i | ||||||||
\(218\) | − 1170.00i | − 0.363497i | ||||||||
\(219\) | 656.000 | 0.202413 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7332.00 | 2.23169 | ||||||||
\(222\) | − 3472.00i | − 1.04966i | ||||||||
\(223\) | − 1728.00i | − 0.518903i | −0.965756 | − | 0.259452i | \(-0.916458\pi\) | ||||
0.965756 | − | 0.259452i | \(-0.0835418\pi\) | |||||||
\(224\) | −1127.00 | −0.336165 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −798.000 | −0.234877 | ||||||||
\(227\) | 4864.00i | 1.42218i | 0.703101 | + | 0.711090i | \(0.251798\pi\) | ||||
−0.703101 | + | 0.711090i | \(0.748202\pi\) | |||||||
\(228\) | 2240.00i | 0.650647i | ||||||||
\(229\) | 5510.00 | 1.59000 | 0.795002 | − | 0.606606i | \(-0.207470\pi\) | ||||
0.795002 | + | 0.606606i | \(0.207470\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −672.000 | −0.191404 | ||||||||
\(232\) | − 750.000i | − 0.212241i | ||||||||
\(233\) | 5322.00i | 1.49638i | 0.663486 | + | 0.748188i | \(0.269076\pi\) | ||||
−0.663486 | + | 0.748188i | \(0.730924\pi\) | |||||||
\(234\) | 2886.00 | 0.806255 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3920.00 | 1.08123 | ||||||||
\(237\) | − 8000.00i | − 2.19264i | ||||||||
\(238\) | − 658.000i | − 0.179209i | ||||||||
\(239\) | 1840.00 | 0.497990 | 0.248995 | − | 0.968505i | \(-0.419900\pi\) | ||||
0.248995 | + | 0.968505i | \(0.419900\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −438.000 | −0.117071 | −0.0585354 | − | 0.998285i | \(-0.518643\pi\) | ||||
−0.0585354 | + | 0.998285i | \(0.518643\pi\) | |||||||
\(242\) | 1187.00i | 0.315303i | ||||||||
\(243\) | 5032.00i | 1.32841i | ||||||||
\(244\) | −1946.00 | −0.510573 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3216.00 | −0.833515 | ||||||||
\(247\) | 3120.00i | 0.803728i | ||||||||
\(248\) | 3720.00i | 0.952501i | ||||||||
\(249\) | −3584.00 | −0.912156 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5592.00 | 1.40623 | 0.703115 | − | 0.711076i | \(-0.251792\pi\) | ||||
0.703115 | + | 0.711076i | \(0.251792\pi\) | |||||||
\(252\) | 1813.00i | 0.453207i | ||||||||
\(253\) | 384.000i | 0.0954224i | ||||||||
\(254\) | −776.000 | −0.191695 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −119.000 | −0.0290527 | ||||||||
\(257\) | 1974.00i | 0.479123i | 0.970881 | + | 0.239562i | \(0.0770038\pi\) | ||||
−0.970881 | + | 0.239562i | \(0.922996\pi\) | |||||||
\(258\) | 544.000i | 0.131271i | ||||||||
\(259\) | 3038.00 | 0.728850 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1850.00 | −0.438744 | ||||||||
\(262\) | − 1112.00i | − 0.262212i | ||||||||
\(263\) | − 728.000i | − 0.170686i | −0.996352 | − | 0.0853430i | \(-0.972801\pi\) | ||||
0.996352 | − | 0.0853430i | \(-0.0271986\pi\) | |||||||
\(264\) | −1440.00 | −0.335704 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 280.000 | 0.0645410 | ||||||||
\(267\) | − 6960.00i | − 1.59530i | ||||||||
\(268\) | 1148.00i | 0.261661i | ||||||||
\(269\) | −5810.00 | −1.31688 | −0.658442 | − | 0.752631i | \(-0.728784\pi\) | ||||
−0.658442 | + | 0.752631i | \(0.728784\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6528.00 | −1.46328 | −0.731638 | − | 0.681693i | \(-0.761244\pi\) | ||||
−0.731638 | + | 0.681693i | \(0.761244\pi\) | |||||||
\(272\) | 3854.00i | 0.859129i | ||||||||
\(273\) | 4368.00i | 0.968364i | ||||||||
\(274\) | 694.000 | 0.153015 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1792.00 | 0.390818 | ||||||||
\(277\) | − 5126.00i | − 1.11188i | −0.831222 | − | 0.555941i | \(-0.812358\pi\) | ||||
0.831222 | − | 0.555941i | \(-0.187642\pi\) | |||||||
\(278\) | 360.000i | 0.0776668i | ||||||||
\(279\) | 9176.00 | 1.96901 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2358.00 | −0.500592 | −0.250296 | − | 0.968169i | \(-0.580528\pi\) | ||||
−0.250296 | + | 0.968169i | \(0.580528\pi\) | |||||||
\(282\) | 4288.00i | 0.905485i | ||||||||
\(283\) | 392.000i | 0.0823392i | 0.999152 | + | 0.0411696i | \(0.0131084\pi\) | ||||
−0.999152 | + | 0.0411696i | \(0.986892\pi\) | |||||||
\(284\) | 4704.00 | 0.982856 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −936.000 | −0.193520 | ||||||||
\(287\) | − 2814.00i | − 0.578764i | ||||||||
\(288\) | 5957.00i | 1.21882i | ||||||||
\(289\) | −3923.00 | −0.798494 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8208.00 | −1.65348 | ||||||||
\(292\) | 574.000i | 0.115037i | ||||||||
\(293\) | 1202.00i | 0.239664i | 0.992794 | + | 0.119832i | \(0.0382356\pi\) | ||||
−0.992794 | + | 0.119832i | \(0.961764\pi\) | |||||||
\(294\) | 392.000 | 0.0777616 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 6510.00 | 1.27833 | ||||||||
\(297\) | 960.000i | 0.187558i | ||||||||
\(298\) | 2270.00i | 0.441267i | ||||||||
\(299\) | 2496.00 | 0.482767 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −476.000 | −0.0911501 | ||||||||
\(302\) | − 632.000i | − 0.120422i | ||||||||
\(303\) | − 3856.00i | − 0.731094i | ||||||||
\(304\) | −1640.00 | −0.309409 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3478.00 | −0.649752 | ||||||||
\(307\) | 6384.00i | 1.18682i | 0.804900 | + | 0.593411i | \(0.202219\pi\) | ||||
−0.804900 | + | 0.593411i | \(0.797781\pi\) | |||||||
\(308\) | − 588.000i | − 0.108781i | ||||||||
\(309\) | 2176.00 | 0.400609 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4968.00 | −0.905818 | −0.452909 | − | 0.891557i | \(-0.649614\pi\) | ||||
−0.452909 | + | 0.891557i | \(0.649614\pi\) | |||||||
\(312\) | 9360.00i | 1.69842i | ||||||||
\(313\) | − 2758.00i | − 0.498056i | −0.968496 | − | 0.249028i | \(-0.919889\pi\) | ||||
0.968496 | − | 0.249028i | \(-0.0801110\pi\) | |||||||
\(314\) | 734.000 | 0.131917 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7000.00 | 1.24614 | ||||||||
\(317\) | 6274.00i | 1.11162i | 0.831310 | + | 0.555809i | \(0.187591\pi\) | ||||
−0.831310 | + | 0.555809i | \(0.812409\pi\) | |||||||
\(318\) | − 176.000i | − 0.0310364i | ||||||||
\(319\) | 600.000 | 0.105309 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3552.00 | 0.617612 | ||||||||
\(322\) | − 224.000i | − 0.0387672i | ||||||||
\(323\) | − 3760.00i | − 0.647715i | ||||||||
\(324\) | −2513.00 | −0.430898 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2532.00 | 0.430167 | ||||||||
\(327\) | − 9360.00i | − 1.58290i | ||||||||
\(328\) | − 6030.00i | − 1.01509i | ||||||||
\(329\) | −3752.00 | −0.628737 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1932.00 | 0.320823 | 0.160411 | − | 0.987050i | \(-0.448718\pi\) | ||||
0.160411 | + | 0.987050i | \(0.448718\pi\) | |||||||
\(332\) | − 3136.00i | − 0.518405i | ||||||||
\(333\) | − 16058.0i | − 2.64256i | ||||||||
\(334\) | −416.000 | −0.0681512 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2296.00 | −0.372789 | ||||||||
\(337\) | − 2386.00i | − 0.385679i | −0.981230 | − | 0.192839i | \(-0.938230\pi\) | ||||
0.981230 | − | 0.192839i | \(-0.0617696\pi\) | |||||||
\(338\) | 3887.00i | 0.625518i | ||||||||
\(339\) | −6384.00 | −1.02281 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2976.00 | −0.472608 | ||||||||
\(342\) | − 1480.00i | − 0.234004i | ||||||||
\(343\) | 343.000i | 0.0539949i | ||||||||
\(344\) | −1020.00 | −0.159868 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3042.00 | 0.472656 | ||||||||
\(347\) | − 6076.00i | − 0.939991i | −0.882669 | − | 0.469995i | \(-0.844256\pi\) | ||||
0.882669 | − | 0.469995i | \(-0.155744\pi\) | |||||||
\(348\) | − 2800.00i | − 0.431310i | ||||||||
\(349\) | −2210.00 | −0.338964 | −0.169482 | − | 0.985533i | \(-0.554210\pi\) | ||||
−0.169482 | + | 0.985533i | \(0.554210\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6240.00 | 0.948908 | ||||||||
\(352\) | − 1932.00i | − 0.292545i | ||||||||
\(353\) | − 2598.00i | − 0.391721i | −0.980632 | − | 0.195861i | \(-0.937250\pi\) | ||||
0.980632 | − | 0.195861i | \(-0.0627500\pi\) | |||||||
\(354\) | −4480.00 | −0.672625 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6090.00 | 0.906655 | ||||||||
\(357\) | − 5264.00i | − 0.780393i | ||||||||
\(358\) | − 180.000i | − 0.0265735i | ||||||||
\(359\) | 13320.0 | 1.95822 | 0.979112 | − | 0.203320i | \(-0.0651731\pi\) | ||||
0.979112 | + | 0.203320i | \(0.0651731\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5259.00 | −0.766730 | ||||||||
\(362\) | 1958.00i | 0.284282i | ||||||||
\(363\) | 9496.00i | 1.37303i | ||||||||
\(364\) | −3822.00 | −0.550350 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2224.00 | 0.317624 | ||||||||
\(367\) | − 10816.0i | − 1.53839i | −0.639012 | − | 0.769197i | \(-0.720656\pi\) | ||||
0.639012 | − | 0.769197i | \(-0.279344\pi\) | |||||||
\(368\) | 1312.00i | 0.185850i | ||||||||
\(369\) | −14874.0 | −2.09840 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 154.000 | 0.0215506 | ||||||||
\(372\) | 13888.0i | 1.93564i | ||||||||
\(373\) | − 11098.0i | − 1.54057i | −0.637700 | − | 0.770285i | \(-0.720114\pi\) | ||||
0.637700 | − | 0.770285i | \(-0.279886\pi\) | |||||||
\(374\) | 1128.00 | 0.155956 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8040.00 | −1.10274 | ||||||||
\(377\) | − 3900.00i | − 0.532786i | ||||||||
\(378\) | − 560.000i | − 0.0761992i | ||||||||
\(379\) | −7100.00 | −0.962276 | −0.481138 | − | 0.876645i | \(-0.659776\pi\) | ||||
−0.481138 | + | 0.876645i | \(0.659776\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6208.00 | −0.834765 | ||||||||
\(382\) | 2888.00i | 0.386814i | ||||||||
\(383\) | − 728.000i | − 0.0971255i | −0.998820 | − | 0.0485627i | \(-0.984536\pi\) | ||||
0.998820 | − | 0.0485627i | \(-0.0154641\pi\) | |||||||
\(384\) | −11640.0 | −1.54688 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1602.00 | 0.211243 | ||||||||
\(387\) | 2516.00i | 0.330479i | ||||||||
\(388\) | − 7182.00i | − 0.939719i | ||||||||
\(389\) | 6810.00 | 0.887611 | 0.443806 | − | 0.896123i | \(-0.353628\pi\) | ||||
0.443806 | + | 0.896123i | \(0.353628\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3008.00 | −0.389057 | ||||||||
\(392\) | 735.000i | 0.0947018i | ||||||||
\(393\) | − 8896.00i | − 1.14184i | ||||||||
\(394\) | 4794.00 | 0.612990 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3108.00 | −0.394401 | ||||||||
\(397\) | 574.000i | 0.0725648i | 0.999342 | + | 0.0362824i | \(0.0115516\pi\) | ||||
−0.999342 | + | 0.0362824i | \(0.988448\pi\) | |||||||
\(398\) | 1280.00i | 0.161208i | ||||||||
\(399\) | 2240.00 | 0.281053 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6162.00 | 0.767371 | 0.383685 | − | 0.923464i | \(-0.374655\pi\) | ||||
0.383685 | + | 0.923464i | \(0.374655\pi\) | |||||||
\(402\) | − 1312.00i | − 0.162778i | ||||||||
\(403\) | 19344.0i | 2.39105i | ||||||||
\(404\) | 3374.00 | 0.415502 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −350.000 | −0.0427838 | ||||||||
\(407\) | 5208.00i | 0.634278i | ||||||||
\(408\) | − 11280.0i | − 1.36873i | ||||||||
\(409\) | −8210.00 | −0.992563 | −0.496282 | − | 0.868162i | \(-0.665302\pi\) | ||||
−0.496282 | + | 0.868162i | \(0.665302\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5552.00 | 0.666326 | ||||||||
\(412\) | 1904.00i | 0.227678i | ||||||||
\(413\) | − 3920.00i | − 0.467047i | ||||||||
\(414\) | −1184.00 | −0.140557 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −12558.0 | −1.48006 | ||||||||
\(417\) | 2880.00i | 0.338212i | ||||||||
\(418\) | 480.000i | 0.0561664i | ||||||||
\(419\) | −4800.00 | −0.559655 | −0.279827 | − | 0.960050i | \(-0.590277\pi\) | ||||
−0.279827 | + | 0.960050i | \(0.590277\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9938.00 | −1.15047 | −0.575236 | − | 0.817988i | \(-0.695090\pi\) | ||||
−0.575236 | + | 0.817988i | \(0.695090\pi\) | |||||||
\(422\) | 68.0000i | 0.00784405i | ||||||||
\(423\) | 19832.0i | 2.27959i | ||||||||
\(424\) | 330.000 | 0.0377977 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −5376.00 | −0.611427 | ||||||||
\(427\) | 1946.00i | 0.220547i | ||||||||
\(428\) | 3108.00i | 0.351007i | ||||||||
\(429\) | −7488.00 | −0.842713 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9248.00 | −1.03355 | −0.516776 | − | 0.856121i | \(-0.672868\pi\) | ||||
−0.516776 | + | 0.856121i | \(0.672868\pi\) | |||||||
\(432\) | 3280.00i | 0.365299i | ||||||||
\(433\) | − 1118.00i | − 0.124082i | −0.998074 | − | 0.0620412i | \(-0.980239\pi\) | ||||
0.998074 | − | 0.0620412i | \(-0.0197610\pi\) | |||||||
\(434\) | 1736.00 | 0.192006 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8190.00 | 0.899610 | ||||||||
\(437\) | − 1280.00i | − 0.140116i | ||||||||
\(438\) | − 656.000i | − 0.0715637i | ||||||||
\(439\) | 11960.0 | 1.30027 | 0.650136 | − | 0.759818i | \(-0.274712\pi\) | ||||
0.650136 | + | 0.759818i | \(0.274712\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1813.00 | 0.195767 | ||||||||
\(442\) | − 7332.00i | − 0.789022i | ||||||||
\(443\) | 7332.00i | 0.786352i | 0.919463 | + | 0.393176i | \(0.128624\pi\) | ||||
−0.919463 | + | 0.393176i | \(0.871376\pi\) | |||||||
\(444\) | 24304.0 | 2.59779 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1728.00 | −0.183460 | ||||||||
\(447\) | 18160.0i | 1.92156i | ||||||||
\(448\) | − 1169.00i | − 0.123281i | ||||||||
\(449\) | −1890.00 | −0.198652 | −0.0993259 | − | 0.995055i | \(-0.531669\pi\) | ||||
−0.0993259 | + | 0.995055i | \(0.531669\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4824.00 | 0.503666 | ||||||||
\(452\) | − 5586.00i | − 0.581291i | ||||||||
\(453\) | − 5056.00i | − 0.524396i | ||||||||
\(454\) | 4864.00 | 0.502817 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4800.00 | 0.492940 | ||||||||
\(457\) | 7014.00i | 0.717945i | 0.933348 | + | 0.358973i | \(0.116873\pi\) | ||||
−0.933348 | + | 0.358973i | \(0.883127\pi\) | |||||||
\(458\) | − 5510.00i | − 0.562152i | ||||||||
\(459\) | −7520.00 | −0.764714 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8318.00 | −0.840364 | −0.420182 | − | 0.907440i | \(-0.638034\pi\) | ||||
−0.420182 | + | 0.907440i | \(0.638034\pi\) | |||||||
\(462\) | 672.000i | 0.0676716i | ||||||||
\(463\) | 6432.00i | 0.645616i | 0.946464 | + | 0.322808i | \(0.104627\pi\) | ||||
−0.946464 | + | 0.322808i | \(0.895373\pi\) | |||||||
\(464\) | 2050.00 | 0.205105 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5322.00 | 0.529049 | ||||||||
\(467\) | 10064.0i | 0.997230i | 0.866824 | + | 0.498615i | \(0.166158\pi\) | ||||
−0.866824 | + | 0.498615i | \(0.833842\pi\) | |||||||
\(468\) | 20202.0i | 1.99538i | ||||||||
\(469\) | 1148.00 | 0.113027 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5872.00 | 0.574453 | ||||||||
\(472\) | − 8400.00i | − 0.819155i | ||||||||
\(473\) | − 816.000i | − 0.0793229i | ||||||||
\(474\) | −8000.00 | −0.775216 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4606.00 | 0.443520 | ||||||||
\(477\) | − 814.000i | − 0.0781352i | ||||||||
\(478\) | − 1840.00i | − 0.176066i | ||||||||
\(479\) | −1400.00 | −0.133544 | −0.0667721 | − | 0.997768i | \(-0.521270\pi\) | ||||
−0.0667721 | + | 0.997768i | \(0.521270\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 33852.0 | 3.20898 | ||||||||
\(482\) | 438.000i | 0.0413908i | ||||||||
\(483\) | − 1792.00i | − 0.168817i | ||||||||
\(484\) | −8309.00 | −0.780334 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 5032.00 | 0.469663 | ||||||||
\(487\) | − 13376.0i | − 1.24461i | −0.782775 | − | 0.622304i | \(-0.786197\pi\) | ||||
0.782775 | − | 0.622304i | \(-0.213803\pi\) | |||||||
\(488\) | 4170.00i | 0.386818i | ||||||||
\(489\) | 20256.0 | 1.87323 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7092.00 | 0.651848 | 0.325924 | − | 0.945396i | \(-0.394325\pi\) | ||||
0.325924 | + | 0.945396i | \(0.394325\pi\) | |||||||
\(492\) | − 22512.0i | − 2.06284i | ||||||||
\(493\) | 4700.00i | 0.429366i | ||||||||
\(494\) | 3120.00 | 0.284161 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10168.0 | −0.920477 | ||||||||
\(497\) | − 4704.00i | − 0.424554i | ||||||||
\(498\) | 3584.00i | 0.322496i | ||||||||
\(499\) | 820.000 | 0.0735636 | 0.0367818 | − | 0.999323i | \(-0.488289\pi\) | ||||
0.0367818 | + | 0.999323i | \(0.488289\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3328.00 | −0.296775 | ||||||||
\(502\) | − 5592.00i | − 0.497178i | ||||||||
\(503\) | − 4568.00i | − 0.404925i | −0.979290 | − | 0.202462i | \(-0.935106\pi\) | ||||
0.979290 | − | 0.202462i | \(-0.0648944\pi\) | |||||||
\(504\) | 3885.00 | 0.343356 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 384.000 | 0.0337369 | ||||||||
\(507\) | 31096.0i | 2.72391i | ||||||||
\(508\) | − 5432.00i | − 0.474421i | ||||||||
\(509\) | −19810.0 | −1.72507 | −0.862537 | − | 0.505994i | \(-0.831126\pi\) | ||||
−0.862537 | + | 0.505994i | \(0.831126\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 574.000 | 0.0496913 | ||||||||
\(512\) | − 11521.0i | − 0.994455i | ||||||||
\(513\) | − 3200.00i | − 0.275406i | ||||||||
\(514\) | 1974.00 | 0.169396 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −3808.00 | −0.324880 | ||||||||
\(517\) | − 6432.00i | − 0.547155i | ||||||||
\(518\) | − 3038.00i | − 0.257687i | ||||||||
\(519\) | 24336.0 | 2.05825 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1838.00 | −0.154557 | −0.0772785 | − | 0.997010i | \(-0.524623\pi\) | ||||
−0.0772785 | + | 0.997010i | \(0.524623\pi\) | |||||||
\(522\) | 1850.00i | 0.155119i | ||||||||
\(523\) | 2072.00i | 0.173236i | 0.996242 | + | 0.0866178i | \(0.0276059\pi\) | ||||
−0.996242 | + | 0.0866178i | \(0.972394\pi\) | |||||||
\(524\) | 7784.00 | 0.648942 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −728.000 | −0.0603466 | ||||||||
\(527\) | − 23312.0i | − 1.92692i | ||||||||
\(528\) | − 3936.00i | − 0.324417i | ||||||||
\(529\) | 11143.0 | 0.915838 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −20720.0 | −1.69335 | ||||||||
\(532\) | 1960.00i | 0.159731i | ||||||||
\(533\) | − 31356.0i | − 2.54818i | ||||||||
\(534\) | −6960.00 | −0.564024 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2460.00 | 0.198238 | ||||||||
\(537\) | − 1440.00i | − 0.115718i | ||||||||
\(538\) | 5810.00i | 0.465589i | ||||||||
\(539\) | −588.000 | −0.0469888 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3498.00 | −0.277987 | −0.138993 | − | 0.990293i | \(-0.544387\pi\) | ||||
−0.138993 | + | 0.990293i | \(0.544387\pi\) | |||||||
\(542\) | 6528.00i | 0.517346i | ||||||||
\(543\) | 15664.0i | 1.23795i | ||||||||
\(544\) | 15134.0 | 1.19277 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 4368.00 | 0.342368 | ||||||||
\(547\) | − 5076.00i | − 0.396772i | −0.980124 | − | 0.198386i | \(-0.936430\pi\) | ||||
0.980124 | − | 0.198386i | \(-0.0635699\pi\) | |||||||
\(548\) | 4858.00i | 0.378692i | ||||||||
\(549\) | 10286.0 | 0.799628 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2000.00 | −0.154633 | ||||||||
\(552\) | − 3840.00i | − 0.296089i | ||||||||
\(553\) | − 7000.00i | − 0.538283i | ||||||||
\(554\) | −5126.00 | −0.393110 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2520.00 | −0.192215 | ||||||||
\(557\) | 8674.00i | 0.659837i | 0.944009 | + | 0.329918i | \(0.107021\pi\) | ||||
−0.944009 | + | 0.329918i | \(0.892979\pi\) | |||||||
\(558\) | − 9176.00i | − 0.696149i | ||||||||
\(559\) | −5304.00 | −0.401315 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9024.00 | 0.679133 | ||||||||
\(562\) | 2358.00i | 0.176986i | ||||||||
\(563\) | 16072.0i | 1.20312i | 0.798829 | + | 0.601558i | \(0.205453\pi\) | ||||
−0.798829 | + | 0.601558i | \(0.794547\pi\) | |||||||
\(564\) | −30016.0 | −2.24096 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 392.000 | 0.0291113 | ||||||||
\(567\) | 2513.00i | 0.186131i | ||||||||
\(568\) | − 10080.0i | − 0.744626i | ||||||||
\(569\) | −2730.00 | −0.201138 | −0.100569 | − | 0.994930i | \(-0.532066\pi\) | ||||
−0.100569 | + | 0.994930i | \(0.532066\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19932.0 | 1.46082 | 0.730410 | − | 0.683009i | \(-0.239329\pi\) | ||||
0.730410 | + | 0.683009i | \(0.239329\pi\) | |||||||
\(572\) | − 6552.00i | − 0.478939i | ||||||||
\(573\) | 23104.0i | 1.68444i | ||||||||
\(574\) | −2814.00 | −0.204624 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −6179.00 | −0.446976 | ||||||||
\(577\) | 20054.0i | 1.44690i | 0.690379 | + | 0.723448i | \(0.257444\pi\) | ||||
−0.690379 | + | 0.723448i | \(0.742556\pi\) | |||||||
\(578\) | 3923.00i | 0.282310i | ||||||||
\(579\) | 12816.0 | 0.919887 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3136.00 | −0.223930 | ||||||||
\(582\) | 8208.00i | 0.584592i | ||||||||
\(583\) | 264.000i | 0.0187543i | ||||||||
\(584\) | 1230.00 | 0.0871537 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1202.00 | 0.0847341 | ||||||||
\(587\) | 2544.00i | 0.178879i | 0.995992 | + | 0.0894396i | \(0.0285076\pi\) | ||||
−0.995992 | + | 0.0894396i | \(0.971492\pi\) | |||||||
\(588\) | 2744.00i | 0.192450i | ||||||||
\(589\) | 9920.00 | 0.693967 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 38352.0 | 2.66936 | ||||||||
\(592\) | 17794.0i | 1.23535i | ||||||||
\(593\) | 14202.0i | 0.983484i | 0.870741 | + | 0.491742i | \(0.163640\pi\) | ||||
−0.870741 | + | 0.491742i | \(0.836360\pi\) | |||||||
\(594\) | 960.000 | 0.0663119 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −15890.0 | −1.09208 | ||||||||
\(597\) | 10240.0i | 0.702002i | ||||||||
\(598\) | − 2496.00i | − 0.170684i | ||||||||
\(599\) | 19600.0 | 1.33695 | 0.668476 | − | 0.743734i | \(-0.266947\pi\) | ||||
0.668476 | + | 0.743734i | \(0.266947\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −27078.0 | −1.83783 | −0.918914 | − | 0.394458i | \(-0.870932\pi\) | ||||
−0.918914 | + | 0.394458i | \(0.870932\pi\) | |||||||
\(602\) | 476.000i | 0.0322264i | ||||||||
\(603\) | − 6068.00i | − 0.409798i | ||||||||
\(604\) | 4424.00 | 0.298030 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −3856.00 | −0.258481 | ||||||||
\(607\) | 2704.00i | 0.180811i | 0.995905 | + | 0.0904053i | \(0.0288162\pi\) | ||||
−0.995905 | + | 0.0904053i | \(0.971184\pi\) | |||||||
\(608\) | 6440.00i | 0.429567i | ||||||||
\(609\) | −2800.00 | −0.186308 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −41808.0 | −2.76820 | ||||||||
\(612\) | − 24346.0i | − 1.60805i | ||||||||
\(613\) | 12702.0i | 0.836915i | 0.908236 | + | 0.418458i | \(0.137429\pi\) | ||||
−0.908236 | + | 0.418458i | \(0.862571\pi\) | |||||||
\(614\) | 6384.00 | 0.419605 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1260.00 | −0.0824137 | ||||||||
\(617\) | − 12666.0i | − 0.826441i | −0.910631 | − | 0.413220i | \(-0.864404\pi\) | ||||
0.910631 | − | 0.413220i | \(-0.135596\pi\) | |||||||
\(618\) | − 2176.00i | − 0.141637i | ||||||||
\(619\) | −960.000 | −0.0623355 | −0.0311677 | − | 0.999514i | \(-0.509923\pi\) | ||||
−0.0311677 | + | 0.999514i | \(0.509923\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2560.00 | −0.165426 | ||||||||
\(622\) | 4968.00i | 0.320255i | ||||||||
\(623\) | − 6090.00i | − 0.391638i | ||||||||
\(624\) | −25584.0 | −1.64131 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −2758.00 | −0.176089 | ||||||||
\(627\) | 3840.00i | 0.244585i | ||||||||
\(628\) | 5138.00i | 0.326479i | ||||||||
\(629\) | −40796.0 | −2.58608 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23232.0 | 1.46569 | 0.732846 | − | 0.680395i | \(-0.238192\pi\) | ||||
0.732846 | + | 0.680395i | \(0.238192\pi\) | |||||||
\(632\) | − 15000.0i | − 0.944095i | ||||||||
\(633\) | 544.000i | 0.0341581i | ||||||||
\(634\) | 6274.00 | 0.393016 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1232.00 | 0.0768113 | ||||||||
\(637\) | 3822.00i | 0.237729i | ||||||||
\(638\) | − 600.000i | − 0.0372323i | ||||||||
\(639\) | −24864.0 | −1.53929 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12162.0 | 0.749407 | 0.374704 | − | 0.927145i | \(-0.377744\pi\) | ||||
0.374704 | + | 0.927145i | \(0.377744\pi\) | |||||||
\(642\) | − 3552.00i | − 0.218359i | ||||||||
\(643\) | − 488.000i | − 0.0299298i | −0.999888 | − | 0.0149649i | \(-0.995236\pi\) | ||||
0.999888 | − | 0.0149649i | \(-0.00476365\pi\) | |||||||
\(644\) | 1568.00 | 0.0959439 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3760.00 | −0.229002 | ||||||||
\(647\) | 3984.00i | 0.242082i | 0.992647 | + | 0.121041i | \(0.0386233\pi\) | ||||
−0.992647 | + | 0.121041i | \(0.961377\pi\) | |||||||
\(648\) | 5385.00i | 0.326455i | ||||||||
\(649\) | 6720.00 | 0.406445 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 13888.0 | 0.836119 | ||||||||
\(652\) | 17724.0i | 1.06461i | ||||||||
\(653\) | − 30538.0i | − 1.83008i | −0.403360 | − | 0.915042i | \(-0.632158\pi\) | ||||
0.403360 | − | 0.915042i | \(-0.367842\pi\) | |||||||
\(654\) | −9360.00 | −0.559641 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 16482.0 | 0.980966 | ||||||||
\(657\) | − 3034.00i | − 0.180164i | ||||||||
\(658\) | 3752.00i | 0.222292i | ||||||||
\(659\) | −22740.0 | −1.34420 | −0.672098 | − | 0.740463i | \(-0.734606\pi\) | ||||
−0.672098 | + | 0.740463i | \(0.734606\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18718.0 | −1.10143 | −0.550715 | − | 0.834693i | \(-0.685645\pi\) | ||||
−0.550715 | + | 0.834693i | \(0.685645\pi\) | |||||||
\(662\) | − 1932.00i | − 0.113428i | ||||||||
\(663\) | − 58656.0i | − 3.43591i | ||||||||
\(664\) | −6720.00 | −0.392751 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −16058.0 | −0.934287 | ||||||||
\(667\) | 1600.00i | 0.0928819i | ||||||||
\(668\) | − 2912.00i | − 0.168666i | ||||||||
\(669\) | −13824.0 | −0.798904 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3336.00 | −0.191930 | ||||||||
\(672\) | 9016.00i | 0.517559i | ||||||||
\(673\) | 10802.0i | 0.618702i | 0.950948 | + | 0.309351i | \(0.100112\pi\) | ||||
−0.950948 | + | 0.309351i | \(0.899888\pi\) | |||||||
\(674\) | −2386.00 | −0.136358 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −27209.0 | −1.54808 | ||||||||
\(677\) | − 346.000i | − 0.0196423i | −0.999952 | − | 0.00982117i | \(-0.996874\pi\) | ||||
0.999952 | − | 0.00982117i | \(-0.00312622\pi\) | |||||||
\(678\) | 6384.00i | 0.361617i | ||||||||
\(679\) | −7182.00 | −0.405920 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 38912.0 | 2.18959 | ||||||||
\(682\) | 2976.00i | 0.167092i | ||||||||
\(683\) | − 11628.0i | − 0.651439i | −0.945466 | − | 0.325720i | \(-0.894393\pi\) | ||||
0.945466 | − | 0.325720i | \(-0.105607\pi\) | |||||||
\(684\) | 10360.0 | 0.579129 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 343.000 | 0.0190901 | ||||||||
\(687\) | − 44080.0i | − 2.44797i | ||||||||
\(688\) | − 2788.00i | − 0.154493i | ||||||||
\(689\) | 1716.00 | 0.0948830 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2472.00 | 0.136092 | 0.0680458 | − | 0.997682i | \(-0.478324\pi\) | ||||
0.0680458 | + | 0.997682i | \(0.478324\pi\) | |||||||
\(692\) | 21294.0i | 1.16976i | ||||||||
\(693\) | 3108.00i | 0.170365i | ||||||||
\(694\) | −6076.00 | −0.332337 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −6000.00 | −0.326766 | ||||||||
\(697\) | 37788.0i | 2.05355i | ||||||||
\(698\) | 2210.00i | 0.119842i | ||||||||
\(699\) | 42576.0 | 2.30382 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2018.00 | −0.108729 | −0.0543643 | − | 0.998521i | \(-0.517313\pi\) | ||||
−0.0543643 | + | 0.998521i | \(0.517313\pi\) | |||||||
\(702\) | − 6240.00i | − 0.335489i | ||||||||
\(703\) | − 17360.0i | − 0.931358i | ||||||||
\(704\) | 2004.00 | 0.107285 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2598.00 | −0.138494 | ||||||||
\(707\) | − 3374.00i | − 0.179480i | ||||||||
\(708\) | − 31360.0i | − 1.66466i | ||||||||
\(709\) | −790.000 | −0.0418464 | −0.0209232 | − | 0.999781i | \(-0.506661\pi\) | ||||
−0.0209232 | + | 0.999781i | \(0.506661\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −37000.0 | −1.95163 | ||||||||
\(712\) | − 13050.0i | − 0.686895i | ||||||||
\(713\) | − 7936.00i | − 0.416838i | ||||||||
\(714\) | −5264.00 | −0.275911 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1260.00 | 0.0657659 | ||||||||
\(717\) | − 14720.0i | − 0.766706i | ||||||||
\(718\) | − 13320.0i | − 0.692337i | ||||||||
\(719\) | −18200.0 | −0.944013 | −0.472007 | − | 0.881595i | \(-0.656470\pi\) | ||||
−0.472007 | + | 0.881595i | \(0.656470\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1904.00 | 0.0983477 | ||||||||
\(722\) | 5259.00i | 0.271080i | ||||||||
\(723\) | 3504.00i | 0.180242i | ||||||||
\(724\) | −13706.0 | −0.703563 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 9496.00 | 0.485440 | ||||||||
\(727\) | − 29056.0i | − 1.48229i | −0.671343 | − | 0.741147i | \(-0.734282\pi\) | ||||
0.671343 | − | 0.741147i | \(-0.265718\pi\) | |||||||
\(728\) | 8190.00i | 0.416953i | ||||||||
\(729\) | 30563.0 | 1.55276 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6392.00 | 0.323415 | ||||||||
\(732\) | 15568.0i | 0.786079i | ||||||||
\(733\) | 7082.00i | 0.356862i | 0.983952 | + | 0.178431i | \(0.0571021\pi\) | ||||
−0.983952 | + | 0.178431i | \(0.942898\pi\) | |||||||
\(734\) | −10816.0 | −0.543904 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5152.00 | 0.258023 | ||||||||
\(737\) | 1968.00i | 0.0983612i | ||||||||
\(738\) | 14874.0i | 0.741896i | ||||||||
\(739\) | −11060.0 | −0.550539 | −0.275270 | − | 0.961367i | \(-0.588767\pi\) | ||||
−0.275270 | + | 0.961367i | \(0.588767\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 24960.0 | 1.23742 | ||||||||
\(742\) | − 154.000i | − 0.00761930i | ||||||||
\(743\) | 33072.0i | 1.63297i | 0.577369 | + | 0.816483i | \(0.304079\pi\) | ||||
−0.577369 | + | 0.816483i | \(0.695921\pi\) | |||||||
\(744\) | 29760.0 | 1.46647 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −11098.0 | −0.544674 | ||||||||
\(747\) | 16576.0i | 0.811893i | ||||||||
\(748\) | 7896.00i | 0.385971i | ||||||||
\(749\) | 3108.00 | 0.151621 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29072.0 | 1.41259 | 0.706293 | − | 0.707919i | \(-0.250366\pi\) | ||||
0.706293 | + | 0.707919i | \(0.250366\pi\) | |||||||
\(752\) | − 21976.0i | − 1.06567i | ||||||||
\(753\) | − 44736.0i | − 2.16503i | ||||||||
\(754\) | −3900.00 | −0.188368 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 3920.00 | 0.188583 | ||||||||
\(757\) | 13234.0i | 0.635400i | 0.948191 | + | 0.317700i | \(0.102911\pi\) | ||||
−0.948191 | + | 0.317700i | \(0.897089\pi\) | |||||||
\(758\) | 7100.00i | 0.340216i | ||||||||
\(759\) | 3072.00 | 0.146912 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −22398.0 | −1.06692 | −0.533460 | − | 0.845825i | \(-0.679109\pi\) | ||||
−0.533460 | + | 0.845825i | \(0.679109\pi\) | |||||||
\(762\) | 6208.00i | 0.295134i | ||||||||
\(763\) | − 8190.00i | − 0.388595i | ||||||||
\(764\) | −20216.0 | −0.957316 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −728.000 | −0.0343390 | ||||||||
\(767\) | − 43680.0i | − 2.05631i | ||||||||
\(768\) | 952.000i | 0.0447296i | ||||||||
\(769\) | −6890.00 | −0.323095 | −0.161547 | − | 0.986865i | \(-0.551648\pi\) | ||||
−0.161547 | + | 0.986865i | \(0.551648\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15792.0 | 0.737659 | ||||||||
\(772\) | 11214.0i | 0.522799i | ||||||||
\(773\) | 16722.0i | 0.778071i | 0.921223 | + | 0.389035i | \(0.127192\pi\) | ||||
−0.921223 | + | 0.389035i | \(0.872808\pi\) | |||||||
\(774\) | 2516.00 | 0.116842 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −15390.0 | −0.711944 | ||||||||
\(777\) | − 24304.0i | − 1.12214i | ||||||||
\(778\) | − 6810.00i | − 0.313818i | ||||||||
\(779\) | −16080.0 | −0.739571 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8064.00 | 0.369466 | ||||||||
\(782\) | 3008.00i | 0.137552i | ||||||||
\(783\) | 4000.00i | 0.182565i | ||||||||
\(784\) | −2009.00 | −0.0915179 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −8896.00 | −0.403702 | ||||||||
\(787\) | 32624.0i | 1.47766i | 0.673891 | + | 0.738831i | \(0.264622\pi\) | ||||
−0.673891 | + | 0.738831i | \(0.735378\pi\) | |||||||
\(788\) | 33558.0i | 1.51707i | ||||||||
\(789\) | −5824.00 | −0.262788 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5586.00 | −0.251094 | ||||||||
\(792\) | 6660.00i | 0.298804i | ||||||||
\(793\) | 21684.0i | 0.971023i | ||||||||
\(794\) | 574.000 | 0.0256555 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8960.00 | −0.398968 | ||||||||
\(797\) | − 11346.0i | − 0.504261i | −0.967693 | − | 0.252130i | \(-0.918869\pi\) | ||||
0.967693 | − | 0.252130i | \(-0.0811312\pi\) | |||||||
\(798\) | − 2240.00i | − 0.0993673i | ||||||||
\(799\) | 50384.0 | 2.23086 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −32190.0 | −1.41995 | ||||||||
\(802\) | − 6162.00i | − 0.271306i | ||||||||
\(803\) | 984.000i | 0.0432436i | ||||||||
\(804\) | 9184.00 | 0.402854 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 19344.0 | 0.845364 | ||||||||
\(807\) | 46480.0i | 2.02748i | ||||||||
\(808\) | − 7230.00i | − 0.314790i | ||||||||
\(809\) | 35190.0 | 1.52931 | 0.764657 | − | 0.644438i | \(-0.222909\pi\) | ||||
0.764657 | + | 0.644438i | \(0.222909\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30432.0 | 1.31765 | 0.658824 | − | 0.752297i | \(-0.271054\pi\) | ||||
0.658824 | + | 0.752297i | \(0.271054\pi\) | |||||||
\(812\) | − 2450.00i | − 0.105884i | ||||||||
\(813\) | 52224.0i | 2.25286i | ||||||||
\(814\) | 5208.00 | 0.224251 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 30832.0 | 1.32272 | ||||||||
\(817\) | 2720.00i | 0.116476i | ||||||||
\(818\) | 8210.00i | 0.350924i | ||||||||
\(819\) | 20202.0 | 0.861923 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12702.0 | 0.539955 | 0.269977 | − | 0.962867i | \(-0.412984\pi\) | ||||
0.269977 | + | 0.962867i | \(0.412984\pi\) | |||||||
\(822\) | − 5552.00i | − 0.235582i | ||||||||
\(823\) | 16952.0i | 0.717995i | 0.933339 | + | 0.358997i | \(0.116881\pi\) | ||||
−0.933339 | + | 0.358997i | \(0.883119\pi\) | |||||||
\(824\) | 4080.00 | 0.172492 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3920.00 | −0.165126 | ||||||||
\(827\) | 25404.0i | 1.06818i | 0.845428 | + | 0.534089i | \(0.179345\pi\) | ||||
−0.845428 | + | 0.534089i | \(0.820655\pi\) | |||||||
\(828\) | − 8288.00i | − 0.347860i | ||||||||
\(829\) | −26250.0 | −1.09976 | −0.549879 | − | 0.835244i | \(-0.685326\pi\) | ||||
−0.549879 | + | 0.835244i | \(0.685326\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −41008.0 | −1.71186 | ||||||||
\(832\) | − 13026.0i | − 0.542783i | ||||||||
\(833\) | − 4606.00i | − 0.191583i | ||||||||
\(834\) | 2880.00 | 0.119576 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3360.00 | −0.139005 | ||||||||
\(837\) | − 19840.0i | − 0.819320i | ||||||||
\(838\) | 4800.00i | 0.197868i | ||||||||
\(839\) | 15360.0 | 0.632045 | 0.316023 | − | 0.948752i | \(-0.397652\pi\) | ||||
0.316023 | + | 0.948752i | \(0.397652\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21889.0 | −0.897495 | ||||||||
\(842\) | 9938.00i | 0.406753i | ||||||||
\(843\) | 18864.0i | 0.770713i | ||||||||
\(844\) | −476.000 | −0.0194130 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 19832.0 | 0.805955 | ||||||||
\(847\) | 8309.00i | 0.337073i | ||||||||
\(848\) | 902.000i | 0.0365269i | ||||||||
\(849\) | 3136.00 | 0.126769 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13888.0 | −0.559430 | ||||||||
\(852\) | − 37632.0i | − 1.51321i | ||||||||
\(853\) | 10362.0i | 0.415930i | 0.978136 | + | 0.207965i | \(0.0666840\pi\) | ||||
−0.978136 | + | 0.207965i | \(0.933316\pi\) | |||||||
\(854\) | 1946.00 | 0.0779751 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6660.00 | 0.265928 | ||||||||
\(857\) | − 4506.00i | − 0.179606i | −0.995960 | − | 0.0898028i | \(-0.971376\pi\) | ||||
0.995960 | − | 0.0898028i | \(-0.0286237\pi\) | |||||||
\(858\) | 7488.00i | 0.297944i | ||||||||
\(859\) | −24200.0 | −0.961226 | −0.480613 | − | 0.876933i | \(-0.659586\pi\) | ||||
−0.480613 | + | 0.876933i | \(0.659586\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −22512.0 | −0.891065 | ||||||||
\(862\) | 9248.00i | 0.365415i | ||||||||
\(863\) | − 37008.0i | − 1.45975i | −0.683579 | − | 0.729877i | \(-0.739578\pi\) | ||||
0.683579 | − | 0.729877i | \(-0.260422\pi\) | |||||||
\(864\) | 12880.0 | 0.507160 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1118.00 | −0.0438697 | ||||||||
\(867\) | 31384.0i | 1.22936i | ||||||||
\(868\) | 12152.0i | 0.475191i | ||||||||
\(869\) | 12000.0 | 0.468437 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12792.0 | 0.497635 | ||||||||
\(872\) | − 17550.0i | − 0.681557i | ||||||||
\(873\) | 37962.0i | 1.47173i | ||||||||
\(874\) | −1280.00 | −0.0495385 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4592.00 | 0.177111 | ||||||||
\(877\) | − 3446.00i | − 0.132683i | −0.997797 | − | 0.0663416i | \(-0.978867\pi\) | ||||
0.997797 | − | 0.0663416i | \(-0.0211327\pi\) | |||||||
\(878\) | − 11960.0i | − 0.459716i | ||||||||
\(879\) | 9616.00 | 0.368987 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −16158.0 | −0.617908 | −0.308954 | − | 0.951077i | \(-0.599979\pi\) | ||||
−0.308954 | + | 0.951077i | \(0.599979\pi\) | |||||||
\(882\) | − 1813.00i | − 0.0692142i | ||||||||
\(883\) | − 44708.0i | − 1.70390i | −0.523623 | − | 0.851950i | \(-0.675420\pi\) | ||||
0.523623 | − | 0.851950i | \(-0.324580\pi\) | |||||||
\(884\) | 51324.0 | 1.95273 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7332.00 | 0.278017 | ||||||||
\(887\) | 23504.0i | 0.889726i | 0.895599 | + | 0.444863i | \(0.146748\pi\) | ||||
−0.895599 | + | 0.444863i | \(0.853252\pi\) | |||||||
\(888\) | − 52080.0i | − 1.96812i | ||||||||
\(889\) | −5432.00 | −0.204931 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4308.00 | −0.161979 | ||||||||
\(892\) | − 12096.0i | − 0.454040i | ||||||||
\(893\) | 21440.0i | 0.803429i | ||||||||
\(894\) | 18160.0 | 0.679375 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −10185.0 | −0.379751 | ||||||||
\(897\) | − 19968.0i | − 0.743269i | ||||||||
\(898\) | 1890.00i | 0.0702340i | ||||||||
\(899\) | −12400.0 | −0.460026 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2068.00 | −0.0764651 | ||||||||
\(902\) | − 4824.00i | − 0.178073i | ||||||||
\(903\) | 3808.00i | 0.140335i | ||||||||
\(904\) | −11970.0 | −0.440394 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −5056.00 | −0.185402 | ||||||||
\(907\) | − 42436.0i | − 1.55354i | −0.629782 | − | 0.776772i | \(-0.716856\pi\) | ||||
0.629782 | − | 0.776772i | \(-0.283144\pi\) | |||||||
\(908\) | 34048.0i | 1.24441i | ||||||||
\(909\) | −17834.0 | −0.650733 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7968.00 | −0.289782 | −0.144891 | − | 0.989448i | \(-0.546283\pi\) | ||||
−0.144891 | + | 0.989448i | \(0.546283\pi\) | |||||||
\(912\) | 13120.0i | 0.476367i | ||||||||
\(913\) | − 5376.00i | − 0.194874i | ||||||||
\(914\) | 7014.00 | 0.253832 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 38570.0 | 1.39125 | ||||||||
\(917\) | − 7784.00i | − 0.280317i | ||||||||
\(918\) | 7520.00i | 0.270367i | ||||||||
\(919\) | −14880.0 | −0.534109 | −0.267054 | − | 0.963681i | \(-0.586050\pi\) | ||||
−0.267054 | + | 0.963681i | \(0.586050\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 51072.0 | 1.82723 | ||||||||
\(922\) | 8318.00i | 0.297114i | ||||||||
\(923\) | − 52416.0i | − 1.86922i | ||||||||
\(924\) | −4704.00 | −0.167479 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 6432.00 | 0.228260 | ||||||||
\(927\) | − 10064.0i | − 0.356575i | ||||||||
\(928\) | − 8050.00i | − 0.284757i | ||||||||
\(929\) | −27610.0 | −0.975086 | −0.487543 | − | 0.873099i | \(-0.662107\pi\) | ||||
−0.487543 | + | 0.873099i | \(0.662107\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1960.00 | 0.0689972 | ||||||||
\(932\) | 37254.0i | 1.30933i | ||||||||
\(933\) | 39744.0i | 1.39460i | ||||||||
\(934\) | 10064.0 | 0.352574 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 43290.0 | 1.51173 | ||||||||
\(937\) | 28094.0i | 0.979499i | 0.871863 | + | 0.489750i | \(0.162912\pi\) | ||||
−0.871863 | + | 0.489750i | \(0.837088\pi\) | |||||||
\(938\) | − 1148.00i | − 0.0399611i | ||||||||
\(939\) | −22064.0 | −0.766807 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12198.0 | −0.422575 | −0.211288 | − | 0.977424i | \(-0.567766\pi\) | ||||
−0.211288 | + | 0.977424i | \(0.567766\pi\) | |||||||
\(942\) | − 5872.00i | − 0.203100i | ||||||||
\(943\) | 12864.0i | 0.444231i | ||||||||
\(944\) | 22960.0 | 0.791615 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −816.000 | −0.0280449 | ||||||||
\(947\) | − 31316.0i | − 1.07459i | −0.843396 | − | 0.537293i | \(-0.819447\pi\) | ||||
0.843396 | − | 0.537293i | \(-0.180553\pi\) | |||||||
\(948\) | − 56000.0i | − 1.91856i | ||||||||
\(949\) | 6396.00 | 0.218781 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 50192.0 | 1.71145 | ||||||||
\(952\) | − 9870.00i | − 0.336017i | ||||||||
\(953\) | 27322.0i | 0.928695i | 0.885653 | + | 0.464348i | \(0.153711\pi\) | ||||
−0.885653 | + | 0.464348i | \(0.846289\pi\) | |||||||
\(954\) | −814.000 | −0.0276250 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 12880.0 | 0.435742 | ||||||||
\(957\) | − 4800.00i | − 0.162134i | ||||||||
\(958\) | 1400.00i | 0.0472150i | ||||||||
\(959\) | 4858.00 | 0.163580 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 31713.0 | 1.06452 | ||||||||
\(962\) | − 33852.0i | − 1.13454i | ||||||||
\(963\) | − 16428.0i | − 0.549725i | ||||||||
\(964\) | −3066.00 | −0.102437 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1792.00 | −0.0596860 | ||||||||
\(967\) | − 5296.00i | − 0.176120i | −0.996115 | − | 0.0880599i | \(-0.971933\pi\) | ||||
0.996115 | − | 0.0880599i | \(-0.0280667\pi\) | |||||||
\(968\) | 17805.0i | 0.591193i | ||||||||
\(969\) | −30080.0 | −0.997223 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 512.000 | 0.0169216 | 0.00846079 | − | 0.999964i | \(-0.497307\pi\) | ||||
0.00846079 | + | 0.999964i | \(0.497307\pi\) | |||||||
\(972\) | 35224.0i | 1.16236i | ||||||||
\(973\) | 2520.00i | 0.0830293i | ||||||||
\(974\) | −13376.0 | −0.440036 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11398.0 | −0.373813 | ||||||||
\(977\) | 20734.0i | 0.678955i | 0.940614 | + | 0.339478i | \(0.110250\pi\) | ||||
−0.940614 | + | 0.339478i | \(0.889750\pi\) | |||||||
\(978\) | − 20256.0i | − 0.662286i | ||||||||
\(979\) | 10440.0 | 0.340821 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −43290.0 | −1.40891 | ||||||||
\(982\) | − 7092.00i | − 0.230463i | ||||||||
\(983\) | − 61168.0i | − 1.98470i | −0.123472 | − | 0.992348i | \(-0.539403\pi\) | ||||
0.123472 | − | 0.992348i | \(-0.460597\pi\) | |||||||
\(984\) | −48240.0 | −1.56284 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 4700.00 | 0.151804 | ||||||||
\(987\) | 30016.0i | 0.968004i | ||||||||
\(988\) | 21840.0i | 0.703262i | ||||||||
\(989\) | 2176.00 | 0.0699624 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −47928.0 | −1.53631 | −0.768155 | − | 0.640264i | \(-0.778825\pi\) | ||||
−0.768155 | + | 0.640264i | \(0.778825\pi\) | |||||||
\(992\) | 39928.0i | 1.27794i | ||||||||
\(993\) | − 15456.0i | − 0.493939i | ||||||||
\(994\) | −4704.00 | −0.150102 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −25088.0 | −0.798136 | ||||||||
\(997\) | 9454.00i | 0.300312i | 0.988662 | + | 0.150156i | \(0.0479776\pi\) | ||||
−0.988662 | + | 0.150156i | \(0.952022\pi\) | |||||||
\(998\) | − 820.000i | − 0.0260087i | ||||||||
\(999\) | −34720.0 | −1.09959 |
(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 | 175.4.b.a.99.1 | 2 | ||
5.2 | odd | 4 | 35.4.a.a.1.1 | ✓ | 1 | ||
5.3 | odd | 4 | 175.4.a.a.1.1 | 1 | |||
5.4 | even | 2 | inner | 175.4.b.a.99.2 | 2 | ||
15.2 | even | 4 | 315.4.a.c.1.1 | 1 | |||
15.8 | even | 4 | 1575.4.a.g.1.1 | 1 | |||
20.7 | even | 4 | 560.4.a.p.1.1 | 1 | |||
35.2 | odd | 12 | 245.4.e.e.116.1 | 2 | |||
35.12 | even | 12 | 245.4.e.b.116.1 | 2 | |||
35.13 | even | 4 | 1225.4.a.e.1.1 | 1 | |||
35.17 | even | 12 | 245.4.e.b.226.1 | 2 | |||
35.27 | even | 4 | 245.4.a.d.1.1 | 1 | |||
35.32 | odd | 12 | 245.4.e.e.226.1 | 2 | |||
40.27 | even | 4 | 2240.4.a.b.1.1 | 1 | |||
40.37 | odd | 4 | 2240.4.a.bk.1.1 | 1 | |||
105.62 | odd | 4 | 2205.4.a.i.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.4.a.a.1.1 | ✓ | 1 | 5.2 | odd | 4 | ||
175.4.a.a.1.1 | 1 | 5.3 | odd | 4 | |||
175.4.b.a.99.1 | 2 | 1.1 | even | 1 | trivial | ||
175.4.b.a.99.2 | 2 | 5.4 | even | 2 | inner | ||
245.4.a.d.1.1 | 1 | 35.27 | even | 4 | |||
245.4.e.b.116.1 | 2 | 35.12 | even | 12 | |||
245.4.e.b.226.1 | 2 | 35.17 | even | 12 | |||
245.4.e.e.116.1 | 2 | 35.2 | odd | 12 | |||
245.4.e.e.226.1 | 2 | 35.32 | odd | 12 | |||
315.4.a.c.1.1 | 1 | 15.2 | even | 4 | |||
560.4.a.p.1.1 | 1 | 20.7 | even | 4 | |||
1225.4.a.e.1.1 | 1 | 35.13 | even | 4 | |||
1575.4.a.g.1.1 | 1 | 15.8 | even | 4 | |||
2205.4.a.i.1.1 | 1 | 105.62 | odd | 4 | |||
2240.4.a.b.1.1 | 1 | 40.27 | even | 4 | |||
2240.4.a.bk.1.1 | 1 | 40.37 | odd | 4 |