Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1225,4,Mod(1,1225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1225, 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("1225.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1225 = 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1225.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: | \(72.2773397570\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 32x^{2} - 35x + 120 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 175) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-3.53510\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1225.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.53510 | −1.60340 | −0.801700 | − | 0.597727i | \(-0.796071\pi\) | ||||
−0.801700 | + | 0.597727i | \(0.796071\pi\) | |||||||
\(3\) | 6.46622 | 1.24442 | 0.622212 | − | 0.782849i | \(-0.286234\pi\) | ||||
0.622212 | + | 0.782849i | \(0.286234\pi\) | |||||||
\(4\) | 12.5671 | 1.57089 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −29.3249 | −1.99531 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −20.7124 | −0.915365 | ||||||||
\(9\) | 14.8119 | 0.548591 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −54.0684 | −1.48202 | −0.741011 | − | 0.671493i | \(-0.765653\pi\) | ||||
−0.741011 | + | 0.671493i | \(0.765653\pi\) | |||||||
\(12\) | 81.2617 | 1.95485 | ||||||||
\(13\) | 75.2159 | 1.60470 | 0.802351 | − | 0.596853i | \(-0.203582\pi\) | ||||
0.802351 | + | 0.596853i | \(0.203582\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −6.60441 | −0.103194 | ||||||||
\(17\) | −71.2538 | −1.01656 | −0.508282 | − | 0.861191i | \(-0.669719\pi\) | ||||
−0.508282 | + | 0.861191i | \(0.669719\pi\) | |||||||
\(18\) | −67.1736 | −0.879610 | ||||||||
\(19\) | 65.5100 | 0.791002 | 0.395501 | − | 0.918466i | \(-0.370571\pi\) | ||||
0.395501 | + | 0.918466i | \(0.370571\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 245.206 | 2.37627 | ||||||||
\(23\) | −125.688 | −1.13947 | −0.569733 | − | 0.821830i | \(-0.692953\pi\) | ||||
−0.569733 | + | 0.821830i | \(0.692953\pi\) | |||||||
\(24\) | −133.931 | −1.13910 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −341.111 | −2.57298 | ||||||||
\(27\) | −78.8106 | −0.561745 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 190.405 | 1.21922 | 0.609608 | − | 0.792703i | \(-0.291327\pi\) | ||||
0.609608 | + | 0.792703i | \(0.291327\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 193.105 | 1.11879 | 0.559397 | − | 0.828900i | \(-0.311033\pi\) | ||||
0.559397 | + | 0.828900i | \(0.311033\pi\) | |||||||
\(32\) | 195.650 | 1.08083 | ||||||||
\(33\) | −349.618 | −1.84426 | ||||||||
\(34\) | 323.143 | 1.62996 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 186.144 | 0.861776 | ||||||||
\(37\) | −114.673 | −0.509516 | −0.254758 | − | 0.967005i | \(-0.581996\pi\) | ||||
−0.254758 | + | 0.967005i | \(0.581996\pi\) | |||||||
\(38\) | −297.094 | −1.26829 | ||||||||
\(39\) | 486.362 | 1.99693 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −216.896 | −0.826180 | −0.413090 | − | 0.910690i | \(-0.635551\pi\) | ||||
−0.413090 | + | 0.910690i | \(0.635551\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 413.032 | 1.46481 | 0.732405 | − | 0.680870i | \(-0.238398\pi\) | ||||
0.732405 | + | 0.680870i | \(0.238398\pi\) | |||||||
\(44\) | −679.484 | −2.32809 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 570.007 | 1.82702 | ||||||||
\(47\) | −113.555 | −0.352421 | −0.176210 | − | 0.984353i | \(-0.556384\pi\) | ||||
−0.176210 | + | 0.984353i | \(0.556384\pi\) | |||||||
\(48\) | −42.7055 | −0.128417 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −460.743 | −1.26504 | ||||||||
\(52\) | 945.247 | 2.52081 | ||||||||
\(53\) | −584.366 | −1.51451 | −0.757253 | − | 0.653122i | \(-0.773459\pi\) | ||||
−0.757253 | + | 0.653122i | \(0.773459\pi\) | |||||||
\(54\) | 357.414 | 0.900701 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 423.602 | 0.984341 | ||||||||
\(58\) | −863.504 | −1.95489 | ||||||||
\(59\) | −203.748 | −0.449589 | −0.224795 | − | 0.974406i | \(-0.572171\pi\) | ||||
−0.224795 | + | 0.974406i | \(0.572171\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 162.539 | 0.341163 | 0.170581 | − | 0.985344i | \(-0.445435\pi\) | ||||
0.170581 | + | 0.985344i | \(0.445435\pi\) | |||||||
\(62\) | −875.749 | −1.79387 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −834.459 | −1.62980 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1585.55 | 2.95709 | ||||||||
\(67\) | −477.534 | −0.870747 | −0.435374 | − | 0.900250i | \(-0.643384\pi\) | ||||
−0.435374 | + | 0.900250i | \(0.643384\pi\) | |||||||
\(68\) | −895.456 | −1.59691 | ||||||||
\(69\) | −812.725 | −1.41798 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 822.294 | 1.37448 | 0.687242 | − | 0.726429i | \(-0.258821\pi\) | ||||
0.687242 | + | 0.726429i | \(0.258821\pi\) | |||||||
\(72\) | −306.790 | −0.502161 | ||||||||
\(73\) | −798.993 | −1.28103 | −0.640514 | − | 0.767947i | \(-0.721279\pi\) | ||||
−0.640514 | + | 0.767947i | \(0.721279\pi\) | |||||||
\(74\) | 520.052 | 0.816957 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 823.273 | 1.24258 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2205.70 | −3.20188 | ||||||||
\(79\) | −468.087 | −0.666632 | −0.333316 | − | 0.942815i | \(-0.608168\pi\) | ||||
−0.333316 | + | 0.942815i | \(0.608168\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −909.529 | −1.24764 | ||||||||
\(82\) | 983.643 | 1.32470 | ||||||||
\(83\) | −310.333 | −0.410403 | −0.205202 | − | 0.978720i | \(-0.565785\pi\) | ||||
−0.205202 | + | 0.978720i | \(0.565785\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1873.14 | −2.34867 | ||||||||
\(87\) | 1231.20 | 1.51722 | ||||||||
\(88\) | 1119.88 | 1.35659 | ||||||||
\(89\) | −1314.90 | −1.56606 | −0.783029 | − | 0.621985i | \(-0.786326\pi\) | ||||
−0.783029 | + | 0.621985i | \(0.786326\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1579.53 | −1.78998 | ||||||||
\(93\) | 1248.66 | 1.39225 | ||||||||
\(94\) | 514.985 | 0.565071 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1265.12 | 1.34501 | ||||||||
\(97\) | −1314.66 | −1.37612 | −0.688058 | − | 0.725656i | \(-0.741537\pi\) | ||||
−0.688058 | + | 0.725656i | \(0.741537\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −800.858 | −0.813023 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 401.240 | 0.395296 | 0.197648 | − | 0.980273i | \(-0.436670\pi\) | ||||
0.197648 | + | 0.980273i | \(0.436670\pi\) | |||||||
\(102\) | 2089.51 | 2.02836 | ||||||||
\(103\) | 291.844 | 0.279187 | 0.139594 | − | 0.990209i | \(-0.455420\pi\) | ||||
0.139594 | + | 0.990209i | \(0.455420\pi\) | |||||||
\(104\) | −1557.90 | −1.46889 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2650.16 | 2.42836 | ||||||||
\(107\) | 21.9594 | 0.0198402 | 0.00992009 | − | 0.999951i | \(-0.496842\pi\) | ||||
0.00992009 | + | 0.999951i | \(0.496842\pi\) | |||||||
\(108\) | −990.422 | −0.882439 | ||||||||
\(109\) | −17.3019 | −0.0152039 | −0.00760194 | − | 0.999971i | \(-0.502420\pi\) | ||||
−0.00760194 | + | 0.999971i | \(0.502420\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −741.498 | −0.634053 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −58.8182 | −0.0489660 | −0.0244830 | − | 0.999700i | \(-0.507794\pi\) | ||||
−0.0244830 | + | 0.999700i | \(0.507794\pi\) | |||||||
\(114\) | −1921.08 | −1.57829 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2392.84 | 1.91526 | ||||||||
\(117\) | 1114.09 | 0.880324 | ||||||||
\(118\) | 924.018 | 0.720871 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1592.39 | 1.19639 | ||||||||
\(122\) | −737.129 | −0.547020 | ||||||||
\(123\) | −1402.49 | −1.02812 | ||||||||
\(124\) | 2426.77 | 1.75750 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1862.03 | −1.30101 | −0.650507 | − | 0.759501i | \(-0.725443\pi\) | ||||
−0.650507 | + | 0.759501i | \(0.725443\pi\) | |||||||
\(128\) | 2219.15 | 1.53240 | ||||||||
\(129\) | 2670.75 | 1.82284 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −775.161 | −0.516994 | −0.258497 | − | 0.966012i | \(-0.583227\pi\) | ||||
−0.258497 | + | 0.966012i | \(0.583227\pi\) | |||||||
\(132\) | −4393.69 | −2.89714 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2165.66 | 1.39616 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1475.83 | 0.930528 | ||||||||
\(137\) | 1027.95 | 0.641051 | 0.320525 | − | 0.947240i | \(-0.396141\pi\) | ||||
0.320525 | + | 0.947240i | \(0.396141\pi\) | |||||||
\(138\) | 3685.79 | 2.27359 | ||||||||
\(139\) | 1029.66 | 0.628309 | 0.314154 | − | 0.949372i | \(-0.398279\pi\) | ||||
0.314154 | + | 0.949372i | \(0.398279\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −734.274 | −0.438561 | ||||||||
\(142\) | −3729.18 | −2.20385 | ||||||||
\(143\) | −4066.80 | −2.37820 | ||||||||
\(144\) | −97.8241 | −0.0566112 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 3623.51 | 2.05400 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1441.11 | −0.800393 | ||||||||
\(149\) | 1414.67 | 0.777814 | 0.388907 | − | 0.921277i | \(-0.372853\pi\) | ||||
0.388907 | + | 0.921277i | \(0.372853\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2094.96 | 1.12904 | 0.564522 | − | 0.825418i | \(-0.309060\pi\) | ||||
0.564522 | + | 0.825418i | \(0.309060\pi\) | |||||||
\(152\) | −1356.87 | −0.724056 | ||||||||
\(153\) | −1055.41 | −0.557678 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6112.17 | 3.13696 | ||||||||
\(157\) | −709.495 | −0.360662 | −0.180331 | − | 0.983606i | \(-0.557717\pi\) | ||||
−0.180331 | + | 0.983606i | \(0.557717\pi\) | |||||||
\(158\) | 2122.82 | 1.06888 | ||||||||
\(159\) | −3778.64 | −1.88469 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 4124.80 | 2.00046 | ||||||||
\(163\) | −3276.23 | −1.57432 | −0.787160 | − | 0.616749i | \(-0.788449\pi\) | ||||
−0.787160 | + | 0.616749i | \(0.788449\pi\) | |||||||
\(164\) | −2725.75 | −1.29784 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1407.39 | 0.658040 | ||||||||
\(167\) | 2860.69 | 1.32555 | 0.662775 | − | 0.748819i | \(-0.269379\pi\) | ||||
0.662775 | + | 0.748819i | \(0.269379\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3460.42 | 1.57507 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 970.331 | 0.433936 | ||||||||
\(172\) | 5190.62 | 2.30105 | ||||||||
\(173\) | 2803.44 | 1.23203 | 0.616015 | − | 0.787734i | \(-0.288746\pi\) | ||||
0.616015 | + | 0.787734i | \(0.288746\pi\) | |||||||
\(174\) | −5583.61 | −2.43271 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 357.090 | 0.152936 | ||||||||
\(177\) | −1317.48 | −0.559479 | ||||||||
\(178\) | 5963.20 | 2.51102 | ||||||||
\(179\) | 248.617 | 0.103813 | 0.0519064 | − | 0.998652i | \(-0.483470\pi\) | ||||
0.0519064 | + | 0.998652i | \(0.483470\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2075.56 | −0.852347 | −0.426174 | − | 0.904641i | \(-0.640139\pi\) | ||||
−0.426174 | + | 0.904641i | \(0.640139\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1051.01 | 0.424551 | ||||||||
\(184\) | 2603.29 | 1.04303 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −5662.78 | −2.23234 | ||||||||
\(187\) | 3852.58 | 1.50657 | ||||||||
\(188\) | −1427.07 | −0.553614 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1252.95 | −0.474663 | −0.237331 | − | 0.971429i | \(-0.576273\pi\) | ||||
−0.237331 | + | 0.971429i | \(0.576273\pi\) | |||||||
\(192\) | −5395.79 | −2.02817 | ||||||||
\(193\) | −1602.12 | −0.597527 | −0.298764 | − | 0.954327i | \(-0.596574\pi\) | ||||
−0.298764 | + | 0.954327i | \(0.596574\pi\) | |||||||
\(194\) | 5962.10 | 2.20646 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2346.38 | −0.848593 | −0.424296 | − | 0.905523i | \(-0.639479\pi\) | ||||
−0.424296 | + | 0.905523i | \(0.639479\pi\) | |||||||
\(198\) | 3631.97 | 1.30360 | ||||||||
\(199\) | 1993.53 | 0.710140 | 0.355070 | − | 0.934840i | \(-0.384457\pi\) | ||||
0.355070 | + | 0.934840i | \(0.384457\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3087.84 | −1.08358 | ||||||||
\(202\) | −1819.67 | −0.633818 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −5790.21 | −1.98723 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1323.54 | −0.447649 | ||||||||
\(207\) | −1861.68 | −0.625101 | ||||||||
\(208\) | −496.756 | −0.165595 | ||||||||
\(209\) | −3542.02 | −1.17228 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5852.55 | −1.90951 | −0.954754 | − | 0.297396i | \(-0.903882\pi\) | ||||
−0.954754 | + | 0.297396i | \(0.903882\pi\) | |||||||
\(212\) | −7343.80 | −2.37912 | ||||||||
\(213\) | 5317.13 | 1.71044 | ||||||||
\(214\) | −99.5883 | −0.0318117 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1632.35 | 0.514202 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 78.4659 | 0.0243779 | ||||||||
\(219\) | −5166.46 | −1.59414 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5359.42 | −1.63128 | ||||||||
\(222\) | 3362.77 | 1.01664 | ||||||||
\(223\) | −1719.58 | −0.516374 | −0.258187 | − | 0.966095i | \(-0.583125\pi\) | ||||
−0.258187 | + | 0.966095i | \(0.583125\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 266.747 | 0.0785120 | ||||||||
\(227\) | −5686.00 | −1.66252 | −0.831262 | − | 0.555881i | \(-0.812381\pi\) | ||||
−0.831262 | + | 0.555881i | \(0.812381\pi\) | |||||||
\(228\) | 5323.46 | 1.54629 | ||||||||
\(229\) | 3087.40 | 0.890923 | 0.445461 | − | 0.895301i | \(-0.353040\pi\) | ||||
0.445461 | + | 0.895301i | \(0.353040\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3943.73 | −1.11603 | ||||||||
\(233\) | −3997.55 | −1.12398 | −0.561991 | − | 0.827143i | \(-0.689965\pi\) | ||||
−0.561991 | + | 0.827143i | \(0.689965\pi\) | |||||||
\(234\) | −5052.52 | −1.41151 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2560.53 | −0.706255 | ||||||||
\(237\) | −3026.75 | −0.829573 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4499.79 | −1.21786 | −0.608928 | − | 0.793226i | \(-0.708400\pi\) | ||||
−0.608928 | + | 0.793226i | \(0.708400\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3633.26 | −0.971115 | −0.485557 | − | 0.874205i | \(-0.661383\pi\) | ||||
−0.485557 | + | 0.874205i | \(0.661383\pi\) | |||||||
\(242\) | −7221.66 | −1.91829 | ||||||||
\(243\) | −3753.32 | −0.990847 | ||||||||
\(244\) | 2042.64 | 0.535929 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6360.45 | 1.64849 | ||||||||
\(247\) | 4927.39 | 1.26932 | ||||||||
\(248\) | −3999.65 | −1.02411 | ||||||||
\(249\) | −2006.68 | −0.510715 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1211.21 | 0.304585 | 0.152292 | − | 0.988335i | \(-0.451334\pi\) | ||||
0.152292 | + | 0.988335i | \(0.451334\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6795.74 | 1.68871 | ||||||||
\(254\) | 8444.50 | 2.08604 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3388.39 | −0.827245 | ||||||||
\(257\) | −6225.81 | −1.51111 | −0.755556 | − | 0.655085i | \(-0.772633\pi\) | ||||
−0.755556 | + | 0.655085i | \(0.772633\pi\) | |||||||
\(258\) | −12112.1 | −2.92275 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2820.27 | 0.668851 | ||||||||
\(262\) | 3515.43 | 0.828947 | ||||||||
\(263\) | 757.377 | 0.177574 | 0.0887869 | − | 0.996051i | \(-0.471701\pi\) | ||||
0.0887869 | + | 0.996051i | \(0.471701\pi\) | |||||||
\(264\) | 7241.41 | 1.68817 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8502.43 | −1.94884 | ||||||||
\(268\) | −6001.23 | −1.36785 | ||||||||
\(269\) | −1750.59 | −0.396786 | −0.198393 | − | 0.980123i | \(-0.563572\pi\) | ||||
−0.198393 | + | 0.980123i | \(0.563572\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4451.86 | −0.997902 | −0.498951 | − | 0.866630i | \(-0.666281\pi\) | ||||
−0.498951 | + | 0.866630i | \(0.666281\pi\) | |||||||
\(272\) | 470.589 | 0.104903 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4661.87 | −1.02786 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −10213.6 | −2.22749 | ||||||||
\(277\) | 7691.69 | 1.66841 | 0.834204 | − | 0.551456i | \(-0.185928\pi\) | ||||
0.834204 | + | 0.551456i | \(0.185928\pi\) | |||||||
\(278\) | −4669.62 | −1.00743 | ||||||||
\(279\) | 2860.26 | 0.613760 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −199.034 | −0.0422540 | −0.0211270 | − | 0.999777i | \(-0.506725\pi\) | ||||
−0.0211270 | + | 0.999777i | \(0.506725\pi\) | |||||||
\(282\) | 3330.01 | 0.703188 | ||||||||
\(283\) | −799.307 | −0.167893 | −0.0839467 | − | 0.996470i | \(-0.526753\pi\) | ||||
−0.0839467 | + | 0.996470i | \(0.526753\pi\) | |||||||
\(284\) | 10333.9 | 2.15916 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 18443.3 | 3.81321 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2897.96 | 0.592931 | ||||||||
\(289\) | 164.110 | 0.0334031 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8500.86 | −1.71247 | ||||||||
\(292\) | −10041.0 | −2.01235 | ||||||||
\(293\) | 3302.75 | 0.658528 | 0.329264 | − | 0.944238i | \(-0.393199\pi\) | ||||
0.329264 | + | 0.944238i | \(0.393199\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2375.14 | 0.466393 | ||||||||
\(297\) | 4261.16 | 0.832518 | ||||||||
\(298\) | −6415.67 | −1.24715 | ||||||||
\(299\) | −9453.72 | −1.82850 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −9500.87 | −1.81031 | ||||||||
\(303\) | 2594.51 | 0.491916 | ||||||||
\(304\) | −432.655 | −0.0816265 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 4786.38 | 0.894180 | ||||||||
\(307\) | −8628.17 | −1.60402 | −0.802012 | − | 0.597308i | \(-0.796237\pi\) | ||||
−0.802012 | + | 0.597308i | \(0.796237\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1887.13 | 0.347427 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4900.60 | 0.893530 | 0.446765 | − | 0.894651i | \(-0.352576\pi\) | ||||
0.446765 | + | 0.894651i | \(0.352576\pi\) | |||||||
\(312\) | −10073.7 | −1.82792 | ||||||||
\(313\) | −9114.26 | −1.64590 | −0.822952 | − | 0.568110i | \(-0.807675\pi\) | ||||
−0.822952 | + | 0.568110i | \(0.807675\pi\) | |||||||
\(314\) | 3217.63 | 0.578285 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5882.51 | −1.04721 | ||||||||
\(317\) | 8022.82 | 1.42147 | 0.710736 | − | 0.703459i | \(-0.248362\pi\) | ||||
0.710736 | + | 0.703459i | \(0.248362\pi\) | |||||||
\(318\) | 17136.5 | 3.02191 | ||||||||
\(319\) | −10294.9 | −1.80691 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 141.995 | 0.0246896 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4667.84 | −0.804104 | ||||||||
\(324\) | −11430.2 | −1.95990 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 14858.0 | 2.52426 | ||||||||
\(327\) | −111.878 | −0.0189201 | ||||||||
\(328\) | 4492.42 | 0.756257 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1333.58 | −0.221451 | −0.110725 | − | 0.993851i | \(-0.535317\pi\) | ||||
−0.110725 | + | 0.993851i | \(0.535317\pi\) | |||||||
\(332\) | −3899.99 | −0.644698 | ||||||||
\(333\) | −1698.53 | −0.279515 | ||||||||
\(334\) | −12973.5 | −2.12539 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1687.33 | 0.272744 | 0.136372 | − | 0.990658i | \(-0.456456\pi\) | ||||
0.136372 | + | 0.990658i | \(0.456456\pi\) | |||||||
\(338\) | −15693.4 | −2.52546 | ||||||||
\(339\) | −380.331 | −0.0609344 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10440.9 | −1.65808 | ||||||||
\(342\) | −4400.55 | −0.695773 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −8554.87 | −1.34084 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12713.9 | −1.97544 | ||||||||
\(347\) | −5955.18 | −0.921299 | −0.460649 | − | 0.887582i | \(-0.652383\pi\) | ||||
−0.460649 | + | 0.887582i | \(0.652383\pi\) | |||||||
\(348\) | 15472.6 | 2.38339 | ||||||||
\(349\) | −6876.59 | −1.05471 | −0.527357 | − | 0.849644i | \(-0.676817\pi\) | ||||
−0.527357 | + | 0.849644i | \(0.676817\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5927.81 | −0.901433 | ||||||||
\(352\) | −10578.5 | −1.60181 | ||||||||
\(353\) | 1395.95 | 0.210479 | 0.105239 | − | 0.994447i | \(-0.466439\pi\) | ||||
0.105239 | + | 0.994447i | \(0.466439\pi\) | |||||||
\(354\) | 5974.90 | 0.897069 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −16524.5 | −2.46011 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1127.50 | −0.166453 | ||||||||
\(359\) | −382.988 | −0.0563046 | −0.0281523 | − | 0.999604i | \(-0.508962\pi\) | ||||
−0.0281523 | + | 0.999604i | \(0.508962\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2567.44 | −0.374316 | ||||||||
\(362\) | 9412.85 | 1.36665 | ||||||||
\(363\) | 10296.8 | 1.48881 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −4766.43 | −0.680725 | ||||||||
\(367\) | −10178.4 | −1.44771 | −0.723856 | − | 0.689951i | \(-0.757632\pi\) | ||||
−0.723856 | + | 0.689951i | \(0.757632\pi\) | |||||||
\(368\) | 830.094 | 0.117586 | ||||||||
\(369\) | −3212.65 | −0.453235 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 15692.0 | 2.18708 | ||||||||
\(373\) | 2991.00 | 0.415196 | 0.207598 | − | 0.978214i | \(-0.433435\pi\) | ||||
0.207598 | + | 0.978214i | \(0.433435\pi\) | |||||||
\(374\) | −17471.8 | −2.41563 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2352.00 | 0.322594 | ||||||||
\(377\) | 14321.5 | 1.95648 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7400.66 | 1.00302 | 0.501512 | − | 0.865150i | \(-0.332777\pi\) | ||||
0.501512 | + | 0.865150i | \(0.332777\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12040.3 | −1.61901 | ||||||||
\(382\) | 5682.27 | 0.761074 | ||||||||
\(383\) | −10769.6 | −1.43682 | −0.718408 | − | 0.695622i | \(-0.755129\pi\) | ||||
−0.718408 | + | 0.695622i | \(0.755129\pi\) | |||||||
\(384\) | 14349.5 | 1.90695 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7265.75 | 0.958075 | ||||||||
\(387\) | 6117.81 | 0.803580 | ||||||||
\(388\) | −16521.5 | −2.16173 | ||||||||
\(389\) | −11193.3 | −1.45893 | −0.729466 | − | 0.684017i | \(-0.760231\pi\) | ||||
−0.729466 | + | 0.684017i | \(0.760231\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8955.74 | 1.15834 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5012.36 | −0.643359 | ||||||||
\(394\) | 10641.1 | 1.36063 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −10064.5 | −1.27717 | ||||||||
\(397\) | 10371.9 | 1.31121 | 0.655605 | − | 0.755104i | \(-0.272414\pi\) | ||||
0.655605 | + | 0.755104i | \(0.272414\pi\) | |||||||
\(398\) | −9040.88 | −1.13864 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5402.20 | 0.672751 | 0.336375 | − | 0.941728i | \(-0.390799\pi\) | ||||
0.336375 | + | 0.941728i | \(0.390799\pi\) | |||||||
\(402\) | 14003.7 | 1.73741 | ||||||||
\(403\) | 14524.5 | 1.79533 | ||||||||
\(404\) | 5042.44 | 0.620967 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6200.17 | 0.755113 | ||||||||
\(408\) | 9543.07 | 1.15797 | ||||||||
\(409\) | 12829.9 | 1.55110 | 0.775549 | − | 0.631288i | \(-0.217473\pi\) | ||||
0.775549 | + | 0.631288i | \(0.217473\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6646.97 | 0.797739 | ||||||||
\(412\) | 3667.64 | 0.438572 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 8442.91 | 1.00229 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 14716.0 | 1.73440 | ||||||||
\(417\) | 6658.02 | 0.781882 | ||||||||
\(418\) | 16063.4 | 1.87964 | ||||||||
\(419\) | −5620.85 | −0.655362 | −0.327681 | − | 0.944788i | \(-0.606267\pi\) | ||||
−0.327681 | + | 0.944788i | \(0.606267\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2177.11 | −0.252033 | −0.126017 | − | 0.992028i | \(-0.540219\pi\) | ||||
−0.126017 | + | 0.992028i | \(0.540219\pi\) | |||||||
\(422\) | 26541.9 | 3.06171 | ||||||||
\(423\) | −1681.98 | −0.193335 | ||||||||
\(424\) | 12103.6 | 1.38633 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −24113.7 | −2.74252 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 275.967 | 0.0311668 | ||||||||
\(429\) | −26296.8 | −2.95949 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10396.4 | 1.16190 | 0.580950 | − | 0.813939i | \(-0.302681\pi\) | ||||
0.580950 | + | 0.813939i | \(0.302681\pi\) | |||||||
\(432\) | 520.497 | 0.0579686 | ||||||||
\(433\) | 11875.6 | 1.31803 | 0.659015 | − | 0.752129i | \(-0.270973\pi\) | ||||
0.659015 | + | 0.752129i | \(0.270973\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −217.435 | −0.0238836 | ||||||||
\(437\) | −8233.81 | −0.901320 | ||||||||
\(438\) | 23430.4 | 2.55605 | ||||||||
\(439\) | −640.369 | −0.0696200 | −0.0348100 | − | 0.999394i | \(-0.511083\pi\) | ||||
−0.0348100 | + | 0.999394i | \(0.511083\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 24305.5 | 2.61560 | ||||||||
\(443\) | 854.852 | 0.0916823 | 0.0458411 | − | 0.998949i | \(-0.485403\pi\) | ||||
0.0458411 | + | 0.998949i | \(0.485403\pi\) | |||||||
\(444\) | −9318.50 | −0.996028 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 7798.46 | 0.827954 | ||||||||
\(447\) | 9147.56 | 0.967930 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3427.44 | 0.360247 | 0.180123 | − | 0.983644i | \(-0.442350\pi\) | ||||
0.180123 | + | 0.983644i | \(0.442350\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11727.2 | 1.22442 | ||||||||
\(452\) | −739.176 | −0.0769202 | ||||||||
\(453\) | 13546.5 | 1.40501 | ||||||||
\(454\) | 25786.6 | 2.66569 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −8773.79 | −0.901032 | ||||||||
\(457\) | −1709.31 | −0.174963 | −0.0874814 | − | 0.996166i | \(-0.527882\pi\) | ||||
−0.0874814 | + | 0.996166i | \(0.527882\pi\) | |||||||
\(458\) | −14001.7 | −1.42851 | ||||||||
\(459\) | 5615.56 | 0.571050 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2251.18 | −0.227436 | −0.113718 | − | 0.993513i | \(-0.536276\pi\) | ||||
−0.113718 | + | 0.993513i | \(0.536276\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3200.80 | 0.321282 | 0.160641 | − | 0.987013i | \(-0.448644\pi\) | ||||
0.160641 | + | 0.987013i | \(0.448644\pi\) | |||||||
\(464\) | −1257.51 | −0.125816 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 18129.3 | 1.80219 | ||||||||
\(467\) | 5477.39 | 0.542748 | 0.271374 | − | 0.962474i | \(-0.412522\pi\) | ||||
0.271374 | + | 0.962474i | \(0.412522\pi\) | |||||||
\(468\) | 14000.9 | 1.38289 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4587.75 | −0.448816 | ||||||||
\(472\) | 4220.11 | 0.411538 | ||||||||
\(473\) | −22332.0 | −2.17088 | ||||||||
\(474\) | 13726.6 | 1.33014 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8655.60 | −0.830844 | ||||||||
\(478\) | 20407.0 | 1.95271 | ||||||||
\(479\) | 14182.0 | 1.35280 | 0.676399 | − | 0.736535i | \(-0.263539\pi\) | ||||
0.676399 | + | 0.736535i | \(0.263539\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8625.20 | −0.817620 | ||||||||
\(482\) | 16477.2 | 1.55709 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 20011.8 | 1.87940 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 17021.7 | 1.58872 | ||||||||
\(487\) | 5320.83 | 0.495092 | 0.247546 | − | 0.968876i | \(-0.420376\pi\) | ||||
0.247546 | + | 0.968876i | \(0.420376\pi\) | |||||||
\(488\) | −3366.56 | −0.312289 | ||||||||
\(489\) | −21184.8 | −1.95912 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6574.80 | −0.604311 | −0.302155 | − | 0.953259i | \(-0.597706\pi\) | ||||
−0.302155 | + | 0.953259i | \(0.597706\pi\) | |||||||
\(492\) | −17625.3 | −1.61506 | ||||||||
\(493\) | −13567.1 | −1.23941 | ||||||||
\(494\) | −22346.2 | −2.03523 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1275.34 | −0.115453 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 9100.49 | 0.818881 | ||||||||
\(499\) | −1507.68 | −0.135256 | −0.0676282 | − | 0.997711i | \(-0.521543\pi\) | ||||
−0.0676282 | + | 0.997711i | \(0.521543\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 18497.8 | 1.64955 | ||||||||
\(502\) | −5492.95 | −0.488371 | ||||||||
\(503\) | −8782.24 | −0.778491 | −0.389245 | − | 0.921134i | \(-0.627264\pi\) | ||||
−0.389245 | + | 0.921134i | \(0.627264\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −30819.4 | −2.70768 | ||||||||
\(507\) | 22375.9 | 1.96005 | ||||||||
\(508\) | −23400.4 | −2.04375 | ||||||||
\(509\) | −12696.6 | −1.10563 | −0.552815 | − | 0.833304i | \(-0.686447\pi\) | ||||
−0.552815 | + | 0.833304i | \(0.686447\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −2386.50 | −0.205995 | ||||||||
\(513\) | −5162.88 | −0.444341 | ||||||||
\(514\) | 28234.7 | 2.42291 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 33563.7 | 2.86349 | ||||||||
\(517\) | 6139.76 | 0.522295 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18127.6 | 1.53317 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10434.7 | 0.877455 | 0.438727 | − | 0.898620i | \(-0.355429\pi\) | ||||
0.438727 | + | 0.898620i | \(0.355429\pi\) | |||||||
\(522\) | −12790.2 | −1.07243 | ||||||||
\(523\) | −8403.03 | −0.702560 | −0.351280 | − | 0.936270i | \(-0.614254\pi\) | ||||
−0.351280 | + | 0.936270i | \(0.614254\pi\) | |||||||
\(524\) | −9741.55 | −0.812140 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3434.78 | −0.284722 | ||||||||
\(527\) | −13759.4 | −1.13733 | ||||||||
\(528\) | 2309.02 | 0.190317 | ||||||||
\(529\) | 3630.43 | 0.298384 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3017.91 | −0.246640 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −16314.0 | −1.32577 | ||||||||
\(534\) | 38559.4 | 3.12477 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 9890.85 | 0.797052 | ||||||||
\(537\) | 1607.61 | 0.129187 | ||||||||
\(538\) | 7939.11 | 0.636207 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8349.66 | 0.663549 | 0.331775 | − | 0.943359i | \(-0.392353\pi\) | ||||
0.331775 | + | 0.943359i | \(0.392353\pi\) | |||||||
\(542\) | 20189.6 | 1.60004 | ||||||||
\(543\) | −13421.0 | −1.06068 | ||||||||
\(544\) | −13940.8 | −1.09873 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12185.7 | −0.952509 | −0.476254 | − | 0.879308i | \(-0.658006\pi\) | ||||
−0.476254 | + | 0.879308i | \(0.658006\pi\) | |||||||
\(548\) | 12918.4 | 1.00702 | ||||||||
\(549\) | 2407.51 | 0.187159 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12473.4 | 0.964402 | ||||||||
\(552\) | 16833.4 | 1.29797 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −34882.6 | −2.67512 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 12939.9 | 0.987004 | ||||||||
\(557\) | 540.209 | 0.0410940 | 0.0205470 | − | 0.999789i | \(-0.493459\pi\) | ||||
0.0205470 | + | 0.999789i | \(0.493459\pi\) | |||||||
\(558\) | −12971.5 | −0.984103 | ||||||||
\(559\) | 31066.6 | 2.35058 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 24911.6 | 1.87481 | ||||||||
\(562\) | 902.639 | 0.0677501 | ||||||||
\(563\) | −1949.26 | −0.145917 | −0.0729587 | − | 0.997335i | \(-0.523244\pi\) | ||||
−0.0729587 | + | 0.997335i | \(0.523244\pi\) | |||||||
\(564\) | −9227.71 | −0.688930 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 3624.94 | 0.269200 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −17031.6 | −1.25815 | ||||||||
\(569\) | 9487.28 | 0.698994 | 0.349497 | − | 0.936938i | \(-0.386353\pi\) | ||||
0.349497 | + | 0.936938i | \(0.386353\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20172.3 | −1.47843 | −0.739215 | − | 0.673470i | \(-0.764803\pi\) | ||||
−0.739215 | + | 0.673470i | \(0.764803\pi\) | |||||||
\(572\) | −51108.0 | −3.73590 | ||||||||
\(573\) | −8101.87 | −0.590681 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −12360.0 | −0.894094 | ||||||||
\(577\) | 12937.3 | 0.933423 | 0.466712 | − | 0.884410i | \(-0.345439\pi\) | ||||
0.466712 | + | 0.884410i | \(0.345439\pi\) | |||||||
\(578\) | −744.254 | −0.0535586 | ||||||||
\(579\) | −10359.6 | −0.743577 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 38552.2 | 2.74578 | ||||||||
\(583\) | 31595.7 | 2.24453 | ||||||||
\(584\) | 16549.0 | 1.17261 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14978.3 | −1.05588 | ||||||||
\(587\) | −6489.43 | −0.456299 | −0.228149 | − | 0.973626i | \(-0.573267\pi\) | ||||
−0.228149 | + | 0.973626i | \(0.573267\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12650.3 | 0.884968 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −15172.2 | −1.05601 | ||||||||
\(592\) | 757.345 | 0.0525789 | ||||||||
\(593\) | −16803.6 | −1.16364 | −0.581821 | − | 0.813317i | \(-0.697660\pi\) | ||||
−0.581821 | + | 0.813317i | \(0.697660\pi\) | |||||||
\(594\) | −19324.8 | −1.33486 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 17778.3 | 1.22186 | ||||||||
\(597\) | 12890.6 | 0.883716 | ||||||||
\(598\) | 42873.5 | 2.93182 | ||||||||
\(599\) | 19139.6 | 1.30554 | 0.652772 | − | 0.757554i | \(-0.273606\pi\) | ||||
0.652772 | + | 0.757554i | \(0.273606\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14304.0 | −0.970838 | −0.485419 | − | 0.874282i | \(-0.661333\pi\) | ||||
−0.485419 | + | 0.874282i | \(0.661333\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7073.21 | −0.477684 | ||||||||
\(604\) | 26327.7 | 1.77361 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −11766.3 | −0.788738 | ||||||||
\(607\) | −2018.10 | −0.134946 | −0.0674730 | − | 0.997721i | \(-0.521494\pi\) | ||||
−0.0674730 | + | 0.997721i | \(0.521494\pi\) | |||||||
\(608\) | 12817.1 | 0.854935 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8541.17 | −0.565530 | ||||||||
\(612\) | −13263.4 | −0.876050 | ||||||||
\(613\) | −21479.4 | −1.41524 | −0.707621 | − | 0.706592i | \(-0.750232\pi\) | ||||
−0.707621 | + | 0.706592i | \(0.750232\pi\) | |||||||
\(614\) | 39129.6 | 2.57189 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5856.83 | 0.382151 | 0.191075 | − | 0.981575i | \(-0.438803\pi\) | ||||
0.191075 | + | 0.981575i | \(0.438803\pi\) | |||||||
\(618\) | −8558.31 | −0.557065 | ||||||||
\(619\) | 17619.3 | 1.14407 | 0.572035 | − | 0.820229i | \(-0.306154\pi\) | ||||
0.572035 | + | 0.820229i | \(0.306154\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9905.53 | 0.640089 | ||||||||
\(622\) | −22224.7 | −1.43269 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −3212.13 | −0.206071 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 41334.1 | 2.63904 | ||||||||
\(627\) | −22903.5 | −1.45882 | ||||||||
\(628\) | −8916.31 | −0.566560 | ||||||||
\(629\) | 8170.87 | 0.517955 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26395.7 | 1.66529 | 0.832643 | − | 0.553810i | \(-0.186827\pi\) | ||||
0.832643 | + | 0.553810i | \(0.186827\pi\) | |||||||
\(632\) | 9695.19 | 0.610212 | ||||||||
\(633\) | −37843.9 | −2.37624 | ||||||||
\(634\) | −36384.3 | −2.27919 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −47486.6 | −2.96064 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 46688.3 | 2.89719 | ||||||||
\(639\) | 12179.8 | 0.754029 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3209.30 | 0.197753 | 0.0988764 | − | 0.995100i | \(-0.468475\pi\) | ||||
0.0988764 | + | 0.995100i | \(0.468475\pi\) | |||||||
\(642\) | −643.959 | −0.0395873 | ||||||||
\(643\) | −1762.48 | −0.108096 | −0.0540478 | − | 0.998538i | \(-0.517212\pi\) | ||||
−0.0540478 | + | 0.998538i | \(0.517212\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 21169.1 | 1.28930 | ||||||||
\(647\) | −24372.7 | −1.48098 | −0.740488 | − | 0.672070i | \(-0.765405\pi\) | ||||
−0.740488 | + | 0.672070i | \(0.765405\pi\) | |||||||
\(648\) | 18838.5 | 1.14205 | ||||||||
\(649\) | 11016.3 | 0.666301 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −41172.8 | −2.47308 | ||||||||
\(653\) | −6389.97 | −0.382938 | −0.191469 | − | 0.981499i | \(-0.561325\pi\) | ||||
−0.191469 | + | 0.981499i | \(0.561325\pi\) | |||||||
\(654\) | 507.377 | 0.0303364 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1432.47 | 0.0852567 | ||||||||
\(657\) | −11834.6 | −0.702760 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6111.68 | −0.361270 | −0.180635 | − | 0.983550i | \(-0.557815\pi\) | ||||
−0.180635 | + | 0.983550i | \(0.557815\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16391.1 | −0.964510 | −0.482255 | − | 0.876031i | \(-0.660182\pi\) | ||||
−0.482255 | + | 0.876031i | \(0.660182\pi\) | |||||||
\(662\) | 6047.92 | 0.355074 | ||||||||
\(663\) | −34655.2 | −2.03001 | ||||||||
\(664\) | 6427.72 | 0.375669 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 7702.98 | 0.448175 | ||||||||
\(667\) | −23931.6 | −1.38926 | ||||||||
\(668\) | 35950.6 | 2.08229 | ||||||||
\(669\) | −11119.2 | −0.642588 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8788.20 | −0.505611 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13055.9 | 0.747799 | 0.373900 | − | 0.927469i | \(-0.378020\pi\) | ||||
0.373900 | + | 0.927469i | \(0.378020\pi\) | |||||||
\(674\) | −7652.20 | −0.437317 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 43487.6 | 2.47426 | ||||||||
\(677\) | −3154.53 | −0.179082 | −0.0895410 | − | 0.995983i | \(-0.528540\pi\) | ||||
−0.0895410 | + | 0.995983i | \(0.528540\pi\) | |||||||
\(678\) | 1724.84 | 0.0977022 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −36766.9 | −2.06888 | ||||||||
\(682\) | 47350.4 | 2.65856 | ||||||||
\(683\) | −17282.7 | −0.968233 | −0.484117 | − | 0.875004i | \(-0.660859\pi\) | ||||
−0.484117 | + | 0.875004i | \(0.660859\pi\) | |||||||
\(684\) | 12194.3 | 0.681666 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 19963.8 | 1.10869 | ||||||||
\(688\) | −2727.83 | −0.151159 | ||||||||
\(689\) | −43953.6 | −2.43033 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26838.3 | −1.47753 | −0.738766 | − | 0.673961i | \(-0.764591\pi\) | ||||
−0.738766 | + | 0.673961i | \(0.764591\pi\) | |||||||
\(692\) | 35231.1 | 1.93538 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 27007.3 | 1.47721 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −25501.0 | −1.38881 | ||||||||
\(697\) | 15454.6 | 0.839866 | ||||||||
\(698\) | 31186.0 | 1.69113 | ||||||||
\(699\) | −25849.0 | −1.39871 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8374.52 | −0.451214 | −0.225607 | − | 0.974218i | \(-0.572437\pi\) | ||||
−0.225607 | + | 0.974218i | \(0.572437\pi\) | |||||||
\(702\) | 26883.2 | 1.44536 | ||||||||
\(703\) | −7512.21 | −0.403028 | ||||||||
\(704\) | 45117.9 | 2.41540 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6330.79 | −0.337482 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −16556.9 | −0.878881 | ||||||||
\(709\) | 11929.4 | 0.631902 | 0.315951 | − | 0.948775i | \(-0.397676\pi\) | ||||
0.315951 | + | 0.948775i | \(0.397676\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6933.28 | −0.365708 | ||||||||
\(712\) | 27234.7 | 1.43352 | ||||||||
\(713\) | −24270.9 | −1.27483 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3124.40 | 0.163078 | ||||||||
\(717\) | −29096.6 | −1.51553 | ||||||||
\(718\) | 1736.89 | 0.0902788 | ||||||||
\(719\) | 23392.3 | 1.21333 | 0.606666 | − | 0.794957i | \(-0.292507\pi\) | ||||
0.606666 | + | 0.794957i | \(0.292507\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 11643.6 | 0.600179 | ||||||||
\(723\) | −23493.4 | −1.20848 | ||||||||
\(724\) | −26083.8 | −1.33894 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −46696.8 | −2.38717 | ||||||||
\(727\) | 10659.8 | 0.543810 | 0.271905 | − | 0.962324i | \(-0.412346\pi\) | ||||
0.271905 | + | 0.962324i | \(0.412346\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 287.476 | 0.0146053 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −29430.1 | −1.48907 | ||||||||
\(732\) | 13208.2 | 0.666923 | ||||||||
\(733\) | 23919.1 | 1.20528 | 0.602642 | − | 0.798011i | \(-0.294115\pi\) | ||||
0.602642 | + | 0.798011i | \(0.294115\pi\) | |||||||
\(734\) | 46160.2 | 2.32126 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −24590.9 | −1.23157 | ||||||||
\(737\) | 25819.5 | 1.29047 | ||||||||
\(738\) | 14569.7 | 0.726717 | ||||||||
\(739\) | 34535.1 | 1.71907 | 0.859536 | − | 0.511074i | \(-0.170752\pi\) | ||||
0.859536 | + | 0.511074i | \(0.170752\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 31861.6 | 1.57957 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −17526.8 | −0.865403 | −0.432702 | − | 0.901537i | \(-0.642440\pi\) | ||||
−0.432702 | + | 0.901537i | \(0.642440\pi\) | |||||||
\(744\) | −25862.6 | −1.27442 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −13564.5 | −0.665725 | ||||||||
\(747\) | −4596.63 | −0.225143 | ||||||||
\(748\) | 48415.9 | 2.36666 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18534.3 | 0.900565 | 0.450283 | − | 0.892886i | \(-0.351323\pi\) | ||||
0.450283 | + | 0.892886i | \(0.351323\pi\) | |||||||
\(752\) | 749.966 | 0.0363676 | ||||||||
\(753\) | 7831.94 | 0.379033 | ||||||||
\(754\) | −64949.2 | −3.13702 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9309.64 | 0.446981 | 0.223491 | − | 0.974706i | \(-0.428255\pi\) | ||||
0.223491 | + | 0.974706i | \(0.428255\pi\) | |||||||
\(758\) | −33562.7 | −1.60825 | ||||||||
\(759\) | 43942.7 | 2.10148 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2968.41 | 0.141399 | 0.0706996 | − | 0.997498i | \(-0.477477\pi\) | ||||
0.0706996 | + | 0.997498i | \(0.477477\pi\) | |||||||
\(762\) | 54604.0 | 2.59592 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −15746.0 | −0.745643 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 48841.1 | 2.30379 | ||||||||
\(767\) | −15325.1 | −0.721457 | ||||||||
\(768\) | −21910.1 | −1.02944 | ||||||||
\(769\) | 34932.9 | 1.63812 | 0.819060 | − | 0.573708i | \(-0.194495\pi\) | ||||
0.819060 | + | 0.573708i | \(0.194495\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −40257.5 | −1.88046 | ||||||||
\(772\) | −20134.0 | −0.938650 | ||||||||
\(773\) | −13595.4 | −0.632591 | −0.316295 | − | 0.948661i | \(-0.602439\pi\) | ||||
−0.316295 | + | 0.948661i | \(0.602439\pi\) | |||||||
\(774\) | −27744.9 | −1.28846 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 27229.7 | 1.25965 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 50762.9 | 2.33925 | ||||||||
\(779\) | −14208.8 | −0.653510 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −44460.1 | −2.03701 | ||||||||
\(782\) | −40615.2 | −1.85728 | ||||||||
\(783\) | −15005.9 | −0.684888 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 22731.6 | 1.03156 | ||||||||
\(787\) | −14228.1 | −0.644444 | −0.322222 | − | 0.946664i | \(-0.604430\pi\) | ||||
−0.322222 | + | 0.946664i | \(0.604430\pi\) | |||||||
\(788\) | −29487.3 | −1.33305 | ||||||||
\(789\) | 4897.36 | 0.220977 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 16587.7 | 0.744213 | ||||||||
\(793\) | 12225.5 | 0.547465 | ||||||||
\(794\) | −47037.5 | −2.10239 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 25053.0 | 1.11555 | ||||||||
\(797\) | 11442.3 | 0.508539 | 0.254270 | − | 0.967133i | \(-0.418165\pi\) | ||||
0.254270 | + | 0.967133i | \(0.418165\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8091.26 | 0.358258 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −19476.2 | −0.859125 | ||||||||
\(802\) | −24499.5 | −1.07869 | ||||||||
\(803\) | 43200.3 | 1.89851 | ||||||||
\(804\) | −38805.2 | −1.70218 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −65870.2 | −2.87863 | ||||||||
\(807\) | −11319.7 | −0.493770 | ||||||||
\(808\) | −8310.63 | −0.361840 | ||||||||
\(809\) | 22732.9 | 0.987944 | 0.493972 | − | 0.869478i | \(-0.335545\pi\) | ||||
0.493972 | + | 0.869478i | \(0.335545\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29768.2 | 1.28890 | 0.644452 | − | 0.764644i | \(-0.277085\pi\) | ||||
0.644452 | + | 0.764644i | \(0.277085\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −28786.7 | −1.24181 | ||||||||
\(814\) | −28118.4 | −1.21075 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3042.93 | 0.130544 | ||||||||
\(817\) | 27057.7 | 1.15867 | ||||||||
\(818\) | −58185.0 | −2.48703 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6408.35 | 0.272416 | 0.136208 | − | 0.990680i | \(-0.456509\pi\) | ||||
0.136208 | + | 0.990680i | \(0.456509\pi\) | |||||||
\(822\) | −30144.6 | −1.27909 | ||||||||
\(823\) | 20876.0 | 0.884194 | 0.442097 | − | 0.896967i | \(-0.354235\pi\) | ||||
0.442097 | + | 0.896967i | \(0.354235\pi\) | |||||||
\(824\) | −6044.78 | −0.255558 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 41650.1 | 1.75129 | 0.875645 | − | 0.482955i | \(-0.160437\pi\) | ||||
0.875645 | + | 0.482955i | \(0.160437\pi\) | |||||||
\(828\) | −23396.0 | −0.981964 | ||||||||
\(829\) | −17194.7 | −0.720380 | −0.360190 | − | 0.932879i | \(-0.617288\pi\) | ||||
−0.360190 | + | 0.932879i | \(0.617288\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 49736.1 | 2.07621 | ||||||||
\(832\) | −62764.5 | −2.61535 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −30194.8 | −1.25367 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −44513.0 | −1.84153 | ||||||||
\(837\) | −15218.7 | −0.628477 | ||||||||
\(838\) | 25491.1 | 1.05081 | ||||||||
\(839\) | −40583.7 | −1.66997 | −0.834985 | − | 0.550273i | \(-0.814524\pi\) | ||||
−0.834985 | + | 0.550273i | \(0.814524\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11865.0 | 0.486489 | ||||||||
\(842\) | 9873.42 | 0.404110 | ||||||||
\(843\) | −1287.00 | −0.0525819 | ||||||||
\(844\) | −73549.7 | −2.99963 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 7627.93 | 0.309993 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 3859.39 | 0.156288 | ||||||||
\(849\) | −5168.49 | −0.208931 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14413.0 | 0.580576 | ||||||||
\(852\) | 66821.0 | 2.68691 | ||||||||
\(853\) | 23020.1 | 0.924023 | 0.462012 | − | 0.886874i | \(-0.347128\pi\) | ||||
0.462012 | + | 0.886874i | \(0.347128\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −454.832 | −0.0181610 | ||||||||
\(857\) | −18075.5 | −0.720476 | −0.360238 | − | 0.932861i | \(-0.617304\pi\) | ||||
−0.360238 | + | 0.932861i | \(0.617304\pi\) | |||||||
\(858\) | 119259. | 4.74525 | ||||||||
\(859\) | −20308.2 | −0.806643 | −0.403321 | − | 0.915058i | \(-0.632144\pi\) | ||||
−0.403321 | + | 0.915058i | \(0.632144\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −47148.9 | −1.86299 | ||||||||
\(863\) | 31023.5 | 1.22370 | 0.611849 | − | 0.790975i | \(-0.290426\pi\) | ||||
0.611849 | + | 0.790975i | \(0.290426\pi\) | |||||||
\(864\) | −15419.3 | −0.607148 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −53857.2 | −2.11333 | ||||||||
\(867\) | 1061.17 | 0.0415677 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 25308.7 | 0.987963 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −35918.1 | −1.39729 | ||||||||
\(872\) | 358.363 | 0.0139171 | ||||||||
\(873\) | −19472.6 | −0.754924 | ||||||||
\(874\) | 37341.2 | 1.44518 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −64927.5 | −2.50422 | ||||||||
\(877\) | 28344.1 | 1.09135 | 0.545674 | − | 0.837997i | \(-0.316274\pi\) | ||||
0.545674 | + | 0.837997i | \(0.316274\pi\) | |||||||
\(878\) | 2904.14 | 0.111629 | ||||||||
\(879\) | 21356.3 | 0.819488 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −41264.5 | −1.57802 | −0.789010 | − | 0.614380i | \(-0.789406\pi\) | ||||
−0.789010 | + | 0.614380i | \(0.789406\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7995.59 | 0.304726 | 0.152363 | − | 0.988325i | \(-0.451312\pi\) | ||||
0.152363 | + | 0.988325i | \(0.451312\pi\) | |||||||
\(884\) | −67352.5 | −2.56257 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3876.84 | −0.147003 | ||||||||
\(887\) | 24438.3 | 0.925093 | 0.462547 | − | 0.886595i | \(-0.346936\pi\) | ||||
0.462547 | + | 0.886595i | \(0.346936\pi\) | |||||||
\(888\) | 15358.2 | 0.580390 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 49176.8 | 1.84903 | ||||||||
\(892\) | −21610.1 | −0.811167 | ||||||||
\(893\) | −7439.02 | −0.278765 | ||||||||
\(894\) | −41485.1 | −1.55198 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −61129.8 | −2.27543 | ||||||||
\(898\) | −15543.8 | −0.577620 | ||||||||
\(899\) | 36768.0 | 1.36405 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 41638.3 | 1.53959 | ||||||||
\(902\) | −53184.0 | −1.96323 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1218.26 | 0.0448218 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −61434.7 | −2.25279 | ||||||||
\(907\) | −17241.6 | −0.631201 | −0.315601 | − | 0.948892i | \(-0.602206\pi\) | ||||
−0.315601 | + | 0.948892i | \(0.602206\pi\) | |||||||
\(908\) | −71456.6 | −2.61164 | ||||||||
\(909\) | 5943.15 | 0.216856 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17407.8 | 0.633092 | 0.316546 | − | 0.948577i | \(-0.397477\pi\) | ||||
0.316546 | + | 0.948577i | \(0.397477\pi\) | |||||||
\(912\) | −2797.64 | −0.101578 | ||||||||
\(913\) | 16779.2 | 0.608226 | ||||||||
\(914\) | 7751.87 | 0.280535 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 38799.8 | 1.39954 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −25467.1 | −0.915621 | ||||||||
\(919\) | 7704.64 | 0.276553 | 0.138277 | − | 0.990394i | \(-0.455844\pi\) | ||||
0.138277 | + | 0.990394i | \(0.455844\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −55791.6 | −1.99609 | ||||||||
\(922\) | 10209.3 | 0.364671 | ||||||||
\(923\) | 61849.5 | 2.20564 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −14515.9 | −0.515144 | ||||||||
\(927\) | 4322.78 | 0.153159 | ||||||||
\(928\) | 37252.8 | 1.31776 | ||||||||
\(929\) | 48184.3 | 1.70170 | 0.850849 | − | 0.525411i | \(-0.176088\pi\) | ||||
0.850849 | + | 0.525411i | \(0.176088\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −50237.7 | −1.76565 | ||||||||
\(933\) | 31688.4 | 1.11193 | ||||||||
\(934\) | −24840.5 | −0.870242 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −23075.5 | −0.805818 | ||||||||
\(937\) | 23371.6 | 0.814853 | 0.407427 | − | 0.913238i | \(-0.366426\pi\) | ||||
0.407427 | + | 0.913238i | \(0.366426\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −58934.7 | −2.04820 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −18048.6 | −0.625258 | −0.312629 | − | 0.949875i | \(-0.601210\pi\) | ||||
−0.312629 | + | 0.949875i | \(0.601210\pi\) | |||||||
\(942\) | 20805.9 | 0.719631 | ||||||||
\(943\) | 27261.1 | 0.941405 | ||||||||
\(944\) | 1345.64 | 0.0463948 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 101278. | 3.48079 | ||||||||
\(947\) | −10346.2 | −0.355022 | −0.177511 | − | 0.984119i | \(-0.556805\pi\) | ||||
−0.177511 | + | 0.984119i | \(0.556805\pi\) | |||||||
\(948\) | −38037.6 | −1.30317 | ||||||||
\(949\) | −60096.9 | −2.05567 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 51877.3 | 1.76891 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8691.77 | −0.295440 | −0.147720 | − | 0.989029i | \(-0.547193\pi\) | ||||
−0.147720 | + | 0.989029i | \(0.547193\pi\) | |||||||
\(954\) | 39254.0 | 1.33217 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −56549.5 | −1.91312 | ||||||||
\(957\) | −66568.9 | −2.24856 | ||||||||
\(958\) | −64316.6 | −2.16908 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7498.41 | 0.251701 | ||||||||
\(962\) | 39116.2 | 1.31097 | ||||||||
\(963\) | 325.262 | 0.0108841 | ||||||||
\(964\) | −45659.6 | −1.52552 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8971.58 | −0.298352 | −0.149176 | − | 0.988811i | \(-0.547662\pi\) | ||||
−0.149176 | + | 0.988811i | \(0.547662\pi\) | |||||||
\(968\) | −32982.2 | −1.09513 | ||||||||
\(969\) | −30183.3 | −1.00065 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −29275.1 | −0.967541 | −0.483771 | − | 0.875195i | \(-0.660733\pi\) | ||||
−0.483771 | + | 0.875195i | \(0.660733\pi\) | |||||||
\(972\) | −47168.5 | −1.55651 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −24130.5 | −0.793831 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1073.47 | −0.0352059 | ||||||||
\(977\) | 16477.5 | 0.539572 | 0.269786 | − | 0.962920i | \(-0.413047\pi\) | ||||
0.269786 | + | 0.962920i | \(0.413047\pi\) | |||||||
\(978\) | 96075.2 | 3.14125 | ||||||||
\(979\) | 71094.6 | 2.32093 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −256.275 | −0.00834071 | ||||||||
\(982\) | 29817.4 | 0.968952 | ||||||||
\(983\) | 45912.9 | 1.48972 | 0.744859 | − | 0.667222i | \(-0.232517\pi\) | ||||
0.744859 | + | 0.667222i | \(0.232517\pi\) | |||||||
\(984\) | 29048.9 | 0.941104 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 61528.0 | 1.98727 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 61923.2 | 1.99397 | ||||||||
\(989\) | −51913.1 | −1.66910 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 46124.8 | 1.47851 | 0.739255 | − | 0.673426i | \(-0.235178\pi\) | ||||
0.739255 | + | 0.673426i | \(0.235178\pi\) | |||||||
\(992\) | 37781.0 | 1.20922 | ||||||||
\(993\) | −8623.22 | −0.275579 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −25218.2 | −0.802278 | ||||||||
\(997\) | −30984.5 | −0.984240 | −0.492120 | − | 0.870527i | \(-0.663778\pi\) | ||||
−0.492120 | + | 0.870527i | \(0.663778\pi\) | |||||||
\(998\) | 6837.47 | 0.216870 | ||||||||
\(999\) | 9037.42 | 0.286218 |
(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 | 1225.4.a.z.1.2 | 4 | ||
5.4 | even | 2 | 1225.4.a.bd.1.3 | 4 | |||
7.6 | odd | 2 | 175.4.a.g.1.2 | ✓ | 4 | ||
21.20 | even | 2 | 1575.4.a.bl.1.3 | 4 | |||
35.13 | even | 4 | 175.4.b.f.99.6 | 8 | |||
35.27 | even | 4 | 175.4.b.f.99.3 | 8 | |||
35.34 | odd | 2 | 175.4.a.h.1.3 | yes | 4 | ||
105.104 | even | 2 | 1575.4.a.bg.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
175.4.a.g.1.2 | ✓ | 4 | 7.6 | odd | 2 | ||
175.4.a.h.1.3 | yes | 4 | 35.34 | odd | 2 | ||
175.4.b.f.99.3 | 8 | 35.27 | even | 4 | |||
175.4.b.f.99.6 | 8 | 35.13 | even | 4 | |||
1225.4.a.z.1.2 | 4 | 1.1 | even | 1 | trivial | ||
1225.4.a.bd.1.3 | 4 | 5.4 | even | 2 | |||
1575.4.a.bg.1.2 | 4 | 105.104 | even | 2 | |||
1575.4.a.bl.1.3 | 4 | 21.20 | even | 2 |