Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [720,4,Mod(1,720)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(720, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("720.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 720.a (trivial) |
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: | yes |
Analytic conductor: | \(42.4813752041\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 60) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 720.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 28.0000 | 1.51186 | 0.755929 | − | 0.654654i | \(-0.227186\pi\) | ||||
0.755929 | + | 0.654654i | \(0.227186\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −24.0000 | −0.657843 | −0.328921 | − | 0.944357i | \(-0.606685\pi\) | ||||
−0.328921 | + | 0.944357i | \(0.606685\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −70.0000 | −1.49342 | −0.746712 | − | 0.665148i | \(-0.768369\pi\) | ||||
−0.746712 | + | 0.665148i | \(0.768369\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −102.000 | −1.45521 | −0.727607 | − | 0.685994i | \(-0.759367\pi\) | ||||
−0.727607 | + | 0.685994i | \(0.759367\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −20.0000 | −0.241490 | −0.120745 | − | 0.992684i | \(-0.538528\pi\) | ||||
−0.120745 | + | 0.992684i | \(0.538528\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −72.0000 | −0.652741 | −0.326370 | − | 0.945242i | \(-0.605826\pi\) | ||||
−0.326370 | + | 0.945242i | \(0.605826\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −306.000 | −1.95941 | −0.979703 | − | 0.200455i | \(-0.935758\pi\) | ||||
−0.979703 | + | 0.200455i | \(0.935758\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 136.000 | 0.787946 | 0.393973 | − | 0.919122i | \(-0.371100\pi\) | ||||
0.393973 | + | 0.919122i | \(0.371100\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 140.000 | 0.676123 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −214.000 | −0.950848 | −0.475424 | − | 0.879757i | \(-0.657705\pi\) | ||||
−0.475424 | + | 0.879757i | \(0.657705\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 150.000 | 0.571367 | 0.285684 | − | 0.958324i | \(-0.407779\pi\) | ||||
0.285684 | + | 0.958324i | \(0.407779\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 292.000 | 1.03557 | 0.517786 | − | 0.855510i | \(-0.326756\pi\) | ||||
0.517786 | + | 0.855510i | \(0.326756\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −72.0000 | −0.223453 | −0.111726 | − | 0.993739i | \(-0.535638\pi\) | ||||
−0.111726 | + | 0.993739i | \(0.535638\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 441.000 | 1.28571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 414.000 | 1.07297 | 0.536484 | − | 0.843911i | \(-0.319752\pi\) | ||||
0.536484 | + | 0.843911i | \(0.319752\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −120.000 | −0.294196 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −744.000 | −1.64170 | −0.820852 | − | 0.571141i | \(-0.806501\pi\) | ||||
−0.820852 | + | 0.571141i | \(0.806501\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −418.000 | −0.877367 | −0.438684 | − | 0.898642i | \(-0.644555\pi\) | ||||
−0.438684 | + | 0.898642i | \(0.644555\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −350.000 | −0.667879 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −188.000 | −0.342804 | −0.171402 | − | 0.985201i | \(-0.554830\pi\) | ||||
−0.171402 | + | 0.985201i | \(0.554830\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 480.000 | 0.802331 | 0.401166 | − | 0.916006i | \(-0.368605\pi\) | ||||
0.401166 | + | 0.916006i | \(0.368605\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 434.000 | 0.695834 | 0.347917 | − | 0.937525i | \(-0.386889\pi\) | ||||
0.347917 | + | 0.937525i | \(0.386889\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −672.000 | −0.994565 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1352.00 | −1.92547 | −0.962733 | − | 0.270452i | \(-0.912827\pi\) | ||||
−0.962733 | + | 0.270452i | \(0.912827\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −612.000 | −0.809346 | −0.404673 | − | 0.914461i | \(-0.632615\pi\) | ||||
−0.404673 | + | 0.914461i | \(0.632615\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −510.000 | −0.650791 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 30.0000 | 0.0357303 | 0.0178651 | − | 0.999840i | \(-0.494313\pi\) | ||||
0.0178651 | + | 0.999840i | \(0.494313\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1960.00 | −2.25784 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −100.000 | −0.107998 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −286.000 | −0.299370 | −0.149685 | − | 0.988734i | \(-0.547826\pi\) | ||||
−0.149685 | + | 0.988734i | \(0.547826\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1542.00 | 1.51916 | 0.759578 | − | 0.650416i | \(-0.225406\pi\) | ||||
0.759578 | + | 0.650416i | \(0.225406\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1172.00 | −1.12117 | −0.560585 | − | 0.828097i | \(-0.689424\pi\) | ||||
−0.560585 | + | 0.828097i | \(0.689424\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1956.00 | 1.76723 | 0.883615 | − | 0.468214i | \(-0.155102\pi\) | ||||
0.883615 | + | 0.468214i | \(0.155102\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1858.00 | −1.63270 | −0.816349 | − | 0.577559i | \(-0.804005\pi\) | ||||
−0.816349 | + | 0.577559i | \(0.804005\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −174.000 | −0.144854 | −0.0724272 | − | 0.997374i | \(-0.523074\pi\) | ||||
−0.0724272 | + | 0.997374i | \(0.523074\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −360.000 | −0.291915 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2856.00 | −2.20008 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −755.000 | −0.567243 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2068.00 | 1.44492 | 0.722462 | − | 0.691411i | \(-0.243010\pi\) | ||||
0.722462 | + | 0.691411i | \(0.243010\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 312.000 | 0.208088 | 0.104044 | − | 0.994573i | \(-0.466822\pi\) | ||||
0.104044 | + | 0.994573i | \(0.466822\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −560.000 | −0.365099 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2646.00 | −1.65010 | −0.825048 | − | 0.565063i | \(-0.808852\pi\) | ||||
−0.825048 | + | 0.565063i | \(0.808852\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1276.00 | 0.778625 | 0.389313 | − | 0.921106i | \(-0.372713\pi\) | ||||
0.389313 | + | 0.921106i | \(0.372713\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1680.00 | 0.982438 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1530.00 | −0.876273 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3198.00 | 1.75832 | 0.879162 | − | 0.476522i | \(-0.158103\pi\) | ||||
0.879162 | + | 0.476522i | \(0.158103\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 760.000 | 0.409589 | 0.204794 | − | 0.978805i | \(-0.434347\pi\) | ||||
0.204794 | + | 0.978805i | \(0.434347\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 680.000 | 0.352380 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −166.000 | −0.0843837 | −0.0421919 | − | 0.999110i | \(-0.513434\pi\) | ||||
−0.0421919 | + | 0.999110i | \(0.513434\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2016.00 | −0.986851 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3020.00 | −1.45119 | −0.725597 | − | 0.688120i | \(-0.758436\pi\) | ||||
−0.725597 | + | 0.688120i | \(0.758436\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −984.000 | −0.455953 | −0.227977 | − | 0.973667i | \(-0.573211\pi\) | ||||
−0.227977 | + | 0.973667i | \(0.573211\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2703.00 | 1.23031 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1962.00 | −0.862243 | −0.431122 | − | 0.902294i | \(-0.641882\pi\) | ||||
−0.431122 | + | 0.902294i | \(0.641882\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 700.000 | 0.302372 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 576.000 | 0.240515 | 0.120258 | − | 0.992743i | \(-0.461628\pi\) | ||||
0.120258 | + | 0.992743i | \(0.461628\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1210.00 | −0.496898 | −0.248449 | − | 0.968645i | \(-0.579921\pi\) | ||||
−0.248449 | + | 0.968645i | \(0.579921\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1070.00 | −0.425232 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2448.00 | 0.957302 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3384.00 | 1.28198 | 0.640989 | − | 0.767550i | \(-0.278525\pi\) | ||||
0.640989 | + | 0.767550i | \(0.278525\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2038.00 | −0.760096 | −0.380048 | − | 0.924967i | \(-0.624092\pi\) | ||||
−0.380048 | + | 0.924967i | \(0.624092\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4098.00 | −1.48208 | −0.741042 | − | 0.671459i | \(-0.765668\pi\) | ||||
−0.741042 | + | 0.671459i | \(0.765668\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2248.00 | 0.800786 | 0.400393 | − | 0.916343i | \(-0.368874\pi\) | ||||
0.400393 | + | 0.916343i | \(0.368874\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8568.00 | −2.96234 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 750.000 | 0.255523 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 480.000 | 0.158863 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3260.00 | −1.06364 | −0.531819 | − | 0.846858i | \(-0.678491\pi\) | ||||
−0.531819 | + | 0.846858i | \(0.678491\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1460.00 | 0.463122 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3808.00 | 1.19126 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7140.00 | 2.17325 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2980.00 | 0.894868 | 0.447434 | − | 0.894317i | \(-0.352338\pi\) | ||||
0.447434 | + | 0.894317i | \(0.352338\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3180.00 | −0.929797 | −0.464899 | − | 0.885364i | \(-0.653909\pi\) | ||||
−0.464899 | + | 0.885364i | \(0.653909\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3374.00 | 0.973625 | 0.486813 | − | 0.873506i | \(-0.338159\pi\) | ||||
0.486813 | + | 0.873506i | \(0.338159\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1950.00 | −0.548278 | −0.274139 | − | 0.961690i | \(-0.588393\pi\) | ||||
−0.274139 | + | 0.961690i | \(0.588393\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −360.000 | −0.0999311 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2232.00 | 0.604084 | 0.302042 | − | 0.953295i | \(-0.402332\pi\) | ||||
0.302042 | + | 0.953295i | \(0.402332\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1822.00 | −0.486993 | −0.243497 | − | 0.969902i | \(-0.578294\pi\) | ||||
−0.243497 | + | 0.969902i | \(0.578294\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2205.00 | 0.574989 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1400.00 | 0.360647 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1488.00 | 0.374190 | 0.187095 | − | 0.982342i | \(-0.440093\pi\) | ||||
0.187095 | + | 0.982342i | \(0.440093\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1728.00 | 0.429401 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2994.00 | 0.726695 | 0.363347 | − | 0.931654i | \(-0.381634\pi\) | ||||
0.363347 | + | 0.931654i | \(0.381634\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5992.00 | −1.43755 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2472.00 | −0.579582 | −0.289791 | − | 0.957090i | \(-0.593586\pi\) | ||||
−0.289791 | + | 0.957090i | \(0.593586\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2070.00 | 0.479846 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3954.00 | −0.896207 | −0.448103 | − | 0.893982i | \(-0.647900\pi\) | ||||
−0.448103 | + | 0.893982i | \(0.647900\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2176.00 | 0.487759 | 0.243879 | − | 0.969806i | \(-0.421580\pi\) | ||||
0.243879 | + | 0.969806i | \(0.421580\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −600.000 | −0.131569 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1034.00 | 0.224285 | 0.112143 | − | 0.993692i | \(-0.464229\pi\) | ||||
0.112143 | + | 0.993692i | \(0.464229\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6654.00 | 1.41261 | 0.706307 | − | 0.707906i | \(-0.250360\pi\) | ||||
0.706307 | + | 0.707906i | \(0.250360\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1756.00 | 0.368846 | 0.184423 | − | 0.982847i | \(-0.440958\pi\) | ||||
0.184423 | + | 0.982847i | \(0.440958\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4200.00 | 0.863826 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5491.00 | 1.11765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3234.00 | −0.644820 | −0.322410 | − | 0.946600i | \(-0.604493\pi\) | ||||
−0.322410 | + | 0.946600i | \(0.604493\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3720.00 | −0.734192 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5040.00 | 0.974818 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8176.00 | 1.56564 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2090.00 | −0.392371 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2036.00 | −0.378504 | −0.189252 | − | 0.981929i | \(-0.560606\pi\) | ||||
−0.189252 | + | 0.981929i | \(0.560606\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −96.0000 | −0.0175037 | −0.00875187 | − | 0.999962i | \(-0.502786\pi\) | ||||
−0.00875187 | + | 0.999962i | \(0.502786\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1202.00 | 0.217064 | 0.108532 | − | 0.994093i | \(-0.465385\pi\) | ||||
0.108532 | + | 0.994093i | \(0.465385\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3798.00 | 0.672924 | 0.336462 | − | 0.941697i | \(-0.390770\pi\) | ||||
0.336462 | + | 0.941697i | \(0.390770\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7344.00 | 1.28898 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2040.00 | 0.351420 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1750.00 | −0.298685 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2016.00 | −0.337829 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5668.00 | 0.941213 | 0.470606 | − | 0.882343i | \(-0.344035\pi\) | ||||
0.470606 | + | 0.882343i | \(0.344035\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −940.000 | −0.153307 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −454.000 | −0.0733856 | −0.0366928 | − | 0.999327i | \(-0.511682\pi\) | ||||
−0.0366928 | + | 0.999327i | \(0.511682\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3264.00 | −0.518345 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2744.00 | 0.431959 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5604.00 | −0.866970 | −0.433485 | − | 0.901161i | \(-0.642716\pi\) | ||||
−0.433485 | + | 0.901161i | \(0.642716\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11266.0 | −1.72795 | −0.863976 | − | 0.503533i | \(-0.832033\pi\) | ||||
−0.863976 | + | 0.503533i | \(0.832033\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6426.00 | 0.968899 | 0.484450 | − | 0.874819i | \(-0.339020\pi\) | ||||
0.484450 | + | 0.874819i | \(0.339020\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2400.00 | 0.358813 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6936.00 | 1.01969 | 0.509844 | − | 0.860267i | \(-0.329703\pi\) | ||||
0.509844 | + | 0.860267i | \(0.329703\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6459.00 | −0.941682 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2170.00 | 0.311186 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 388.000 | 0.0551865 | 0.0275932 | − | 0.999619i | \(-0.491216\pi\) | ||||
0.0275932 | + | 0.999619i | \(0.491216\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11592.0 | 1.62217 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8062.00 | −1.11913 | −0.559564 | − | 0.828787i | \(-0.689031\pi\) | ||||
−0.559564 | + | 0.828787i | \(0.689031\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 21420.0 | 2.92622 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3388.00 | 0.459182 | 0.229591 | − | 0.973287i | \(-0.426261\pi\) | ||||
0.229591 | + | 0.973287i | \(0.426261\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6984.00 | 0.931764 | 0.465882 | − | 0.884847i | \(-0.345737\pi\) | ||||
0.465882 | + | 0.884847i | \(0.345737\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3360.00 | −0.444783 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2526.00 | 0.329237 | 0.164619 | − | 0.986357i | \(-0.447361\pi\) | ||||
0.164619 | + | 0.986357i | \(0.447361\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7344.00 | 0.949877 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6760.00 | −0.861095 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6146.00 | 0.776975 | 0.388487 | − | 0.921454i | \(-0.372998\pi\) | ||||
0.388487 | + | 0.921454i | \(0.372998\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9786.00 | −1.21868 | −0.609339 | − | 0.792910i | \(-0.708565\pi\) | ||||
−0.609339 | + | 0.792910i | \(0.708565\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9520.00 | −1.17674 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5136.00 | 0.625509 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −886.000 | −0.107115 | −0.0535573 | − | 0.998565i | \(-0.517056\pi\) | ||||
−0.0535573 | + | 0.998565i | \(0.517056\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −20832.0 | −2.48202 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3060.00 | −0.361951 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11352.0 | −1.32358 | −0.661792 | − | 0.749688i | \(-0.730204\pi\) | ||||
−0.661792 | + | 0.749688i | \(0.730204\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10190.0 | 1.17964 | 0.589822 | − | 0.807533i | \(-0.299198\pi\) | ||||
0.589822 | + | 0.807533i | \(0.299198\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2550.00 | −0.291043 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11704.0 | −1.32645 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2448.00 | 0.273587 | 0.136794 | − | 0.990600i | \(-0.456320\pi\) | ||||
0.136794 | + | 0.990600i | \(0.456320\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7078.00 | −0.785559 | −0.392779 | − | 0.919633i | \(-0.628486\pi\) | ||||
−0.392779 | + | 0.919633i | \(0.628486\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1440.00 | 0.157631 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18088.0 | 1.96650 | 0.983250 | − | 0.182264i | \(-0.0583426\pi\) | ||||
0.983250 | + | 0.182264i | \(0.0583426\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3852.00 | 0.413124 | 0.206562 | − | 0.978433i | \(-0.433772\pi\) | ||||
0.206562 | + | 0.978433i | \(0.433772\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 150.000 | 0.0159791 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6522.00 | −0.685506 | −0.342753 | − | 0.939426i | \(-0.611359\pi\) | ||||
−0.342753 | + | 0.939426i | \(0.611359\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3600.00 | −0.375870 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9800.00 | −1.00974 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2090.00 | 0.213930 | 0.106965 | − | 0.994263i | \(-0.465887\pi\) | ||||
0.106965 | + | 0.994263i | \(0.465887\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9894.00 | 0.999587 | 0.499793 | − | 0.866145i | \(-0.333409\pi\) | ||||
0.499793 | + | 0.866145i | \(0.333409\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3044.00 | −0.305544 | −0.152772 | − | 0.988261i | \(-0.548820\pi\) | ||||
−0.152772 | + | 0.988261i | \(0.548820\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10236.0 | 1.01427 | 0.507137 | − | 0.861866i | \(-0.330704\pi\) | ||||
0.507137 | + | 0.861866i | \(0.330704\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5264.00 | −0.518271 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7008.00 | −0.681244 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −500.000 | −0.0482980 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11496.0 | 1.09659 | 0.548294 | − | 0.836286i | \(-0.315277\pi\) | ||||
0.548294 | + | 0.836286i | \(0.315277\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14980.0 | 1.42002 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1430.00 | −0.133882 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15316.0 | 1.42512 | 0.712561 | − | 0.701610i | \(-0.247535\pi\) | ||||
0.712561 | + | 0.701610i | \(0.247535\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11616.0 | −1.06766 | −0.533832 | − | 0.845591i | \(-0.679248\pi\) | ||||
−0.533832 | + | 0.845591i | \(0.679248\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 31212.0 | 2.85135 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13440.0 | 1.21301 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14996.0 | −1.34532 | −0.672658 | − | 0.739953i | \(-0.734848\pi\) | ||||
−0.672658 | + | 0.739953i | \(0.734848\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −21648.0 | −1.91896 | −0.959480 | − | 0.281778i | \(-0.909076\pi\) | ||||
−0.959480 | + | 0.281778i | \(0.909076\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7710.00 | 0.679387 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3378.00 | −0.294160 | −0.147080 | − | 0.989125i | \(-0.546987\pi\) | ||||
−0.147080 | + | 0.989125i | \(0.546987\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12152.0 | 1.05200 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5860.00 | −0.501403 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1728.00 | 0.146997 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16158.0 | 1.35872 | 0.679362 | − | 0.733804i | \(-0.262257\pi\) | ||||
0.679362 | + | 0.733804i | \(0.262257\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 76.0000 | 0.00635420 | 0.00317710 | − | 0.999995i | \(-0.498989\pi\) | ||||
0.00317710 | + | 0.999995i | \(0.498989\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −13872.0 | −1.14663 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6983.00 | −0.573929 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10500.0 | −0.853294 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9780.00 | 0.790329 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10584.0 | −0.845798 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9278.00 | 0.737324 | 0.368662 | − | 0.929563i | \(-0.379816\pi\) | ||||
0.368662 | + | 0.929563i | \(0.379816\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9290.00 | −0.730165 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14564.0 | −1.13841 | −0.569206 | − | 0.822195i | \(-0.692749\pi\) | ||||
−0.569206 | + | 0.822195i | \(0.692749\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6120.00 | 0.473177 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −37856.0 | −2.91103 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2154.00 | −0.163856 | −0.0819281 | − | 0.996638i | \(-0.526108\pi\) | ||||
−0.0819281 | + | 0.996638i | \(0.526108\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −20440.0 | −1.54655 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8700.00 | −0.651263 | −0.325632 | − | 0.945497i | \(-0.605577\pi\) | ||||
−0.325632 | + | 0.945497i | \(0.605577\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −870.000 | −0.0647808 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4194.00 | −0.309001 | −0.154501 | − | 0.987993i | \(-0.549377\pi\) | ||||
−0.154501 | + | 0.987993i | \(0.549377\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8020.00 | 0.587787 | 0.293894 | − | 0.955838i | \(-0.405049\pi\) | ||||
0.293894 | + | 0.955838i | \(0.405049\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1800.00 | −0.130548 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2686.00 | −0.193795 | −0.0968974 | − | 0.995294i | \(-0.530892\pi\) | ||||
−0.0968974 | + | 0.995294i | \(0.530892\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −17136.0 | −1.22362 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9936.00 | −0.705844 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3012.00 | 0.211786 | 0.105893 | − | 0.994378i | \(-0.466230\pi\) | ||||
0.105893 | + | 0.994378i | \(0.466230\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2720.00 | −0.190281 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15522.0 | 1.07489 | 0.537447 | − | 0.843298i | \(-0.319389\pi\) | ||||
0.537447 | + | 0.843298i | \(0.319389\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −14280.0 | −0.983904 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19224.0 | 1.31130 | 0.655652 | − | 0.755063i | \(-0.272394\pi\) | ||||
0.655652 | + | 0.755063i | \(0.272394\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6502.00 | −0.441301 | −0.220651 | − | 0.975353i | \(-0.570818\pi\) | ||||
−0.220651 | + | 0.975353i | \(0.570818\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3775.00 | −0.253679 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −29396.0 | −1.96565 | −0.982823 | − | 0.184552i | \(-0.940917\pi\) | ||||
−0.982823 | + | 0.184552i | \(0.940917\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5040.00 | 0.333710 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10006.0 | −0.659280 | −0.329640 | − | 0.944107i | \(-0.606927\pi\) | ||||
−0.329640 | + | 0.944107i | \(0.606927\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23118.0 | −1.50842 | −0.754210 | − | 0.656633i | \(-0.771980\pi\) | ||||
−0.754210 | + | 0.656633i | \(0.771980\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14036.0 | −0.911397 | −0.455698 | − | 0.890134i | \(-0.650610\pi\) | ||||
−0.455698 | + | 0.890134i | \(0.650610\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 840.000 | 0.0540191 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 21828.0 | 1.38369 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4288.00 | 0.270527 | 0.135264 | − | 0.990810i | \(-0.456812\pi\) | ||||
0.135264 | + | 0.990810i | \(0.456812\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10340.0 | 0.646190 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −30870.0 | −1.92012 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1314.00 | −0.0809671 | −0.0404835 | − | 0.999180i | \(-0.512890\pi\) | ||||
−0.0404835 | + | 0.999180i | \(0.512890\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 628.000 | 0.0385162 | 0.0192581 | − | 0.999815i | \(-0.493870\pi\) | ||||
0.0192581 | + | 0.999815i | \(0.493870\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10944.0 | −0.664997 | −0.332498 | − | 0.943104i | \(-0.607892\pi\) | ||||
−0.332498 | + | 0.943104i | \(0.607892\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17856.0 | 1.07998 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1098.00 | −0.0658010 | −0.0329005 | − | 0.999459i | \(-0.510474\pi\) | ||||
−0.0329005 | + | 0.999459i | \(0.510474\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1560.00 | 0.0930599 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 312.000 | 0.0184428 | 0.00922139 | − | 0.999957i | \(-0.497065\pi\) | ||||
0.00922139 | + | 0.999957i | \(0.497065\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8678.00 | 0.510643 | 0.255322 | − | 0.966856i | \(-0.417819\pi\) | ||||
0.255322 | + | 0.966856i | \(0.417819\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2800.00 | −0.163277 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 22032.0 | 1.27898 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10032.0 | 0.577170 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14470.0 | −0.828793 | −0.414396 | − | 0.910097i | \(-0.636007\pi\) | ||||
−0.414396 | + | 0.910097i | \(0.636007\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11838.0 | 0.672040 | 0.336020 | − | 0.941855i | \(-0.390919\pi\) | ||||
0.336020 | + | 0.941855i | \(0.390919\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8008.00 | −0.452605 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −25548.0 | −1.43128 | −0.715642 | − | 0.698467i | \(-0.753866\pi\) | ||||
−0.715642 | + | 0.698467i | \(0.753866\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13230.0 | −0.737945 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −28980.0 | −1.60239 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18412.0 | 1.01364 | 0.506820 | − | 0.862052i | \(-0.330821\pi\) | ||||
0.506820 | + | 0.862052i | \(0.330821\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6380.00 | 0.348212 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15300.0 | −0.831462 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8814.00 | 0.474893 | 0.237447 | − | 0.971401i | \(-0.423690\pi\) | ||||
0.237447 | + | 0.971401i | \(0.423690\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4280.00 | 0.229621 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 43176.0 | 2.29675 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17314.0 | −0.917124 | −0.458562 | − | 0.888662i | \(-0.651635\pi\) | ||||
−0.458562 | + | 0.888662i | \(0.651635\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9792.00 | −0.514324 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8400.00 | 0.439360 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −768.000 | −0.0398353 | −0.0199176 | − | 0.999802i | \(-0.506340\pi\) | ||||
−0.0199176 | + | 0.999802i | \(0.506340\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −32816.0 | −1.69505 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7650.00 | −0.391881 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18196.0 | 0.928270 | 0.464135 | − | 0.885764i | \(-0.346365\pi\) | ||||
0.464135 | + | 0.885764i | \(0.346365\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −29784.0 | −1.50698 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18142.0 | −0.914175 | −0.457087 | − | 0.889422i | \(-0.651107\pi\) | ||||
−0.457087 | + | 0.889422i | \(0.651107\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4512.00 | 0.225511 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13660.0 | 0.679961 | 0.339981 | − | 0.940432i | \(-0.389580\pi\) | ||||
0.339981 | + | 0.940432i | \(0.389580\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12768.0 | −0.630434 | −0.315217 | − | 0.949020i | \(-0.602077\pi\) | ||||
−0.315217 | + | 0.949020i | \(0.602077\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15990.0 | 0.786347 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 54768.0 | 2.67180 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22952.0 | −1.11522 | −0.557610 | − | 0.830103i | \(-0.688282\pi\) | ||||
−0.557610 | + | 0.830103i | \(0.688282\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3800.00 | 0.183174 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15818.0 | 0.759465 | 0.379732 | − | 0.925096i | \(-0.376016\pi\) | ||||
0.379732 | + | 0.925096i | \(0.376016\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18558.0 | 0.884004 | 0.442002 | − | 0.897014i | \(-0.354268\pi\) | ||||
0.442002 | + | 0.897014i | \(0.354268\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −52024.0 | −2.46841 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 52080.0 | 2.45176 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14978.0 | 0.702367 | 0.351184 | − | 0.936307i | \(-0.385779\pi\) | ||||
0.351184 | + | 0.936307i | \(0.385779\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8946.00 | −0.416255 | −0.208128 | − | 0.978102i | \(-0.566737\pi\) | ||||
−0.208128 | + | 0.978102i | \(0.566737\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3400.00 | 0.157589 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3000.00 | −0.137980 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11520.0 | −0.527808 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −830.000 | −0.0377375 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18436.0 | 0.835035 | 0.417517 | − | 0.908669i | \(-0.362900\pi\) | ||||
0.417517 | + | 0.908669i | \(0.362900\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4872.00 | −0.218999 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 29260.0 | 1.31028 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −16314.0 | −0.725058 | −0.362529 | − | 0.931972i | \(-0.618087\pi\) | ||||
−0.362529 | + | 0.931972i | \(0.618087\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7344.00 | 0.325172 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10416.0 | −0.457749 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10080.0 | −0.441333 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 25446.0 | 1.10585 | 0.552926 | − | 0.833231i | \(-0.313511\pi\) | ||||
0.552926 | + | 0.833231i | \(0.313511\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −42740.0 | −1.85056 | −0.925280 | − | 0.379284i | \(-0.876170\pi\) | ||||
−0.925280 | + | 0.379284i | \(0.876170\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −15100.0 | −0.648994 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5840.00 | −0.250080 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29946.0 | −1.27299 | −0.636494 | − | 0.771282i | \(-0.719616\pi\) | ||||
−0.636494 | + | 0.771282i | \(0.719616\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32596.0 | 1.38059 | 0.690295 | − | 0.723528i | \(-0.257481\pi\) | ||||
0.690295 | + | 0.723528i | \(0.257481\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3804.00 | 0.159949 | 0.0799746 | − | 0.996797i | \(-0.474516\pi\) | ||||
0.0799746 | + | 0.996797i | \(0.474516\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3278.00 | 0.137334 | 0.0686669 | − | 0.997640i | \(-0.478125\pi\) | ||||
0.0686669 | + | 0.997640i | \(0.478125\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −44982.0 | −1.87099 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4920.00 | −0.203909 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5784.00 | −0.238005 | −0.119002 | − | 0.992894i | \(-0.537970\pi\) | ||||
−0.119002 | + | 0.992894i | \(0.537970\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 69247.0 | 2.83927 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 13515.0 | 0.550213 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −21140.0 | −0.857590 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15408.0 | 0.620657 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17306.0 | 0.694661 | 0.347331 | − | 0.937743i | \(-0.387088\pi\) | ||||
0.347331 | + | 0.937743i | \(0.387088\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −31134.0 | −1.24098 | −0.620488 | − | 0.784216i | \(-0.713066\pi\) | ||||
−0.620488 | + | 0.784216i | \(0.713066\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10780.0 | 0.428183 | 0.214091 | − | 0.976814i | \(-0.431321\pi\) | ||||
0.214091 | + | 0.976814i | \(0.431321\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3456.00 | 0.136319 | 0.0681597 | − | 0.997674i | \(-0.478287\pi\) | ||||
0.0681597 | + | 0.997674i | \(0.478287\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9810.00 | −0.385607 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 32448.0 | 1.26665 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13160.0 | 0.511951 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3500.00 | 0.135225 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2618.00 | 0.100802 | 0.0504011 | − | 0.998729i | \(-0.483950\pi\) | ||||
0.0504011 | + | 0.998729i | \(0.483950\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26550.0 | 1.01531 | 0.507657 | − | 0.861559i | \(-0.330512\pi\) | ||||
0.507657 | + | 0.861559i | \(0.330512\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −27596.0 | −1.05173 | −0.525866 | − | 0.850567i | \(-0.676259\pi\) | ||||
−0.525866 | + | 0.850567i | \(0.676259\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −37848.0 | −1.43271 | −0.716354 | − | 0.697737i | \(-0.754190\pi\) | ||||
−0.716354 | + | 0.697737i | \(0.754190\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 57904.0 | 2.18452 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1440.00 | 0.0539617 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2880.00 | 0.107562 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −41616.0 | −1.54391 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −42228.0 | −1.56140 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6050.00 | −0.222220 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4804.00 | 0.175870 | 0.0879351 | − | 0.996126i | \(-0.471973\pi\) | ||||
0.0879351 | + | 0.996126i | \(0.471973\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28608.0 | 1.04042 | 0.520211 | − | 0.854037i | \(-0.325853\pi\) | ||||
0.520211 | + | 0.854037i | \(0.325853\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14688.0 | 0.532423 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8736.00 | 0.314600 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40768.0 | 1.46334 | 0.731672 | − | 0.681657i | \(-0.238741\pi\) | ||||
0.731672 | + | 0.681657i | \(0.238741\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −33600.0 | −1.19822 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5350.00 | −0.190170 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −27642.0 | −0.976216 | −0.488108 | − | 0.872783i | \(-0.662313\pi\) | ||||
−0.488108 | + | 0.872783i | \(0.662313\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8820.00 | −0.310487 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12240.0 | 0.428119 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28106.0 | 0.979918 | 0.489959 | − | 0.871746i | \(-0.337012\pi\) | ||||
0.489959 | + | 0.871746i | \(0.337012\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14730.0 | −0.510291 | −0.255146 | − | 0.966903i | \(-0.582123\pi\) | ||||
−0.255146 | + | 0.966903i | \(0.582123\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10800.0 | −0.372955 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9564.00 | −0.328182 | −0.164091 | − | 0.986445i | \(-0.552469\pi\) | ||||
−0.164091 | + | 0.986445i | \(0.552469\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −30380.0 | −1.03917 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 53898.0 | 1.83203 | 0.916017 | − | 0.401141i | \(-0.131386\pi\) | ||||
0.916017 | + | 0.401141i | \(0.131386\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16920.0 | 0.573318 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −74088.0 | −2.49471 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11295.0 | −0.379141 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −10190.0 | −0.339925 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15140.0 | −0.503485 | −0.251742 | − | 0.967794i | \(-0.581004\pi\) | ||||
−0.251742 | + | 0.967794i | \(0.581004\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23808.0 | 0.786854 | 0.393427 | − | 0.919356i | \(-0.371289\pi\) | ||||
0.393427 | + | 0.919356i | \(0.371289\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 35728.0 | 1.17717 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −23094.0 | −0.756236 | −0.378118 | − | 0.925757i | \(-0.623429\pi\) | ||||
−0.378118 | + | 0.925757i | \(0.623429\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −720.000 | −0.0235049 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7584.00 | 0.246075 | 0.123038 | − | 0.992402i | \(-0.460736\pi\) | ||||
0.123038 | + | 0.992402i | \(0.460736\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20490.0 | −0.662808 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −21024.0 | −0.675960 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26752.0 | 0.857523 | 0.428761 | − | 0.903418i | \(-0.358950\pi\) | ||||
0.428761 | + | 0.903418i | \(0.358950\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11240.0 | 0.358123 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7778.00 | 0.247073 | 0.123536 | − | 0.992340i | \(-0.460576\pi\) | ||||
0.123536 | + | 0.992340i | \(0.460576\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 720.4.a.bb.1.1 | 1 | ||
3.2 | odd | 2 | 240.4.a.i.1.1 | 1 | |||
4.3 | odd | 2 | 180.4.a.d.1.1 | 1 | |||
12.11 | even | 2 | 60.4.a.a.1.1 | ✓ | 1 | ||
15.2 | even | 4 | 1200.4.f.n.49.1 | 2 | |||
15.8 | even | 4 | 1200.4.f.n.49.2 | 2 | |||
15.14 | odd | 2 | 1200.4.a.a.1.1 | 1 | |||
20.3 | even | 4 | 900.4.d.h.649.2 | 2 | |||
20.7 | even | 4 | 900.4.d.h.649.1 | 2 | |||
20.19 | odd | 2 | 900.4.a.q.1.1 | 1 | |||
24.5 | odd | 2 | 960.4.a.r.1.1 | 1 | |||
24.11 | even | 2 | 960.4.a.bc.1.1 | 1 | |||
36.7 | odd | 6 | 1620.4.i.f.1081.1 | 2 | |||
36.11 | even | 6 | 1620.4.i.l.1081.1 | 2 | |||
36.23 | even | 6 | 1620.4.i.l.541.1 | 2 | |||
36.31 | odd | 6 | 1620.4.i.f.541.1 | 2 | |||
60.23 | odd | 4 | 300.4.d.b.49.1 | 2 | |||
60.47 | odd | 4 | 300.4.d.b.49.2 | 2 | |||
60.59 | even | 2 | 300.4.a.i.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.4.a.a.1.1 | ✓ | 1 | 12.11 | even | 2 | ||
180.4.a.d.1.1 | 1 | 4.3 | odd | 2 | |||
240.4.a.i.1.1 | 1 | 3.2 | odd | 2 | |||
300.4.a.i.1.1 | 1 | 60.59 | even | 2 | |||
300.4.d.b.49.1 | 2 | 60.23 | odd | 4 | |||
300.4.d.b.49.2 | 2 | 60.47 | odd | 4 | |||
720.4.a.bb.1.1 | 1 | 1.1 | even | 1 | trivial | ||
900.4.a.q.1.1 | 1 | 20.19 | odd | 2 | |||
900.4.d.h.649.1 | 2 | 20.7 | even | 4 | |||
900.4.d.h.649.2 | 2 | 20.3 | even | 4 | |||
960.4.a.r.1.1 | 1 | 24.5 | odd | 2 | |||
960.4.a.bc.1.1 | 1 | 24.11 | even | 2 | |||
1200.4.a.a.1.1 | 1 | 15.14 | odd | 2 | |||
1200.4.f.n.49.1 | 2 | 15.2 | even | 4 | |||
1200.4.f.n.49.2 | 2 | 15.8 | even | 4 | |||
1620.4.i.f.541.1 | 2 | 36.31 | odd | 6 | |||
1620.4.i.f.1081.1 | 2 | 36.7 | odd | 6 | |||
1620.4.i.l.541.1 | 2 | 36.23 | even | 6 | |||
1620.4.i.l.1081.1 | 2 | 36.11 | even | 6 |