Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2475,4,Mod(1,2475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2475, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2475.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2475 = 3^{2} \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2475.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: | \(146.029727264\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 825) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 2475.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.00000 | 1.41421 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 8.00000 | 1.00000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 21.0000 | 1.13389 | 0.566947 | − | 0.823754i | \(-0.308125\pi\) | ||||
0.566947 | + | 0.823754i | \(0.308125\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −68.0000 | −1.45075 | −0.725377 | − | 0.688352i | \(-0.758335\pi\) | ||||
−0.725377 | + | 0.688352i | \(0.758335\pi\) | |||||||
\(14\) | 84.0000 | 1.60357 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −64.0000 | −1.00000 | ||||||||
\(17\) | −21.0000 | −0.299603 | −0.149801 | − | 0.988716i | \(-0.547863\pi\) | ||||
−0.149801 | + | 0.988716i | \(0.547863\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 125.000 | 1.50931 | 0.754657 | − | 0.656119i | \(-0.227803\pi\) | ||||
0.754657 | + | 0.656119i | \(0.227803\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −44.0000 | −0.426401 | ||||||||
\(23\) | −137.000 | −1.24202 | −0.621010 | − | 0.783802i | \(-0.713278\pi\) | ||||
−0.621010 | + | 0.783802i | \(0.713278\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −272.000 | −2.05168 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 168.000 | 1.13389 | ||||||||
\(29\) | 150.000 | 0.960493 | 0.480247 | − | 0.877134i | \(-0.340547\pi\) | ||||
0.480247 | + | 0.877134i | \(0.340547\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 292.000 | 1.69177 | 0.845883 | − | 0.533368i | \(-0.179074\pi\) | ||||
0.845883 | + | 0.533368i | \(0.179074\pi\) | |||||||
\(32\) | −256.000 | −1.41421 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −84.0000 | −0.423702 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −349.000 | −1.55068 | −0.775341 | − | 0.631543i | \(-0.782422\pi\) | ||||
−0.775341 | + | 0.631543i | \(0.782422\pi\) | |||||||
\(38\) | 500.000 | 2.13449 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −497.000 | −1.89313 | −0.946565 | − | 0.322512i | \(-0.895473\pi\) | ||||
−0.946565 | + | 0.322512i | \(0.895473\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −208.000 | −0.737668 | −0.368834 | − | 0.929495i | \(-0.620243\pi\) | ||||
−0.368834 | + | 0.929495i | \(0.620243\pi\) | |||||||
\(44\) | −88.0000 | −0.301511 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −548.000 | −1.75648 | ||||||||
\(47\) | 369.000 | 1.14520 | 0.572598 | − | 0.819837i | \(-0.305936\pi\) | ||||
0.572598 | + | 0.819837i | \(0.305936\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 98.0000 | 0.285714 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −544.000 | −1.45075 | ||||||||
\(53\) | −542.000 | −1.40471 | −0.702353 | − | 0.711829i | \(-0.747867\pi\) | ||||
−0.702353 | + | 0.711829i | \(0.747867\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 600.000 | 1.35834 | ||||||||
\(59\) | −235.000 | −0.518549 | −0.259275 | − | 0.965804i | \(-0.583483\pi\) | ||||
−0.259275 | + | 0.965804i | \(0.583483\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 482.000 | 1.01170 | 0.505851 | − | 0.862621i | \(-0.331179\pi\) | ||||
0.505851 | + | 0.862621i | \(0.331179\pi\) | |||||||
\(62\) | 1168.00 | 2.39252 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −512.000 | −1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −734.000 | −1.33839 | −0.669197 | − | 0.743085i | \(-0.733362\pi\) | ||||
−0.669197 | + | 0.743085i | \(0.733362\pi\) | |||||||
\(68\) | −168.000 | −0.299603 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −587.000 | −0.981184 | −0.490592 | − | 0.871389i | \(-0.663219\pi\) | ||||
−0.490592 | + | 0.871389i | \(0.663219\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −518.000 | −0.830511 | −0.415256 | − | 0.909705i | \(-0.636308\pi\) | ||||
−0.415256 | + | 0.909705i | \(0.636308\pi\) | |||||||
\(74\) | −1396.00 | −2.19300 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1000.00 | 1.50931 | ||||||||
\(77\) | −231.000 | −0.341882 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1045.00 | −1.48825 | −0.744125 | − | 0.668041i | \(-0.767133\pi\) | ||||
−0.744125 | + | 0.668041i | \(0.767133\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1988.00 | −2.67729 | ||||||||
\(83\) | 608.000 | 0.804056 | 0.402028 | − | 0.915627i | \(-0.368305\pi\) | ||||
0.402028 | + | 0.915627i | \(0.368305\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −832.000 | −1.04322 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 770.000 | 0.917077 | 0.458538 | − | 0.888675i | \(-0.348373\pi\) | ||||
0.458538 | + | 0.888675i | \(0.348373\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1428.00 | −1.64500 | ||||||||
\(92\) | −1096.00 | −1.24202 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1476.00 | 1.61955 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1541.00 | 1.61304 | 0.806520 | − | 0.591207i | \(-0.201348\pi\) | ||||
0.806520 | + | 0.591207i | \(0.201348\pi\) | |||||||
\(98\) | 392.000 | 0.404061 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −827.000 | −0.814748 | −0.407374 | − | 0.913261i | \(-0.633555\pi\) | ||||
−0.407374 | + | 0.913261i | \(0.633555\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −248.000 | −0.237244 | −0.118622 | − | 0.992939i | \(-0.537848\pi\) | ||||
−0.118622 | + | 0.992939i | \(0.537848\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2168.00 | −1.98655 | ||||||||
\(107\) | −366.000 | −0.330678 | −0.165339 | − | 0.986237i | \(-0.552872\pi\) | ||||
−0.165339 | + | 0.986237i | \(0.552872\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 270.000 | 0.237260 | 0.118630 | − | 0.992939i | \(-0.462150\pi\) | ||||
0.118630 | + | 0.992939i | \(0.462150\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1344.00 | −1.13389 | ||||||||
\(113\) | −1002.00 | −0.834161 | −0.417081 | − | 0.908869i | \(-0.636947\pi\) | ||||
−0.417081 | + | 0.908869i | \(0.636947\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1200.00 | 0.960493 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −940.000 | −0.733339 | ||||||||
\(119\) | −441.000 | −0.339718 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 1928.00 | 1.43076 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2336.00 | 1.69177 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −469.000 | −0.327693 | −0.163847 | − | 0.986486i | \(-0.552390\pi\) | ||||
−0.163847 | + | 0.986486i | \(0.552390\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 408.000 | 0.272115 | 0.136058 | − | 0.990701i | \(-0.456557\pi\) | ||||
0.136058 | + | 0.990701i | \(0.456557\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2625.00 | 1.71140 | ||||||||
\(134\) | −2936.00 | −1.89277 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2466.00 | −1.53784 | −0.768922 | − | 0.639343i | \(-0.779207\pi\) | ||||
−0.768922 | + | 0.639343i | \(0.779207\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1020.00 | 0.622412 | 0.311206 | − | 0.950342i | \(-0.399267\pi\) | ||||
0.311206 | + | 0.950342i | \(0.399267\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2348.00 | −1.38760 | ||||||||
\(143\) | 748.000 | 0.437419 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2072.00 | −1.17452 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2792.00 | −1.55068 | ||||||||
\(149\) | −5.00000 | −0.00274910 | −0.00137455 | − | 0.999999i | \(-0.500438\pi\) | ||||
−0.00137455 | + | 0.999999i | \(0.500438\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 452.000 | 0.243598 | 0.121799 | − | 0.992555i | \(-0.461134\pi\) | ||||
0.121799 | + | 0.992555i | \(0.461134\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −924.000 | −0.483494 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1766.00 | 0.897721 | 0.448860 | − | 0.893602i | \(-0.351830\pi\) | ||||
0.448860 | + | 0.893602i | \(0.351830\pi\) | |||||||
\(158\) | −4180.00 | −2.10470 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2877.00 | −1.40832 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2068.00 | −0.993732 | −0.496866 | − | 0.867827i | \(-0.665516\pi\) | ||||
−0.496866 | + | 0.867827i | \(0.665516\pi\) | |||||||
\(164\) | −3976.00 | −1.89313 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2432.00 | 1.13711 | ||||||||
\(167\) | −3386.00 | −1.56896 | −0.784481 | − | 0.620153i | \(-0.787070\pi\) | ||||
−0.784481 | + | 0.620153i | \(0.787070\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2427.00 | 1.10469 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1664.00 | −0.737668 | ||||||||
\(173\) | −117.000 | −0.0514182 | −0.0257091 | − | 0.999669i | \(-0.508184\pi\) | ||||
−0.0257091 | + | 0.999669i | \(0.508184\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 704.000 | 0.301511 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3080.00 | 1.29694 | ||||||||
\(179\) | −2995.00 | −1.25060 | −0.625298 | − | 0.780386i | \(-0.715023\pi\) | ||||
−0.625298 | + | 0.780386i | \(0.715023\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4067.00 | 1.67015 | 0.835077 | − | 0.550134i | \(-0.185423\pi\) | ||||
0.835077 | + | 0.550134i | \(0.185423\pi\) | |||||||
\(182\) | −5712.00 | −2.32638 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 231.000 | 0.0903337 | ||||||||
\(188\) | 2952.00 | 1.14520 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3047.00 | −1.15431 | −0.577155 | − | 0.816635i | \(-0.695837\pi\) | ||||
−0.577155 | + | 0.816635i | \(0.695837\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1232.00 | 0.459489 | 0.229744 | − | 0.973251i | \(-0.426211\pi\) | ||||
0.229744 | + | 0.973251i | \(0.426211\pi\) | |||||||
\(194\) | 6164.00 | 2.28118 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 784.000 | 0.285714 | ||||||||
\(197\) | 4979.00 | 1.80071 | 0.900353 | − | 0.435160i | \(-0.143308\pi\) | ||||
0.900353 | + | 0.435160i | \(0.143308\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 600.000 | 0.213733 | 0.106867 | − | 0.994273i | \(-0.465918\pi\) | ||||
0.106867 | + | 0.994273i | \(0.465918\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3308.00 | −1.15223 | ||||||||
\(203\) | 3150.00 | 1.08910 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −992.000 | −0.335514 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4352.00 | 1.45075 | ||||||||
\(209\) | −1375.00 | −0.455075 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2468.00 | −0.805233 | −0.402616 | − | 0.915369i | \(-0.631899\pi\) | ||||
−0.402616 | + | 0.915369i | \(0.631899\pi\) | |||||||
\(212\) | −4336.00 | −1.40471 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1464.00 | −0.467649 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6132.00 | 1.91828 | ||||||||
\(218\) | 1080.00 | 0.335536 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1428.00 | 0.434650 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5392.00 | 1.61917 | 0.809585 | − | 0.587002i | \(-0.199692\pi\) | ||||
0.809585 | + | 0.587002i | \(0.199692\pi\) | |||||||
\(224\) | −5376.00 | −1.60357 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4008.00 | −1.17968 | ||||||||
\(227\) | −2366.00 | −0.691793 | −0.345896 | − | 0.938273i | \(-0.612425\pi\) | ||||
−0.345896 | + | 0.938273i | \(0.612425\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4645.00 | −1.34039 | −0.670197 | − | 0.742183i | \(-0.733790\pi\) | ||||
−0.670197 | + | 0.742183i | \(0.733790\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 513.000 | 0.144239 | 0.0721196 | − | 0.997396i | \(-0.477024\pi\) | ||||
0.0721196 | + | 0.997396i | \(0.477024\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1880.00 | −0.518549 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1764.00 | −0.480433 | ||||||||
\(239\) | −2690.00 | −0.728040 | −0.364020 | − | 0.931391i | \(-0.618596\pi\) | ||||
−0.364020 | + | 0.931391i | \(0.618596\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3728.00 | −0.996438 | −0.498219 | − | 0.867051i | \(-0.666012\pi\) | ||||
−0.498219 | + | 0.867051i | \(0.666012\pi\) | |||||||
\(242\) | 484.000 | 0.128565 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3856.00 | 1.01170 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8500.00 | −2.18964 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2352.00 | −0.591462 | −0.295731 | − | 0.955271i | \(-0.595563\pi\) | ||||
−0.295731 | + | 0.955271i | \(0.595563\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1507.00 | 0.374483 | ||||||||
\(254\) | −1876.00 | −0.463428 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4096.00 | 1.00000 | ||||||||
\(257\) | −3846.00 | −0.933490 | −0.466745 | − | 0.884392i | \(-0.654573\pi\) | ||||
−0.466745 | + | 0.884392i | \(0.654573\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7329.00 | −1.75831 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1632.00 | 0.384829 | ||||||||
\(263\) | −522.000 | −0.122387 | −0.0611937 | − | 0.998126i | \(-0.519491\pi\) | ||||
−0.0611937 | + | 0.998126i | \(0.519491\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 10500.0 | 2.42029 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5872.00 | −1.33839 | ||||||||
\(269\) | −4020.00 | −0.911166 | −0.455583 | − | 0.890193i | \(-0.650569\pi\) | ||||
−0.455583 | + | 0.890193i | \(0.650569\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6687.00 | 1.49892 | 0.749458 | − | 0.662052i | \(-0.230314\pi\) | ||||
0.749458 | + | 0.662052i | \(0.230314\pi\) | |||||||
\(272\) | 1344.00 | 0.299603 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9864.00 | −2.17484 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3746.00 | 0.812546 | 0.406273 | − | 0.913752i | \(-0.366828\pi\) | ||||
0.406273 | + | 0.913752i | \(0.366828\pi\) | |||||||
\(278\) | 4080.00 | 0.880224 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5883.00 | 1.24893 | 0.624467 | − | 0.781051i | \(-0.285316\pi\) | ||||
0.624467 | + | 0.781051i | \(0.285316\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3943.00 | −0.828223 | −0.414111 | − | 0.910226i | \(-0.635908\pi\) | ||||
−0.414111 | + | 0.910226i | \(0.635908\pi\) | |||||||
\(284\) | −4696.00 | −0.981184 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2992.00 | 0.618604 | ||||||||
\(287\) | −10437.0 | −2.14661 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4472.00 | −0.910238 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4144.00 | −0.830511 | ||||||||
\(293\) | −1487.00 | −0.296490 | −0.148245 | − | 0.988951i | \(-0.547362\pi\) | ||||
−0.148245 | + | 0.988951i | \(0.547362\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −20.0000 | −0.00388782 | ||||||||
\(299\) | 9316.00 | 1.80187 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4368.00 | −0.836436 | ||||||||
\(302\) | 1808.00 | 0.344499 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −8000.00 | −1.50931 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4844.00 | −0.900527 | −0.450263 | − | 0.892896i | \(-0.648670\pi\) | ||||
−0.450263 | + | 0.892896i | \(0.648670\pi\) | |||||||
\(308\) | −1848.00 | −0.341882 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4632.00 | −0.844555 | −0.422278 | − | 0.906467i | \(-0.638769\pi\) | ||||
−0.422278 | + | 0.906467i | \(0.638769\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8437.00 | 1.52360 | 0.761801 | − | 0.647811i | \(-0.224315\pi\) | ||||
0.761801 | + | 0.647811i | \(0.224315\pi\) | |||||||
\(314\) | 7064.00 | 1.26957 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8360.00 | −1.48825 | ||||||||
\(317\) | −3636.00 | −0.644221 | −0.322111 | − | 0.946702i | \(-0.604392\pi\) | ||||
−0.322111 | + | 0.946702i | \(0.604392\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1650.00 | −0.289600 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −11508.0 | −1.99166 | ||||||||
\(323\) | −2625.00 | −0.452195 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −8272.00 | −1.40535 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7749.00 | 1.29853 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −758.000 | −0.125871 | −0.0629357 | − | 0.998018i | \(-0.520046\pi\) | ||||
−0.0629357 | + | 0.998018i | \(0.520046\pi\) | |||||||
\(332\) | 4864.00 | 0.804056 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −13544.0 | −2.21885 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7374.00 | −1.19195 | −0.595975 | − | 0.803003i | \(-0.703234\pi\) | ||||
−0.595975 | + | 0.803003i | \(0.703234\pi\) | |||||||
\(338\) | 9708.00 | 1.56227 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3212.00 | −0.510087 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5145.00 | −0.809924 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −468.000 | −0.0727163 | ||||||||
\(347\) | 6524.00 | 1.00930 | 0.504649 | − | 0.863324i | \(-0.331622\pi\) | ||||
0.504649 | + | 0.863324i | \(0.331622\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3710.00 | 0.569031 | 0.284515 | − | 0.958671i | \(-0.408167\pi\) | ||||
0.284515 | + | 0.958671i | \(0.408167\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2816.00 | 0.426401 | ||||||||
\(353\) | −2832.00 | −0.427003 | −0.213502 | − | 0.976943i | \(-0.568487\pi\) | ||||
−0.213502 | + | 0.976943i | \(0.568487\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6160.00 | 0.917077 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −11980.0 | −1.76861 | ||||||||
\(359\) | 7040.00 | 1.03498 | 0.517489 | − | 0.855690i | \(-0.326867\pi\) | ||||
0.517489 | + | 0.855690i | \(0.326867\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8766.00 | 1.27803 | ||||||||
\(362\) | 16268.0 | 2.36195 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −11424.0 | −1.64500 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6206.00 | 0.882699 | 0.441350 | − | 0.897335i | \(-0.354500\pi\) | ||||
0.441350 | + | 0.897335i | \(0.354500\pi\) | |||||||
\(368\) | 8768.00 | 1.24202 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11382.0 | −1.59279 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1962.00 | 0.272355 | 0.136178 | − | 0.990684i | \(-0.456518\pi\) | ||||
0.136178 | + | 0.990684i | \(0.456518\pi\) | |||||||
\(374\) | 924.000 | 0.127751 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10200.0 | −1.39344 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7960.00 | −1.07883 | −0.539417 | − | 0.842039i | \(-0.681355\pi\) | ||||
−0.539417 | + | 0.842039i | \(0.681355\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −12188.0 | −1.63244 | ||||||||
\(383\) | 7188.00 | 0.958981 | 0.479490 | − | 0.877547i | \(-0.340822\pi\) | ||||
0.479490 | + | 0.877547i | \(0.340822\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4928.00 | 0.649815 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 12328.0 | 1.61304 | ||||||||
\(389\) | −7920.00 | −1.03229 | −0.516144 | − | 0.856502i | \(-0.672633\pi\) | ||||
−0.516144 | + | 0.856502i | \(0.672633\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2877.00 | 0.372113 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 19916.0 | 2.54658 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9654.00 | −1.22045 | −0.610227 | − | 0.792226i | \(-0.708922\pi\) | ||||
−0.610227 | + | 0.792226i | \(0.708922\pi\) | |||||||
\(398\) | 2400.00 | 0.302264 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1952.00 | −0.243088 | −0.121544 | − | 0.992586i | \(-0.538785\pi\) | ||||
−0.121544 | + | 0.992586i | \(0.538785\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −19856.0 | −2.45434 | ||||||||
\(404\) | −6616.00 | −0.814748 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 12600.0 | 1.54022 | ||||||||
\(407\) | 3839.00 | 0.467548 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9690.00 | 1.17149 | 0.585745 | − | 0.810495i | \(-0.300802\pi\) | ||||
0.585745 | + | 0.810495i | \(0.300802\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1984.00 | −0.237244 | ||||||||
\(413\) | −4935.00 | −0.587979 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 17408.0 | 2.05168 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −5500.00 | −0.643574 | ||||||||
\(419\) | 2935.00 | 0.342206 | 0.171103 | − | 0.985253i | \(-0.445267\pi\) | ||||
0.171103 | + | 0.985253i | \(0.445267\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12837.0 | 1.48607 | 0.743037 | − | 0.669250i | \(-0.233385\pi\) | ||||
0.743037 | + | 0.669250i | \(0.233385\pi\) | |||||||
\(422\) | −9872.00 | −1.13877 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10122.0 | 1.14716 | ||||||||
\(428\) | −2928.00 | −0.330678 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6108.00 | 0.682626 | 0.341313 | − | 0.939950i | \(-0.389128\pi\) | ||||
0.341313 | + | 0.939950i | \(0.389128\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9278.00 | −1.02973 | −0.514864 | − | 0.857272i | \(-0.672158\pi\) | ||||
−0.514864 | + | 0.857272i | \(0.672158\pi\) | |||||||
\(434\) | 24528.0 | 2.71286 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2160.00 | 0.237260 | ||||||||
\(437\) | −17125.0 | −1.87460 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2455.00 | 0.266904 | 0.133452 | − | 0.991055i | \(-0.457394\pi\) | ||||
0.133452 | + | 0.991055i | \(0.457394\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5712.00 | 0.614688 | ||||||||
\(443\) | 3503.00 | 0.375694 | 0.187847 | − | 0.982198i | \(-0.439849\pi\) | ||||
0.187847 | + | 0.982198i | \(0.439849\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 21568.0 | 2.28985 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −10752.0 | −1.13389 | ||||||||
\(449\) | 7630.00 | 0.801964 | 0.400982 | − | 0.916086i | \(-0.368669\pi\) | ||||
0.400982 | + | 0.916086i | \(0.368669\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5467.00 | 0.570800 | ||||||||
\(452\) | −8016.00 | −0.834161 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −9464.00 | −0.978343 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7414.00 | −0.758889 | −0.379445 | − | 0.925214i | \(-0.623885\pi\) | ||||
−0.379445 | + | 0.925214i | \(0.623885\pi\) | |||||||
\(458\) | −18580.0 | −1.89560 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4982.00 | −0.503329 | −0.251665 | − | 0.967814i | \(-0.580978\pi\) | ||||
−0.251665 | + | 0.967814i | \(0.580978\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13422.0 | 1.34724 | 0.673621 | − | 0.739077i | \(-0.264738\pi\) | ||||
0.673621 | + | 0.739077i | \(0.264738\pi\) | |||||||
\(464\) | −9600.00 | −0.960493 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2052.00 | 0.203985 | ||||||||
\(467\) | 15804.0 | 1.56600 | 0.783000 | − | 0.622022i | \(-0.213689\pi\) | ||||
0.783000 | + | 0.622022i | \(0.213689\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15414.0 | −1.51760 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2288.00 | 0.222415 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3528.00 | −0.339718 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −10760.0 | −1.02960 | ||||||||
\(479\) | 9060.00 | 0.864221 | 0.432111 | − | 0.901821i | \(-0.357769\pi\) | ||||
0.432111 | + | 0.901821i | \(0.357769\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 23732.0 | 2.24966 | ||||||||
\(482\) | −14912.0 | −1.40918 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 968.000 | 0.0909091 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2854.00 | −0.265559 | −0.132779 | − | 0.991146i | \(-0.542390\pi\) | ||||
−0.132779 | + | 0.991146i | \(0.542390\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2278.00 | 0.209378 | 0.104689 | − | 0.994505i | \(-0.466615\pi\) | ||||
0.104689 | + | 0.994505i | \(0.466615\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3150.00 | −0.287766 | ||||||||
\(494\) | −34000.0 | −3.09662 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −18688.0 | −1.69177 | ||||||||
\(497\) | −12327.0 | −1.11256 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13290.0 | 1.19227 | 0.596134 | − | 0.802885i | \(-0.296703\pi\) | ||||
0.596134 | + | 0.802885i | \(0.296703\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −9408.00 | −0.836453 | ||||||||
\(503\) | −10762.0 | −0.953984 | −0.476992 | − | 0.878908i | \(-0.658273\pi\) | ||||
−0.476992 | + | 0.878908i | \(0.658273\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 6028.00 | 0.529599 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3752.00 | −0.327693 | ||||||||
\(509\) | 1570.00 | 0.136717 | 0.0683586 | − | 0.997661i | \(-0.478224\pi\) | ||||
0.0683586 | + | 0.997661i | \(0.478224\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10878.0 | −0.941711 | ||||||||
\(512\) | 16384.0 | 1.41421 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −15384.0 | −1.32015 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4059.00 | −0.345289 | ||||||||
\(518\) | −29316.0 | −2.48662 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22638.0 | 1.90363 | 0.951813 | − | 0.306680i | \(-0.0992182\pi\) | ||||
0.951813 | + | 0.306680i | \(0.0992182\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10273.0 | −0.858904 | −0.429452 | − | 0.903090i | \(-0.641293\pi\) | ||||
−0.429452 | + | 0.903090i | \(0.641293\pi\) | |||||||
\(524\) | 3264.00 | 0.272115 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2088.00 | −0.173082 | ||||||||
\(527\) | −6132.00 | −0.506858 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6602.00 | 0.542615 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 21000.0 | 1.71140 | ||||||||
\(533\) | 33796.0 | 2.74647 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −16080.0 | −1.28858 | ||||||||
\(539\) | −1078.00 | −0.0861461 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6628.00 | −0.526728 | −0.263364 | − | 0.964697i | \(-0.584832\pi\) | ||||
−0.263364 | + | 0.964697i | \(0.584832\pi\) | |||||||
\(542\) | 26748.0 | 2.11979 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5376.00 | 0.423702 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1131.00 | 0.0884060 | 0.0442030 | − | 0.999023i | \(-0.485925\pi\) | ||||
0.0442030 | + | 0.999023i | \(0.485925\pi\) | |||||||
\(548\) | −19728.0 | −1.53784 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 18750.0 | 1.44969 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −21945.0 | −1.68752 | ||||||||
\(554\) | 14984.0 | 1.14911 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8160.00 | 0.622412 | ||||||||
\(557\) | 22954.0 | 1.74613 | 0.873063 | − | 0.487607i | \(-0.162130\pi\) | ||||
0.873063 | + | 0.487607i | \(0.162130\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14144.0 | 1.07017 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 23532.0 | 1.76626 | ||||||||
\(563\) | −5532.00 | −0.414114 | −0.207057 | − | 0.978329i | \(-0.566389\pi\) | ||||
−0.207057 | + | 0.978329i | \(0.566389\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −15772.0 | −1.17128 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25225.0 | 1.85850 | 0.929250 | − | 0.369450i | \(-0.120454\pi\) | ||||
0.929250 | + | 0.369450i | \(0.120454\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2088.00 | −0.153030 | −0.0765150 | − | 0.997068i | \(-0.524379\pi\) | ||||
−0.0765150 | + | 0.997068i | \(0.524379\pi\) | |||||||
\(572\) | 5984.00 | 0.437419 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −41748.0 | −3.03576 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7831.00 | 0.565007 | 0.282503 | − | 0.959266i | \(-0.408835\pi\) | ||||
0.282503 | + | 0.959266i | \(0.408835\pi\) | |||||||
\(578\) | −17888.0 | −1.28727 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12768.0 | 0.911714 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5962.00 | 0.423535 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5948.00 | −0.419300 | ||||||||
\(587\) | 8199.00 | 0.576506 | 0.288253 | − | 0.957554i | \(-0.406926\pi\) | ||||
0.288253 | + | 0.957554i | \(0.406926\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 36500.0 | 2.55341 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 22336.0 | 1.55068 | ||||||||
\(593\) | −9542.00 | −0.660781 | −0.330390 | − | 0.943844i | \(-0.607180\pi\) | ||||
−0.330390 | + | 0.943844i | \(0.607180\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −40.0000 | −0.00274910 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 37264.0 | 2.54822 | ||||||||
\(599\) | −24705.0 | −1.68517 | −0.842587 | − | 0.538561i | \(-0.818968\pi\) | ||||
−0.842587 | + | 0.538561i | \(0.818968\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15452.0 | 1.04875 | 0.524376 | − | 0.851487i | \(-0.324299\pi\) | ||||
0.524376 | + | 0.851487i | \(0.324299\pi\) | |||||||
\(602\) | −17472.0 | −1.18290 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3616.00 | 0.243598 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6176.00 | 0.412975 | 0.206488 | − | 0.978449i | \(-0.433797\pi\) | ||||
0.206488 | + | 0.978449i | \(0.433797\pi\) | |||||||
\(608\) | −32000.0 | −2.13449 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −25092.0 | −1.66140 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13198.0 | −0.869596 | −0.434798 | − | 0.900528i | \(-0.643180\pi\) | ||||
−0.434798 | + | 0.900528i | \(0.643180\pi\) | |||||||
\(614\) | −19376.0 | −1.27354 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19216.0 | −1.25382 | −0.626910 | − | 0.779092i | \(-0.715681\pi\) | ||||
−0.626910 | + | 0.779092i | \(0.715681\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 27700.0 | 1.79864 | 0.899319 | − | 0.437293i | \(-0.144063\pi\) | ||||
0.899319 | + | 0.437293i | \(0.144063\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −18528.0 | −1.19438 | ||||||||
\(623\) | 16170.0 | 1.03987 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 33748.0 | 2.15470 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 14128.0 | 0.897721 | ||||||||
\(629\) | 7329.00 | 0.464589 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5108.00 | −0.322260 | −0.161130 | − | 0.986933i | \(-0.551514\pi\) | ||||
−0.161130 | + | 0.986933i | \(0.551514\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −14544.0 | −0.911066 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6664.00 | −0.414501 | ||||||||
\(638\) | −6600.00 | −0.409556 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −322.000 | −0.0198412 | −0.00992062 | − | 0.999951i | \(-0.503158\pi\) | ||||
−0.00992062 | + | 0.999951i | \(0.503158\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7432.00 | 0.455816 | 0.227908 | − | 0.973683i | \(-0.426812\pi\) | ||||
0.227908 | + | 0.973683i | \(0.426812\pi\) | |||||||
\(644\) | −23016.0 | −1.40832 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −10500.0 | −0.639500 | ||||||||
\(647\) | 1409.00 | 0.0856159 | 0.0428080 | − | 0.999083i | \(-0.486370\pi\) | ||||
0.0428080 | + | 0.999083i | \(0.486370\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2585.00 | 0.156348 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −16544.0 | −0.993732 | ||||||||
\(653\) | 21548.0 | 1.29133 | 0.645665 | − | 0.763621i | \(-0.276580\pi\) | ||||
0.645665 | + | 0.763621i | \(0.276580\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 31808.0 | 1.89313 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 30996.0 | 1.83640 | ||||||||
\(659\) | 13380.0 | 0.790912 | 0.395456 | − | 0.918485i | \(-0.370587\pi\) | ||||
0.395456 | + | 0.918485i | \(0.370587\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10907.0 | 0.641805 | 0.320903 | − | 0.947112i | \(-0.396014\pi\) | ||||
0.320903 | + | 0.947112i | \(0.396014\pi\) | |||||||
\(662\) | −3032.00 | −0.178009 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −20550.0 | −1.19295 | ||||||||
\(668\) | −27088.0 | −1.56896 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5302.00 | −0.305039 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17522.0 | 1.00360 | 0.501800 | − | 0.864983i | \(-0.332671\pi\) | ||||
0.501800 | + | 0.864983i | \(0.332671\pi\) | |||||||
\(674\) | −29496.0 | −1.68567 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 19416.0 | 1.10469 | ||||||||
\(677\) | −8306.00 | −0.471530 | −0.235765 | − | 0.971810i | \(-0.575759\pi\) | ||||
−0.235765 | + | 0.971810i | \(0.575759\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 32361.0 | 1.82902 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −12848.0 | −0.721371 | ||||||||
\(683\) | −18427.0 | −1.03234 | −0.516171 | − | 0.856486i | \(-0.672643\pi\) | ||||
−0.516171 | + | 0.856486i | \(0.672643\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −20580.0 | −1.14541 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 13312.0 | 0.737668 | ||||||||
\(689\) | 36856.0 | 2.03788 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8278.00 | −0.455731 | −0.227865 | − | 0.973693i | \(-0.573175\pi\) | ||||
−0.227865 | + | 0.973693i | \(0.573175\pi\) | |||||||
\(692\) | −936.000 | −0.0514182 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 26096.0 | 1.42736 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10437.0 | 0.567187 | ||||||||
\(698\) | 14840.0 | 0.804731 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21923.0 | 1.18120 | 0.590599 | − | 0.806965i | \(-0.298891\pi\) | ||||
0.590599 | + | 0.806965i | \(0.298891\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −43625.0 | −2.34047 | ||||||||
\(704\) | 5632.00 | 0.301511 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −11328.0 | −0.603874 | ||||||||
\(707\) | −17367.0 | −0.923838 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11425.0 | −0.605183 | −0.302592 | − | 0.953120i | \(-0.597852\pi\) | ||||
−0.302592 | + | 0.953120i | \(0.597852\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −40004.0 | −2.10121 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −23960.0 | −1.25060 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 28160.0 | 1.46368 | ||||||||
\(719\) | −7380.00 | −0.382792 | −0.191396 | − | 0.981513i | \(-0.561301\pi\) | ||||
−0.191396 | + | 0.981513i | \(0.561301\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5208.00 | −0.269010 | ||||||||
\(722\) | 35064.0 | 1.80741 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 32536.0 | 1.67015 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10924.0 | −0.557288 | −0.278644 | − | 0.960394i | \(-0.589885\pi\) | ||||
−0.278644 | + | 0.960394i | \(0.589885\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4368.00 | 0.221007 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13578.0 | −0.684195 | −0.342097 | − | 0.939664i | \(-0.611137\pi\) | ||||
−0.342097 | + | 0.939664i | \(0.611137\pi\) | |||||||
\(734\) | 24824.0 | 1.24833 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 35072.0 | 1.75648 | ||||||||
\(737\) | 8074.00 | 0.403541 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2875.00 | 0.143110 | 0.0715552 | − | 0.997437i | \(-0.477204\pi\) | ||||
0.0715552 | + | 0.997437i | \(0.477204\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −45528.0 | −2.25254 | ||||||||
\(743\) | 9568.00 | 0.472431 | 0.236215 | − | 0.971701i | \(-0.424093\pi\) | ||||
0.236215 | + | 0.971701i | \(0.424093\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 7848.00 | 0.385168 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1848.00 | 0.0903337 | ||||||||
\(749\) | −7686.00 | −0.374954 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −35048.0 | −1.70296 | −0.851478 | − | 0.524391i | \(-0.824293\pi\) | ||||
−0.851478 | + | 0.524391i | \(0.824293\pi\) | |||||||
\(752\) | −23616.0 | −1.14520 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −40800.0 | −1.97062 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8226.00 | 0.394953 | 0.197476 | − | 0.980308i | \(-0.436725\pi\) | ||||
0.197476 | + | 0.980308i | \(0.436725\pi\) | |||||||
\(758\) | −31840.0 | −1.52570 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6818.00 | 0.324773 | 0.162387 | − | 0.986727i | \(-0.448081\pi\) | ||||
0.162387 | + | 0.986727i | \(0.448081\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5670.00 | 0.269027 | ||||||||
\(764\) | −24376.0 | −1.15431 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 28752.0 | 1.35620 | ||||||||
\(767\) | 15980.0 | 0.752287 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29390.0 | 1.37819 | 0.689097 | − | 0.724670i | \(-0.258008\pi\) | ||||
0.689097 | + | 0.724670i | \(0.258008\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 9856.00 | 0.459489 | ||||||||
\(773\) | 34358.0 | 1.59867 | 0.799335 | − | 0.600886i | \(-0.205185\pi\) | ||||
0.799335 | + | 0.600886i | \(0.205185\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −31680.0 | −1.45988 | ||||||||
\(779\) | −62125.0 | −2.85733 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6457.00 | 0.295838 | ||||||||
\(782\) | 11508.0 | 0.526247 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6272.00 | −0.285714 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14291.0 | 0.647292 | 0.323646 | − | 0.946178i | \(-0.395091\pi\) | ||||
0.323646 | + | 0.946178i | \(0.395091\pi\) | |||||||
\(788\) | 39832.0 | 1.80071 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −21042.0 | −0.945850 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −32776.0 | −1.46773 | ||||||||
\(794\) | −38616.0 | −1.72598 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4800.00 | 0.213733 | ||||||||
\(797\) | −11576.0 | −0.514483 | −0.257242 | − | 0.966347i | \(-0.582814\pi\) | ||||
−0.257242 | + | 0.966347i | \(0.582814\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7749.00 | −0.343104 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −7808.00 | −0.343778 | ||||||||
\(803\) | 5698.00 | 0.250409 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −79424.0 | −3.47096 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12825.0 | 0.557358 | 0.278679 | − | 0.960384i | \(-0.410103\pi\) | ||||
0.278679 | + | 0.960384i | \(0.410103\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36843.0 | −1.59523 | −0.797616 | − | 0.603166i | \(-0.793906\pi\) | ||||
−0.797616 | + | 0.603166i | \(0.793906\pi\) | |||||||
\(812\) | 25200.0 | 1.08910 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 15356.0 | 0.661213 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −26000.0 | −1.11337 | ||||||||
\(818\) | 38760.0 | 1.65674 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −43962.0 | −1.86880 | −0.934400 | − | 0.356226i | \(-0.884063\pi\) | ||||
−0.934400 | + | 0.356226i | \(0.884063\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 33522.0 | 1.41981 | 0.709905 | − | 0.704298i | \(-0.248738\pi\) | ||||
0.709905 | + | 0.704298i | \(0.248738\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −19740.0 | −0.831528 | ||||||||
\(827\) | 1704.00 | 0.0716492 | 0.0358246 | − | 0.999358i | \(-0.488594\pi\) | ||||
0.0358246 | + | 0.999358i | \(0.488594\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1750.00 | 0.0733173 | 0.0366586 | − | 0.999328i | \(-0.488329\pi\) | ||||
0.0366586 | + | 0.999328i | \(0.488329\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 34816.0 | 1.45075 | ||||||||
\(833\) | −2058.00 | −0.0856008 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −11000.0 | −0.455075 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 11740.0 | 0.483952 | ||||||||
\(839\) | 15260.0 | 0.627931 | 0.313965 | − | 0.949434i | \(-0.398342\pi\) | ||||
0.313965 | + | 0.949434i | \(0.398342\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1889.00 | −0.0774530 | ||||||||
\(842\) | 51348.0 | 2.10163 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −19744.0 | −0.805233 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2541.00 | 0.103081 | ||||||||
\(848\) | 34688.0 | 1.40471 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 47813.0 | 1.92598 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −878.000 | −0.0352428 | −0.0176214 | − | 0.999845i | \(-0.505609\pi\) | ||||
−0.0176214 | + | 0.999845i | \(0.505609\pi\) | |||||||
\(854\) | 40488.0 | 1.62233 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 35019.0 | 1.39583 | 0.697915 | − | 0.716181i | \(-0.254111\pi\) | ||||
0.697915 | + | 0.716181i | \(0.254111\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1280.00 | −0.0508417 | −0.0254209 | − | 0.999677i | \(-0.508093\pi\) | ||||
−0.0254209 | + | 0.999677i | \(0.508093\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 24432.0 | 0.965380 | ||||||||
\(863\) | 16888.0 | 0.666135 | 0.333067 | − | 0.942903i | \(-0.391916\pi\) | ||||
0.333067 | + | 0.942903i | \(0.391916\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −37112.0 | −1.45626 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 49056.0 | 1.91828 | ||||||||
\(869\) | 11495.0 | 0.448724 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 49912.0 | 1.94168 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −68500.0 | −2.65108 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 29836.0 | 1.14879 | 0.574396 | − | 0.818578i | \(-0.305237\pi\) | ||||
0.574396 | + | 0.818578i | \(0.305237\pi\) | |||||||
\(878\) | 9820.00 | 0.377459 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29292.0 | −1.12017 | −0.560087 | − | 0.828434i | \(-0.689232\pi\) | ||||
−0.560087 | + | 0.828434i | \(0.689232\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6532.00 | 0.248946 | 0.124473 | − | 0.992223i | \(-0.460276\pi\) | ||||
0.124473 | + | 0.992223i | \(0.460276\pi\) | |||||||
\(884\) | 11424.0 | 0.434650 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 14012.0 | 0.531312 | ||||||||
\(887\) | −20476.0 | −0.775103 | −0.387552 | − | 0.921848i | \(-0.626679\pi\) | ||||
−0.387552 | + | 0.921848i | \(0.626679\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9849.00 | −0.371569 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 43136.0 | 1.61917 | ||||||||
\(893\) | 46125.0 | 1.72846 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 30520.0 | 1.13415 | ||||||||
\(899\) | 43800.0 | 1.62493 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11382.0 | 0.420854 | ||||||||
\(902\) | 21868.0 | 0.807234 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −51914.0 | −1.90052 | −0.950262 | − | 0.311450i | \(-0.899185\pi\) | ||||
−0.950262 | + | 0.311450i | \(0.899185\pi\) | |||||||
\(908\) | −18928.0 | −0.691793 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 41893.0 | 1.52358 | 0.761788 | − | 0.647827i | \(-0.224322\pi\) | ||||
0.761788 | + | 0.647827i | \(0.224322\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6688.00 | −0.242432 | ||||||||
\(914\) | −29656.0 | −1.07323 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −37160.0 | −1.34039 | ||||||||
\(917\) | 8568.00 | 0.308550 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 495.000 | 0.0177677 | 0.00888386 | − | 0.999961i | \(-0.497172\pi\) | ||||
0.00888386 | + | 0.999961i | \(0.497172\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −19928.0 | −0.711815 | ||||||||
\(923\) | 39916.0 | 1.42346 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 53688.0 | 1.90529 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −38400.0 | −1.35834 | ||||||||
\(929\) | 16310.0 | 0.576010 | 0.288005 | − | 0.957629i | \(-0.407008\pi\) | ||||
0.288005 | + | 0.957629i | \(0.407008\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12250.0 | 0.431233 | ||||||||
\(932\) | 4104.00 | 0.144239 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 63216.0 | 2.21466 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18744.0 | −0.653511 | −0.326755 | − | 0.945109i | \(-0.605955\pi\) | ||||
−0.326755 | + | 0.945109i | \(0.605955\pi\) | |||||||
\(938\) | −61656.0 | −2.14620 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25553.0 | 0.885233 | 0.442616 | − | 0.896711i | \(-0.354050\pi\) | ||||
0.442616 | + | 0.896711i | \(0.354050\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 68089.0 | 2.35131 | ||||||||
\(944\) | 15040.0 | 0.518549 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9152.00 | 0.314542 | ||||||||
\(947\) | 6879.00 | 0.236048 | 0.118024 | − | 0.993011i | \(-0.462344\pi\) | ||||
0.118024 | + | 0.993011i | \(0.462344\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 35224.0 | 1.20487 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −13677.0 | −0.464891 | −0.232446 | − | 0.972609i | \(-0.574673\pi\) | ||||
−0.232446 | + | 0.972609i | \(0.574673\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −21520.0 | −0.728040 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 36240.0 | 1.22219 | ||||||||
\(959\) | −51786.0 | −1.74375 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 55473.0 | 1.86207 | ||||||||
\(962\) | 94928.0 | 3.18150 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −29824.0 | −0.996438 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26984.0 | −0.897360 | −0.448680 | − | 0.893693i | \(-0.648106\pi\) | ||||
−0.448680 | + | 0.893693i | \(0.648106\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −41937.0 | −1.38602 | −0.693008 | − | 0.720929i | \(-0.743715\pi\) | ||||
−0.693008 | + | 0.720929i | \(0.743715\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21420.0 | 0.705749 | ||||||||
\(974\) | −11416.0 | −0.375557 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −30848.0 | −1.01170 | ||||||||
\(977\) | 13504.0 | 0.442202 | 0.221101 | − | 0.975251i | \(-0.429035\pi\) | ||||
0.221101 | + | 0.975251i | \(0.429035\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8470.00 | −0.276509 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 9112.00 | 0.296106 | ||||||||
\(983\) | 33353.0 | 1.08219 | 0.541096 | − | 0.840961i | \(-0.318009\pi\) | ||||
0.541096 | + | 0.840961i | \(0.318009\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −12600.0 | −0.406963 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −68000.0 | −2.18964 | ||||||||
\(989\) | 28496.0 | 0.916198 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16978.0 | −0.544222 | −0.272111 | − | 0.962266i | \(-0.587722\pi\) | ||||
−0.272111 | + | 0.962266i | \(0.587722\pi\) | |||||||
\(992\) | −74752.0 | −2.39252 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −49308.0 | −1.57340 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2714.00 | −0.0862119 | −0.0431059 | − | 0.999071i | \(-0.513725\pi\) | ||||
−0.0431059 | + | 0.999071i | \(0.513725\pi\) | |||||||
\(998\) | 53160.0 | 1.68612 | ||||||||
\(999\) | 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 | 2475.4.a.j.1.1 | 1 | ||
3.2 | odd | 2 | 825.4.a.b.1.1 | ✓ | 1 | ||
5.4 | even | 2 | 2475.4.a.c.1.1 | 1 | |||
15.2 | even | 4 | 825.4.c.c.199.1 | 2 | |||
15.8 | even | 4 | 825.4.c.c.199.2 | 2 | |||
15.14 | odd | 2 | 825.4.a.h.1.1 | yes | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.4.a.b.1.1 | ✓ | 1 | 3.2 | odd | 2 | ||
825.4.a.h.1.1 | yes | 1 | 15.14 | odd | 2 | ||
825.4.c.c.199.1 | 2 | 15.2 | even | 4 | |||
825.4.c.c.199.2 | 2 | 15.8 | even | 4 | |||
2475.4.a.c.1.1 | 1 | 5.4 | even | 2 | |||
2475.4.a.j.1.1 | 1 | 1.1 | even | 1 | trivial |