Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1849,4,Mod(1,1849)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1849, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1849.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1849 = 43^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1849.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: | \(109.094531601\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 62x^{8} + 1289x^{6} - 11252x^{4} + 39376x^{2} - 35688 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-3.05512\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1849.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.05512 | −1.08015 | −0.540074 | − | 0.841618i | \(-0.681604\pi\) | ||||
−0.540074 | + | 0.841618i | \(0.681604\pi\) | |||||||
\(3\) | −4.99167 | −0.960647 | −0.480323 | − | 0.877091i | \(-0.659481\pi\) | ||||
−0.480323 | + | 0.877091i | \(0.659481\pi\) | |||||||
\(4\) | 1.33374 | 0.166718 | ||||||||
\(5\) | 15.7813 | 1.41152 | 0.705759 | − | 0.708452i | \(-0.250606\pi\) | ||||
0.705759 | + | 0.708452i | \(0.250606\pi\) | |||||||
\(6\) | 15.2501 | 1.03764 | ||||||||
\(7\) | −15.1156 | −0.816168 | −0.408084 | − | 0.912944i | \(-0.633803\pi\) | ||||
−0.408084 | + | 0.912944i | \(0.633803\pi\) | |||||||
\(8\) | 20.3662 | 0.900068 | ||||||||
\(9\) | −2.08325 | −0.0771575 | ||||||||
\(10\) | −48.2136 | −1.52465 | ||||||||
\(11\) | −21.4756 | −0.588648 | −0.294324 | − | 0.955706i | \(-0.595094\pi\) | ||||
−0.294324 | + | 0.955706i | \(0.595094\pi\) | |||||||
\(12\) | −6.65759 | −0.160157 | ||||||||
\(13\) | 59.1204 | 1.26131 | 0.630656 | − | 0.776063i | \(-0.282786\pi\) | ||||
0.630656 | + | 0.776063i | \(0.282786\pi\) | |||||||
\(14\) | 46.1801 | 0.881581 | ||||||||
\(15\) | −78.7748 | −1.35597 | ||||||||
\(16\) | −72.8911 | −1.13892 | ||||||||
\(17\) | −89.2363 | −1.27312 | −0.636558 | − | 0.771228i | \(-0.719643\pi\) | ||||
−0.636558 | + | 0.771228i | \(0.719643\pi\) | |||||||
\(18\) | 6.36458 | 0.0833414 | ||||||||
\(19\) | 3.71618 | 0.0448711 | 0.0224355 | − | 0.999748i | \(-0.492858\pi\) | ||||
0.0224355 | + | 0.999748i | \(0.492858\pi\) | |||||||
\(20\) | 21.0481 | 0.235325 | ||||||||
\(21\) | 75.4523 | 0.784049 | ||||||||
\(22\) | 65.6104 | 0.635827 | ||||||||
\(23\) | 132.040 | 1.19705 | 0.598526 | − | 0.801103i | \(-0.295753\pi\) | ||||
0.598526 | + | 0.801103i | \(0.295753\pi\) | |||||||
\(24\) | −101.661 | −0.864647 | ||||||||
\(25\) | 124.048 | 0.992384 | ||||||||
\(26\) | −180.620 | −1.36240 | ||||||||
\(27\) | 145.174 | 1.03477 | ||||||||
\(28\) | −20.1603 | −0.136070 | ||||||||
\(29\) | −220.497 | −1.41191 | −0.705954 | − | 0.708257i | \(-0.749482\pi\) | ||||
−0.705954 | + | 0.708257i | \(0.749482\pi\) | |||||||
\(30\) | 240.666 | 1.46465 | ||||||||
\(31\) | −173.787 | −1.00687 | −0.503437 | − | 0.864032i | \(-0.667931\pi\) | ||||
−0.503437 | + | 0.864032i | \(0.667931\pi\) | |||||||
\(32\) | 59.7611 | 0.330137 | ||||||||
\(33\) | 107.199 | 0.565483 | ||||||||
\(34\) | 272.627 | 1.37515 | ||||||||
\(35\) | −238.544 | −1.15204 | ||||||||
\(36\) | −2.77852 | −0.0128635 | ||||||||
\(37\) | −341.140 | −1.51576 | −0.757880 | − | 0.652394i | \(-0.773765\pi\) | ||||
−0.757880 | + | 0.652394i | \(0.773765\pi\) | |||||||
\(38\) | −11.3534 | −0.0484674 | ||||||||
\(39\) | −295.109 | −1.21167 | ||||||||
\(40\) | 321.404 | 1.27046 | ||||||||
\(41\) | 334.536 | 1.27429 | 0.637144 | − | 0.770745i | \(-0.280116\pi\) | ||||
0.637144 | + | 0.770745i | \(0.280116\pi\) | |||||||
\(42\) | −230.515 | −0.846888 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | −28.6428 | −0.0981380 | ||||||||
\(45\) | −32.8763 | −0.108909 | ||||||||
\(46\) | −403.397 | −1.29299 | ||||||||
\(47\) | 182.605 | 0.566717 | 0.283358 | − | 0.959014i | \(-0.408551\pi\) | ||||
0.283358 | + | 0.959014i | \(0.408551\pi\) | |||||||
\(48\) | 363.848 | 1.09410 | ||||||||
\(49\) | −114.517 | −0.333870 | ||||||||
\(50\) | −378.981 | −1.07192 | ||||||||
\(51\) | 445.438 | 1.22302 | ||||||||
\(52\) | 78.8513 | 0.210283 | ||||||||
\(53\) | 296.886 | 0.769442 | 0.384721 | − | 0.923033i | \(-0.374298\pi\) | ||||
0.384721 | + | 0.923033i | \(0.374298\pi\) | |||||||
\(54\) | −443.523 | −1.11770 | ||||||||
\(55\) | −338.911 | −0.830888 | ||||||||
\(56\) | −307.848 | −0.734606 | ||||||||
\(57\) | −18.5499 | −0.0431053 | ||||||||
\(58\) | 673.646 | 1.52507 | ||||||||
\(59\) | 668.255 | 1.47457 | 0.737283 | − | 0.675584i | \(-0.236109\pi\) | ||||
0.737283 | + | 0.675584i | \(0.236109\pi\) | |||||||
\(60\) | −105.065 | −0.226064 | ||||||||
\(61\) | 461.669 | 0.969026 | 0.484513 | − | 0.874784i | \(-0.338997\pi\) | ||||
0.484513 | + | 0.874784i | \(0.338997\pi\) | |||||||
\(62\) | 530.940 | 1.08757 | ||||||||
\(63\) | 31.4897 | 0.0629735 | ||||||||
\(64\) | 400.551 | 0.782327 | ||||||||
\(65\) | 932.994 | 1.78036 | ||||||||
\(66\) | −327.505 | −0.610805 | ||||||||
\(67\) | 485.027 | 0.884411 | 0.442205 | − | 0.896914i | \(-0.354196\pi\) | ||||
0.442205 | + | 0.896914i | \(0.354196\pi\) | |||||||
\(68\) | −119.018 | −0.212251 | ||||||||
\(69\) | −659.099 | −1.14994 | ||||||||
\(70\) | 728.779 | 1.24437 | ||||||||
\(71\) | −358.344 | −0.598981 | −0.299490 | − | 0.954099i | \(-0.596817\pi\) | ||||
−0.299490 | + | 0.954099i | \(0.596817\pi\) | |||||||
\(72\) | −42.4279 | −0.0694470 | ||||||||
\(73\) | 136.162 | 0.218309 | 0.109155 | − | 0.994025i | \(-0.465186\pi\) | ||||
0.109155 | + | 0.994025i | \(0.465186\pi\) | |||||||
\(74\) | 1042.22 | 1.63724 | ||||||||
\(75\) | −619.206 | −0.953330 | ||||||||
\(76\) | 4.95642 | 0.00748080 | ||||||||
\(77\) | 324.617 | 0.480436 | ||||||||
\(78\) | 901.594 | 1.30879 | ||||||||
\(79\) | −590.322 | −0.840713 | −0.420357 | − | 0.907359i | \(-0.638095\pi\) | ||||
−0.420357 | + | 0.907359i | \(0.638095\pi\) | |||||||
\(80\) | −1150.31 | −1.60761 | ||||||||
\(81\) | −668.412 | −0.916889 | ||||||||
\(82\) | −1022.05 | −1.37642 | ||||||||
\(83\) | −45.5071 | −0.0601814 | −0.0300907 | − | 0.999547i | \(-0.509580\pi\) | ||||
−0.0300907 | + | 0.999547i | \(0.509580\pi\) | |||||||
\(84\) | 100.634 | 0.130715 | ||||||||
\(85\) | −1408.26 | −1.79703 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1100.65 | 1.35635 | ||||||||
\(88\) | −437.376 | −0.529823 | ||||||||
\(89\) | −1615.18 | −1.92369 | −0.961847 | − | 0.273589i | \(-0.911789\pi\) | ||||
−0.961847 | + | 0.273589i | \(0.911789\pi\) | |||||||
\(90\) | 100.441 | 0.117638 | ||||||||
\(91\) | −893.643 | −1.02944 | ||||||||
\(92\) | 176.107 | 0.199570 | ||||||||
\(93\) | 867.487 | 0.967250 | ||||||||
\(94\) | −557.880 | −0.612137 | ||||||||
\(95\) | 58.6460 | 0.0633363 | ||||||||
\(96\) | −298.308 | −0.317145 | ||||||||
\(97\) | 1569.66 | 1.64303 | 0.821517 | − | 0.570184i | \(-0.193128\pi\) | ||||
0.821517 | + | 0.570184i | \(0.193128\pi\) | |||||||
\(98\) | 349.864 | 0.360629 | ||||||||
\(99\) | 44.7390 | 0.0454186 | ||||||||
\(100\) | 165.448 | 0.165448 | ||||||||
\(101\) | −1985.34 | −1.95593 | −0.977965 | − | 0.208771i | \(-0.933054\pi\) | ||||
−0.977965 | + | 0.208771i | \(0.933054\pi\) | |||||||
\(102\) | −1360.87 | −1.32104 | ||||||||
\(103\) | 119.966 | 0.114763 | 0.0573815 | − | 0.998352i | \(-0.481725\pi\) | ||||
0.0573815 | + | 0.998352i | \(0.481725\pi\) | |||||||
\(104\) | 1204.06 | 1.13527 | ||||||||
\(105\) | 1190.73 | 1.10670 | ||||||||
\(106\) | −907.021 | −0.831110 | ||||||||
\(107\) | −684.291 | −0.618252 | −0.309126 | − | 0.951021i | \(-0.600036\pi\) | ||||
−0.309126 | + | 0.951021i | \(0.600036\pi\) | |||||||
\(108\) | 193.624 | 0.172514 | ||||||||
\(109\) | −880.341 | −0.773590 | −0.386795 | − | 0.922166i | \(-0.626418\pi\) | ||||
−0.386795 | + | 0.922166i | \(0.626418\pi\) | |||||||
\(110\) | 1035.41 | 0.897481 | ||||||||
\(111\) | 1702.86 | 1.45611 | ||||||||
\(112\) | 1101.80 | 0.929552 | ||||||||
\(113\) | −1051.95 | −0.875747 | −0.437874 | − | 0.899037i | \(-0.644268\pi\) | ||||
−0.437874 | + | 0.899037i | \(0.644268\pi\) | |||||||
\(114\) | 56.6723 | 0.0465600 | ||||||||
\(115\) | 2083.75 | 1.68966 | ||||||||
\(116\) | −294.086 | −0.235390 | ||||||||
\(117\) | −123.163 | −0.0973196 | ||||||||
\(118\) | −2041.60 | −1.59275 | ||||||||
\(119\) | 1348.86 | 1.03908 | ||||||||
\(120\) | −1604.34 | −1.22047 | ||||||||
\(121\) | −869.800 | −0.653493 | ||||||||
\(122\) | −1410.45 | −1.04669 | ||||||||
\(123\) | −1669.89 | −1.22414 | ||||||||
\(124\) | −231.787 | −0.167864 | ||||||||
\(125\) | −15.0243 | −0.0107505 | ||||||||
\(126\) | −96.2047 | −0.0680206 | ||||||||
\(127\) | −594.064 | −0.415076 | −0.207538 | − | 0.978227i | \(-0.566545\pi\) | ||||
−0.207538 | + | 0.978227i | \(0.566545\pi\) | |||||||
\(128\) | −1701.82 | −1.17516 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2850.41 | −1.92305 | ||||||||
\(131\) | −1980.10 | −1.32063 | −0.660313 | − | 0.750990i | \(-0.729576\pi\) | ||||
−0.660313 | + | 0.750990i | \(0.729576\pi\) | |||||||
\(132\) | 142.976 | 0.0942760 | ||||||||
\(133\) | −56.1725 | −0.0366223 | ||||||||
\(134\) | −1481.82 | −0.955294 | ||||||||
\(135\) | 2291.03 | 1.46059 | ||||||||
\(136\) | −1817.41 | −1.14589 | ||||||||
\(137\) | 692.962 | 0.432144 | 0.216072 | − | 0.976377i | \(-0.430675\pi\) | ||||
0.216072 | + | 0.976377i | \(0.430675\pi\) | |||||||
\(138\) | 2013.62 | 1.24211 | ||||||||
\(139\) | 2752.84 | 1.67981 | 0.839903 | − | 0.542737i | \(-0.182612\pi\) | ||||
0.839903 | + | 0.542737i | \(0.182612\pi\) | |||||||
\(140\) | −318.155 | −0.192065 | ||||||||
\(141\) | −911.504 | −0.544415 | ||||||||
\(142\) | 1094.78 | 0.646987 | ||||||||
\(143\) | −1269.64 | −0.742469 | ||||||||
\(144\) | 151.850 | 0.0878764 | ||||||||
\(145\) | −3479.73 | −1.99293 | ||||||||
\(146\) | −415.991 | −0.235806 | ||||||||
\(147\) | 571.633 | 0.320731 | ||||||||
\(148\) | −454.993 | −0.252704 | ||||||||
\(149\) | 800.322 | 0.440033 | 0.220016 | − | 0.975496i | \(-0.429389\pi\) | ||||
0.220016 | + | 0.975496i | \(0.429389\pi\) | |||||||
\(150\) | 1891.75 | 1.02974 | ||||||||
\(151\) | 1188.66 | 0.640606 | 0.320303 | − | 0.947315i | \(-0.396215\pi\) | ||||
0.320303 | + | 0.947315i | \(0.396215\pi\) | |||||||
\(152\) | 75.6845 | 0.0403870 | ||||||||
\(153\) | 185.902 | 0.0982305 | ||||||||
\(154\) | −991.743 | −0.518941 | ||||||||
\(155\) | −2742.58 | −1.42122 | ||||||||
\(156\) | −393.599 | −0.202007 | ||||||||
\(157\) | 127.963 | 0.0650483 | 0.0325242 | − | 0.999471i | \(-0.489645\pi\) | ||||
0.0325242 | + | 0.999471i | \(0.489645\pi\) | |||||||
\(158\) | 1803.50 | 0.908094 | ||||||||
\(159\) | −1481.96 | −0.739162 | ||||||||
\(160\) | 943.105 | 0.465994 | ||||||||
\(161\) | −1995.87 | −0.976995 | ||||||||
\(162\) | 2042.08 | 0.990375 | ||||||||
\(163\) | −3889.35 | −1.86894 | −0.934470 | − | 0.356043i | \(-0.884126\pi\) | ||||
−0.934470 | + | 0.356043i | \(0.884126\pi\) | |||||||
\(164\) | 446.184 | 0.212446 | ||||||||
\(165\) | 1691.73 | 0.798190 | ||||||||
\(166\) | 139.030 | 0.0650047 | ||||||||
\(167\) | 2043.08 | 0.946695 | 0.473348 | − | 0.880876i | \(-0.343045\pi\) | ||||
0.473348 | + | 0.880876i | \(0.343045\pi\) | |||||||
\(168\) | 1536.68 | 0.705697 | ||||||||
\(169\) | 1298.22 | 0.590906 | ||||||||
\(170\) | 4302.40 | 1.94105 | ||||||||
\(171\) | −7.74174 | −0.00346214 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2540.34 | −1.11641 | −0.558203 | − | 0.829704i | \(-0.688509\pi\) | ||||
−0.558203 | + | 0.829704i | \(0.688509\pi\) | |||||||
\(174\) | −3362.62 | −1.46505 | ||||||||
\(175\) | −1875.06 | −0.809952 | ||||||||
\(176\) | 1565.38 | 0.670425 | ||||||||
\(177\) | −3335.71 | −1.41654 | ||||||||
\(178\) | 4934.56 | 2.07787 | ||||||||
\(179\) | 3910.87 | 1.63303 | 0.816514 | − | 0.577325i | \(-0.195904\pi\) | ||||
0.816514 | + | 0.577325i | \(0.195904\pi\) | |||||||
\(180\) | −43.8485 | −0.0181571 | ||||||||
\(181\) | 570.165 | 0.234144 | 0.117072 | − | 0.993123i | \(-0.462649\pi\) | ||||
0.117072 | + | 0.993123i | \(0.462649\pi\) | |||||||
\(182\) | 2730.18 | 1.11195 | ||||||||
\(183\) | −2304.50 | −0.930892 | ||||||||
\(184\) | 2689.15 | 1.07743 | ||||||||
\(185\) | −5383.62 | −2.13952 | ||||||||
\(186\) | −2650.28 | −1.04477 | ||||||||
\(187\) | 1916.40 | 0.749418 | ||||||||
\(188\) | 243.548 | 0.0944816 | ||||||||
\(189\) | −2194.40 | −0.844544 | ||||||||
\(190\) | −179.170 | −0.0684126 | ||||||||
\(191\) | −2303.16 | −0.872518 | −0.436259 | − | 0.899821i | \(-0.643697\pi\) | ||||
−0.436259 | + | 0.899821i | \(0.643697\pi\) | |||||||
\(192\) | −1999.42 | −0.751540 | ||||||||
\(193\) | 2322.35 | 0.866147 | 0.433074 | − | 0.901359i | \(-0.357429\pi\) | ||||
0.433074 | + | 0.901359i | \(0.357429\pi\) | |||||||
\(194\) | −4795.48 | −1.77472 | ||||||||
\(195\) | −4657.20 | −1.71030 | ||||||||
\(196\) | −152.737 | −0.0556620 | ||||||||
\(197\) | 3293.02 | 1.19095 | 0.595476 | − | 0.803373i | \(-0.296963\pi\) | ||||
0.595476 | + | 0.803373i | \(0.296963\pi\) | |||||||
\(198\) | −136.683 | −0.0490588 | ||||||||
\(199\) | −3266.88 | −1.16373 | −0.581866 | − | 0.813284i | \(-0.697677\pi\) | ||||
−0.581866 | + | 0.813284i | \(0.697677\pi\) | |||||||
\(200\) | 2526.39 | 0.893212 | ||||||||
\(201\) | −2421.10 | −0.849607 | ||||||||
\(202\) | 6065.45 | 2.11269 | ||||||||
\(203\) | 3332.96 | 1.15235 | ||||||||
\(204\) | 594.099 | 0.203898 | ||||||||
\(205\) | 5279.40 | 1.79868 | ||||||||
\(206\) | −366.510 | −0.123961 | ||||||||
\(207\) | −275.072 | −0.0923615 | ||||||||
\(208\) | −4309.35 | −1.43654 | ||||||||
\(209\) | −79.8071 | −0.0264133 | ||||||||
\(210\) | −3637.82 | −1.19540 | ||||||||
\(211\) | 2236.86 | 0.729819 | 0.364909 | − | 0.931043i | \(-0.381100\pi\) | ||||
0.364909 | + | 0.931043i | \(0.381100\pi\) | |||||||
\(212\) | 395.969 | 0.128279 | ||||||||
\(213\) | 1788.73 | 0.575409 | ||||||||
\(214\) | 2090.59 | 0.667803 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2956.64 | 0.931361 | ||||||||
\(217\) | 2626.90 | 0.821778 | ||||||||
\(218\) | 2689.54 | 0.835591 | ||||||||
\(219\) | −679.676 | −0.209718 | ||||||||
\(220\) | −452.020 | −0.138524 | ||||||||
\(221\) | −5275.69 | −1.60580 | ||||||||
\(222\) | −5202.44 | −1.57281 | ||||||||
\(223\) | 5277.70 | 1.58485 | 0.792423 | − | 0.609972i | \(-0.208819\pi\) | ||||
0.792423 | + | 0.609972i | \(0.208819\pi\) | |||||||
\(224\) | −903.327 | −0.269447 | ||||||||
\(225\) | −258.423 | −0.0765698 | ||||||||
\(226\) | 3213.84 | 0.945936 | ||||||||
\(227\) | −5243.93 | −1.53327 | −0.766635 | − | 0.642084i | \(-0.778070\pi\) | ||||
−0.766635 | + | 0.642084i | \(0.778070\pi\) | |||||||
\(228\) | −24.7408 | −0.00718641 | ||||||||
\(229\) | 1658.73 | 0.478655 | 0.239328 | − | 0.970939i | \(-0.423073\pi\) | ||||
0.239328 | + | 0.970939i | \(0.423073\pi\) | |||||||
\(230\) | −6366.11 | −1.82508 | ||||||||
\(231\) | −1620.38 | −0.461529 | ||||||||
\(232\) | −4490.70 | −1.27081 | ||||||||
\(233\) | −290.160 | −0.0815837 | −0.0407919 | − | 0.999168i | \(-0.512988\pi\) | ||||
−0.0407919 | + | 0.999168i | \(0.512988\pi\) | |||||||
\(234\) | 376.277 | 0.105120 | ||||||||
\(235\) | 2881.74 | 0.799931 | ||||||||
\(236\) | 891.278 | 0.245836 | ||||||||
\(237\) | 2946.69 | 0.807629 | ||||||||
\(238\) | −4120.94 | −1.12236 | ||||||||
\(239\) | 5851.40 | 1.58366 | 0.791832 | − | 0.610739i | \(-0.209128\pi\) | ||||
0.791832 | + | 0.610739i | \(0.209128\pi\) | |||||||
\(240\) | 5741.98 | 1.54435 | ||||||||
\(241\) | −1736.35 | −0.464100 | −0.232050 | − | 0.972704i | \(-0.574543\pi\) | ||||
−0.232050 | + | 0.972704i | \(0.574543\pi\) | |||||||
\(242\) | 2657.34 | 0.705869 | ||||||||
\(243\) | −583.204 | −0.153961 | ||||||||
\(244\) | 615.746 | 0.161554 | ||||||||
\(245\) | −1807.23 | −0.471264 | ||||||||
\(246\) | 5101.72 | 1.32225 | ||||||||
\(247\) | 219.702 | 0.0565964 | ||||||||
\(248\) | −3539.38 | −0.906254 | ||||||||
\(249\) | 227.156 | 0.0578130 | ||||||||
\(250\) | 45.9011 | 0.0116122 | ||||||||
\(251\) | −6882.85 | −1.73084 | −0.865421 | − | 0.501045i | \(-0.832949\pi\) | ||||
−0.865421 | + | 0.501045i | \(0.832949\pi\) | |||||||
\(252\) | 41.9991 | 0.0104988 | ||||||||
\(253\) | −2835.63 | −0.704642 | ||||||||
\(254\) | 1814.93 | 0.448343 | ||||||||
\(255\) | 7029.57 | 1.72631 | ||||||||
\(256\) | 1994.85 | 0.487024 | ||||||||
\(257\) | 1572.19 | 0.381598 | 0.190799 | − | 0.981629i | \(-0.438892\pi\) | ||||
0.190799 | + | 0.981629i | \(0.438892\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5156.56 | 1.23711 | ||||||||
\(260\) | 1244.37 | 0.296818 | ||||||||
\(261\) | 459.352 | 0.108939 | ||||||||
\(262\) | 6049.43 | 1.42647 | ||||||||
\(263\) | 3425.31 | 0.803095 | 0.401547 | − | 0.915838i | \(-0.368473\pi\) | ||||
0.401547 | + | 0.915838i | \(0.368473\pi\) | |||||||
\(264\) | 2183.24 | 0.508973 | ||||||||
\(265\) | 4685.23 | 1.08608 | ||||||||
\(266\) | 171.613 | 0.0395575 | ||||||||
\(267\) | 8062.44 | 1.84799 | ||||||||
\(268\) | 646.901 | 0.147447 | ||||||||
\(269\) | 3907.21 | 0.885601 | 0.442801 | − | 0.896620i | \(-0.353985\pi\) | ||||
0.442801 | + | 0.896620i | \(0.353985\pi\) | |||||||
\(270\) | −6999.35 | −1.57766 | ||||||||
\(271\) | 2862.10 | 0.641551 | 0.320775 | − | 0.947155i | \(-0.396057\pi\) | ||||
0.320775 | + | 0.947155i | \(0.396057\pi\) | |||||||
\(272\) | 6504.53 | 1.44998 | ||||||||
\(273\) | 4460.77 | 0.988930 | ||||||||
\(274\) | −2117.08 | −0.466779 | ||||||||
\(275\) | −2664.00 | −0.584165 | ||||||||
\(276\) | −879.066 | −0.191716 | ||||||||
\(277\) | −1361.01 | −0.295218 | −0.147609 | − | 0.989046i | \(-0.547158\pi\) | ||||
−0.147609 | + | 0.989046i | \(0.547158\pi\) | |||||||
\(278\) | −8410.26 | −1.81444 | ||||||||
\(279\) | 362.042 | 0.0776879 | ||||||||
\(280\) | −4858.23 | −1.03691 | ||||||||
\(281\) | 3455.07 | 0.733494 | 0.366747 | − | 0.930321i | \(-0.380471\pi\) | ||||
0.366747 | + | 0.930321i | \(0.380471\pi\) | |||||||
\(282\) | 2784.75 | 0.588048 | ||||||||
\(283\) | −547.918 | −0.115090 | −0.0575448 | − | 0.998343i | \(-0.518327\pi\) | ||||
−0.0575448 | + | 0.998343i | \(0.518327\pi\) | |||||||
\(284\) | −477.938 | −0.0998606 | ||||||||
\(285\) | −292.741 | −0.0608439 | ||||||||
\(286\) | 3878.91 | 0.801975 | ||||||||
\(287\) | −5056.73 | −1.04003 | ||||||||
\(288\) | −124.497 | −0.0254725 | ||||||||
\(289\) | 3050.12 | 0.620827 | ||||||||
\(290\) | 10631.0 | 2.15266 | ||||||||
\(291\) | −7835.20 | −1.57838 | ||||||||
\(292\) | 181.605 | 0.0363960 | ||||||||
\(293\) | 4349.89 | 0.867315 | 0.433657 | − | 0.901078i | \(-0.357223\pi\) | ||||
0.433657 | + | 0.901078i | \(0.357223\pi\) | |||||||
\(294\) | −1746.41 | −0.346437 | ||||||||
\(295\) | 10545.9 | 2.08138 | ||||||||
\(296\) | −6947.73 | −1.36429 | ||||||||
\(297\) | −3117.69 | −0.609114 | ||||||||
\(298\) | −2445.08 | −0.475300 | ||||||||
\(299\) | 7806.24 | 1.50985 | ||||||||
\(300\) | −825.860 | −0.158937 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3631.49 | −0.691949 | ||||||||
\(303\) | 9910.16 | 1.87896 | ||||||||
\(304\) | −270.876 | −0.0511047 | ||||||||
\(305\) | 7285.71 | 1.36780 | ||||||||
\(306\) | −567.952 | −0.106103 | ||||||||
\(307\) | 4215.70 | 0.783723 | 0.391861 | − | 0.920024i | \(-0.371831\pi\) | ||||
0.391861 | + | 0.920024i | \(0.371831\pi\) | |||||||
\(308\) | 432.955 | 0.0800971 | ||||||||
\(309\) | −598.829 | −0.110247 | ||||||||
\(310\) | 8378.90 | 1.53513 | ||||||||
\(311\) | 3421.26 | 0.623801 | 0.311900 | − | 0.950115i | \(-0.399034\pi\) | ||||
0.311900 | + | 0.950115i | \(0.399034\pi\) | |||||||
\(312\) | −6010.26 | −1.09059 | ||||||||
\(313\) | 5650.32 | 1.02037 | 0.510184 | − | 0.860065i | \(-0.329577\pi\) | ||||
0.510184 | + | 0.860065i | \(0.329577\pi\) | |||||||
\(314\) | −390.943 | −0.0702617 | ||||||||
\(315\) | 496.947 | 0.0888882 | ||||||||
\(316\) | −787.336 | −0.140162 | ||||||||
\(317\) | −2209.08 | −0.391402 | −0.195701 | − | 0.980664i | \(-0.562698\pi\) | ||||
−0.195701 | + | 0.980664i | \(0.562698\pi\) | |||||||
\(318\) | 4527.55 | 0.798404 | ||||||||
\(319\) | 4735.31 | 0.831117 | ||||||||
\(320\) | 6321.20 | 1.10427 | ||||||||
\(321\) | 3415.75 | 0.593921 | ||||||||
\(322\) | 6097.60 | 1.05530 | ||||||||
\(323\) | −331.618 | −0.0571261 | ||||||||
\(324\) | −891.489 | −0.152862 | ||||||||
\(325\) | 7333.76 | 1.25170 | ||||||||
\(326\) | 11882.4 | 2.01873 | ||||||||
\(327\) | 4394.37 | 0.743147 | ||||||||
\(328\) | 6813.23 | 1.14694 | ||||||||
\(329\) | −2760.19 | −0.462536 | ||||||||
\(330\) | −5168.44 | −0.862162 | ||||||||
\(331\) | 5378.50 | 0.893140 | 0.446570 | − | 0.894749i | \(-0.352645\pi\) | ||||
0.446570 | + | 0.894749i | \(0.352645\pi\) | |||||||
\(332\) | −60.6947 | −0.0100333 | ||||||||
\(333\) | 710.682 | 0.116952 | ||||||||
\(334\) | −6241.84 | −1.02257 | ||||||||
\(335\) | 7654.34 | 1.24836 | ||||||||
\(336\) | −5499.80 | −0.892971 | ||||||||
\(337\) | −3423.39 | −0.553365 | −0.276683 | − | 0.960961i | \(-0.589235\pi\) | ||||
−0.276683 | + | 0.960961i | \(0.589235\pi\) | |||||||
\(338\) | −3966.22 | −0.638266 | ||||||||
\(339\) | 5251.00 | 0.841284 | ||||||||
\(340\) | −1878.25 | −0.299596 | ||||||||
\(341\) | 3732.18 | 0.592694 | ||||||||
\(342\) | 23.6519 | 0.00373962 | ||||||||
\(343\) | 6915.67 | 1.08866 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −10401.4 | −1.62317 | ||||||||
\(346\) | 7761.03 | 1.20588 | ||||||||
\(347\) | 2323.39 | 0.359441 | 0.179720 | − | 0.983718i | \(-0.442481\pi\) | ||||
0.179720 | + | 0.983718i | \(0.442481\pi\) | |||||||
\(348\) | 1467.98 | 0.226127 | ||||||||
\(349\) | 11472.1 | 1.75956 | 0.879782 | − | 0.475378i | \(-0.157689\pi\) | ||||
0.879782 | + | 0.475378i | \(0.157689\pi\) | |||||||
\(350\) | 5728.54 | 0.874867 | ||||||||
\(351\) | 8582.74 | 1.30516 | ||||||||
\(352\) | −1283.40 | −0.194334 | ||||||||
\(353\) | −7136.51 | −1.07603 | −0.538014 | − | 0.842936i | \(-0.680825\pi\) | ||||
−0.538014 | + | 0.842936i | \(0.680825\pi\) | |||||||
\(354\) | 10191.0 | 1.53007 | ||||||||
\(355\) | −5655.12 | −0.845472 | ||||||||
\(356\) | −2154.23 | −0.320713 | ||||||||
\(357\) | −6733.08 | −0.998186 | ||||||||
\(358\) | −11948.2 | −1.76391 | ||||||||
\(359\) | −3801.33 | −0.558848 | −0.279424 | − | 0.960168i | \(-0.590144\pi\) | ||||
−0.279424 | + | 0.960168i | \(0.590144\pi\) | |||||||
\(360\) | −669.566 | −0.0980257 | ||||||||
\(361\) | −6845.19 | −0.997987 | ||||||||
\(362\) | −1741.92 | −0.252910 | ||||||||
\(363\) | 4341.75 | 0.627776 | ||||||||
\(364\) | −1191.89 | −0.171626 | ||||||||
\(365\) | 2148.81 | 0.308147 | ||||||||
\(366\) | 7040.51 | 1.00550 | ||||||||
\(367\) | −970.263 | −0.138004 | −0.0690018 | − | 0.997617i | \(-0.521981\pi\) | ||||
−0.0690018 | + | 0.997617i | \(0.521981\pi\) | |||||||
\(368\) | −9624.52 | −1.36335 | ||||||||
\(369\) | −696.923 | −0.0983208 | ||||||||
\(370\) | 16447.6 | 2.31100 | ||||||||
\(371\) | −4487.62 | −0.627994 | ||||||||
\(372\) | 1157.00 | 0.161258 | ||||||||
\(373\) | 4565.98 | 0.633827 | 0.316913 | − | 0.948454i | \(-0.397354\pi\) | ||||
0.316913 | + | 0.948454i | \(0.397354\pi\) | |||||||
\(374\) | −5854.83 | −0.809481 | ||||||||
\(375\) | 74.9965 | 0.0103275 | ||||||||
\(376\) | 3718.97 | 0.510083 | ||||||||
\(377\) | −13035.9 | −1.78086 | ||||||||
\(378\) | 6704.14 | 0.912232 | ||||||||
\(379\) | 1211.00 | 0.164129 | 0.0820643 | − | 0.996627i | \(-0.473849\pi\) | ||||
0.0820643 | + | 0.996627i | \(0.473849\pi\) | |||||||
\(380\) | 78.2186 | 0.0105593 | ||||||||
\(381\) | 2965.37 | 0.398741 | ||||||||
\(382\) | 7036.43 | 0.942447 | ||||||||
\(383\) | 4576.99 | 0.610635 | 0.305317 | − | 0.952251i | \(-0.401237\pi\) | ||||
0.305317 | + | 0.952251i | \(0.401237\pi\) | |||||||
\(384\) | 8494.92 | 1.12892 | ||||||||
\(385\) | 5122.86 | 0.678144 | ||||||||
\(386\) | −7095.05 | −0.935566 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2093.51 | 0.273923 | ||||||||
\(389\) | 1490.12 | 0.194221 | 0.0971105 | − | 0.995274i | \(-0.469040\pi\) | ||||
0.0971105 | + | 0.995274i | \(0.469040\pi\) | |||||||
\(390\) | 14228.3 | 1.84738 | ||||||||
\(391\) | −11782.7 | −1.52399 | ||||||||
\(392\) | −2332.28 | −0.300506 | ||||||||
\(393\) | 9884.00 | 1.26866 | ||||||||
\(394\) | −10060.5 | −1.28640 | ||||||||
\(395\) | −9316.01 | −1.18668 | ||||||||
\(396\) | 59.6703 | 0.00757208 | ||||||||
\(397\) | 3177.79 | 0.401734 | 0.200867 | − | 0.979618i | \(-0.435624\pi\) | ||||
0.200867 | + | 0.979618i | \(0.435624\pi\) | |||||||
\(398\) | 9980.69 | 1.25700 | ||||||||
\(399\) | 280.394 | 0.0351811 | ||||||||
\(400\) | −9041.99 | −1.13025 | ||||||||
\(401\) | −7617.68 | −0.948651 | −0.474325 | − | 0.880350i | \(-0.657308\pi\) | ||||
−0.474325 | + | 0.880350i | \(0.657308\pi\) | |||||||
\(402\) | 7396.73 | 0.917700 | ||||||||
\(403\) | −10274.4 | −1.26998 | ||||||||
\(404\) | −2647.93 | −0.326088 | ||||||||
\(405\) | −10548.4 | −1.29421 | ||||||||
\(406\) | −10182.6 | −1.24471 | ||||||||
\(407\) | 7326.19 | 0.892249 | ||||||||
\(408\) | 9071.88 | 1.10080 | ||||||||
\(409\) | −1427.26 | −0.172551 | −0.0862753 | − | 0.996271i | \(-0.527496\pi\) | ||||
−0.0862753 | + | 0.996271i | \(0.527496\pi\) | |||||||
\(410\) | −16129.2 | −1.94284 | ||||||||
\(411\) | −3459.04 | −0.415138 | ||||||||
\(412\) | 160.003 | 0.0191330 | ||||||||
\(413\) | −10101.1 | −1.20349 | ||||||||
\(414\) | 840.378 | 0.0997640 | ||||||||
\(415\) | −718.159 | −0.0849471 | ||||||||
\(416\) | 3533.10 | 0.416405 | ||||||||
\(417\) | −13741.3 | −1.61370 | ||||||||
\(418\) | 243.820 | 0.0285302 | ||||||||
\(419\) | 8478.74 | 0.988576 | 0.494288 | − | 0.869298i | \(-0.335429\pi\) | ||||
0.494288 | + | 0.869298i | \(0.335429\pi\) | |||||||
\(420\) | 1588.13 | 0.184506 | ||||||||
\(421\) | −6824.96 | −0.790091 | −0.395045 | − | 0.918662i | \(-0.629271\pi\) | ||||
−0.395045 | + | 0.918662i | \(0.629271\pi\) | |||||||
\(422\) | −6833.87 | −0.788312 | ||||||||
\(423\) | −380.412 | −0.0437264 | ||||||||
\(424\) | 6046.44 | 0.692550 | ||||||||
\(425\) | −11069.6 | −1.26342 | ||||||||
\(426\) | −5464.79 | −0.621526 | ||||||||
\(427\) | −6978.42 | −0.790888 | ||||||||
\(428\) | −912.667 | −0.103073 | ||||||||
\(429\) | 6337.64 | 0.713250 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5594.86 | 0.625279 | 0.312639 | − | 0.949872i | \(-0.398787\pi\) | ||||
0.312639 | + | 0.949872i | \(0.398787\pi\) | |||||||
\(432\) | −10581.9 | −1.17852 | ||||||||
\(433\) | −6469.41 | −0.718014 | −0.359007 | − | 0.933335i | \(-0.616885\pi\) | ||||
−0.359007 | + | 0.933335i | \(0.616885\pi\) | |||||||
\(434\) | −8025.50 | −0.887641 | ||||||||
\(435\) | 17369.6 | 1.91451 | ||||||||
\(436\) | −1174.15 | −0.128971 | ||||||||
\(437\) | 490.684 | 0.0537130 | ||||||||
\(438\) | 2076.49 | 0.226526 | ||||||||
\(439\) | −5772.38 | −0.627564 | −0.313782 | − | 0.949495i | \(-0.601596\pi\) | ||||
−0.313782 | + | 0.949495i | \(0.601596\pi\) | |||||||
\(440\) | −6902.34 | −0.747855 | ||||||||
\(441\) | 238.569 | 0.0257606 | ||||||||
\(442\) | 16117.8 | 1.73450 | ||||||||
\(443\) | 12893.5 | 1.38282 | 0.691409 | − | 0.722463i | \(-0.256990\pi\) | ||||
0.691409 | + | 0.722463i | \(0.256990\pi\) | |||||||
\(444\) | 2271.17 | 0.242759 | ||||||||
\(445\) | −25489.6 | −2.71533 | ||||||||
\(446\) | −16124.0 | −1.71187 | ||||||||
\(447\) | −3994.94 | −0.422716 | ||||||||
\(448\) | −6054.59 | −0.638510 | ||||||||
\(449\) | −5360.01 | −0.563373 | −0.281687 | − | 0.959506i | \(-0.590894\pi\) | ||||
−0.281687 | + | 0.959506i | \(0.590894\pi\) | |||||||
\(450\) | 789.513 | 0.0827067 | ||||||||
\(451\) | −7184.36 | −0.750107 | ||||||||
\(452\) | −1403.03 | −0.146002 | ||||||||
\(453\) | −5933.38 | −0.615396 | ||||||||
\(454\) | 16020.8 | 1.65616 | ||||||||
\(455\) | −14102.8 | −1.45308 | ||||||||
\(456\) | −377.792 | −0.0387976 | ||||||||
\(457\) | −327.885 | −0.0335620 | −0.0167810 | − | 0.999859i | \(-0.505342\pi\) | ||||
−0.0167810 | + | 0.999859i | \(0.505342\pi\) | |||||||
\(458\) | −5067.62 | −0.517018 | ||||||||
\(459\) | −12954.8 | −1.31738 | ||||||||
\(460\) | 2779.19 | 0.281696 | ||||||||
\(461\) | 10444.8 | 1.05524 | 0.527618 | − | 0.849482i | \(-0.323085\pi\) | ||||
0.527618 | + | 0.849482i | \(0.323085\pi\) | |||||||
\(462\) | 4950.45 | 0.498519 | ||||||||
\(463\) | 11801.3 | 1.18456 | 0.592282 | − | 0.805731i | \(-0.298227\pi\) | ||||
0.592282 | + | 0.805731i | \(0.298227\pi\) | |||||||
\(464\) | 16072.3 | 1.60806 | ||||||||
\(465\) | 13690.0 | 1.36529 | ||||||||
\(466\) | 886.473 | 0.0881224 | ||||||||
\(467\) | 8957.03 | 0.887541 | 0.443771 | − | 0.896140i | \(-0.353641\pi\) | ||||
0.443771 | + | 0.896140i | \(0.353641\pi\) | |||||||
\(468\) | −164.267 | −0.0162249 | ||||||||
\(469\) | −7331.50 | −0.721828 | ||||||||
\(470\) | −8804.04 | −0.864043 | ||||||||
\(471\) | −638.750 | −0.0624885 | ||||||||
\(472\) | 13609.8 | 1.32721 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −9002.48 | −0.872358 | ||||||||
\(475\) | 460.985 | 0.0445293 | ||||||||
\(476\) | 1799.03 | 0.173232 | ||||||||
\(477\) | −618.488 | −0.0593682 | ||||||||
\(478\) | −17876.7 | −1.71059 | ||||||||
\(479\) | 777.002 | 0.0741172 | 0.0370586 | − | 0.999313i | \(-0.488201\pi\) | ||||
0.0370586 | + | 0.999313i | \(0.488201\pi\) | |||||||
\(480\) | −4707.67 | −0.447655 | ||||||||
\(481\) | −20168.4 | −1.91185 | ||||||||
\(482\) | 5304.76 | 0.501297 | ||||||||
\(483\) | 9962.70 | 0.938547 | ||||||||
\(484\) | −1160.09 | −0.108949 | ||||||||
\(485\) | 24771.1 | 2.31917 | ||||||||
\(486\) | 1781.76 | 0.166301 | ||||||||
\(487\) | 14184.9 | 1.31988 | 0.659938 | − | 0.751320i | \(-0.270583\pi\) | ||||
0.659938 | + | 0.751320i | \(0.270583\pi\) | |||||||
\(488\) | 9402.44 | 0.872189 | ||||||||
\(489\) | 19414.3 | 1.79539 | ||||||||
\(490\) | 5521.29 | 0.509034 | ||||||||
\(491\) | 2677.72 | 0.246117 | 0.123059 | − | 0.992399i | \(-0.460730\pi\) | ||||
0.123059 | + | 0.992399i | \(0.460730\pi\) | |||||||
\(492\) | −2227.20 | −0.204086 | ||||||||
\(493\) | 19676.4 | 1.79752 | ||||||||
\(494\) | −671.216 | −0.0611324 | ||||||||
\(495\) | 706.038 | 0.0641092 | ||||||||
\(496\) | 12667.5 | 1.14675 | ||||||||
\(497\) | 5416.60 | 0.488869 | ||||||||
\(498\) | −693.989 | −0.0624466 | ||||||||
\(499\) | 11775.2 | 1.05638 | 0.528188 | − | 0.849127i | \(-0.322871\pi\) | ||||
0.528188 | + | 0.849127i | \(0.322871\pi\) | |||||||
\(500\) | −20.0386 | −0.00179230 | ||||||||
\(501\) | −10198.4 | −0.909440 | ||||||||
\(502\) | 21027.9 | 1.86956 | ||||||||
\(503\) | 1095.68 | 0.0971248 | 0.0485624 | − | 0.998820i | \(-0.484536\pi\) | ||||
0.0485624 | + | 0.998820i | \(0.484536\pi\) | |||||||
\(504\) | 641.326 | 0.0566804 | ||||||||
\(505\) | −31331.2 | −2.76083 | ||||||||
\(506\) | 8663.18 | 0.761117 | ||||||||
\(507\) | −6480.29 | −0.567652 | ||||||||
\(508\) | −792.327 | −0.0692005 | ||||||||
\(509\) | 2497.55 | 0.217489 | 0.108744 | − | 0.994070i | \(-0.465317\pi\) | ||||
0.108744 | + | 0.994070i | \(0.465317\pi\) | |||||||
\(510\) | −21476.2 | −1.86467 | ||||||||
\(511\) | −2058.18 | −0.178177 | ||||||||
\(512\) | 7520.06 | 0.649107 | ||||||||
\(513\) | 539.493 | 0.0464312 | ||||||||
\(514\) | −4803.23 | −0.412182 | ||||||||
\(515\) | 1893.21 | 0.161990 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3921.55 | −0.333597 | ||||||||
\(518\) | −15753.9 | −1.33627 | ||||||||
\(519\) | 12680.5 | 1.07247 | ||||||||
\(520\) | 19001.5 | 1.60245 | ||||||||
\(521\) | 9002.64 | 0.757030 | 0.378515 | − | 0.925595i | \(-0.376435\pi\) | ||||
0.378515 | + | 0.925595i | \(0.376435\pi\) | |||||||
\(522\) | −1403.37 | −0.117671 | ||||||||
\(523\) | −11093.0 | −0.927465 | −0.463732 | − | 0.885975i | \(-0.653490\pi\) | ||||
−0.463732 | + | 0.885975i | \(0.653490\pi\) | |||||||
\(524\) | −2640.94 | −0.220172 | ||||||||
\(525\) | 9359.70 | 0.778078 | ||||||||
\(526\) | −10464.7 | −0.867460 | ||||||||
\(527\) | 15508.1 | 1.28187 | ||||||||
\(528\) | −7813.84 | −0.644041 | ||||||||
\(529\) | 5267.49 | 0.432933 | ||||||||
\(530\) | −14313.9 | −1.17313 | ||||||||
\(531\) | −1392.14 | −0.113774 | ||||||||
\(532\) | −74.9195 | −0.00610559 | ||||||||
\(533\) | 19777.9 | 1.60727 | ||||||||
\(534\) | −24631.7 | −1.99610 | ||||||||
\(535\) | −10799.0 | −0.872673 | ||||||||
\(536\) | 9878.17 | 0.796030 | ||||||||
\(537\) | −19521.8 | −1.56876 | ||||||||
\(538\) | −11937.0 | −0.956579 | ||||||||
\(539\) | 2459.33 | 0.196532 | ||||||||
\(540\) | 3055.64 | 0.243507 | ||||||||
\(541\) | 14140.7 | 1.12376 | 0.561881 | − | 0.827218i | \(-0.310078\pi\) | ||||
0.561881 | + | 0.827218i | \(0.310078\pi\) | |||||||
\(542\) | −8744.05 | −0.692969 | ||||||||
\(543\) | −2846.08 | −0.224930 | ||||||||
\(544\) | −5332.86 | −0.420302 | ||||||||
\(545\) | −13892.9 | −1.09194 | ||||||||
\(546\) | −13628.2 | −1.06819 | ||||||||
\(547\) | 8289.93 | 0.647992 | 0.323996 | − | 0.946058i | \(-0.394974\pi\) | ||||
0.323996 | + | 0.946058i | \(0.394974\pi\) | |||||||
\(548\) | 924.231 | 0.0720460 | ||||||||
\(549\) | −961.772 | −0.0747677 | ||||||||
\(550\) | 8138.84 | 0.630984 | ||||||||
\(551\) | −819.409 | −0.0633539 | ||||||||
\(552\) | −13423.3 | −1.03503 | ||||||||
\(553\) | 8923.09 | 0.686163 | ||||||||
\(554\) | 4158.05 | 0.318878 | ||||||||
\(555\) | 26873.3 | 2.05533 | ||||||||
\(556\) | 3671.58 | 0.280053 | ||||||||
\(557\) | −8299.84 | −0.631374 | −0.315687 | − | 0.948863i | \(-0.602235\pi\) | ||||
−0.315687 | + | 0.948863i | \(0.602235\pi\) | |||||||
\(558\) | −1106.08 | −0.0839143 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 17387.7 | 1.31208 | ||||||||
\(561\) | −9566.04 | −0.719926 | ||||||||
\(562\) | −10555.6 | −0.792282 | ||||||||
\(563\) | 22079.4 | 1.65282 | 0.826408 | − | 0.563071i | \(-0.190380\pi\) | ||||
0.826408 | + | 0.563071i | \(0.190380\pi\) | |||||||
\(564\) | −1215.71 | −0.0907635 | ||||||||
\(565\) | −16601.1 | −1.23613 | ||||||||
\(566\) | 1673.96 | 0.124314 | ||||||||
\(567\) | 10103.5 | 0.748336 | ||||||||
\(568\) | −7298.11 | −0.539123 | ||||||||
\(569\) | 6483.18 | 0.477661 | 0.238831 | − | 0.971061i | \(-0.423236\pi\) | ||||
0.238831 | + | 0.971061i | \(0.423236\pi\) | |||||||
\(570\) | 894.359 | 0.0657203 | ||||||||
\(571\) | 8403.34 | 0.615882 | 0.307941 | − | 0.951405i | \(-0.400360\pi\) | ||||
0.307941 | + | 0.951405i | \(0.400360\pi\) | |||||||
\(572\) | −1693.38 | −0.123783 | ||||||||
\(573\) | 11496.6 | 0.838181 | ||||||||
\(574\) | 15448.9 | 1.12339 | ||||||||
\(575\) | 16379.3 | 1.18793 | ||||||||
\(576\) | −834.450 | −0.0603624 | ||||||||
\(577\) | 3579.80 | 0.258282 | 0.129141 | − | 0.991626i | \(-0.458778\pi\) | ||||
0.129141 | + | 0.991626i | \(0.458778\pi\) | |||||||
\(578\) | −9318.48 | −0.670584 | ||||||||
\(579\) | −11592.4 | −0.832062 | ||||||||
\(580\) | −4641.05 | −0.332257 | ||||||||
\(581\) | 687.869 | 0.0491181 | ||||||||
\(582\) | 23937.4 | 1.70488 | ||||||||
\(583\) | −6375.80 | −0.452931 | ||||||||
\(584\) | 2773.10 | 0.196493 | ||||||||
\(585\) | −1943.66 | −0.137368 | ||||||||
\(586\) | −13289.4 | −0.936827 | ||||||||
\(587\) | −10896.7 | −0.766191 | −0.383096 | − | 0.923709i | \(-0.625142\pi\) | ||||
−0.383096 | + | 0.923709i | \(0.625142\pi\) | |||||||
\(588\) | 762.410 | 0.0534715 | ||||||||
\(589\) | −645.824 | −0.0451795 | ||||||||
\(590\) | −32218.9 | −2.24819 | ||||||||
\(591\) | −16437.6 | −1.14408 | ||||||||
\(592\) | 24866.1 | 1.72633 | ||||||||
\(593\) | 1858.08 | 0.128672 | 0.0643358 | − | 0.997928i | \(-0.479507\pi\) | ||||
0.0643358 | + | 0.997928i | \(0.479507\pi\) | |||||||
\(594\) | 9524.92 | 0.657933 | ||||||||
\(595\) | 21286.8 | 1.46668 | ||||||||
\(596\) | 1067.42 | 0.0733612 | ||||||||
\(597\) | 16307.2 | 1.11794 | ||||||||
\(598\) | −23849.0 | −1.63087 | ||||||||
\(599\) | 5459.07 | 0.372373 | 0.186186 | − | 0.982514i | \(-0.440387\pi\) | ||||
0.186186 | + | 0.982514i | \(0.440387\pi\) | |||||||
\(600\) | −12610.9 | −0.858062 | ||||||||
\(601\) | −7307.36 | −0.495962 | −0.247981 | − | 0.968765i | \(-0.579767\pi\) | ||||
−0.247981 | + | 0.968765i | \(0.579767\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1010.43 | −0.0682389 | ||||||||
\(604\) | 1585.36 | 0.106800 | ||||||||
\(605\) | −13726.5 | −0.922418 | ||||||||
\(606\) | −30276.7 | −2.02955 | ||||||||
\(607\) | 548.992 | 0.0367099 | 0.0183550 | − | 0.999832i | \(-0.494157\pi\) | ||||
0.0183550 | + | 0.999832i | \(0.494157\pi\) | |||||||
\(608\) | 222.083 | 0.0148136 | ||||||||
\(609\) | −16637.0 | −1.10701 | ||||||||
\(610\) | −22258.7 | −1.47742 | ||||||||
\(611\) | 10795.7 | 0.714806 | ||||||||
\(612\) | 247.945 | 0.0163768 | ||||||||
\(613\) | −20952.2 | −1.38051 | −0.690255 | − | 0.723566i | \(-0.742502\pi\) | ||||
−0.690255 | + | 0.723566i | \(0.742502\pi\) | |||||||
\(614\) | −12879.5 | −0.846536 | ||||||||
\(615\) | −26353.0 | −1.72790 | ||||||||
\(616\) | 6611.22 | 0.432425 | ||||||||
\(617\) | 15844.2 | 1.03381 | 0.516907 | − | 0.856042i | \(-0.327083\pi\) | ||||
0.516907 | + | 0.856042i | \(0.327083\pi\) | |||||||
\(618\) | 1829.49 | 0.119083 | ||||||||
\(619\) | 879.578 | 0.0571135 | 0.0285567 | − | 0.999592i | \(-0.490909\pi\) | ||||
0.0285567 | + | 0.999592i | \(0.490909\pi\) | |||||||
\(620\) | −3657.89 | −0.236942 | ||||||||
\(621\) | 19168.7 | 1.23867 | ||||||||
\(622\) | −10452.4 | −0.673797 | ||||||||
\(623\) | 24414.5 | 1.57006 | ||||||||
\(624\) | 21510.8 | 1.38000 | ||||||||
\(625\) | −15743.1 | −1.00756 | ||||||||
\(626\) | −17262.4 | −1.10215 | ||||||||
\(627\) | 398.371 | 0.0253738 | ||||||||
\(628\) | 170.670 | 0.0108447 | ||||||||
\(629\) | 30442.1 | 1.92974 | ||||||||
\(630\) | −1518.23 | −0.0960123 | ||||||||
\(631\) | 20975.5 | 1.32333 | 0.661667 | − | 0.749798i | \(-0.269849\pi\) | ||||
0.661667 | + | 0.749798i | \(0.269849\pi\) | |||||||
\(632\) | −12022.6 | −0.756699 | ||||||||
\(633\) | −11165.7 | −0.701098 | ||||||||
\(634\) | 6749.01 | 0.422772 | ||||||||
\(635\) | −9375.07 | −0.585887 | ||||||||
\(636\) | −1976.54 | −0.123231 | ||||||||
\(637\) | −6770.31 | −0.421114 | ||||||||
\(638\) | −14466.9 | −0.897729 | ||||||||
\(639\) | 746.521 | 0.0462158 | ||||||||
\(640\) | −26856.9 | −1.65877 | ||||||||
\(641\) | −24275.9 | −1.49585 | −0.747925 | − | 0.663784i | \(-0.768950\pi\) | ||||
−0.747925 | + | 0.663784i | \(0.768950\pi\) | |||||||
\(642\) | −10435.5 | −0.641523 | ||||||||
\(643\) | 19783.9 | 1.21338 | 0.606688 | − | 0.794940i | \(-0.292498\pi\) | ||||
0.606688 | + | 0.794940i | \(0.292498\pi\) | |||||||
\(644\) | −2661.97 | −0.162882 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1013.13 | 0.0617046 | ||||||||
\(647\) | −7539.98 | −0.458157 | −0.229078 | − | 0.973408i | \(-0.573571\pi\) | ||||
−0.229078 | + | 0.973408i | \(0.573571\pi\) | |||||||
\(648\) | −13613.0 | −0.825262 | ||||||||
\(649\) | −14351.2 | −0.868000 | ||||||||
\(650\) | −22405.5 | −1.35203 | ||||||||
\(651\) | −13112.6 | −0.789438 | ||||||||
\(652\) | −5187.38 | −0.311585 | ||||||||
\(653\) | 1288.35 | 0.0772081 | 0.0386041 | − | 0.999255i | \(-0.487709\pi\) | ||||
0.0386041 | + | 0.999255i | \(0.487709\pi\) | |||||||
\(654\) | −13425.3 | −0.802708 | ||||||||
\(655\) | −31248.4 | −1.86409 | ||||||||
\(656\) | −24384.7 | −1.45131 | ||||||||
\(657\) | −283.660 | −0.0168442 | ||||||||
\(658\) | 8432.71 | 0.499607 | ||||||||
\(659\) | 13574.7 | 0.802420 | 0.401210 | − | 0.915986i | \(-0.368590\pi\) | ||||
0.401210 | + | 0.915986i | \(0.368590\pi\) | |||||||
\(660\) | 2256.33 | 0.133072 | ||||||||
\(661\) | 14332.4 | 0.843368 | 0.421684 | − | 0.906743i | \(-0.361439\pi\) | ||||
0.421684 | + | 0.906743i | \(0.361439\pi\) | |||||||
\(662\) | −16432.0 | −0.964722 | ||||||||
\(663\) | 26334.5 | 1.54260 | ||||||||
\(664\) | −926.807 | −0.0541673 | ||||||||
\(665\) | −886.472 | −0.0516931 | ||||||||
\(666\) | −2171.22 | −0.126326 | ||||||||
\(667\) | −29114.4 | −1.69013 | ||||||||
\(668\) | 2724.94 | 0.157831 | ||||||||
\(669\) | −26344.5 | −1.52248 | ||||||||
\(670\) | −23384.9 | −1.34841 | ||||||||
\(671\) | −9914.60 | −0.570416 | ||||||||
\(672\) | 4509.11 | 0.258843 | ||||||||
\(673\) | 8301.11 | 0.475460 | 0.237730 | − | 0.971331i | \(-0.423597\pi\) | ||||
0.237730 | + | 0.971331i | \(0.423597\pi\) | |||||||
\(674\) | 10458.9 | 0.597716 | ||||||||
\(675\) | 18008.5 | 1.02689 | ||||||||
\(676\) | 1731.49 | 0.0985145 | ||||||||
\(677\) | −11712.0 | −0.664888 | −0.332444 | − | 0.943123i | \(-0.607873\pi\) | ||||
−0.332444 | + | 0.943123i | \(0.607873\pi\) | |||||||
\(678\) | −16042.4 | −0.908710 | ||||||||
\(679\) | −23726.3 | −1.34099 | ||||||||
\(680\) | −28680.9 | −1.61745 | ||||||||
\(681\) | 26176.0 | 1.47293 | ||||||||
\(682\) | −11402.2 | −0.640197 | ||||||||
\(683\) | 30661.5 | 1.71776 | 0.858881 | − | 0.512175i | \(-0.171160\pi\) | ||||
0.858881 | + | 0.512175i | \(0.171160\pi\) | |||||||
\(684\) | −10.3255 | −0.000577200 0 | ||||||||
\(685\) | 10935.8 | 0.609979 | ||||||||
\(686\) | −21128.2 | −1.17591 | ||||||||
\(687\) | −8279.84 | −0.459819 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 17552.0 | 0.970506 | ||||||||
\(690\) | 31777.5 | 1.75326 | ||||||||
\(691\) | 2530.11 | 0.139291 | 0.0696454 | − | 0.997572i | \(-0.477813\pi\) | ||||
0.0696454 | + | 0.997572i | \(0.477813\pi\) | |||||||
\(692\) | −3388.15 | −0.186125 | ||||||||
\(693\) | −676.259 | −0.0370692 | ||||||||
\(694\) | −7098.21 | −0.388249 | ||||||||
\(695\) | 43443.3 | 2.37108 | ||||||||
\(696\) | 22416.1 | 1.22080 | ||||||||
\(697\) | −29852.8 | −1.62232 | ||||||||
\(698\) | −35048.6 | −1.90059 | ||||||||
\(699\) | 1448.38 | 0.0783732 | ||||||||
\(700\) | −2500.85 | −0.135033 | ||||||||
\(701\) | 29878.4 | 1.60983 | 0.804915 | − | 0.593390i | \(-0.202211\pi\) | ||||
0.804915 | + | 0.593390i | \(0.202211\pi\) | |||||||
\(702\) | −26221.3 | −1.40977 | ||||||||
\(703\) | −1267.74 | −0.0680138 | ||||||||
\(704\) | −8602.07 | −0.460515 | ||||||||
\(705\) | −14384.7 | −0.768451 | ||||||||
\(706\) | 21802.9 | 1.16227 | ||||||||
\(707\) | 30009.7 | 1.59637 | ||||||||
\(708\) | −4448.97 | −0.236162 | ||||||||
\(709\) | −1455.09 | −0.0770765 | −0.0385382 | − | 0.999257i | \(-0.512270\pi\) | ||||
−0.0385382 | + | 0.999257i | \(0.512270\pi\) | |||||||
\(710\) | 17277.0 | 0.913234 | ||||||||
\(711\) | 1229.79 | 0.0648673 | ||||||||
\(712\) | −32895.1 | −1.73145 | ||||||||
\(713\) | −22946.8 | −1.20528 | ||||||||
\(714\) | 20570.4 | 1.07819 | ||||||||
\(715\) | −20036.6 | −1.04801 | ||||||||
\(716\) | 5216.08 | 0.272255 | ||||||||
\(717\) | −29208.3 | −1.52134 | ||||||||
\(718\) | 11613.5 | 0.603638 | ||||||||
\(719\) | 2748.33 | 0.142553 | 0.0712765 | − | 0.997457i | \(-0.477293\pi\) | ||||
0.0712765 | + | 0.997457i | \(0.477293\pi\) | |||||||
\(720\) | 2396.39 | 0.124039 | ||||||||
\(721\) | −1813.36 | −0.0936658 | ||||||||
\(722\) | 20912.9 | 1.07797 | ||||||||
\(723\) | 8667.29 | 0.445837 | ||||||||
\(724\) | 760.453 | 0.0390359 | ||||||||
\(725\) | −27352.3 | −1.40116 | ||||||||
\(726\) | −13264.6 | −0.678091 | ||||||||
\(727\) | 29119.3 | 1.48552 | 0.742761 | − | 0.669556i | \(-0.233516\pi\) | ||||
0.742761 | + | 0.669556i | \(0.233516\pi\) | |||||||
\(728\) | −18200.1 | −0.926567 | ||||||||
\(729\) | 20958.3 | 1.06479 | ||||||||
\(730\) | −6564.86 | −0.332844 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −3073.60 | −0.155196 | ||||||||
\(733\) | −22990.6 | −1.15850 | −0.579248 | − | 0.815151i | \(-0.696654\pi\) | ||||
−0.579248 | + | 0.815151i | \(0.696654\pi\) | |||||||
\(734\) | 2964.27 | 0.149064 | ||||||||
\(735\) | 9021.08 | 0.452718 | ||||||||
\(736\) | 7890.84 | 0.395191 | ||||||||
\(737\) | −10416.2 | −0.520607 | ||||||||
\(738\) | 2129.18 | 0.106201 | ||||||||
\(739\) | 12574.0 | 0.625905 | 0.312952 | − | 0.949769i | \(-0.398682\pi\) | ||||
0.312952 | + | 0.949769i | \(0.398682\pi\) | |||||||
\(740\) | −7180.36 | −0.356696 | ||||||||
\(741\) | −1096.68 | −0.0543692 | ||||||||
\(742\) | 13710.2 | 0.678326 | ||||||||
\(743\) | −36672.3 | −1.81073 | −0.905367 | − | 0.424631i | \(-0.860404\pi\) | ||||
−0.905367 | + | 0.424631i | \(0.860404\pi\) | |||||||
\(744\) | 17667.4 | 0.870590 | ||||||||
\(745\) | 12630.1 | 0.621115 | ||||||||
\(746\) | −13949.6 | −0.684626 | ||||||||
\(747\) | 94.8028 | 0.00464344 | ||||||||
\(748\) | 2555.98 | 0.124941 | ||||||||
\(749\) | 10343.5 | 0.504597 | ||||||||
\(750\) | −229.123 | −0.0111552 | ||||||||
\(751\) | −14516.0 | −0.705322 | −0.352661 | − | 0.935751i | \(-0.614723\pi\) | ||||
−0.352661 | + | 0.935751i | \(0.614723\pi\) | |||||||
\(752\) | −13310.3 | −0.645446 | ||||||||
\(753\) | 34356.9 | 1.66273 | ||||||||
\(754\) | 39826.2 | 1.92359 | ||||||||
\(755\) | 18758.5 | 0.904227 | ||||||||
\(756\) | −2926.76 | −0.140800 | ||||||||
\(757\) | −25899.1 | −1.24348 | −0.621742 | − | 0.783222i | \(-0.713575\pi\) | ||||
−0.621742 | + | 0.783222i | \(0.713575\pi\) | |||||||
\(758\) | −3699.74 | −0.177283 | ||||||||
\(759\) | 14154.5 | 0.676912 | ||||||||
\(760\) | 1194.40 | 0.0570070 | ||||||||
\(761\) | 18599.9 | 0.886002 | 0.443001 | − | 0.896521i | \(-0.353914\pi\) | ||||
0.443001 | + | 0.896521i | \(0.353914\pi\) | |||||||
\(762\) | −9059.55 | −0.430699 | ||||||||
\(763\) | 13306.9 | 0.631380 | ||||||||
\(764\) | −3071.82 | −0.145464 | ||||||||
\(765\) | 2933.76 | 0.138654 | ||||||||
\(766\) | −13983.2 | −0.659575 | ||||||||
\(767\) | 39507.5 | 1.85989 | ||||||||
\(768\) | −9957.62 | −0.467858 | ||||||||
\(769\) | 24888.9 | 1.16712 | 0.583560 | − | 0.812070i | \(-0.301659\pi\) | ||||
0.583560 | + | 0.812070i | \(0.301659\pi\) | |||||||
\(770\) | −15651.0 | −0.732495 | ||||||||
\(771\) | −7847.87 | −0.366581 | ||||||||
\(772\) | 3097.41 | 0.144402 | ||||||||
\(773\) | −41420.2 | −1.92727 | −0.963636 | − | 0.267217i | \(-0.913896\pi\) | ||||
−0.963636 | + | 0.267217i | \(0.913896\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −21557.9 | −0.999205 | ||||||||
\(776\) | 31967.9 | 1.47884 | ||||||||
\(777\) | −25739.8 | −1.18843 | ||||||||
\(778\) | −4552.48 | −0.209787 | ||||||||
\(779\) | 1243.20 | 0.0571786 | ||||||||
\(780\) | −6211.49 | −0.285137 | ||||||||
\(781\) | 7695.64 | 0.352589 | ||||||||
\(782\) | 35997.7 | 1.64613 | ||||||||
\(783\) | −32010.5 | −1.46100 | ||||||||
\(784\) | 8347.29 | 0.380252 | ||||||||
\(785\) | 2019.42 | 0.0918169 | ||||||||
\(786\) | −30196.8 | −1.37033 | ||||||||
\(787\) | −9546.36 | −0.432390 | −0.216195 | − | 0.976350i | \(-0.569365\pi\) | ||||
−0.216195 | + | 0.976350i | \(0.569365\pi\) | |||||||
\(788\) | 4392.03 | 0.198553 | ||||||||
\(789\) | −17098.0 | −0.771491 | ||||||||
\(790\) | 28461.5 | 1.28179 | ||||||||
\(791\) | 15900.9 | 0.714757 | ||||||||
\(792\) | 911.165 | 0.0408798 | ||||||||
\(793\) | 27294.0 | 1.22224 | ||||||||
\(794\) | −9708.51 | −0.433932 | ||||||||
\(795\) | −23387.1 | −1.04334 | ||||||||
\(796\) | −4357.17 | −0.194015 | ||||||||
\(797\) | 1574.59 | 0.0699808 | 0.0349904 | − | 0.999388i | \(-0.488860\pi\) | ||||
0.0349904 | + | 0.999388i | \(0.488860\pi\) | |||||||
\(798\) | −856.637 | −0.0380008 | ||||||||
\(799\) | −16295.0 | −0.721496 | ||||||||
\(800\) | 7413.24 | 0.327622 | ||||||||
\(801\) | 3364.83 | 0.148427 | ||||||||
\(802\) | 23272.9 | 1.02468 | ||||||||
\(803\) | −2924.16 | −0.128507 | ||||||||
\(804\) | −3229.11 | −0.141644 | ||||||||
\(805\) | −31497.3 | −1.37905 | ||||||||
\(806\) | 31389.4 | 1.37177 | ||||||||
\(807\) | −19503.5 | −0.850750 | ||||||||
\(808\) | −40433.9 | −1.76047 | ||||||||
\(809\) | −2642.40 | −0.114835 | −0.0574176 | − | 0.998350i | \(-0.518287\pi\) | ||||
−0.0574176 | + | 0.998350i | \(0.518287\pi\) | |||||||
\(810\) | 32226.5 | 1.39793 | ||||||||
\(811\) | 8604.81 | 0.372572 | 0.186286 | − | 0.982496i | \(-0.440355\pi\) | ||||
0.186286 | + | 0.982496i | \(0.440355\pi\) | |||||||
\(812\) | 4445.30 | 0.192118 | ||||||||
\(813\) | −14286.7 | −0.616304 | ||||||||
\(814\) | −22382.4 | −0.963761 | ||||||||
\(815\) | −61378.8 | −2.63804 | ||||||||
\(816\) | −32468.5 | −1.39292 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 4360.43 | 0.186380 | ||||||||
\(819\) | 1861.68 | 0.0794292 | ||||||||
\(820\) | 7041.35 | 0.299871 | ||||||||
\(821\) | −13653.9 | −0.580417 | −0.290209 | − | 0.956963i | \(-0.593725\pi\) | ||||
−0.290209 | + | 0.956963i | \(0.593725\pi\) | |||||||
\(822\) | 10567.8 | 0.448410 | ||||||||
\(823\) | −35324.1 | −1.49614 | −0.748068 | − | 0.663622i | \(-0.769018\pi\) | ||||
−0.748068 | + | 0.663622i | \(0.769018\pi\) | |||||||
\(824\) | 2443.25 | 0.103294 | ||||||||
\(825\) | 13297.8 | 0.561176 | ||||||||
\(826\) | 30860.0 | 1.29995 | ||||||||
\(827\) | 36897.8 | 1.55147 | 0.775733 | − | 0.631061i | \(-0.217380\pi\) | ||||
0.775733 | + | 0.631061i | \(0.217380\pi\) | |||||||
\(828\) | −366.875 | −0.0153983 | ||||||||
\(829\) | 25449.6 | 1.06623 | 0.533113 | − | 0.846044i | \(-0.321022\pi\) | ||||
0.533113 | + | 0.846044i | \(0.321022\pi\) | |||||||
\(830\) | 2194.06 | 0.0917553 | ||||||||
\(831\) | 6793.72 | 0.283600 | ||||||||
\(832\) | 23680.8 | 0.986758 | ||||||||
\(833\) | 10219.1 | 0.425056 | ||||||||
\(834\) | 41981.2 | 1.74303 | ||||||||
\(835\) | 32242.3 | 1.33628 | ||||||||
\(836\) | −106.442 | −0.00440356 | ||||||||
\(837\) | −25229.4 | −1.04188 | ||||||||
\(838\) | −25903.5 | −1.06781 | ||||||||
\(839\) | 11708.4 | 0.481789 | 0.240894 | − | 0.970551i | \(-0.422559\pi\) | ||||
0.240894 | + | 0.970551i | \(0.422559\pi\) | |||||||
\(840\) | 24250.7 | 0.996104 | ||||||||
\(841\) | 24230.1 | 0.993486 | ||||||||
\(842\) | 20851.1 | 0.853414 | ||||||||
\(843\) | −17246.5 | −0.704629 | ||||||||
\(844\) | 2983.39 | 0.121674 | ||||||||
\(845\) | 20487.6 | 0.834075 | ||||||||
\(846\) | 1162.20 | 0.0472310 | ||||||||
\(847\) | 13147.6 | 0.533360 | ||||||||
\(848\) | −21640.3 | −0.876335 | ||||||||
\(849\) | 2735.03 | 0.110561 | ||||||||
\(850\) | 33818.9 | 1.36468 | ||||||||
\(851\) | −45044.1 | −1.81444 | ||||||||
\(852\) | 2385.71 | 0.0959308 | ||||||||
\(853\) | −30324.8 | −1.21723 | −0.608617 | − | 0.793464i | \(-0.708275\pi\) | ||||
−0.608617 | + | 0.793464i | \(0.708275\pi\) | |||||||
\(854\) | 21319.9 | 0.854276 | ||||||||
\(855\) | −122.174 | −0.00488687 | ||||||||
\(856\) | −13936.4 | −0.556468 | ||||||||
\(857\) | −13821.8 | −0.550924 | −0.275462 | − | 0.961312i | \(-0.588831\pi\) | ||||
−0.275462 | + | 0.961312i | \(0.588831\pi\) | |||||||
\(858\) | −19362.2 | −0.770415 | ||||||||
\(859\) | 43930.5 | 1.74493 | 0.872463 | − | 0.488681i | \(-0.162522\pi\) | ||||
0.872463 | + | 0.488681i | \(0.162522\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 25241.5 | 0.999104 | ||||||||
\(862\) | −17093.0 | −0.675393 | ||||||||
\(863\) | 644.396 | 0.0254177 | 0.0127089 | − | 0.999919i | \(-0.495955\pi\) | ||||
0.0127089 | + | 0.999919i | \(0.495955\pi\) | |||||||
\(864\) | 8675.75 | 0.341615 | ||||||||
\(865\) | −40089.7 | −1.57583 | ||||||||
\(866\) | 19764.8 | 0.775561 | ||||||||
\(867\) | −15225.2 | −0.596395 | ||||||||
\(868\) | 3503.61 | 0.137005 | ||||||||
\(869\) | 12677.5 | 0.494884 | ||||||||
\(870\) | −53066.3 | −2.06795 | ||||||||
\(871\) | 28675.0 | 1.11552 | ||||||||
\(872\) | −17929.2 | −0.696284 | ||||||||
\(873\) | −3269.99 | −0.126772 | ||||||||
\(874\) | −1499.10 | −0.0580179 | ||||||||
\(875\) | 227.102 | 0.00877424 | ||||||||
\(876\) | −906.511 | −0.0349637 | ||||||||
\(877\) | 21633.7 | 0.832975 | 0.416488 | − | 0.909141i | \(-0.363261\pi\) | ||||
0.416488 | + | 0.909141i | \(0.363261\pi\) | |||||||
\(878\) | 17635.3 | 0.677862 | ||||||||
\(879\) | −21713.2 | −0.833183 | ||||||||
\(880\) | 24703.6 | 0.946317 | ||||||||
\(881\) | −23264.2 | −0.889661 | −0.444830 | − | 0.895615i | \(-0.646736\pi\) | ||||
−0.444830 | + | 0.895615i | \(0.646736\pi\) | |||||||
\(882\) | −728.855 | −0.0278252 | ||||||||
\(883\) | 7201.01 | 0.274443 | 0.137222 | − | 0.990540i | \(-0.456183\pi\) | ||||
0.137222 | + | 0.990540i | \(0.456183\pi\) | |||||||
\(884\) | −7036.40 | −0.267715 | ||||||||
\(885\) | −52641.6 | −1.99947 | ||||||||
\(886\) | −39391.2 | −1.49365 | ||||||||
\(887\) | 34582.1 | 1.30908 | 0.654540 | − | 0.756027i | \(-0.272862\pi\) | ||||
0.654540 | + | 0.756027i | \(0.272862\pi\) | |||||||
\(888\) | 34680.8 | 1.31060 | ||||||||
\(889\) | 8979.66 | 0.338772 | ||||||||
\(890\) | 77873.6 | 2.93295 | ||||||||
\(891\) | 14354.5 | 0.539725 | ||||||||
\(892\) | 7039.08 | 0.264222 | ||||||||
\(893\) | 678.593 | 0.0254292 | ||||||||
\(894\) | 12205.0 | 0.456596 | ||||||||
\(895\) | 61718.4 | 2.30505 | ||||||||
\(896\) | 25724.1 | 0.959132 | ||||||||
\(897\) | −38966.2 | −1.45044 | ||||||||
\(898\) | 16375.5 | 0.608526 | ||||||||
\(899\) | 38319.6 | 1.42161 | ||||||||
\(900\) | −344.670 | −0.0127655 | ||||||||
\(901\) | −26493.0 | −0.979589 | ||||||||
\(902\) | 21949.0 | 0.810226 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −21424.3 | −0.788231 | ||||||||
\(905\) | 8997.92 | 0.330498 | ||||||||
\(906\) | 18127.2 | 0.664718 | ||||||||
\(907\) | −38466.5 | −1.40822 | −0.704111 | − | 0.710090i | \(-0.748654\pi\) | ||||
−0.704111 | + | 0.710090i | \(0.748654\pi\) | |||||||
\(908\) | −6994.05 | −0.255623 | ||||||||
\(909\) | 4135.97 | 0.150915 | ||||||||
\(910\) | 43085.7 | 1.56954 | ||||||||
\(911\) | 40167.6 | 1.46083 | 0.730413 | − | 0.683005i | \(-0.239327\pi\) | ||||
0.730413 | + | 0.683005i | \(0.239327\pi\) | |||||||
\(912\) | 1352.13 | 0.0490936 | ||||||||
\(913\) | 977.291 | 0.0354256 | ||||||||
\(914\) | 1001.73 | 0.0362519 | ||||||||
\(915\) | −36367.8 | −1.31397 | ||||||||
\(916\) | 2212.32 | 0.0798002 | ||||||||
\(917\) | 29930.5 | 1.07785 | ||||||||
\(918\) | 39578.4 | 1.42296 | ||||||||
\(919\) | 11458.8 | 0.411305 | 0.205653 | − | 0.978625i | \(-0.434068\pi\) | ||||
0.205653 | + | 0.978625i | \(0.434068\pi\) | |||||||
\(920\) | 42438.1 | 1.52081 | ||||||||
\(921\) | −21043.4 | −0.752881 | ||||||||
\(922\) | −31910.1 | −1.13981 | ||||||||
\(923\) | −21185.4 | −0.755501 | ||||||||
\(924\) | −2161.17 | −0.0769450 | ||||||||
\(925\) | −42317.8 | −1.50422 | ||||||||
\(926\) | −36054.4 | −1.27950 | ||||||||
\(927\) | −249.919 | −0.00885482 | ||||||||
\(928\) | −13177.2 | −0.466123 | ||||||||
\(929\) | −6550.23 | −0.231330 | −0.115665 | − | 0.993288i | \(-0.536900\pi\) | ||||
−0.115665 | + | 0.993288i | \(0.536900\pi\) | |||||||
\(930\) | −41824.7 | −1.47472 | ||||||||
\(931\) | −425.567 | −0.0149811 | ||||||||
\(932\) | −386.998 | −0.0136014 | ||||||||
\(933\) | −17077.8 | −0.599252 | ||||||||
\(934\) | −27364.8 | −0.958675 | ||||||||
\(935\) | 30243.2 | 1.05782 | ||||||||
\(936\) | −2508.36 | −0.0875942 | ||||||||
\(937\) | 6402.67 | 0.223230 | 0.111615 | − | 0.993752i | \(-0.464398\pi\) | ||||
0.111615 | + | 0.993752i | \(0.464398\pi\) | |||||||
\(938\) | 22398.6 | 0.779680 | ||||||||
\(939\) | −28204.5 | −0.980214 | ||||||||
\(940\) | 3843.49 | 0.133363 | ||||||||
\(941\) | 21377.3 | 0.740573 | 0.370286 | − | 0.928918i | \(-0.379260\pi\) | ||||
0.370286 | + | 0.928918i | \(0.379260\pi\) | |||||||
\(942\) | 1951.46 | 0.0674967 | ||||||||
\(943\) | 44172.1 | 1.52539 | ||||||||
\(944\) | −48709.8 | −1.67942 | ||||||||
\(945\) | −34630.3 | −1.19209 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4062.88 | 0.139415 | 0.0697074 | − | 0.997567i | \(-0.477793\pi\) | ||||
0.0697074 | + | 0.997567i | \(0.477793\pi\) | |||||||
\(948\) | 3930.12 | 0.134646 | ||||||||
\(949\) | 8049.95 | 0.275356 | ||||||||
\(950\) | −1408.36 | −0.0480982 | ||||||||
\(951\) | 11027.0 | 0.375999 | ||||||||
\(952\) | 27471.2 | 0.935240 | ||||||||
\(953\) | −25971.9 | −0.882803 | −0.441402 | − | 0.897310i | \(-0.645519\pi\) | ||||
−0.441402 | + | 0.897310i | \(0.645519\pi\) | |||||||
\(954\) | 1889.55 | 0.0641264 | ||||||||
\(955\) | −36346.8 | −1.23157 | ||||||||
\(956\) | 7804.25 | 0.264025 | ||||||||
\(957\) | −23637.1 | −0.798410 | ||||||||
\(958\) | −2373.83 | −0.0800575 | ||||||||
\(959\) | −10474.6 | −0.352702 | ||||||||
\(960\) | −31553.3 | −1.06081 | ||||||||
\(961\) | 410.955 | 0.0137946 | ||||||||
\(962\) | 61616.7 | 2.06507 | ||||||||
\(963\) | 1425.55 | 0.0477028 | ||||||||
\(964\) | −2315.84 | −0.0773737 | ||||||||
\(965\) | 36649.6 | 1.22258 | ||||||||
\(966\) | −30437.2 | −1.01377 | ||||||||
\(967\) | −30978.6 | −1.03020 | −0.515100 | − | 0.857130i | \(-0.672245\pi\) | ||||
−0.515100 | + | 0.857130i | \(0.672245\pi\) | |||||||
\(968\) | −17714.5 | −0.588188 | ||||||||
\(969\) | 1655.33 | 0.0548780 | ||||||||
\(970\) | −75678.7 | −2.50505 | ||||||||
\(971\) | −15282.5 | −0.505085 | −0.252543 | − | 0.967586i | \(-0.581267\pi\) | ||||
−0.252543 | + | 0.967586i | \(0.581267\pi\) | |||||||
\(972\) | −777.843 | −0.0256680 | ||||||||
\(973\) | −41611.0 | −1.37100 | ||||||||
\(974\) | −43336.6 | −1.42566 | ||||||||
\(975\) | −36607.7 | −1.20245 | ||||||||
\(976\) | −33651.5 | −1.10365 | ||||||||
\(977\) | 19872.6 | 0.650748 | 0.325374 | − | 0.945585i | \(-0.394510\pi\) | ||||
0.325374 | + | 0.945585i | \(0.394510\pi\) | |||||||
\(978\) | −59313.0 | −1.93929 | ||||||||
\(979\) | 34686.9 | 1.13238 | ||||||||
\(980\) | −2410.37 | −0.0785679 | ||||||||
\(981\) | 1833.97 | 0.0596883 | ||||||||
\(982\) | −8180.73 | −0.265843 | ||||||||
\(983\) | 23591.4 | 0.765463 | 0.382732 | − | 0.923860i | \(-0.374983\pi\) | ||||
0.382732 | + | 0.923860i | \(0.374983\pi\) | |||||||
\(984\) | −34009.4 | −1.10181 | ||||||||
\(985\) | 51967.9 | 1.68105 | ||||||||
\(986\) | −60113.7 | −1.94159 | ||||||||
\(987\) | 13778.0 | 0.444334 | ||||||||
\(988\) | 293.026 | 0.00943561 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −2157.03 | −0.0692474 | ||||||||
\(991\) | −43277.7 | −1.38725 | −0.693624 | − | 0.720337i | \(-0.743987\pi\) | ||||
−0.693624 | + | 0.720337i | \(0.743987\pi\) | |||||||
\(992\) | −10385.7 | −0.332406 | ||||||||
\(993\) | −26847.7 | −0.857992 | ||||||||
\(994\) | −16548.3 | −0.528050 | ||||||||
\(995\) | −51555.4 | −1.64263 | ||||||||
\(996\) | 302.968 | 0.00963845 | ||||||||
\(997\) | 8111.07 | 0.257653 | 0.128826 | − | 0.991667i | \(-0.458879\pi\) | ||||
0.128826 | + | 0.991667i | \(0.458879\pi\) | |||||||
\(998\) | −35974.7 | −1.14104 | ||||||||
\(999\) | −49524.7 | −1.56846 |
(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 | 1849.4.a.e.1.3 | ✓ | 10 | |
43.42 | odd | 2 | inner | 1849.4.a.e.1.8 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1849.4.a.e.1.3 | ✓ | 10 | 1.1 | even | 1 | trivial | |
1849.4.a.e.1.8 | yes | 10 | 43.42 | odd | 2 | inner |