Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,4,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(10.4433380710\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 45x^{6} + 47x^{5} + 654x^{4} - 157x^{3} - 2898x^{2} + 96x + 2432 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-3.08481\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.08481 | 1.44420 | 0.722099 | − | 0.691790i | \(-0.243178\pi\) | ||||
0.722099 | + | 0.691790i | \(0.243178\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 8.68564 | 1.08571 | ||||||||
\(5\) | −7.45529 | −0.666822 | −0.333411 | − | 0.942782i | \(-0.608200\pi\) | ||||
−0.333411 | + | 0.942782i | \(0.608200\pi\) | |||||||
\(6\) | 12.2544 | 0.833808 | ||||||||
\(7\) | 34.0237 | 1.83711 | 0.918554 | − | 0.395296i | \(-0.129358\pi\) | ||||
0.918554 | + | 0.395296i | \(0.129358\pi\) | |||||||
\(8\) | 2.80073 | 0.123776 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −30.4534 | −0.963022 | ||||||||
\(11\) | 30.1014 | 0.825083 | 0.412542 | − | 0.910939i | \(-0.364641\pi\) | ||||
0.412542 | + | 0.910939i | \(0.364641\pi\) | |||||||
\(12\) | 26.0569 | 0.626832 | ||||||||
\(13\) | −5.30717 | −0.113226 | −0.0566132 | − | 0.998396i | \(-0.518030\pi\) | ||||
−0.0566132 | + | 0.998396i | \(0.518030\pi\) | |||||||
\(14\) | 138.980 | 2.65315 | ||||||||
\(15\) | −22.3659 | −0.384990 | ||||||||
\(16\) | −58.0447 | −0.906949 | ||||||||
\(17\) | 63.2506 | 0.902384 | 0.451192 | − | 0.892427i | \(-0.350999\pi\) | ||||
0.451192 | + | 0.892427i | \(0.350999\pi\) | |||||||
\(18\) | 36.7633 | 0.481399 | ||||||||
\(19\) | −86.0442 | −1.03894 | −0.519471 | − | 0.854488i | \(-0.673871\pi\) | ||||
−0.519471 | + | 0.854488i | \(0.673871\pi\) | |||||||
\(20\) | −64.7540 | −0.723972 | ||||||||
\(21\) | 102.071 | 1.06065 | ||||||||
\(22\) | 122.958 | 1.19158 | ||||||||
\(23\) | 83.0398 | 0.752826 | 0.376413 | − | 0.926452i | \(-0.377157\pi\) | ||||
0.376413 | + | 0.926452i | \(0.377157\pi\) | |||||||
\(24\) | 8.40218 | 0.0714620 | ||||||||
\(25\) | −69.4186 | −0.555349 | ||||||||
\(26\) | −21.6788 | −0.163521 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 295.518 | 1.99456 | ||||||||
\(29\) | −27.8076 | −0.178060 | −0.0890299 | − | 0.996029i | \(-0.528377\pi\) | ||||
−0.0890299 | + | 0.996029i | \(0.528377\pi\) | |||||||
\(30\) | −91.3603 | −0.556001 | ||||||||
\(31\) | −48.3051 | −0.279866 | −0.139933 | − | 0.990161i | \(-0.544689\pi\) | ||||
−0.139933 | + | 0.990161i | \(0.544689\pi\) | |||||||
\(32\) | −259.507 | −1.43359 | ||||||||
\(33\) | 90.3042 | 0.476362 | ||||||||
\(34\) | 258.366 | 1.30322 | ||||||||
\(35\) | −253.657 | −1.22502 | ||||||||
\(36\) | 78.1708 | 0.361902 | ||||||||
\(37\) | −358.130 | −1.59125 | −0.795625 | − | 0.605789i | \(-0.792857\pi\) | ||||
−0.795625 | + | 0.605789i | \(0.792857\pi\) | |||||||
\(38\) | −351.474 | −1.50044 | ||||||||
\(39\) | −15.9215 | −0.0653713 | ||||||||
\(40\) | −20.8802 | −0.0825363 | ||||||||
\(41\) | −139.953 | −0.533096 | −0.266548 | − | 0.963822i | \(-0.585883\pi\) | ||||
−0.266548 | + | 0.963822i | \(0.585883\pi\) | |||||||
\(42\) | 416.941 | 1.53179 | ||||||||
\(43\) | −366.669 | −1.30038 | −0.650192 | − | 0.759770i | \(-0.725312\pi\) | ||||
−0.650192 | + | 0.759770i | \(0.725312\pi\) | |||||||
\(44\) | 261.450 | 0.895797 | ||||||||
\(45\) | −67.0976 | −0.222274 | ||||||||
\(46\) | 339.202 | 1.08723 | ||||||||
\(47\) | −130.162 | −0.403959 | −0.201979 | − | 0.979390i | \(-0.564737\pi\) | ||||
−0.201979 | + | 0.979390i | \(0.564737\pi\) | |||||||
\(48\) | −174.134 | −0.523627 | ||||||||
\(49\) | 814.613 | 2.37497 | ||||||||
\(50\) | −283.562 | −0.802034 | ||||||||
\(51\) | 189.752 | 0.520992 | ||||||||
\(52\) | −46.0962 | −0.122931 | ||||||||
\(53\) | 608.850 | 1.57796 | 0.788982 | − | 0.614417i | \(-0.210609\pi\) | ||||
0.788982 | + | 0.614417i | \(0.210609\pi\) | |||||||
\(54\) | 110.290 | 0.277936 | ||||||||
\(55\) | −224.415 | −0.550183 | ||||||||
\(56\) | 95.2911 | 0.227389 | ||||||||
\(57\) | −258.133 | −0.599833 | ||||||||
\(58\) | −113.588 | −0.257153 | ||||||||
\(59\) | 59.0000 | 0.130189 | ||||||||
\(60\) | −194.262 | −0.417985 | ||||||||
\(61\) | −361.223 | −0.758194 | −0.379097 | − | 0.925357i | \(-0.623765\pi\) | ||||
−0.379097 | + | 0.925357i | \(0.623765\pi\) | |||||||
\(62\) | −197.317 | −0.404182 | ||||||||
\(63\) | 306.213 | 0.612369 | ||||||||
\(64\) | −595.679 | −1.16344 | ||||||||
\(65\) | 39.5665 | 0.0755018 | ||||||||
\(66\) | 368.875 | 0.687961 | ||||||||
\(67\) | −519.397 | −0.947082 | −0.473541 | − | 0.880772i | \(-0.657024\pi\) | ||||
−0.473541 | + | 0.880772i | \(0.657024\pi\) | |||||||
\(68\) | 549.372 | 0.979723 | ||||||||
\(69\) | 249.120 | 0.434644 | ||||||||
\(70\) | −1036.14 | −1.76917 | ||||||||
\(71\) | −733.270 | −1.22568 | −0.612839 | − | 0.790208i | \(-0.709973\pi\) | ||||
−0.612839 | + | 0.790208i | \(0.709973\pi\) | |||||||
\(72\) | 25.2065 | 0.0412586 | ||||||||
\(73\) | 1132.20 | 1.81525 | 0.907626 | − | 0.419779i | \(-0.137893\pi\) | ||||
0.907626 | + | 0.419779i | \(0.137893\pi\) | |||||||
\(74\) | −1462.89 | −2.29808 | ||||||||
\(75\) | −208.256 | −0.320631 | ||||||||
\(76\) | −747.349 | −1.12798 | ||||||||
\(77\) | 1024.16 | 1.51577 | ||||||||
\(78\) | −65.0363 | −0.0944091 | ||||||||
\(79\) | 280.538 | 0.399532 | 0.199766 | − | 0.979844i | \(-0.435982\pi\) | ||||
0.199766 | + | 0.979844i | \(0.435982\pi\) | |||||||
\(80\) | 432.740 | 0.604773 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −571.680 | −0.769896 | ||||||||
\(83\) | 239.288 | 0.316450 | 0.158225 | − | 0.987403i | \(-0.449423\pi\) | ||||
0.158225 | + | 0.987403i | \(0.449423\pi\) | |||||||
\(84\) | 886.554 | 1.15156 | ||||||||
\(85\) | −471.552 | −0.601729 | ||||||||
\(86\) | −1497.77 | −1.87801 | ||||||||
\(87\) | −83.4227 | −0.102803 | ||||||||
\(88\) | 84.3058 | 0.102125 | ||||||||
\(89\) | 1214.72 | 1.44674 | 0.723372 | − | 0.690459i | \(-0.242591\pi\) | ||||
0.723372 | + | 0.690459i | \(0.242591\pi\) | |||||||
\(90\) | −274.081 | −0.321007 | ||||||||
\(91\) | −180.570 | −0.208009 | ||||||||
\(92\) | 721.255 | 0.817348 | ||||||||
\(93\) | −144.915 | −0.161581 | ||||||||
\(94\) | −531.686 | −0.583396 | ||||||||
\(95\) | 641.485 | 0.692789 | ||||||||
\(96\) | −778.522 | −0.827683 | ||||||||
\(97\) | 149.047 | 0.156015 | 0.0780074 | − | 0.996953i | \(-0.475144\pi\) | ||||
0.0780074 | + | 0.996953i | \(0.475144\pi\) | |||||||
\(98\) | 3327.54 | 3.42992 | ||||||||
\(99\) | 270.913 | 0.275028 | ||||||||
\(100\) | −602.946 | −0.602946 | ||||||||
\(101\) | −491.208 | −0.483931 | −0.241965 | − | 0.970285i | \(-0.577792\pi\) | ||||
−0.241965 | + | 0.970285i | \(0.577792\pi\) | |||||||
\(102\) | 775.099 | 0.752415 | ||||||||
\(103\) | −1710.99 | −1.63679 | −0.818393 | − | 0.574658i | \(-0.805135\pi\) | ||||
−0.818393 | + | 0.574658i | \(0.805135\pi\) | |||||||
\(104\) | −14.8639 | −0.0140147 | ||||||||
\(105\) | −760.970 | −0.707267 | ||||||||
\(106\) | 2487.04 | 2.27889 | ||||||||
\(107\) | 19.6195 | 0.0177261 | 0.00886304 | − | 0.999961i | \(-0.497179\pi\) | ||||
0.00886304 | + | 0.999961i | \(0.497179\pi\) | |||||||
\(108\) | 234.512 | 0.208944 | ||||||||
\(109\) | 227.070 | 0.199535 | 0.0997677 | − | 0.995011i | \(-0.468190\pi\) | ||||
0.0997677 | + | 0.995011i | \(0.468190\pi\) | |||||||
\(110\) | −916.691 | −0.794573 | ||||||||
\(111\) | −1074.39 | −0.918709 | ||||||||
\(112\) | −1974.90 | −1.66616 | ||||||||
\(113\) | −406.168 | −0.338134 | −0.169067 | − | 0.985605i | \(-0.554075\pi\) | ||||
−0.169067 | + | 0.985605i | \(0.554075\pi\) | |||||||
\(114\) | −1054.42 | −0.866278 | ||||||||
\(115\) | −619.086 | −0.502001 | ||||||||
\(116\) | −241.527 | −0.193320 | ||||||||
\(117\) | −47.7645 | −0.0377421 | ||||||||
\(118\) | 241.004 | 0.188018 | ||||||||
\(119\) | 2152.02 | 1.65778 | ||||||||
\(120\) | −62.6407 | −0.0476524 | ||||||||
\(121\) | −424.905 | −0.319238 | ||||||||
\(122\) | −1475.52 | −1.09498 | ||||||||
\(123\) | −419.858 | −0.307783 | ||||||||
\(124\) | −419.561 | −0.303852 | ||||||||
\(125\) | 1449.45 | 1.03714 | ||||||||
\(126\) | 1250.82 | 0.884382 | ||||||||
\(127\) | 1305.00 | 0.911810 | 0.455905 | − | 0.890028i | \(-0.349316\pi\) | ||||
0.455905 | + | 0.890028i | \(0.349316\pi\) | |||||||
\(128\) | −357.176 | −0.246642 | ||||||||
\(129\) | −1100.01 | −0.750777 | ||||||||
\(130\) | 161.621 | 0.109040 | ||||||||
\(131\) | 1256.06 | 0.837727 | 0.418863 | − | 0.908049i | \(-0.362429\pi\) | ||||
0.418863 | + | 0.908049i | \(0.362429\pi\) | |||||||
\(132\) | 784.350 | 0.517189 | ||||||||
\(133\) | −2927.54 | −1.90865 | ||||||||
\(134\) | −2121.64 | −1.36777 | ||||||||
\(135\) | −201.293 | −0.128330 | ||||||||
\(136\) | 177.148 | 0.111693 | ||||||||
\(137\) | −1061.86 | −0.662198 | −0.331099 | − | 0.943596i | \(-0.607419\pi\) | ||||
−0.331099 | + | 0.943596i | \(0.607419\pi\) | |||||||
\(138\) | 1017.61 | 0.627712 | ||||||||
\(139\) | −1006.82 | −0.614368 | −0.307184 | − | 0.951650i | \(-0.599387\pi\) | ||||
−0.307184 | + | 0.951650i | \(0.599387\pi\) | |||||||
\(140\) | −2203.17 | −1.33001 | ||||||||
\(141\) | −390.485 | −0.233226 | ||||||||
\(142\) | −2995.27 | −1.77012 | ||||||||
\(143\) | −159.753 | −0.0934212 | ||||||||
\(144\) | −522.403 | −0.302316 | ||||||||
\(145\) | 207.313 | 0.118734 | ||||||||
\(146\) | 4624.80 | 2.62158 | ||||||||
\(147\) | 2443.84 | 1.37119 | ||||||||
\(148\) | −3110.59 | −1.72763 | ||||||||
\(149\) | 971.154 | 0.533960 | 0.266980 | − | 0.963702i | \(-0.413974\pi\) | ||||
0.266980 | + | 0.963702i | \(0.413974\pi\) | |||||||
\(150\) | −850.685 | −0.463054 | ||||||||
\(151\) | 3599.13 | 1.93969 | 0.969843 | − | 0.243729i | \(-0.0783708\pi\) | ||||
0.969843 | + | 0.243729i | \(0.0783708\pi\) | |||||||
\(152\) | −240.986 | −0.128596 | ||||||||
\(153\) | 569.255 | 0.300795 | ||||||||
\(154\) | 4183.50 | 2.18907 | ||||||||
\(155\) | 360.129 | 0.186621 | ||||||||
\(156\) | −138.289 | −0.0709740 | ||||||||
\(157\) | 1208.64 | 0.614393 | 0.307197 | − | 0.951646i | \(-0.400609\pi\) | ||||
0.307197 | + | 0.951646i | \(0.400609\pi\) | |||||||
\(158\) | 1145.94 | 0.577003 | ||||||||
\(159\) | 1826.55 | 0.911037 | ||||||||
\(160\) | 1934.70 | 0.955948 | ||||||||
\(161\) | 2825.32 | 1.38302 | ||||||||
\(162\) | 330.869 | 0.160466 | ||||||||
\(163\) | 686.989 | 0.330118 | 0.165059 | − | 0.986284i | \(-0.447219\pi\) | ||||
0.165059 | + | 0.986284i | \(0.447219\pi\) | |||||||
\(164\) | −1215.58 | −0.578785 | ||||||||
\(165\) | −673.244 | −0.317648 | ||||||||
\(166\) | 977.447 | 0.457016 | ||||||||
\(167\) | 3111.46 | 1.44175 | 0.720874 | − | 0.693066i | \(-0.243740\pi\) | ||||
0.720874 | + | 0.693066i | \(0.243740\pi\) | |||||||
\(168\) | 285.873 | 0.131283 | ||||||||
\(169\) | −2168.83 | −0.987180 | ||||||||
\(170\) | −1926.20 | −0.869015 | ||||||||
\(171\) | −774.398 | −0.346314 | ||||||||
\(172\) | −3184.76 | −1.41183 | ||||||||
\(173\) | 574.070 | 0.252288 | 0.126144 | − | 0.992012i | \(-0.459740\pi\) | ||||
0.126144 | + | 0.992012i | \(0.459740\pi\) | |||||||
\(174\) | −340.765 | −0.148468 | ||||||||
\(175\) | −2361.88 | −1.02024 | ||||||||
\(176\) | −1747.23 | −0.748308 | ||||||||
\(177\) | 177.000 | 0.0751646 | ||||||||
\(178\) | 4961.90 | 2.08938 | ||||||||
\(179\) | 3296.00 | 1.37628 | 0.688142 | − | 0.725576i | \(-0.258426\pi\) | ||||
0.688142 | + | 0.725576i | \(0.258426\pi\) | |||||||
\(180\) | −582.786 | −0.241324 | ||||||||
\(181\) | 2022.64 | 0.830616 | 0.415308 | − | 0.909681i | \(-0.363674\pi\) | ||||
0.415308 | + | 0.909681i | \(0.363674\pi\) | |||||||
\(182\) | −737.592 | −0.300406 | ||||||||
\(183\) | −1083.67 | −0.437743 | ||||||||
\(184\) | 232.572 | 0.0931816 | ||||||||
\(185\) | 2669.97 | 1.06108 | ||||||||
\(186\) | −591.951 | −0.233355 | ||||||||
\(187\) | 1903.93 | 0.744542 | ||||||||
\(188\) | −1130.54 | −0.438580 | ||||||||
\(189\) | 918.640 | 0.353552 | ||||||||
\(190\) | 2620.34 | 1.00052 | ||||||||
\(191\) | −3437.29 | −1.30216 | −0.651082 | − | 0.759007i | \(-0.725685\pi\) | ||||
−0.651082 | + | 0.759007i | \(0.725685\pi\) | |||||||
\(192\) | −1787.04 | −0.671710 | ||||||||
\(193\) | 4382.77 | 1.63460 | 0.817301 | − | 0.576210i | \(-0.195469\pi\) | ||||
0.817301 | + | 0.576210i | \(0.195469\pi\) | |||||||
\(194\) | 608.828 | 0.225316 | ||||||||
\(195\) | 118.699 | 0.0435910 | ||||||||
\(196\) | 7075.44 | 2.57851 | ||||||||
\(197\) | −5031.35 | −1.81964 | −0.909819 | − | 0.415004i | \(-0.863780\pi\) | ||||
−0.909819 | + | 0.415004i | \(0.863780\pi\) | |||||||
\(198\) | 1106.63 | 0.397194 | ||||||||
\(199\) | 4357.76 | 1.55233 | 0.776164 | − | 0.630532i | \(-0.217163\pi\) | ||||
0.776164 | + | 0.630532i | \(0.217163\pi\) | |||||||
\(200\) | −194.423 | −0.0687387 | ||||||||
\(201\) | −1558.19 | −0.546798 | ||||||||
\(202\) | −2006.49 | −0.698891 | ||||||||
\(203\) | −946.116 | −0.327115 | ||||||||
\(204\) | 1648.12 | 0.565643 | ||||||||
\(205\) | 1043.39 | 0.355480 | ||||||||
\(206\) | −6989.07 | −2.36384 | ||||||||
\(207\) | 747.359 | 0.250942 | ||||||||
\(208\) | 308.053 | 0.102691 | ||||||||
\(209\) | −2590.05 | −0.857213 | ||||||||
\(210\) | −3108.42 | −1.02143 | ||||||||
\(211\) | −4436.30 | −1.44743 | −0.723715 | − | 0.690099i | \(-0.757567\pi\) | ||||
−0.723715 | + | 0.690099i | \(0.757567\pi\) | |||||||
\(212\) | 5288.26 | 1.71320 | ||||||||
\(213\) | −2199.81 | −0.707645 | ||||||||
\(214\) | 80.1420 | 0.0256000 | ||||||||
\(215\) | 2733.63 | 0.867124 | ||||||||
\(216\) | 75.6196 | 0.0238207 | ||||||||
\(217\) | −1643.52 | −0.514144 | ||||||||
\(218\) | 927.536 | 0.288168 | ||||||||
\(219\) | 3396.59 | 1.04804 | ||||||||
\(220\) | −1949.19 | −0.597337 | ||||||||
\(221\) | −335.682 | −0.102174 | ||||||||
\(222\) | −4388.68 | −1.32680 | ||||||||
\(223\) | −518.147 | −0.155595 | −0.0777975 | − | 0.996969i | \(-0.524789\pi\) | ||||
−0.0777975 | + | 0.996969i | \(0.524789\pi\) | |||||||
\(224\) | −8829.40 | −2.63366 | ||||||||
\(225\) | −624.768 | −0.185116 | ||||||||
\(226\) | −1659.12 | −0.488332 | ||||||||
\(227\) | −5358.31 | −1.56671 | −0.783355 | − | 0.621574i | \(-0.786493\pi\) | ||||
−0.783355 | + | 0.621574i | \(0.786493\pi\) | |||||||
\(228\) | −2242.05 | −0.651242 | ||||||||
\(229\) | 2805.75 | 0.809647 | 0.404823 | − | 0.914395i | \(-0.367333\pi\) | ||||
0.404823 | + | 0.914395i | \(0.367333\pi\) | |||||||
\(230\) | −2528.85 | −0.724988 | ||||||||
\(231\) | 3072.48 | 0.875128 | ||||||||
\(232\) | −77.8813 | −0.0220395 | ||||||||
\(233\) | −4221.06 | −1.18683 | −0.593414 | − | 0.804897i | \(-0.702220\pi\) | ||||
−0.593414 | + | 0.804897i | \(0.702220\pi\) | |||||||
\(234\) | −195.109 | −0.0545071 | ||||||||
\(235\) | 970.394 | 0.269368 | ||||||||
\(236\) | 512.453 | 0.141347 | ||||||||
\(237\) | 841.614 | 0.230670 | ||||||||
\(238\) | 8790.59 | 2.39416 | ||||||||
\(239\) | 5412.00 | 1.46474 | 0.732371 | − | 0.680905i | \(-0.238414\pi\) | ||||
0.732371 | + | 0.680905i | \(0.238414\pi\) | |||||||
\(240\) | 1298.22 | 0.349166 | ||||||||
\(241\) | −3003.56 | −0.802806 | −0.401403 | − | 0.915902i | \(-0.631477\pi\) | ||||
−0.401403 | + | 0.915902i | \(0.631477\pi\) | |||||||
\(242\) | −1735.66 | −0.461042 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | −3137.45 | −0.823175 | ||||||||
\(245\) | −6073.18 | −1.58368 | ||||||||
\(246\) | −1715.04 | −0.444500 | ||||||||
\(247\) | 456.651 | 0.117636 | ||||||||
\(248\) | −135.289 | −0.0346407 | ||||||||
\(249\) | 717.865 | 0.182702 | ||||||||
\(250\) | 5920.71 | 1.49784 | ||||||||
\(251\) | −900.091 | −0.226348 | −0.113174 | − | 0.993575i | \(-0.536102\pi\) | ||||
−0.113174 | + | 0.993575i | \(0.536102\pi\) | |||||||
\(252\) | 2659.66 | 0.664853 | ||||||||
\(253\) | 2499.62 | 0.621144 | ||||||||
\(254\) | 5330.67 | 1.31683 | ||||||||
\(255\) | −1414.66 | −0.347408 | ||||||||
\(256\) | 3306.44 | 0.807236 | ||||||||
\(257\) | 3419.24 | 0.829907 | 0.414953 | − | 0.909843i | \(-0.363798\pi\) | ||||
0.414953 | + | 0.909843i | \(0.363798\pi\) | |||||||
\(258\) | −4493.32 | −1.08427 | ||||||||
\(259\) | −12184.9 | −2.92330 | ||||||||
\(260\) | 343.660 | 0.0819727 | ||||||||
\(261\) | −250.268 | −0.0593533 | ||||||||
\(262\) | 5130.75 | 1.20984 | ||||||||
\(263\) | 1273.15 | 0.298501 | 0.149250 | − | 0.988799i | \(-0.452314\pi\) | ||||
0.149250 | + | 0.988799i | \(0.452314\pi\) | |||||||
\(264\) | 252.917 | 0.0589621 | ||||||||
\(265\) | −4539.16 | −1.05222 | ||||||||
\(266\) | −11958.4 | −2.75646 | ||||||||
\(267\) | 3644.16 | 0.835278 | ||||||||
\(268\) | −4511.30 | −1.02825 | ||||||||
\(269\) | 3437.51 | 0.779141 | 0.389570 | − | 0.920997i | \(-0.372624\pi\) | ||||
0.389570 | + | 0.920997i | \(0.372624\pi\) | |||||||
\(270\) | −822.242 | −0.185334 | ||||||||
\(271\) | −2409.95 | −0.540199 | −0.270100 | − | 0.962832i | \(-0.587057\pi\) | ||||
−0.270100 | + | 0.962832i | \(0.587057\pi\) | |||||||
\(272\) | −3671.36 | −0.818416 | ||||||||
\(273\) | −541.709 | −0.120094 | ||||||||
\(274\) | −4337.51 | −0.956344 | ||||||||
\(275\) | −2089.60 | −0.458209 | ||||||||
\(276\) | 2163.76 | 0.471896 | ||||||||
\(277\) | −7279.05 | −1.57890 | −0.789450 | − | 0.613814i | \(-0.789634\pi\) | ||||
−0.789450 | + | 0.613814i | \(0.789634\pi\) | |||||||
\(278\) | −4112.66 | −0.887269 | ||||||||
\(279\) | −434.746 | −0.0932887 | ||||||||
\(280\) | −710.423 | −0.151628 | ||||||||
\(281\) | 6298.57 | 1.33716 | 0.668579 | − | 0.743641i | \(-0.266903\pi\) | ||||
0.668579 | + | 0.743641i | \(0.266903\pi\) | |||||||
\(282\) | −1595.06 | −0.336824 | ||||||||
\(283\) | −3561.67 | −0.748124 | −0.374062 | − | 0.927404i | \(-0.622035\pi\) | ||||
−0.374062 | + | 0.927404i | \(0.622035\pi\) | |||||||
\(284\) | −6368.92 | −1.33072 | ||||||||
\(285\) | 1924.45 | 0.399982 | ||||||||
\(286\) | −652.561 | −0.134919 | ||||||||
\(287\) | −4761.71 | −0.979355 | ||||||||
\(288\) | −2335.57 | −0.477863 | ||||||||
\(289\) | −912.361 | −0.185703 | ||||||||
\(290\) | 846.835 | 0.171475 | ||||||||
\(291\) | 447.141 | 0.0900752 | ||||||||
\(292\) | 9833.84 | 1.97083 | ||||||||
\(293\) | −4374.10 | −0.872142 | −0.436071 | − | 0.899912i | \(-0.643630\pi\) | ||||
−0.436071 | + | 0.899912i | \(0.643630\pi\) | |||||||
\(294\) | 9982.61 | 1.98026 | ||||||||
\(295\) | −439.862 | −0.0868128 | ||||||||
\(296\) | −1003.02 | −0.196958 | ||||||||
\(297\) | 812.738 | 0.158787 | ||||||||
\(298\) | 3966.98 | 0.771144 | ||||||||
\(299\) | −440.706 | −0.0852398 | ||||||||
\(300\) | −1808.84 | −0.348111 | ||||||||
\(301\) | −12475.4 | −2.38895 | ||||||||
\(302\) | 14701.7 | 2.80129 | ||||||||
\(303\) | −1473.62 | −0.279397 | ||||||||
\(304\) | 4994.41 | 0.942267 | ||||||||
\(305\) | 2693.02 | 0.505580 | ||||||||
\(306\) | 2325.30 | 0.434407 | ||||||||
\(307\) | 5264.64 | 0.978726 | 0.489363 | − | 0.872080i | \(-0.337229\pi\) | ||||
0.489363 | + | 0.872080i | \(0.337229\pi\) | |||||||
\(308\) | 8895.50 | 1.64568 | ||||||||
\(309\) | −5132.98 | −0.944999 | ||||||||
\(310\) | 1471.06 | 0.269517 | ||||||||
\(311\) | 3889.00 | 0.709083 | 0.354542 | − | 0.935040i | \(-0.384637\pi\) | ||||
0.354542 | + | 0.935040i | \(0.384637\pi\) | |||||||
\(312\) | −44.5918 | −0.00809138 | ||||||||
\(313\) | −8815.40 | −1.59194 | −0.795968 | − | 0.605339i | \(-0.793038\pi\) | ||||
−0.795968 | + | 0.605339i | \(0.793038\pi\) | |||||||
\(314\) | 4937.05 | 0.887305 | ||||||||
\(315\) | −2282.91 | −0.408341 | ||||||||
\(316\) | 2436.65 | 0.433774 | ||||||||
\(317\) | −10172.7 | −1.80239 | −0.901196 | − | 0.433412i | \(-0.857309\pi\) | ||||
−0.901196 | + | 0.433412i | \(0.857309\pi\) | |||||||
\(318\) | 7461.11 | 1.31572 | ||||||||
\(319\) | −837.047 | −0.146914 | ||||||||
\(320\) | 4440.96 | 0.775804 | ||||||||
\(321\) | 58.8586 | 0.0102342 | ||||||||
\(322\) | 11540.9 | 1.99736 | ||||||||
\(323\) | −5442.35 | −0.937524 | ||||||||
\(324\) | 703.537 | 0.120634 | ||||||||
\(325\) | 368.416 | 0.0628802 | ||||||||
\(326\) | 2806.22 | 0.476755 | ||||||||
\(327\) | 681.210 | 0.115202 | ||||||||
\(328\) | −391.969 | −0.0659844 | ||||||||
\(329\) | −4428.59 | −0.742115 | ||||||||
\(330\) | −2750.07 | −0.458747 | ||||||||
\(331\) | −2899.09 | −0.481415 | −0.240707 | − | 0.970598i | \(-0.577379\pi\) | ||||
−0.240707 | + | 0.970598i | \(0.577379\pi\) | |||||||
\(332\) | 2078.37 | 0.343571 | ||||||||
\(333\) | −3223.17 | −0.530417 | ||||||||
\(334\) | 12709.7 | 2.08217 | ||||||||
\(335\) | 3872.26 | 0.631534 | ||||||||
\(336\) | −5924.69 | −0.961960 | ||||||||
\(337\) | −11201.0 | −1.81055 | −0.905277 | − | 0.424821i | \(-0.860337\pi\) | ||||
−0.905277 | + | 0.424821i | \(0.860337\pi\) | |||||||
\(338\) | −8859.27 | −1.42568 | ||||||||
\(339\) | −1218.51 | −0.195222 | ||||||||
\(340\) | −4095.73 | −0.653300 | ||||||||
\(341\) | −1454.05 | −0.230913 | ||||||||
\(342\) | −3163.27 | −0.500146 | ||||||||
\(343\) | 16046.0 | 2.52596 | ||||||||
\(344\) | −1026.94 | −0.160956 | ||||||||
\(345\) | −1857.26 | −0.289830 | ||||||||
\(346\) | 2344.97 | 0.364353 | ||||||||
\(347\) | 9034.82 | 1.39774 | 0.698868 | − | 0.715251i | \(-0.253687\pi\) | ||||
0.698868 | + | 0.715251i | \(0.253687\pi\) | |||||||
\(348\) | −724.580 | −0.111614 | ||||||||
\(349\) | 2985.35 | 0.457886 | 0.228943 | − | 0.973440i | \(-0.426473\pi\) | ||||
0.228943 | + | 0.973440i | \(0.426473\pi\) | |||||||
\(350\) | −9647.82 | −1.47342 | ||||||||
\(351\) | −143.294 | −0.0217904 | ||||||||
\(352\) | −7811.54 | −1.18283 | ||||||||
\(353\) | 10272.8 | 1.54892 | 0.774458 | − | 0.632626i | \(-0.218023\pi\) | ||||
0.774458 | + | 0.632626i | \(0.218023\pi\) | |||||||
\(354\) | 723.011 | 0.108553 | ||||||||
\(355\) | 5466.74 | 0.817308 | ||||||||
\(356\) | 10550.6 | 1.57074 | ||||||||
\(357\) | 6456.06 | 0.957118 | ||||||||
\(358\) | 13463.5 | 1.98763 | ||||||||
\(359\) | −4648.82 | −0.683442 | −0.341721 | − | 0.939802i | \(-0.611010\pi\) | ||||
−0.341721 | + | 0.939802i | \(0.611010\pi\) | |||||||
\(360\) | −187.922 | −0.0275121 | ||||||||
\(361\) | 544.604 | 0.0793999 | ||||||||
\(362\) | 8262.08 | 1.19957 | ||||||||
\(363\) | −1274.72 | −0.184312 | ||||||||
\(364\) | −1568.36 | −0.225837 | ||||||||
\(365\) | −8440.84 | −1.21045 | ||||||||
\(366\) | −4426.57 | −0.632188 | ||||||||
\(367\) | −1646.71 | −0.234216 | −0.117108 | − | 0.993119i | \(-0.537362\pi\) | ||||
−0.117108 | + | 0.993119i | \(0.537362\pi\) | |||||||
\(368\) | −4820.03 | −0.682775 | ||||||||
\(369\) | −1259.57 | −0.177699 | ||||||||
\(370\) | 10906.3 | 1.53241 | ||||||||
\(371\) | 20715.4 | 2.89889 | ||||||||
\(372\) | −1258.68 | −0.175429 | ||||||||
\(373\) | 6528.88 | 0.906307 | 0.453154 | − | 0.891432i | \(-0.350299\pi\) | ||||
0.453154 | + | 0.891432i | \(0.350299\pi\) | |||||||
\(374\) | 7777.19 | 1.07527 | ||||||||
\(375\) | 4348.34 | 0.598793 | ||||||||
\(376\) | −364.548 | −0.0500003 | ||||||||
\(377\) | 147.579 | 0.0201611 | ||||||||
\(378\) | 3752.47 | 0.510598 | ||||||||
\(379\) | 6421.70 | 0.870344 | 0.435172 | − | 0.900347i | \(-0.356688\pi\) | ||||
0.435172 | + | 0.900347i | \(0.356688\pi\) | |||||||
\(380\) | 5571.71 | 0.752165 | ||||||||
\(381\) | 3915.00 | 0.526434 | ||||||||
\(382\) | −14040.7 | −1.88058 | ||||||||
\(383\) | −3048.13 | −0.406663 | −0.203332 | − | 0.979110i | \(-0.565177\pi\) | ||||
−0.203332 | + | 0.979110i | \(0.565177\pi\) | |||||||
\(384\) | −1071.53 | −0.142399 | ||||||||
\(385\) | −7635.42 | −1.01075 | ||||||||
\(386\) | 17902.7 | 2.36069 | ||||||||
\(387\) | −3300.02 | −0.433461 | ||||||||
\(388\) | 1294.57 | 0.169386 | ||||||||
\(389\) | 8129.80 | 1.05963 | 0.529816 | − | 0.848112i | \(-0.322261\pi\) | ||||
0.529816 | + | 0.848112i | \(0.322261\pi\) | |||||||
\(390\) | 484.864 | 0.0629540 | ||||||||
\(391\) | 5252.32 | 0.679338 | ||||||||
\(392\) | 2281.51 | 0.293963 | ||||||||
\(393\) | 3768.17 | 0.483662 | ||||||||
\(394\) | −20552.1 | −2.62792 | ||||||||
\(395\) | −2091.49 | −0.266416 | ||||||||
\(396\) | 2353.05 | 0.298599 | ||||||||
\(397\) | −5072.35 | −0.641244 | −0.320622 | − | 0.947207i | \(-0.603892\pi\) | ||||
−0.320622 | + | 0.947207i | \(0.603892\pi\) | |||||||
\(398\) | 17800.6 | 2.24187 | ||||||||
\(399\) | −8782.63 | −1.10196 | ||||||||
\(400\) | 4029.39 | 0.503673 | ||||||||
\(401\) | 9539.59 | 1.18799 | 0.593996 | − | 0.804468i | \(-0.297550\pi\) | ||||
0.593996 | + | 0.804468i | \(0.297550\pi\) | |||||||
\(402\) | −6364.91 | −0.789684 | ||||||||
\(403\) | 256.363 | 0.0316883 | ||||||||
\(404\) | −4266.46 | −0.525406 | ||||||||
\(405\) | −603.879 | −0.0740913 | ||||||||
\(406\) | −3864.70 | −0.472419 | ||||||||
\(407\) | −10780.2 | −1.31291 | ||||||||
\(408\) | 531.443 | 0.0644861 | ||||||||
\(409\) | 10696.8 | 1.29321 | 0.646605 | − | 0.762825i | \(-0.276188\pi\) | ||||
0.646605 | + | 0.762825i | \(0.276188\pi\) | |||||||
\(410\) | 4262.04 | 0.513383 | ||||||||
\(411\) | −3185.59 | −0.382320 | ||||||||
\(412\) | −14861.1 | −1.77707 | ||||||||
\(413\) | 2007.40 | 0.239171 | ||||||||
\(414\) | 3052.82 | 0.362410 | ||||||||
\(415\) | −1783.96 | −0.211015 | ||||||||
\(416\) | 1377.25 | 0.162320 | ||||||||
\(417\) | −3020.45 | −0.354706 | ||||||||
\(418\) | −10579.9 | −1.23799 | ||||||||
\(419\) | −2134.24 | −0.248841 | −0.124421 | − | 0.992230i | \(-0.539707\pi\) | ||||
−0.124421 | + | 0.992230i | \(0.539707\pi\) | |||||||
\(420\) | −6609.52 | −0.767884 | ||||||||
\(421\) | 6780.72 | 0.784970 | 0.392485 | − | 0.919758i | \(-0.371616\pi\) | ||||
0.392485 | + | 0.919758i | \(0.371616\pi\) | |||||||
\(422\) | −18121.4 | −2.09037 | ||||||||
\(423\) | −1171.46 | −0.134653 | ||||||||
\(424\) | 1705.22 | 0.195314 | ||||||||
\(425\) | −4390.77 | −0.501138 | ||||||||
\(426\) | −8985.80 | −1.02198 | ||||||||
\(427\) | −12290.1 | −1.39288 | ||||||||
\(428\) | 170.408 | 0.0192453 | ||||||||
\(429\) | −479.260 | −0.0539368 | ||||||||
\(430\) | 11166.3 | 1.25230 | ||||||||
\(431\) | −16691.4 | −1.86542 | −0.932708 | − | 0.360633i | \(-0.882561\pi\) | ||||
−0.932708 | + | 0.360633i | \(0.882561\pi\) | |||||||
\(432\) | −1567.21 | −0.174542 | ||||||||
\(433\) | −2902.98 | −0.322190 | −0.161095 | − | 0.986939i | \(-0.551503\pi\) | ||||
−0.161095 | + | 0.986939i | \(0.551503\pi\) | |||||||
\(434\) | −6713.46 | −0.742526 | ||||||||
\(435\) | 621.940 | 0.0685512 | ||||||||
\(436\) | 1972.25 | 0.216637 | ||||||||
\(437\) | −7145.10 | −0.782143 | ||||||||
\(438\) | 13874.4 | 1.51357 | ||||||||
\(439\) | 8526.93 | 0.927034 | 0.463517 | − | 0.886088i | \(-0.346587\pi\) | ||||
0.463517 | + | 0.886088i | \(0.346587\pi\) | |||||||
\(440\) | −628.524 | −0.0680993 | ||||||||
\(441\) | 7331.52 | 0.791655 | ||||||||
\(442\) | −1371.19 | −0.147559 | ||||||||
\(443\) | −3174.04 | −0.340413 | −0.170207 | − | 0.985408i | \(-0.554444\pi\) | ||||
−0.170207 | + | 0.985408i | \(0.554444\pi\) | |||||||
\(444\) | −9331.78 | −0.997447 | ||||||||
\(445\) | −9056.10 | −0.964720 | ||||||||
\(446\) | −2116.53 | −0.224710 | ||||||||
\(447\) | 2913.46 | 0.308282 | ||||||||
\(448\) | −20267.2 | −2.13736 | ||||||||
\(449\) | −2111.09 | −0.221889 | −0.110945 | − | 0.993827i | \(-0.535388\pi\) | ||||
−0.110945 | + | 0.993827i | \(0.535388\pi\) | |||||||
\(450\) | −2552.06 | −0.267345 | ||||||||
\(451\) | −4212.77 | −0.439849 | ||||||||
\(452\) | −3527.83 | −0.367114 | ||||||||
\(453\) | 10797.4 | 1.11988 | ||||||||
\(454\) | −21887.6 | −2.26264 | ||||||||
\(455\) | 1346.20 | 0.138705 | ||||||||
\(456\) | −722.959 | −0.0742448 | ||||||||
\(457\) | −6995.71 | −0.716074 | −0.358037 | − | 0.933707i | \(-0.616554\pi\) | ||||
−0.358037 | + | 0.933707i | \(0.616554\pi\) | |||||||
\(458\) | 11460.9 | 1.16929 | ||||||||
\(459\) | 1707.77 | 0.173664 | ||||||||
\(460\) | −5377.16 | −0.545025 | ||||||||
\(461\) | 426.893 | 0.0431288 | 0.0215644 | − | 0.999767i | \(-0.493135\pi\) | ||||
0.0215644 | + | 0.999767i | \(0.493135\pi\) | |||||||
\(462\) | 12550.5 | 1.26386 | ||||||||
\(463\) | 2901.91 | 0.291281 | 0.145641 | − | 0.989338i | \(-0.453476\pi\) | ||||
0.145641 | + | 0.989338i | \(0.453476\pi\) | |||||||
\(464\) | 1614.08 | 0.161491 | ||||||||
\(465\) | 1080.39 | 0.107746 | ||||||||
\(466\) | −17242.2 | −1.71401 | ||||||||
\(467\) | 8424.34 | 0.834758 | 0.417379 | − | 0.908733i | \(-0.362949\pi\) | ||||
0.417379 | + | 0.908733i | \(0.362949\pi\) | |||||||
\(468\) | −414.866 | −0.0409769 | ||||||||
\(469\) | −17671.8 | −1.73989 | ||||||||
\(470\) | 3963.87 | 0.389021 | ||||||||
\(471\) | 3625.91 | 0.354720 | ||||||||
\(472\) | 165.243 | 0.0161142 | ||||||||
\(473\) | −11037.3 | −1.07293 | ||||||||
\(474\) | 3437.83 | 0.333133 | ||||||||
\(475\) | 5973.07 | 0.576975 | ||||||||
\(476\) | 18691.7 | 1.79986 | ||||||||
\(477\) | 5479.65 | 0.525988 | ||||||||
\(478\) | 22107.0 | 2.11538 | ||||||||
\(479\) | −10436.0 | −0.995476 | −0.497738 | − | 0.867327i | \(-0.665836\pi\) | ||||
−0.497738 | + | 0.867327i | \(0.665836\pi\) | |||||||
\(480\) | 5804.11 | 0.551917 | ||||||||
\(481\) | 1900.66 | 0.180172 | ||||||||
\(482\) | −12269.0 | −1.15941 | ||||||||
\(483\) | 8475.97 | 0.798489 | ||||||||
\(484\) | −3690.58 | −0.346598 | ||||||||
\(485\) | −1111.19 | −0.104034 | ||||||||
\(486\) | 992.608 | 0.0926453 | ||||||||
\(487\) | 6183.28 | 0.575341 | 0.287671 | − | 0.957729i | \(-0.407119\pi\) | ||||
0.287671 | + | 0.957729i | \(0.407119\pi\) | |||||||
\(488\) | −1011.69 | −0.0938460 | ||||||||
\(489\) | 2060.97 | 0.190593 | ||||||||
\(490\) | −24807.8 | −2.28714 | ||||||||
\(491\) | −4039.61 | −0.371293 | −0.185647 | − | 0.982617i | \(-0.559438\pi\) | ||||
−0.185647 | + | 0.982617i | \(0.559438\pi\) | |||||||
\(492\) | −3646.74 | −0.334162 | ||||||||
\(493\) | −1758.84 | −0.160678 | ||||||||
\(494\) | 1865.33 | 0.169889 | ||||||||
\(495\) | −2019.73 | −0.183394 | ||||||||
\(496\) | 2803.86 | 0.253824 | ||||||||
\(497\) | −24948.6 | −2.25170 | ||||||||
\(498\) | 2932.34 | 0.263858 | ||||||||
\(499\) | −17134.6 | −1.53718 | −0.768589 | − | 0.639743i | \(-0.779041\pi\) | ||||
−0.768589 | + | 0.639743i | \(0.779041\pi\) | |||||||
\(500\) | 12589.4 | 1.12603 | ||||||||
\(501\) | 9334.38 | 0.832394 | ||||||||
\(502\) | −3676.70 | −0.326890 | ||||||||
\(503\) | 19616.1 | 1.73884 | 0.869422 | − | 0.494069i | \(-0.164491\pi\) | ||||
0.869422 | + | 0.494069i | \(0.164491\pi\) | |||||||
\(504\) | 857.620 | 0.0757965 | ||||||||
\(505\) | 3662.10 | 0.322695 | ||||||||
\(506\) | 10210.4 | 0.897055 | ||||||||
\(507\) | −6506.50 | −0.569949 | ||||||||
\(508\) | 11334.8 | 0.989957 | ||||||||
\(509\) | 15281.4 | 1.33072 | 0.665358 | − | 0.746524i | \(-0.268279\pi\) | ||||
0.665358 | + | 0.746524i | \(0.268279\pi\) | |||||||
\(510\) | −5778.59 | −0.501726 | ||||||||
\(511\) | 38521.5 | 3.33481 | ||||||||
\(512\) | 16363.6 | 1.41245 | ||||||||
\(513\) | −2323.19 | −0.199944 | ||||||||
\(514\) | 13966.9 | 1.19855 | ||||||||
\(515\) | 12755.9 | 1.09144 | ||||||||
\(516\) | −9554.28 | −0.815123 | ||||||||
\(517\) | −3918.05 | −0.333299 | ||||||||
\(518\) | −49773.1 | −4.22182 | ||||||||
\(519\) | 1722.21 | 0.145658 | ||||||||
\(520\) | 110.815 | 0.00934530 | ||||||||
\(521\) | 20973.2 | 1.76363 | 0.881816 | − | 0.471593i | \(-0.156321\pi\) | ||||
0.881816 | + | 0.471593i | \(0.156321\pi\) | |||||||
\(522\) | −1022.30 | −0.0857178 | ||||||||
\(523\) | 7587.00 | 0.634334 | 0.317167 | − | 0.948370i | \(-0.397268\pi\) | ||||
0.317167 | + | 0.948370i | \(0.397268\pi\) | |||||||
\(524\) | 10909.7 | 0.909525 | ||||||||
\(525\) | −7085.64 | −0.589034 | ||||||||
\(526\) | 5200.57 | 0.431094 | ||||||||
\(527\) | −3055.33 | −0.252547 | ||||||||
\(528\) | −5241.68 | −0.432036 | ||||||||
\(529\) | −5271.39 | −0.433253 | ||||||||
\(530\) | −18541.6 | −1.51961 | ||||||||
\(531\) | 531.000 | 0.0433963 | ||||||||
\(532\) | −25427.6 | −2.07223 | ||||||||
\(533\) | 742.753 | 0.0603606 | ||||||||
\(534\) | 14885.7 | 1.20631 | ||||||||
\(535\) | −146.269 | −0.0118201 | ||||||||
\(536\) | −1454.69 | −0.117226 | ||||||||
\(537\) | 9888.01 | 0.794598 | ||||||||
\(538\) | 14041.6 | 1.12523 | ||||||||
\(539\) | 24521.0 | 1.95954 | ||||||||
\(540\) | −1748.36 | −0.139328 | ||||||||
\(541\) | 1078.04 | 0.0856721 | 0.0428360 | − | 0.999082i | \(-0.486361\pi\) | ||||
0.0428360 | + | 0.999082i | \(0.486361\pi\) | |||||||
\(542\) | −9844.18 | −0.780154 | ||||||||
\(543\) | 6067.91 | 0.479556 | ||||||||
\(544\) | −16414.0 | −1.29365 | ||||||||
\(545\) | −1692.87 | −0.133054 | ||||||||
\(546\) | −2212.78 | −0.173440 | ||||||||
\(547\) | −318.365 | −0.0248854 | −0.0124427 | − | 0.999923i | \(-0.503961\pi\) | ||||
−0.0124427 | + | 0.999923i | \(0.503961\pi\) | |||||||
\(548\) | −9222.97 | −0.718952 | ||||||||
\(549\) | −3251.00 | −0.252731 | ||||||||
\(550\) | −8535.61 | −0.661744 | ||||||||
\(551\) | 2392.68 | 0.184994 | ||||||||
\(552\) | 697.715 | 0.0537984 | ||||||||
\(553\) | 9544.95 | 0.733983 | ||||||||
\(554\) | −29733.5 | −2.28024 | ||||||||
\(555\) | 8009.90 | 0.612615 | ||||||||
\(556\) | −8744.87 | −0.667023 | ||||||||
\(557\) | −7357.32 | −0.559676 | −0.279838 | − | 0.960047i | \(-0.590281\pi\) | ||||
−0.279838 | + | 0.960047i | \(0.590281\pi\) | |||||||
\(558\) | −1775.85 | −0.134727 | ||||||||
\(559\) | 1945.98 | 0.147238 | ||||||||
\(560\) | 14723.4 | 1.11103 | ||||||||
\(561\) | 5711.80 | 0.429861 | ||||||||
\(562\) | 25728.5 | 1.93112 | ||||||||
\(563\) | −10907.4 | −0.816505 | −0.408253 | − | 0.912869i | \(-0.633862\pi\) | ||||
−0.408253 | + | 0.912869i | \(0.633862\pi\) | |||||||
\(564\) | −3391.62 | −0.253214 | ||||||||
\(565\) | 3028.10 | 0.225475 | ||||||||
\(566\) | −14548.7 | −1.08044 | ||||||||
\(567\) | 2755.92 | 0.204123 | ||||||||
\(568\) | −2053.69 | −0.151709 | ||||||||
\(569\) | −8712.06 | −0.641878 | −0.320939 | − | 0.947100i | \(-0.603998\pi\) | ||||
−0.320939 | + | 0.947100i | \(0.603998\pi\) | |||||||
\(570\) | 7861.02 | 0.577653 | ||||||||
\(571\) | 120.132 | 0.00880446 | 0.00440223 | − | 0.999990i | \(-0.498599\pi\) | ||||
0.00440223 | + | 0.999990i | \(0.498599\pi\) | |||||||
\(572\) | −1387.56 | −0.101428 | ||||||||
\(573\) | −10311.9 | −0.751805 | ||||||||
\(574\) | −19450.7 | −1.41438 | ||||||||
\(575\) | −5764.51 | −0.418081 | ||||||||
\(576\) | −5361.11 | −0.387812 | ||||||||
\(577\) | 2169.26 | 0.156512 | 0.0782560 | − | 0.996933i | \(-0.475065\pi\) | ||||
0.0782560 | + | 0.996933i | \(0.475065\pi\) | |||||||
\(578\) | −3726.82 | −0.268192 | ||||||||
\(579\) | 13148.3 | 0.943738 | ||||||||
\(580\) | 1800.65 | 0.128910 | ||||||||
\(581\) | 8141.48 | 0.581352 | ||||||||
\(582\) | 1826.48 | 0.130086 | ||||||||
\(583\) | 18327.3 | 1.30195 | ||||||||
\(584\) | 3170.97 | 0.224684 | ||||||||
\(585\) | 356.098 | 0.0251673 | ||||||||
\(586\) | −17867.3 | −1.25954 | ||||||||
\(587\) | −1300.42 | −0.0914378 | −0.0457189 | − | 0.998954i | \(-0.514558\pi\) | ||||
−0.0457189 | + | 0.998954i | \(0.514558\pi\) | |||||||
\(588\) | 21226.3 | 1.48871 | ||||||||
\(589\) | 4156.37 | 0.290765 | ||||||||
\(590\) | −1796.75 | −0.125375 | ||||||||
\(591\) | −15094.1 | −1.05057 | ||||||||
\(592\) | 20787.6 | 1.44318 | ||||||||
\(593\) | −13449.8 | −0.931395 | −0.465698 | − | 0.884944i | \(-0.654197\pi\) | ||||
−0.465698 | + | 0.884944i | \(0.654197\pi\) | |||||||
\(594\) | 3319.88 | 0.229320 | ||||||||
\(595\) | −16043.9 | −1.10544 | ||||||||
\(596\) | 8435.10 | 0.579724 | ||||||||
\(597\) | 13073.3 | 0.896237 | ||||||||
\(598\) | −1800.20 | −0.123103 | ||||||||
\(599\) | −11679.1 | −0.796652 | −0.398326 | − | 0.917244i | \(-0.630409\pi\) | ||||
−0.398326 | + | 0.917244i | \(0.630409\pi\) | |||||||
\(600\) | −583.268 | −0.0396863 | ||||||||
\(601\) | −7992.33 | −0.542452 | −0.271226 | − | 0.962516i | \(-0.587429\pi\) | ||||
−0.271226 | + | 0.962516i | \(0.587429\pi\) | |||||||
\(602\) | −50959.8 | −3.45011 | ||||||||
\(603\) | −4674.57 | −0.315694 | ||||||||
\(604\) | 31260.7 | 2.10593 | ||||||||
\(605\) | 3167.79 | 0.212875 | ||||||||
\(606\) | −6019.46 | −0.403505 | ||||||||
\(607\) | 9263.57 | 0.619434 | 0.309717 | − | 0.950829i | \(-0.399766\pi\) | ||||
0.309717 | + | 0.950829i | \(0.399766\pi\) | |||||||
\(608\) | 22329.1 | 1.48942 | ||||||||
\(609\) | −2838.35 | −0.188860 | ||||||||
\(610\) | 11000.5 | 0.730157 | ||||||||
\(611\) | 690.791 | 0.0457388 | ||||||||
\(612\) | 4944.35 | 0.326574 | ||||||||
\(613\) | −11447.6 | −0.754267 | −0.377134 | − | 0.926159i | \(-0.623090\pi\) | ||||
−0.377134 | + | 0.926159i | \(0.623090\pi\) | |||||||
\(614\) | 21505.0 | 1.41347 | ||||||||
\(615\) | 3130.16 | 0.205236 | ||||||||
\(616\) | 2868.40 | 0.187615 | ||||||||
\(617\) | −27000.2 | −1.76173 | −0.880863 | − | 0.473371i | \(-0.843037\pi\) | ||||
−0.880863 | + | 0.473371i | \(0.843037\pi\) | |||||||
\(618\) | −20967.2 | −1.36477 | ||||||||
\(619\) | 22497.9 | 1.46085 | 0.730425 | − | 0.682993i | \(-0.239322\pi\) | ||||
0.730425 | + | 0.682993i | \(0.239322\pi\) | |||||||
\(620\) | 3127.95 | 0.202615 | ||||||||
\(621\) | 2242.08 | 0.144881 | ||||||||
\(622\) | 15885.8 | 1.02406 | ||||||||
\(623\) | 41329.3 | 2.65782 | ||||||||
\(624\) | 924.160 | 0.0592884 | ||||||||
\(625\) | −2128.72 | −0.136238 | ||||||||
\(626\) | −36009.2 | −2.29907 | ||||||||
\(627\) | −7770.15 | −0.494912 | ||||||||
\(628\) | 10497.8 | 0.667050 | ||||||||
\(629\) | −22652.0 | −1.43592 | ||||||||
\(630\) | −9325.25 | −0.589725 | ||||||||
\(631\) | 20510.4 | 1.29399 | 0.646994 | − | 0.762495i | \(-0.276026\pi\) | ||||
0.646994 | + | 0.762495i | \(0.276026\pi\) | |||||||
\(632\) | 785.710 | 0.0494523 | ||||||||
\(633\) | −13308.9 | −0.835674 | ||||||||
\(634\) | −41553.7 | −2.60301 | ||||||||
\(635\) | −9729.14 | −0.608015 | ||||||||
\(636\) | 15864.8 | 0.989118 | ||||||||
\(637\) | −4323.29 | −0.268909 | ||||||||
\(638\) | −3419.17 | −0.212173 | ||||||||
\(639\) | −6599.43 | −0.408559 | ||||||||
\(640\) | 2662.85 | 0.164466 | ||||||||
\(641\) | 9877.54 | 0.608642 | 0.304321 | − | 0.952570i | \(-0.401570\pi\) | ||||
0.304321 | + | 0.952570i | \(0.401570\pi\) | |||||||
\(642\) | 240.426 | 0.0147801 | ||||||||
\(643\) | 9789.87 | 0.600427 | 0.300214 | − | 0.953872i | \(-0.402942\pi\) | ||||
0.300214 | + | 0.953872i | \(0.402942\pi\) | |||||||
\(644\) | 24539.8 | 1.50156 | ||||||||
\(645\) | 8200.88 | 0.500634 | ||||||||
\(646\) | −22230.9 | −1.35397 | ||||||||
\(647\) | −9704.28 | −0.589667 | −0.294834 | − | 0.955549i | \(-0.595264\pi\) | ||||
−0.294834 | + | 0.955549i | \(0.595264\pi\) | |||||||
\(648\) | 226.859 | 0.0137529 | ||||||||
\(649\) | 1775.98 | 0.107417 | ||||||||
\(650\) | 1504.91 | 0.0908114 | ||||||||
\(651\) | −4930.56 | −0.296841 | ||||||||
\(652\) | 5966.95 | 0.358410 | ||||||||
\(653\) | 19355.5 | 1.15994 | 0.579970 | − | 0.814638i | \(-0.303064\pi\) | ||||
0.579970 | + | 0.814638i | \(0.303064\pi\) | |||||||
\(654\) | 2782.61 | 0.166374 | ||||||||
\(655\) | −9364.27 | −0.558614 | ||||||||
\(656\) | 8123.52 | 0.483491 | ||||||||
\(657\) | 10189.8 | 0.605084 | ||||||||
\(658\) | −18089.9 | −1.07176 | ||||||||
\(659\) | −9598.00 | −0.567352 | −0.283676 | − | 0.958920i | \(-0.591554\pi\) | ||||
−0.283676 | + | 0.958920i | \(0.591554\pi\) | |||||||
\(660\) | −5847.56 | −0.344873 | ||||||||
\(661\) | −30099.9 | −1.77118 | −0.885591 | − | 0.464465i | \(-0.846247\pi\) | ||||
−0.885591 | + | 0.464465i | \(0.846247\pi\) | |||||||
\(662\) | −11842.2 | −0.695258 | ||||||||
\(663\) | −1007.04 | −0.0589900 | ||||||||
\(664\) | 670.181 | 0.0391688 | ||||||||
\(665\) | 21825.7 | 1.27273 | ||||||||
\(666\) | −13166.0 | −0.766026 | ||||||||
\(667\) | −2309.14 | −0.134048 | ||||||||
\(668\) | 27025.0 | 1.56531 | ||||||||
\(669\) | −1554.44 | −0.0898328 | ||||||||
\(670\) | 15817.4 | 0.912060 | ||||||||
\(671\) | −10873.3 | −0.625573 | ||||||||
\(672\) | −26488.2 | −1.52054 | ||||||||
\(673\) | 4334.61 | 0.248272 | 0.124136 | − | 0.992265i | \(-0.460384\pi\) | ||||
0.124136 | + | 0.992265i | \(0.460384\pi\) | |||||||
\(674\) | −45753.9 | −2.61480 | ||||||||
\(675\) | −1874.30 | −0.106877 | ||||||||
\(676\) | −18837.7 | −1.07179 | ||||||||
\(677\) | 26966.0 | 1.53085 | 0.765427 | − | 0.643523i | \(-0.222528\pi\) | ||||
0.765427 | + | 0.643523i | \(0.222528\pi\) | |||||||
\(678\) | −4977.36 | −0.281938 | ||||||||
\(679\) | 5071.13 | 0.286616 | ||||||||
\(680\) | −1320.69 | −0.0744795 | ||||||||
\(681\) | −16074.9 | −0.904541 | ||||||||
\(682\) | −5939.52 | −0.333484 | ||||||||
\(683\) | 4741.14 | 0.265615 | 0.132807 | − | 0.991142i | \(-0.457601\pi\) | ||||
0.132807 | + | 0.991142i | \(0.457601\pi\) | |||||||
\(684\) | −6726.14 | −0.375995 | ||||||||
\(685\) | 7916.50 | 0.441568 | ||||||||
\(686\) | 65544.9 | 3.64798 | ||||||||
\(687\) | 8417.25 | 0.467450 | ||||||||
\(688\) | 21283.2 | 1.17938 | ||||||||
\(689\) | −3231.27 | −0.178667 | ||||||||
\(690\) | −7586.54 | −0.418572 | ||||||||
\(691\) | 7335.54 | 0.403845 | 0.201923 | − | 0.979401i | \(-0.435281\pi\) | ||||
0.201923 | + | 0.979401i | \(0.435281\pi\) | |||||||
\(692\) | 4986.17 | 0.273910 | ||||||||
\(693\) | 9217.45 | 0.505256 | ||||||||
\(694\) | 36905.5 | 2.01861 | ||||||||
\(695\) | 7506.12 | 0.409674 | ||||||||
\(696\) | −233.644 | −0.0127245 | ||||||||
\(697\) | −8852.09 | −0.481057 | ||||||||
\(698\) | 12194.6 | 0.661277 | ||||||||
\(699\) | −12663.2 | −0.685216 | ||||||||
\(700\) | −20514.4 | −1.10768 | ||||||||
\(701\) | 8441.52 | 0.454824 | 0.227412 | − | 0.973799i | \(-0.426974\pi\) | ||||
0.227412 | + | 0.973799i | \(0.426974\pi\) | |||||||
\(702\) | −585.326 | −0.0314697 | ||||||||
\(703\) | 30815.0 | 1.65322 | ||||||||
\(704\) | −17930.8 | −0.959932 | ||||||||
\(705\) | 2911.18 | 0.155520 | ||||||||
\(706\) | 41962.5 | 2.23694 | ||||||||
\(707\) | −16712.7 | −0.889033 | ||||||||
\(708\) | 1537.36 | 0.0816066 | ||||||||
\(709\) | 9530.08 | 0.504809 | 0.252405 | − | 0.967622i | \(-0.418779\pi\) | ||||
0.252405 | + | 0.967622i | \(0.418779\pi\) | |||||||
\(710\) | 22330.6 | 1.18035 | ||||||||
\(711\) | 2524.84 | 0.133177 | ||||||||
\(712\) | 3402.10 | 0.179072 | ||||||||
\(713\) | −4011.25 | −0.210691 | ||||||||
\(714\) | 26371.8 | 1.38227 | ||||||||
\(715\) | 1191.01 | 0.0622953 | ||||||||
\(716\) | 28627.9 | 1.49424 | ||||||||
\(717\) | 16236.0 | 0.845670 | ||||||||
\(718\) | −18989.5 | −0.987024 | ||||||||
\(719\) | −8740.89 | −0.453380 | −0.226690 | − | 0.973967i | \(-0.572790\pi\) | ||||
−0.226690 | + | 0.973967i | \(0.572790\pi\) | |||||||
\(720\) | 3894.66 | 0.201591 | ||||||||
\(721\) | −58214.3 | −3.00695 | ||||||||
\(722\) | 2224.60 | 0.114669 | ||||||||
\(723\) | −9010.68 | −0.463500 | ||||||||
\(724\) | 17567.9 | 0.901804 | ||||||||
\(725\) | 1930.36 | 0.0988853 | ||||||||
\(726\) | −5206.97 | −0.266183 | ||||||||
\(727\) | 19162.5 | 0.977575 | 0.488788 | − | 0.872403i | \(-0.337439\pi\) | ||||
0.488788 | + | 0.872403i | \(0.337439\pi\) | |||||||
\(728\) | −505.726 | −0.0257465 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −34479.2 | −1.74813 | ||||||||
\(731\) | −23192.0 | −1.17345 | ||||||||
\(732\) | −9412.35 | −0.475260 | ||||||||
\(733\) | 14807.2 | 0.746134 | 0.373067 | − | 0.927804i | \(-0.378306\pi\) | ||||
0.373067 | + | 0.927804i | \(0.378306\pi\) | |||||||
\(734\) | −6726.48 | −0.338255 | ||||||||
\(735\) | −18219.5 | −0.914337 | ||||||||
\(736\) | −21549.4 | −1.07924 | ||||||||
\(737\) | −15634.6 | −0.781421 | ||||||||
\(738\) | −5145.12 | −0.256632 | ||||||||
\(739\) | −22838.8 | −1.13686 | −0.568430 | − | 0.822732i | \(-0.692449\pi\) | ||||
−0.568430 | + | 0.822732i | \(0.692449\pi\) | |||||||
\(740\) | 23190.4 | 1.15202 | ||||||||
\(741\) | 1369.95 | 0.0679170 | ||||||||
\(742\) | 84618.2 | 4.18657 | ||||||||
\(743\) | −2638.81 | −0.130294 | −0.0651472 | − | 0.997876i | \(-0.520752\pi\) | ||||
−0.0651472 | + | 0.997876i | \(0.520752\pi\) | |||||||
\(744\) | −405.868 | −0.0199998 | ||||||||
\(745\) | −7240.24 | −0.356056 | ||||||||
\(746\) | 26669.2 | 1.30889 | ||||||||
\(747\) | 2153.60 | 0.105483 | ||||||||
\(748\) | 16536.9 | 0.808353 | ||||||||
\(749\) | 667.529 | 0.0325647 | ||||||||
\(750\) | 17762.1 | 0.864775 | ||||||||
\(751\) | −6880.34 | −0.334311 | −0.167155 | − | 0.985931i | \(-0.553458\pi\) | ||||
−0.167155 | + | 0.985931i | \(0.553458\pi\) | |||||||
\(752\) | 7555.21 | 0.366370 | ||||||||
\(753\) | −2700.27 | −0.130682 | ||||||||
\(754\) | 602.833 | 0.0291166 | ||||||||
\(755\) | −26832.5 | −1.29342 | ||||||||
\(756\) | 7978.98 | 0.383853 | ||||||||
\(757\) | 41277.3 | 1.98183 | 0.990916 | − | 0.134479i | \(-0.0429359\pi\) | ||||
0.990916 | + | 0.134479i | \(0.0429359\pi\) | |||||||
\(758\) | 26231.4 | 1.25695 | ||||||||
\(759\) | 7498.85 | 0.358618 | ||||||||
\(760\) | 1796.62 | 0.0857504 | ||||||||
\(761\) | 16764.5 | 0.798570 | 0.399285 | − | 0.916827i | \(-0.369258\pi\) | ||||
0.399285 | + | 0.916827i | \(0.369258\pi\) | |||||||
\(762\) | 15992.0 | 0.760274 | ||||||||
\(763\) | 7725.76 | 0.366568 | ||||||||
\(764\) | −29855.1 | −1.41377 | ||||||||
\(765\) | −4243.97 | −0.200576 | ||||||||
\(766\) | −12451.0 | −0.587302 | ||||||||
\(767\) | −313.123 | −0.0147408 | ||||||||
\(768\) | 9919.32 | 0.466058 | ||||||||
\(769\) | −29667.0 | −1.39118 | −0.695591 | − | 0.718438i | \(-0.744858\pi\) | ||||
−0.695591 | + | 0.718438i | \(0.744858\pi\) | |||||||
\(770\) | −31189.2 | −1.45972 | ||||||||
\(771\) | 10257.7 | 0.479147 | ||||||||
\(772\) | 38067.1 | 1.77470 | ||||||||
\(773\) | −1557.94 | −0.0724904 | −0.0362452 | − | 0.999343i | \(-0.511540\pi\) | ||||
−0.0362452 | + | 0.999343i | \(0.511540\pi\) | |||||||
\(774\) | −13480.0 | −0.626004 | ||||||||
\(775\) | 3353.27 | 0.155423 | ||||||||
\(776\) | 417.440 | 0.0193108 | ||||||||
\(777\) | −36554.8 | −1.68777 | ||||||||
\(778\) | 33208.7 | 1.53032 | ||||||||
\(779\) | 12042.1 | 0.553856 | ||||||||
\(780\) | 1030.98 | 0.0473270 | ||||||||
\(781\) | −22072.5 | −1.01129 | ||||||||
\(782\) | 21454.7 | 0.981098 | ||||||||
\(783\) | −750.804 | −0.0342676 | ||||||||
\(784\) | −47284.0 | −2.15397 | ||||||||
\(785\) | −9010.74 | −0.409691 | ||||||||
\(786\) | 15392.2 | 0.698503 | ||||||||
\(787\) | 8898.56 | 0.403049 | 0.201524 | − | 0.979483i | \(-0.435410\pi\) | ||||
0.201524 | + | 0.979483i | \(0.435410\pi\) | |||||||
\(788\) | −43700.5 | −1.97559 | ||||||||
\(789\) | 3819.45 | 0.172340 | ||||||||
\(790\) | −8543.35 | −0.384758 | ||||||||
\(791\) | −13819.4 | −0.621188 | ||||||||
\(792\) | 758.752 | 0.0340418 | ||||||||
\(793\) | 1917.07 | 0.0858476 | ||||||||
\(794\) | −20719.6 | −0.926083 | ||||||||
\(795\) | −13617.5 | −0.607499 | ||||||||
\(796\) | 37849.9 | 1.68537 | ||||||||
\(797\) | 25724.7 | 1.14331 | 0.571654 | − | 0.820495i | \(-0.306302\pi\) | ||||
0.571654 | + | 0.820495i | \(0.306302\pi\) | |||||||
\(798\) | −35875.3 | −1.59145 | ||||||||
\(799\) | −8232.81 | −0.364526 | ||||||||
\(800\) | 18014.6 | 0.796142 | ||||||||
\(801\) | 10932.5 | 0.482248 | ||||||||
\(802\) | 38967.4 | 1.71569 | ||||||||
\(803\) | 34080.7 | 1.49773 | ||||||||
\(804\) | −13533.9 | −0.593661 | ||||||||
\(805\) | −21063.6 | −0.922229 | ||||||||
\(806\) | 1047.19 | 0.0457641 | ||||||||
\(807\) | 10312.5 | 0.449837 | ||||||||
\(808\) | −1375.74 | −0.0598989 | ||||||||
\(809\) | −25187.9 | −1.09463 | −0.547317 | − | 0.836926i | \(-0.684351\pi\) | ||||
−0.547317 | + | 0.836926i | \(0.684351\pi\) | |||||||
\(810\) | −2466.73 | −0.107002 | ||||||||
\(811\) | −1555.98 | −0.0673709 | −0.0336854 | − | 0.999432i | \(-0.510724\pi\) | ||||
−0.0336854 | + | 0.999432i | \(0.510724\pi\) | |||||||
\(812\) | −8217.63 | −0.355151 | ||||||||
\(813\) | −7229.85 | −0.311884 | ||||||||
\(814\) | −44035.1 | −1.89611 | ||||||||
\(815\) | −5121.71 | −0.220129 | ||||||||
\(816\) | −11014.1 | −0.472513 | ||||||||
\(817\) | 31549.8 | 1.35102 | ||||||||
\(818\) | 43694.3 | 1.86765 | ||||||||
\(819\) | −1625.13 | −0.0693364 | ||||||||
\(820\) | 9062.50 | 0.385947 | ||||||||
\(821\) | −10402.0 | −0.442182 | −0.221091 | − | 0.975253i | \(-0.570962\pi\) | ||||
−0.221091 | + | 0.975253i | \(0.570962\pi\) | |||||||
\(822\) | −13012.5 | −0.552146 | ||||||||
\(823\) | −3211.80 | −0.136035 | −0.0680173 | − | 0.997684i | \(-0.521667\pi\) | ||||
−0.0680173 | + | 0.997684i | \(0.521667\pi\) | |||||||
\(824\) | −4792.02 | −0.202595 | ||||||||
\(825\) | −6268.80 | −0.264547 | ||||||||
\(826\) | 8199.84 | 0.345410 | ||||||||
\(827\) | −14355.4 | −0.603612 | −0.301806 | − | 0.953369i | \(-0.597589\pi\) | ||||
−0.301806 | + | 0.953369i | \(0.597589\pi\) | |||||||
\(828\) | 6491.29 | 0.272449 | ||||||||
\(829\) | 40266.3 | 1.68698 | 0.843490 | − | 0.537145i | \(-0.180497\pi\) | ||||
0.843490 | + | 0.537145i | \(0.180497\pi\) | |||||||
\(830\) | −7287.15 | −0.304748 | ||||||||
\(831\) | −21837.1 | −0.911579 | ||||||||
\(832\) | 3161.37 | 0.131732 | ||||||||
\(833\) | 51524.8 | 2.14313 | ||||||||
\(834\) | −12338.0 | −0.512265 | ||||||||
\(835\) | −23196.8 | −0.961389 | ||||||||
\(836\) | −22496.3 | −0.930681 | ||||||||
\(837\) | −1304.24 | −0.0538603 | ||||||||
\(838\) | −8717.96 | −0.359376 | ||||||||
\(839\) | −32142.4 | −1.32262 | −0.661310 | − | 0.750113i | \(-0.729999\pi\) | ||||
−0.661310 | + | 0.750113i | \(0.729999\pi\) | |||||||
\(840\) | −2131.27 | −0.0875426 | ||||||||
\(841\) | −23615.7 | −0.968295 | ||||||||
\(842\) | 27697.9 | 1.13365 | ||||||||
\(843\) | 18895.7 | 0.772008 | ||||||||
\(844\) | −38532.2 | −1.57148 | ||||||||
\(845\) | 16169.3 | 0.658273 | ||||||||
\(846\) | −4785.17 | −0.194465 | ||||||||
\(847\) | −14456.9 | −0.586474 | ||||||||
\(848\) | −35340.6 | −1.43113 | ||||||||
\(849\) | −10685.0 | −0.431930 | ||||||||
\(850\) | −17935.4 | −0.723742 | ||||||||
\(851\) | −29739.1 | −1.19793 | ||||||||
\(852\) | −19106.8 | −0.768294 | ||||||||
\(853\) | 3961.96 | 0.159033 | 0.0795164 | − | 0.996834i | \(-0.474662\pi\) | ||||
0.0795164 | + | 0.996834i | \(0.474662\pi\) | |||||||
\(854\) | −50202.8 | −2.01160 | ||||||||
\(855\) | 5773.36 | 0.230930 | ||||||||
\(856\) | 54.9489 | 0.00219406 | ||||||||
\(857\) | −38708.1 | −1.54287 | −0.771437 | − | 0.636306i | \(-0.780462\pi\) | ||||
−0.771437 | + | 0.636306i | \(0.780462\pi\) | |||||||
\(858\) | −1957.68 | −0.0778953 | ||||||||
\(859\) | −6725.04 | −0.267119 | −0.133560 | − | 0.991041i | \(-0.542641\pi\) | ||||
−0.133560 | + | 0.991041i | \(0.542641\pi\) | |||||||
\(860\) | 23743.3 | 0.941442 | ||||||||
\(861\) | −14285.1 | −0.565431 | ||||||||
\(862\) | −68180.9 | −2.69403 | ||||||||
\(863\) | 22856.4 | 0.901554 | 0.450777 | − | 0.892637i | \(-0.351147\pi\) | ||||
0.450777 | + | 0.892637i | \(0.351147\pi\) | |||||||
\(864\) | −7006.70 | −0.275894 | ||||||||
\(865\) | −4279.86 | −0.168231 | ||||||||
\(866\) | −11858.1 | −0.465306 | ||||||||
\(867\) | −2737.08 | −0.107216 | ||||||||
\(868\) | −14275.0 | −0.558209 | ||||||||
\(869\) | 8444.59 | 0.329647 | ||||||||
\(870\) | 2540.51 | 0.0990014 | ||||||||
\(871\) | 2756.53 | 0.107235 | ||||||||
\(872\) | 635.960 | 0.0246976 | ||||||||
\(873\) | 1341.42 | 0.0520049 | ||||||||
\(874\) | −29186.3 | −1.12957 | ||||||||
\(875\) | 49315.6 | 1.90534 | ||||||||
\(876\) | 29501.5 | 1.13786 | ||||||||
\(877\) | 25523.5 | 0.982744 | 0.491372 | − | 0.870950i | \(-0.336496\pi\) | ||||
0.491372 | + | 0.870950i | \(0.336496\pi\) | |||||||
\(878\) | 34830.8 | 1.33882 | ||||||||
\(879\) | −13122.3 | −0.503531 | ||||||||
\(880\) | 13026.1 | 0.498988 | ||||||||
\(881\) | 37925.5 | 1.45033 | 0.725166 | − | 0.688574i | \(-0.241763\pi\) | ||||
0.725166 | + | 0.688574i | \(0.241763\pi\) | |||||||
\(882\) | 29947.8 | 1.14331 | ||||||||
\(883\) | −44752.5 | −1.70560 | −0.852798 | − | 0.522241i | \(-0.825096\pi\) | ||||
−0.852798 | + | 0.522241i | \(0.825096\pi\) | |||||||
\(884\) | −2915.61 | −0.110931 | ||||||||
\(885\) | −1319.59 | −0.0501214 | ||||||||
\(886\) | −12965.3 | −0.491624 | ||||||||
\(887\) | 27284.8 | 1.03285 | 0.516423 | − | 0.856334i | \(-0.327263\pi\) | ||||
0.516423 | + | 0.856334i | \(0.327263\pi\) | |||||||
\(888\) | −3009.07 | −0.113714 | ||||||||
\(889\) | 44400.9 | 1.67509 | ||||||||
\(890\) | −36992.4 | −1.39325 | ||||||||
\(891\) | 2438.21 | 0.0916759 | ||||||||
\(892\) | −4500.44 | −0.168930 | ||||||||
\(893\) | 11199.7 | 0.419689 | ||||||||
\(894\) | 11900.9 | 0.445220 | ||||||||
\(895\) | −24572.7 | −0.917736 | ||||||||
\(896\) | −12152.5 | −0.453109 | ||||||||
\(897\) | −1322.12 | −0.0492132 | ||||||||
\(898\) | −8623.38 | −0.320452 | ||||||||
\(899\) | 1343.25 | 0.0498329 | ||||||||
\(900\) | −5426.51 | −0.200982 | ||||||||
\(901\) | 38510.2 | 1.42393 | ||||||||
\(902\) | −17208.4 | −0.635228 | ||||||||
\(903\) | −37426.3 | −1.37926 | ||||||||
\(904\) | −1137.57 | −0.0418528 | ||||||||
\(905\) | −15079.4 | −0.553873 | ||||||||
\(906\) | 44105.2 | 1.61733 | ||||||||
\(907\) | 22037.7 | 0.806779 | 0.403390 | − | 0.915028i | \(-0.367832\pi\) | ||||
0.403390 | + | 0.915028i | \(0.367832\pi\) | |||||||
\(908\) | −46540.3 | −1.70099 | ||||||||
\(909\) | −4420.87 | −0.161310 | ||||||||
\(910\) | 5498.96 | 0.200317 | ||||||||
\(911\) | 53768.1 | 1.95545 | 0.977726 | − | 0.209884i | \(-0.0673087\pi\) | ||||
0.977726 | + | 0.209884i | \(0.0673087\pi\) | |||||||
\(912\) | 14983.2 | 0.544018 | ||||||||
\(913\) | 7202.92 | 0.261097 | ||||||||
\(914\) | −28576.1 | −1.03415 | ||||||||
\(915\) | 8079.06 | 0.291897 | ||||||||
\(916\) | 24369.7 | 0.879038 | ||||||||
\(917\) | 42735.7 | 1.53899 | ||||||||
\(918\) | 6975.90 | 0.250805 | ||||||||
\(919\) | 12821.6 | 0.460224 | 0.230112 | − | 0.973164i | \(-0.426091\pi\) | ||||
0.230112 | + | 0.973164i | \(0.426091\pi\) | |||||||
\(920\) | −1733.89 | −0.0621355 | ||||||||
\(921\) | 15793.9 | 0.565068 | ||||||||
\(922\) | 1743.77 | 0.0622865 | ||||||||
\(923\) | 3891.59 | 0.138779 | ||||||||
\(924\) | 26686.5 | 0.950132 | ||||||||
\(925\) | 24860.9 | 0.883699 | ||||||||
\(926\) | 11853.7 | 0.420667 | ||||||||
\(927\) | −15398.9 | −0.545596 | ||||||||
\(928\) | 7216.26 | 0.255265 | ||||||||
\(929\) | −20227.5 | −0.714361 | −0.357181 | − | 0.934035i | \(-0.616262\pi\) | ||||
−0.357181 | + | 0.934035i | \(0.616262\pi\) | |||||||
\(930\) | 4413.17 | 0.155606 | ||||||||
\(931\) | −70092.7 | −2.46745 | ||||||||
\(932\) | −36662.7 | −1.28855 | ||||||||
\(933\) | 11667.0 | 0.409389 | ||||||||
\(934\) | 34411.8 | 1.20555 | ||||||||
\(935\) | −14194.4 | −0.496476 | ||||||||
\(936\) | −133.775 | −0.00467156 | ||||||||
\(937\) | −43813.7 | −1.52757 | −0.763784 | − | 0.645471i | \(-0.776661\pi\) | ||||
−0.763784 | + | 0.645471i | \(0.776661\pi\) | |||||||
\(938\) | −72186.0 | −2.51275 | ||||||||
\(939\) | −26446.2 | −0.919104 | ||||||||
\(940\) | 8428.50 | 0.292455 | ||||||||
\(941\) | 36622.2 | 1.26870 | 0.634351 | − | 0.773045i | \(-0.281267\pi\) | ||||
0.634351 | + | 0.773045i | \(0.281267\pi\) | |||||||
\(942\) | 14811.1 | 0.512286 | ||||||||
\(943\) | −11621.7 | −0.401329 | ||||||||
\(944\) | −3424.64 | −0.118075 | ||||||||
\(945\) | −6848.73 | −0.235756 | ||||||||
\(946\) | −45085.1 | −1.54952 | ||||||||
\(947\) | −15181.8 | −0.520952 | −0.260476 | − | 0.965480i | \(-0.583879\pi\) | ||||
−0.260476 | + | 0.965480i | \(0.583879\pi\) | |||||||
\(948\) | 7309.96 | 0.250439 | ||||||||
\(949\) | −6008.75 | −0.205535 | ||||||||
\(950\) | 24398.8 | 0.833266 | ||||||||
\(951\) | −30518.2 | −1.04061 | ||||||||
\(952\) | 6027.22 | 0.205193 | ||||||||
\(953\) | −17530.8 | −0.595885 | −0.297942 | − | 0.954584i | \(-0.596300\pi\) | ||||
−0.297942 | + | 0.954584i | \(0.596300\pi\) | |||||||
\(954\) | 22383.3 | 0.759630 | ||||||||
\(955\) | 25626.0 | 0.868311 | ||||||||
\(956\) | 47006.7 | 1.59028 | ||||||||
\(957\) | −2511.14 | −0.0848209 | ||||||||
\(958\) | −42629.0 | −1.43766 | ||||||||
\(959\) | −36128.5 | −1.21653 | ||||||||
\(960\) | 13322.9 | 0.447911 | ||||||||
\(961\) | −27457.6 | −0.921675 | ||||||||
\(962\) | 7763.82 | 0.260203 | ||||||||
\(963\) | 176.576 | 0.00590869 | ||||||||
\(964\) | −26087.9 | −0.871611 | ||||||||
\(965\) | −32674.8 | −1.08999 | ||||||||
\(966\) | 34622.7 | 1.15318 | ||||||||
\(967\) | 50857.1 | 1.69127 | 0.845633 | − | 0.533765i | \(-0.179223\pi\) | ||||
0.845633 | + | 0.533765i | \(0.179223\pi\) | |||||||
\(968\) | −1190.04 | −0.0395139 | ||||||||
\(969\) | −16327.0 | −0.541280 | ||||||||
\(970\) | −4538.99 | −0.150246 | ||||||||
\(971\) | −24239.2 | −0.801105 | −0.400553 | − | 0.916274i | \(-0.631182\pi\) | ||||
−0.400553 | + | 0.916274i | \(0.631182\pi\) | |||||||
\(972\) | 2110.61 | 0.0696480 | ||||||||
\(973\) | −34255.7 | −1.12866 | ||||||||
\(974\) | 25257.5 | 0.830906 | ||||||||
\(975\) | 1105.25 | 0.0363039 | ||||||||
\(976\) | 20967.1 | 0.687643 | ||||||||
\(977\) | −52188.5 | −1.70896 | −0.854482 | − | 0.519481i | \(-0.826125\pi\) | ||||
−0.854482 | + | 0.519481i | \(0.826125\pi\) | |||||||
\(978\) | 8418.66 | 0.275255 | ||||||||
\(979\) | 36564.8 | 1.19368 | ||||||||
\(980\) | −52749.5 | −1.71941 | ||||||||
\(981\) | 2043.63 | 0.0665118 | ||||||||
\(982\) | −16501.0 | −0.536221 | ||||||||
\(983\) | −6206.63 | −0.201384 | −0.100692 | − | 0.994918i | \(-0.532106\pi\) | ||||
−0.100692 | + | 0.994918i | \(0.532106\pi\) | |||||||
\(984\) | −1175.91 | −0.0380961 | ||||||||
\(985\) | 37510.2 | 1.21337 | ||||||||
\(986\) | −7184.54 | −0.232051 | ||||||||
\(987\) | −13285.8 | −0.428460 | ||||||||
\(988\) | 3966.31 | 0.127718 | ||||||||
\(989\) | −30448.2 | −0.978964 | ||||||||
\(990\) | −8250.22 | −0.264858 | ||||||||
\(991\) | 11627.8 | 0.372724 | 0.186362 | − | 0.982481i | \(-0.440330\pi\) | ||||
0.186362 | + | 0.982481i | \(0.440330\pi\) | |||||||
\(992\) | 12535.5 | 0.401213 | ||||||||
\(993\) | −8697.27 | −0.277945 | ||||||||
\(994\) | −101910. | −3.25190 | ||||||||
\(995\) | −32488.3 | −1.03513 | ||||||||
\(996\) | 6235.12 | 0.198361 | ||||||||
\(997\) | 27404.9 | 0.870533 | 0.435266 | − | 0.900302i | \(-0.356654\pi\) | ||||
0.435266 | + | 0.900302i | \(0.356654\pi\) | |||||||
\(998\) | −69991.7 | −2.21999 | ||||||||
\(999\) | −9669.52 | −0.306236 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 177.4.a.d.1.7 | ✓ | 8 | |
3.2 | odd | 2 | 531.4.a.e.1.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.4.a.d.1.7 | ✓ | 8 | 1.1 | even | 1 | trivial | |
531.4.a.e.1.2 | 8 | 3.2 | odd | 2 |