Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [65,4,Mod(1,65)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(65, 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("65.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 65 = 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 65.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: | \(3.83512415037\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 65.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.56155 | −0.552092 | −0.276046 | − | 0.961144i | \(-0.589024\pi\) | ||||
−0.276046 | + | 0.961144i | \(0.589024\pi\) | |||||||
\(3\) | −8.24621 | −1.58698 | −0.793492 | − | 0.608581i | \(-0.791739\pi\) | ||||
−0.793492 | + | 0.608581i | \(0.791739\pi\) | |||||||
\(4\) | −5.56155 | −0.695194 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 12.8769 | 0.876162 | ||||||||
\(7\) | 33.1231 | 1.78848 | 0.894240 | − | 0.447588i | \(-0.147717\pi\) | ||||
0.894240 | + | 0.447588i | \(0.147717\pi\) | |||||||
\(8\) | 21.1771 | 0.935904 | ||||||||
\(9\) | 41.0000 | 1.51852 | ||||||||
\(10\) | 7.80776 | 0.246903 | ||||||||
\(11\) | −47.1231 | −1.29165 | −0.645825 | − | 0.763485i | \(-0.723486\pi\) | ||||
−0.645825 | + | 0.763485i | \(0.723486\pi\) | |||||||
\(12\) | 45.8617 | 1.10326 | ||||||||
\(13\) | −13.0000 | −0.277350 | ||||||||
\(14\) | −51.7235 | −0.987406 | ||||||||
\(15\) | 41.2311 | 0.709721 | ||||||||
\(16\) | 11.4233 | 0.178489 | ||||||||
\(17\) | 51.9697 | 0.741441 | 0.370721 | − | 0.928744i | \(-0.379111\pi\) | ||||
0.370721 | + | 0.928744i | \(0.379111\pi\) | |||||||
\(18\) | −64.0237 | −0.838362 | ||||||||
\(19\) | 37.6458 | 0.454555 | 0.227278 | − | 0.973830i | \(-0.427018\pi\) | ||||
0.227278 | + | 0.973830i | \(0.427018\pi\) | |||||||
\(20\) | 27.8078 | 0.310900 | ||||||||
\(21\) | −273.140 | −2.83829 | ||||||||
\(22\) | 73.5852 | 0.713110 | ||||||||
\(23\) | 161.939 | 1.46812 | 0.734059 | − | 0.679086i | \(-0.237624\pi\) | ||||
0.734059 | + | 0.679086i | \(0.237624\pi\) | |||||||
\(24\) | −174.631 | −1.48526 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 20.3002 | 0.153123 | ||||||||
\(27\) | −115.447 | −0.822881 | ||||||||
\(28\) | −184.216 | −1.24334 | ||||||||
\(29\) | 2.27652 | 0.0145772 | 0.00728861 | − | 0.999973i | \(-0.497680\pi\) | ||||
0.00728861 | + | 0.999973i | \(0.497680\pi\) | |||||||
\(30\) | −64.3845 | −0.391831 | ||||||||
\(31\) | 220.756 | 1.27900 | 0.639498 | − | 0.768793i | \(-0.279142\pi\) | ||||
0.639498 | + | 0.768793i | \(0.279142\pi\) | |||||||
\(32\) | −187.255 | −1.03445 | ||||||||
\(33\) | 388.587 | 2.04983 | ||||||||
\(34\) | −81.1534 | −0.409344 | ||||||||
\(35\) | −165.616 | −0.799832 | ||||||||
\(36\) | −228.024 | −1.05567 | ||||||||
\(37\) | 105.784 | 0.470022 | 0.235011 | − | 0.971993i | \(-0.424487\pi\) | ||||
0.235011 | + | 0.971993i | \(0.424487\pi\) | |||||||
\(38\) | −58.7860 | −0.250956 | ||||||||
\(39\) | 107.201 | 0.440150 | ||||||||
\(40\) | −105.885 | −0.418549 | ||||||||
\(41\) | −291.633 | −1.11086 | −0.555431 | − | 0.831563i | \(-0.687447\pi\) | ||||
−0.555431 | + | 0.831563i | \(0.687447\pi\) | |||||||
\(42\) | 426.523 | 1.56700 | ||||||||
\(43\) | 60.4621 | 0.214428 | 0.107214 | − | 0.994236i | \(-0.465807\pi\) | ||||
0.107214 | + | 0.994236i | \(0.465807\pi\) | |||||||
\(44\) | 262.078 | 0.897948 | ||||||||
\(45\) | −205.000 | −0.679102 | ||||||||
\(46\) | −252.877 | −0.810536 | ||||||||
\(47\) | 53.1837 | 0.165056 | 0.0825281 | − | 0.996589i | \(-0.473701\pi\) | ||||
0.0825281 | + | 0.996589i | \(0.473701\pi\) | |||||||
\(48\) | −94.1989 | −0.283259 | ||||||||
\(49\) | 754.140 | 2.19866 | ||||||||
\(50\) | −39.0388 | −0.110418 | ||||||||
\(51\) | −428.553 | −1.17666 | ||||||||
\(52\) | 72.3002 | 0.192812 | ||||||||
\(53\) | −395.909 | −1.02608 | −0.513041 | − | 0.858364i | \(-0.671481\pi\) | ||||
−0.513041 | + | 0.858364i | \(0.671481\pi\) | |||||||
\(54\) | 180.277 | 0.454306 | ||||||||
\(55\) | 235.616 | 0.577643 | ||||||||
\(56\) | 701.451 | 1.67384 | ||||||||
\(57\) | −310.436 | −0.721372 | ||||||||
\(58\) | −3.55491 | −0.00804797 | ||||||||
\(59\) | 367.710 | 0.811386 | 0.405693 | − | 0.914009i | \(-0.367030\pi\) | ||||
0.405693 | + | 0.914009i | \(0.367030\pi\) | |||||||
\(60\) | −229.309 | −0.493394 | ||||||||
\(61\) | 442.000 | 0.927743 | 0.463871 | − | 0.885903i | \(-0.346460\pi\) | ||||
0.463871 | + | 0.885903i | \(0.346460\pi\) | |||||||
\(62\) | −344.722 | −0.706124 | ||||||||
\(63\) | 1358.05 | 2.71584 | ||||||||
\(64\) | 201.022 | 0.392621 | ||||||||
\(65\) | 65.0000 | 0.124035 | ||||||||
\(66\) | −606.799 | −1.13169 | ||||||||
\(67\) | 1093.93 | 1.99469 | 0.997346 | − | 0.0728098i | \(-0.0231966\pi\) | ||||
0.997346 | + | 0.0728098i | \(0.0231966\pi\) | |||||||
\(68\) | −289.032 | −0.515446 | ||||||||
\(69\) | −1335.39 | −2.32988 | ||||||||
\(70\) | 258.617 | 0.441581 | ||||||||
\(71\) | −330.328 | −0.552150 | −0.276075 | − | 0.961136i | \(-0.589034\pi\) | ||||
−0.276075 | + | 0.961136i | \(0.589034\pi\) | |||||||
\(72\) | 868.260 | 1.42119 | ||||||||
\(73\) | −722.682 | −1.15868 | −0.579339 | − | 0.815087i | \(-0.696689\pi\) | ||||
−0.579339 | + | 0.815087i | \(0.696689\pi\) | |||||||
\(74\) | −165.187 | −0.259495 | ||||||||
\(75\) | −206.155 | −0.317397 | ||||||||
\(76\) | −209.369 | −0.316004 | ||||||||
\(77\) | −1560.86 | −2.31009 | ||||||||
\(78\) | −167.400 | −0.243004 | ||||||||
\(79\) | −114.739 | −0.163406 | −0.0817032 | − | 0.996657i | \(-0.526036\pi\) | ||||
−0.0817032 | + | 0.996657i | \(0.526036\pi\) | |||||||
\(80\) | −57.1165 | −0.0798227 | ||||||||
\(81\) | −155.000 | −0.212620 | ||||||||
\(82\) | 455.400 | 0.613298 | ||||||||
\(83\) | 806.419 | 1.06646 | 0.533229 | − | 0.845971i | \(-0.320979\pi\) | ||||
0.533229 | + | 0.845971i | \(0.320979\pi\) | |||||||
\(84\) | 1519.08 | 1.97316 | ||||||||
\(85\) | −259.848 | −0.331583 | ||||||||
\(86\) | −94.4148 | −0.118384 | ||||||||
\(87\) | −18.7727 | −0.0231338 | ||||||||
\(88\) | −997.930 | −1.20886 | ||||||||
\(89\) | −673.386 | −0.802009 | −0.401005 | − | 0.916076i | \(-0.631339\pi\) | ||||
−0.401005 | + | 0.916076i | \(0.631339\pi\) | |||||||
\(90\) | 320.118 | 0.374927 | ||||||||
\(91\) | −430.600 | −0.496035 | ||||||||
\(92\) | −900.634 | −1.02063 | ||||||||
\(93\) | −1820.40 | −2.02975 | ||||||||
\(94\) | −83.0492 | −0.0911263 | ||||||||
\(95\) | −188.229 | −0.203283 | ||||||||
\(96\) | 1544.14 | 1.64165 | ||||||||
\(97\) | 1739.46 | 1.82078 | 0.910388 | − | 0.413756i | \(-0.135783\pi\) | ||||
0.910388 | + | 0.413756i | \(0.135783\pi\) | |||||||
\(98\) | −1177.63 | −1.21386 | ||||||||
\(99\) | −1932.05 | −1.96139 | ||||||||
\(100\) | −139.039 | −0.139039 | ||||||||
\(101\) | 648.038 | 0.638437 | 0.319219 | − | 0.947681i | \(-0.396580\pi\) | ||||
0.319219 | + | 0.947681i | \(0.396580\pi\) | |||||||
\(102\) | 669.208 | 0.649622 | ||||||||
\(103\) | 1080.83 | 1.03396 | 0.516979 | − | 0.855998i | \(-0.327057\pi\) | ||||
0.516979 | + | 0.855998i | \(0.327057\pi\) | |||||||
\(104\) | −275.302 | −0.259573 | ||||||||
\(105\) | 1365.70 | 1.26932 | ||||||||
\(106\) | 618.233 | 0.566491 | ||||||||
\(107\) | 1002.09 | 0.905385 | 0.452692 | − | 0.891667i | \(-0.350464\pi\) | ||||
0.452692 | + | 0.891667i | \(0.350464\pi\) | |||||||
\(108\) | 642.064 | 0.572062 | ||||||||
\(109\) | −734.932 | −0.645814 | −0.322907 | − | 0.946431i | \(-0.604660\pi\) | ||||
−0.322907 | + | 0.946431i | \(0.604660\pi\) | |||||||
\(110\) | −367.926 | −0.318913 | ||||||||
\(111\) | −872.318 | −0.745917 | ||||||||
\(112\) | 378.375 | 0.319224 | ||||||||
\(113\) | −1167.11 | −0.971612 | −0.485806 | − | 0.874067i | \(-0.661474\pi\) | ||||
−0.485806 | + | 0.874067i | \(0.661474\pi\) | |||||||
\(114\) | 484.761 | 0.398264 | ||||||||
\(115\) | −809.697 | −0.656562 | ||||||||
\(116\) | −12.6610 | −0.0101340 | ||||||||
\(117\) | −533.000 | −0.421161 | ||||||||
\(118\) | −574.199 | −0.447960 | ||||||||
\(119\) | 1721.40 | 1.32605 | ||||||||
\(120\) | 873.153 | 0.664230 | ||||||||
\(121\) | 889.587 | 0.668360 | ||||||||
\(122\) | −690.206 | −0.512200 | ||||||||
\(123\) | 2404.86 | 1.76292 | ||||||||
\(124\) | −1227.74 | −0.889151 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | −2120.66 | −1.49939 | ||||||||
\(127\) | −2737.33 | −1.91259 | −0.956295 | − | 0.292402i | \(-0.905545\pi\) | ||||
−0.956295 | + | 0.292402i | \(0.905545\pi\) | |||||||
\(128\) | 1184.13 | 0.817683 | ||||||||
\(129\) | −498.583 | −0.340293 | ||||||||
\(130\) | −101.501 | −0.0684786 | ||||||||
\(131\) | 1447.49 | 0.965402 | 0.482701 | − | 0.875785i | \(-0.339656\pi\) | ||||
0.482701 | + | 0.875785i | \(0.339656\pi\) | |||||||
\(132\) | −2161.15 | −1.42503 | ||||||||
\(133\) | 1246.95 | 0.812963 | ||||||||
\(134\) | −1708.22 | −1.10125 | ||||||||
\(135\) | 577.235 | 0.368003 | ||||||||
\(136\) | 1100.57 | 0.693918 | ||||||||
\(137\) | 1955.20 | 1.21930 | 0.609650 | − | 0.792671i | \(-0.291310\pi\) | ||||
0.609650 | + | 0.792671i | \(0.291310\pi\) | |||||||
\(138\) | 2085.28 | 1.28631 | ||||||||
\(139\) | 53.5113 | 0.0326530 | 0.0163265 | − | 0.999867i | \(-0.494803\pi\) | ||||
0.0163265 | + | 0.999867i | \(0.494803\pi\) | |||||||
\(140\) | 921.080 | 0.556039 | ||||||||
\(141\) | −438.564 | −0.261942 | ||||||||
\(142\) | 515.824 | 0.304838 | ||||||||
\(143\) | 612.600 | 0.358239 | ||||||||
\(144\) | 468.355 | 0.271039 | ||||||||
\(145\) | −11.3826 | −0.00651913 | ||||||||
\(146\) | 1128.51 | 0.639697 | ||||||||
\(147\) | −6218.80 | −3.48924 | ||||||||
\(148\) | −588.324 | −0.326756 | ||||||||
\(149\) | 108.901 | 0.0598762 | 0.0299381 | − | 0.999552i | \(-0.490469\pi\) | ||||
0.0299381 | + | 0.999552i | \(0.490469\pi\) | |||||||
\(150\) | 321.922 | 0.175232 | ||||||||
\(151\) | −359.710 | −0.193860 | −0.0969298 | − | 0.995291i | \(-0.530902\pi\) | ||||
−0.0969298 | + | 0.995291i | \(0.530902\pi\) | |||||||
\(152\) | 797.229 | 0.425420 | ||||||||
\(153\) | 2130.76 | 1.12589 | ||||||||
\(154\) | 2437.37 | 1.27538 | ||||||||
\(155\) | −1103.78 | −0.571985 | ||||||||
\(156\) | −596.203 | −0.305990 | ||||||||
\(157\) | −249.682 | −0.126922 | −0.0634611 | − | 0.997984i | \(-0.520214\pi\) | ||||
−0.0634611 | + | 0.997984i | \(0.520214\pi\) | |||||||
\(158\) | 179.170 | 0.0902154 | ||||||||
\(159\) | 3264.75 | 1.62837 | ||||||||
\(160\) | 936.274 | 0.462618 | ||||||||
\(161\) | 5363.94 | 2.62570 | ||||||||
\(162\) | 242.041 | 0.117386 | ||||||||
\(163\) | 883.505 | 0.424549 | 0.212275 | − | 0.977210i | \(-0.431913\pi\) | ||||
0.212275 | + | 0.977210i | \(0.431913\pi\) | |||||||
\(164\) | 1621.93 | 0.772265 | ||||||||
\(165\) | −1942.94 | −0.916711 | ||||||||
\(166\) | −1259.27 | −0.588783 | ||||||||
\(167\) | −945.036 | −0.437899 | −0.218949 | − | 0.975736i | \(-0.570263\pi\) | ||||
−0.218949 | + | 0.975736i | \(0.570263\pi\) | |||||||
\(168\) | −5784.31 | −2.65636 | ||||||||
\(169\) | 169.000 | 0.0769231 | ||||||||
\(170\) | 405.767 | 0.183064 | ||||||||
\(171\) | 1543.48 | 0.690250 | ||||||||
\(172\) | −336.263 | −0.149069 | ||||||||
\(173\) | −2125.83 | −0.934240 | −0.467120 | − | 0.884194i | \(-0.654708\pi\) | ||||
−0.467120 | + | 0.884194i | \(0.654708\pi\) | |||||||
\(174\) | 29.3145 | 0.0127720 | ||||||||
\(175\) | 828.078 | 0.357696 | ||||||||
\(176\) | −538.301 | −0.230545 | ||||||||
\(177\) | −3032.22 | −1.28766 | ||||||||
\(178\) | 1051.53 | 0.442783 | ||||||||
\(179\) | −3448.13 | −1.43981 | −0.719903 | − | 0.694075i | \(-0.755814\pi\) | ||||
−0.719903 | + | 0.694075i | \(0.755814\pi\) | |||||||
\(180\) | 1140.12 | 0.472108 | ||||||||
\(181\) | 3273.24 | 1.34419 | 0.672094 | − | 0.740466i | \(-0.265395\pi\) | ||||
0.672094 | + | 0.740466i | \(0.265395\pi\) | |||||||
\(182\) | 672.405 | 0.273857 | ||||||||
\(183\) | −3644.83 | −1.47231 | ||||||||
\(184\) | 3429.40 | 1.37402 | ||||||||
\(185\) | −528.920 | −0.210200 | ||||||||
\(186\) | 2842.65 | 1.12061 | ||||||||
\(187\) | −2448.97 | −0.957683 | ||||||||
\(188\) | −295.784 | −0.114746 | ||||||||
\(189\) | −3823.96 | −1.47171 | ||||||||
\(190\) | 293.930 | 0.112231 | ||||||||
\(191\) | −443.973 | −0.168193 | −0.0840963 | − | 0.996458i | \(-0.526800\pi\) | ||||
−0.0840963 | + | 0.996458i | \(0.526800\pi\) | |||||||
\(192\) | −1657.67 | −0.623083 | ||||||||
\(193\) | −4188.38 | −1.56211 | −0.781053 | − | 0.624465i | \(-0.785317\pi\) | ||||
−0.781053 | + | 0.624465i | \(0.785317\pi\) | |||||||
\(194\) | −2716.26 | −1.00524 | ||||||||
\(195\) | −536.004 | −0.196841 | ||||||||
\(196\) | −4194.19 | −1.52849 | ||||||||
\(197\) | 481.204 | 0.174032 | 0.0870162 | − | 0.996207i | \(-0.472267\pi\) | ||||
0.0870162 | + | 0.996207i | \(0.472267\pi\) | |||||||
\(198\) | 3016.99 | 1.08287 | ||||||||
\(199\) | −3500.02 | −1.24678 | −0.623392 | − | 0.781909i | \(-0.714246\pi\) | ||||
−0.623392 | + | 0.781909i | \(0.714246\pi\) | |||||||
\(200\) | 529.427 | 0.187181 | ||||||||
\(201\) | −9020.75 | −3.16554 | ||||||||
\(202\) | −1011.95 | −0.352476 | ||||||||
\(203\) | 75.4055 | 0.0260711 | ||||||||
\(204\) | 2383.42 | 0.818004 | ||||||||
\(205\) | 1458.16 | 0.496793 | ||||||||
\(206\) | −1687.78 | −0.570840 | ||||||||
\(207\) | 6639.51 | 2.22936 | ||||||||
\(208\) | −148.503 | −0.0495039 | ||||||||
\(209\) | −1773.99 | −0.587126 | ||||||||
\(210\) | −2132.61 | −0.700782 | ||||||||
\(211\) | 1206.57 | 0.393667 | 0.196834 | − | 0.980437i | \(-0.436934\pi\) | ||||
0.196834 | + | 0.980437i | \(0.436934\pi\) | |||||||
\(212\) | 2201.87 | 0.713325 | ||||||||
\(213\) | 2723.95 | 0.876254 | ||||||||
\(214\) | −1564.82 | −0.499856 | ||||||||
\(215\) | −302.311 | −0.0958949 | ||||||||
\(216\) | −2444.83 | −0.770137 | ||||||||
\(217\) | 7312.11 | 2.28746 | ||||||||
\(218\) | 1147.63 | 0.356549 | ||||||||
\(219\) | 5959.39 | 1.83880 | ||||||||
\(220\) | −1310.39 | −0.401574 | ||||||||
\(221\) | −675.606 | −0.205639 | ||||||||
\(222\) | 1362.17 | 0.411815 | ||||||||
\(223\) | 202.733 | 0.0608790 | 0.0304395 | − | 0.999537i | \(-0.490309\pi\) | ||||
0.0304395 | + | 0.999537i | \(0.490309\pi\) | |||||||
\(224\) | −6202.46 | −1.85009 | ||||||||
\(225\) | 1025.00 | 0.303704 | ||||||||
\(226\) | 1822.50 | 0.536419 | ||||||||
\(227\) | 5345.87 | 1.56307 | 0.781536 | − | 0.623860i | \(-0.214436\pi\) | ||||
0.781536 | + | 0.623860i | \(0.214436\pi\) | |||||||
\(228\) | 1726.50 | 0.501493 | ||||||||
\(229\) | 1003.45 | 0.289563 | 0.144781 | − | 0.989464i | \(-0.453752\pi\) | ||||
0.144781 | + | 0.989464i | \(0.453752\pi\) | |||||||
\(230\) | 1264.38 | 0.362483 | ||||||||
\(231\) | 12871.2 | 3.66608 | ||||||||
\(232\) | 48.2101 | 0.0136429 | ||||||||
\(233\) | 1948.83 | 0.547950 | 0.273975 | − | 0.961737i | \(-0.411661\pi\) | ||||
0.273975 | + | 0.961737i | \(0.411661\pi\) | |||||||
\(234\) | 832.308 | 0.232520 | ||||||||
\(235\) | −265.919 | −0.0738154 | ||||||||
\(236\) | −2045.04 | −0.564071 | ||||||||
\(237\) | 946.159 | 0.259323 | ||||||||
\(238\) | −2688.05 | −0.732103 | ||||||||
\(239\) | 602.725 | 0.163126 | 0.0815629 | − | 0.996668i | \(-0.474009\pi\) | ||||
0.0815629 | + | 0.996668i | \(0.474009\pi\) | |||||||
\(240\) | 470.994 | 0.126677 | ||||||||
\(241\) | −492.171 | −0.131550 | −0.0657749 | − | 0.997834i | \(-0.520952\pi\) | ||||
−0.0657749 | + | 0.997834i | \(0.520952\pi\) | |||||||
\(242\) | −1389.14 | −0.368996 | ||||||||
\(243\) | 4395.23 | 1.16031 | ||||||||
\(244\) | −2458.21 | −0.644961 | ||||||||
\(245\) | −3770.70 | −0.983270 | ||||||||
\(246\) | −3755.32 | −0.973295 | ||||||||
\(247\) | −489.396 | −0.126071 | ||||||||
\(248\) | 4674.96 | 1.19702 | ||||||||
\(249\) | −6649.90 | −1.69245 | ||||||||
\(250\) | 195.194 | 0.0493806 | ||||||||
\(251\) | 2990.29 | 0.751973 | 0.375987 | − | 0.926625i | \(-0.377304\pi\) | ||||
0.375987 | + | 0.926625i | \(0.377304\pi\) | |||||||
\(252\) | −7552.85 | −1.88804 | ||||||||
\(253\) | −7631.09 | −1.89629 | ||||||||
\(254\) | 4274.49 | 1.05593 | ||||||||
\(255\) | 2142.77 | 0.526216 | ||||||||
\(256\) | −3457.26 | −0.844057 | ||||||||
\(257\) | 4254.24 | 1.03258 | 0.516288 | − | 0.856415i | \(-0.327314\pi\) | ||||
0.516288 | + | 0.856415i | \(0.327314\pi\) | |||||||
\(258\) | 778.564 | 0.187873 | ||||||||
\(259\) | 3503.90 | 0.840624 | ||||||||
\(260\) | −361.501 | −0.0862282 | ||||||||
\(261\) | 93.3374 | 0.0221358 | ||||||||
\(262\) | −2260.33 | −0.532991 | ||||||||
\(263\) | −4166.84 | −0.976953 | −0.488476 | − | 0.872577i | \(-0.662447\pi\) | ||||
−0.488476 | + | 0.872577i | \(0.662447\pi\) | |||||||
\(264\) | 8229.14 | 1.91844 | ||||||||
\(265\) | 1979.55 | 0.458877 | ||||||||
\(266\) | −1947.17 | −0.448830 | ||||||||
\(267\) | 5552.89 | 1.27278 | ||||||||
\(268\) | −6083.93 | −1.38670 | ||||||||
\(269\) | −4209.91 | −0.954212 | −0.477106 | − | 0.878846i | \(-0.658314\pi\) | ||||
−0.477106 | + | 0.878846i | \(0.658314\pi\) | |||||||
\(270\) | −901.383 | −0.203172 | ||||||||
\(271\) | −4951.69 | −1.10994 | −0.554970 | − | 0.831871i | \(-0.687270\pi\) | ||||
−0.554970 | + | 0.831871i | \(0.687270\pi\) | |||||||
\(272\) | 593.665 | 0.132339 | ||||||||
\(273\) | 3550.82 | 0.787200 | ||||||||
\(274\) | −3053.15 | −0.673166 | ||||||||
\(275\) | −1178.08 | −0.258330 | ||||||||
\(276\) | 7426.82 | 1.61972 | ||||||||
\(277\) | 4348.35 | 0.943202 | 0.471601 | − | 0.881812i | \(-0.343676\pi\) | ||||
0.471601 | + | 0.881812i | \(0.343676\pi\) | |||||||
\(278\) | −83.5607 | −0.0180275 | ||||||||
\(279\) | 9050.98 | 1.94218 | ||||||||
\(280\) | −3507.25 | −0.748566 | ||||||||
\(281\) | 1217.69 | 0.258509 | 0.129254 | − | 0.991611i | \(-0.458742\pi\) | ||||
0.129254 | + | 0.991611i | \(0.458742\pi\) | |||||||
\(282\) | 684.841 | 0.144616 | ||||||||
\(283\) | −1142.98 | −0.240081 | −0.120041 | − | 0.992769i | \(-0.538302\pi\) | ||||
−0.120041 | + | 0.992769i | \(0.538302\pi\) | |||||||
\(284\) | 1837.13 | 0.383852 | ||||||||
\(285\) | 1552.18 | 0.322607 | ||||||||
\(286\) | −956.608 | −0.197781 | ||||||||
\(287\) | −9659.78 | −1.98675 | ||||||||
\(288\) | −7677.44 | −1.57083 | ||||||||
\(289\) | −2212.15 | −0.450265 | ||||||||
\(290\) | 17.7745 | 0.00359916 | ||||||||
\(291\) | −14343.9 | −2.88954 | ||||||||
\(292\) | 4019.23 | 0.805506 | ||||||||
\(293\) | 8222.16 | 1.63940 | 0.819699 | − | 0.572795i | \(-0.194141\pi\) | ||||
0.819699 | + | 0.572795i | \(0.194141\pi\) | |||||||
\(294\) | 9710.98 | 1.92638 | ||||||||
\(295\) | −1838.55 | −0.362863 | ||||||||
\(296\) | 2240.20 | 0.439895 | ||||||||
\(297\) | 5440.22 | 1.06287 | ||||||||
\(298\) | −170.055 | −0.0330572 | ||||||||
\(299\) | −2105.21 | −0.407182 | ||||||||
\(300\) | 1146.54 | 0.220652 | ||||||||
\(301\) | 2002.69 | 0.383499 | ||||||||
\(302\) | 561.706 | 0.107028 | ||||||||
\(303\) | −5343.86 | −1.01319 | ||||||||
\(304\) | 430.039 | 0.0811331 | ||||||||
\(305\) | −2210.00 | −0.414899 | ||||||||
\(306\) | −3327.29 | −0.621596 | ||||||||
\(307\) | −2543.07 | −0.472771 | −0.236385 | − | 0.971659i | \(-0.575963\pi\) | ||||
−0.236385 | + | 0.971659i | \(0.575963\pi\) | |||||||
\(308\) | 8680.83 | 1.60596 | ||||||||
\(309\) | −8912.78 | −1.64087 | ||||||||
\(310\) | 1723.61 | 0.315788 | ||||||||
\(311\) | 2028.16 | 0.369795 | 0.184898 | − | 0.982758i | \(-0.440805\pi\) | ||||
0.184898 | + | 0.982758i | \(0.440805\pi\) | |||||||
\(312\) | 2270.20 | 0.411938 | ||||||||
\(313\) | 7321.83 | 1.32222 | 0.661109 | − | 0.750290i | \(-0.270086\pi\) | ||||
0.661109 | + | 0.750290i | \(0.270086\pi\) | |||||||
\(314\) | 389.892 | 0.0700728 | ||||||||
\(315\) | −6790.24 | −1.21456 | ||||||||
\(316\) | 638.125 | 0.113599 | ||||||||
\(317\) | −2484.31 | −0.440167 | −0.220084 | − | 0.975481i | \(-0.570633\pi\) | ||||
−0.220084 | + | 0.975481i | \(0.570633\pi\) | |||||||
\(318\) | −5098.08 | −0.899013 | ||||||||
\(319\) | −107.277 | −0.0188287 | ||||||||
\(320\) | −1005.11 | −0.175585 | ||||||||
\(321\) | −8263.48 | −1.43683 | ||||||||
\(322\) | −8376.07 | −1.44963 | ||||||||
\(323\) | 1956.44 | 0.337026 | ||||||||
\(324\) | 862.041 | 0.147812 | ||||||||
\(325\) | −325.000 | −0.0554700 | ||||||||
\(326\) | −1379.64 | −0.234390 | ||||||||
\(327\) | 6060.40 | 1.02490 | ||||||||
\(328\) | −6175.93 | −1.03966 | ||||||||
\(329\) | 1761.61 | 0.295200 | ||||||||
\(330\) | 3034.00 | 0.506109 | ||||||||
\(331\) | −6914.29 | −1.14817 | −0.574085 | − | 0.818796i | \(-0.694642\pi\) | ||||
−0.574085 | + | 0.818796i | \(0.694642\pi\) | |||||||
\(332\) | −4484.94 | −0.741395 | ||||||||
\(333\) | 4337.15 | 0.713736 | ||||||||
\(334\) | 1475.72 | 0.241760 | ||||||||
\(335\) | −5469.63 | −0.892053 | ||||||||
\(336\) | −3120.16 | −0.506603 | ||||||||
\(337\) | −5456.98 | −0.882080 | −0.441040 | − | 0.897488i | \(-0.645390\pi\) | ||||
−0.441040 | + | 0.897488i | \(0.645390\pi\) | |||||||
\(338\) | −263.902 | −0.0424686 | ||||||||
\(339\) | 9624.20 | 1.54193 | ||||||||
\(340\) | 1445.16 | 0.230514 | ||||||||
\(341\) | −10402.7 | −1.65202 | ||||||||
\(342\) | −2410.22 | −0.381082 | ||||||||
\(343\) | 13618.2 | 2.14378 | ||||||||
\(344\) | 1280.41 | 0.200684 | ||||||||
\(345\) | 6676.93 | 1.04195 | ||||||||
\(346\) | 3319.59 | 0.515787 | ||||||||
\(347\) | −710.943 | −0.109987 | −0.0549934 | − | 0.998487i | \(-0.517514\pi\) | ||||
−0.0549934 | + | 0.998487i | \(0.517514\pi\) | |||||||
\(348\) | 104.405 | 0.0160825 | ||||||||
\(349\) | −5108.22 | −0.783486 | −0.391743 | − | 0.920075i | \(-0.628128\pi\) | ||||
−0.391743 | + | 0.920075i | \(0.628128\pi\) | |||||||
\(350\) | −1293.09 | −0.197481 | ||||||||
\(351\) | 1500.81 | 0.228226 | ||||||||
\(352\) | 8824.02 | 1.33614 | ||||||||
\(353\) | 3605.90 | 0.543691 | 0.271845 | − | 0.962341i | \(-0.412366\pi\) | ||||
0.271845 | + | 0.962341i | \(0.412366\pi\) | |||||||
\(354\) | 4734.97 | 0.710906 | ||||||||
\(355\) | 1651.64 | 0.246929 | ||||||||
\(356\) | 3745.07 | 0.557552 | ||||||||
\(357\) | −14195.0 | −2.10442 | ||||||||
\(358\) | 5384.44 | 0.794906 | ||||||||
\(359\) | 87.8655 | 0.0129174 | 0.00645872 | − | 0.999979i | \(-0.497944\pi\) | ||||
0.00645872 | + | 0.999979i | \(0.497944\pi\) | |||||||
\(360\) | −4341.30 | −0.635574 | ||||||||
\(361\) | −5441.79 | −0.793380 | ||||||||
\(362\) | −5111.33 | −0.742115 | ||||||||
\(363\) | −7335.72 | −1.06068 | ||||||||
\(364\) | 2394.81 | 0.344841 | ||||||||
\(365\) | 3613.41 | 0.518177 | ||||||||
\(366\) | 5691.59 | 0.812853 | ||||||||
\(367\) | −2379.95 | −0.338508 | −0.169254 | − | 0.985572i | \(-0.554136\pi\) | ||||
−0.169254 | + | 0.985572i | \(0.554136\pi\) | |||||||
\(368\) | 1849.88 | 0.262043 | ||||||||
\(369\) | −11956.9 | −1.68686 | ||||||||
\(370\) | 825.937 | 0.116050 | ||||||||
\(371\) | −13113.7 | −1.83512 | ||||||||
\(372\) | 10124.2 | 1.41107 | ||||||||
\(373\) | −7291.14 | −1.01212 | −0.506060 | − | 0.862498i | \(-0.668899\pi\) | ||||
−0.506060 | + | 0.862498i | \(0.668899\pi\) | |||||||
\(374\) | 3824.20 | 0.528729 | ||||||||
\(375\) | 1030.78 | 0.141944 | ||||||||
\(376\) | 1126.28 | 0.154477 | ||||||||
\(377\) | −29.5948 | −0.00404299 | ||||||||
\(378\) | 5971.32 | 0.812517 | ||||||||
\(379\) | 5827.67 | 0.789834 | 0.394917 | − | 0.918717i | \(-0.370773\pi\) | ||||
0.394917 | + | 0.918717i | \(0.370773\pi\) | |||||||
\(380\) | 1046.85 | 0.141321 | ||||||||
\(381\) | 22572.6 | 3.03525 | ||||||||
\(382\) | 693.288 | 0.0928578 | ||||||||
\(383\) | 6029.95 | 0.804481 | 0.402240 | − | 0.915534i | \(-0.368232\pi\) | ||||
0.402240 | + | 0.915534i | \(0.368232\pi\) | |||||||
\(384\) | −9764.60 | −1.29765 | ||||||||
\(385\) | 7804.32 | 1.03310 | ||||||||
\(386\) | 6540.38 | 0.862426 | ||||||||
\(387\) | 2478.95 | 0.325612 | ||||||||
\(388\) | −9674.09 | −1.26579 | ||||||||
\(389\) | 7929.38 | 1.03351 | 0.516755 | − | 0.856133i | \(-0.327140\pi\) | ||||
0.516755 | + | 0.856133i | \(0.327140\pi\) | |||||||
\(390\) | 836.998 | 0.108674 | ||||||||
\(391\) | 8415.94 | 1.08852 | ||||||||
\(392\) | 15970.5 | 2.05773 | ||||||||
\(393\) | −11936.3 | −1.53208 | ||||||||
\(394\) | −751.426 | −0.0960820 | ||||||||
\(395\) | 573.693 | 0.0730776 | ||||||||
\(396\) | 10745.2 | 1.36355 | ||||||||
\(397\) | −3677.91 | −0.464959 | −0.232480 | − | 0.972601i | \(-0.574684\pi\) | ||||
−0.232480 | + | 0.972601i | \(0.574684\pi\) | |||||||
\(398\) | 5465.47 | 0.688340 | ||||||||
\(399\) | −10282.6 | −1.29016 | ||||||||
\(400\) | 285.582 | 0.0356978 | ||||||||
\(401\) | 7770.69 | 0.967705 | 0.483852 | − | 0.875150i | \(-0.339237\pi\) | ||||
0.483852 | + | 0.875150i | \(0.339237\pi\) | |||||||
\(402\) | 14086.4 | 1.74767 | ||||||||
\(403\) | −2869.82 | −0.354730 | ||||||||
\(404\) | −3604.10 | −0.443838 | ||||||||
\(405\) | 775.000 | 0.0950866 | ||||||||
\(406\) | −117.750 | −0.0143936 | ||||||||
\(407\) | −4984.88 | −0.607103 | ||||||||
\(408\) | −9075.50 | −1.10124 | ||||||||
\(409\) | 7102.25 | 0.858639 | 0.429320 | − | 0.903153i | \(-0.358753\pi\) | ||||
0.429320 | + | 0.903153i | \(0.358753\pi\) | |||||||
\(410\) | −2277.00 | −0.274275 | ||||||||
\(411\) | −16123.0 | −1.93501 | ||||||||
\(412\) | −6011.11 | −0.718801 | ||||||||
\(413\) | 12179.7 | 1.45115 | ||||||||
\(414\) | −10368.0 | −1.23081 | ||||||||
\(415\) | −4032.09 | −0.476934 | ||||||||
\(416\) | 2434.31 | 0.286904 | ||||||||
\(417\) | −441.266 | −0.0518198 | ||||||||
\(418\) | 2770.18 | 0.324148 | ||||||||
\(419\) | −9131.61 | −1.06470 | −0.532349 | − | 0.846525i | \(-0.678691\pi\) | ||||
−0.532349 | + | 0.846525i | \(0.678691\pi\) | |||||||
\(420\) | −7595.42 | −0.882425 | ||||||||
\(421\) | −9425.45 | −1.09114 | −0.545568 | − | 0.838066i | \(-0.683686\pi\) | ||||
−0.545568 | + | 0.838066i | \(0.683686\pi\) | |||||||
\(422\) | −1884.13 | −0.217341 | ||||||||
\(423\) | 2180.53 | 0.250641 | ||||||||
\(424\) | −8384.20 | −0.960313 | ||||||||
\(425\) | 1299.24 | 0.148288 | ||||||||
\(426\) | −4253.59 | −0.483773 | ||||||||
\(427\) | 14640.4 | 1.65925 | ||||||||
\(428\) | −5573.20 | −0.629418 | ||||||||
\(429\) | −5051.63 | −0.568520 | ||||||||
\(430\) | 472.074 | 0.0529428 | ||||||||
\(431\) | 6543.74 | 0.731325 | 0.365662 | − | 0.930748i | \(-0.380843\pi\) | ||||
0.365662 | + | 0.930748i | \(0.380843\pi\) | |||||||
\(432\) | −1318.78 | −0.146875 | ||||||||
\(433\) | −9189.31 | −1.01988 | −0.509942 | − | 0.860209i | \(-0.670333\pi\) | ||||
−0.509942 | + | 0.860209i | \(0.670333\pi\) | |||||||
\(434\) | −11418.3 | −1.26289 | ||||||||
\(435\) | 93.8634 | 0.0103458 | ||||||||
\(436\) | 4087.36 | 0.448966 | ||||||||
\(437\) | 6096.34 | 0.667340 | ||||||||
\(438\) | −9305.90 | −1.01519 | ||||||||
\(439\) | −3024.75 | −0.328846 | −0.164423 | − | 0.986390i | \(-0.552576\pi\) | ||||
−0.164423 | + | 0.986390i | \(0.552576\pi\) | |||||||
\(440\) | 4989.65 | 0.540619 | ||||||||
\(441\) | 30919.7 | 3.33870 | ||||||||
\(442\) | 1054.99 | 0.113532 | ||||||||
\(443\) | −7883.72 | −0.845524 | −0.422762 | − | 0.906241i | \(-0.638939\pi\) | ||||
−0.422762 | + | 0.906241i | \(0.638939\pi\) | |||||||
\(444\) | 4851.44 | 0.518557 | ||||||||
\(445\) | 3366.93 | 0.358669 | ||||||||
\(446\) | −316.579 | −0.0336108 | ||||||||
\(447\) | −898.024 | −0.0950225 | ||||||||
\(448\) | 6658.47 | 0.702194 | ||||||||
\(449\) | 3739.78 | 0.393076 | 0.196538 | − | 0.980496i | \(-0.437030\pi\) | ||||
0.196538 | + | 0.980496i | \(0.437030\pi\) | |||||||
\(450\) | −1600.59 | −0.167672 | ||||||||
\(451\) | 13742.6 | 1.43485 | ||||||||
\(452\) | 6490.92 | 0.675459 | ||||||||
\(453\) | 2966.25 | 0.307652 | ||||||||
\(454\) | −8347.85 | −0.862961 | ||||||||
\(455\) | 2153.00 | 0.221834 | ||||||||
\(456\) | −6574.12 | −0.675134 | ||||||||
\(457\) | −7986.51 | −0.817491 | −0.408745 | − | 0.912648i | \(-0.634034\pi\) | ||||
−0.408745 | + | 0.912648i | \(0.634034\pi\) | |||||||
\(458\) | −1566.94 | −0.159865 | ||||||||
\(459\) | −5999.74 | −0.610118 | ||||||||
\(460\) | 4503.17 | 0.456438 | ||||||||
\(461\) | −80.4439 | −0.00812722 | −0.00406361 | − | 0.999992i | \(-0.501293\pi\) | ||||
−0.00406361 | + | 0.999992i | \(0.501293\pi\) | |||||||
\(462\) | −20099.1 | −2.02401 | ||||||||
\(463\) | 15159.0 | 1.52159 | 0.760796 | − | 0.648991i | \(-0.224809\pi\) | ||||
0.760796 | + | 0.648991i | \(0.224809\pi\) | |||||||
\(464\) | 26.0054 | 0.00260187 | ||||||||
\(465\) | 9101.99 | 0.907730 | ||||||||
\(466\) | −3043.21 | −0.302519 | ||||||||
\(467\) | −18397.2 | −1.82296 | −0.911479 | − | 0.411347i | \(-0.865059\pi\) | ||||
−0.911479 | + | 0.411347i | \(0.865059\pi\) | |||||||
\(468\) | 2964.31 | 0.292789 | ||||||||
\(469\) | 36234.2 | 3.56747 | ||||||||
\(470\) | 415.246 | 0.0407529 | ||||||||
\(471\) | 2058.93 | 0.201424 | ||||||||
\(472\) | 7787.03 | 0.759379 | ||||||||
\(473\) | −2849.16 | −0.276965 | ||||||||
\(474\) | −1477.48 | −0.143170 | ||||||||
\(475\) | 941.146 | 0.0909110 | ||||||||
\(476\) | −9573.64 | −0.921864 | ||||||||
\(477\) | −16232.3 | −1.55812 | ||||||||
\(478\) | −941.187 | −0.0900605 | ||||||||
\(479\) | −3047.92 | −0.290737 | −0.145368 | − | 0.989378i | \(-0.546437\pi\) | ||||
−0.145368 | + | 0.989378i | \(0.546437\pi\) | |||||||
\(480\) | −7720.71 | −0.734168 | ||||||||
\(481\) | −1375.19 | −0.130361 | ||||||||
\(482\) | 768.550 | 0.0726276 | ||||||||
\(483\) | −44232.1 | −4.16694 | ||||||||
\(484\) | −4947.49 | −0.464640 | ||||||||
\(485\) | −8697.29 | −0.814276 | ||||||||
\(486\) | −6863.38 | −0.640596 | ||||||||
\(487\) | 3729.62 | 0.347033 | 0.173517 | − | 0.984831i | \(-0.444487\pi\) | ||||
0.173517 | + | 0.984831i | \(0.444487\pi\) | |||||||
\(488\) | 9360.27 | 0.868278 | ||||||||
\(489\) | −7285.57 | −0.673753 | ||||||||
\(490\) | 5888.15 | 0.542856 | ||||||||
\(491\) | −15519.2 | −1.42641 | −0.713207 | − | 0.700953i | \(-0.752758\pi\) | ||||
−0.713207 | + | 0.700953i | \(0.752758\pi\) | |||||||
\(492\) | −13374.8 | −1.22557 | ||||||||
\(493\) | 118.310 | 0.0108082 | ||||||||
\(494\) | 764.218 | 0.0696028 | ||||||||
\(495\) | 9660.24 | 0.877162 | ||||||||
\(496\) | 2521.76 | 0.228287 | ||||||||
\(497\) | −10941.5 | −0.987510 | ||||||||
\(498\) | 10384.2 | 0.934389 | ||||||||
\(499\) | 10975.7 | 0.984652 | 0.492326 | − | 0.870411i | \(-0.336147\pi\) | ||||
0.492326 | + | 0.870411i | \(0.336147\pi\) | |||||||
\(500\) | 695.194 | 0.0621801 | ||||||||
\(501\) | 7792.97 | 0.694938 | ||||||||
\(502\) | −4669.49 | −0.415159 | ||||||||
\(503\) | 13173.2 | 1.16772 | 0.583861 | − | 0.811854i | \(-0.301541\pi\) | ||||
0.583861 | + | 0.811854i | \(0.301541\pi\) | |||||||
\(504\) | 28759.5 | 2.54176 | ||||||||
\(505\) | −3240.19 | −0.285518 | ||||||||
\(506\) | 11916.3 | 1.04693 | ||||||||
\(507\) | −1393.61 | −0.122076 | ||||||||
\(508\) | 15223.8 | 1.32962 | ||||||||
\(509\) | 950.065 | 0.0827326 | 0.0413663 | − | 0.999144i | \(-0.486829\pi\) | ||||
0.0413663 | + | 0.999144i | \(0.486829\pi\) | |||||||
\(510\) | −3346.04 | −0.290520 | ||||||||
\(511\) | −23937.5 | −2.07227 | ||||||||
\(512\) | −4074.36 | −0.351686 | ||||||||
\(513\) | −4346.10 | −0.374045 | ||||||||
\(514\) | −6643.21 | −0.570077 | ||||||||
\(515\) | −5404.17 | −0.462400 | ||||||||
\(516\) | 2772.90 | 0.236570 | ||||||||
\(517\) | −2506.18 | −0.213195 | ||||||||
\(518\) | −5471.52 | −0.464102 | ||||||||
\(519\) | 17530.0 | 1.48262 | ||||||||
\(520\) | 1376.51 | 0.116085 | ||||||||
\(521\) | −16813.2 | −1.41382 | −0.706908 | − | 0.707305i | \(-0.749911\pi\) | ||||
−0.706908 | + | 0.707305i | \(0.749911\pi\) | |||||||
\(522\) | −145.751 | −0.0122210 | ||||||||
\(523\) | −6938.06 | −0.580077 | −0.290038 | − | 0.957015i | \(-0.593668\pi\) | ||||
−0.290038 | + | 0.957015i | \(0.593668\pi\) | |||||||
\(524\) | −8050.28 | −0.671142 | ||||||||
\(525\) | −6828.50 | −0.567658 | ||||||||
\(526\) | 6506.75 | 0.539368 | ||||||||
\(527\) | 11472.6 | 0.948301 | ||||||||
\(528\) | 4438.94 | 0.365872 | ||||||||
\(529\) | 14057.4 | 1.15537 | ||||||||
\(530\) | −3091.16 | −0.253343 | ||||||||
\(531\) | 15076.1 | 1.23211 | ||||||||
\(532\) | −6934.96 | −0.565167 | ||||||||
\(533\) | 3791.22 | 0.308098 | ||||||||
\(534\) | −8671.12 | −0.702690 | ||||||||
\(535\) | −5010.47 | −0.404900 | ||||||||
\(536\) | 23166.2 | 1.86684 | ||||||||
\(537\) | 28434.0 | 2.28495 | ||||||||
\(538\) | 6574.00 | 0.526813 | ||||||||
\(539\) | −35537.4 | −2.83990 | ||||||||
\(540\) | −3210.32 | −0.255834 | ||||||||
\(541\) | 23180.2 | 1.84213 | 0.921066 | − | 0.389407i | \(-0.127320\pi\) | ||||
0.921066 | + | 0.389407i | \(0.127320\pi\) | |||||||
\(542\) | 7732.32 | 0.612789 | ||||||||
\(543\) | −26991.8 | −2.13320 | ||||||||
\(544\) | −9731.57 | −0.766981 | ||||||||
\(545\) | 3674.66 | 0.288817 | ||||||||
\(546\) | −5544.80 | −0.434607 | ||||||||
\(547\) | −20408.1 | −1.59522 | −0.797612 | − | 0.603171i | \(-0.793904\pi\) | ||||
−0.797612 | + | 0.603171i | \(0.793904\pi\) | |||||||
\(548\) | −10874.0 | −0.847650 | ||||||||
\(549\) | 18122.0 | 1.40879 | ||||||||
\(550\) | 1839.63 | 0.142622 | ||||||||
\(551\) | 85.7016 | 0.00662615 | ||||||||
\(552\) | −28279.6 | −2.18054 | ||||||||
\(553\) | −3800.50 | −0.292249 | ||||||||
\(554\) | −6790.18 | −0.520735 | ||||||||
\(555\) | 4361.59 | 0.333584 | ||||||||
\(556\) | −297.606 | −0.0227002 | ||||||||
\(557\) | −4882.71 | −0.371431 | −0.185715 | − | 0.982604i | \(-0.559460\pi\) | ||||
−0.185715 | + | 0.982604i | \(0.559460\pi\) | |||||||
\(558\) | −14133.6 | −1.07226 | ||||||||
\(559\) | −786.007 | −0.0594715 | ||||||||
\(560\) | −1891.87 | −0.142761 | ||||||||
\(561\) | 20194.8 | 1.51983 | ||||||||
\(562\) | −1901.48 | −0.142721 | ||||||||
\(563\) | 18374.1 | 1.37545 | 0.687724 | − | 0.725972i | \(-0.258610\pi\) | ||||
0.687724 | + | 0.725972i | \(0.258610\pi\) | |||||||
\(564\) | 2439.10 | 0.182100 | ||||||||
\(565\) | 5835.53 | 0.434518 | ||||||||
\(566\) | 1784.82 | 0.132547 | ||||||||
\(567\) | −5134.08 | −0.380267 | ||||||||
\(568\) | −6995.37 | −0.516759 | ||||||||
\(569\) | −5478.72 | −0.403655 | −0.201828 | − | 0.979421i | \(-0.564688\pi\) | ||||
−0.201828 | + | 0.979421i | \(0.564688\pi\) | |||||||
\(570\) | −2423.81 | −0.178109 | ||||||||
\(571\) | −9766.61 | −0.715797 | −0.357898 | − | 0.933761i | \(-0.616507\pi\) | ||||
−0.357898 | + | 0.933761i | \(0.616507\pi\) | |||||||
\(572\) | −3407.01 | −0.249046 | ||||||||
\(573\) | 3661.10 | 0.266919 | ||||||||
\(574\) | 15084.2 | 1.09687 | ||||||||
\(575\) | 4048.48 | 0.293623 | ||||||||
\(576\) | 8241.89 | 0.596202 | ||||||||
\(577\) | 18623.4 | 1.34368 | 0.671840 | − | 0.740696i | \(-0.265504\pi\) | ||||
0.671840 | + | 0.740696i | \(0.265504\pi\) | |||||||
\(578\) | 3454.39 | 0.248588 | ||||||||
\(579\) | 34538.3 | 2.47904 | ||||||||
\(580\) | 63.3050 | 0.00453206 | ||||||||
\(581\) | 26711.1 | 1.90734 | ||||||||
\(582\) | 22398.8 | 1.59529 | ||||||||
\(583\) | 18656.5 | 1.32534 | ||||||||
\(584\) | −15304.3 | −1.08441 | ||||||||
\(585\) | 2665.00 | 0.188349 | ||||||||
\(586\) | −12839.3 | −0.905099 | ||||||||
\(587\) | 16290.0 | 1.14542 | 0.572710 | − | 0.819758i | \(-0.305892\pi\) | ||||
0.572710 | + | 0.819758i | \(0.305892\pi\) | |||||||
\(588\) | 34586.2 | 2.42570 | ||||||||
\(589\) | 8310.53 | 0.581374 | ||||||||
\(590\) | 2870.99 | 0.200334 | ||||||||
\(591\) | −3968.11 | −0.276187 | ||||||||
\(592\) | 1208.40 | 0.0838937 | ||||||||
\(593\) | 8431.78 | 0.583898 | 0.291949 | − | 0.956434i | \(-0.405696\pi\) | ||||
0.291949 | + | 0.956434i | \(0.405696\pi\) | |||||||
\(594\) | −8495.19 | −0.586804 | ||||||||
\(595\) | −8606.99 | −0.593029 | ||||||||
\(596\) | −605.661 | −0.0416256 | ||||||||
\(597\) | 28861.9 | 1.97863 | ||||||||
\(598\) | 3287.40 | 0.224802 | ||||||||
\(599\) | −26227.6 | −1.78903 | −0.894516 | − | 0.447035i | \(-0.852480\pi\) | ||||
−0.894516 | + | 0.447035i | \(0.852480\pi\) | |||||||
\(600\) | −4365.77 | −0.297053 | ||||||||
\(601\) | −24169.8 | −1.64045 | −0.820223 | − | 0.572044i | \(-0.806151\pi\) | ||||
−0.820223 | + | 0.572044i | \(0.806151\pi\) | |||||||
\(602\) | −3127.31 | −0.211727 | ||||||||
\(603\) | 44851.0 | 3.02898 | ||||||||
\(604\) | 2000.55 | 0.134770 | ||||||||
\(605\) | −4447.94 | −0.298900 | ||||||||
\(606\) | 8344.71 | 0.559374 | ||||||||
\(607\) | −11155.6 | −0.745953 | −0.372977 | − | 0.927841i | \(-0.621663\pi\) | ||||
−0.372977 | + | 0.927841i | \(0.621663\pi\) | |||||||
\(608\) | −7049.36 | −0.470213 | ||||||||
\(609\) | −621.809 | −0.0413744 | ||||||||
\(610\) | 3451.03 | 0.229063 | ||||||||
\(611\) | −691.388 | −0.0457784 | ||||||||
\(612\) | −11850.3 | −0.782714 | ||||||||
\(613\) | −24816.7 | −1.63513 | −0.817567 | − | 0.575834i | \(-0.804677\pi\) | ||||
−0.817567 | + | 0.575834i | \(0.804677\pi\) | |||||||
\(614\) | 3971.14 | 0.261013 | ||||||||
\(615\) | −12024.3 | −0.788402 | ||||||||
\(616\) | −33054.5 | −2.16202 | ||||||||
\(617\) | −5299.65 | −0.345795 | −0.172898 | − | 0.984940i | \(-0.555313\pi\) | ||||
−0.172898 | + | 0.984940i | \(0.555313\pi\) | |||||||
\(618\) | 13917.8 | 0.905914 | ||||||||
\(619\) | 4104.30 | 0.266504 | 0.133252 | − | 0.991082i | \(-0.457458\pi\) | ||||
0.133252 | + | 0.991082i | \(0.457458\pi\) | |||||||
\(620\) | 6138.72 | 0.397640 | ||||||||
\(621\) | −18695.4 | −1.20809 | ||||||||
\(622\) | −3167.08 | −0.204161 | ||||||||
\(623\) | −22304.6 | −1.43438 | ||||||||
\(624\) | 1224.59 | 0.0785619 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −11433.4 | −0.729986 | ||||||||
\(627\) | 14628.7 | 0.931760 | ||||||||
\(628\) | 1388.62 | 0.0882356 | ||||||||
\(629\) | 5497.57 | 0.348493 | ||||||||
\(630\) | 10603.3 | 0.670549 | ||||||||
\(631\) | 13060.9 | 0.824004 | 0.412002 | − | 0.911183i | \(-0.364830\pi\) | ||||
0.412002 | + | 0.911183i | \(0.364830\pi\) | |||||||
\(632\) | −2429.83 | −0.152933 | ||||||||
\(633\) | −9949.65 | −0.624744 | ||||||||
\(634\) | 3879.39 | 0.243013 | ||||||||
\(635\) | 13686.7 | 0.855337 | ||||||||
\(636\) | −18157.1 | −1.13204 | ||||||||
\(637\) | −9803.82 | −0.609798 | ||||||||
\(638\) | 167.518 | 0.0103952 | ||||||||
\(639\) | −13543.4 | −0.838450 | ||||||||
\(640\) | −5920.66 | −0.365679 | ||||||||
\(641\) | 995.223 | 0.0613244 | 0.0306622 | − | 0.999530i | \(-0.490238\pi\) | ||||
0.0306622 | + | 0.999530i | \(0.490238\pi\) | |||||||
\(642\) | 12903.9 | 0.793263 | ||||||||
\(643\) | −499.256 | −0.0306201 | −0.0153100 | − | 0.999883i | \(-0.504874\pi\) | ||||
−0.0153100 | + | 0.999883i | \(0.504874\pi\) | |||||||
\(644\) | −29831.8 | −1.82537 | ||||||||
\(645\) | 2492.92 | 0.152184 | ||||||||
\(646\) | −3055.09 | −0.186069 | ||||||||
\(647\) | 30522.4 | 1.85465 | 0.927325 | − | 0.374256i | \(-0.122102\pi\) | ||||
0.927325 | + | 0.374256i | \(0.122102\pi\) | |||||||
\(648\) | −3282.45 | −0.198992 | ||||||||
\(649\) | −17327.6 | −1.04803 | ||||||||
\(650\) | 507.505 | 0.0306246 | ||||||||
\(651\) | −60297.2 | −3.63016 | ||||||||
\(652\) | −4913.66 | −0.295144 | ||||||||
\(653\) | −9837.63 | −0.589550 | −0.294775 | − | 0.955567i | \(-0.595245\pi\) | ||||
−0.294775 | + | 0.955567i | \(0.595245\pi\) | |||||||
\(654\) | −9463.64 | −0.565837 | ||||||||
\(655\) | −7237.44 | −0.431741 | ||||||||
\(656\) | −3331.40 | −0.198277 | ||||||||
\(657\) | −29630.0 | −1.75947 | ||||||||
\(658\) | −2750.85 | −0.162977 | ||||||||
\(659\) | −6309.40 | −0.372958 | −0.186479 | − | 0.982459i | \(-0.559708\pi\) | ||||
−0.186479 | + | 0.982459i | \(0.559708\pi\) | |||||||
\(660\) | 10805.7 | 0.637292 | ||||||||
\(661\) | 10067.3 | 0.592393 | 0.296196 | − | 0.955127i | \(-0.404282\pi\) | ||||
0.296196 | + | 0.955127i | \(0.404282\pi\) | |||||||
\(662\) | 10797.0 | 0.633895 | ||||||||
\(663\) | 5571.19 | 0.326346 | ||||||||
\(664\) | 17077.6 | 0.998101 | ||||||||
\(665\) | −6234.74 | −0.363568 | ||||||||
\(666\) | −6772.69 | −0.394048 | ||||||||
\(667\) | 368.658 | 0.0214011 | ||||||||
\(668\) | 5255.87 | 0.304425 | ||||||||
\(669\) | −1671.78 | −0.0966141 | ||||||||
\(670\) | 8541.12 | 0.492496 | ||||||||
\(671\) | −20828.4 | −1.19832 | ||||||||
\(672\) | 51146.8 | 2.93606 | ||||||||
\(673\) | 23938.7 | 1.37113 | 0.685564 | − | 0.728012i | \(-0.259556\pi\) | ||||
0.685564 | + | 0.728012i | \(0.259556\pi\) | |||||||
\(674\) | 8521.37 | 0.486989 | ||||||||
\(675\) | −2886.17 | −0.164576 | ||||||||
\(676\) | −939.902 | −0.0534765 | ||||||||
\(677\) | −5102.53 | −0.289669 | −0.144835 | − | 0.989456i | \(-0.546265\pi\) | ||||
−0.144835 | + | 0.989456i | \(0.546265\pi\) | |||||||
\(678\) | −15028.7 | −0.851289 | ||||||||
\(679\) | 57616.3 | 3.25642 | ||||||||
\(680\) | −5502.83 | −0.310329 | ||||||||
\(681\) | −44083.1 | −2.48057 | ||||||||
\(682\) | 16244.4 | 0.912065 | ||||||||
\(683\) | −27531.8 | −1.54242 | −0.771210 | − | 0.636580i | \(-0.780348\pi\) | ||||
−0.771210 | + | 0.636580i | \(0.780348\pi\) | |||||||
\(684\) | −8584.14 | −0.479858 | ||||||||
\(685\) | −9776.00 | −0.545287 | ||||||||
\(686\) | −21265.6 | −1.18356 | ||||||||
\(687\) | −8274.67 | −0.459532 | ||||||||
\(688\) | 690.676 | 0.0382730 | ||||||||
\(689\) | 5146.82 | 0.284584 | ||||||||
\(690\) | −10426.4 | −0.575254 | ||||||||
\(691\) | 31475.4 | 1.73282 | 0.866412 | − | 0.499330i | \(-0.166421\pi\) | ||||
0.866412 | + | 0.499330i | \(0.166421\pi\) | |||||||
\(692\) | 11822.9 | 0.649478 | ||||||||
\(693\) | −63995.4 | −3.50791 | ||||||||
\(694\) | 1110.18 | 0.0607229 | ||||||||
\(695\) | −267.557 | −0.0146029 | ||||||||
\(696\) | −397.550 | −0.0216510 | ||||||||
\(697\) | −15156.1 | −0.823639 | ||||||||
\(698\) | 7976.75 | 0.432556 | ||||||||
\(699\) | −16070.5 | −0.869588 | ||||||||
\(700\) | −4605.40 | −0.248668 | ||||||||
\(701\) | 34138.6 | 1.83937 | 0.919684 | − | 0.392660i | \(-0.128445\pi\) | ||||
0.919684 | + | 0.392660i | \(0.128445\pi\) | |||||||
\(702\) | −2343.59 | −0.126002 | ||||||||
\(703\) | 3982.33 | 0.213651 | ||||||||
\(704\) | −9472.77 | −0.507129 | ||||||||
\(705\) | 2192.82 | 0.117144 | ||||||||
\(706\) | −5630.81 | −0.300167 | ||||||||
\(707\) | 21465.0 | 1.14183 | ||||||||
\(708\) | 16863.8 | 0.895172 | ||||||||
\(709\) | −6114.73 | −0.323898 | −0.161949 | − | 0.986799i | \(-0.551778\pi\) | ||||
−0.161949 | + | 0.986799i | \(0.551778\pi\) | |||||||
\(710\) | −2579.12 | −0.136328 | ||||||||
\(711\) | −4704.28 | −0.248136 | ||||||||
\(712\) | −14260.4 | −0.750603 | ||||||||
\(713\) | 35749.0 | 1.87772 | ||||||||
\(714\) | 22166.3 | 1.16184 | ||||||||
\(715\) | −3063.00 | −0.160209 | ||||||||
\(716\) | 19176.9 | 1.00094 | ||||||||
\(717\) | −4970.20 | −0.258878 | ||||||||
\(718\) | −137.207 | −0.00713162 | ||||||||
\(719\) | 26415.4 | 1.37014 | 0.685069 | − | 0.728478i | \(-0.259772\pi\) | ||||
0.685069 | + | 0.728478i | \(0.259772\pi\) | |||||||
\(720\) | −2341.77 | −0.121212 | ||||||||
\(721\) | 35800.6 | 1.84921 | ||||||||
\(722\) | 8497.64 | 0.438019 | ||||||||
\(723\) | 4058.54 | 0.208767 | ||||||||
\(724\) | −18204.3 | −0.934471 | ||||||||
\(725\) | 56.9130 | 0.00291544 | ||||||||
\(726\) | 11455.1 | 0.585591 | ||||||||
\(727\) | 36222.5 | 1.84789 | 0.923946 | − | 0.382524i | \(-0.124945\pi\) | ||||
0.923946 | + | 0.382524i | \(0.124945\pi\) | |||||||
\(728\) | −9118.86 | −0.464241 | ||||||||
\(729\) | −32059.0 | −1.62877 | ||||||||
\(730\) | −5642.53 | −0.286081 | ||||||||
\(731\) | 3142.20 | 0.158985 | ||||||||
\(732\) | 20270.9 | 1.02354 | ||||||||
\(733\) | −14555.7 | −0.733463 | −0.366731 | − | 0.930327i | \(-0.619523\pi\) | ||||
−0.366731 | + | 0.930327i | \(0.619523\pi\) | |||||||
\(734\) | 3716.42 | 0.186888 | ||||||||
\(735\) | 31094.0 | 1.56043 | ||||||||
\(736\) | −30323.9 | −1.51869 | ||||||||
\(737\) | −51549.2 | −2.57644 | ||||||||
\(738\) | 18671.4 | 0.931305 | ||||||||
\(739\) | −27876.6 | −1.38763 | −0.693814 | − | 0.720155i | \(-0.744071\pi\) | ||||
−0.693814 | + | 0.720155i | \(0.744071\pi\) | |||||||
\(740\) | 2941.62 | 0.146130 | ||||||||
\(741\) | 4035.66 | 0.200073 | ||||||||
\(742\) | 20477.8 | 1.01316 | ||||||||
\(743\) | 3226.10 | 0.159292 | 0.0796460 | − | 0.996823i | \(-0.474621\pi\) | ||||
0.0796460 | + | 0.996823i | \(0.474621\pi\) | |||||||
\(744\) | −38550.7 | −1.89965 | ||||||||
\(745\) | −544.507 | −0.0267774 | ||||||||
\(746\) | 11385.5 | 0.558784 | ||||||||
\(747\) | 33063.2 | 1.61943 | ||||||||
\(748\) | 13620.1 | 0.665775 | ||||||||
\(749\) | 33192.5 | 1.61926 | ||||||||
\(750\) | −1609.61 | −0.0783663 | ||||||||
\(751\) | 27690.7 | 1.34547 | 0.672735 | − | 0.739884i | \(-0.265120\pi\) | ||||
0.672735 | + | 0.739884i | \(0.265120\pi\) | |||||||
\(752\) | 607.533 | 0.0294607 | ||||||||
\(753\) | −24658.5 | −1.19337 | ||||||||
\(754\) | 46.2138 | 0.00223211 | ||||||||
\(755\) | 1798.55 | 0.0866967 | ||||||||
\(756\) | 21267.2 | 1.02312 | ||||||||
\(757\) | −12300.3 | −0.590571 | −0.295285 | − | 0.955409i | \(-0.595415\pi\) | ||||
−0.295285 | + | 0.955409i | \(0.595415\pi\) | |||||||
\(758\) | −9100.21 | −0.436061 | ||||||||
\(759\) | 62927.6 | 3.00939 | ||||||||
\(760\) | −3986.14 | −0.190254 | ||||||||
\(761\) | −25188.7 | −1.19986 | −0.599928 | − | 0.800054i | \(-0.704804\pi\) | ||||
−0.599928 | + | 0.800054i | \(0.704804\pi\) | |||||||
\(762\) | −35248.4 | −1.67574 | ||||||||
\(763\) | −24343.2 | −1.15502 | ||||||||
\(764\) | 2469.18 | 0.116927 | ||||||||
\(765\) | −10653.8 | −0.503514 | ||||||||
\(766\) | −9416.09 | −0.444148 | ||||||||
\(767\) | −4780.23 | −0.225038 | ||||||||
\(768\) | 28509.3 | 1.33951 | ||||||||
\(769\) | 4955.84 | 0.232396 | 0.116198 | − | 0.993226i | \(-0.462929\pi\) | ||||
0.116198 | + | 0.993226i | \(0.462929\pi\) | |||||||
\(770\) | −12186.9 | −0.570369 | ||||||||
\(771\) | −35081.3 | −1.63868 | ||||||||
\(772\) | 23293.9 | 1.08597 | ||||||||
\(773\) | −14186.7 | −0.660106 | −0.330053 | − | 0.943962i | \(-0.607067\pi\) | ||||
−0.330053 | + | 0.943962i | \(0.607067\pi\) | |||||||
\(774\) | −3871.01 | −0.179768 | ||||||||
\(775\) | 5518.89 | 0.255799 | ||||||||
\(776\) | 36836.6 | 1.70407 | ||||||||
\(777\) | −28893.9 | −1.33406 | ||||||||
\(778\) | −12382.1 | −0.570593 | ||||||||
\(779\) | −10978.8 | −0.504948 | ||||||||
\(780\) | 2981.01 | 0.136843 | ||||||||
\(781\) | 15566.1 | 0.713185 | ||||||||
\(782\) | −13141.9 | −0.600965 | ||||||||
\(783\) | −262.817 | −0.0119953 | ||||||||
\(784\) | 8614.76 | 0.392436 | ||||||||
\(785\) | 1248.41 | 0.0567613 | ||||||||
\(786\) | 18639.2 | 0.845848 | ||||||||
\(787\) | −27311.8 | −1.23705 | −0.618526 | − | 0.785764i | \(-0.712270\pi\) | ||||
−0.618526 | + | 0.785764i | \(0.712270\pi\) | |||||||
\(788\) | −2676.24 | −0.120986 | ||||||||
\(789\) | 34360.7 | 1.55041 | ||||||||
\(790\) | −895.852 | −0.0403456 | ||||||||
\(791\) | −38658.2 | −1.73771 | ||||||||
\(792\) | −40915.1 | −1.83568 | ||||||||
\(793\) | −5746.00 | −0.257310 | ||||||||
\(794\) | 5743.24 | 0.256700 | ||||||||
\(795\) | −16323.7 | −0.728231 | ||||||||
\(796\) | 19465.6 | 0.866757 | ||||||||
\(797\) | −3313.27 | −0.147255 | −0.0736274 | − | 0.997286i | \(-0.523458\pi\) | ||||
−0.0736274 | + | 0.997286i | \(0.523458\pi\) | |||||||
\(798\) | 16056.8 | 0.712287 | ||||||||
\(799\) | 2763.94 | 0.122380 | ||||||||
\(800\) | −4681.37 | −0.206889 | ||||||||
\(801\) | −27608.8 | −1.21787 | ||||||||
\(802\) | −12134.3 | −0.534262 | ||||||||
\(803\) | 34055.0 | 1.49661 | ||||||||
\(804\) | 50169.4 | 2.20067 | ||||||||
\(805\) | −26819.7 | −1.17425 | ||||||||
\(806\) | 4481.38 | 0.195844 | ||||||||
\(807\) | 34715.8 | 1.51432 | ||||||||
\(808\) | 13723.5 | 0.597516 | ||||||||
\(809\) | 3606.84 | 0.156749 | 0.0783744 | − | 0.996924i | \(-0.475027\pi\) | ||||
0.0783744 | + | 0.996924i | \(0.475027\pi\) | |||||||
\(810\) | −1210.20 | −0.0524966 | ||||||||
\(811\) | 4908.14 | 0.212513 | 0.106257 | − | 0.994339i | \(-0.466113\pi\) | ||||
0.106257 | + | 0.994339i | \(0.466113\pi\) | |||||||
\(812\) | −419.371 | −0.0181244 | ||||||||
\(813\) | 40832.7 | 1.76146 | ||||||||
\(814\) | 7784.15 | 0.335177 | ||||||||
\(815\) | −4417.53 | −0.189864 | ||||||||
\(816\) | −4895.49 | −0.210020 | ||||||||
\(817\) | 2276.15 | 0.0974692 | ||||||||
\(818\) | −11090.5 | −0.474048 | ||||||||
\(819\) | −17654.6 | −0.753238 | ||||||||
\(820\) | −8109.65 | −0.345367 | ||||||||
\(821\) | 25125.8 | 1.06808 | 0.534042 | − | 0.845458i | \(-0.320672\pi\) | ||||
0.534042 | + | 0.845458i | \(0.320672\pi\) | |||||||
\(822\) | 25176.9 | 1.06830 | ||||||||
\(823\) | −32032.1 | −1.35671 | −0.678353 | − | 0.734736i | \(-0.737306\pi\) | ||||
−0.678353 | + | 0.734736i | \(0.737306\pi\) | |||||||
\(824\) | 22888.9 | 0.967685 | ||||||||
\(825\) | 9714.68 | 0.409966 | ||||||||
\(826\) | −19019.3 | −0.801167 | ||||||||
\(827\) | 4182.06 | 0.175846 | 0.0879229 | − | 0.996127i | \(-0.471977\pi\) | ||||
0.0879229 | + | 0.996127i | \(0.471977\pi\) | |||||||
\(828\) | −36926.0 | −1.54984 | ||||||||
\(829\) | −39983.0 | −1.67511 | −0.837556 | − | 0.546351i | \(-0.816017\pi\) | ||||
−0.837556 | + | 0.546351i | \(0.816017\pi\) | |||||||
\(830\) | 6296.33 | 0.263312 | ||||||||
\(831\) | −35857.4 | −1.49685 | ||||||||
\(832\) | −2613.28 | −0.108893 | ||||||||
\(833\) | 39192.4 | 1.63018 | ||||||||
\(834\) | 689.059 | 0.0286093 | ||||||||
\(835\) | 4725.18 | 0.195834 | ||||||||
\(836\) | 9866.13 | 0.408167 | ||||||||
\(837\) | −25485.6 | −1.05246 | ||||||||
\(838\) | 14259.5 | 0.587811 | ||||||||
\(839\) | 28100.7 | 1.15631 | 0.578155 | − | 0.815927i | \(-0.303773\pi\) | ||||
0.578155 | + | 0.815927i | \(0.303773\pi\) | |||||||
\(840\) | 28921.6 | 1.18796 | ||||||||
\(841\) | −24383.8 | −0.999788 | ||||||||
\(842\) | 14718.3 | 0.602408 | ||||||||
\(843\) | −10041.3 | −0.410250 | ||||||||
\(844\) | −6710.41 | −0.273675 | ||||||||
\(845\) | −845.000 | −0.0344010 | ||||||||
\(846\) | −3405.02 | −0.138377 | ||||||||
\(847\) | 29465.9 | 1.19535 | ||||||||
\(848\) | −4522.58 | −0.183144 | ||||||||
\(849\) | 9425.23 | 0.381005 | ||||||||
\(850\) | −2028.84 | −0.0818688 | ||||||||
\(851\) | 17130.6 | 0.690047 | ||||||||
\(852\) | −15149.4 | −0.609166 | ||||||||
\(853\) | −10845.1 | −0.435321 | −0.217661 | − | 0.976024i | \(-0.569843\pi\) | ||||
−0.217661 | + | 0.976024i | \(0.569843\pi\) | |||||||
\(854\) | −22861.8 | −0.916058 | ||||||||
\(855\) | −7717.40 | −0.308689 | ||||||||
\(856\) | 21221.4 | 0.847353 | ||||||||
\(857\) | −20977.4 | −0.836144 | −0.418072 | − | 0.908414i | \(-0.637294\pi\) | ||||
−0.418072 | + | 0.908414i | \(0.637294\pi\) | |||||||
\(858\) | 7888.39 | 0.313876 | ||||||||
\(859\) | −18440.5 | −0.732458 | −0.366229 | − | 0.930525i | \(-0.619351\pi\) | ||||
−0.366229 | + | 0.930525i | \(0.619351\pi\) | |||||||
\(860\) | 1681.32 | 0.0666656 | ||||||||
\(861\) | 79656.6 | 3.15295 | ||||||||
\(862\) | −10218.4 | −0.403759 | ||||||||
\(863\) | 28960.1 | 1.14231 | 0.571154 | − | 0.820843i | \(-0.306496\pi\) | ||||
0.571154 | + | 0.820843i | \(0.306496\pi\) | |||||||
\(864\) | 21618.0 | 0.851226 | ||||||||
\(865\) | 10629.1 | 0.417805 | ||||||||
\(866\) | 14349.6 | 0.563071 | ||||||||
\(867\) | 18241.9 | 0.714563 | ||||||||
\(868\) | −40666.7 | −1.59023 | ||||||||
\(869\) | 5406.84 | 0.211064 | ||||||||
\(870\) | −146.573 | −0.00571181 | ||||||||
\(871\) | −14221.0 | −0.553228 | ||||||||
\(872\) | −15563.7 | −0.604419 | ||||||||
\(873\) | 71317.8 | 2.76488 | ||||||||
\(874\) | −9519.76 | −0.368433 | ||||||||
\(875\) | −4140.39 | −0.159966 | ||||||||
\(876\) | −33143.4 | −1.27833 | ||||||||
\(877\) | −34736.4 | −1.33747 | −0.668737 | − | 0.743499i | \(-0.733165\pi\) | ||||
−0.668737 | + | 0.743499i | \(0.733165\pi\) | |||||||
\(878\) | 4723.31 | 0.181553 | ||||||||
\(879\) | −67801.6 | −2.60170 | ||||||||
\(880\) | 2691.51 | 0.103103 | ||||||||
\(881\) | −4957.71 | −0.189591 | −0.0947953 | − | 0.995497i | \(-0.530220\pi\) | ||||
−0.0947953 | + | 0.995497i | \(0.530220\pi\) | |||||||
\(882\) | −48282.8 | −1.84327 | ||||||||
\(883\) | 10146.6 | 0.386704 | 0.193352 | − | 0.981129i | \(-0.438064\pi\) | ||||
0.193352 | + | 0.981129i | \(0.438064\pi\) | |||||||
\(884\) | 3757.42 | 0.142959 | ||||||||
\(885\) | 15161.1 | 0.575858 | ||||||||
\(886\) | 12310.8 | 0.466807 | ||||||||
\(887\) | 29481.3 | 1.11599 | 0.557997 | − | 0.829843i | \(-0.311570\pi\) | ||||
0.557997 | + | 0.829843i | \(0.311570\pi\) | |||||||
\(888\) | −18473.1 | −0.698106 | ||||||||
\(889\) | −90669.0 | −3.42063 | ||||||||
\(890\) | −5257.64 | −0.198019 | ||||||||
\(891\) | 7304.08 | 0.274631 | ||||||||
\(892\) | −1127.51 | −0.0423227 | ||||||||
\(893\) | 2002.15 | 0.0750272 | ||||||||
\(894\) | 1402.31 | 0.0524612 | ||||||||
\(895\) | 17240.6 | 0.643901 | ||||||||
\(896\) | 39222.1 | 1.46241 | ||||||||
\(897\) | 17360.0 | 0.646192 | ||||||||
\(898\) | −5839.86 | −0.217014 | ||||||||
\(899\) | 502.555 | 0.0186442 | ||||||||
\(900\) | −5700.59 | −0.211133 | ||||||||
\(901\) | −20575.3 | −0.760779 | ||||||||
\(902\) | −21459.8 | −0.792167 | ||||||||
\(903\) | −16514.6 | −0.608607 | ||||||||
\(904\) | −24715.9 | −0.909335 | ||||||||
\(905\) | −16366.2 | −0.601139 | ||||||||
\(906\) | −4631.95 | −0.169852 | ||||||||
\(907\) | −34640.7 | −1.26817 | −0.634083 | − | 0.773265i | \(-0.718622\pi\) | ||||
−0.634083 | + | 0.773265i | \(0.718622\pi\) | |||||||
\(908\) | −29731.3 | −1.08664 | ||||||||
\(909\) | 26569.5 | 0.969479 | ||||||||
\(910\) | −3362.03 | −0.122473 | ||||||||
\(911\) | −14409.8 | −0.524059 | −0.262029 | − | 0.965060i | \(-0.584392\pi\) | ||||
−0.262029 | + | 0.965060i | \(0.584392\pi\) | |||||||
\(912\) | −3546.20 | −0.128757 | ||||||||
\(913\) | −38000.9 | −1.37749 | ||||||||
\(914\) | 12471.4 | 0.451330 | ||||||||
\(915\) | 18224.1 | 0.658438 | ||||||||
\(916\) | −5580.74 | −0.201302 | ||||||||
\(917\) | 47945.3 | 1.72660 | ||||||||
\(918\) | 9368.91 | 0.336841 | ||||||||
\(919\) | −17403.1 | −0.624672 | −0.312336 | − | 0.949972i | \(-0.601112\pi\) | ||||
−0.312336 | + | 0.949972i | \(0.601112\pi\) | |||||||
\(920\) | −17147.0 | −0.614479 | ||||||||
\(921\) | 20970.7 | 0.750280 | ||||||||
\(922\) | 125.617 | 0.00448697 | ||||||||
\(923\) | 4294.26 | 0.153139 | ||||||||
\(924\) | −71583.9 | −2.54863 | ||||||||
\(925\) | 2644.60 | 0.0940043 | ||||||||
\(926\) | −23671.5 | −0.840060 | ||||||||
\(927\) | 44314.2 | 1.57008 | ||||||||
\(928\) | −426.289 | −0.0150793 | ||||||||
\(929\) | −11474.1 | −0.405223 | −0.202612 | − | 0.979259i | \(-0.564943\pi\) | ||||
−0.202612 | + | 0.979259i | \(0.564943\pi\) | |||||||
\(930\) | −14213.2 | −0.501151 | ||||||||
\(931\) | 28390.2 | 0.999412 | ||||||||
\(932\) | −10838.5 | −0.380932 | ||||||||
\(933\) | −16724.6 | −0.586859 | ||||||||
\(934\) | 28728.2 | 1.00644 | ||||||||
\(935\) | 12244.9 | 0.428289 | ||||||||
\(936\) | −11287.4 | −0.394166 | ||||||||
\(937\) | 15121.6 | 0.527216 | 0.263608 | − | 0.964630i | \(-0.415087\pi\) | ||||
0.263608 | + | 0.964630i | \(0.415087\pi\) | |||||||
\(938\) | −56581.7 | −1.96957 | ||||||||
\(939\) | −60377.3 | −2.09834 | ||||||||
\(940\) | 1478.92 | 0.0513160 | ||||||||
\(941\) | 18152.2 | 0.628846 | 0.314423 | − | 0.949283i | \(-0.398189\pi\) | ||||
0.314423 | + | 0.949283i | \(0.398189\pi\) | |||||||
\(942\) | −3215.13 | −0.111204 | ||||||||
\(943\) | −47226.8 | −1.63088 | ||||||||
\(944\) | 4200.46 | 0.144823 | ||||||||
\(945\) | 19119.8 | 0.658167 | ||||||||
\(946\) | 4449.12 | 0.152910 | ||||||||
\(947\) | 19041.0 | 0.653378 | 0.326689 | − | 0.945132i | \(-0.394067\pi\) | ||||
0.326689 | + | 0.945132i | \(0.394067\pi\) | |||||||
\(948\) | −5262.11 | −0.180280 | ||||||||
\(949\) | 9394.86 | 0.321359 | ||||||||
\(950\) | −1469.65 | −0.0501913 | ||||||||
\(951\) | 20486.2 | 0.698538 | ||||||||
\(952\) | 36454.2 | 1.24106 | ||||||||
\(953\) | −22836.0 | −0.776213 | −0.388106 | − | 0.921615i | \(-0.626871\pi\) | ||||
−0.388106 | + | 0.921615i | \(0.626871\pi\) | |||||||
\(954\) | 25347.5 | 0.860228 | ||||||||
\(955\) | 2219.87 | 0.0752180 | ||||||||
\(956\) | −3352.09 | −0.113404 | ||||||||
\(957\) | 884.627 | 0.0298808 | ||||||||
\(958\) | 4759.48 | 0.160513 | ||||||||
\(959\) | 64762.3 | 2.18069 | ||||||||
\(960\) | 8288.34 | 0.278651 | ||||||||
\(961\) | 18942.1 | 0.635832 | ||||||||
\(962\) | 2147.44 | 0.0719710 | ||||||||
\(963\) | 41085.9 | 1.37484 | ||||||||
\(964\) | 2737.23 | 0.0914526 | ||||||||
\(965\) | 20941.9 | 0.698595 | ||||||||
\(966\) | 69070.8 | 2.30054 | ||||||||
\(967\) | −32917.6 | −1.09468 | −0.547342 | − | 0.836909i | \(-0.684360\pi\) | ||||
−0.547342 | + | 0.836909i | \(0.684360\pi\) | |||||||
\(968\) | 18838.9 | 0.625520 | ||||||||
\(969\) | −16133.2 | −0.534855 | ||||||||
\(970\) | 13581.3 | 0.449555 | ||||||||
\(971\) | −52645.6 | −1.73994 | −0.869968 | − | 0.493108i | \(-0.835861\pi\) | ||||
−0.869968 | + | 0.493108i | \(0.835861\pi\) | |||||||
\(972\) | −24444.3 | −0.806637 | ||||||||
\(973\) | 1772.46 | 0.0583993 | ||||||||
\(974\) | −5824.00 | −0.191594 | ||||||||
\(975\) | 2680.02 | 0.0880300 | ||||||||
\(976\) | 5049.10 | 0.165592 | ||||||||
\(977\) | −11301.4 | −0.370075 | −0.185038 | − | 0.982731i | \(-0.559241\pi\) | ||||
−0.185038 | + | 0.982731i | \(0.559241\pi\) | |||||||
\(978\) | 11376.8 | 0.371974 | ||||||||
\(979\) | 31732.1 | 1.03592 | ||||||||
\(980\) | 20971.0 | 0.683564 | ||||||||
\(981\) | −30132.2 | −0.980680 | ||||||||
\(982\) | 24234.0 | 0.787512 | ||||||||
\(983\) | −57289.3 | −1.85884 | −0.929422 | − | 0.369018i | \(-0.879694\pi\) | ||||
−0.929422 | + | 0.369018i | \(0.879694\pi\) | |||||||
\(984\) | 50928.0 | 1.64992 | ||||||||
\(985\) | −2406.02 | −0.0778297 | ||||||||
\(986\) | −184.747 | −0.00596710 | ||||||||
\(987\) | −14526.6 | −0.468477 | ||||||||
\(988\) | 2721.80 | 0.0876438 | ||||||||
\(989\) | 9791.20 | 0.314805 | ||||||||
\(990\) | −15085.0 | −0.484275 | ||||||||
\(991\) | 3413.94 | 0.109432 | 0.0547162 | − | 0.998502i | \(-0.482575\pi\) | ||||
0.0547162 | + | 0.998502i | \(0.482575\pi\) | |||||||
\(992\) | −41337.5 | −1.32305 | ||||||||
\(993\) | 57016.7 | 1.82213 | ||||||||
\(994\) | 17085.7 | 0.545196 | ||||||||
\(995\) | 17500.1 | 0.557579 | ||||||||
\(996\) | 36983.8 | 1.17658 | ||||||||
\(997\) | −46243.7 | −1.46896 | −0.734480 | − | 0.678630i | \(-0.762574\pi\) | ||||
−0.734480 | + | 0.678630i | \(0.762574\pi\) | |||||||
\(998\) | −17139.2 | −0.543619 | ||||||||
\(999\) | −12212.5 | −0.386772 |
(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 | 65.4.a.c.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 585.4.a.h.1.2 | 2 | |||
4.3 | odd | 2 | 1040.4.a.k.1.2 | 2 | |||
5.2 | odd | 4 | 325.4.b.f.274.2 | 4 | |||
5.3 | odd | 4 | 325.4.b.f.274.3 | 4 | |||
5.4 | even | 2 | 325.4.a.g.1.2 | 2 | |||
13.12 | even | 2 | 845.4.a.d.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
65.4.a.c.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
325.4.a.g.1.2 | 2 | 5.4 | even | 2 | |||
325.4.b.f.274.2 | 4 | 5.2 | odd | 4 | |||
325.4.b.f.274.3 | 4 | 5.3 | odd | 4 | |||
585.4.a.h.1.2 | 2 | 3.2 | odd | 2 | |||
845.4.a.d.1.2 | 2 | 13.12 | even | 2 | |||
1040.4.a.k.1.2 | 2 | 4.3 | odd | 2 |