Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [675,4,Mod(1,675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(675, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("675.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 675 = 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 675.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: | \(39.8262892539\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.183945.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 12x^{2} + 3x + 18 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2^{3}\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-2.82516\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 675.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.52654 | 1.60037 | 0.800187 | − | 0.599750i | \(-0.204733\pi\) | ||||
0.800187 | + | 0.599750i | \(0.204733\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 12.4896 | 1.56120 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 30.8119 | 1.66368 | 0.831842 | − | 0.555013i | \(-0.187287\pi\) | ||||
0.831842 | + | 0.555013i | \(0.187287\pi\) | |||||||
\(8\) | 20.3223 | 0.898126 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.79573 | −0.186272 | −0.0931359 | − | 0.995653i | \(-0.529689\pi\) | ||||
−0.0931359 | + | 0.995653i | \(0.529689\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 31.2493 | 0.666692 | 0.333346 | − | 0.942805i | \(-0.391822\pi\) | ||||
0.333346 | + | 0.942805i | \(0.391822\pi\) | |||||||
\(14\) | 139.471 | 2.66252 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −7.92702 | −0.123860 | ||||||||
\(17\) | 112.418 | 1.60385 | 0.801923 | − | 0.597427i | \(-0.203810\pi\) | ||||
0.801923 | + | 0.597427i | \(0.203810\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −60.9161 | −0.735533 | −0.367766 | − | 0.929918i | \(-0.619877\pi\) | ||||
−0.367766 | + | 0.929918i | \(0.619877\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −30.7612 | −0.298105 | ||||||||
\(23\) | −31.1821 | −0.282692 | −0.141346 | − | 0.989960i | \(-0.545143\pi\) | ||||
−0.141346 | + | 0.989960i | \(0.545143\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 141.451 | 1.06696 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 384.827 | 2.59734 | ||||||||
\(29\) | 189.228 | 1.21168 | 0.605839 | − | 0.795587i | \(-0.292837\pi\) | ||||
0.605839 | + | 0.795587i | \(0.292837\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −343.933 | −1.99265 | −0.996327 | − | 0.0856357i | \(-0.972708\pi\) | ||||
−0.996327 | + | 0.0856357i | \(0.972708\pi\) | |||||||
\(32\) | −198.460 | −1.09635 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 508.865 | 2.56675 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 206.503 | 0.917538 | 0.458769 | − | 0.888556i | \(-0.348291\pi\) | ||||
0.458769 | + | 0.888556i | \(0.348291\pi\) | |||||||
\(38\) | −275.739 | −1.17713 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 435.018 | 1.65704 | 0.828518 | − | 0.559963i | \(-0.189184\pi\) | ||||
0.828518 | + | 0.559963i | \(0.189184\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 60.9569 | 0.216183 | 0.108091 | − | 0.994141i | \(-0.465526\pi\) | ||||
0.108091 | + | 0.994141i | \(0.465526\pi\) | |||||||
\(44\) | −84.8758 | −0.290807 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −141.147 | −0.452412 | ||||||||
\(47\) | 251.239 | 0.779721 | 0.389861 | − | 0.920874i | \(-0.372523\pi\) | ||||
0.389861 | + | 0.920874i | \(0.372523\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 606.370 | 1.76784 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 390.291 | 1.04084 | ||||||||
\(53\) | 248.620 | 0.644350 | 0.322175 | − | 0.946680i | \(-0.395586\pi\) | ||||
0.322175 | + | 0.946680i | \(0.395586\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 626.167 | 1.49420 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 856.547 | 1.93914 | ||||||||
\(59\) | −571.583 | −1.26125 | −0.630626 | − | 0.776087i | \(-0.717202\pi\) | ||||
−0.630626 | + | 0.776087i | \(0.717202\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −329.038 | −0.690639 | −0.345319 | − | 0.938485i | \(-0.612229\pi\) | ||||
−0.345319 | + | 0.938485i | \(0.612229\pi\) | |||||||
\(62\) | −1556.83 | −3.18899 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −834.922 | −1.63071 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −677.273 | −1.23496 | −0.617478 | − | 0.786588i | \(-0.711845\pi\) | ||||
−0.617478 | + | 0.786588i | \(0.711845\pi\) | |||||||
\(68\) | 1404.05 | 2.50392 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −453.668 | −0.758317 | −0.379159 | − | 0.925332i | \(-0.623787\pi\) | ||||
−0.379159 | + | 0.925332i | \(0.623787\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1024.66 | 1.64283 | 0.821417 | − | 0.570328i | \(-0.193184\pi\) | ||||
0.821417 | + | 0.570328i | \(0.193184\pi\) | |||||||
\(74\) | 934.745 | 1.46840 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −760.817 | −1.14831 | ||||||||
\(77\) | −209.389 | −0.309897 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 238.142 | 0.339153 | 0.169576 | − | 0.985517i | \(-0.445760\pi\) | ||||
0.169576 | + | 0.985517i | \(0.445760\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1969.13 | 2.65188 | ||||||||
\(83\) | 826.853 | 1.09348 | 0.546740 | − | 0.837302i | \(-0.315869\pi\) | ||||
0.546740 | + | 0.837302i | \(0.315869\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 275.924 | 0.345973 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −138.105 | −0.167296 | ||||||||
\(89\) | −1140.55 | −1.35840 | −0.679201 | − | 0.733953i | \(-0.737673\pi\) | ||||
−0.679201 | + | 0.733953i | \(0.737673\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 962.849 | 1.10916 | ||||||||
\(92\) | −389.451 | −0.441337 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1137.24 | 1.24785 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1308.77 | −1.36995 | −0.684977 | − | 0.728565i | \(-0.740188\pi\) | ||||
−0.684977 | + | 0.728565i | \(0.740188\pi\) | |||||||
\(98\) | 2744.76 | 2.82921 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1448.64 | 1.42718 | 0.713589 | − | 0.700565i | \(-0.247069\pi\) | ||||
0.713589 | + | 0.700565i | \(0.247069\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1355.83 | −1.29703 | −0.648513 | − | 0.761204i | \(-0.724609\pi\) | ||||
−0.648513 | + | 0.761204i | \(0.724609\pi\) | |||||||
\(104\) | 635.057 | 0.598773 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1125.39 | 1.03120 | ||||||||
\(107\) | −390.807 | −0.353091 | −0.176545 | − | 0.984292i | \(-0.556492\pi\) | ||||
−0.176545 | + | 0.984292i | \(0.556492\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 770.512 | 0.677080 | 0.338540 | − | 0.940952i | \(-0.390067\pi\) | ||||
0.338540 | + | 0.940952i | \(0.390067\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −244.246 | −0.206063 | ||||||||
\(113\) | −1625.10 | −1.35289 | −0.676446 | − | 0.736493i | \(-0.736481\pi\) | ||||
−0.676446 | + | 0.736493i | \(0.736481\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2363.37 | 1.89167 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2587.30 | −2.01847 | ||||||||
\(119\) | 3463.81 | 2.66829 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1284.82 | −0.965303 | ||||||||
\(122\) | −1489.40 | −1.10528 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4295.58 | −3.11093 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1615.40 | −1.12869 | −0.564346 | − | 0.825538i | \(-0.690872\pi\) | ||||
−0.564346 | + | 0.825538i | \(0.690872\pi\) | |||||||
\(128\) | −2191.63 | −1.51339 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 51.2371 | 0.0341726 | 0.0170863 | − | 0.999854i | \(-0.494561\pi\) | ||||
0.0170863 | + | 0.999854i | \(0.494561\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1876.94 | −1.22369 | ||||||||
\(134\) | −3065.70 | −1.97639 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2284.59 | 1.44046 | ||||||||
\(137\) | 1601.46 | 0.998703 | 0.499351 | − | 0.866400i | \(-0.333572\pi\) | ||||
0.499351 | + | 0.866400i | \(0.333572\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −436.476 | −0.266341 | −0.133170 | − | 0.991093i | \(-0.542516\pi\) | ||||
−0.133170 | + | 0.991093i | \(0.542516\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2053.55 | −1.21359 | ||||||||
\(143\) | −212.362 | −0.124186 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4638.15 | 2.62915 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2579.14 | 1.43246 | ||||||||
\(149\) | 1447.05 | 0.795615 | 0.397807 | − | 0.917469i | \(-0.369771\pi\) | ||||
0.397807 | + | 0.917469i | \(0.369771\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −748.431 | −0.403354 | −0.201677 | − | 0.979452i | \(-0.564639\pi\) | ||||
−0.201677 | + | 0.979452i | \(0.564639\pi\) | |||||||
\(152\) | −1237.95 | −0.660601 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −947.809 | −0.495952 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 987.755 | 0.502111 | 0.251056 | − | 0.967973i | \(-0.419222\pi\) | ||||
0.251056 | + | 0.967973i | \(0.419222\pi\) | |||||||
\(158\) | 1077.96 | 0.542771 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −960.777 | −0.470309 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2947.21 | −1.41621 | −0.708107 | − | 0.706105i | \(-0.750451\pi\) | ||||
−0.708107 | + | 0.706105i | \(0.750451\pi\) | |||||||
\(164\) | 5433.20 | 2.58696 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3742.78 | 1.74998 | ||||||||
\(167\) | −445.456 | −0.206410 | −0.103205 | − | 0.994660i | \(-0.532910\pi\) | ||||
−0.103205 | + | 0.994660i | \(0.532910\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1220.48 | −0.555522 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 761.327 | 0.337504 | ||||||||
\(173\) | −4548.52 | −1.99895 | −0.999473 | − | 0.0324524i | \(-0.989668\pi\) | ||||
−0.999473 | + | 0.0324524i | \(0.989668\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 53.8699 | 0.0230716 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5162.73 | −2.17395 | ||||||||
\(179\) | 1866.03 | 0.779181 | 0.389591 | − | 0.920988i | \(-0.372616\pi\) | ||||
0.389591 | + | 0.920988i | \(0.372616\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −273.461 | −0.112300 | −0.0561498 | − | 0.998422i | \(-0.517882\pi\) | ||||
−0.0561498 | + | 0.998422i | \(0.517882\pi\) | |||||||
\(182\) | 4358.38 | 1.77508 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −633.690 | −0.253893 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −763.963 | −0.298751 | ||||||||
\(188\) | 3137.86 | 1.21730 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1935.50 | −0.733235 | −0.366618 | − | 0.930372i | \(-0.619484\pi\) | ||||
−0.366618 | + | 0.930372i | \(0.619484\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1428.51 | −0.532779 | −0.266389 | − | 0.963866i | \(-0.585831\pi\) | ||||
−0.266389 | + | 0.963866i | \(0.585831\pi\) | |||||||
\(194\) | −5924.21 | −2.19244 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7573.31 | 2.75995 | ||||||||
\(197\) | −2779.85 | −1.00536 | −0.502680 | − | 0.864473i | \(-0.667653\pi\) | ||||
−0.502680 | + | 0.864473i | \(0.667653\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2155.10 | 0.767695 | 0.383847 | − | 0.923397i | \(-0.374599\pi\) | ||||
0.383847 | + | 0.923397i | \(0.374599\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6557.32 | 2.28402 | ||||||||
\(203\) | 5830.45 | 2.01585 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −6137.21 | −2.07573 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −247.714 | −0.0825763 | ||||||||
\(209\) | 413.970 | 0.137009 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4577.31 | −1.49344 | −0.746718 | − | 0.665140i | \(-0.768372\pi\) | ||||
−0.746718 | + | 0.665140i | \(0.768372\pi\) | |||||||
\(212\) | 3105.16 | 1.00596 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1769.00 | −0.565078 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10597.2 | −3.31514 | ||||||||
\(218\) | 3487.76 | 1.08358 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3512.99 | 1.06927 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 892.931 | 0.268140 | 0.134070 | − | 0.990972i | \(-0.457195\pi\) | ||||
0.134070 | + | 0.990972i | \(0.457195\pi\) | |||||||
\(224\) | −6114.93 | −1.82398 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7356.09 | −2.16513 | ||||||||
\(227\) | 1036.61 | 0.303093 | 0.151546 | − | 0.988450i | \(-0.451575\pi\) | ||||
0.151546 | + | 0.988450i | \(0.451575\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1450.92 | 0.418688 | 0.209344 | − | 0.977842i | \(-0.432867\pi\) | ||||
0.209344 | + | 0.977842i | \(0.432867\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3845.53 | 1.08824 | ||||||||
\(233\) | −974.736 | −0.274065 | −0.137032 | − | 0.990567i | \(-0.543756\pi\) | ||||
−0.137032 | + | 0.990567i | \(0.543756\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −7138.84 | −1.96906 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 15679.1 | 4.27027 | ||||||||
\(239\) | 3761.95 | 1.01816 | 0.509080 | − | 0.860719i | \(-0.329986\pi\) | ||||
0.509080 | + | 0.860719i | \(0.329986\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −356.827 | −0.0953744 | −0.0476872 | − | 0.998862i | \(-0.515185\pi\) | ||||
−0.0476872 | + | 0.998862i | \(0.515185\pi\) | |||||||
\(242\) | −5815.78 | −1.54485 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4109.54 | −1.07822 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1903.59 | −0.490374 | ||||||||
\(248\) | −6989.51 | −1.78965 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3161.78 | −0.795098 | −0.397549 | − | 0.917581i | \(-0.630139\pi\) | ||||
−0.397549 | + | 0.917581i | \(0.630139\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 211.905 | 0.0526575 | ||||||||
\(254\) | −7312.19 | −1.80633 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3241.12 | −0.791289 | ||||||||
\(257\) | −1683.47 | −0.408607 | −0.204304 | − | 0.978908i | \(-0.565493\pi\) | ||||
−0.204304 | + | 0.978908i | \(0.565493\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6362.74 | 1.52649 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 231.927 | 0.0546889 | ||||||||
\(263\) | −5030.48 | −1.17944 | −0.589720 | − | 0.807608i | \(-0.700762\pi\) | ||||
−0.589720 | + | 0.807608i | \(0.700762\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −8496.04 | −1.95837 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −8458.85 | −1.92801 | ||||||||
\(269\) | −6050.81 | −1.37147 | −0.685733 | − | 0.727853i | \(-0.740518\pi\) | ||||
−0.685733 | + | 0.727853i | \(0.740518\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2836.60 | −0.635834 | −0.317917 | − | 0.948119i | \(-0.602983\pi\) | ||||
−0.317917 | + | 0.948119i | \(0.602983\pi\) | |||||||
\(272\) | −891.140 | −0.198652 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7249.09 | 1.59830 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1917.59 | 0.415946 | 0.207973 | − | 0.978135i | \(-0.433313\pi\) | ||||
0.207973 | + | 0.978135i | \(0.433313\pi\) | |||||||
\(278\) | −1975.73 | −0.426245 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4694.31 | 0.996580 | 0.498290 | − | 0.867011i | \(-0.333962\pi\) | ||||
0.498290 | + | 0.867011i | \(0.333962\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7108.90 | 1.49322 | 0.746608 | − | 0.665265i | \(-0.231681\pi\) | ||||
0.746608 | + | 0.665265i | \(0.231681\pi\) | |||||||
\(284\) | −5666.13 | −1.18388 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −961.265 | −0.198744 | ||||||||
\(287\) | 13403.7 | 2.75678 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7724.82 | 1.57232 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 12797.5 | 2.56479 | ||||||||
\(293\) | −2401.20 | −0.478770 | −0.239385 | − | 0.970925i | \(-0.576946\pi\) | ||||
−0.239385 | + | 0.970925i | \(0.576946\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4196.61 | 0.824064 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6550.11 | 1.27328 | ||||||||
\(299\) | −974.417 | −0.188468 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1878.20 | 0.359659 | ||||||||
\(302\) | −3387.80 | −0.645517 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 482.883 | 0.0911029 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1623.62 | 0.301840 | 0.150920 | − | 0.988546i | \(-0.451776\pi\) | ||||
0.150920 | + | 0.988546i | \(0.451776\pi\) | |||||||
\(308\) | −2615.18 | −0.483811 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2062.80 | −0.376111 | −0.188056 | − | 0.982158i | \(-0.560219\pi\) | ||||
−0.188056 | + | 0.982158i | \(0.560219\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −207.093 | −0.0373980 | −0.0186990 | − | 0.999825i | \(-0.505952\pi\) | ||||
−0.0186990 | + | 0.999825i | \(0.505952\pi\) | |||||||
\(314\) | 4471.12 | 0.803566 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2974.29 | 0.529484 | ||||||||
\(317\) | 699.087 | 0.123863 | 0.0619316 | − | 0.998080i | \(-0.480274\pi\) | ||||
0.0619316 | + | 0.998080i | \(0.480274\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1285.94 | −0.225702 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4349.00 | −0.752671 | ||||||||
\(323\) | −6848.07 | −1.17968 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −13340.6 | −2.26647 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8840.56 | 1.48823 | ||||||||
\(329\) | 7741.12 | 1.29721 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2662.58 | 0.442140 | 0.221070 | − | 0.975258i | \(-0.429045\pi\) | ||||
0.221070 | + | 0.975258i | \(0.429045\pi\) | |||||||
\(332\) | 10327.0 | 1.70714 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2016.38 | −0.330333 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2552.84 | 0.412647 | 0.206323 | − | 0.978484i | \(-0.433850\pi\) | ||||
0.206323 | + | 0.978484i | \(0.433850\pi\) | |||||||
\(338\) | −5524.56 | −0.889043 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2337.28 | 0.371175 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8114.93 | 1.27745 | ||||||||
\(344\) | 1238.78 | 0.194159 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −20589.1 | −3.19906 | ||||||||
\(347\) | 8835.70 | 1.36693 | 0.683466 | − | 0.729983i | \(-0.260472\pi\) | ||||
0.683466 | + | 0.729983i | \(0.260472\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8837.73 | −1.35551 | −0.677755 | − | 0.735288i | \(-0.737047\pi\) | ||||
−0.677755 | + | 0.735288i | \(0.737047\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1348.68 | 0.204219 | ||||||||
\(353\) | 3128.88 | 0.471766 | 0.235883 | − | 0.971781i | \(-0.424202\pi\) | ||||
0.235883 | + | 0.971781i | \(0.424202\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −14245.0 | −2.12073 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8446.65 | 1.24698 | ||||||||
\(359\) | 10823.3 | 1.59118 | 0.795588 | − | 0.605838i | \(-0.207162\pi\) | ||||
0.795588 | + | 0.605838i | \(0.207162\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3148.22 | −0.458992 | ||||||||
\(362\) | −1237.83 | −0.179721 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 12025.6 | 1.73163 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −426.157 | −0.0606137 | −0.0303068 | − | 0.999541i | \(-0.509648\pi\) | ||||
−0.0303068 | + | 0.999541i | \(0.509648\pi\) | |||||||
\(368\) | 247.181 | 0.0350141 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7660.44 | 1.07200 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2607.13 | −0.361909 | −0.180955 | − | 0.983491i | \(-0.557919\pi\) | ||||
−0.180955 | + | 0.983491i | \(0.557919\pi\) | |||||||
\(374\) | −3458.11 | −0.478114 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5105.74 | 0.700288 | ||||||||
\(377\) | 5913.23 | 0.807816 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3453.71 | −0.468087 | −0.234044 | − | 0.972226i | \(-0.575196\pi\) | ||||
−0.234044 | + | 0.972226i | \(0.575196\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −8761.13 | −1.17345 | ||||||||
\(383\) | 1424.88 | 0.190100 | 0.0950498 | − | 0.995473i | \(-0.469699\pi\) | ||||
0.0950498 | + | 0.995473i | \(0.469699\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6466.20 | −0.852645 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −16346.0 | −2.13877 | ||||||||
\(389\) | 6040.34 | 0.787294 | 0.393647 | − | 0.919262i | \(-0.371213\pi\) | ||||
0.393647 | + | 0.919262i | \(0.371213\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3505.43 | −0.453394 | ||||||||
\(392\) | 12322.8 | 1.58775 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −12583.1 | −1.60895 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10652.4 | 1.34667 | 0.673336 | − | 0.739337i | \(-0.264861\pi\) | ||||
0.673336 | + | 0.739337i | \(0.264861\pi\) | |||||||
\(398\) | 9755.17 | 1.22860 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13110.4 | 1.63267 | 0.816334 | − | 0.577580i | \(-0.196003\pi\) | ||||
0.816334 | + | 0.577580i | \(0.196003\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10747.7 | −1.32849 | ||||||||
\(404\) | 18092.9 | 2.22811 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 26391.8 | 3.22611 | ||||||||
\(407\) | −1403.34 | −0.170911 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9195.93 | 1.11176 | 0.555880 | − | 0.831263i | \(-0.312381\pi\) | ||||
0.555880 | + | 0.831263i | \(0.312381\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −16933.7 | −2.02491 | ||||||||
\(413\) | −17611.5 | −2.09832 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −6201.74 | −0.730926 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1873.85 | 0.219266 | ||||||||
\(419\) | −5.87977 | −0.000685550 0 | −0.000342775 | − | 1.00000i | \(-0.500109\pi\) | ||||
−0.000342775 | 1.00000i | \(0.500109\pi\) | ||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4757.16 | −0.550712 | −0.275356 | − | 0.961342i | \(-0.588796\pi\) | ||||
−0.275356 | + | 0.961342i | \(0.588796\pi\) | |||||||
\(422\) | −20719.4 | −2.39006 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5052.52 | 0.578708 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10138.3 | −1.14900 | ||||||||
\(428\) | −4881.01 | −0.551245 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12028.0 | −1.34424 | −0.672121 | − | 0.740441i | \(-0.734617\pi\) | ||||
−0.672121 | + | 0.740441i | \(0.734617\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15071.2 | −1.67269 | −0.836346 | − | 0.548203i | \(-0.815312\pi\) | ||||
−0.836346 | + | 0.548203i | \(0.815312\pi\) | |||||||
\(434\) | −47968.8 | −5.30547 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9623.38 | 1.05706 | ||||||||
\(437\) | 1899.49 | 0.207929 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1394.31 | −0.151588 | −0.0757938 | − | 0.997124i | \(-0.524149\pi\) | ||||
−0.0757938 | + | 0.997124i | \(0.524149\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 15901.7 | 1.71123 | ||||||||
\(443\) | 16363.0 | 1.75492 | 0.877462 | − | 0.479646i | \(-0.159235\pi\) | ||||
0.877462 | + | 0.479646i | \(0.159235\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4041.89 | 0.429124 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −25725.5 | −2.71298 | ||||||||
\(449\) | 8133.05 | 0.854838 | 0.427419 | − | 0.904054i | \(-0.359423\pi\) | ||||
0.427419 | + | 0.904054i | \(0.359423\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2956.27 | −0.308659 | ||||||||
\(452\) | −20296.8 | −2.11213 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4692.25 | 0.485062 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1780.59 | −0.182259 | −0.0911297 | − | 0.995839i | \(-0.529048\pi\) | ||||
−0.0911297 | + | 0.995839i | \(0.529048\pi\) | |||||||
\(458\) | 6567.65 | 0.670057 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6751.82 | −0.682133 | −0.341067 | − | 0.940039i | \(-0.610788\pi\) | ||||
−0.341067 | + | 0.940039i | \(0.610788\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4496.61 | −0.451350 | −0.225675 | − | 0.974203i | \(-0.572459\pi\) | ||||
−0.225675 | + | 0.974203i | \(0.572459\pi\) | |||||||
\(464\) | −1500.01 | −0.150078 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4412.18 | −0.438606 | ||||||||
\(467\) | 12171.4 | 1.20605 | 0.603027 | − | 0.797721i | \(-0.293961\pi\) | ||||
0.603027 | + | 0.797721i | \(0.293961\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −20868.0 | −2.05458 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −11615.9 | −1.13276 | ||||||||
\(473\) | −414.247 | −0.0402687 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 43261.5 | 4.16573 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 17028.6 | 1.62944 | ||||||||
\(479\) | −11601.8 | −1.10668 | −0.553338 | − | 0.832957i | \(-0.686646\pi\) | ||||
−0.553338 | + | 0.832957i | \(0.686646\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6453.07 | 0.611715 | ||||||||
\(482\) | −1615.19 | −0.152635 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −16046.8 | −1.50703 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9713.05 | 0.903779 | 0.451889 | − | 0.892074i | \(-0.350750\pi\) | ||||
0.451889 | + | 0.892074i | \(0.350750\pi\) | |||||||
\(488\) | −6686.79 | −0.620281 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15375.7 | 1.41323 | 0.706616 | − | 0.707597i | \(-0.250221\pi\) | ||||
0.706616 | + | 0.707597i | \(0.250221\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 21272.6 | 1.94335 | ||||||||
\(494\) | −8616.66 | −0.784781 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2726.37 | 0.246809 | ||||||||
\(497\) | −13978.4 | −1.26160 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7115.58 | −0.638351 | −0.319176 | − | 0.947696i | \(-0.603406\pi\) | ||||
−0.319176 | + | 0.947696i | \(0.603406\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −14311.9 | −1.27245 | ||||||||
\(503\) | −13438.6 | −1.19125 | −0.595623 | − | 0.803264i | \(-0.703095\pi\) | ||||
−0.595623 | + | 0.803264i | \(0.703095\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 959.196 | 0.0842717 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −20175.7 | −1.76211 | ||||||||
\(509\) | 7175.20 | 0.624823 | 0.312412 | − | 0.949947i | \(-0.398863\pi\) | ||||
0.312412 | + | 0.949947i | \(0.398863\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 31571.5 | 2.73316 | ||||||||
\(512\) | 2861.96 | 0.247035 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −7620.30 | −0.653924 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1707.35 | −0.145240 | ||||||||
\(518\) | 28801.2 | 2.44296 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21486.2 | −1.80677 | −0.903385 | − | 0.428830i | \(-0.858926\pi\) | ||||
−0.903385 | + | 0.428830i | \(0.858926\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11699.9 | −0.978205 | −0.489103 | − | 0.872226i | \(-0.662676\pi\) | ||||
−0.489103 | + | 0.872226i | \(0.662676\pi\) | |||||||
\(524\) | 639.930 | 0.0533502 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −22770.7 | −1.88755 | ||||||||
\(527\) | −38664.3 | −3.19591 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11194.7 | −0.920085 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −23442.2 | −1.91043 | ||||||||
\(533\) | 13594.0 | 1.10473 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −13763.7 | −1.10915 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −27389.2 | −2.19486 | ||||||||
\(539\) | −4120.73 | −0.329300 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17032.0 | 1.35354 | 0.676769 | − | 0.736195i | \(-0.263379\pi\) | ||||
0.676769 | + | 0.736195i | \(0.263379\pi\) | |||||||
\(542\) | −12840.0 | −1.01757 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −22310.5 | −1.75837 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23325.5 | 1.82327 | 0.911633 | − | 0.411005i | \(-0.134822\pi\) | ||||
0.911633 | + | 0.411005i | \(0.134822\pi\) | |||||||
\(548\) | 20001.6 | 1.55917 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11527.0 | −0.891229 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7337.59 | 0.564243 | ||||||||
\(554\) | 8680.07 | 0.665670 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5451.40 | −0.415811 | ||||||||
\(557\) | 16735.1 | 1.27305 | 0.636525 | − | 0.771256i | \(-0.280371\pi\) | ||||
0.636525 | + | 0.771256i | \(0.280371\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1904.86 | 0.144127 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 21249.0 | 1.59490 | ||||||||
\(563\) | −20154.6 | −1.50873 | −0.754366 | − | 0.656454i | \(-0.772056\pi\) | ||||
−0.754366 | + | 0.656454i | \(0.772056\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 32178.7 | 2.38970 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9219.57 | −0.681065 | ||||||||
\(569\) | 13838.5 | 1.01958 | 0.509789 | − | 0.860299i | \(-0.329723\pi\) | ||||
0.509789 | + | 0.860299i | \(0.329723\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16171.3 | 1.18520 | 0.592598 | − | 0.805499i | \(-0.298102\pi\) | ||||
0.592598 | + | 0.805499i | \(0.298102\pi\) | |||||||
\(572\) | −2652.31 | −0.193879 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 60672.5 | 4.41189 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5270.22 | −0.380246 | −0.190123 | − | 0.981760i | \(-0.560889\pi\) | ||||
−0.190123 | + | 0.981760i | \(0.560889\pi\) | |||||||
\(578\) | 34966.7 | 2.51630 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 25476.9 | 1.81921 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1689.55 | −0.120024 | ||||||||
\(584\) | 20823.3 | 1.47547 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −10869.1 | −0.766211 | ||||||||
\(587\) | 16540.2 | 1.16301 | 0.581504 | − | 0.813544i | \(-0.302465\pi\) | ||||
0.581504 | + | 0.813544i | \(0.302465\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20951.1 | 1.46566 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1636.95 | −0.113646 | ||||||||
\(593\) | 12053.1 | 0.834673 | 0.417336 | − | 0.908752i | \(-0.362964\pi\) | ||||
0.417336 | + | 0.908752i | \(0.362964\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 18073.0 | 1.24211 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4410.74 | −0.301620 | ||||||||
\(599\) | 16683.3 | 1.13800 | 0.569000 | − | 0.822337i | \(-0.307330\pi\) | ||||
0.569000 | + | 0.822337i | \(0.307330\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4852.77 | −0.329366 | −0.164683 | − | 0.986347i | \(-0.552660\pi\) | ||||
−0.164683 | + | 0.986347i | \(0.552660\pi\) | |||||||
\(602\) | 8501.74 | 0.575590 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −9347.59 | −0.629715 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −868.698 | −0.0580879 | −0.0290440 | − | 0.999578i | \(-0.509246\pi\) | ||||
−0.0290440 | + | 0.999578i | \(0.509246\pi\) | |||||||
\(608\) | 12089.4 | 0.806400 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7851.03 | 0.519834 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22753.0 | 1.49916 | 0.749579 | − | 0.661915i | \(-0.230256\pi\) | ||||
0.749579 | + | 0.661915i | \(0.230256\pi\) | |||||||
\(614\) | 7349.38 | 0.483057 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4255.26 | −0.278327 | ||||||||
\(617\) | −872.076 | −0.0569019 | −0.0284510 | − | 0.999595i | \(-0.509057\pi\) | ||||
−0.0284510 | + | 0.999595i | \(0.509057\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10397.0 | −0.675105 | −0.337553 | − | 0.941307i | \(-0.609599\pi\) | ||||
−0.337553 | + | 0.941307i | \(0.609599\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −9337.35 | −0.601919 | ||||||||
\(623\) | −35142.4 | −2.25995 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −937.414 | −0.0598508 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 12336.7 | 0.783895 | ||||||||
\(629\) | 23214.7 | 1.47159 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23474.9 | −1.48102 | −0.740508 | − | 0.672047i | \(-0.765415\pi\) | ||||
−0.740508 | + | 0.672047i | \(0.765415\pi\) | |||||||
\(632\) | 4839.59 | 0.304602 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3164.45 | 0.198228 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 18948.6 | 1.17861 | ||||||||
\(638\) | −5820.86 | −0.361207 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7948.00 | 0.489746 | 0.244873 | − | 0.969555i | \(-0.421254\pi\) | ||||
0.244873 | + | 0.969555i | \(0.421254\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24194.7 | 1.48390 | 0.741949 | − | 0.670456i | \(-0.233901\pi\) | ||||
0.741949 | + | 0.670456i | \(0.233901\pi\) | |||||||
\(644\) | −11999.7 | −0.734246 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −30998.1 | −1.88793 | ||||||||
\(647\) | −11011.7 | −0.669113 | −0.334556 | − | 0.942376i | \(-0.608586\pi\) | ||||
−0.334556 | + | 0.942376i | \(0.608586\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3884.33 | 0.234936 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −36809.4 | −2.21099 | ||||||||
\(653\) | 23121.1 | 1.38560 | 0.692800 | − | 0.721130i | \(-0.256377\pi\) | ||||
0.692800 | + | 0.721130i | \(0.256377\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3448.40 | −0.205240 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 35040.5 | 2.07602 | ||||||||
\(659\) | 13152.6 | 0.777470 | 0.388735 | − | 0.921350i | \(-0.372912\pi\) | ||||
0.388735 | + | 0.921350i | \(0.372912\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13205.9 | 0.777077 | 0.388539 | − | 0.921432i | \(-0.372980\pi\) | ||||
0.388539 | + | 0.921432i | \(0.372980\pi\) | |||||||
\(662\) | 12052.3 | 0.707590 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 16803.5 | 0.982083 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5900.50 | −0.342531 | ||||||||
\(668\) | −5563.56 | −0.322247 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2236.05 | 0.128647 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15527.3 | 0.889351 | 0.444675 | − | 0.895692i | \(-0.353319\pi\) | ||||
0.444675 | + | 0.895692i | \(0.353319\pi\) | |||||||
\(674\) | 11555.5 | 0.660389 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −15243.3 | −0.867279 | ||||||||
\(677\) | −2917.34 | −0.165616 | −0.0828082 | − | 0.996566i | \(-0.526389\pi\) | ||||
−0.0828082 | + | 0.996566i | \(0.526389\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −40325.7 | −2.27917 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 10579.8 | 0.594019 | ||||||||
\(683\) | −30803.5 | −1.72571 | −0.862856 | − | 0.505449i | \(-0.831327\pi\) | ||||
−0.862856 | + | 0.505449i | \(0.831327\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 36732.6 | 2.04440 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −483.207 | −0.0267763 | ||||||||
\(689\) | 7769.20 | 0.429583 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6315.91 | 0.347711 | 0.173856 | − | 0.984771i | \(-0.444377\pi\) | ||||
0.173856 | + | 0.984771i | \(0.444377\pi\) | |||||||
\(692\) | −56809.1 | −3.12075 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 39995.2 | 2.18760 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 48903.9 | 2.65763 | ||||||||
\(698\) | −40004.4 | −2.16932 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3545.05 | 0.191006 | 0.0955028 | − | 0.995429i | \(-0.469554\pi\) | ||||
0.0955028 | + | 0.995429i | \(0.469554\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12579.4 | −0.674879 | ||||||||
\(704\) | 5673.91 | 0.303755 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 14163.0 | 0.755002 | ||||||||
\(707\) | 44635.2 | 2.37437 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12214.3 | −0.646991 | −0.323495 | − | 0.946230i | \(-0.604858\pi\) | ||||
−0.323495 | + | 0.946230i | \(0.604858\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −23178.5 | −1.22002 | ||||||||
\(713\) | 10724.5 | 0.563306 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 23305.9 | 1.21646 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 48992.2 | 2.54648 | ||||||||
\(719\) | −36175.4 | −1.87638 | −0.938189 | − | 0.346122i | \(-0.887498\pi\) | ||||
−0.938189 | + | 0.346122i | \(0.887498\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −41775.5 | −2.15784 | ||||||||
\(722\) | −14250.6 | −0.734559 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3415.42 | −0.175322 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 29209.3 | 1.49012 | 0.745058 | − | 0.667000i | \(-0.232422\pi\) | ||||
0.745058 | + | 0.667000i | \(0.232422\pi\) | |||||||
\(728\) | 19567.3 | 0.996170 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6852.66 | 0.346723 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −30189.6 | −1.52125 | −0.760625 | − | 0.649191i | \(-0.775108\pi\) | ||||
−0.760625 | + | 0.649191i | \(0.775108\pi\) | |||||||
\(734\) | −1929.02 | −0.0970046 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6188.40 | 0.309928 | ||||||||
\(737\) | 4602.56 | 0.230037 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 34356.0 | 1.71016 | 0.855079 | − | 0.518498i | \(-0.173509\pi\) | ||||
0.855079 | + | 0.518498i | \(0.173509\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 34675.3 | 1.71559 | ||||||||
\(743\) | 12730.6 | 0.628589 | 0.314294 | − | 0.949326i | \(-0.398232\pi\) | ||||
0.314294 | + | 0.949326i | \(0.398232\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −11801.3 | −0.579190 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −9541.58 | −0.466410 | ||||||||
\(749\) | −12041.5 | −0.587432 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5514.18 | −0.267930 | −0.133965 | − | 0.990986i | \(-0.542771\pi\) | ||||
−0.133965 | + | 0.990986i | \(0.542771\pi\) | |||||||
\(752\) | −1991.57 | −0.0965761 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 26766.5 | 1.29281 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9205.95 | −0.442003 | −0.221001 | − | 0.975274i | \(-0.570933\pi\) | ||||
−0.221001 | + | 0.975274i | \(0.570933\pi\) | |||||||
\(758\) | −15633.4 | −0.749115 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5372.53 | −0.255918 | −0.127959 | − | 0.991779i | \(-0.540843\pi\) | ||||
−0.127959 | + | 0.991779i | \(0.540843\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 23740.9 | 1.12645 | ||||||||
\(764\) | −24173.6 | −1.14473 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6449.79 | 0.304230 | ||||||||
\(767\) | −17861.6 | −0.840866 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4467.86 | 0.209513 | 0.104756 | − | 0.994498i | \(-0.466594\pi\) | ||||
0.104756 | + | 0.994498i | \(0.466594\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −17841.5 | −0.831773 | ||||||||
\(773\) | 23496.7 | 1.09329 | 0.546647 | − | 0.837363i | \(-0.315904\pi\) | ||||
0.546647 | + | 0.837363i | \(0.315904\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −26597.2 | −1.23039 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 27341.9 | 1.25997 | ||||||||
\(779\) | −26499.6 | −1.21880 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3083.01 | 0.141253 | ||||||||
\(782\) | −15867.5 | −0.725600 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4806.71 | −0.218965 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5324.68 | 0.241174 | 0.120587 | − | 0.992703i | \(-0.461522\pi\) | ||||
0.120587 | + | 0.992703i | \(0.461522\pi\) | |||||||
\(788\) | −34719.1 | −1.56957 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −50072.4 | −2.25078 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10282.2 | −0.460443 | ||||||||
\(794\) | 48218.6 | 2.15518 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 26916.3 | 1.19852 | ||||||||
\(797\) | −34413.0 | −1.52945 | −0.764724 | − | 0.644358i | \(-0.777125\pi\) | ||||
−0.764724 | + | 0.644358i | \(0.777125\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 28243.7 | 1.25055 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 59344.6 | 2.61288 | ||||||||
\(803\) | −6963.29 | −0.306014 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −48649.8 | −2.12607 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 29439.6 | 1.28179 | ||||||||
\(809\) | −17213.2 | −0.748062 | −0.374031 | − | 0.927416i | \(-0.622025\pi\) | ||||
−0.374031 | + | 0.927416i | \(0.622025\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10256.4 | 0.444084 | 0.222042 | − | 0.975037i | \(-0.428728\pi\) | ||||
0.222042 | + | 0.975037i | \(0.428728\pi\) | |||||||
\(812\) | 72819.9 | 3.14714 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −6352.27 | −0.273522 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3713.26 | −0.159009 | ||||||||
\(818\) | 41625.8 | 1.77923 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 46354.4 | 1.97050 | 0.985250 | − | 0.171122i | \(-0.0547393\pi\) | ||||
0.985250 | + | 0.171122i | \(0.0547393\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24429.4 | 1.03470 | 0.517348 | − | 0.855775i | \(-0.326919\pi\) | ||||
0.517348 | + | 0.855775i | \(0.326919\pi\) | |||||||
\(824\) | −27553.5 | −1.16489 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −79719.4 | −3.35810 | ||||||||
\(827\) | 9681.38 | 0.407079 | 0.203540 | − | 0.979067i | \(-0.434755\pi\) | ||||
0.203540 | + | 0.979067i | \(0.434755\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13781.5 | 0.577382 | 0.288691 | − | 0.957422i | \(-0.406780\pi\) | ||||
0.288691 | + | 0.957422i | \(0.406780\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −26090.7 | −1.08718 | ||||||||
\(833\) | 68167.0 | 2.83535 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 5170.31 | 0.213898 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −26.6150 | −0.00109714 | ||||||||
\(839\) | 5290.63 | 0.217703 | 0.108852 | − | 0.994058i | \(-0.465283\pi\) | ||||
0.108852 | + | 0.994058i | \(0.465283\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11418.1 | 0.468165 | ||||||||
\(842\) | −21533.5 | −0.881345 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −57168.7 | −2.33155 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −39587.6 | −1.60596 | ||||||||
\(848\) | −1970.82 | −0.0798091 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6439.19 | −0.259380 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13788.1 | −0.553451 | −0.276726 | − | 0.960949i | \(-0.589249\pi\) | ||||
−0.276726 | + | 0.960949i | \(0.589249\pi\) | |||||||
\(854\) | −45891.3 | −1.83884 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7942.09 | −0.317120 | ||||||||
\(857\) | 34665.3 | 1.38173 | 0.690865 | − | 0.722983i | \(-0.257230\pi\) | ||||
0.690865 | + | 0.722983i | \(0.257230\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25914.7 | −1.02933 | −0.514667 | − | 0.857390i | \(-0.672085\pi\) | ||||
−0.514667 | + | 0.857390i | \(0.672085\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −54445.3 | −2.15129 | ||||||||
\(863\) | 256.730 | 0.0101265 | 0.00506327 | − | 0.999987i | \(-0.498388\pi\) | ||||
0.00506327 | + | 0.999987i | \(0.498388\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −68220.4 | −2.67693 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −132355. | −5.17560 | ||||||||
\(869\) | −1618.35 | −0.0631746 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21164.3 | −0.823335 | ||||||||
\(872\) | 15658.6 | 0.608103 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 8598.12 | 0.332764 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −35072.4 | −1.35041 | −0.675207 | − | 0.737629i | \(-0.735946\pi\) | ||||
−0.675207 | + | 0.737629i | \(0.735946\pi\) | |||||||
\(878\) | −6311.42 | −0.242597 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9294.28 | 0.355428 | 0.177714 | − | 0.984082i | \(-0.443130\pi\) | ||||
0.177714 | + | 0.984082i | \(0.443130\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9642.26 | 0.367483 | 0.183742 | − | 0.982975i | \(-0.441179\pi\) | ||||
0.183742 | + | 0.982975i | \(0.441179\pi\) | |||||||
\(884\) | 43875.7 | 1.66934 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 74068.0 | 2.80854 | ||||||||
\(887\) | −7224.57 | −0.273481 | −0.136740 | − | 0.990607i | \(-0.543663\pi\) | ||||
−0.136740 | + | 0.990607i | \(0.543663\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −49773.6 | −1.87779 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 11152.3 | 0.418619 | ||||||||
\(893\) | −15304.5 | −0.573510 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −67528.1 | −2.51781 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 36814.6 | 1.36806 | ||||||||
\(899\) | −65081.7 | −2.41446 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 27949.4 | 1.03344 | ||||||||
\(902\) | −13381.7 | −0.493970 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −33025.8 | −1.21507 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24903.1 | 0.911681 | 0.455840 | − | 0.890061i | \(-0.349339\pi\) | ||||
0.455840 | + | 0.890061i | \(0.349339\pi\) | |||||||
\(908\) | 12946.8 | 0.473188 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18055.5 | −0.656647 | −0.328324 | − | 0.944565i | \(-0.606484\pi\) | ||||
−0.328324 | + | 0.944565i | \(0.606484\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5619.07 | −0.203685 | ||||||||
\(914\) | −8059.92 | −0.291683 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 18121.4 | 0.653654 | ||||||||
\(917\) | 1578.71 | 0.0568524 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 374.785 | 0.0134527 | 0.00672634 | − | 0.999977i | \(-0.497859\pi\) | ||||
0.00672634 | + | 0.999977i | \(0.497859\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −30562.4 | −1.09167 | ||||||||
\(923\) | −14176.8 | −0.505564 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −20354.1 | −0.722329 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −37554.1 | −1.32842 | ||||||||
\(929\) | 7051.65 | 0.249039 | 0.124519 | − | 0.992217i | \(-0.460261\pi\) | ||||
0.124519 | + | 0.992217i | \(0.460261\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −36937.7 | −1.30031 | ||||||||
\(932\) | −12174.0 | −0.427869 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 55094.5 | 1.93014 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21558.0 | −0.751623 | −0.375811 | − | 0.926696i | \(-0.622636\pi\) | ||||
−0.375811 | + | 0.926696i | \(0.622636\pi\) | |||||||
\(938\) | −94460.0 | −3.28809 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16659.3 | −0.577130 | −0.288565 | − | 0.957460i | \(-0.593178\pi\) | ||||
−0.288565 | + | 0.957460i | \(0.593178\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13564.8 | −0.468430 | ||||||||
\(944\) | 4530.95 | 0.156218 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1875.11 | −0.0644450 | ||||||||
\(947\) | 26547.4 | 0.910956 | 0.455478 | − | 0.890247i | \(-0.349468\pi\) | ||||
0.455478 | + | 0.890247i | \(0.349468\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 32019.8 | 1.09526 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 70392.5 | 2.39646 | ||||||||
\(953\) | −32158.1 | −1.09308 | −0.546539 | − | 0.837434i | \(-0.684055\pi\) | ||||
−0.546539 | + | 0.837434i | \(0.684055\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 46985.2 | 1.58955 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −52515.8 | −1.77110 | ||||||||
\(959\) | 49344.1 | 1.66153 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 88499.1 | 2.97067 | ||||||||
\(962\) | 29210.1 | 0.978973 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −4456.62 | −0.148898 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27131.2 | −0.902254 | −0.451127 | − | 0.892460i | \(-0.648978\pi\) | ||||
−0.451127 | + | 0.892460i | \(0.648978\pi\) | |||||||
\(968\) | −26110.4 | −0.866964 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −31358.9 | −1.03641 | −0.518206 | − | 0.855256i | \(-0.673400\pi\) | ||||
−0.518206 | + | 0.855256i | \(0.673400\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13448.6 | −0.443107 | ||||||||
\(974\) | 43966.5 | 1.44638 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2608.29 | 0.0855423 | ||||||||
\(977\) | −23459.2 | −0.768193 | −0.384097 | − | 0.923293i | \(-0.625487\pi\) | ||||
−0.384097 | + | 0.923293i | \(0.625487\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7750.85 | 0.253032 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 69598.9 | 2.26170 | ||||||||
\(983\) | −37086.9 | −1.20334 | −0.601672 | − | 0.798743i | \(-0.705499\pi\) | ||||
−0.601672 | + | 0.798743i | \(0.705499\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 96291.3 | 3.11008 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −23775.0 | −0.765570 | ||||||||
\(989\) | −1900.76 | −0.0611130 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45468.4 | 1.45747 | 0.728735 | − | 0.684796i | \(-0.240109\pi\) | ||||
0.728735 | + | 0.684796i | \(0.240109\pi\) | |||||||
\(992\) | 68257.1 | 2.18464 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −63273.6 | −2.01903 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7102.47 | −0.225614 | −0.112807 | − | 0.993617i | \(-0.535984\pi\) | ||||
−0.112807 | + | 0.993617i | \(0.535984\pi\) | |||||||
\(998\) | −32209.0 | −1.02160 | ||||||||
\(999\) | 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 | 675.4.a.y.1.4 | yes | 4 | |
3.2 | odd | 2 | 675.4.a.u.1.1 | ✓ | 4 | ||
5.2 | odd | 4 | 675.4.b.q.649.7 | 8 | |||
5.3 | odd | 4 | 675.4.b.q.649.2 | 8 | |||
5.4 | even | 2 | 675.4.a.v.1.1 | yes | 4 | ||
15.2 | even | 4 | 675.4.b.p.649.2 | 8 | |||
15.8 | even | 4 | 675.4.b.p.649.7 | 8 | |||
15.14 | odd | 2 | 675.4.a.z.1.4 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
675.4.a.u.1.1 | ✓ | 4 | 3.2 | odd | 2 | ||
675.4.a.v.1.1 | yes | 4 | 5.4 | even | 2 | ||
675.4.a.y.1.4 | yes | 4 | 1.1 | even | 1 | trivial | |
675.4.a.z.1.4 | yes | 4 | 15.14 | odd | 2 | ||
675.4.b.p.649.2 | 8 | 15.2 | even | 4 | |||
675.4.b.p.649.7 | 8 | 15.8 | even | 4 | |||
675.4.b.q.649.2 | 8 | 5.3 | odd | 4 | |||
675.4.b.q.649.7 | 8 | 5.2 | odd | 4 |