Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [531,4,Mod(1,531)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(531, 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("531.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 531 = 3^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 531.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: | \(31.3300142130\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 41x^{5} - 7x^{4} + 484x^{3} + 63x^{2} - 1736x - 44 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 177) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-2.74916\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 531.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.74916 | −0.971974 | −0.485987 | − | 0.873966i | \(-0.661540\pi\) | ||||
−0.485987 | + | 0.873966i | \(0.661540\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.442134 | −0.0552668 | ||||||||
\(5\) | −13.7745 | −1.23203 | −0.616015 | − | 0.787734i | \(-0.711254\pi\) | ||||
−0.616015 | + | 0.787734i | \(0.711254\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −35.6462 | −1.92471 | −0.962357 | − | 0.271790i | \(-0.912384\pi\) | ||||
−0.962357 | + | 0.271790i | \(0.912384\pi\) | |||||||
\(8\) | 23.2088 | 1.02569 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 37.8683 | 1.19750 | ||||||||
\(11\) | 30.8537 | 0.845703 | 0.422851 | − | 0.906199i | \(-0.361029\pi\) | ||||
0.422851 | + | 0.906199i | \(0.361029\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 14.6435 | 0.312413 | 0.156206 | − | 0.987724i | \(-0.450074\pi\) | ||||
0.156206 | + | 0.987724i | \(0.450074\pi\) | |||||||
\(14\) | 97.9970 | 1.87077 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −60.2674 | −0.941679 | ||||||||
\(17\) | 77.8827 | 1.11114 | 0.555568 | − | 0.831471i | \(-0.312501\pi\) | ||||
0.555568 | + | 0.831471i | \(0.312501\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 98.6377 | 1.19100 | 0.595501 | − | 0.803355i | \(-0.296954\pi\) | ||||
0.595501 | + | 0.803355i | \(0.296954\pi\) | |||||||
\(20\) | 6.09019 | 0.0680904 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −84.8216 | −0.822001 | ||||||||
\(23\) | 117.065 | 1.06129 | 0.530647 | − | 0.847593i | \(-0.321949\pi\) | ||||
0.530647 | + | 0.847593i | \(0.321949\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 64.7375 | 0.517900 | ||||||||
\(26\) | −40.2572 | −0.303657 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 15.7604 | 0.106373 | ||||||||
\(29\) | 54.2015 | 0.347068 | 0.173534 | − | 0.984828i | \(-0.444481\pi\) | ||||
0.173534 | + | 0.984828i | \(0.444481\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −231.433 | −1.34086 | −0.670428 | − | 0.741975i | \(-0.733890\pi\) | ||||
−0.670428 | + | 0.741975i | \(0.733890\pi\) | |||||||
\(32\) | −19.9854 | −0.110405 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −214.112 | −1.08000 | ||||||||
\(35\) | 491.009 | 2.37131 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −258.311 | −1.14773 | −0.573866 | − | 0.818950i | \(-0.694557\pi\) | ||||
−0.573866 | + | 0.818950i | \(0.694557\pi\) | |||||||
\(38\) | −271.171 | −1.15762 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −319.690 | −1.26368 | ||||||||
\(41\) | −326.921 | −1.24528 | −0.622639 | − | 0.782509i | \(-0.713940\pi\) | ||||
−0.622639 | + | 0.782509i | \(0.713940\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 250.920 | 0.889882 | 0.444941 | − | 0.895560i | \(-0.353225\pi\) | ||||
0.444941 | + | 0.895560i | \(0.353225\pi\) | |||||||
\(44\) | −13.6415 | −0.0467393 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −321.830 | −1.03155 | ||||||||
\(47\) | −509.390 | −1.58090 | −0.790449 | − | 0.612528i | \(-0.790153\pi\) | ||||
−0.790449 | + | 0.612528i | \(0.790153\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 927.650 | 2.70452 | ||||||||
\(50\) | −177.974 | −0.503385 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.47437 | −0.0172660 | ||||||||
\(53\) | 313.730 | 0.813097 | 0.406549 | − | 0.913629i | \(-0.366732\pi\) | ||||
0.406549 | + | 0.913629i | \(0.366732\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −424.994 | −1.04193 | ||||||||
\(56\) | −827.304 | −1.97416 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −149.008 | −0.337341 | ||||||||
\(59\) | −59.0000 | −0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 528.854 | 1.11005 | 0.555023 | − | 0.831835i | \(-0.312709\pi\) | ||||
0.555023 | + | 0.831835i | \(0.312709\pi\) | |||||||
\(62\) | 636.245 | 1.30328 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 537.082 | 1.04899 | ||||||||
\(65\) | −201.707 | −0.384902 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −373.284 | −0.680656 | −0.340328 | − | 0.940307i | \(-0.610538\pi\) | ||||
−0.340328 | + | 0.940307i | \(0.610538\pi\) | |||||||
\(68\) | −34.4346 | −0.0614090 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1349.86 | −2.30485 | ||||||||
\(71\) | 521.969 | 0.872483 | 0.436241 | − | 0.899830i | \(-0.356309\pi\) | ||||
0.436241 | + | 0.899830i | \(0.356309\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 809.404 | 1.29772 | 0.648860 | − | 0.760908i | \(-0.275246\pi\) | ||||
0.648860 | + | 0.760908i | \(0.275246\pi\) | |||||||
\(74\) | 710.137 | 1.11556 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −43.6111 | −0.0658229 | ||||||||
\(77\) | −1099.82 | −1.62773 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −926.088 | −1.31890 | −0.659449 | − | 0.751749i | \(-0.729211\pi\) | ||||
−0.659449 | + | 0.751749i | \(0.729211\pi\) | |||||||
\(80\) | 830.155 | 1.16018 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 898.756 | 1.21038 | ||||||||
\(83\) | 1311.77 | 1.73476 | 0.867380 | − | 0.497646i | \(-0.165802\pi\) | ||||
0.867380 | + | 0.497646i | \(0.165802\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1072.80 | −1.36895 | ||||||||
\(86\) | −689.818 | −0.864942 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 716.075 | 0.867430 | ||||||||
\(89\) | −510.201 | −0.607654 | −0.303827 | − | 0.952727i | \(-0.598265\pi\) | ||||
−0.303827 | + | 0.952727i | \(0.598265\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −521.983 | −0.601305 | ||||||||
\(92\) | −51.7585 | −0.0586543 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1400.39 | 1.53659 | ||||||||
\(95\) | −1358.69 | −1.46735 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −856.449 | −0.896486 | −0.448243 | − | 0.893912i | \(-0.647950\pi\) | ||||
−0.448243 | + | 0.893912i | \(0.647950\pi\) | |||||||
\(98\) | −2550.26 | −2.62872 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −28.6227 | −0.0286227 | ||||||||
\(101\) | −811.456 | −0.799435 | −0.399717 | − | 0.916638i | \(-0.630892\pi\) | ||||
−0.399717 | + | 0.916638i | \(0.630892\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −419.340 | −0.401153 | −0.200577 | − | 0.979678i | \(-0.564282\pi\) | ||||
−0.200577 | + | 0.979678i | \(0.564282\pi\) | |||||||
\(104\) | 339.856 | 0.320439 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −862.494 | −0.790309 | ||||||||
\(107\) | 1165.05 | 1.05261 | 0.526305 | − | 0.850296i | \(-0.323577\pi\) | ||||
0.526305 | + | 0.850296i | \(0.323577\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2016.17 | −1.77169 | −0.885844 | − | 0.463984i | \(-0.846419\pi\) | ||||
−0.885844 | + | 0.463984i | \(0.846419\pi\) | |||||||
\(110\) | 1168.38 | 1.01273 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2148.30 | 1.81246 | ||||||||
\(113\) | 731.760 | 0.609188 | 0.304594 | − | 0.952482i | \(-0.401479\pi\) | ||||
0.304594 | + | 0.952482i | \(0.401479\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1612.51 | −1.30755 | ||||||||
\(116\) | −23.9643 | −0.0191813 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 162.200 | 0.126540 | ||||||||
\(119\) | −2776.22 | −2.13862 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −379.051 | −0.284787 | ||||||||
\(122\) | −1453.90 | −1.07894 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 102.324 | 0.0741048 | ||||||||
\(125\) | 830.087 | 0.593962 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1187.43 | −0.829666 | −0.414833 | − | 0.909898i | \(-0.636160\pi\) | ||||
−0.414833 | + | 0.909898i | \(0.636160\pi\) | |||||||
\(128\) | −1316.64 | −0.909185 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 554.523 | 0.374115 | ||||||||
\(131\) | 250.996 | 0.167402 | 0.0837008 | − | 0.996491i | \(-0.473326\pi\) | ||||
0.0837008 | + | 0.996491i | \(0.473326\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3516.06 | −2.29234 | ||||||||
\(134\) | 1026.22 | 0.661580 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1807.56 | 1.13968 | ||||||||
\(137\) | −2474.51 | −1.54315 | −0.771576 | − | 0.636137i | \(-0.780531\pi\) | ||||
−0.771576 | + | 0.636137i | \(0.780531\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2067.65 | 1.26169 | 0.630847 | − | 0.775907i | \(-0.282708\pi\) | ||||
0.630847 | + | 0.775907i | \(0.282708\pi\) | |||||||
\(140\) | −217.092 | −0.131054 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1434.97 | −0.848031 | ||||||||
\(143\) | 451.804 | 0.264208 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −746.600 | −0.427598 | ||||||||
\(146\) | −2225.18 | −1.26135 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 114.208 | 0.0634314 | ||||||||
\(149\) | −70.2921 | −0.0386480 | −0.0193240 | − | 0.999813i | \(-0.506151\pi\) | ||||
−0.0193240 | + | 0.999813i | \(0.506151\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2156.31 | 1.16211 | 0.581054 | − | 0.813865i | \(-0.302641\pi\) | ||||
0.581054 | + | 0.813865i | \(0.302641\pi\) | |||||||
\(152\) | 2289.26 | 1.22160 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3023.57 | 1.58212 | ||||||||
\(155\) | 3187.88 | 1.65198 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 105.729 | 0.0537459 | 0.0268729 | − | 0.999639i | \(-0.491445\pi\) | ||||
0.0268729 | + | 0.999639i | \(0.491445\pi\) | |||||||
\(158\) | 2545.96 | 1.28194 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 275.289 | 0.136022 | ||||||||
\(161\) | −4172.92 | −2.04268 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1006.11 | −0.483463 | −0.241731 | − | 0.970343i | \(-0.577715\pi\) | ||||
−0.241731 | + | 0.970343i | \(0.577715\pi\) | |||||||
\(164\) | 144.543 | 0.0688226 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3606.25 | −1.68614 | ||||||||
\(167\) | 668.739 | 0.309872 | 0.154936 | − | 0.987925i | \(-0.450483\pi\) | ||||
0.154936 | + | 0.987925i | \(0.450483\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1982.57 | −0.902398 | ||||||||
\(170\) | 2949.29 | 1.33059 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −110.940 | −0.0491809 | ||||||||
\(173\) | 2879.96 | 1.26566 | 0.632831 | − | 0.774290i | \(-0.281893\pi\) | ||||
0.632831 | + | 0.774290i | \(0.281893\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2307.64 | −0.996809 | ||||||||
\(176\) | −1859.47 | −0.796380 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1402.62 | 0.590624 | ||||||||
\(179\) | −1700.00 | −0.709856 | −0.354928 | − | 0.934894i | \(-0.615495\pi\) | ||||
−0.354928 | + | 0.934894i | \(0.615495\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1750.62 | −0.718910 | −0.359455 | − | 0.933162i | \(-0.617037\pi\) | ||||
−0.359455 | + | 0.933162i | \(0.617037\pi\) | |||||||
\(182\) | 1435.01 | 0.584452 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2716.93 | 1.08856 | ||||||||
\(185\) | 3558.11 | 1.41404 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2402.97 | 0.939691 | ||||||||
\(188\) | 225.219 | 0.0873711 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3735.24 | 1.42623 | ||||||||
\(191\) | −1504.78 | −0.570062 | −0.285031 | − | 0.958518i | \(-0.592004\pi\) | ||||
−0.285031 | + | 0.958518i | \(0.592004\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −803.437 | −0.299651 | −0.149826 | − | 0.988712i | \(-0.547871\pi\) | ||||
−0.149826 | + | 0.988712i | \(0.547871\pi\) | |||||||
\(194\) | 2354.51 | 0.871361 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −410.146 | −0.149470 | ||||||||
\(197\) | 1329.45 | 0.480808 | 0.240404 | − | 0.970673i | \(-0.422720\pi\) | ||||
0.240404 | + | 0.970673i | \(0.422720\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2857.91 | −1.01805 | −0.509025 | − | 0.860752i | \(-0.669994\pi\) | ||||
−0.509025 | + | 0.860752i | \(0.669994\pi\) | |||||||
\(200\) | 1502.48 | 0.531206 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2230.82 | 0.777030 | ||||||||
\(203\) | −1932.08 | −0.668006 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4503.18 | 1.53422 | ||||||||
\(206\) | 1152.83 | 0.389911 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −882.524 | −0.294192 | ||||||||
\(209\) | 3043.33 | 1.00723 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3121.15 | −1.01834 | −0.509168 | − | 0.860667i | \(-0.670047\pi\) | ||||
−0.509168 | + | 0.860667i | \(0.670047\pi\) | |||||||
\(212\) | −138.711 | −0.0449373 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3202.89 | −1.02311 | ||||||||
\(215\) | −3456.30 | −1.09636 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8249.69 | 2.58076 | ||||||||
\(218\) | 5542.76 | 1.72203 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 187.905 | 0.0575842 | ||||||||
\(221\) | 1140.47 | 0.347133 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2100.41 | −0.630734 | −0.315367 | − | 0.948970i | \(-0.602128\pi\) | ||||
−0.315367 | + | 0.948970i | \(0.602128\pi\) | |||||||
\(224\) | 712.402 | 0.212497 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2011.72 | −0.592114 | ||||||||
\(227\) | −2601.37 | −0.760613 | −0.380306 | − | 0.924861i | \(-0.624181\pi\) | ||||
−0.380306 | + | 0.924861i | \(0.624181\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1502.73 | −0.433637 | −0.216819 | − | 0.976212i | \(-0.569568\pi\) | ||||
−0.216819 | + | 0.976212i | \(0.569568\pi\) | |||||||
\(230\) | 4433.06 | 1.27090 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1257.95 | 0.355984 | ||||||||
\(233\) | 1672.77 | 0.470329 | 0.235164 | − | 0.971956i | \(-0.424437\pi\) | ||||
0.235164 | + | 0.971956i | \(0.424437\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7016.60 | 1.94771 | ||||||||
\(236\) | 26.0859 | 0.00719512 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 7632.27 | 2.07868 | ||||||||
\(239\) | −3489.49 | −0.944420 | −0.472210 | − | 0.881486i | \(-0.656544\pi\) | ||||
−0.472210 | + | 0.881486i | \(0.656544\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −872.061 | −0.233089 | −0.116544 | − | 0.993185i | \(-0.537182\pi\) | ||||
−0.116544 | + | 0.993185i | \(0.537182\pi\) | |||||||
\(242\) | 1042.07 | 0.276806 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −233.825 | −0.0613487 | ||||||||
\(245\) | −12777.9 | −3.33205 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1444.40 | 0.372084 | ||||||||
\(248\) | −5371.26 | −1.37531 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2282.04 | −0.577316 | ||||||||
\(251\) | 463.531 | 0.116565 | 0.0582825 | − | 0.998300i | \(-0.481438\pi\) | ||||
0.0582825 | + | 0.998300i | \(0.481438\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3611.88 | 0.897538 | ||||||||
\(254\) | 3264.44 | 0.806413 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −677.006 | −0.165285 | ||||||||
\(257\) | −2168.52 | −0.526338 | −0.263169 | − | 0.964750i | \(-0.584768\pi\) | ||||
−0.263169 | + | 0.964750i | \(0.584768\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9207.80 | 2.20905 | ||||||||
\(260\) | 89.1814 | 0.0212723 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −690.027 | −0.162710 | ||||||||
\(263\) | −567.749 | −0.133114 | −0.0665569 | − | 0.997783i | \(-0.521201\pi\) | ||||
−0.0665569 | + | 0.997783i | \(0.521201\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4321.48 | −1.00176 | ||||||||
\(266\) | 9666.20 | 2.22809 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 165.042 | 0.0376177 | ||||||||
\(269\) | 326.225 | 0.0739415 | 0.0369708 | − | 0.999316i | \(-0.488229\pi\) | ||||
0.0369708 | + | 0.999316i | \(0.488229\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1478.00 | 0.331300 | 0.165650 | − | 0.986185i | \(-0.447028\pi\) | ||||
0.165650 | + | 0.986185i | \(0.447028\pi\) | |||||||
\(272\) | −4693.79 | −1.04633 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6802.82 | 1.49990 | ||||||||
\(275\) | 1997.39 | 0.437989 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8647.79 | 1.87580 | 0.937898 | − | 0.346911i | \(-0.112769\pi\) | ||||
0.937898 | + | 0.346911i | \(0.112769\pi\) | |||||||
\(278\) | −5684.29 | −1.22633 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 11395.7 | 2.43223 | ||||||||
\(281\) | 4653.34 | 0.987882 | 0.493941 | − | 0.869495i | \(-0.335556\pi\) | ||||
0.493941 | + | 0.869495i | \(0.335556\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2594.93 | −0.545062 | −0.272531 | − | 0.962147i | \(-0.587861\pi\) | ||||
−0.272531 | + | 0.962147i | \(0.587861\pi\) | |||||||
\(284\) | −230.780 | −0.0482193 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1242.08 | −0.256803 | ||||||||
\(287\) | 11653.5 | 2.39680 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1152.71 | 0.234625 | ||||||||
\(290\) | 2052.52 | 0.415614 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −357.865 | −0.0717208 | ||||||||
\(293\) | 7299.73 | 1.45548 | 0.727739 | − | 0.685854i | \(-0.240571\pi\) | ||||
0.727739 | + | 0.685854i | \(0.240571\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 812.697 | 0.160397 | ||||||||
\(296\) | −5995.07 | −1.17722 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 193.244 | 0.0375648 | ||||||||
\(299\) | 1714.24 | 0.331561 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8944.34 | −1.71277 | ||||||||
\(302\) | −5928.04 | −1.12954 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5944.64 | −1.12154 | ||||||||
\(305\) | −7284.72 | −1.36761 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3677.41 | 0.683651 | 0.341826 | − | 0.939763i | \(-0.388955\pi\) | ||||
0.341826 | + | 0.939763i | \(0.388955\pi\) | |||||||
\(308\) | 486.266 | 0.0899597 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −8763.97 | −1.60568 | ||||||||
\(311\) | −3389.46 | −0.618002 | −0.309001 | − | 0.951062i | \(-0.599995\pi\) | ||||
−0.309001 | + | 0.951062i | \(0.599995\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4847.47 | −0.875384 | −0.437692 | − | 0.899125i | \(-0.644204\pi\) | ||||
−0.437692 | + | 0.899125i | \(0.644204\pi\) | |||||||
\(314\) | −290.666 | −0.0522396 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 409.455 | 0.0728913 | ||||||||
\(317\) | −10460.9 | −1.85344 | −0.926721 | − | 0.375750i | \(-0.877385\pi\) | ||||
−0.926721 | + | 0.375750i | \(0.877385\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1672.31 | 0.293516 | ||||||||
\(320\) | −7398.05 | −1.29239 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 11472.0 | 1.98544 | ||||||||
\(323\) | 7682.17 | 1.32337 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 947.980 | 0.161798 | ||||||||
\(326\) | 2765.95 | 0.469913 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −7587.42 | −1.27727 | ||||||||
\(329\) | 18157.8 | 3.04277 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2859.84 | −0.474898 | −0.237449 | − | 0.971400i | \(-0.576311\pi\) | ||||
−0.237449 | + | 0.971400i | \(0.576311\pi\) | |||||||
\(332\) | −579.977 | −0.0958747 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1838.47 | −0.301187 | ||||||||
\(335\) | 5141.82 | 0.838589 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4699.94 | 0.759710 | 0.379855 | − | 0.925046i | \(-0.375974\pi\) | ||||
0.379855 | + | 0.925046i | \(0.375974\pi\) | |||||||
\(338\) | 5450.39 | 0.877108 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 474.320 | 0.0756577 | ||||||||
\(341\) | −7140.55 | −1.13397 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20840.6 | −3.28071 | ||||||||
\(344\) | 5823.54 | 0.912745 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7917.47 | −1.23019 | ||||||||
\(347\) | −951.938 | −0.147270 | −0.0736350 | − | 0.997285i | \(-0.523460\pi\) | ||||
−0.0736350 | + | 0.997285i | \(0.523460\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10647.9 | −1.63315 | −0.816575 | − | 0.577239i | \(-0.804130\pi\) | ||||
−0.816575 | + | 0.577239i | \(0.804130\pi\) | |||||||
\(350\) | 6344.08 | 0.968872 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −616.622 | −0.0933695 | ||||||||
\(353\) | −11818.1 | −1.78191 | −0.890957 | − | 0.454088i | \(-0.849965\pi\) | ||||
−0.890957 | + | 0.454088i | \(0.849965\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7189.87 | −1.07493 | ||||||||
\(356\) | 225.578 | 0.0335831 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4673.58 | 0.689962 | ||||||||
\(359\) | −8794.89 | −1.29297 | −0.646485 | − | 0.762926i | \(-0.723762\pi\) | ||||
−0.646485 | + | 0.762926i | \(0.723762\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2870.40 | 0.418486 | ||||||||
\(362\) | 4812.74 | 0.698762 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 230.787 | 0.0332322 | ||||||||
\(365\) | −11149.2 | −1.59883 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13284.1 | 1.88945 | 0.944723 | − | 0.327869i | \(-0.106331\pi\) | ||||
0.944723 | + | 0.327869i | \(0.106331\pi\) | |||||||
\(368\) | −7055.21 | −0.999397 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −9781.80 | −1.37441 | ||||||||
\(371\) | −11183.3 | −1.56498 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11897.3 | −1.65153 | −0.825763 | − | 0.564018i | \(-0.809255\pi\) | ||||
−0.825763 | + | 0.564018i | \(0.809255\pi\) | |||||||
\(374\) | −6606.13 | −0.913355 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −11822.3 | −1.62151 | ||||||||
\(377\) | 793.697 | 0.108428 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1743.93 | 0.236357 | 0.118179 | − | 0.992992i | \(-0.462294\pi\) | ||||
0.118179 | + | 0.992992i | \(0.462294\pi\) | |||||||
\(380\) | 600.722 | 0.0810958 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4136.87 | 0.554085 | ||||||||
\(383\) | −1572.59 | −0.209806 | −0.104903 | − | 0.994482i | \(-0.533453\pi\) | ||||
−0.104903 | + | 0.994482i | \(0.533453\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 15149.4 | 2.00542 | ||||||||
\(386\) | 2208.77 | 0.291253 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 378.665 | 0.0495459 | ||||||||
\(389\) | 3545.77 | 0.462153 | 0.231077 | − | 0.972936i | \(-0.425775\pi\) | ||||
0.231077 | + | 0.972936i | \(0.425775\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9117.34 | 1.17924 | ||||||||
\(392\) | 21529.6 | 2.77400 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3654.86 | −0.467333 | ||||||||
\(395\) | 12756.4 | 1.62492 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7176.14 | 0.907205 | 0.453602 | − | 0.891204i | \(-0.350139\pi\) | ||||
0.453602 | + | 0.891204i | \(0.350139\pi\) | |||||||
\(398\) | 7856.85 | 0.989518 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3901.56 | −0.487695 | ||||||||
\(401\) | −7431.68 | −0.925487 | −0.462744 | − | 0.886492i | \(-0.653135\pi\) | ||||
−0.462744 | + | 0.886492i | \(0.653135\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3388.97 | −0.418900 | ||||||||
\(404\) | 358.773 | 0.0441822 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5311.58 | 0.649284 | ||||||||
\(407\) | −7969.84 | −0.970639 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5038.83 | −0.609179 | −0.304589 | − | 0.952484i | \(-0.598519\pi\) | ||||
−0.304589 | + | 0.952484i | \(0.598519\pi\) | |||||||
\(410\) | −12379.9 | −1.49122 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 185.405 | 0.0221705 | ||||||||
\(413\) | 2103.12 | 0.250576 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18069.0 | −2.13728 | ||||||||
\(416\) | −292.655 | −0.0344918 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −8366.60 | −0.979005 | ||||||||
\(419\) | 3543.16 | 0.413114 | 0.206557 | − | 0.978435i | \(-0.433774\pi\) | ||||
0.206557 | + | 0.978435i | \(0.433774\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13131.9 | 1.52022 | 0.760109 | − | 0.649796i | \(-0.225145\pi\) | ||||
0.760109 | + | 0.649796i | \(0.225145\pi\) | |||||||
\(422\) | 8580.54 | 0.989797 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 7281.29 | 0.833987 | ||||||||
\(425\) | 5041.93 | 0.575458 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −18851.6 | −2.13652 | ||||||||
\(428\) | −515.107 | −0.0581744 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 9501.92 | 1.06564 | ||||||||
\(431\) | 9117.45 | 1.01896 | 0.509480 | − | 0.860482i | \(-0.329838\pi\) | ||||
0.509480 | + | 0.860482i | \(0.329838\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2554.40 | −0.283502 | −0.141751 | − | 0.989902i | \(-0.545273\pi\) | ||||
−0.141751 | + | 0.989902i | \(0.545273\pi\) | |||||||
\(434\) | −22679.7 | −2.50843 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 891.417 | 0.0979155 | ||||||||
\(437\) | 11547.0 | 1.26400 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1523.94 | 0.165681 | 0.0828404 | − | 0.996563i | \(-0.473601\pi\) | ||||
0.0828404 | + | 0.996563i | \(0.473601\pi\) | |||||||
\(440\) | −9863.59 | −1.06870 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3135.34 | −0.337404 | ||||||||
\(443\) | −10110.8 | −1.08437 | −0.542186 | − | 0.840258i | \(-0.682403\pi\) | ||||
−0.542186 | + | 0.840258i | \(0.682403\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7027.78 | 0.748649 | ||||||||
\(446\) | 5774.35 | 0.613057 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −19144.9 | −2.01900 | ||||||||
\(449\) | −17927.7 | −1.88432 | −0.942162 | − | 0.335158i | \(-0.891210\pi\) | ||||
−0.942162 | + | 0.335158i | \(0.891210\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10086.7 | −1.05314 | ||||||||
\(452\) | −323.536 | −0.0336678 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7151.58 | 0.739296 | ||||||||
\(455\) | 7190.07 | 0.740826 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8911.04 | −0.912125 | −0.456062 | − | 0.889948i | \(-0.650741\pi\) | ||||
−0.456062 | + | 0.889948i | \(0.650741\pi\) | |||||||
\(458\) | 4131.23 | 0.421484 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 712.948 | 0.0722639 | ||||||||
\(461\) | −16724.3 | −1.68965 | −0.844825 | − | 0.535042i | \(-0.820296\pi\) | ||||
−0.844825 | + | 0.535042i | \(0.820296\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14050.4 | −1.41031 | −0.705157 | − | 0.709051i | \(-0.749123\pi\) | ||||
−0.705157 | + | 0.709051i | \(0.749123\pi\) | |||||||
\(464\) | −3266.58 | −0.326826 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4598.70 | −0.457147 | ||||||||
\(467\) | −10526.3 | −1.04304 | −0.521520 | − | 0.853239i | \(-0.674635\pi\) | ||||
−0.521520 | + | 0.853239i | \(0.674635\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13306.2 | 1.31007 | ||||||||
\(470\) | −19289.7 | −1.89313 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1369.32 | −0.133534 | ||||||||
\(473\) | 7741.80 | 0.752576 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6385.56 | 0.616820 | ||||||||
\(476\) | 1227.46 | 0.118195 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 9593.16 | 0.917952 | ||||||||
\(479\) | 6393.78 | 0.609894 | 0.304947 | − | 0.952369i | \(-0.401361\pi\) | ||||
0.304947 | + | 0.952369i | \(0.401361\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3782.56 | −0.358566 | ||||||||
\(482\) | 2397.43 | 0.226556 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 167.592 | 0.0157393 | ||||||||
\(485\) | 11797.2 | 1.10450 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14196.4 | 1.32095 | 0.660473 | − | 0.750850i | \(-0.270356\pi\) | ||||
0.660473 | + | 0.750850i | \(0.270356\pi\) | |||||||
\(488\) | 12274.1 | 1.13857 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 35128.6 | 3.23867 | ||||||||
\(491\) | 5867.49 | 0.539299 | 0.269650 | − | 0.962958i | \(-0.413092\pi\) | ||||
0.269650 | + | 0.962958i | \(0.413092\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4221.36 | 0.385640 | ||||||||
\(494\) | −3970.87 | −0.361656 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 13947.9 | 1.26266 | ||||||||
\(497\) | −18606.2 | −1.67928 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8345.43 | −0.748683 | −0.374341 | − | 0.927291i | \(-0.622131\pi\) | ||||
−0.374341 | + | 0.927291i | \(0.622131\pi\) | |||||||
\(500\) | −367.010 | −0.0328264 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1274.32 | −0.113298 | ||||||||
\(503\) | 1607.53 | 0.142498 | 0.0712488 | − | 0.997459i | \(-0.477302\pi\) | ||||
0.0712488 | + | 0.997459i | \(0.477302\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11177.4 | 0.984929 | ||||||||
\(506\) | −9929.64 | −0.872384 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 525.004 | 0.0458530 | ||||||||
\(509\) | 9106.68 | 0.793018 | 0.396509 | − | 0.918031i | \(-0.370221\pi\) | ||||
0.396509 | + | 0.918031i | \(0.370221\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −28852.2 | −2.49774 | ||||||||
\(512\) | 12394.3 | 1.06984 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5961.61 | 0.511586 | ||||||||
\(515\) | 5776.21 | 0.494233 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15716.5 | −1.33697 | ||||||||
\(518\) | −25313.7 | −2.14714 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4681.36 | −0.394791 | ||||||||
\(521\) | 7301.03 | 0.613942 | 0.306971 | − | 0.951719i | \(-0.400684\pi\) | ||||
0.306971 | + | 0.951719i | \(0.400684\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4874.89 | 0.407579 | 0.203790 | − | 0.979015i | \(-0.434674\pi\) | ||||
0.203790 | + | 0.979015i | \(0.434674\pi\) | |||||||
\(524\) | −110.974 | −0.00925175 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1560.83 | 0.129383 | ||||||||
\(527\) | −18024.6 | −1.48987 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1537.22 | 0.126343 | ||||||||
\(530\) | 11880.4 | 0.973685 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1554.57 | 0.126690 | ||||||||
\(533\) | −4787.25 | −0.389041 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16047.9 | −1.29685 | ||||||||
\(536\) | −8663.47 | −0.698143 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −896.843 | −0.0718692 | ||||||||
\(539\) | 28621.4 | 2.28722 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1382.28 | −0.109850 | −0.0549249 | − | 0.998490i | \(-0.517492\pi\) | ||||
−0.0549249 | + | 0.998490i | \(0.517492\pi\) | |||||||
\(542\) | −4063.26 | −0.322015 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1556.51 | −0.122675 | ||||||||
\(545\) | 27771.8 | 2.18277 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20117.5 | −1.57251 | −0.786255 | − | 0.617902i | \(-0.787983\pi\) | ||||
−0.786255 | + | 0.617902i | \(0.787983\pi\) | |||||||
\(548\) | 1094.07 | 0.0852851 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −5491.14 | −0.425714 | ||||||||
\(551\) | 5346.31 | 0.413358 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 33011.5 | 2.53850 | ||||||||
\(554\) | −23774.1 | −1.82322 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −914.178 | −0.0697298 | ||||||||
\(557\) | 12926.3 | 0.983311 | 0.491655 | − | 0.870790i | \(-0.336392\pi\) | ||||
0.491655 | + | 0.870790i | \(0.336392\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3674.33 | 0.278010 | ||||||||
\(560\) | −29591.9 | −2.23301 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −12792.8 | −0.960195 | ||||||||
\(563\) | −1483.56 | −0.111056 | −0.0555279 | − | 0.998457i | \(-0.517684\pi\) | ||||
−0.0555279 | + | 0.998457i | \(0.517684\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10079.6 | −0.750538 | ||||||||
\(566\) | 7133.87 | 0.529786 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12114.2 | 0.894899 | ||||||||
\(569\) | −535.139 | −0.0394274 | −0.0197137 | − | 0.999806i | \(-0.506275\pi\) | ||||
−0.0197137 | + | 0.999806i | \(0.506275\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11303.3 | 0.828420 | 0.414210 | − | 0.910181i | \(-0.364058\pi\) | ||||
0.414210 | + | 0.910181i | \(0.364058\pi\) | |||||||
\(572\) | −199.758 | −0.0146019 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −32037.2 | −2.32963 | ||||||||
\(575\) | 7578.50 | 0.549644 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22867.6 | −1.64990 | −0.824950 | − | 0.565206i | \(-0.808797\pi\) | ||||
−0.824950 | + | 0.565206i | \(0.808797\pi\) | |||||||
\(578\) | −3168.99 | −0.228049 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 330.097 | 0.0236320 | ||||||||
\(581\) | −46759.5 | −3.33892 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9679.73 | 0.687639 | ||||||||
\(584\) | 18785.3 | 1.33106 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −20068.1 | −1.41469 | ||||||||
\(587\) | 17589.4 | 1.23679 | 0.618393 | − | 0.785869i | \(-0.287784\pi\) | ||||
0.618393 | + | 0.785869i | \(0.287784\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −22828.0 | −1.59696 | ||||||||
\(590\) | −2234.23 | −0.155901 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 15567.7 | 1.08079 | ||||||||
\(593\) | 16110.5 | 1.11565 | 0.557825 | − | 0.829959i | \(-0.311636\pi\) | ||||
0.557825 | + | 0.829959i | \(0.311636\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 38241.1 | 2.63485 | ||||||||
\(596\) | 31.0785 | 0.00213595 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4712.70 | −0.322269 | ||||||||
\(599\) | −22231.7 | −1.51646 | −0.758231 | − | 0.651986i | \(-0.773936\pi\) | ||||
−0.758231 | + | 0.651986i | \(0.773936\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16668.9 | −1.13135 | −0.565673 | − | 0.824629i | \(-0.691384\pi\) | ||||
−0.565673 | + | 0.824629i | \(0.691384\pi\) | |||||||
\(602\) | 24589.4 | 1.66477 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −953.380 | −0.0642259 | ||||||||
\(605\) | 5221.25 | 0.350866 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11293.3 | 0.755155 | 0.377577 | − | 0.925978i | \(-0.376757\pi\) | ||||
0.377577 | + | 0.925978i | \(0.376757\pi\) | |||||||
\(608\) | −1971.31 | −0.131492 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 20026.8 | 1.32928 | ||||||||
\(611\) | −7459.23 | −0.493892 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9187.06 | −0.605321 | −0.302661 | − | 0.953098i | \(-0.597875\pi\) | ||||
−0.302661 | + | 0.953098i | \(0.597875\pi\) | |||||||
\(614\) | −10109.8 | −0.664491 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −25525.3 | −1.66955 | ||||||||
\(617\) | 5405.24 | 0.352685 | 0.176342 | − | 0.984329i | \(-0.443573\pi\) | ||||
0.176342 | + | 0.984329i | \(0.443573\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 26890.8 | 1.74610 | 0.873049 | − | 0.487633i | \(-0.162140\pi\) | ||||
0.873049 | + | 0.487633i | \(0.162140\pi\) | |||||||
\(620\) | −1409.47 | −0.0912994 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 9318.16 | 0.600682 | ||||||||
\(623\) | 18186.7 | 1.16956 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19526.2 | −1.24968 | ||||||||
\(626\) | 13326.5 | 0.850850 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −46.7465 | −0.00297036 | ||||||||
\(629\) | −20117.9 | −1.27529 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13088.1 | 0.825718 | 0.412859 | − | 0.910795i | \(-0.364530\pi\) | ||||
0.412859 | + | 0.910795i | \(0.364530\pi\) | |||||||
\(632\) | −21493.3 | −1.35278 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 28758.6 | 1.80150 | ||||||||
\(635\) | 16356.3 | 1.02217 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13584.0 | 0.844926 | ||||||||
\(638\) | −4597.46 | −0.285290 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 18136.1 | 1.12014 | ||||||||
\(641\) | −11372.4 | −0.700754 | −0.350377 | − | 0.936609i | \(-0.613947\pi\) | ||||
−0.350377 | + | 0.936609i | \(0.613947\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28882.8 | 1.77142 | 0.885712 | − | 0.464236i | \(-0.153671\pi\) | ||||
0.885712 | + | 0.464236i | \(0.153671\pi\) | |||||||
\(644\) | 1844.99 | 0.112893 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −21119.5 | −1.28628 | ||||||||
\(647\) | −3509.03 | −0.213222 | −0.106611 | − | 0.994301i | \(-0.534000\pi\) | ||||
−0.106611 | + | 0.994301i | \(0.534000\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1820.37 | −0.110101 | ||||||||
\(650\) | −2606.15 | −0.157264 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 444.835 | 0.0267194 | ||||||||
\(653\) | 12551.5 | 0.752185 | 0.376092 | − | 0.926582i | \(-0.377268\pi\) | ||||
0.376092 | + | 0.926582i | \(0.377268\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3457.35 | −0.206244 | ||||||||
\(656\) | 19702.7 | 1.17265 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −49918.7 | −2.95750 | ||||||||
\(659\) | 26042.1 | 1.53938 | 0.769692 | − | 0.638415i | \(-0.220410\pi\) | ||||
0.769692 | + | 0.638415i | \(0.220410\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8841.43 | 0.520260 | 0.260130 | − | 0.965574i | \(-0.416235\pi\) | ||||
0.260130 | + | 0.965574i | \(0.416235\pi\) | |||||||
\(662\) | 7862.16 | 0.461588 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 30444.5 | 1.77933 | ||||||||
\(665\) | 48432.0 | 2.82423 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6345.10 | 0.368341 | ||||||||
\(668\) | −295.673 | −0.0171256 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −14135.7 | −0.815087 | ||||||||
\(671\) | 16317.1 | 0.938770 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5539.99 | 0.317312 | 0.158656 | − | 0.987334i | \(-0.449284\pi\) | ||||
0.158656 | + | 0.987334i | \(0.449284\pi\) | |||||||
\(674\) | −12920.9 | −0.738418 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 876.562 | 0.0498727 | ||||||||
\(677\) | −6105.80 | −0.346625 | −0.173312 | − | 0.984867i | \(-0.555447\pi\) | ||||
−0.173312 | + | 0.984867i | \(0.555447\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 30529.1 | 1.72548 | ||||||||
\(680\) | −24898.3 | −1.40413 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 19630.5 | 1.10218 | ||||||||
\(683\) | −6169.93 | −0.345660 | −0.172830 | − | 0.984952i | \(-0.555291\pi\) | ||||
−0.172830 | + | 0.984952i | \(0.555291\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 34085.2 | 1.90121 | ||||||||
\(686\) | 57294.0 | 3.18877 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −15122.3 | −0.837983 | ||||||||
\(689\) | 4594.09 | 0.254022 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24137.5 | −1.32885 | −0.664423 | − | 0.747357i | \(-0.731323\pi\) | ||||
−0.664423 | + | 0.747357i | \(0.731323\pi\) | |||||||
\(692\) | −1273.33 | −0.0699491 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2617.03 | 0.143143 | ||||||||
\(695\) | −28480.8 | −1.55445 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −25461.5 | −1.38368 | ||||||||
\(698\) | 29272.8 | 1.58738 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1020.29 | 0.0550904 | ||||||||
\(701\) | −1381.52 | −0.0744354 | −0.0372177 | − | 0.999307i | \(-0.511849\pi\) | ||||
−0.0372177 | + | 0.999307i | \(0.511849\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −25479.2 | −1.36695 | ||||||||
\(704\) | 16571.0 | 0.887133 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 32489.9 | 1.73197 | ||||||||
\(707\) | 28925.3 | 1.53868 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11440.3 | 0.605995 | 0.302998 | − | 0.952991i | \(-0.402013\pi\) | ||||
0.302998 | + | 0.952991i | \(0.402013\pi\) | |||||||
\(710\) | 19766.1 | 1.04480 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −11841.1 | −0.623266 | ||||||||
\(713\) | −27092.7 | −1.42304 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6223.39 | −0.325513 | ||||||||
\(716\) | 751.630 | 0.0392315 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 24178.5 | 1.25673 | ||||||||
\(719\) | −23773.0 | −1.23308 | −0.616539 | − | 0.787324i | \(-0.711466\pi\) | ||||
−0.616539 | + | 0.787324i | \(0.711466\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14947.9 | 0.772105 | ||||||||
\(722\) | −7891.17 | −0.406757 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 774.010 | 0.0397319 | ||||||||
\(725\) | 3508.87 | 0.179746 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −38328.7 | −1.95534 | −0.977670 | − | 0.210146i | \(-0.932606\pi\) | ||||
−0.977670 | + | 0.210146i | \(0.932606\pi\) | |||||||
\(728\) | −12114.6 | −0.616753 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 30650.8 | 1.55402 | ||||||||
\(731\) | 19542.3 | 0.988781 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23440.6 | −1.18117 | −0.590586 | − | 0.806975i | \(-0.701103\pi\) | ||||
−0.590586 | + | 0.806975i | \(0.701103\pi\) | |||||||
\(734\) | −36520.2 | −1.83649 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2339.59 | −0.117172 | ||||||||
\(737\) | −11517.2 | −0.575633 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20289.0 | −1.00994 | −0.504968 | − | 0.863138i | \(-0.668496\pi\) | ||||
−0.504968 | + | 0.863138i | \(0.668496\pi\) | |||||||
\(740\) | −1573.16 | −0.0781495 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 30744.6 | 1.52112 | ||||||||
\(743\) | 21978.5 | 1.08521 | 0.542607 | − | 0.839987i | \(-0.317437\pi\) | ||||
0.542607 | + | 0.839987i | \(0.317437\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 968.240 | 0.0476155 | ||||||||
\(746\) | 32707.6 | 1.60524 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1062.43 | −0.0519337 | ||||||||
\(749\) | −41529.4 | −2.02597 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11321.9 | −0.550122 | −0.275061 | − | 0.961427i | \(-0.588698\pi\) | ||||
−0.275061 | + | 0.961427i | \(0.588698\pi\) | |||||||
\(752\) | 30699.6 | 1.48870 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2182.00 | −0.105389 | ||||||||
\(755\) | −29702.2 | −1.43175 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −29868.4 | −1.43406 | −0.717031 | − | 0.697042i | \(-0.754499\pi\) | ||||
−0.717031 | + | 0.697042i | \(0.754499\pi\) | |||||||
\(758\) | −4794.33 | −0.229733 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −31533.4 | −1.50505 | ||||||||
\(761\) | −25711.9 | −1.22478 | −0.612388 | − | 0.790557i | \(-0.709791\pi\) | ||||
−0.612388 | + | 0.790557i | \(0.709791\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 71868.7 | 3.40999 | ||||||||
\(764\) | 665.313 | 0.0315055 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4323.31 | 0.203926 | ||||||||
\(767\) | −863.964 | −0.0406727 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16360.5 | −0.767199 | −0.383600 | − | 0.923500i | \(-0.625316\pi\) | ||||
−0.383600 | + | 0.923500i | \(0.625316\pi\) | |||||||
\(770\) | −41648.2 | −1.94922 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 355.227 | 0.0165608 | ||||||||
\(773\) | 8952.62 | 0.416563 | 0.208282 | − | 0.978069i | \(-0.433213\pi\) | ||||
0.208282 | + | 0.978069i | \(0.433213\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −14982.4 | −0.694429 | ||||||||
\(776\) | −19877.1 | −0.919519 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9747.88 | −0.449201 | ||||||||
\(779\) | −32246.7 | −1.48313 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16104.6 | 0.737861 | ||||||||
\(782\) | −25065.0 | −1.14619 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −55907.1 | −2.54679 | ||||||||
\(785\) | −1456.37 | −0.0662166 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1427.86 | −0.0646731 | −0.0323365 | − | 0.999477i | \(-0.510295\pi\) | ||||
−0.0323365 | + | 0.999477i | \(0.510295\pi\) | |||||||
\(788\) | −587.794 | −0.0265727 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −35069.4 | −1.57938 | ||||||||
\(791\) | −26084.5 | −1.17251 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7744.25 | 0.346793 | ||||||||
\(794\) | −19728.3 | −0.881779 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1263.58 | 0.0562644 | ||||||||
\(797\) | −33475.6 | −1.48779 | −0.743894 | − | 0.668297i | \(-0.767023\pi\) | ||||
−0.743894 | + | 0.668297i | \(0.767023\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −39672.7 | −1.75659 | ||||||||
\(800\) | −1293.80 | −0.0571785 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 20430.9 | 0.899549 | ||||||||
\(803\) | 24973.1 | 1.09749 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 57480.0 | 2.51665 | ||||||||
\(806\) | 9316.82 | 0.407160 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −18832.9 | −0.819974 | ||||||||
\(809\) | −18354.9 | −0.797679 | −0.398839 | − | 0.917021i | \(-0.630587\pi\) | ||||
−0.398839 | + | 0.917021i | \(0.630587\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18590.6 | 0.804937 | 0.402469 | − | 0.915434i | \(-0.368152\pi\) | ||||
0.402469 | + | 0.915434i | \(0.368152\pi\) | |||||||
\(812\) | 854.237 | 0.0369185 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 21910.3 | 0.943436 | ||||||||
\(815\) | 13858.7 | 0.595641 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24750.2 | 1.05985 | ||||||||
\(818\) | 13852.5 | 0.592106 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1991.01 | −0.0847915 | ||||||||
\(821\) | −11083.4 | −0.471151 | −0.235575 | − | 0.971856i | \(-0.575697\pi\) | ||||
−0.235575 | + | 0.971856i | \(0.575697\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11533.7 | −0.488506 | −0.244253 | − | 0.969712i | \(-0.578543\pi\) | ||||
−0.244253 | + | 0.969712i | \(0.578543\pi\) | |||||||
\(824\) | −9732.36 | −0.411460 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5781.82 | −0.243554 | ||||||||
\(827\) | 25859.7 | 1.08734 | 0.543670 | − | 0.839299i | \(-0.317034\pi\) | ||||
0.543670 | + | 0.839299i | \(0.317034\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20734.3 | −0.868674 | −0.434337 | − | 0.900750i | \(-0.643017\pi\) | ||||
−0.434337 | + | 0.900750i | \(0.643017\pi\) | |||||||
\(830\) | 49674.4 | 2.07738 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 7864.74 | 0.327717 | ||||||||
\(833\) | 72247.9 | 3.00509 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9211.56 | −0.381772 | ||||||||
\(836\) | −1345.56 | −0.0556666 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −9740.71 | −0.401536 | ||||||||
\(839\) | −8282.44 | −0.340812 | −0.170406 | − | 0.985374i | \(-0.554508\pi\) | ||||
−0.170406 | + | 0.985374i | \(0.554508\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21451.2 | −0.879544 | ||||||||
\(842\) | −36101.8 | −1.47761 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1379.97 | 0.0562802 | ||||||||
\(845\) | 27308.9 | 1.11178 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13511.7 | 0.548133 | ||||||||
\(848\) | −18907.7 | −0.765676 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −13861.1 | −0.559330 | ||||||||
\(851\) | −30239.2 | −1.21808 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 27976.9 | 1.12299 | 0.561495 | − | 0.827480i | \(-0.310226\pi\) | ||||
0.561495 | + | 0.827480i | \(0.310226\pi\) | |||||||
\(854\) | 51826.1 | 2.07664 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 27039.3 | 1.07965 | ||||||||
\(857\) | 30334.1 | 1.20910 | 0.604548 | − | 0.796569i | \(-0.293354\pi\) | ||||
0.604548 | + | 0.796569i | \(0.293354\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 35079.4 | 1.39336 | 0.696679 | − | 0.717383i | \(-0.254660\pi\) | ||||
0.696679 | + | 0.717383i | \(0.254660\pi\) | |||||||
\(860\) | 1528.15 | 0.0605924 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −25065.3 | −0.990403 | ||||||||
\(863\) | 8904.72 | 0.351240 | 0.175620 | − | 0.984458i | \(-0.443807\pi\) | ||||
0.175620 | + | 0.984458i | \(0.443807\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −39670.1 | −1.55934 | ||||||||
\(866\) | 7022.44 | 0.275557 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3647.47 | −0.142631 | ||||||||
\(869\) | −28573.2 | −1.11540 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5466.17 | −0.212645 | ||||||||
\(872\) | −46792.8 | −1.81720 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −31744.6 | −1.22858 | ||||||||
\(875\) | −29589.4 | −1.14321 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5487.15 | 0.211275 | 0.105637 | − | 0.994405i | \(-0.466312\pi\) | ||||
0.105637 | + | 0.994405i | \(0.466312\pi\) | |||||||
\(878\) | −4189.56 | −0.161037 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 25613.3 | 0.981165 | ||||||||
\(881\) | 12650.9 | 0.483792 | 0.241896 | − | 0.970302i | \(-0.422231\pi\) | ||||
0.241896 | + | 0.970302i | \(0.422231\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31973.4 | 1.21856 | 0.609282 | − | 0.792954i | \(-0.291458\pi\) | ||||
0.609282 | + | 0.792954i | \(0.291458\pi\) | |||||||
\(884\) | −504.242 | −0.0191849 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 27796.1 | 1.05398 | ||||||||
\(887\) | 48252.3 | 1.82655 | 0.913277 | − | 0.407338i | \(-0.133543\pi\) | ||||
0.913277 | + | 0.407338i | \(0.133543\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 42327.4 | 1.59687 | ||||||||
\(890\) | −19320.5 | −0.727667 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 928.662 | 0.0348586 | ||||||||
\(893\) | −50245.1 | −1.88285 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 23416.8 | 0.874565 | ||||||||
\(896\) | 46933.2 | 1.74992 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 49286.1 | 1.83151 | ||||||||
\(899\) | −12544.0 | −0.465368 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24434.1 | 0.903462 | ||||||||
\(902\) | 27729.9 | 1.02362 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 16983.2 | 0.624839 | ||||||||
\(905\) | 24114.0 | 0.885719 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33861.7 | 1.23964 | 0.619822 | − | 0.784742i | \(-0.287205\pi\) | ||||
0.619822 | + | 0.784742i | \(0.287205\pi\) | |||||||
\(908\) | 1150.16 | 0.0420366 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −19766.6 | −0.720063 | ||||||||
\(911\) | −45845.4 | −1.66732 | −0.833659 | − | 0.552280i | \(-0.813758\pi\) | ||||
−0.833659 | + | 0.552280i | \(0.813758\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 40472.8 | 1.46709 | ||||||||
\(914\) | 24497.9 | 0.886561 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 664.407 | 0.0239657 | ||||||||
\(917\) | −8947.05 | −0.322200 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14126.6 | −0.507066 | −0.253533 | − | 0.967327i | \(-0.581593\pi\) | ||||
−0.253533 | + | 0.967327i | \(0.581593\pi\) | |||||||
\(920\) | −37424.5 | −1.34114 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 45977.8 | 1.64230 | ||||||||
\(923\) | 7643.42 | 0.272575 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16722.4 | −0.594410 | ||||||||
\(926\) | 38626.6 | 1.37079 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1083.24 | −0.0383179 | ||||||||
\(929\) | −27790.5 | −0.981461 | −0.490730 | − | 0.871311i | \(-0.663270\pi\) | ||||
−0.490730 | + | 0.871311i | \(0.663270\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 91501.3 | 3.22109 | ||||||||
\(932\) | −739.588 | −0.0259936 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 28938.5 | 1.01381 | ||||||||
\(935\) | −33099.7 | −1.15773 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6472.88 | −0.225677 | −0.112839 | − | 0.993613i | \(-0.535994\pi\) | ||||
−0.112839 | + | 0.993613i | \(0.535994\pi\) | |||||||
\(938\) | −36580.7 | −1.27335 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3102.28 | −0.107644 | ||||||||
\(941\) | 12312.7 | 0.426550 | 0.213275 | − | 0.976992i | \(-0.431587\pi\) | ||||
0.213275 | + | 0.976992i | \(0.431587\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −38271.0 | −1.32161 | ||||||||
\(944\) | 3555.78 | 0.122596 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −21283.4 | −0.731484 | ||||||||
\(947\) | −4368.65 | −0.149907 | −0.0749536 | − | 0.997187i | \(-0.523881\pi\) | ||||
−0.0749536 | + | 0.997187i | \(0.523881\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11852.5 | 0.405424 | ||||||||
\(950\) | −17554.9 | −0.599533 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −64432.6 | −2.19356 | ||||||||
\(953\) | −2917.34 | −0.0991627 | −0.0495814 | − | 0.998770i | \(-0.515789\pi\) | ||||
−0.0495814 | + | 0.998770i | \(0.515789\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 20727.6 | 0.702333 | ||||||||
\(956\) | 1542.82 | 0.0521951 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −17577.5 | −0.592801 | ||||||||
\(959\) | 88206.9 | 2.97012 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23770.1 | 0.797895 | ||||||||
\(962\) | 10398.9 | 0.348516 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 385.568 | 0.0128821 | ||||||||
\(965\) | 11067.0 | 0.369179 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 42945.5 | 1.42816 | 0.714082 | − | 0.700062i | \(-0.246845\pi\) | ||||
0.714082 | + | 0.700062i | \(0.246845\pi\) | |||||||
\(968\) | −8797.31 | −0.292104 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −32432.3 | −1.07354 | ||||||||
\(971\) | −43742.9 | −1.44570 | −0.722851 | − | 0.691004i | \(-0.757169\pi\) | ||||
−0.722851 | + | 0.691004i | \(0.757169\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −73703.7 | −2.42840 | ||||||||
\(974\) | −39028.1 | −1.28392 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −31872.7 | −1.04531 | ||||||||
\(977\) | 29917.5 | 0.979679 | 0.489839 | − | 0.871813i | \(-0.337055\pi\) | ||||
0.489839 | + | 0.871813i | \(0.337055\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15741.6 | −0.513895 | ||||||||
\(980\) | 5649.57 | 0.184152 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −16130.6 | −0.524185 | ||||||||
\(983\) | 48495.4 | 1.57351 | 0.786756 | − | 0.617264i | \(-0.211759\pi\) | ||||
0.786756 | + | 0.617264i | \(0.211759\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18312.5 | −0.592370 | ||||||||
\(986\) | −11605.2 | −0.374832 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −638.617 | −0.0205639 | ||||||||
\(989\) | 29373.9 | 0.944426 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14192.8 | −0.454944 | −0.227472 | − | 0.973785i | \(-0.573046\pi\) | ||||
−0.227472 | + | 0.973785i | \(0.573046\pi\) | |||||||
\(992\) | 4625.27 | 0.148037 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 51151.4 | 1.63222 | ||||||||
\(995\) | 39366.4 | 1.25427 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −49366.8 | −1.56817 | −0.784083 | − | 0.620656i | \(-0.786866\pi\) | ||||
−0.784083 | + | 0.620656i | \(0.786866\pi\) | |||||||
\(998\) | 22942.9 | 0.727700 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 531.4.a.c.1.3 | 7 | ||
3.2 | odd | 2 | 177.4.a.b.1.5 | ✓ | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.4.a.b.1.5 | ✓ | 7 | 3.2 | odd | 2 | ||
531.4.a.c.1.3 | 7 | 1.1 | even | 1 | trivial |