Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,4,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, 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("177.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(10.4433380710\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 41x^{5} - 7x^{4} + 484x^{3} + 63x^{2} - 1736x - 44 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(5.07078\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.07078 | −1.79279 | −0.896396 | − | 0.443253i | \(-0.853824\pi\) | ||||
−0.896396 | + | 0.443253i | \(0.853824\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 17.7128 | 2.21411 | ||||||||
\(5\) | 5.77165 | 0.516232 | 0.258116 | − | 0.966114i | \(-0.416898\pi\) | ||||
0.258116 | + | 0.966114i | \(0.416898\pi\) | |||||||
\(6\) | 15.2123 | 1.03507 | ||||||||
\(7\) | −31.1296 | −1.68084 | −0.840420 | − | 0.541936i | \(-0.817692\pi\) | ||||
−0.840420 | + | 0.541936i | \(0.817692\pi\) | |||||||
\(8\) | −49.2517 | −2.17664 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −29.2668 | −0.925497 | ||||||||
\(11\) | 52.2494 | 1.43216 | 0.716081 | − | 0.698018i | \(-0.245934\pi\) | ||||
0.716081 | + | 0.698018i | \(0.245934\pi\) | |||||||
\(12\) | −53.1385 | −1.27831 | ||||||||
\(13\) | −16.2393 | −0.346459 | −0.173230 | − | 0.984881i | \(-0.555420\pi\) | ||||
−0.173230 | + | 0.984881i | \(0.555420\pi\) | |||||||
\(14\) | 157.851 | 3.01340 | ||||||||
\(15\) | −17.3150 | −0.298047 | ||||||||
\(16\) | 108.042 | 1.68816 | ||||||||
\(17\) | 102.687 | 1.46501 | 0.732507 | − | 0.680760i | \(-0.238350\pi\) | ||||
0.732507 | + | 0.680760i | \(0.238350\pi\) | |||||||
\(18\) | −45.6370 | −0.597598 | ||||||||
\(19\) | 46.2494 | 0.558439 | 0.279219 | − | 0.960227i | \(-0.409924\pi\) | ||||
0.279219 | + | 0.960227i | \(0.409924\pi\) | |||||||
\(20\) | 102.232 | 1.14299 | ||||||||
\(21\) | 93.3888 | 0.970433 | ||||||||
\(22\) | −264.945 | −2.56757 | ||||||||
\(23\) | −99.1068 | −0.898487 | −0.449243 | − | 0.893409i | \(-0.648306\pi\) | ||||
−0.449243 | + | 0.893409i | \(0.648306\pi\) | |||||||
\(24\) | 147.755 | 1.25668 | ||||||||
\(25\) | −91.6880 | −0.733504 | ||||||||
\(26\) | 82.3459 | 0.621129 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | −551.394 | −3.72156 | ||||||||
\(29\) | −119.005 | −0.762024 | −0.381012 | − | 0.924570i | \(-0.624424\pi\) | ||||
−0.381012 | + | 0.924570i | \(0.624424\pi\) | |||||||
\(30\) | 87.8004 | 0.534336 | ||||||||
\(31\) | 20.2372 | 0.117249 | 0.0586243 | − | 0.998280i | \(-0.481329\pi\) | ||||
0.0586243 | + | 0.998280i | \(0.481329\pi\) | |||||||
\(32\) | −153.844 | −0.849877 | ||||||||
\(33\) | −156.748 | −0.826859 | ||||||||
\(34\) | −520.703 | −2.62647 | ||||||||
\(35\) | −179.669 | −0.867704 | ||||||||
\(36\) | 159.416 | 0.738035 | ||||||||
\(37\) | 117.880 | 0.523766 | 0.261883 | − | 0.965100i | \(-0.415657\pi\) | ||||
0.261883 | + | 0.965100i | \(0.415657\pi\) | |||||||
\(38\) | −234.521 | −1.00117 | ||||||||
\(39\) | 48.7179 | 0.200028 | ||||||||
\(40\) | −284.264 | −1.12365 | ||||||||
\(41\) | −278.005 | −1.05895 | −0.529476 | − | 0.848325i | \(-0.677611\pi\) | ||||
−0.529476 | + | 0.848325i | \(0.677611\pi\) | |||||||
\(42\) | −473.554 | −1.73979 | ||||||||
\(43\) | −484.571 | −1.71852 | −0.859260 | − | 0.511539i | \(-0.829076\pi\) | ||||
−0.859260 | + | 0.511539i | \(0.829076\pi\) | |||||||
\(44\) | 925.485 | 3.17096 | ||||||||
\(45\) | 51.9449 | 0.172077 | ||||||||
\(46\) | 502.549 | 1.61080 | ||||||||
\(47\) | −347.541 | −1.07860 | −0.539299 | − | 0.842114i | \(-0.681311\pi\) | ||||
−0.539299 | + | 0.842114i | \(0.681311\pi\) | |||||||
\(48\) | −324.126 | −0.974658 | ||||||||
\(49\) | 626.051 | 1.82522 | ||||||||
\(50\) | 464.930 | 1.31502 | ||||||||
\(51\) | −308.061 | −0.845826 | ||||||||
\(52\) | −287.644 | −0.767097 | ||||||||
\(53\) | 161.039 | 0.417367 | 0.208684 | − | 0.977983i | \(-0.433082\pi\) | ||||
0.208684 | + | 0.977983i | \(0.433082\pi\) | |||||||
\(54\) | 136.911 | 0.345023 | ||||||||
\(55\) | 301.565 | 0.739328 | ||||||||
\(56\) | 1533.19 | 3.65858 | ||||||||
\(57\) | −138.748 | −0.322415 | ||||||||
\(58\) | 603.449 | 1.36615 | ||||||||
\(59\) | 59.0000 | 0.130189 | ||||||||
\(60\) | −306.697 | −0.659907 | ||||||||
\(61\) | −845.543 | −1.77477 | −0.887383 | − | 0.461033i | \(-0.847479\pi\) | ||||
−0.887383 | + | 0.461033i | \(0.847479\pi\) | |||||||
\(62\) | −102.618 | −0.210203 | ||||||||
\(63\) | −280.166 | −0.560280 | ||||||||
\(64\) | −84.2264 | −0.164505 | ||||||||
\(65\) | −93.7275 | −0.178853 | ||||||||
\(66\) | 794.836 | 1.48239 | ||||||||
\(67\) | −740.885 | −1.35095 | −0.675474 | − | 0.737384i | \(-0.736061\pi\) | ||||
−0.675474 | + | 0.737384i | \(0.736061\pi\) | |||||||
\(68\) | 1818.88 | 3.24369 | ||||||||
\(69\) | 297.320 | 0.518742 | ||||||||
\(70\) | 911.063 | 1.55561 | ||||||||
\(71\) | −738.136 | −1.23381 | −0.616906 | − | 0.787037i | \(-0.711614\pi\) | ||||
−0.616906 | + | 0.787037i | \(0.711614\pi\) | |||||||
\(72\) | −443.265 | −0.725546 | ||||||||
\(73\) | 539.769 | 0.865413 | 0.432706 | − | 0.901535i | \(-0.357559\pi\) | ||||
0.432706 | + | 0.901535i | \(0.357559\pi\) | |||||||
\(74\) | −597.743 | −0.939003 | ||||||||
\(75\) | 275.064 | 0.423489 | ||||||||
\(76\) | 819.208 | 1.23644 | ||||||||
\(77\) | −1626.50 | −2.40723 | ||||||||
\(78\) | −247.038 | −0.358609 | ||||||||
\(79\) | −412.312 | −0.587199 | −0.293599 | − | 0.955929i | \(-0.594853\pi\) | ||||
−0.293599 | + | 0.955929i | \(0.594853\pi\) | |||||||
\(80\) | 623.581 | 0.871481 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 1409.70 | 1.89848 | ||||||||
\(83\) | −75.5904 | −0.0999654 | −0.0499827 | − | 0.998750i | \(-0.515917\pi\) | ||||
−0.0499827 | + | 0.998750i | \(0.515917\pi\) | |||||||
\(84\) | 1654.18 | 2.14864 | ||||||||
\(85\) | 592.673 | 0.756287 | ||||||||
\(86\) | 2457.15 | 3.08095 | ||||||||
\(87\) | 357.016 | 0.439955 | ||||||||
\(88\) | −2573.37 | −3.11730 | ||||||||
\(89\) | 163.421 | 0.194635 | 0.0973177 | − | 0.995253i | \(-0.468974\pi\) | ||||
0.0973177 | + | 0.995253i | \(0.468974\pi\) | |||||||
\(90\) | −263.401 | −0.308499 | ||||||||
\(91\) | 505.523 | 0.582342 | ||||||||
\(92\) | −1755.46 | −1.98934 | ||||||||
\(93\) | −60.7116 | −0.0676936 | ||||||||
\(94\) | 1762.31 | 1.93370 | ||||||||
\(95\) | 266.935 | 0.288284 | ||||||||
\(96\) | 461.532 | 0.490676 | ||||||||
\(97\) | 857.136 | 0.897205 | 0.448603 | − | 0.893731i | \(-0.351922\pi\) | ||||
0.448603 | + | 0.893731i | \(0.351922\pi\) | |||||||
\(98\) | −3174.57 | −3.27225 | ||||||||
\(99\) | 470.244 | 0.477387 | ||||||||
\(100\) | −1624.06 | −1.62406 | ||||||||
\(101\) | 1635.06 | 1.61083 | 0.805417 | − | 0.592708i | \(-0.201941\pi\) | ||||
0.805417 | + | 0.592708i | \(0.201941\pi\) | |||||||
\(102\) | 1562.11 | 1.51639 | ||||||||
\(103\) | −127.175 | −0.121659 | −0.0608296 | − | 0.998148i | \(-0.519375\pi\) | ||||
−0.0608296 | + | 0.998148i | \(0.519375\pi\) | |||||||
\(104\) | 799.813 | 0.754117 | ||||||||
\(105\) | 539.008 | 0.500969 | ||||||||
\(106\) | −816.596 | −0.748253 | ||||||||
\(107\) | −1769.35 | −1.59859 | −0.799296 | − | 0.600938i | \(-0.794794\pi\) | ||||
−0.799296 | + | 0.600938i | \(0.794794\pi\) | |||||||
\(108\) | −478.247 | −0.426105 | ||||||||
\(109\) | −1862.08 | −1.63628 | −0.818140 | − | 0.575019i | \(-0.804995\pi\) | ||||
−0.818140 | + | 0.575019i | \(0.804995\pi\) | |||||||
\(110\) | −1529.17 | −1.32546 | ||||||||
\(111\) | −353.640 | −0.302396 | ||||||||
\(112\) | −3363.31 | −2.83752 | ||||||||
\(113\) | 2135.01 | 1.77739 | 0.888694 | − | 0.458501i | \(-0.151614\pi\) | ||||
0.888694 | + | 0.458501i | \(0.151614\pi\) | |||||||
\(114\) | 703.562 | 0.578023 | ||||||||
\(115\) | −572.010 | −0.463828 | ||||||||
\(116\) | −2107.92 | −1.68720 | ||||||||
\(117\) | −146.154 | −0.115486 | ||||||||
\(118\) | −299.176 | −0.233402 | ||||||||
\(119\) | −3196.60 | −2.46245 | ||||||||
\(120\) | 852.791 | 0.648740 | ||||||||
\(121\) | 1399.00 | 1.05109 | ||||||||
\(122\) | 4287.57 | 3.18179 | ||||||||
\(123\) | 834.014 | 0.611386 | ||||||||
\(124\) | 358.458 | 0.259601 | ||||||||
\(125\) | −1250.65 | −0.894891 | ||||||||
\(126\) | 1420.66 | 1.00447 | ||||||||
\(127\) | 487.180 | 0.340396 | 0.170198 | − | 0.985410i | \(-0.445559\pi\) | ||||
0.170198 | + | 0.985410i | \(0.445559\pi\) | |||||||
\(128\) | 1657.85 | 1.14480 | ||||||||
\(129\) | 1453.71 | 0.992188 | ||||||||
\(130\) | 475.272 | 0.320647 | ||||||||
\(131\) | 1162.04 | 0.775022 | 0.387511 | − | 0.921865i | \(-0.373335\pi\) | ||||
0.387511 | + | 0.921865i | \(0.373335\pi\) | |||||||
\(132\) | −2776.45 | −1.83075 | ||||||||
\(133\) | −1439.72 | −0.938647 | ||||||||
\(134\) | 3756.87 | 2.42197 | ||||||||
\(135\) | −155.835 | −0.0993489 | ||||||||
\(136\) | −5057.51 | −3.18881 | ||||||||
\(137\) | 47.9021 | 0.0298727 | 0.0149363 | − | 0.999888i | \(-0.495245\pi\) | ||||
0.0149363 | + | 0.999888i | \(0.495245\pi\) | |||||||
\(138\) | −1507.65 | −0.929996 | ||||||||
\(139\) | −2217.52 | −1.35315 | −0.676573 | − | 0.736375i | \(-0.736536\pi\) | ||||
−0.676573 | + | 0.736375i | \(0.736536\pi\) | |||||||
\(140\) | −3182.45 | −1.92119 | ||||||||
\(141\) | 1042.62 | 0.622729 | ||||||||
\(142\) | 3742.93 | 2.21197 | ||||||||
\(143\) | −848.493 | −0.496185 | ||||||||
\(144\) | 972.379 | 0.562719 | ||||||||
\(145\) | −686.856 | −0.393382 | ||||||||
\(146\) | −2737.05 | −1.55151 | ||||||||
\(147\) | −1878.15 | −1.05379 | ||||||||
\(148\) | 2087.99 | 1.15967 | ||||||||
\(149\) | −830.176 | −0.456448 | −0.228224 | − | 0.973609i | \(-0.573292\pi\) | ||||
−0.228224 | + | 0.973609i | \(0.573292\pi\) | |||||||
\(150\) | −1394.79 | −0.759228 | ||||||||
\(151\) | −2874.89 | −1.54937 | −0.774685 | − | 0.632347i | \(-0.782092\pi\) | ||||
−0.774685 | + | 0.632347i | \(0.782092\pi\) | |||||||
\(152\) | −2277.86 | −1.21552 | ||||||||
\(153\) | 924.182 | 0.488338 | ||||||||
\(154\) | 8247.64 | 4.31567 | ||||||||
\(155\) | 116.802 | 0.0605275 | ||||||||
\(156\) | 862.932 | 0.442884 | ||||||||
\(157\) | −341.385 | −0.173538 | −0.0867691 | − | 0.996228i | \(-0.527654\pi\) | ||||
−0.0867691 | + | 0.996228i | \(0.527654\pi\) | |||||||
\(158\) | 2090.74 | 1.05273 | ||||||||
\(159\) | −483.118 | −0.240967 | ||||||||
\(160\) | −887.935 | −0.438734 | ||||||||
\(161\) | 3085.15 | 1.51021 | ||||||||
\(162\) | −410.733 | −0.199199 | ||||||||
\(163\) | 3435.09 | 1.65065 | 0.825327 | − | 0.564655i | \(-0.190991\pi\) | ||||
0.825327 | + | 0.564655i | \(0.190991\pi\) | |||||||
\(164\) | −4924.25 | −2.34463 | ||||||||
\(165\) | −904.695 | −0.426851 | ||||||||
\(166\) | 383.303 | 0.179217 | ||||||||
\(167\) | −2320.44 | −1.07522 | −0.537608 | − | 0.843195i | \(-0.680672\pi\) | ||||
−0.537608 | + | 0.843195i | \(0.680672\pi\) | |||||||
\(168\) | −4599.56 | −2.11228 | ||||||||
\(169\) | −1933.29 | −0.879966 | ||||||||
\(170\) | −3005.32 | −1.35587 | ||||||||
\(171\) | 416.245 | 0.186146 | ||||||||
\(172\) | −8583.13 | −3.80498 | ||||||||
\(173\) | −2665.42 | −1.17138 | −0.585689 | − | 0.810536i | \(-0.699176\pi\) | ||||
−0.585689 | + | 0.810536i | \(0.699176\pi\) | |||||||
\(174\) | −1810.35 | −0.788748 | ||||||||
\(175\) | 2854.21 | 1.23290 | ||||||||
\(176\) | 5645.13 | 2.41771 | ||||||||
\(177\) | −177.000 | −0.0751646 | ||||||||
\(178\) | −828.670 | −0.348941 | ||||||||
\(179\) | 771.425 | 0.322117 | 0.161059 | − | 0.986945i | \(-0.448509\pi\) | ||||
0.161059 | + | 0.986945i | \(0.448509\pi\) | |||||||
\(180\) | 920.091 | 0.380998 | ||||||||
\(181\) | 1057.15 | 0.434129 | 0.217065 | − | 0.976157i | \(-0.430352\pi\) | ||||
0.217065 | + | 0.976157i | \(0.430352\pi\) | |||||||
\(182\) | −2563.40 | −1.04402 | ||||||||
\(183\) | 2536.63 | 1.02466 | ||||||||
\(184\) | 4881.18 | 1.95568 | ||||||||
\(185\) | 680.362 | 0.270385 | ||||||||
\(186\) | 307.855 | 0.121360 | ||||||||
\(187\) | 5365.32 | 2.09814 | ||||||||
\(188\) | −6155.95 | −2.38813 | ||||||||
\(189\) | 840.499 | 0.323478 | ||||||||
\(190\) | −1353.57 | −0.516834 | ||||||||
\(191\) | 2555.11 | 0.967966 | 0.483983 | − | 0.875078i | \(-0.339190\pi\) | ||||
0.483983 | + | 0.875078i | \(0.339190\pi\) | |||||||
\(192\) | 252.679 | 0.0949768 | ||||||||
\(193\) | −2038.27 | −0.760197 | −0.380098 | − | 0.924946i | \(-0.624110\pi\) | ||||
−0.380098 | + | 0.924946i | \(0.624110\pi\) | |||||||
\(194\) | −4346.35 | −1.60850 | ||||||||
\(195\) | 281.183 | 0.103261 | ||||||||
\(196\) | 11089.2 | 4.04124 | ||||||||
\(197\) | 1204.93 | 0.435776 | 0.217888 | − | 0.975974i | \(-0.430083\pi\) | ||||
0.217888 | + | 0.975974i | \(0.430083\pi\) | |||||||
\(198\) | −2384.51 | −0.855856 | ||||||||
\(199\) | 3829.73 | 1.36423 | 0.682116 | − | 0.731244i | \(-0.261060\pi\) | ||||
0.682116 | + | 0.731244i | \(0.261060\pi\) | |||||||
\(200\) | 4515.79 | 1.59657 | ||||||||
\(201\) | 2222.65 | 0.779970 | ||||||||
\(202\) | −8291.02 | −2.88789 | ||||||||
\(203\) | 3704.58 | 1.28084 | ||||||||
\(204\) | −5456.63 | −1.87275 | ||||||||
\(205\) | −1604.55 | −0.546665 | ||||||||
\(206\) | 644.876 | 0.218110 | ||||||||
\(207\) | −891.961 | −0.299496 | ||||||||
\(208\) | −1754.53 | −0.584878 | ||||||||
\(209\) | 2416.50 | 0.799775 | ||||||||
\(210\) | −2733.19 | −0.898134 | ||||||||
\(211\) | 3285.19 | 1.07186 | 0.535929 | − | 0.844263i | \(-0.319961\pi\) | ||||
0.535929 | + | 0.844263i | \(0.319961\pi\) | |||||||
\(212\) | 2852.46 | 0.924095 | ||||||||
\(213\) | 2214.41 | 0.712342 | ||||||||
\(214\) | 8971.98 | 2.86594 | ||||||||
\(215\) | −2796.77 | −0.887155 | ||||||||
\(216\) | 1329.80 | 0.418894 | ||||||||
\(217\) | −629.976 | −0.197076 | ||||||||
\(218\) | 9442.19 | 2.93351 | ||||||||
\(219\) | −1619.31 | −0.499646 | ||||||||
\(220\) | 5341.58 | 1.63695 | ||||||||
\(221\) | −1667.56 | −0.507567 | ||||||||
\(222\) | 1793.23 | 0.542134 | ||||||||
\(223\) | 426.083 | 0.127949 | 0.0639745 | − | 0.997952i | \(-0.479622\pi\) | ||||
0.0639745 | + | 0.997952i | \(0.479622\pi\) | |||||||
\(224\) | 4789.10 | 1.42851 | ||||||||
\(225\) | −825.192 | −0.244501 | ||||||||
\(226\) | −10826.2 | −3.18649 | ||||||||
\(227\) | −4529.34 | −1.32433 | −0.662164 | − | 0.749359i | \(-0.730362\pi\) | ||||
−0.662164 | + | 0.749359i | \(0.730362\pi\) | |||||||
\(228\) | −2457.63 | −0.713861 | ||||||||
\(229\) | 2137.81 | 0.616900 | 0.308450 | − | 0.951241i | \(-0.400190\pi\) | ||||
0.308450 | + | 0.951241i | \(0.400190\pi\) | |||||||
\(230\) | 2900.54 | 0.831547 | ||||||||
\(231\) | 4879.50 | 1.38982 | ||||||||
\(232\) | 5861.21 | 1.65865 | ||||||||
\(233\) | 5634.00 | 1.58410 | 0.792051 | − | 0.610455i | \(-0.209013\pi\) | ||||
0.792051 | + | 0.610455i | \(0.209013\pi\) | |||||||
\(234\) | 741.113 | 0.207043 | ||||||||
\(235\) | −2005.89 | −0.556807 | ||||||||
\(236\) | 1045.06 | 0.288252 | ||||||||
\(237\) | 1236.93 | 0.339019 | ||||||||
\(238\) | 16209.3 | 4.41467 | ||||||||
\(239\) | −4143.54 | −1.12144 | −0.560718 | − | 0.828007i | \(-0.689475\pi\) | ||||
−0.560718 | + | 0.828007i | \(0.689475\pi\) | |||||||
\(240\) | −1870.74 | −0.503150 | ||||||||
\(241\) | −5880.72 | −1.57183 | −0.785914 | − | 0.618335i | \(-0.787807\pi\) | ||||
−0.785914 | + | 0.618335i | \(0.787807\pi\) | |||||||
\(242\) | −7094.00 | −1.88438 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | −14977.0 | −3.92952 | ||||||||
\(245\) | 3613.35 | 0.942239 | ||||||||
\(246\) | −4229.10 | −1.09609 | ||||||||
\(247\) | −751.057 | −0.193476 | ||||||||
\(248\) | −996.717 | −0.255208 | ||||||||
\(249\) | 226.771 | 0.0577150 | ||||||||
\(250\) | 6341.76 | 1.60435 | ||||||||
\(251\) | −2345.45 | −0.589814 | −0.294907 | − | 0.955526i | \(-0.595289\pi\) | ||||
−0.294907 | + | 0.955526i | \(0.595289\pi\) | |||||||
\(252\) | −4962.54 | −1.24052 | ||||||||
\(253\) | −5178.27 | −1.28678 | ||||||||
\(254\) | −2470.38 | −0.610259 | ||||||||
\(255\) | −1778.02 | −0.436643 | ||||||||
\(256\) | −7732.77 | −1.88788 | ||||||||
\(257\) | −4401.18 | −1.06824 | −0.534120 | − | 0.845409i | \(-0.679357\pi\) | ||||
−0.534120 | + | 0.845409i | \(0.679357\pi\) | |||||||
\(258\) | −7371.46 | −1.77879 | ||||||||
\(259\) | −3669.55 | −0.880366 | ||||||||
\(260\) | −1660.18 | −0.396000 | ||||||||
\(261\) | −1071.05 | −0.254008 | ||||||||
\(262\) | −5892.45 | −1.38945 | ||||||||
\(263\) | 6751.11 | 1.58286 | 0.791428 | − | 0.611262i | \(-0.209338\pi\) | ||||
0.791428 | + | 0.611262i | \(0.209338\pi\) | |||||||
\(264\) | 7720.11 | 1.79977 | ||||||||
\(265\) | 929.463 | 0.215458 | ||||||||
\(266\) | 7300.53 | 1.68280 | ||||||||
\(267\) | −490.262 | −0.112373 | ||||||||
\(268\) | −13123.2 | −2.99114 | ||||||||
\(269\) | 2097.51 | 0.475419 | 0.237709 | − | 0.971336i | \(-0.423603\pi\) | ||||
0.237709 | + | 0.971336i | \(0.423603\pi\) | |||||||
\(270\) | 790.204 | 0.178112 | ||||||||
\(271\) | −5765.27 | −1.29231 | −0.646153 | − | 0.763208i | \(-0.723623\pi\) | ||||
−0.646153 | + | 0.763208i | \(0.723623\pi\) | |||||||
\(272\) | 11094.5 | 2.47317 | ||||||||
\(273\) | −1516.57 | −0.336216 | ||||||||
\(274\) | −242.901 | −0.0535555 | ||||||||
\(275\) | −4790.64 | −1.05050 | ||||||||
\(276\) | 5266.39 | 1.14855 | ||||||||
\(277\) | −3383.35 | −0.733884 | −0.366942 | − | 0.930244i | \(-0.619595\pi\) | ||||
−0.366942 | + | 0.930244i | \(0.619595\pi\) | |||||||
\(278\) | 11244.5 | 2.42591 | ||||||||
\(279\) | 182.135 | 0.0390829 | ||||||||
\(280\) | 8849.02 | 1.88868 | ||||||||
\(281\) | −2239.18 | −0.475368 | −0.237684 | − | 0.971343i | \(-0.576388\pi\) | ||||
−0.237684 | + | 0.971343i | \(0.576388\pi\) | |||||||
\(282\) | −5286.92 | −1.11642 | ||||||||
\(283\) | −4303.21 | −0.903884 | −0.451942 | − | 0.892047i | \(-0.649269\pi\) | ||||
−0.451942 | + | 0.892047i | \(0.649269\pi\) | |||||||
\(284\) | −13074.5 | −2.73179 | ||||||||
\(285\) | −800.806 | −0.166441 | ||||||||
\(286\) | 4302.52 | 0.889558 | ||||||||
\(287\) | 8654.17 | 1.77993 | ||||||||
\(288\) | −1384.60 | −0.283292 | ||||||||
\(289\) | 5631.60 | 1.14626 | ||||||||
\(290\) | 3482.90 | 0.705252 | ||||||||
\(291\) | −2571.41 | −0.518002 | ||||||||
\(292\) | 9560.83 | 1.91611 | ||||||||
\(293\) | −3649.23 | −0.727612 | −0.363806 | − | 0.931475i | \(-0.618523\pi\) | ||||
−0.363806 | + | 0.931475i | \(0.618523\pi\) | |||||||
\(294\) | 9523.71 | 1.88923 | ||||||||
\(295\) | 340.527 | 0.0672077 | ||||||||
\(296\) | −5805.79 | −1.14005 | ||||||||
\(297\) | −1410.73 | −0.275620 | ||||||||
\(298\) | 4209.64 | 0.818316 | ||||||||
\(299\) | 1609.42 | 0.311289 | ||||||||
\(300\) | 4872.17 | 0.937649 | ||||||||
\(301\) | 15084.5 | 2.88856 | ||||||||
\(302\) | 14577.9 | 2.77770 | ||||||||
\(303\) | −4905.17 | −0.930016 | ||||||||
\(304\) | 4996.88 | 0.942733 | ||||||||
\(305\) | −4880.18 | −0.916192 | ||||||||
\(306\) | −4686.33 | −0.875488 | ||||||||
\(307\) | −4242.25 | −0.788658 | −0.394329 | − | 0.918969i | \(-0.629023\pi\) | ||||
−0.394329 | + | 0.918969i | \(0.629023\pi\) | |||||||
\(308\) | −28810.0 | −5.32987 | ||||||||
\(309\) | 381.524 | 0.0702400 | ||||||||
\(310\) | −592.278 | −0.108513 | ||||||||
\(311\) | −292.249 | −0.0532859 | −0.0266430 | − | 0.999645i | \(-0.508482\pi\) | ||||
−0.0266430 | + | 0.999645i | \(0.508482\pi\) | |||||||
\(312\) | −2399.44 | −0.435389 | ||||||||
\(313\) | 5053.05 | 0.912509 | 0.456254 | − | 0.889849i | \(-0.349191\pi\) | ||||
0.456254 | + | 0.889849i | \(0.349191\pi\) | |||||||
\(314\) | 1731.09 | 0.311118 | ||||||||
\(315\) | −1617.02 | −0.289235 | ||||||||
\(316\) | −7303.21 | −1.30012 | ||||||||
\(317\) | −7858.38 | −1.39234 | −0.696168 | − | 0.717879i | \(-0.745113\pi\) | ||||
−0.696168 | + | 0.717879i | \(0.745113\pi\) | |||||||
\(318\) | 2449.79 | 0.432004 | ||||||||
\(319\) | −6217.94 | −1.09134 | ||||||||
\(320\) | −486.126 | −0.0849226 | ||||||||
\(321\) | 5308.04 | 0.922947 | ||||||||
\(322\) | −15644.2 | −2.70750 | ||||||||
\(323\) | 4749.21 | 0.818121 | ||||||||
\(324\) | 1434.74 | 0.246012 | ||||||||
\(325\) | 1488.95 | 0.254129 | ||||||||
\(326\) | −17418.6 | −2.95928 | ||||||||
\(327\) | 5586.23 | 0.944707 | ||||||||
\(328\) | 13692.2 | 2.30496 | ||||||||
\(329\) | 10818.8 | 1.81295 | ||||||||
\(330\) | 4587.51 | 0.765256 | ||||||||
\(331\) | 6703.97 | 1.11324 | 0.556622 | − | 0.830766i | \(-0.312097\pi\) | ||||
0.556622 | + | 0.830766i | \(0.312097\pi\) | |||||||
\(332\) | −1338.92 | −0.221334 | ||||||||
\(333\) | 1060.92 | 0.174589 | ||||||||
\(334\) | 11766.4 | 1.92764 | ||||||||
\(335\) | −4276.13 | −0.697403 | ||||||||
\(336\) | 10089.9 | 1.63824 | ||||||||
\(337\) | −1034.27 | −0.167182 | −0.0835910 | − | 0.996500i | \(-0.526639\pi\) | ||||
−0.0835910 | + | 0.996500i | \(0.526639\pi\) | |||||||
\(338\) | 9803.27 | 1.57760 | ||||||||
\(339\) | −6405.03 | −1.02618 | ||||||||
\(340\) | 10497.9 | 1.67450 | ||||||||
\(341\) | 1057.38 | 0.167919 | ||||||||
\(342\) | −2110.69 | −0.333722 | ||||||||
\(343\) | −8811.28 | −1.38707 | ||||||||
\(344\) | 23865.9 | 3.74060 | ||||||||
\(345\) | 1716.03 | 0.267791 | ||||||||
\(346\) | 13515.8 | 2.10004 | ||||||||
\(347\) | −2414.72 | −0.373571 | −0.186785 | − | 0.982401i | \(-0.559807\pi\) | ||||
−0.186785 | + | 0.982401i | \(0.559807\pi\) | |||||||
\(348\) | 6323.76 | 0.974107 | ||||||||
\(349\) | 1429.79 | 0.219298 | 0.109649 | − | 0.993970i | \(-0.465027\pi\) | ||||
0.109649 | + | 0.993970i | \(0.465027\pi\) | |||||||
\(350\) | −14473.1 | −2.21034 | ||||||||
\(351\) | 438.461 | 0.0666761 | ||||||||
\(352\) | −8038.26 | −1.21716 | ||||||||
\(353\) | 9657.60 | 1.45615 | 0.728077 | − | 0.685496i | \(-0.240415\pi\) | ||||
0.728077 | + | 0.685496i | \(0.240415\pi\) | |||||||
\(354\) | 897.529 | 0.134755 | ||||||||
\(355\) | −4260.27 | −0.636934 | ||||||||
\(356\) | 2894.64 | 0.430943 | ||||||||
\(357\) | 9589.80 | 1.42170 | ||||||||
\(358\) | −3911.73 | −0.577490 | ||||||||
\(359\) | 1728.23 | 0.254074 | 0.127037 | − | 0.991898i | \(-0.459453\pi\) | ||||
0.127037 | + | 0.991898i | \(0.459453\pi\) | |||||||
\(360\) | −2558.37 | −0.374550 | ||||||||
\(361\) | −4719.99 | −0.688146 | ||||||||
\(362\) | −5360.58 | −0.778304 | ||||||||
\(363\) | −4196.99 | −0.606845 | ||||||||
\(364\) | 8954.24 | 1.28937 | ||||||||
\(365\) | 3115.36 | 0.446754 | ||||||||
\(366\) | −12862.7 | −1.83701 | ||||||||
\(367\) | −2452.53 | −0.348831 | −0.174416 | − | 0.984672i | \(-0.555804\pi\) | ||||
−0.174416 | + | 0.984672i | \(0.555804\pi\) | |||||||
\(368\) | −10707.7 | −1.51679 | ||||||||
\(369\) | −2502.04 | −0.352984 | ||||||||
\(370\) | −3449.97 | −0.484744 | ||||||||
\(371\) | −5013.09 | −0.701527 | ||||||||
\(372\) | −1075.38 | −0.149881 | ||||||||
\(373\) | 8584.89 | 1.19171 | 0.595856 | − | 0.803091i | \(-0.296813\pi\) | ||||
0.595856 | + | 0.803091i | \(0.296813\pi\) | |||||||
\(374\) | −27206.4 | −3.76152 | ||||||||
\(375\) | 3751.94 | 0.516665 | ||||||||
\(376\) | 17117.0 | 2.34772 | ||||||||
\(377\) | 1932.56 | 0.264010 | ||||||||
\(378\) | −4261.99 | −0.579929 | ||||||||
\(379\) | −6441.28 | −0.872998 | −0.436499 | − | 0.899705i | \(-0.643782\pi\) | ||||
−0.436499 | + | 0.899705i | \(0.643782\pi\) | |||||||
\(380\) | 4728.19 | 0.638292 | ||||||||
\(381\) | −1461.54 | −0.196527 | ||||||||
\(382\) | −12956.4 | −1.73536 | ||||||||
\(383\) | −10167.8 | −1.35653 | −0.678264 | − | 0.734818i | \(-0.737268\pi\) | ||||
−0.678264 | + | 0.734818i | \(0.737268\pi\) | |||||||
\(384\) | −4973.54 | −0.660950 | ||||||||
\(385\) | −9387.60 | −1.24269 | ||||||||
\(386\) | 10335.6 | 1.36288 | ||||||||
\(387\) | −4361.14 | −0.572840 | ||||||||
\(388\) | 15182.3 | 1.98651 | ||||||||
\(389\) | 3426.40 | 0.446595 | 0.223297 | − | 0.974750i | \(-0.428318\pi\) | ||||
0.223297 | + | 0.974750i | \(0.428318\pi\) | |||||||
\(390\) | −1425.82 | −0.185126 | ||||||||
\(391\) | −10177.0 | −1.31630 | ||||||||
\(392\) | −30834.1 | −3.97285 | ||||||||
\(393\) | −3486.12 | −0.447459 | ||||||||
\(394\) | −6109.95 | −0.781256 | ||||||||
\(395\) | −2379.72 | −0.303131 | ||||||||
\(396\) | 8329.36 | 1.05699 | ||||||||
\(397\) | −8161.03 | −1.03171 | −0.515857 | − | 0.856675i | \(-0.672526\pi\) | ||||
−0.515857 | + | 0.856675i | \(0.672526\pi\) | |||||||
\(398\) | −19419.7 | −2.44578 | ||||||||
\(399\) | 4319.17 | 0.541928 | ||||||||
\(400\) | −9906.16 | −1.23827 | ||||||||
\(401\) | 8303.40 | 1.03404 | 0.517022 | − | 0.855972i | \(-0.327040\pi\) | ||||
0.517022 | + | 0.855972i | \(0.327040\pi\) | |||||||
\(402\) | −11270.6 | −1.39832 | ||||||||
\(403\) | −328.638 | −0.0406219 | ||||||||
\(404\) | 28961.5 | 3.56656 | ||||||||
\(405\) | 467.504 | 0.0573591 | ||||||||
\(406\) | −18785.1 | −2.29628 | ||||||||
\(407\) | 6159.15 | 0.750117 | ||||||||
\(408\) | 15172.5 | 1.84106 | ||||||||
\(409\) | −1611.03 | −0.194769 | −0.0973844 | − | 0.995247i | \(-0.531048\pi\) | ||||
−0.0973844 | + | 0.995247i | \(0.531048\pi\) | |||||||
\(410\) | 8136.31 | 0.980057 | ||||||||
\(411\) | −143.706 | −0.0172470 | ||||||||
\(412\) | −2252.63 | −0.269366 | ||||||||
\(413\) | −1836.65 | −0.218827 | ||||||||
\(414\) | 4522.94 | 0.536934 | ||||||||
\(415\) | −436.282 | −0.0516053 | ||||||||
\(416\) | 2498.32 | 0.294448 | ||||||||
\(417\) | 6652.55 | 0.781239 | ||||||||
\(418\) | −12253.6 | −1.43383 | ||||||||
\(419\) | 12278.0 | 1.43155 | 0.715776 | − | 0.698330i | \(-0.246073\pi\) | ||||
0.715776 | + | 0.698330i | \(0.246073\pi\) | |||||||
\(420\) | 9547.36 | 1.10920 | ||||||||
\(421\) | −2402.19 | −0.278089 | −0.139045 | − | 0.990286i | \(-0.544403\pi\) | ||||
−0.139045 | + | 0.990286i | \(0.544403\pi\) | |||||||
\(422\) | −16658.5 | −1.92162 | ||||||||
\(423\) | −3127.87 | −0.359533 | ||||||||
\(424\) | −7931.46 | −0.908457 | ||||||||
\(425\) | −9415.16 | −1.07459 | ||||||||
\(426\) | −11228.8 | −1.27708 | ||||||||
\(427\) | 26321.4 | 2.98310 | ||||||||
\(428\) | −31340.2 | −3.53945 | ||||||||
\(429\) | 2545.48 | 0.286473 | ||||||||
\(430\) | 14181.8 | 1.59049 | ||||||||
\(431\) | 7294.64 | 0.815245 | 0.407622 | − | 0.913151i | \(-0.366358\pi\) | ||||
0.407622 | + | 0.913151i | \(0.366358\pi\) | |||||||
\(432\) | −2917.14 | −0.324886 | ||||||||
\(433\) | 13340.5 | 1.48060 | 0.740302 | − | 0.672275i | \(-0.234683\pi\) | ||||
0.740302 | + | 0.672275i | \(0.234683\pi\) | |||||||
\(434\) | 3194.47 | 0.353317 | ||||||||
\(435\) | 2060.57 | 0.227119 | ||||||||
\(436\) | −32982.7 | −3.62290 | ||||||||
\(437\) | −4583.63 | −0.501750 | ||||||||
\(438\) | 8211.15 | 0.895762 | ||||||||
\(439\) | 7920.79 | 0.861136 | 0.430568 | − | 0.902558i | \(-0.358313\pi\) | ||||
0.430568 | + | 0.902558i | \(0.358313\pi\) | |||||||
\(440\) | −14852.6 | −1.60925 | ||||||||
\(441\) | 5634.46 | 0.608408 | ||||||||
\(442\) | 8455.85 | 0.909963 | ||||||||
\(443\) | 776.340 | 0.0832619 | 0.0416310 | − | 0.999133i | \(-0.486745\pi\) | ||||
0.0416310 | + | 0.999133i | \(0.486745\pi\) | |||||||
\(444\) | −6263.96 | −0.669537 | ||||||||
\(445\) | 943.207 | 0.100477 | ||||||||
\(446\) | −2160.57 | −0.229386 | ||||||||
\(447\) | 2490.53 | 0.263530 | ||||||||
\(448\) | 2621.93 | 0.276506 | ||||||||
\(449\) | 2796.54 | 0.293935 | 0.146968 | − | 0.989141i | \(-0.453049\pi\) | ||||
0.146968 | + | 0.989141i | \(0.453049\pi\) | |||||||
\(450\) | 4184.37 | 0.438340 | ||||||||
\(451\) | −14525.6 | −1.51659 | ||||||||
\(452\) | 37817.1 | 3.93532 | ||||||||
\(453\) | 8624.66 | 0.894529 | ||||||||
\(454\) | 22967.3 | 2.37425 | ||||||||
\(455\) | 2917.70 | 0.300624 | ||||||||
\(456\) | 6833.59 | 0.701781 | ||||||||
\(457\) | −3189.75 | −0.326499 | −0.163250 | − | 0.986585i | \(-0.552198\pi\) | ||||
−0.163250 | + | 0.986585i | \(0.552198\pi\) | |||||||
\(458\) | −10840.3 | −1.10597 | ||||||||
\(459\) | −2772.55 | −0.281942 | ||||||||
\(460\) | −10131.9 | −1.02696 | ||||||||
\(461\) | 11072.8 | 1.11868 | 0.559339 | − | 0.828939i | \(-0.311055\pi\) | ||||
0.559339 | + | 0.828939i | \(0.311055\pi\) | |||||||
\(462\) | −24742.9 | −2.49165 | ||||||||
\(463\) | 15208.6 | 1.52658 | 0.763288 | − | 0.646059i | \(-0.223584\pi\) | ||||
0.763288 | + | 0.646059i | \(0.223584\pi\) | |||||||
\(464\) | −12857.6 | −1.28642 | ||||||||
\(465\) | −350.406 | −0.0349456 | ||||||||
\(466\) | −28568.8 | −2.83997 | ||||||||
\(467\) | −2666.62 | −0.264233 | −0.132116 | − | 0.991234i | \(-0.542177\pi\) | ||||
−0.132116 | + | 0.991234i | \(0.542177\pi\) | |||||||
\(468\) | −2588.80 | −0.255699 | ||||||||
\(469\) | 23063.4 | 2.27073 | ||||||||
\(470\) | 10171.4 | 0.998240 | ||||||||
\(471\) | 1024.16 | 0.100192 | ||||||||
\(472\) | −2905.85 | −0.283374 | ||||||||
\(473\) | −25318.5 | −2.46120 | ||||||||
\(474\) | −6272.23 | −0.607791 | ||||||||
\(475\) | −4240.52 | −0.409617 | ||||||||
\(476\) | −56620.9 | −5.45213 | ||||||||
\(477\) | 1449.35 | 0.139122 | ||||||||
\(478\) | 21011.0 | 2.01050 | ||||||||
\(479\) | −1470.72 | −0.140290 | −0.0701451 | − | 0.997537i | \(-0.522346\pi\) | ||||
−0.0701451 | + | 0.997537i | \(0.522346\pi\) | |||||||
\(480\) | 2663.80 | 0.253303 | ||||||||
\(481\) | −1914.29 | −0.181463 | ||||||||
\(482\) | 29819.9 | 2.81796 | ||||||||
\(483\) | −9255.46 | −0.871922 | ||||||||
\(484\) | 24780.2 | 2.32722 | ||||||||
\(485\) | 4947.09 | 0.463166 | ||||||||
\(486\) | 1232.20 | 0.115008 | ||||||||
\(487\) | −10466.9 | −0.973921 | −0.486960 | − | 0.873424i | \(-0.661894\pi\) | ||||
−0.486960 | + | 0.873424i | \(0.661894\pi\) | |||||||
\(488\) | 41644.5 | 3.86303 | ||||||||
\(489\) | −10305.3 | −0.953006 | ||||||||
\(490\) | −18322.5 | −1.68924 | ||||||||
\(491\) | 8125.93 | 0.746880 | 0.373440 | − | 0.927654i | \(-0.378178\pi\) | ||||
0.373440 | + | 0.927654i | \(0.378178\pi\) | |||||||
\(492\) | 14772.8 | 1.35367 | ||||||||
\(493\) | −12220.3 | −1.11638 | ||||||||
\(494\) | 3808.45 | 0.346863 | ||||||||
\(495\) | 2714.09 | 0.246443 | ||||||||
\(496\) | 2186.47 | 0.197934 | ||||||||
\(497\) | 22977.9 | 2.07384 | ||||||||
\(498\) | −1149.91 | −0.103471 | ||||||||
\(499\) | −14989.0 | −1.34469 | −0.672344 | − | 0.740239i | \(-0.734712\pi\) | ||||
−0.672344 | + | 0.740239i | \(0.734712\pi\) | |||||||
\(500\) | −22152.5 | −1.98138 | ||||||||
\(501\) | 6961.32 | 0.620776 | ||||||||
\(502\) | 11893.2 | 1.05741 | ||||||||
\(503\) | −5526.27 | −0.489869 | −0.244935 | − | 0.969540i | \(-0.578766\pi\) | ||||
−0.244935 | + | 0.969540i | \(0.578766\pi\) | |||||||
\(504\) | 13798.7 | 1.21953 | ||||||||
\(505\) | 9436.98 | 0.831565 | ||||||||
\(506\) | 26257.9 | 2.30693 | ||||||||
\(507\) | 5799.86 | 0.508049 | ||||||||
\(508\) | 8629.34 | 0.753672 | ||||||||
\(509\) | 16053.1 | 1.39792 | 0.698962 | − | 0.715159i | \(-0.253646\pi\) | ||||
0.698962 | + | 0.715159i | \(0.253646\pi\) | |||||||
\(510\) | 9015.95 | 0.782810 | ||||||||
\(511\) | −16802.8 | −1.45462 | ||||||||
\(512\) | 25948.4 | 2.23978 | ||||||||
\(513\) | −1248.73 | −0.107472 | ||||||||
\(514\) | 22317.4 | 1.91513 | ||||||||
\(515\) | −734.008 | −0.0628044 | ||||||||
\(516\) | 25749.4 | 2.19681 | ||||||||
\(517\) | −18158.8 | −1.54473 | ||||||||
\(518\) | 18607.5 | 1.57831 | ||||||||
\(519\) | 7996.26 | 0.676295 | ||||||||
\(520\) | 4616.24 | 0.389299 | ||||||||
\(521\) | −16059.8 | −1.35047 | −0.675234 | − | 0.737604i | \(-0.735957\pi\) | ||||
−0.675234 | + | 0.737604i | \(0.735957\pi\) | |||||||
\(522\) | 5431.05 | 0.455384 | ||||||||
\(523\) | −18602.9 | −1.55535 | −0.777675 | − | 0.628666i | \(-0.783601\pi\) | ||||
−0.777675 | + | 0.628666i | \(0.783601\pi\) | |||||||
\(524\) | 20583.0 | 1.71598 | ||||||||
\(525\) | −8562.63 | −0.711817 | ||||||||
\(526\) | −34233.4 | −2.83773 | ||||||||
\(527\) | 2078.10 | 0.171771 | ||||||||
\(528\) | −16935.4 | −1.39587 | ||||||||
\(529\) | −2344.84 | −0.192721 | ||||||||
\(530\) | −4713.11 | −0.386272 | ||||||||
\(531\) | 531.000 | 0.0433963 | ||||||||
\(532\) | −25501.6 | −2.07826 | ||||||||
\(533\) | 4514.60 | 0.366884 | ||||||||
\(534\) | 2486.01 | 0.201461 | ||||||||
\(535\) | −10212.1 | −0.825245 | ||||||||
\(536\) | 36489.9 | 2.94053 | ||||||||
\(537\) | −2314.27 | −0.185975 | ||||||||
\(538\) | −10636.0 | −0.852327 | ||||||||
\(539\) | 32710.8 | 2.61401 | ||||||||
\(540\) | −2760.27 | −0.219969 | ||||||||
\(541\) | −21283.9 | −1.69144 | −0.845718 | − | 0.533630i | \(-0.820827\pi\) | ||||
−0.845718 | + | 0.533630i | \(0.820827\pi\) | |||||||
\(542\) | 29234.4 | 2.31684 | ||||||||
\(543\) | −3171.45 | −0.250645 | ||||||||
\(544\) | −15797.8 | −1.24508 | ||||||||
\(545\) | −10747.3 | −0.844701 | ||||||||
\(546\) | 7690.19 | 0.602765 | ||||||||
\(547\) | 17983.2 | 1.40568 | 0.702839 | − | 0.711349i | \(-0.251915\pi\) | ||||
0.702839 | + | 0.711349i | \(0.251915\pi\) | |||||||
\(548\) | 848.483 | 0.0661412 | ||||||||
\(549\) | −7609.89 | −0.591589 | ||||||||
\(550\) | 24292.3 | 1.88332 | ||||||||
\(551\) | −5503.92 | −0.425544 | ||||||||
\(552\) | −14643.5 | −1.12911 | ||||||||
\(553\) | 12835.1 | 0.986987 | ||||||||
\(554\) | 17156.2 | 1.31570 | ||||||||
\(555\) | −2041.08 | −0.156107 | ||||||||
\(556\) | −39278.5 | −2.99601 | ||||||||
\(557\) | 22854.0 | 1.73852 | 0.869261 | − | 0.494354i | \(-0.164595\pi\) | ||||
0.869261 | + | 0.494354i | \(0.164595\pi\) | |||||||
\(558\) | −923.566 | −0.0700675 | ||||||||
\(559\) | 7869.09 | 0.595397 | ||||||||
\(560\) | −19411.8 | −1.46482 | ||||||||
\(561\) | −16096.0 | −1.21136 | ||||||||
\(562\) | 11354.4 | 0.852236 | ||||||||
\(563\) | −9314.59 | −0.697271 | −0.348635 | − | 0.937258i | \(-0.613355\pi\) | ||||
−0.348635 | + | 0.937258i | \(0.613355\pi\) | |||||||
\(564\) | 18467.8 | 1.37879 | ||||||||
\(565\) | 12322.5 | 0.917545 | ||||||||
\(566\) | 21820.6 | 1.62048 | ||||||||
\(567\) | −2521.50 | −0.186760 | ||||||||
\(568\) | 36354.5 | 2.68556 | ||||||||
\(569\) | 13990.2 | 1.03075 | 0.515376 | − | 0.856964i | \(-0.327652\pi\) | ||||
0.515376 | + | 0.856964i | \(0.327652\pi\) | |||||||
\(570\) | 4060.72 | 0.298394 | ||||||||
\(571\) | 19287.1 | 1.41355 | 0.706777 | − | 0.707437i | \(-0.250149\pi\) | ||||
0.706777 | + | 0.707437i | \(0.250149\pi\) | |||||||
\(572\) | −15029.2 | −1.09861 | ||||||||
\(573\) | −7665.34 | −0.558855 | ||||||||
\(574\) | −43883.4 | −3.19104 | ||||||||
\(575\) | 9086.91 | 0.659044 | ||||||||
\(576\) | −758.038 | −0.0548349 | ||||||||
\(577\) | −23173.6 | −1.67197 | −0.835986 | − | 0.548750i | \(-0.815104\pi\) | ||||
−0.835986 | + | 0.548750i | \(0.815104\pi\) | |||||||
\(578\) | −28556.6 | −2.05501 | ||||||||
\(579\) | 6114.81 | 0.438900 | ||||||||
\(580\) | −12166.2 | −0.870988 | ||||||||
\(581\) | 2353.10 | 0.168026 | ||||||||
\(582\) | 13039.0 | 0.928670 | ||||||||
\(583\) | 8414.20 | 0.597737 | ||||||||
\(584\) | −26584.5 | −1.88369 | ||||||||
\(585\) | −843.548 | −0.0596178 | ||||||||
\(586\) | 18504.5 | 1.30446 | ||||||||
\(587\) | 26048.4 | 1.83157 | 0.915787 | − | 0.401663i | \(-0.131568\pi\) | ||||
0.915787 | + | 0.401663i | \(0.131568\pi\) | |||||||
\(588\) | −33267.5 | −2.33321 | ||||||||
\(589\) | 935.958 | 0.0654762 | ||||||||
\(590\) | −1726.74 | −0.120489 | ||||||||
\(591\) | −3614.80 | −0.251595 | ||||||||
\(592\) | 12736.0 | 0.884199 | ||||||||
\(593\) | −54.2397 | −0.00375609 | −0.00187804 | − | 0.999998i | \(-0.500598\pi\) | ||||
−0.00187804 | + | 0.999998i | \(0.500598\pi\) | |||||||
\(594\) | 7153.52 | 0.494129 | ||||||||
\(595\) | −18449.7 | −1.27120 | ||||||||
\(596\) | −14704.8 | −1.01062 | ||||||||
\(597\) | −11489.2 | −0.787640 | ||||||||
\(598\) | −8161.04 | −0.558077 | ||||||||
\(599\) | −7953.75 | −0.542540 | −0.271270 | − | 0.962503i | \(-0.587444\pi\) | ||||
−0.271270 | + | 0.962503i | \(0.587444\pi\) | |||||||
\(600\) | −13547.4 | −0.921782 | ||||||||
\(601\) | 10456.8 | 0.709720 | 0.354860 | − | 0.934919i | \(-0.384528\pi\) | ||||
0.354860 | + | 0.934919i | \(0.384528\pi\) | |||||||
\(602\) | −76490.2 | −5.17858 | ||||||||
\(603\) | −6667.96 | −0.450316 | ||||||||
\(604\) | −50922.4 | −3.43047 | ||||||||
\(605\) | 8074.52 | 0.542605 | ||||||||
\(606\) | 24873.1 | 1.66733 | ||||||||
\(607\) | 6233.80 | 0.416840 | 0.208420 | − | 0.978039i | \(-0.433168\pi\) | ||||
0.208420 | + | 0.978039i | \(0.433168\pi\) | |||||||
\(608\) | −7115.20 | −0.474604 | ||||||||
\(609\) | −11113.7 | −0.739494 | ||||||||
\(610\) | 24746.3 | 1.64254 | ||||||||
\(611\) | 5643.83 | 0.373690 | ||||||||
\(612\) | 16369.9 | 1.08123 | ||||||||
\(613\) | −12563.6 | −0.827794 | −0.413897 | − | 0.910324i | \(-0.635833\pi\) | ||||
−0.413897 | + | 0.910324i | \(0.635833\pi\) | |||||||
\(614\) | 21511.5 | 1.41390 | ||||||||
\(615\) | 4813.64 | 0.315617 | ||||||||
\(616\) | 80108.0 | 5.23968 | ||||||||
\(617\) | −14795.6 | −0.965396 | −0.482698 | − | 0.875787i | \(-0.660343\pi\) | ||||
−0.482698 | + | 0.875787i | \(0.660343\pi\) | |||||||
\(618\) | −1934.63 | −0.125926 | ||||||||
\(619\) | −1136.52 | −0.0737976 | −0.0368988 | − | 0.999319i | \(-0.511748\pi\) | ||||
−0.0368988 | + | 0.999319i | \(0.511748\pi\) | |||||||
\(620\) | 2068.90 | 0.134014 | ||||||||
\(621\) | 2675.88 | 0.172914 | ||||||||
\(622\) | 1481.93 | 0.0955306 | ||||||||
\(623\) | −5087.22 | −0.327151 | ||||||||
\(624\) | 5263.58 | 0.337679 | ||||||||
\(625\) | 4242.70 | 0.271533 | ||||||||
\(626\) | −25622.9 | −1.63594 | ||||||||
\(627\) | −7249.50 | −0.461750 | ||||||||
\(628\) | −6046.90 | −0.384232 | ||||||||
\(629\) | 12104.7 | 0.767324 | ||||||||
\(630\) | 8199.57 | 0.518538 | ||||||||
\(631\) | −8230.74 | −0.519272 | −0.259636 | − | 0.965707i | \(-0.583603\pi\) | ||||
−0.259636 | + | 0.965707i | \(0.583603\pi\) | |||||||
\(632\) | 20307.1 | 1.27812 | ||||||||
\(633\) | −9855.58 | −0.618838 | ||||||||
\(634\) | 39848.1 | 2.49617 | ||||||||
\(635\) | 2811.83 | 0.175723 | ||||||||
\(636\) | −8557.39 | −0.533526 | ||||||||
\(637\) | −10166.6 | −0.632365 | ||||||||
\(638\) | 31529.8 | 1.95655 | ||||||||
\(639\) | −6643.23 | −0.411271 | ||||||||
\(640\) | 9568.51 | 0.590982 | ||||||||
\(641\) | −20600.4 | −1.26937 | −0.634685 | − | 0.772771i | \(-0.718870\pi\) | ||||
−0.634685 | + | 0.772771i | \(0.718870\pi\) | |||||||
\(642\) | −26915.9 | −1.65465 | ||||||||
\(643\) | 8955.01 | 0.549224 | 0.274612 | − | 0.961555i | \(-0.411451\pi\) | ||||
0.274612 | + | 0.961555i | \(0.411451\pi\) | |||||||
\(644\) | 54646.9 | 3.34377 | ||||||||
\(645\) | 8390.32 | 0.512199 | ||||||||
\(646\) | −24082.2 | −1.46672 | ||||||||
\(647\) | −19489.8 | −1.18427 | −0.592136 | − | 0.805838i | \(-0.701715\pi\) | ||||
−0.592136 | + | 0.805838i | \(0.701715\pi\) | |||||||
\(648\) | −3989.39 | −0.241849 | ||||||||
\(649\) | 3082.71 | 0.186452 | ||||||||
\(650\) | −7550.14 | −0.455601 | ||||||||
\(651\) | 1889.93 | 0.113782 | ||||||||
\(652\) | 60845.1 | 3.65472 | ||||||||
\(653\) | 24922.7 | 1.49357 | 0.746784 | − | 0.665067i | \(-0.231597\pi\) | ||||
0.746784 | + | 0.665067i | \(0.231597\pi\) | |||||||
\(654\) | −28326.6 | −1.69366 | ||||||||
\(655\) | 6706.89 | 0.400092 | ||||||||
\(656\) | −30036.2 | −1.78768 | ||||||||
\(657\) | 4857.92 | 0.288471 | ||||||||
\(658\) | −54859.9 | −3.25025 | ||||||||
\(659\) | −29532.0 | −1.74568 | −0.872839 | − | 0.488008i | \(-0.837724\pi\) | ||||
−0.872839 | + | 0.488008i | \(0.837724\pi\) | |||||||
\(660\) | −16024.7 | −0.945093 | ||||||||
\(661\) | 23688.8 | 1.39393 | 0.696965 | − | 0.717105i | \(-0.254533\pi\) | ||||
0.696965 | + | 0.717105i | \(0.254533\pi\) | |||||||
\(662\) | −33994.4 | −1.99581 | ||||||||
\(663\) | 5002.69 | 0.293044 | ||||||||
\(664\) | 3722.96 | 0.217589 | ||||||||
\(665\) | −8309.59 | −0.484560 | ||||||||
\(666\) | −5379.69 | −0.313001 | ||||||||
\(667\) | 11794.2 | 0.684669 | ||||||||
\(668\) | −41101.6 | −2.38064 | ||||||||
\(669\) | −1278.25 | −0.0738714 | ||||||||
\(670\) | 21683.3 | 1.25030 | ||||||||
\(671\) | −44179.1 | −2.54175 | ||||||||
\(672\) | −14367.3 | −0.824749 | ||||||||
\(673\) | 11534.1 | 0.660636 | 0.330318 | − | 0.943870i | \(-0.392844\pi\) | ||||
0.330318 | + | 0.943870i | \(0.392844\pi\) | |||||||
\(674\) | 5244.56 | 0.299723 | ||||||||
\(675\) | 2475.58 | 0.141163 | ||||||||
\(676\) | −34244.0 | −1.94834 | ||||||||
\(677\) | 3710.82 | 0.210662 | 0.105331 | − | 0.994437i | \(-0.466410\pi\) | ||||
0.105331 | + | 0.994437i | \(0.466410\pi\) | |||||||
\(678\) | 32478.5 | 1.83972 | ||||||||
\(679\) | −26682.3 | −1.50806 | ||||||||
\(680\) | −29190.2 | −1.64616 | ||||||||
\(681\) | 13588.0 | 0.764601 | ||||||||
\(682\) | −5361.75 | −0.301044 | ||||||||
\(683\) | −8278.65 | −0.463797 | −0.231899 | − | 0.972740i | \(-0.574494\pi\) | ||||
−0.231899 | + | 0.972740i | \(0.574494\pi\) | |||||||
\(684\) | 7372.88 | 0.412148 | ||||||||
\(685\) | 276.474 | 0.0154212 | ||||||||
\(686\) | 44680.1 | 2.48672 | ||||||||
\(687\) | −6413.42 | −0.356167 | ||||||||
\(688\) | −52354.0 | −2.90113 | ||||||||
\(689\) | −2615.16 | −0.144601 | ||||||||
\(690\) | −8701.62 | −0.480094 | ||||||||
\(691\) | 19296.8 | 1.06235 | 0.531176 | − | 0.847261i | \(-0.321750\pi\) | ||||
0.531176 | + | 0.847261i | \(0.321750\pi\) | |||||||
\(692\) | −47212.2 | −2.59355 | ||||||||
\(693\) | −14638.5 | −0.802411 | ||||||||
\(694\) | 12244.5 | 0.669735 | ||||||||
\(695\) | −12798.7 | −0.698538 | ||||||||
\(696\) | −17583.6 | −0.957623 | ||||||||
\(697\) | −28547.4 | −1.55138 | ||||||||
\(698\) | −7250.17 | −0.393156 | ||||||||
\(699\) | −16902.0 | −0.914582 | ||||||||
\(700\) | 50556.2 | 2.72978 | ||||||||
\(701\) | 1826.74 | 0.0984237 | 0.0492119 | − | 0.998788i | \(-0.484329\pi\) | ||||
0.0492119 | + | 0.998788i | \(0.484329\pi\) | |||||||
\(702\) | −2223.34 | −0.119536 | ||||||||
\(703\) | 5451.87 | 0.292491 | ||||||||
\(704\) | −4400.78 | −0.235597 | ||||||||
\(705\) | 6017.66 | 0.321473 | ||||||||
\(706\) | −48971.6 | −2.61058 | ||||||||
\(707\) | −50898.7 | −2.70756 | ||||||||
\(708\) | −3135.17 | −0.166422 | ||||||||
\(709\) | −10531.6 | −0.557862 | −0.278931 | − | 0.960311i | \(-0.589980\pi\) | ||||
−0.278931 | + | 0.960311i | \(0.589980\pi\) | |||||||
\(710\) | 21602.9 | 1.14189 | ||||||||
\(711\) | −3710.80 | −0.195733 | ||||||||
\(712\) | −8048.75 | −0.423651 | ||||||||
\(713\) | −2005.64 | −0.105346 | ||||||||
\(714\) | −48627.8 | −2.54881 | ||||||||
\(715\) | −4897.20 | −0.256147 | ||||||||
\(716\) | 13664.1 | 0.713202 | ||||||||
\(717\) | 12430.6 | 0.647462 | ||||||||
\(718\) | −8763.47 | −0.455501 | ||||||||
\(719\) | 20954.3 | 1.08688 | 0.543438 | − | 0.839449i | \(-0.317122\pi\) | ||||
0.543438 | + | 0.839449i | \(0.317122\pi\) | |||||||
\(720\) | 5612.23 | 0.290494 | ||||||||
\(721\) | 3958.90 | 0.204490 | ||||||||
\(722\) | 23934.1 | 1.23370 | ||||||||
\(723\) | 17642.2 | 0.907496 | ||||||||
\(724\) | 18725.2 | 0.961208 | ||||||||
\(725\) | 10911.4 | 0.558948 | ||||||||
\(726\) | 21282.0 | 1.08795 | ||||||||
\(727\) | 12108.1 | 0.617697 | 0.308849 | − | 0.951111i | \(-0.400056\pi\) | ||||
0.308849 | + | 0.951111i | \(0.400056\pi\) | |||||||
\(728\) | −24897.9 | −1.26755 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −15797.3 | −0.800937 | ||||||||
\(731\) | −49759.1 | −2.51765 | ||||||||
\(732\) | 44930.9 | 2.26871 | ||||||||
\(733\) | 11182.5 | 0.563486 | 0.281743 | − | 0.959490i | \(-0.409087\pi\) | ||||
0.281743 | + | 0.959490i | \(0.409087\pi\) | |||||||
\(734\) | 12436.3 | 0.625382 | ||||||||
\(735\) | −10840.1 | −0.544002 | ||||||||
\(736\) | 15247.0 | 0.763603 | ||||||||
\(737\) | −38710.8 | −1.93477 | ||||||||
\(738\) | 12687.3 | 0.632827 | ||||||||
\(739\) | −9024.78 | −0.449231 | −0.224616 | − | 0.974447i | \(-0.572113\pi\) | ||||
−0.224616 | + | 0.974447i | \(0.572113\pi\) | |||||||
\(740\) | 12051.1 | 0.598660 | ||||||||
\(741\) | 2253.17 | 0.111704 | ||||||||
\(742\) | 25420.3 | 1.25769 | ||||||||
\(743\) | 17214.3 | 0.849974 | 0.424987 | − | 0.905200i | \(-0.360279\pi\) | ||||
0.424987 | + | 0.905200i | \(0.360279\pi\) | |||||||
\(744\) | 2990.15 | 0.147344 | ||||||||
\(745\) | −4791.49 | −0.235633 | ||||||||
\(746\) | −43532.1 | −2.13649 | ||||||||
\(747\) | −680.314 | −0.0333218 | ||||||||
\(748\) | 95035.1 | 4.64549 | ||||||||
\(749\) | 55079.1 | 2.68698 | ||||||||
\(750\) | −19025.3 | −0.926274 | ||||||||
\(751\) | −10115.7 | −0.491517 | −0.245758 | − | 0.969331i | \(-0.579037\pi\) | ||||
−0.245758 | + | 0.969331i | \(0.579037\pi\) | |||||||
\(752\) | −37549.1 | −1.82084 | ||||||||
\(753\) | 7036.34 | 0.340529 | ||||||||
\(754\) | −9799.59 | −0.473316 | ||||||||
\(755\) | −16592.8 | −0.799835 | ||||||||
\(756\) | 14887.6 | 0.716214 | ||||||||
\(757\) | 21416.7 | 1.02827 | 0.514137 | − | 0.857708i | \(-0.328112\pi\) | ||||
0.514137 | + | 0.857708i | \(0.328112\pi\) | |||||||
\(758\) | 32662.3 | 1.56510 | ||||||||
\(759\) | 15534.8 | 0.742922 | ||||||||
\(760\) | −13147.0 | −0.627491 | ||||||||
\(761\) | −26539.8 | −1.26421 | −0.632107 | − | 0.774881i | \(-0.717810\pi\) | ||||
−0.632107 | + | 0.774881i | \(0.717810\pi\) | |||||||
\(762\) | 7411.15 | 0.352333 | ||||||||
\(763\) | 57965.7 | 2.75033 | ||||||||
\(764\) | 45258.3 | 2.14318 | ||||||||
\(765\) | 5334.06 | 0.252096 | ||||||||
\(766\) | 51558.7 | 2.43197 | ||||||||
\(767\) | −958.118 | −0.0451051 | ||||||||
\(768\) | 23198.3 | 1.08997 | ||||||||
\(769\) | −8581.69 | −0.402423 | −0.201212 | − | 0.979548i | \(-0.564488\pi\) | ||||
−0.201212 | + | 0.979548i | \(0.564488\pi\) | |||||||
\(770\) | 47602.5 | 2.22789 | ||||||||
\(771\) | 13203.5 | 0.616749 | ||||||||
\(772\) | −36103.6 | −1.68316 | ||||||||
\(773\) | −9126.70 | −0.424663 | −0.212331 | − | 0.977198i | \(-0.568106\pi\) | ||||
−0.212331 | + | 0.977198i | \(0.568106\pi\) | |||||||
\(774\) | 22114.4 | 1.02698 | ||||||||
\(775\) | −1855.51 | −0.0860024 | ||||||||
\(776\) | −42215.4 | −1.95289 | ||||||||
\(777\) | 11008.7 | 0.508280 | ||||||||
\(778\) | −17374.5 | −0.800652 | ||||||||
\(779\) | −12857.5 | −0.591360 | ||||||||
\(780\) | 4980.54 | 0.228631 | ||||||||
\(781\) | −38567.2 | −1.76702 | ||||||||
\(782\) | 51605.2 | 2.35984 | ||||||||
\(783\) | 3213.14 | 0.146652 | ||||||||
\(784\) | 67639.9 | 3.08126 | ||||||||
\(785\) | −1970.36 | −0.0895860 | ||||||||
\(786\) | 17677.4 | 0.802202 | ||||||||
\(787\) | 29121.3 | 1.31901 | 0.659507 | − | 0.751699i | \(-0.270765\pi\) | ||||
0.659507 | + | 0.751699i | \(0.270765\pi\) | |||||||
\(788\) | 21342.8 | 0.964854 | ||||||||
\(789\) | −20253.3 | −0.913863 | ||||||||
\(790\) | 12067.0 | 0.543451 | ||||||||
\(791\) | −66462.0 | −2.98750 | ||||||||
\(792\) | −23160.3 | −1.03910 | ||||||||
\(793\) | 13731.0 | 0.614884 | ||||||||
\(794\) | 41382.8 | 1.84965 | ||||||||
\(795\) | −2788.39 | −0.124395 | ||||||||
\(796\) | 67835.4 | 3.02055 | ||||||||
\(797\) | −29979.5 | −1.33241 | −0.666204 | − | 0.745770i | \(-0.732082\pi\) | ||||
−0.666204 | + | 0.745770i | \(0.732082\pi\) | |||||||
\(798\) | −21901.6 | −0.971564 | ||||||||
\(799\) | −35687.9 | −1.58016 | ||||||||
\(800\) | 14105.7 | 0.623388 | ||||||||
\(801\) | 1470.79 | 0.0648785 | ||||||||
\(802\) | −42104.7 | −1.85383 | ||||||||
\(803\) | 28202.6 | 1.23941 | ||||||||
\(804\) | 39369.5 | 1.72694 | ||||||||
\(805\) | 17806.4 | 0.779621 | ||||||||
\(806\) | 1666.45 | 0.0728266 | ||||||||
\(807\) | −6292.54 | −0.274483 | ||||||||
\(808\) | −80529.4 | −3.50621 | ||||||||
\(809\) | 14674.6 | 0.637739 | 0.318870 | − | 0.947799i | \(-0.396697\pi\) | ||||
0.318870 | + | 0.947799i | \(0.396697\pi\) | |||||||
\(810\) | −2370.61 | −0.102833 | ||||||||
\(811\) | 23037.9 | 0.997496 | 0.498748 | − | 0.866747i | \(-0.333793\pi\) | ||||
0.498748 | + | 0.866747i | \(0.333793\pi\) | |||||||
\(812\) | 65618.7 | 2.83592 | ||||||||
\(813\) | 17295.8 | 0.746114 | ||||||||
\(814\) | −31231.7 | −1.34480 | ||||||||
\(815\) | 19826.1 | 0.852121 | ||||||||
\(816\) | −33283.5 | −1.42789 | ||||||||
\(817\) | −22411.1 | −0.959689 | ||||||||
\(818\) | 8169.20 | 0.349180 | ||||||||
\(819\) | 4549.70 | 0.194114 | ||||||||
\(820\) | −28421.1 | −1.21037 | ||||||||
\(821\) | 22136.0 | 0.940987 | 0.470494 | − | 0.882403i | \(-0.344076\pi\) | ||||
0.470494 | + | 0.882403i | \(0.344076\pi\) | |||||||
\(822\) | 728.704 | 0.0309203 | ||||||||
\(823\) | −31318.9 | −1.32650 | −0.663249 | − | 0.748399i | \(-0.730823\pi\) | ||||
−0.663249 | + | 0.748399i | \(0.730823\pi\) | |||||||
\(824\) | 6263.58 | 0.264808 | ||||||||
\(825\) | 14371.9 | 0.606504 | ||||||||
\(826\) | 9313.23 | 0.392311 | ||||||||
\(827\) | 17055.7 | 0.717151 | 0.358576 | − | 0.933501i | \(-0.383262\pi\) | ||||
0.358576 | + | 0.933501i | \(0.383262\pi\) | |||||||
\(828\) | −15799.2 | −0.663115 | ||||||||
\(829\) | −23830.8 | −0.998406 | −0.499203 | − | 0.866485i | \(-0.666374\pi\) | ||||
−0.499203 | + | 0.866485i | \(0.666374\pi\) | |||||||
\(830\) | 2212.29 | 0.0925177 | ||||||||
\(831\) | 10150.0 | 0.423708 | ||||||||
\(832\) | 1367.78 | 0.0569942 | ||||||||
\(833\) | 64287.3 | 2.67398 | ||||||||
\(834\) | −33733.6 | −1.40060 | ||||||||
\(835\) | −13392.8 | −0.555061 | ||||||||
\(836\) | 42803.1 | 1.77079 | ||||||||
\(837\) | −546.404 | −0.0225645 | ||||||||
\(838\) | −62259.2 | −2.56648 | ||||||||
\(839\) | −6153.41 | −0.253205 | −0.126603 | − | 0.991954i | \(-0.540407\pi\) | ||||
−0.126603 | + | 0.991954i | \(0.540407\pi\) | |||||||
\(840\) | −26547.0 | −1.09043 | ||||||||
\(841\) | −10226.8 | −0.419319 | ||||||||
\(842\) | 12181.0 | 0.498556 | ||||||||
\(843\) | 6717.55 | 0.274454 | ||||||||
\(844\) | 58190.1 | 2.37321 | ||||||||
\(845\) | −11158.3 | −0.454267 | ||||||||
\(846\) | 15860.8 | 0.644568 | ||||||||
\(847\) | −43550.2 | −1.76671 | ||||||||
\(848\) | 17399.0 | 0.704581 | ||||||||
\(849\) | 12909.6 | 0.521858 | ||||||||
\(850\) | 47742.2 | 1.92652 | ||||||||
\(851\) | −11682.7 | −0.470597 | ||||||||
\(852\) | 39223.5 | 1.57720 | ||||||||
\(853\) | 23127.0 | 0.928318 | 0.464159 | − | 0.885752i | \(-0.346357\pi\) | ||||
0.464159 | + | 0.885752i | \(0.346357\pi\) | |||||||
\(854\) | −133470. | −5.34808 | ||||||||
\(855\) | 2402.42 | 0.0960947 | ||||||||
\(856\) | 87143.4 | 3.47956 | ||||||||
\(857\) | 9069.34 | 0.361497 | 0.180748 | − | 0.983529i | \(-0.442148\pi\) | ||||
0.180748 | + | 0.983529i | \(0.442148\pi\) | |||||||
\(858\) | −12907.6 | −0.513586 | ||||||||
\(859\) | 5101.91 | 0.202649 | 0.101324 | − | 0.994853i | \(-0.467692\pi\) | ||||
0.101324 | + | 0.994853i | \(0.467692\pi\) | |||||||
\(860\) | −49538.8 | −1.96426 | ||||||||
\(861\) | −25962.5 | −1.02764 | ||||||||
\(862\) | −36989.6 | −1.46157 | ||||||||
\(863\) | −28547.6 | −1.12604 | −0.563020 | − | 0.826444i | \(-0.690360\pi\) | ||||
−0.563020 | + | 0.826444i | \(0.690360\pi\) | |||||||
\(864\) | 4153.79 | 0.163559 | ||||||||
\(865\) | −15383.9 | −0.604703 | ||||||||
\(866\) | −67646.5 | −2.65441 | ||||||||
\(867\) | −16894.8 | −0.661796 | ||||||||
\(868\) | −11158.7 | −0.436348 | ||||||||
\(869\) | −21543.0 | −0.840963 | ||||||||
\(870\) | −10448.7 | −0.407177 | ||||||||
\(871\) | 12031.4 | 0.468048 | ||||||||
\(872\) | 91710.5 | 3.56159 | ||||||||
\(873\) | 7714.22 | 0.299068 | ||||||||
\(874\) | 23242.6 | 0.899534 | ||||||||
\(875\) | 38932.2 | 1.50417 | ||||||||
\(876\) | −28682.5 | −1.10627 | ||||||||
\(877\) | −810.103 | −0.0311918 | −0.0155959 | − | 0.999878i | \(-0.504965\pi\) | ||||
−0.0155959 | + | 0.999878i | \(0.504965\pi\) | |||||||
\(878\) | −40164.6 | −1.54384 | ||||||||
\(879\) | 10947.7 | 0.420087 | ||||||||
\(880\) | 32581.7 | 1.24810 | ||||||||
\(881\) | −26009.1 | −0.994630 | −0.497315 | − | 0.867570i | \(-0.665681\pi\) | ||||
−0.497315 | + | 0.867570i | \(0.665681\pi\) | |||||||
\(882\) | −28571.1 | −1.09075 | ||||||||
\(883\) | 19343.3 | 0.737208 | 0.368604 | − | 0.929586i | \(-0.379836\pi\) | ||||
0.368604 | + | 0.929586i | \(0.379836\pi\) | |||||||
\(884\) | −29537.3 | −1.12381 | ||||||||
\(885\) | −1021.58 | −0.0388024 | ||||||||
\(886\) | −3936.65 | −0.149271 | ||||||||
\(887\) | 10442.1 | 0.395279 | 0.197639 | − | 0.980275i | \(-0.436673\pi\) | ||||
0.197639 | + | 0.980275i | \(0.436673\pi\) | |||||||
\(888\) | 17417.4 | 0.658208 | ||||||||
\(889\) | −15165.7 | −0.572150 | ||||||||
\(890\) | −4782.80 | −0.180135 | ||||||||
\(891\) | 4232.20 | 0.159129 | ||||||||
\(892\) | 7547.14 | 0.283293 | ||||||||
\(893\) | −16073.6 | −0.602331 | ||||||||
\(894\) | −12628.9 | −0.472455 | ||||||||
\(895\) | 4452.40 | 0.166287 | ||||||||
\(896\) | −51608.1 | −1.92422 | ||||||||
\(897\) | −4828.27 | −0.179723 | ||||||||
\(898\) | −14180.6 | −0.526965 | ||||||||
\(899\) | −2408.33 | −0.0893463 | ||||||||
\(900\) | −14616.5 | −0.541352 | ||||||||
\(901\) | 16536.6 | 0.611448 | ||||||||
\(902\) | 73656.0 | 2.71893 | ||||||||
\(903\) | −45253.5 | −1.66771 | ||||||||
\(904\) | −105153. | −3.86873 | ||||||||
\(905\) | 6101.51 | 0.224112 | ||||||||
\(906\) | −43733.8 | −1.60371 | ||||||||
\(907\) | 31550.6 | 1.15504 | 0.577519 | − | 0.816377i | \(-0.304021\pi\) | ||||
0.577519 | + | 0.816377i | \(0.304021\pi\) | |||||||
\(908\) | −80227.4 | −2.93220 | ||||||||
\(909\) | 14715.5 | 0.536945 | ||||||||
\(910\) | −14795.0 | −0.538956 | ||||||||
\(911\) | 7389.17 | 0.268731 | 0.134366 | − | 0.990932i | \(-0.457100\pi\) | ||||
0.134366 | + | 0.990932i | \(0.457100\pi\) | |||||||
\(912\) | −14990.6 | −0.544287 | ||||||||
\(913\) | −3949.55 | −0.143167 | ||||||||
\(914\) | 16174.5 | 0.585345 | ||||||||
\(915\) | 14640.5 | 0.528963 | ||||||||
\(916\) | 37866.6 | 1.36588 | ||||||||
\(917\) | −36173.8 | −1.30269 | ||||||||
\(918\) | 14059.0 | 0.505463 | ||||||||
\(919\) | 25793.5 | 0.925842 | 0.462921 | − | 0.886399i | \(-0.346801\pi\) | ||||
0.462921 | + | 0.886399i | \(0.346801\pi\) | |||||||
\(920\) | 28172.5 | 1.00959 | ||||||||
\(921\) | 12726.7 | 0.455332 | ||||||||
\(922\) | −56147.6 | −2.00556 | ||||||||
\(923\) | 11986.8 | 0.427466 | ||||||||
\(924\) | 86429.9 | 3.07720 | ||||||||
\(925\) | −10808.2 | −0.384184 | ||||||||
\(926\) | −77119.6 | −2.73683 | ||||||||
\(927\) | −1144.57 | −0.0405531 | ||||||||
\(928\) | 18308.2 | 0.647627 | ||||||||
\(929\) | −29660.4 | −1.04750 | −0.523749 | − | 0.851872i | \(-0.675467\pi\) | ||||
−0.523749 | + | 0.851872i | \(0.675467\pi\) | |||||||
\(930\) | 1776.83 | 0.0626502 | ||||||||
\(931\) | 28954.5 | 1.01928 | ||||||||
\(932\) | 99794.2 | 3.50737 | ||||||||
\(933\) | 876.747 | 0.0307646 | ||||||||
\(934\) | 13521.9 | 0.473714 | ||||||||
\(935\) | 30966.8 | 1.08313 | ||||||||
\(936\) | 7198.32 | 0.251372 | ||||||||
\(937\) | 29585.3 | 1.03149 | 0.515747 | − | 0.856741i | \(-0.327514\pi\) | ||||
0.515747 | + | 0.856741i | \(0.327514\pi\) | |||||||
\(938\) | −116950. | −4.07094 | ||||||||
\(939\) | −15159.1 | −0.526837 | ||||||||
\(940\) | −35530.0 | −1.23283 | ||||||||
\(941\) | 26146.0 | 0.905778 | 0.452889 | − | 0.891567i | \(-0.350393\pi\) | ||||
0.452889 | + | 0.891567i | \(0.350393\pi\) | |||||||
\(942\) | −5193.27 | −0.179624 | ||||||||
\(943\) | 27552.2 | 0.951454 | ||||||||
\(944\) | 6374.48 | 0.219779 | ||||||||
\(945\) | 4851.07 | 0.166990 | ||||||||
\(946\) | 128385. | 4.41242 | ||||||||
\(947\) | −22905.8 | −0.785998 | −0.392999 | − | 0.919539i | \(-0.628562\pi\) | ||||
−0.392999 | + | 0.919539i | \(0.628562\pi\) | |||||||
\(948\) | 21909.6 | 0.750624 | ||||||||
\(949\) | −8765.46 | −0.299830 | ||||||||
\(950\) | 21502.7 | 0.734359 | ||||||||
\(951\) | 23575.1 | 0.803865 | ||||||||
\(952\) | 157438. | 5.35987 | ||||||||
\(953\) | 2307.17 | 0.0784225 | 0.0392113 | − | 0.999231i | \(-0.487515\pi\) | ||||
0.0392113 | + | 0.999231i | \(0.487515\pi\) | |||||||
\(954\) | −7349.36 | −0.249418 | ||||||||
\(955\) | 14747.2 | 0.499695 | ||||||||
\(956\) | −73393.9 | −2.48298 | ||||||||
\(957\) | 18653.8 | 0.630086 | ||||||||
\(958\) | 7457.71 | 0.251511 | ||||||||
\(959\) | −1491.17 | −0.0502112 | ||||||||
\(960\) | 1458.38 | 0.0490301 | ||||||||
\(961\) | −29381.5 | −0.986253 | ||||||||
\(962\) | 9706.93 | 0.325326 | ||||||||
\(963\) | −15924.1 | −0.532864 | ||||||||
\(964\) | −104164. | −3.48019 | ||||||||
\(965\) | −11764.2 | −0.392438 | ||||||||
\(966\) | 46932.5 | 1.56317 | ||||||||
\(967\) | 13468.7 | 0.447906 | 0.223953 | − | 0.974600i | \(-0.428104\pi\) | ||||
0.223953 | + | 0.974600i | \(0.428104\pi\) | |||||||
\(968\) | −68902.9 | −2.28784 | ||||||||
\(969\) | −14247.6 | −0.472342 | ||||||||
\(970\) | −25085.6 | −0.830361 | ||||||||
\(971\) | 18009.0 | 0.595197 | 0.297598 | − | 0.954691i | \(-0.403814\pi\) | ||||
0.297598 | + | 0.954691i | \(0.403814\pi\) | |||||||
\(972\) | −4304.22 | −0.142035 | ||||||||
\(973\) | 69030.4 | 2.27442 | ||||||||
\(974\) | 53075.3 | 1.74604 | ||||||||
\(975\) | −4466.85 | −0.146722 | ||||||||
\(976\) | −91354.3 | −2.99608 | ||||||||
\(977\) | 39514.9 | 1.29395 | 0.646977 | − | 0.762510i | \(-0.276033\pi\) | ||||
0.646977 | + | 0.762510i | \(0.276033\pi\) | |||||||
\(978\) | 52255.7 | 1.70854 | ||||||||
\(979\) | 8538.62 | 0.278749 | ||||||||
\(980\) | 64002.7 | 2.08622 | ||||||||
\(981\) | −16758.7 | −0.545427 | ||||||||
\(982\) | −41204.8 | −1.33900 | ||||||||
\(983\) | −2941.64 | −0.0954464 | −0.0477232 | − | 0.998861i | \(-0.515197\pi\) | ||||
−0.0477232 | + | 0.998861i | \(0.515197\pi\) | |||||||
\(984\) | −41076.6 | −1.33077 | ||||||||
\(985\) | 6954.45 | 0.224962 | ||||||||
\(986\) | 61966.3 | 2.00143 | ||||||||
\(987\) | −32456.5 | −1.04671 | ||||||||
\(988\) | −13303.4 | −0.428377 | ||||||||
\(989\) | 48024.3 | 1.54407 | ||||||||
\(990\) | −13762.5 | −0.441821 | ||||||||
\(991\) | 22197.7 | 0.711537 | 0.355769 | − | 0.934574i | \(-0.384219\pi\) | ||||
0.355769 | + | 0.934574i | \(0.384219\pi\) | |||||||
\(992\) | −3113.37 | −0.0996469 | ||||||||
\(993\) | −20111.9 | −0.642731 | ||||||||
\(994\) | −116516. | −3.71797 | ||||||||
\(995\) | 22103.9 | 0.704261 | ||||||||
\(996\) | 4016.76 | 0.127787 | ||||||||
\(997\) | 2312.86 | 0.0734695 | 0.0367347 | − | 0.999325i | \(-0.488304\pi\) | ||||
0.0367347 | + | 0.999325i | \(0.488304\pi\) | |||||||
\(998\) | 76005.9 | 2.41074 | ||||||||
\(999\) | −3182.76 | −0.100799 |
(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 | 177.4.a.b.1.1 | ✓ | 7 | |
3.2 | odd | 2 | 531.4.a.c.1.7 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.4.a.b.1.1 | ✓ | 7 | 1.1 | even | 1 | trivial | |
531.4.a.c.1.7 | 7 | 3.2 | odd | 2 |