Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1045,4,Mod(1,1045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1045, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1045.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1045 = 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1045.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: | \(61.6569959560\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 1045.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.998459 | 0.353009 | 0.176504 | − | 0.984300i | \(-0.443521\pi\) | ||||
0.176504 | + | 0.984300i | \(0.443521\pi\) | |||||||
\(3\) | 4.82825 | 0.929197 | 0.464599 | − | 0.885521i | \(-0.346199\pi\) | ||||
0.464599 | + | 0.885521i | \(0.346199\pi\) | |||||||
\(4\) | −7.00308 | −0.875385 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 4.82081 | 0.328015 | ||||||||
\(7\) | −5.45452 | −0.294516 | −0.147258 | − | 0.989098i | \(-0.547045\pi\) | ||||
−0.147258 | + | 0.989098i | \(0.547045\pi\) | |||||||
\(8\) | −14.9800 | −0.662027 | ||||||||
\(9\) | −3.68800 | −0.136593 | ||||||||
\(10\) | 4.99229 | 0.157870 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | −33.8126 | −0.813405 | ||||||||
\(13\) | −28.9587 | −0.617823 | −0.308911 | − | 0.951091i | \(-0.599965\pi\) | ||||
−0.308911 | + | 0.951091i | \(0.599965\pi\) | |||||||
\(14\) | −5.44611 | −0.103967 | ||||||||
\(15\) | 24.1413 | 0.415550 | ||||||||
\(16\) | 41.0678 | 0.641684 | ||||||||
\(17\) | −44.4214 | −0.633751 | −0.316875 | − | 0.948467i | \(-0.602634\pi\) | ||||
−0.316875 | + | 0.948467i | \(0.602634\pi\) | |||||||
\(18\) | −3.68231 | −0.0482183 | ||||||||
\(19\) | 19.0000 | 0.229416 | ||||||||
\(20\) | −35.0154 | −0.391484 | ||||||||
\(21\) | −26.3358 | −0.273664 | ||||||||
\(22\) | −10.9830 | −0.106436 | ||||||||
\(23\) | 152.854 | 1.38575 | 0.692875 | − | 0.721058i | \(-0.256344\pi\) | ||||
0.692875 | + | 0.721058i | \(0.256344\pi\) | |||||||
\(24\) | −72.3270 | −0.615154 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −28.9141 | −0.218097 | ||||||||
\(27\) | −148.169 | −1.05612 | ||||||||
\(28\) | 38.1984 | 0.257815 | ||||||||
\(29\) | 182.157 | 1.16640 | 0.583202 | − | 0.812327i | \(-0.301800\pi\) | ||||
0.583202 | + | 0.812327i | \(0.301800\pi\) | |||||||
\(30\) | 24.1040 | 0.146693 | ||||||||
\(31\) | 182.989 | 1.06019 | 0.530094 | − | 0.847939i | \(-0.322157\pi\) | ||||
0.530094 | + | 0.847939i | \(0.322157\pi\) | |||||||
\(32\) | 160.844 | 0.888547 | ||||||||
\(33\) | −53.1108 | −0.280164 | ||||||||
\(34\) | −44.3529 | −0.223719 | ||||||||
\(35\) | −27.2726 | −0.131712 | ||||||||
\(36\) | 25.8273 | 0.119571 | ||||||||
\(37\) | 279.209 | 1.24058 | 0.620292 | − | 0.784371i | \(-0.287014\pi\) | ||||
0.620292 | + | 0.784371i | \(0.287014\pi\) | |||||||
\(38\) | 18.9707 | 0.0809857 | ||||||||
\(39\) | −139.820 | −0.574079 | ||||||||
\(40\) | −74.8998 | −0.296067 | ||||||||
\(41\) | −41.6226 | −0.158545 | −0.0792727 | − | 0.996853i | \(-0.525260\pi\) | ||||
−0.0792727 | + | 0.996853i | \(0.525260\pi\) | |||||||
\(42\) | −26.2952 | −0.0966056 | ||||||||
\(43\) | 290.563 | 1.03048 | 0.515238 | − | 0.857047i | \(-0.327704\pi\) | ||||
0.515238 | + | 0.857047i | \(0.327704\pi\) | |||||||
\(44\) | 77.0339 | 0.263939 | ||||||||
\(45\) | −18.4400 | −0.0610860 | ||||||||
\(46\) | 152.618 | 0.489182 | ||||||||
\(47\) | 38.6536 | 0.119962 | 0.0599809 | − | 0.998200i | \(-0.480896\pi\) | ||||
0.0599809 | + | 0.998200i | \(0.480896\pi\) | |||||||
\(48\) | 198.285 | 0.596251 | ||||||||
\(49\) | −313.248 | −0.913260 | ||||||||
\(50\) | 24.9615 | 0.0706017 | ||||||||
\(51\) | −214.478 | −0.588880 | ||||||||
\(52\) | 202.800 | 0.540833 | ||||||||
\(53\) | 521.847 | 1.35248 | 0.676238 | − | 0.736684i | \(-0.263609\pi\) | ||||
0.676238 | + | 0.736684i | \(0.263609\pi\) | |||||||
\(54\) | −147.941 | −0.372819 | ||||||||
\(55\) | −55.0000 | −0.134840 | ||||||||
\(56\) | 81.7085 | 0.194978 | ||||||||
\(57\) | 91.7368 | 0.213172 | ||||||||
\(58\) | 181.876 | 0.411751 | ||||||||
\(59\) | 126.032 | 0.278101 | 0.139050 | − | 0.990285i | \(-0.455595\pi\) | ||||
0.139050 | + | 0.990285i | \(0.455595\pi\) | |||||||
\(60\) | −169.063 | −0.363766 | ||||||||
\(61\) | 295.884 | 0.621049 | 0.310525 | − | 0.950565i | \(-0.399495\pi\) | ||||
0.310525 | + | 0.950565i | \(0.399495\pi\) | |||||||
\(62\) | 182.707 | 0.374255 | ||||||||
\(63\) | 20.1162 | 0.0402287 | ||||||||
\(64\) | −167.946 | −0.328019 | ||||||||
\(65\) | −144.793 | −0.276299 | ||||||||
\(66\) | −53.0289 | −0.0989001 | ||||||||
\(67\) | 165.988 | 0.302666 | 0.151333 | − | 0.988483i | \(-0.451643\pi\) | ||||
0.151333 | + | 0.988483i | \(0.451643\pi\) | |||||||
\(68\) | 311.086 | 0.554776 | ||||||||
\(69\) | 738.017 | 1.28764 | ||||||||
\(70\) | −27.2306 | −0.0464953 | ||||||||
\(71\) | 223.721 | 0.373955 | 0.186977 | − | 0.982364i | \(-0.440131\pi\) | ||||
0.186977 | + | 0.982364i | \(0.440131\pi\) | |||||||
\(72\) | 55.2461 | 0.0904279 | ||||||||
\(73\) | −274.718 | −0.440457 | −0.220228 | − | 0.975448i | \(-0.570680\pi\) | ||||
−0.220228 | + | 0.975448i | \(0.570680\pi\) | |||||||
\(74\) | 278.778 | 0.437937 | ||||||||
\(75\) | 120.706 | 0.185839 | ||||||||
\(76\) | −133.059 | −0.200827 | ||||||||
\(77\) | 59.9997 | 0.0888000 | ||||||||
\(78\) | −139.604 | −0.202655 | ||||||||
\(79\) | −16.3617 | −0.0233018 | −0.0116509 | − | 0.999932i | \(-0.503709\pi\) | ||||
−0.0116509 | + | 0.999932i | \(0.503709\pi\) | |||||||
\(80\) | 205.339 | 0.286970 | ||||||||
\(81\) | −615.823 | −0.844750 | ||||||||
\(82\) | −41.5585 | −0.0559679 | ||||||||
\(83\) | −372.736 | −0.492929 | −0.246464 | − | 0.969152i | \(-0.579269\pi\) | ||||
−0.246464 | + | 0.969152i | \(0.579269\pi\) | |||||||
\(84\) | 184.432 | 0.239561 | ||||||||
\(85\) | −222.107 | −0.283422 | ||||||||
\(86\) | 290.115 | 0.363767 | ||||||||
\(87\) | 879.500 | 1.08382 | ||||||||
\(88\) | 164.780 | 0.199609 | ||||||||
\(89\) | 489.012 | 0.582418 | 0.291209 | − | 0.956659i | \(-0.405942\pi\) | ||||
0.291209 | + | 0.956659i | \(0.405942\pi\) | |||||||
\(90\) | −18.4116 | −0.0215639 | ||||||||
\(91\) | 157.956 | 0.181959 | ||||||||
\(92\) | −1070.45 | −1.21306 | ||||||||
\(93\) | 883.518 | 0.985124 | ||||||||
\(94\) | 38.5940 | 0.0423475 | ||||||||
\(95\) | 95.0000 | 0.102598 | ||||||||
\(96\) | 776.596 | 0.825635 | ||||||||
\(97\) | −880.289 | −0.921441 | −0.460721 | − | 0.887545i | \(-0.652409\pi\) | ||||
−0.460721 | + | 0.887545i | \(0.652409\pi\) | |||||||
\(98\) | −312.765 | −0.322389 | ||||||||
\(99\) | 40.5680 | 0.0411842 | ||||||||
\(100\) | −175.077 | −0.175077 | ||||||||
\(101\) | −605.680 | −0.596707 | −0.298353 | − | 0.954455i | \(-0.596437\pi\) | ||||
−0.298353 | + | 0.954455i | \(0.596437\pi\) | |||||||
\(102\) | −214.147 | −0.207880 | ||||||||
\(103\) | −224.049 | −0.214332 | −0.107166 | − | 0.994241i | \(-0.534178\pi\) | ||||
−0.107166 | + | 0.994241i | \(0.534178\pi\) | |||||||
\(104\) | 433.800 | 0.409015 | ||||||||
\(105\) | −131.679 | −0.122386 | ||||||||
\(106\) | 521.043 | 0.477435 | ||||||||
\(107\) | −1586.56 | −1.43344 | −0.716721 | − | 0.697360i | \(-0.754358\pi\) | ||||
−0.716721 | + | 0.697360i | \(0.754358\pi\) | |||||||
\(108\) | 1037.64 | 0.924510 | ||||||||
\(109\) | 666.119 | 0.585345 | 0.292672 | − | 0.956213i | \(-0.405455\pi\) | ||||
0.292672 | + | 0.956213i | \(0.405455\pi\) | |||||||
\(110\) | −54.9152 | −0.0475997 | ||||||||
\(111\) | 1348.09 | 1.15275 | ||||||||
\(112\) | −224.005 | −0.188986 | ||||||||
\(113\) | 2347.13 | 1.95398 | 0.976989 | − | 0.213290i | \(-0.0684178\pi\) | ||||
0.976989 | + | 0.213290i | \(0.0684178\pi\) | |||||||
\(114\) | 91.5954 | 0.0752517 | ||||||||
\(115\) | 764.270 | 0.619726 | ||||||||
\(116\) | −1275.66 | −1.02105 | ||||||||
\(117\) | 106.800 | 0.0843900 | ||||||||
\(118\) | 125.838 | 0.0981719 | ||||||||
\(119\) | 242.297 | 0.186650 | ||||||||
\(120\) | −361.635 | −0.275105 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 295.428 | 0.219236 | ||||||||
\(123\) | −200.965 | −0.147320 | ||||||||
\(124\) | −1281.49 | −0.928073 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 20.0852 | 0.0142011 | ||||||||
\(127\) | 2361.88 | 1.65026 | 0.825129 | − | 0.564944i | \(-0.191102\pi\) | ||||
0.825129 | + | 0.564944i | \(0.191102\pi\) | |||||||
\(128\) | −1454.44 | −1.00434 | ||||||||
\(129\) | 1402.91 | 0.957515 | ||||||||
\(130\) | −144.570 | −0.0975358 | ||||||||
\(131\) | −986.974 | −0.658262 | −0.329131 | − | 0.944284i | \(-0.606756\pi\) | ||||
−0.329131 | + | 0.944284i | \(0.606756\pi\) | |||||||
\(132\) | 371.939 | 0.245251 | ||||||||
\(133\) | −103.636 | −0.0675667 | ||||||||
\(134\) | 165.732 | 0.106844 | ||||||||
\(135\) | −740.847 | −0.472311 | ||||||||
\(136\) | 665.430 | 0.419560 | ||||||||
\(137\) | 2651.56 | 1.65356 | 0.826781 | − | 0.562524i | \(-0.190170\pi\) | ||||
0.826781 | + | 0.562524i | \(0.190170\pi\) | |||||||
\(138\) | 736.880 | 0.454546 | ||||||||
\(139\) | 2360.21 | 1.44022 | 0.720110 | − | 0.693860i | \(-0.244092\pi\) | ||||
0.720110 | + | 0.693860i | \(0.244092\pi\) | |||||||
\(140\) | 190.992 | 0.115298 | ||||||||
\(141\) | 186.629 | 0.111468 | ||||||||
\(142\) | 223.376 | 0.132009 | ||||||||
\(143\) | 318.546 | 0.186281 | ||||||||
\(144\) | −151.458 | −0.0876492 | ||||||||
\(145\) | 910.786 | 0.521632 | ||||||||
\(146\) | −274.295 | −0.155485 | ||||||||
\(147\) | −1512.44 | −0.848599 | ||||||||
\(148\) | −1955.32 | −1.08599 | ||||||||
\(149\) | 655.848 | 0.360598 | 0.180299 | − | 0.983612i | \(-0.442293\pi\) | ||||
0.180299 | + | 0.983612i | \(0.442293\pi\) | |||||||
\(150\) | 120.520 | 0.0656029 | ||||||||
\(151\) | −1222.79 | −0.659001 | −0.329501 | − | 0.944155i | \(-0.606880\pi\) | ||||
−0.329501 | + | 0.944155i | \(0.606880\pi\) | |||||||
\(152\) | −284.619 | −0.151879 | ||||||||
\(153\) | 163.826 | 0.0865656 | ||||||||
\(154\) | 59.9072 | 0.0313472 | ||||||||
\(155\) | 914.946 | 0.474131 | ||||||||
\(156\) | 979.169 | 0.502540 | ||||||||
\(157\) | −860.979 | −0.437666 | −0.218833 | − | 0.975762i | \(-0.570225\pi\) | ||||
−0.218833 | + | 0.975762i | \(0.570225\pi\) | |||||||
\(158\) | −16.3365 | −0.00822573 | ||||||||
\(159\) | 2519.61 | 1.25672 | ||||||||
\(160\) | 804.221 | 0.397370 | ||||||||
\(161\) | −833.745 | −0.408126 | ||||||||
\(162\) | −614.874 | −0.298204 | ||||||||
\(163\) | −1707.69 | −0.820592 | −0.410296 | − | 0.911952i | \(-0.634575\pi\) | ||||
−0.410296 | + | 0.911952i | \(0.634575\pi\) | |||||||
\(164\) | 291.487 | 0.138788 | ||||||||
\(165\) | −265.554 | −0.125293 | ||||||||
\(166\) | −372.162 | −0.174008 | ||||||||
\(167\) | −2733.85 | −1.26678 | −0.633389 | − | 0.773834i | \(-0.718336\pi\) | ||||
−0.633389 | + | 0.773834i | \(0.718336\pi\) | |||||||
\(168\) | 394.509 | 0.181173 | ||||||||
\(169\) | −1358.39 | −0.618295 | ||||||||
\(170\) | −221.765 | −0.100050 | ||||||||
\(171\) | −70.0720 | −0.0313365 | ||||||||
\(172\) | −2034.84 | −0.902063 | ||||||||
\(173\) | 3871.83 | 1.70156 | 0.850779 | − | 0.525523i | \(-0.176130\pi\) | ||||
0.850779 | + | 0.525523i | \(0.176130\pi\) | |||||||
\(174\) | 878.145 | 0.382598 | ||||||||
\(175\) | −136.363 | −0.0589033 | ||||||||
\(176\) | −451.745 | −0.193475 | ||||||||
\(177\) | 608.513 | 0.258410 | ||||||||
\(178\) | 488.259 | 0.205599 | ||||||||
\(179\) | −3334.16 | −1.39222 | −0.696109 | − | 0.717936i | \(-0.745087\pi\) | ||||
−0.696109 | + | 0.717936i | \(0.745087\pi\) | |||||||
\(180\) | 129.137 | 0.0534738 | ||||||||
\(181\) | 3124.85 | 1.28325 | 0.641625 | − | 0.767019i | \(-0.278261\pi\) | ||||
0.641625 | + | 0.767019i | \(0.278261\pi\) | |||||||
\(182\) | 157.712 | 0.0642330 | ||||||||
\(183\) | 1428.60 | 0.577077 | ||||||||
\(184\) | −2289.75 | −0.917404 | ||||||||
\(185\) | 1396.04 | 0.554806 | ||||||||
\(186\) | 882.156 | 0.347757 | ||||||||
\(187\) | 488.635 | 0.191083 | ||||||||
\(188\) | −270.694 | −0.105013 | ||||||||
\(189\) | 808.192 | 0.311044 | ||||||||
\(190\) | 94.8536 | 0.0362179 | ||||||||
\(191\) | 4957.27 | 1.87799 | 0.938994 | − | 0.343933i | \(-0.111759\pi\) | ||||
0.938994 | + | 0.343933i | \(0.111759\pi\) | |||||||
\(192\) | −810.885 | −0.304795 | ||||||||
\(193\) | 336.139 | 0.125367 | 0.0626834 | − | 0.998033i | \(-0.480034\pi\) | ||||
0.0626834 | + | 0.998033i | \(0.480034\pi\) | |||||||
\(194\) | −878.932 | −0.325277 | ||||||||
\(195\) | −699.099 | −0.256736 | ||||||||
\(196\) | 2193.70 | 0.799454 | ||||||||
\(197\) | −3812.32 | −1.37877 | −0.689383 | − | 0.724397i | \(-0.742118\pi\) | ||||
−0.689383 | + | 0.724397i | \(0.742118\pi\) | |||||||
\(198\) | 40.5055 | 0.0145384 | ||||||||
\(199\) | −332.540 | −0.118458 | −0.0592290 | − | 0.998244i | \(-0.518864\pi\) | ||||
−0.0592290 | + | 0.998244i | \(0.518864\pi\) | |||||||
\(200\) | −374.499 | −0.132405 | ||||||||
\(201\) | 801.431 | 0.281237 | ||||||||
\(202\) | −604.746 | −0.210643 | ||||||||
\(203\) | −993.579 | −0.343525 | ||||||||
\(204\) | 1502.00 | 0.515496 | ||||||||
\(205\) | −208.113 | −0.0709037 | ||||||||
\(206\) | −223.704 | −0.0756612 | ||||||||
\(207\) | −563.725 | −0.189283 | ||||||||
\(208\) | −1189.27 | −0.396447 | ||||||||
\(209\) | −209.000 | −0.0691714 | ||||||||
\(210\) | −131.476 | −0.0432033 | ||||||||
\(211\) | −2997.24 | −0.977909 | −0.488954 | − | 0.872309i | \(-0.662622\pi\) | ||||
−0.488954 | + | 0.872309i | \(0.662622\pi\) | |||||||
\(212\) | −3654.54 | −1.18394 | ||||||||
\(213\) | 1080.18 | 0.347478 | ||||||||
\(214\) | −1584.11 | −0.506017 | ||||||||
\(215\) | 1452.82 | 0.460843 | ||||||||
\(216\) | 2219.57 | 0.699179 | ||||||||
\(217\) | −998.118 | −0.312243 | ||||||||
\(218\) | 665.092 | 0.206632 | ||||||||
\(219\) | −1326.41 | −0.409271 | ||||||||
\(220\) | 385.169 | 0.118037 | ||||||||
\(221\) | 1286.39 | 0.391546 | ||||||||
\(222\) | 1346.01 | 0.406930 | ||||||||
\(223\) | 4352.79 | 1.30710 | 0.653552 | − | 0.756882i | \(-0.273278\pi\) | ||||
0.653552 | + | 0.756882i | \(0.273278\pi\) | |||||||
\(224\) | −877.327 | −0.261691 | ||||||||
\(225\) | −92.1999 | −0.0273185 | ||||||||
\(226\) | 2343.51 | 0.689771 | ||||||||
\(227\) | −886.376 | −0.259167 | −0.129583 | − | 0.991569i | \(-0.541364\pi\) | ||||
−0.129583 | + | 0.991569i | \(0.541364\pi\) | |||||||
\(228\) | −642.440 | −0.186608 | ||||||||
\(229\) | 4343.89 | 1.25350 | 0.626752 | − | 0.779218i | \(-0.284384\pi\) | ||||
0.626752 | + | 0.779218i | \(0.284384\pi\) | |||||||
\(230\) | 763.092 | 0.218769 | ||||||||
\(231\) | 289.694 | 0.0825127 | ||||||||
\(232\) | −2728.71 | −0.772191 | ||||||||
\(233\) | −3296.68 | −0.926921 | −0.463461 | − | 0.886117i | \(-0.653392\pi\) | ||||
−0.463461 | + | 0.886117i | \(0.653392\pi\) | |||||||
\(234\) | 106.635 | 0.0297904 | ||||||||
\(235\) | 193.268 | 0.0536485 | ||||||||
\(236\) | −882.611 | −0.243445 | ||||||||
\(237\) | −78.9986 | −0.0216519 | ||||||||
\(238\) | 241.924 | 0.0658890 | ||||||||
\(239\) | 6076.91 | 1.64470 | 0.822348 | − | 0.568985i | \(-0.192664\pi\) | ||||
0.822348 | + | 0.568985i | \(0.192664\pi\) | |||||||
\(240\) | 991.427 | 0.266651 | ||||||||
\(241\) | 285.570 | 0.0763287 | 0.0381643 | − | 0.999271i | \(-0.487849\pi\) | ||||
0.0381643 | + | 0.999271i | \(0.487849\pi\) | |||||||
\(242\) | 120.814 | 0.0320917 | ||||||||
\(243\) | 1027.23 | 0.271179 | ||||||||
\(244\) | −2072.10 | −0.543657 | ||||||||
\(245\) | −1566.24 | −0.408422 | ||||||||
\(246\) | −200.655 | −0.0520052 | ||||||||
\(247\) | −550.215 | −0.141738 | ||||||||
\(248\) | −2741.17 | −0.701873 | ||||||||
\(249\) | −1799.66 | −0.458028 | ||||||||
\(250\) | 124.807 | 0.0315740 | ||||||||
\(251\) | −4454.58 | −1.12020 | −0.560101 | − | 0.828424i | \(-0.689238\pi\) | ||||
−0.560101 | + | 0.828424i | \(0.689238\pi\) | |||||||
\(252\) | −140.876 | −0.0352156 | ||||||||
\(253\) | −1681.39 | −0.417819 | ||||||||
\(254\) | 2358.24 | 0.582555 | ||||||||
\(255\) | −1072.39 | −0.263355 | ||||||||
\(256\) | −108.632 | −0.0265215 | ||||||||
\(257\) | −7030.62 | −1.70645 | −0.853225 | − | 0.521542i | \(-0.825357\pi\) | ||||
−0.853225 | + | 0.521542i | \(0.825357\pi\) | |||||||
\(258\) | 1400.75 | 0.338011 | ||||||||
\(259\) | −1522.95 | −0.365372 | ||||||||
\(260\) | 1014.00 | 0.241868 | ||||||||
\(261\) | −671.795 | −0.159322 | ||||||||
\(262\) | −985.452 | −0.232372 | ||||||||
\(263\) | −4769.61 | −1.11828 | −0.559138 | − | 0.829074i | \(-0.688868\pi\) | ||||
−0.559138 | + | 0.829074i | \(0.688868\pi\) | |||||||
\(264\) | 795.597 | 0.185476 | ||||||||
\(265\) | 2609.23 | 0.604845 | ||||||||
\(266\) | −103.476 | −0.0238516 | ||||||||
\(267\) | 2361.07 | 0.541181 | ||||||||
\(268\) | −1162.43 | −0.264950 | ||||||||
\(269\) | 5513.04 | 1.24958 | 0.624788 | − | 0.780794i | \(-0.285185\pi\) | ||||
0.624788 | + | 0.780794i | \(0.285185\pi\) | |||||||
\(270\) | −739.705 | −0.166730 | ||||||||
\(271\) | 8440.43 | 1.89196 | 0.945978 | − | 0.324232i | \(-0.105106\pi\) | ||||
0.945978 | + | 0.324232i | \(0.105106\pi\) | |||||||
\(272\) | −1824.29 | −0.406668 | ||||||||
\(273\) | 762.650 | 0.169076 | ||||||||
\(274\) | 2647.47 | 0.583721 | ||||||||
\(275\) | −275.000 | −0.0603023 | ||||||||
\(276\) | −5168.39 | −1.12718 | ||||||||
\(277\) | −1579.33 | −0.342572 | −0.171286 | − | 0.985221i | \(-0.554792\pi\) | ||||
−0.171286 | + | 0.985221i | \(0.554792\pi\) | |||||||
\(278\) | 2356.57 | 0.508410 | ||||||||
\(279\) | −674.864 | −0.144814 | ||||||||
\(280\) | 408.542 | 0.0871967 | ||||||||
\(281\) | 8944.42 | 1.89886 | 0.949429 | − | 0.313980i | \(-0.101663\pi\) | ||||
0.949429 | + | 0.313980i | \(0.101663\pi\) | |||||||
\(282\) | 186.341 | 0.0393492 | ||||||||
\(283\) | 4606.18 | 0.967523 | 0.483762 | − | 0.875200i | \(-0.339270\pi\) | ||||
0.483762 | + | 0.875200i | \(0.339270\pi\) | |||||||
\(284\) | −1566.74 | −0.327354 | ||||||||
\(285\) | 458.684 | 0.0953336 | ||||||||
\(286\) | 318.055 | 0.0657586 | ||||||||
\(287\) | 227.031 | 0.0466942 | ||||||||
\(288\) | −593.193 | −0.121369 | ||||||||
\(289\) | −2939.74 | −0.598360 | ||||||||
\(290\) | 909.382 | 0.184141 | ||||||||
\(291\) | −4250.25 | −0.856200 | ||||||||
\(292\) | 1923.87 | 0.385569 | ||||||||
\(293\) | 6623.14 | 1.32057 | 0.660287 | − | 0.751014i | \(-0.270435\pi\) | ||||
0.660287 | + | 0.751014i | \(0.270435\pi\) | |||||||
\(294\) | −1510.11 | −0.299563 | ||||||||
\(295\) | 630.159 | 0.124370 | ||||||||
\(296\) | −4182.53 | −0.821300 | ||||||||
\(297\) | 1629.86 | 0.318432 | ||||||||
\(298\) | 654.837 | 0.127294 | ||||||||
\(299\) | −4426.45 | −0.856148 | ||||||||
\(300\) | −845.316 | −0.162681 | ||||||||
\(301\) | −1584.88 | −0.303492 | ||||||||
\(302\) | −1220.91 | −0.232633 | ||||||||
\(303\) | −2924.37 | −0.554458 | ||||||||
\(304\) | 780.288 | 0.147212 | ||||||||
\(305\) | 1479.42 | 0.277742 | ||||||||
\(306\) | 163.573 | 0.0305584 | ||||||||
\(307\) | 6926.55 | 1.28768 | 0.643842 | − | 0.765158i | \(-0.277339\pi\) | ||||
0.643842 | + | 0.765158i | \(0.277339\pi\) | |||||||
\(308\) | −420.183 | −0.0777342 | ||||||||
\(309\) | −1081.77 | −0.199157 | ||||||||
\(310\) | 913.536 | 0.167372 | ||||||||
\(311\) | −3859.97 | −0.703790 | −0.351895 | − | 0.936039i | \(-0.614463\pi\) | ||||
−0.351895 | + | 0.936039i | \(0.614463\pi\) | |||||||
\(312\) | 2094.50 | 0.380056 | ||||||||
\(313\) | 2522.62 | 0.455550 | 0.227775 | − | 0.973714i | \(-0.426855\pi\) | ||||
0.227775 | + | 0.973714i | \(0.426855\pi\) | |||||||
\(314\) | −859.652 | −0.154500 | ||||||||
\(315\) | 100.581 | 0.0179908 | ||||||||
\(316\) | 114.583 | 0.0203980 | ||||||||
\(317\) | −8532.28 | −1.51174 | −0.755869 | − | 0.654723i | \(-0.772785\pi\) | ||||
−0.755869 | + | 0.654723i | \(0.772785\pi\) | |||||||
\(318\) | 2515.72 | 0.443632 | ||||||||
\(319\) | −2003.73 | −0.351684 | ||||||||
\(320\) | −839.729 | −0.146695 | ||||||||
\(321\) | −7660.29 | −1.33195 | ||||||||
\(322\) | −832.460 | −0.144072 | ||||||||
\(323\) | −844.006 | −0.145392 | ||||||||
\(324\) | 4312.66 | 0.739481 | ||||||||
\(325\) | −723.967 | −0.123565 | ||||||||
\(326\) | −1705.06 | −0.289676 | ||||||||
\(327\) | 3216.19 | 0.543901 | ||||||||
\(328\) | 623.505 | 0.104961 | ||||||||
\(329\) | −210.837 | −0.0353307 | ||||||||
\(330\) | −265.145 | −0.0442295 | ||||||||
\(331\) | −7224.77 | −1.19973 | −0.599863 | − | 0.800103i | \(-0.704778\pi\) | ||||
−0.599863 | + | 0.800103i | \(0.704778\pi\) | |||||||
\(332\) | 2610.30 | 0.431502 | ||||||||
\(333\) | −1029.72 | −0.169454 | ||||||||
\(334\) | −2729.64 | −0.447183 | ||||||||
\(335\) | 829.939 | 0.135356 | ||||||||
\(336\) | −1081.55 | −0.175606 | ||||||||
\(337\) | −7562.26 | −1.22238 | −0.611190 | − | 0.791484i | \(-0.709309\pi\) | ||||
−0.611190 | + | 0.791484i | \(0.709309\pi\) | |||||||
\(338\) | −1356.30 | −0.218263 | ||||||||
\(339\) | 11332.5 | 1.81563 | ||||||||
\(340\) | 1555.43 | 0.248103 | ||||||||
\(341\) | −2012.88 | −0.319659 | ||||||||
\(342\) | −69.9640 | −0.0110620 | ||||||||
\(343\) | 3579.52 | 0.563486 | ||||||||
\(344\) | −4352.62 | −0.682203 | ||||||||
\(345\) | 3690.09 | 0.575848 | ||||||||
\(346\) | 3865.86 | 0.600665 | ||||||||
\(347\) | −7611.70 | −1.17757 | −0.588786 | − | 0.808289i | \(-0.700394\pi\) | ||||
−0.588786 | + | 0.808289i | \(0.700394\pi\) | |||||||
\(348\) | −6159.21 | −0.948760 | ||||||||
\(349\) | 72.3720 | 0.0111002 | 0.00555012 | − | 0.999985i | \(-0.498233\pi\) | ||||
0.00555012 | + | 0.999985i | \(0.498233\pi\) | |||||||
\(350\) | −136.153 | −0.0207934 | ||||||||
\(351\) | 4290.79 | 0.652494 | ||||||||
\(352\) | −1769.29 | −0.267907 | ||||||||
\(353\) | −4364.92 | −0.658134 | −0.329067 | − | 0.944307i | \(-0.606734\pi\) | ||||
−0.329067 | + | 0.944307i | \(0.606734\pi\) | |||||||
\(354\) | 607.575 | 0.0912211 | ||||||||
\(355\) | 1118.60 | 0.167238 | ||||||||
\(356\) | −3424.59 | −0.509840 | ||||||||
\(357\) | 1169.87 | 0.173435 | ||||||||
\(358\) | −3329.03 | −0.491465 | ||||||||
\(359\) | 6094.21 | 0.895933 | 0.447966 | − | 0.894050i | \(-0.352148\pi\) | ||||
0.447966 | + | 0.894050i | \(0.352148\pi\) | |||||||
\(360\) | 276.230 | 0.0404406 | ||||||||
\(361\) | 361.000 | 0.0526316 | ||||||||
\(362\) | 3120.03 | 0.452998 | ||||||||
\(363\) | 584.218 | 0.0844725 | ||||||||
\(364\) | −1106.18 | −0.159284 | ||||||||
\(365\) | −1373.59 | −0.196978 | ||||||||
\(366\) | 1426.40 | 0.203713 | ||||||||
\(367\) | 7299.18 | 1.03819 | 0.519093 | − | 0.854718i | \(-0.326270\pi\) | ||||
0.519093 | + | 0.854718i | \(0.326270\pi\) | |||||||
\(368\) | 6277.37 | 0.889213 | ||||||||
\(369\) | 153.504 | 0.0216561 | ||||||||
\(370\) | 1393.89 | 0.195851 | ||||||||
\(371\) | −2846.42 | −0.398326 | ||||||||
\(372\) | −6187.35 | −0.862363 | ||||||||
\(373\) | 6056.32 | 0.840709 | 0.420355 | − | 0.907360i | \(-0.361906\pi\) | ||||
0.420355 | + | 0.907360i | \(0.361906\pi\) | |||||||
\(374\) | 487.882 | 0.0674540 | ||||||||
\(375\) | 603.531 | 0.0831099 | ||||||||
\(376\) | −579.029 | −0.0794179 | ||||||||
\(377\) | −5275.03 | −0.720631 | ||||||||
\(378\) | 806.947 | 0.109801 | ||||||||
\(379\) | 10524.2 | 1.42637 | 0.713185 | − | 0.700976i | \(-0.247252\pi\) | ||||
0.713185 | + | 0.700976i | \(0.247252\pi\) | |||||||
\(380\) | −665.293 | −0.0898126 | ||||||||
\(381\) | 11403.7 | 1.53342 | ||||||||
\(382\) | 4949.63 | 0.662946 | ||||||||
\(383\) | 2558.18 | 0.341297 | 0.170649 | − | 0.985332i | \(-0.445414\pi\) | ||||
0.170649 | + | 0.985332i | \(0.445414\pi\) | |||||||
\(384\) | −7022.40 | −0.933230 | ||||||||
\(385\) | 299.998 | 0.0397126 | ||||||||
\(386\) | 335.621 | 0.0442555 | ||||||||
\(387\) | −1071.60 | −0.140755 | ||||||||
\(388\) | 6164.73 | 0.806616 | ||||||||
\(389\) | −4038.68 | −0.526399 | −0.263200 | − | 0.964741i | \(-0.584778\pi\) | ||||
−0.263200 | + | 0.964741i | \(0.584778\pi\) | |||||||
\(390\) | −698.022 | −0.0906300 | ||||||||
\(391\) | −6789.98 | −0.878220 | ||||||||
\(392\) | 4692.45 | 0.604603 | ||||||||
\(393\) | −4765.36 | −0.611655 | ||||||||
\(394\) | −3806.45 | −0.486716 | ||||||||
\(395\) | −81.8087 | −0.0104209 | ||||||||
\(396\) | −284.101 | −0.0360520 | ||||||||
\(397\) | 6406.47 | 0.809903 | 0.404951 | − | 0.914338i | \(-0.367288\pi\) | ||||
0.404951 | + | 0.914338i | \(0.367288\pi\) | |||||||
\(398\) | −332.028 | −0.0418167 | ||||||||
\(399\) | −500.380 | −0.0627828 | ||||||||
\(400\) | 1026.69 | 0.128337 | ||||||||
\(401\) | 12365.1 | 1.53986 | 0.769928 | − | 0.638130i | \(-0.220292\pi\) | ||||
0.769928 | + | 0.638130i | \(0.220292\pi\) | |||||||
\(402\) | 800.196 | 0.0992789 | ||||||||
\(403\) | −5299.13 | −0.655008 | ||||||||
\(404\) | 4241.62 | 0.522348 | ||||||||
\(405\) | −3079.11 | −0.377784 | ||||||||
\(406\) | −992.048 | −0.121267 | ||||||||
\(407\) | −3071.29 | −0.374050 | ||||||||
\(408\) | 3212.86 | 0.389854 | ||||||||
\(409\) | −8543.97 | −1.03294 | −0.516469 | − | 0.856306i | \(-0.672754\pi\) | ||||
−0.516469 | + | 0.856306i | \(0.672754\pi\) | |||||||
\(410\) | −207.792 | −0.0250296 | ||||||||
\(411\) | 12802.4 | 1.53648 | ||||||||
\(412\) | 1569.04 | 0.187623 | ||||||||
\(413\) | −687.443 | −0.0819052 | ||||||||
\(414\) | −562.856 | −0.0668185 | ||||||||
\(415\) | −1863.68 | −0.220444 | ||||||||
\(416\) | −4657.84 | −0.548964 | ||||||||
\(417\) | 11395.7 | 1.33825 | ||||||||
\(418\) | −208.678 | −0.0244181 | ||||||||
\(419\) | 5168.26 | 0.602593 | 0.301296 | − | 0.953531i | \(-0.402581\pi\) | ||||
0.301296 | + | 0.953531i | \(0.402581\pi\) | |||||||
\(420\) | 922.158 | 0.107135 | ||||||||
\(421\) | 10451.1 | 1.20987 | 0.604934 | − | 0.796276i | \(-0.293199\pi\) | ||||
0.604934 | + | 0.796276i | \(0.293199\pi\) | |||||||
\(422\) | −2992.62 | −0.345210 | ||||||||
\(423\) | −142.554 | −0.0163859 | ||||||||
\(424\) | −7817.24 | −0.895375 | ||||||||
\(425\) | −1110.53 | −0.126750 | ||||||||
\(426\) | 1078.52 | 0.122663 | ||||||||
\(427\) | −1613.90 | −0.182909 | ||||||||
\(428\) | 11110.8 | 1.25481 | ||||||||
\(429\) | 1538.02 | 0.173091 | ||||||||
\(430\) | 1450.58 | 0.162681 | ||||||||
\(431\) | −13009.8 | −1.45397 | −0.726984 | − | 0.686655i | \(-0.759079\pi\) | ||||
−0.726984 | + | 0.686655i | \(0.759079\pi\) | |||||||
\(432\) | −6084.98 | −0.677694 | ||||||||
\(433\) | 4228.27 | 0.469279 | 0.234640 | − | 0.972082i | \(-0.424609\pi\) | ||||
0.234640 | + | 0.972082i | \(0.424609\pi\) | |||||||
\(434\) | −996.580 | −0.110224 | ||||||||
\(435\) | 4397.50 | 0.484699 | ||||||||
\(436\) | −4664.88 | −0.512402 | ||||||||
\(437\) | 2904.22 | 0.317913 | ||||||||
\(438\) | −1324.36 | −0.144476 | ||||||||
\(439\) | 3566.23 | 0.387715 | 0.193857 | − | 0.981030i | \(-0.437900\pi\) | ||||
0.193857 | + | 0.981030i | \(0.437900\pi\) | |||||||
\(440\) | 823.898 | 0.0892677 | ||||||||
\(441\) | 1155.26 | 0.124744 | ||||||||
\(442\) | 1284.40 | 0.138219 | ||||||||
\(443\) | −1680.04 | −0.180183 | −0.0900916 | − | 0.995933i | \(-0.528716\pi\) | ||||
−0.0900916 | + | 0.995933i | \(0.528716\pi\) | |||||||
\(444\) | −9440.77 | −1.00910 | ||||||||
\(445\) | 2445.06 | 0.260465 | ||||||||
\(446\) | 4346.08 | 0.461419 | ||||||||
\(447\) | 3166.60 | 0.335067 | ||||||||
\(448\) | 916.064 | 0.0966070 | ||||||||
\(449\) | −13705.2 | −1.44051 | −0.720257 | − | 0.693708i | \(-0.755976\pi\) | ||||
−0.720257 | + | 0.693708i | \(0.755976\pi\) | |||||||
\(450\) | −92.0579 | −0.00964366 | ||||||||
\(451\) | 457.849 | 0.0478033 | ||||||||
\(452\) | −16437.1 | −1.71048 | ||||||||
\(453\) | −5903.94 | −0.612342 | ||||||||
\(454\) | −885.010 | −0.0914881 | ||||||||
\(455\) | 789.779 | 0.0813745 | ||||||||
\(456\) | −1374.21 | −0.141126 | ||||||||
\(457\) | −16073.4 | −1.64526 | −0.822630 | − | 0.568576i | \(-0.807494\pi\) | ||||
−0.822630 | + | 0.568576i | \(0.807494\pi\) | |||||||
\(458\) | 4337.20 | 0.442498 | ||||||||
\(459\) | 6581.89 | 0.669316 | ||||||||
\(460\) | −5352.24 | −0.542499 | ||||||||
\(461\) | −1555.96 | −0.157198 | −0.0785992 | − | 0.996906i | \(-0.525045\pi\) | ||||
−0.0785992 | + | 0.996906i | \(0.525045\pi\) | |||||||
\(462\) | 289.247 | 0.0291277 | ||||||||
\(463\) | −9649.31 | −0.968556 | −0.484278 | − | 0.874914i | \(-0.660918\pi\) | ||||
−0.484278 | + | 0.874914i | \(0.660918\pi\) | |||||||
\(464\) | 7480.79 | 0.748463 | ||||||||
\(465\) | 4417.59 | 0.440561 | ||||||||
\(466\) | −3291.60 | −0.327211 | ||||||||
\(467\) | 13894.1 | 1.37675 | 0.688373 | − | 0.725357i | \(-0.258325\pi\) | ||||
0.688373 | + | 0.725357i | \(0.258325\pi\) | |||||||
\(468\) | −747.926 | −0.0738737 | ||||||||
\(469\) | −905.384 | −0.0891402 | ||||||||
\(470\) | 192.970 | 0.0189384 | ||||||||
\(471\) | −4157.02 | −0.406678 | ||||||||
\(472\) | −1887.95 | −0.184110 | ||||||||
\(473\) | −3196.19 | −0.310700 | ||||||||
\(474\) | −78.8769 | −0.00764332 | ||||||||
\(475\) | 475.000 | 0.0458831 | ||||||||
\(476\) | −1696.83 | −0.163391 | ||||||||
\(477\) | −1924.57 | −0.184738 | ||||||||
\(478\) | 6067.54 | 0.580592 | ||||||||
\(479\) | −17265.3 | −1.64691 | −0.823457 | − | 0.567379i | \(-0.807957\pi\) | ||||
−0.823457 | + | 0.567379i | \(0.807957\pi\) | |||||||
\(480\) | 3882.98 | 0.369235 | ||||||||
\(481\) | −8085.52 | −0.766461 | ||||||||
\(482\) | 285.130 | 0.0269447 | ||||||||
\(483\) | −4025.53 | −0.379229 | ||||||||
\(484\) | −847.373 | −0.0795805 | ||||||||
\(485\) | −4401.44 | −0.412081 | ||||||||
\(486\) | 1025.64 | 0.0957286 | ||||||||
\(487\) | −17531.9 | −1.63130 | −0.815652 | − | 0.578542i | \(-0.803622\pi\) | ||||
−0.815652 | + | 0.578542i | \(0.803622\pi\) | |||||||
\(488\) | −4432.32 | −0.411151 | ||||||||
\(489\) | −8245.15 | −0.762492 | ||||||||
\(490\) | −1563.83 | −0.144177 | ||||||||
\(491\) | −5697.92 | −0.523714 | −0.261857 | − | 0.965107i | \(-0.584335\pi\) | ||||
−0.261857 | + | 0.965107i | \(0.584335\pi\) | |||||||
\(492\) | 1407.37 | 0.128962 | ||||||||
\(493\) | −8091.67 | −0.739210 | ||||||||
\(494\) | −549.367 | −0.0500348 | ||||||||
\(495\) | 202.840 | 0.0184181 | ||||||||
\(496\) | 7514.96 | 0.680306 | ||||||||
\(497\) | −1220.29 | −0.110136 | ||||||||
\(498\) | −1796.89 | −0.161688 | ||||||||
\(499\) | −1513.35 | −0.135765 | −0.0678827 | − | 0.997693i | \(-0.521624\pi\) | ||||
−0.0678827 | + | 0.997693i | \(0.521624\pi\) | |||||||
\(500\) | −875.385 | −0.0782968 | ||||||||
\(501\) | −13199.7 | −1.17709 | ||||||||
\(502\) | −4447.72 | −0.395441 | ||||||||
\(503\) | −9687.94 | −0.858775 | −0.429388 | − | 0.903120i | \(-0.641271\pi\) | ||||
−0.429388 | + | 0.903120i | \(0.641271\pi\) | |||||||
\(504\) | −301.341 | −0.0266325 | ||||||||
\(505\) | −3028.40 | −0.266855 | ||||||||
\(506\) | −1678.80 | −0.147494 | ||||||||
\(507\) | −6558.67 | −0.574518 | ||||||||
\(508\) | −16540.4 | −1.44461 | ||||||||
\(509\) | −10573.5 | −0.920750 | −0.460375 | − | 0.887725i | \(-0.652285\pi\) | ||||
−0.460375 | + | 0.887725i | \(0.652285\pi\) | |||||||
\(510\) | −1070.73 | −0.0929665 | ||||||||
\(511\) | 1498.46 | 0.129722 | ||||||||
\(512\) | 11527.1 | 0.994978 | ||||||||
\(513\) | −2815.22 | −0.242290 | ||||||||
\(514\) | −7019.78 | −0.602392 | ||||||||
\(515\) | −1120.25 | −0.0958524 | ||||||||
\(516\) | −9824.70 | −0.838194 | ||||||||
\(517\) | −425.189 | −0.0361698 | ||||||||
\(518\) | −1520.60 | −0.128979 | ||||||||
\(519\) | 18694.2 | 1.58108 | ||||||||
\(520\) | 2169.00 | 0.182917 | ||||||||
\(521\) | −6922.30 | −0.582095 | −0.291047 | − | 0.956709i | \(-0.594004\pi\) | ||||
−0.291047 | + | 0.956709i | \(0.594004\pi\) | |||||||
\(522\) | −670.760 | −0.0562421 | ||||||||
\(523\) | 9395.11 | 0.785506 | 0.392753 | − | 0.919644i | \(-0.371523\pi\) | ||||
0.392753 | + | 0.919644i | \(0.371523\pi\) | |||||||
\(524\) | 6911.85 | 0.576232 | ||||||||
\(525\) | −658.394 | −0.0547327 | ||||||||
\(526\) | −4762.26 | −0.394761 | ||||||||
\(527\) | −8128.63 | −0.671895 | ||||||||
\(528\) | −2181.14 | −0.179776 | ||||||||
\(529\) | 11197.3 | 0.920303 | ||||||||
\(530\) | 2605.21 | 0.213516 | ||||||||
\(531\) | −464.805 | −0.0379865 | ||||||||
\(532\) | 725.770 | 0.0591468 | ||||||||
\(533\) | 1205.34 | 0.0979530 | ||||||||
\(534\) | 2357.44 | 0.191042 | ||||||||
\(535\) | −7932.78 | −0.641054 | ||||||||
\(536\) | −2486.49 | −0.200373 | ||||||||
\(537\) | −16098.2 | −1.29365 | ||||||||
\(538\) | 5504.54 | 0.441111 | ||||||||
\(539\) | 3445.73 | 0.275358 | ||||||||
\(540\) | 5188.21 | 0.413454 | ||||||||
\(541\) | −16286.8 | −1.29431 | −0.647156 | − | 0.762357i | \(-0.724042\pi\) | ||||
−0.647156 | + | 0.762357i | \(0.724042\pi\) | |||||||
\(542\) | 8427.43 | 0.667876 | ||||||||
\(543\) | 15087.5 | 1.19239 | ||||||||
\(544\) | −7144.92 | −0.563117 | ||||||||
\(545\) | 3330.59 | 0.261774 | ||||||||
\(546\) | 761.474 | 0.0596852 | ||||||||
\(547\) | 11621.3 | 0.908389 | 0.454195 | − | 0.890902i | \(-0.349927\pi\) | ||||
0.454195 | + | 0.890902i | \(0.349927\pi\) | |||||||
\(548\) | −18569.1 | −1.44750 | ||||||||
\(549\) | −1091.22 | −0.0848307 | ||||||||
\(550\) | −274.576 | −0.0212872 | ||||||||
\(551\) | 3460.99 | 0.267592 | ||||||||
\(552\) | −11055.5 | −0.852449 | ||||||||
\(553\) | 89.2454 | 0.00686275 | ||||||||
\(554\) | −1576.89 | −0.120931 | ||||||||
\(555\) | 6740.44 | 0.515524 | ||||||||
\(556\) | −16528.7 | −1.26075 | ||||||||
\(557\) | 1281.49 | 0.0974836 | 0.0487418 | − | 0.998811i | \(-0.484479\pi\) | ||||
0.0487418 | + | 0.998811i | \(0.484479\pi\) | |||||||
\(558\) | −673.824 | −0.0511205 | ||||||||
\(559\) | −8414.33 | −0.636651 | ||||||||
\(560\) | −1120.02 | −0.0845173 | ||||||||
\(561\) | 2359.25 | 0.177554 | ||||||||
\(562\) | 8930.64 | 0.670313 | ||||||||
\(563\) | −2831.57 | −0.211965 | −0.105983 | − | 0.994368i | \(-0.533799\pi\) | ||||
−0.105983 | + | 0.994368i | \(0.533799\pi\) | |||||||
\(564\) | −1306.98 | −0.0975775 | ||||||||
\(565\) | 11735.7 | 0.873846 | ||||||||
\(566\) | 4599.08 | 0.341544 | ||||||||
\(567\) | 3359.02 | 0.248793 | ||||||||
\(568\) | −3351.33 | −0.247568 | ||||||||
\(569\) | −2659.84 | −0.195969 | −0.0979845 | − | 0.995188i | \(-0.531240\pi\) | ||||
−0.0979845 | + | 0.995188i | \(0.531240\pi\) | |||||||
\(570\) | 457.977 | 0.0336536 | ||||||||
\(571\) | −14305.1 | −1.04843 | −0.524213 | − | 0.851587i | \(-0.675640\pi\) | ||||
−0.524213 | + | 0.851587i | \(0.675640\pi\) | |||||||
\(572\) | −2230.80 | −0.163067 | ||||||||
\(573\) | 23935.0 | 1.74502 | ||||||||
\(574\) | 226.682 | 0.0164835 | ||||||||
\(575\) | 3821.35 | 0.277150 | ||||||||
\(576\) | 619.384 | 0.0448050 | ||||||||
\(577\) | −17711.9 | −1.27791 | −0.638956 | − | 0.769243i | \(-0.720633\pi\) | ||||
−0.638956 | + | 0.769243i | \(0.720633\pi\) | |||||||
\(578\) | −2935.21 | −0.211226 | ||||||||
\(579\) | 1622.96 | 0.116490 | ||||||||
\(580\) | −6378.30 | −0.456629 | ||||||||
\(581\) | 2033.09 | 0.145176 | ||||||||
\(582\) | −4243.70 | −0.302246 | ||||||||
\(583\) | −5740.32 | −0.407787 | ||||||||
\(584\) | 4115.27 | 0.291594 | ||||||||
\(585\) | 533.998 | 0.0377403 | ||||||||
\(586\) | 6612.93 | 0.466174 | ||||||||
\(587\) | −1709.75 | −0.120220 | −0.0601098 | − | 0.998192i | \(-0.519145\pi\) | ||||
−0.0601098 | + | 0.998192i | \(0.519145\pi\) | |||||||
\(588\) | 10591.7 | 0.742851 | ||||||||
\(589\) | 3476.80 | 0.243224 | ||||||||
\(590\) | 629.188 | 0.0439038 | ||||||||
\(591\) | −18406.9 | −1.28115 | ||||||||
\(592\) | 11466.5 | 0.796063 | ||||||||
\(593\) | −11865.0 | −0.821647 | −0.410823 | − | 0.911715i | \(-0.634759\pi\) | ||||
−0.410823 | + | 0.911715i | \(0.634759\pi\) | |||||||
\(594\) | 1627.35 | 0.112409 | ||||||||
\(595\) | 1211.49 | 0.0834724 | ||||||||
\(596\) | −4592.95 | −0.315662 | ||||||||
\(597\) | −1605.59 | −0.110071 | ||||||||
\(598\) | −4419.63 | −0.302228 | ||||||||
\(599\) | 18384.2 | 1.25402 | 0.627009 | − | 0.779012i | \(-0.284279\pi\) | ||||
0.627009 | + | 0.779012i | \(0.284279\pi\) | |||||||
\(600\) | −1808.17 | −0.123031 | ||||||||
\(601\) | 2605.59 | 0.176845 | 0.0884227 | − | 0.996083i | \(-0.471817\pi\) | ||||
0.0884227 | + | 0.996083i | \(0.471817\pi\) | |||||||
\(602\) | −1582.44 | −0.107135 | ||||||||
\(603\) | −612.163 | −0.0413419 | ||||||||
\(604\) | 8563.29 | 0.576880 | ||||||||
\(605\) | 605.000 | 0.0406558 | ||||||||
\(606\) | −2919.87 | −0.195729 | ||||||||
\(607\) | 8719.58 | 0.583059 | 0.291530 | − | 0.956562i | \(-0.405836\pi\) | ||||
0.291530 | + | 0.956562i | \(0.405836\pi\) | |||||||
\(608\) | 3056.04 | 0.203847 | ||||||||
\(609\) | −4797.25 | −0.319203 | ||||||||
\(610\) | 1477.14 | 0.0980452 | ||||||||
\(611\) | −1119.36 | −0.0741151 | ||||||||
\(612\) | −1147.29 | −0.0757782 | ||||||||
\(613\) | 11894.1 | 0.783682 | 0.391841 | − | 0.920033i | \(-0.371838\pi\) | ||||
0.391841 | + | 0.920033i | \(0.371838\pi\) | |||||||
\(614\) | 6915.88 | 0.454564 | ||||||||
\(615\) | −1004.82 | −0.0658835 | ||||||||
\(616\) | −898.793 | −0.0587880 | ||||||||
\(617\) | 24484.4 | 1.59757 | 0.798787 | − | 0.601614i | \(-0.205475\pi\) | ||||
0.798787 | + | 0.601614i | \(0.205475\pi\) | |||||||
\(618\) | −1080.10 | −0.0703042 | ||||||||
\(619\) | −23343.4 | −1.51575 | −0.757876 | − | 0.652399i | \(-0.773763\pi\) | ||||
−0.757876 | + | 0.652399i | \(0.773763\pi\) | |||||||
\(620\) | −6407.44 | −0.415047 | ||||||||
\(621\) | −22648.3 | −1.46352 | ||||||||
\(622\) | −3854.02 | −0.248444 | ||||||||
\(623\) | −2667.33 | −0.171532 | ||||||||
\(624\) | −5742.09 | −0.368377 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 2518.73 | 0.160813 | ||||||||
\(627\) | −1009.10 | −0.0642739 | ||||||||
\(628\) | 6029.51 | 0.383127 | ||||||||
\(629\) | −12402.8 | −0.786221 | ||||||||
\(630\) | 100.426 | 0.00635092 | ||||||||
\(631\) | −19335.8 | −1.21989 | −0.609943 | − | 0.792445i | \(-0.708808\pi\) | ||||
−0.609943 | + | 0.792445i | \(0.708808\pi\) | |||||||
\(632\) | 245.098 | 0.0154264 | ||||||||
\(633\) | −14471.4 | −0.908670 | ||||||||
\(634\) | −8519.13 | −0.533656 | ||||||||
\(635\) | 11809.4 | 0.738018 | ||||||||
\(636\) | −17645.0 | −1.10011 | ||||||||
\(637\) | 9071.26 | 0.564233 | ||||||||
\(638\) | −2000.64 | −0.124148 | ||||||||
\(639\) | −825.082 | −0.0510794 | ||||||||
\(640\) | −7272.20 | −0.449155 | ||||||||
\(641\) | −16829.4 | −1.03701 | −0.518504 | − | 0.855075i | \(-0.673511\pi\) | ||||
−0.518504 | + | 0.855075i | \(0.673511\pi\) | |||||||
\(642\) | −7648.49 | −0.470190 | ||||||||
\(643\) | 3545.10 | 0.217426 | 0.108713 | − | 0.994073i | \(-0.465327\pi\) | ||||
0.108713 | + | 0.994073i | \(0.465327\pi\) | |||||||
\(644\) | 5838.78 | 0.357267 | ||||||||
\(645\) | 7014.56 | 0.428214 | ||||||||
\(646\) | −842.705 | −0.0513248 | ||||||||
\(647\) | 22433.7 | 1.36315 | 0.681577 | − | 0.731747i | \(-0.261295\pi\) | ||||
0.681577 | + | 0.731747i | \(0.261295\pi\) | |||||||
\(648\) | 9225.00 | 0.559247 | ||||||||
\(649\) | −1386.35 | −0.0838505 | ||||||||
\(650\) | −722.852 | −0.0436193 | ||||||||
\(651\) | −4819.16 | −0.290135 | ||||||||
\(652\) | 11959.1 | 0.718334 | ||||||||
\(653\) | 21081.8 | 1.26339 | 0.631696 | − | 0.775216i | \(-0.282359\pi\) | ||||
0.631696 | + | 0.775216i | \(0.282359\pi\) | |||||||
\(654\) | 3211.23 | 0.192002 | ||||||||
\(655\) | −4934.87 | −0.294384 | ||||||||
\(656\) | −1709.35 | −0.101736 | ||||||||
\(657\) | 1013.16 | 0.0601631 | ||||||||
\(658\) | −210.512 | −0.0124720 | ||||||||
\(659\) | −9423.03 | −0.557009 | −0.278505 | − | 0.960435i | \(-0.589839\pi\) | ||||
−0.278505 | + | 0.960435i | \(0.589839\pi\) | |||||||
\(660\) | 1859.69 | 0.109680 | ||||||||
\(661\) | 1328.37 | 0.0781659 | 0.0390829 | − | 0.999236i | \(-0.487556\pi\) | ||||
0.0390829 | + | 0.999236i | \(0.487556\pi\) | |||||||
\(662\) | −7213.64 | −0.423514 | ||||||||
\(663\) | 6210.99 | 0.363823 | ||||||||
\(664\) | 5583.57 | 0.326332 | ||||||||
\(665\) | −518.179 | −0.0302167 | ||||||||
\(666\) | −1028.13 | −0.0598189 | ||||||||
\(667\) | 27843.4 | 1.61634 | ||||||||
\(668\) | 19145.4 | 1.10892 | ||||||||
\(669\) | 21016.3 | 1.21456 | ||||||||
\(670\) | 828.660 | 0.0477820 | ||||||||
\(671\) | −3254.72 | −0.187253 | ||||||||
\(672\) | −4235.96 | −0.243163 | ||||||||
\(673\) | 14340.8 | 0.821390 | 0.410695 | − | 0.911773i | \(-0.365286\pi\) | ||||
0.410695 | + | 0.911773i | \(0.365286\pi\) | |||||||
\(674\) | −7550.60 | −0.431511 | ||||||||
\(675\) | −3704.23 | −0.211224 | ||||||||
\(676\) | 9512.94 | 0.541246 | ||||||||
\(677\) | 5522.39 | 0.313505 | 0.156752 | − | 0.987638i | \(-0.449898\pi\) | ||||
0.156752 | + | 0.987638i | \(0.449898\pi\) | |||||||
\(678\) | 11315.1 | 0.640933 | ||||||||
\(679\) | 4801.55 | 0.271379 | ||||||||
\(680\) | 3327.15 | 0.187633 | ||||||||
\(681\) | −4279.65 | −0.240817 | ||||||||
\(682\) | −2009.78 | −0.112842 | ||||||||
\(683\) | 15232.8 | 0.853395 | 0.426698 | − | 0.904394i | \(-0.359677\pi\) | ||||
0.426698 | + | 0.904394i | \(0.359677\pi\) | |||||||
\(684\) | 490.719 | 0.0274315 | ||||||||
\(685\) | 13257.8 | 0.739495 | ||||||||
\(686\) | 3574.00 | 0.198915 | ||||||||
\(687\) | 20973.4 | 1.16475 | ||||||||
\(688\) | 11932.8 | 0.661240 | ||||||||
\(689\) | −15112.0 | −0.835590 | ||||||||
\(690\) | 3684.40 | 0.203279 | ||||||||
\(691\) | 2107.11 | 0.116003 | 0.0580015 | − | 0.998316i | \(-0.481527\pi\) | ||||
0.0580015 | + | 0.998316i | \(0.481527\pi\) | |||||||
\(692\) | −27114.7 | −1.48952 | ||||||||
\(693\) | −221.279 | −0.0121294 | ||||||||
\(694\) | −7599.97 | −0.415693 | ||||||||
\(695\) | 11801.1 | 0.644086 | ||||||||
\(696\) | −13174.9 | −0.717518 | ||||||||
\(697\) | 1848.93 | 0.100478 | ||||||||
\(698\) | 72.2605 | 0.00391848 | ||||||||
\(699\) | −15917.2 | −0.861293 | ||||||||
\(700\) | 954.961 | 0.0515630 | ||||||||
\(701\) | −26102.8 | −1.40641 | −0.703203 | − | 0.710989i | \(-0.748248\pi\) | ||||
−0.703203 | + | 0.710989i | \(0.748248\pi\) | |||||||
\(702\) | 4284.18 | 0.230336 | ||||||||
\(703\) | 5304.96 | 0.284609 | ||||||||
\(704\) | 1847.40 | 0.0989015 | ||||||||
\(705\) | 933.145 | 0.0498500 | ||||||||
\(706\) | −4358.19 | −0.232327 | ||||||||
\(707\) | 3303.69 | 0.175740 | ||||||||
\(708\) | −4261.46 | −0.226209 | ||||||||
\(709\) | 19669.9 | 1.04192 | 0.520958 | − | 0.853582i | \(-0.325575\pi\) | ||||
0.520958 | + | 0.853582i | \(0.325575\pi\) | |||||||
\(710\) | 1116.88 | 0.0590363 | ||||||||
\(711\) | 60.3421 | 0.00318285 | ||||||||
\(712\) | −7325.38 | −0.385576 | ||||||||
\(713\) | 27970.6 | 1.46916 | ||||||||
\(714\) | 1168.07 | 0.0612239 | ||||||||
\(715\) | 1592.73 | 0.0833072 | ||||||||
\(716\) | 23349.4 | 1.21873 | ||||||||
\(717\) | 29340.8 | 1.52825 | ||||||||
\(718\) | 6084.81 | 0.316272 | ||||||||
\(719\) | −7374.35 | −0.382499 | −0.191250 | − | 0.981541i | \(-0.561254\pi\) | ||||
−0.191250 | + | 0.981541i | \(0.561254\pi\) | |||||||
\(720\) | −757.289 | −0.0391979 | ||||||||
\(721\) | 1222.08 | 0.0631244 | ||||||||
\(722\) | 360.444 | 0.0185794 | ||||||||
\(723\) | 1378.81 | 0.0709244 | ||||||||
\(724\) | −21883.6 | −1.12334 | ||||||||
\(725\) | 4553.93 | 0.233281 | ||||||||
\(726\) | 583.318 | 0.0298195 | ||||||||
\(727\) | −1129.37 | −0.0576148 | −0.0288074 | − | 0.999585i | \(-0.509171\pi\) | ||||
−0.0288074 | + | 0.999585i | \(0.509171\pi\) | |||||||
\(728\) | −2366.17 | −0.120462 | ||||||||
\(729\) | 21586.9 | 1.09673 | ||||||||
\(730\) | −1371.47 | −0.0695350 | ||||||||
\(731\) | −12907.2 | −0.653065 | ||||||||
\(732\) | −10004.6 | −0.505165 | ||||||||
\(733\) | 30429.8 | 1.53336 | 0.766678 | − | 0.642032i | \(-0.221908\pi\) | ||||
0.766678 | + | 0.642032i | \(0.221908\pi\) | |||||||
\(734\) | 7287.93 | 0.366488 | ||||||||
\(735\) | −7562.20 | −0.379505 | ||||||||
\(736\) | 24585.7 | 1.23130 | ||||||||
\(737\) | −1825.87 | −0.0912573 | ||||||||
\(738\) | 153.268 | 0.00764480 | ||||||||
\(739\) | 16230.8 | 0.807928 | 0.403964 | − | 0.914775i | \(-0.367632\pi\) | ||||
0.403964 | + | 0.914775i | \(0.367632\pi\) | |||||||
\(740\) | −9776.60 | −0.485669 | ||||||||
\(741\) | −2656.58 | −0.131703 | ||||||||
\(742\) | −2842.04 | −0.140612 | ||||||||
\(743\) | 21007.2 | 1.03726 | 0.518628 | − | 0.855000i | \(-0.326443\pi\) | ||||
0.518628 | + | 0.855000i | \(0.326443\pi\) | |||||||
\(744\) | −13235.1 | −0.652179 | ||||||||
\(745\) | 3279.24 | 0.161264 | ||||||||
\(746\) | 6046.99 | 0.296777 | ||||||||
\(747\) | 1374.65 | 0.0673304 | ||||||||
\(748\) | −3421.95 | −0.167271 | ||||||||
\(749\) | 8653.90 | 0.422172 | ||||||||
\(750\) | 602.601 | 0.0293385 | ||||||||
\(751\) | −14406.5 | −0.699999 | −0.350000 | − | 0.936750i | \(-0.613818\pi\) | ||||
−0.350000 | + | 0.936750i | \(0.613818\pi\) | |||||||
\(752\) | 1587.42 | 0.0769775 | ||||||||
\(753\) | −21507.8 | −1.04089 | ||||||||
\(754\) | −5266.90 | −0.254389 | ||||||||
\(755\) | −6113.95 | −0.294714 | ||||||||
\(756\) | −5659.84 | −0.272283 | ||||||||
\(757\) | −12943.9 | −0.621474 | −0.310737 | − | 0.950496i | \(-0.600576\pi\) | ||||
−0.310737 | + | 0.950496i | \(0.600576\pi\) | |||||||
\(758\) | 10508.0 | 0.503521 | ||||||||
\(759\) | −8118.19 | −0.388237 | ||||||||
\(760\) | −1423.10 | −0.0679225 | ||||||||
\(761\) | 24426.1 | 1.16353 | 0.581765 | − | 0.813357i | \(-0.302362\pi\) | ||||
0.581765 | + | 0.813357i | \(0.302362\pi\) | |||||||
\(762\) | 11386.2 | 0.541309 | ||||||||
\(763\) | −3633.36 | −0.172394 | ||||||||
\(764\) | −34716.2 | −1.64396 | ||||||||
\(765\) | 819.130 | 0.0387133 | ||||||||
\(766\) | 2554.24 | 0.120481 | ||||||||
\(767\) | −3649.72 | −0.171817 | ||||||||
\(768\) | −524.502 | −0.0246437 | ||||||||
\(769\) | 10766.1 | 0.504860 | 0.252430 | − | 0.967615i | \(-0.418770\pi\) | ||||
0.252430 | + | 0.967615i | \(0.418770\pi\) | |||||||
\(770\) | 299.536 | 0.0140189 | ||||||||
\(771\) | −33945.6 | −1.58563 | ||||||||
\(772\) | −2354.01 | −0.109744 | ||||||||
\(773\) | 4089.46 | 0.190282 | 0.0951409 | − | 0.995464i | \(-0.469670\pi\) | ||||
0.0951409 | + | 0.995464i | \(0.469670\pi\) | |||||||
\(774\) | −1069.94 | −0.0496878 | ||||||||
\(775\) | 4574.73 | 0.212038 | ||||||||
\(776\) | 13186.7 | 0.610019 | ||||||||
\(777\) | −7353.18 | −0.339503 | ||||||||
\(778\) | −4032.46 | −0.185823 | ||||||||
\(779\) | −790.830 | −0.0363728 | ||||||||
\(780\) | 4895.85 | 0.224743 | ||||||||
\(781\) | −2460.93 | −0.112752 | ||||||||
\(782\) | −6779.52 | −0.310019 | ||||||||
\(783\) | −26990.1 | −1.23186 | ||||||||
\(784\) | −12864.4 | −0.586024 | ||||||||
\(785\) | −4304.90 | −0.195730 | ||||||||
\(786\) | −4758.01 | −0.215919 | ||||||||
\(787\) | 8132.48 | 0.368350 | 0.184175 | − | 0.982893i | \(-0.441039\pi\) | ||||
0.184175 | + | 0.982893i | \(0.441039\pi\) | |||||||
\(788\) | 26698.0 | 1.20695 | ||||||||
\(789\) | −23028.9 | −1.03910 | ||||||||
\(790\) | −81.6827 | −0.00367866 | ||||||||
\(791\) | −12802.5 | −0.575478 | ||||||||
\(792\) | −607.707 | −0.0272650 | ||||||||
\(793\) | −8568.40 | −0.383699 | ||||||||
\(794\) | 6396.59 | 0.285903 | ||||||||
\(795\) | 12598.0 | 0.562021 | ||||||||
\(796\) | 2328.81 | 0.103696 | ||||||||
\(797\) | 18215.1 | 0.809553 | 0.404776 | − | 0.914416i | \(-0.367349\pi\) | ||||
0.404776 | + | 0.914416i | \(0.367349\pi\) | |||||||
\(798\) | −499.609 | −0.0221629 | ||||||||
\(799\) | −1717.04 | −0.0760258 | ||||||||
\(800\) | 4021.10 | 0.177709 | ||||||||
\(801\) | −1803.48 | −0.0795539 | ||||||||
\(802\) | 12346.0 | 0.543583 | ||||||||
\(803\) | 3021.90 | 0.132803 | ||||||||
\(804\) | −5612.48 | −0.246190 | ||||||||
\(805\) | −4168.72 | −0.182519 | ||||||||
\(806\) | −5290.96 | −0.231224 | ||||||||
\(807\) | 26618.3 | 1.16110 | ||||||||
\(808\) | 9073.06 | 0.395036 | ||||||||
\(809\) | 26419.1 | 1.14814 | 0.574071 | − | 0.818805i | \(-0.305363\pi\) | ||||
0.574071 | + | 0.818805i | \(0.305363\pi\) | |||||||
\(810\) | −3074.37 | −0.133361 | ||||||||
\(811\) | −23759.4 | −1.02874 | −0.514368 | − | 0.857569i | \(-0.671974\pi\) | ||||
−0.514368 | + | 0.857569i | \(0.671974\pi\) | |||||||
\(812\) | 6958.11 | 0.300717 | ||||||||
\(813\) | 40752.5 | 1.75800 | ||||||||
\(814\) | −3066.56 | −0.132043 | ||||||||
\(815\) | −8538.45 | −0.366980 | ||||||||
\(816\) | −8808.11 | −0.377875 | ||||||||
\(817\) | 5520.70 | 0.236407 | ||||||||
\(818\) | −8530.80 | −0.364636 | ||||||||
\(819\) | −582.540 | −0.0248542 | ||||||||
\(820\) | 1457.43 | 0.0620680 | ||||||||
\(821\) | −17542.7 | −0.745731 | −0.372865 | − | 0.927885i | \(-0.621625\pi\) | ||||
−0.372865 | + | 0.927885i | \(0.621625\pi\) | |||||||
\(822\) | 12782.7 | 0.542392 | ||||||||
\(823\) | 8113.49 | 0.343643 | 0.171822 | − | 0.985128i | \(-0.445035\pi\) | ||||
0.171822 | + | 0.985128i | \(0.445035\pi\) | |||||||
\(824\) | 3356.25 | 0.141894 | ||||||||
\(825\) | −1327.77 | −0.0560327 | ||||||||
\(826\) | −686.383 | −0.0289132 | ||||||||
\(827\) | −29229.7 | −1.22904 | −0.614520 | − | 0.788901i | \(-0.710650\pi\) | ||||
−0.614520 | + | 0.788901i | \(0.710650\pi\) | |||||||
\(828\) | 3947.81 | 0.165696 | ||||||||
\(829\) | 45007.9 | 1.88563 | 0.942816 | − | 0.333312i | \(-0.108166\pi\) | ||||
0.942816 | + | 0.333312i | \(0.108166\pi\) | |||||||
\(830\) | −1860.81 | −0.0778188 | ||||||||
\(831\) | −7625.38 | −0.318317 | ||||||||
\(832\) | 4863.49 | 0.202658 | ||||||||
\(833\) | 13914.9 | 0.578779 | ||||||||
\(834\) | 11378.1 | 0.472413 | ||||||||
\(835\) | −13669.3 | −0.566520 | ||||||||
\(836\) | 1463.64 | 0.0605516 | ||||||||
\(837\) | −27113.4 | −1.11968 | ||||||||
\(838\) | 5160.30 | 0.212720 | ||||||||
\(839\) | 28183.2 | 1.15970 | 0.579852 | − | 0.814722i | \(-0.303110\pi\) | ||||
0.579852 | + | 0.814722i | \(0.303110\pi\) | |||||||
\(840\) | 1972.54 | 0.0810229 | ||||||||
\(841\) | 8792.22 | 0.360499 | ||||||||
\(842\) | 10435.0 | 0.427094 | ||||||||
\(843\) | 43185.9 | 1.76441 | ||||||||
\(844\) | 20989.9 | 0.856046 | ||||||||
\(845\) | −6791.97 | −0.276510 | ||||||||
\(846\) | −142.335 | −0.00578435 | ||||||||
\(847\) | −659.997 | −0.0267742 | ||||||||
\(848\) | 21431.1 | 0.867861 | ||||||||
\(849\) | 22239.8 | 0.899020 | ||||||||
\(850\) | −1108.82 | −0.0447439 | ||||||||
\(851\) | 42678.1 | 1.71914 | ||||||||
\(852\) | −7564.59 | −0.304177 | ||||||||
\(853\) | −37984.9 | −1.52471 | −0.762356 | − | 0.647158i | \(-0.775957\pi\) | ||||
−0.762356 | + | 0.647158i | \(0.775957\pi\) | |||||||
\(854\) | −1611.42 | −0.0645685 | ||||||||
\(855\) | −350.360 | −0.0140141 | ||||||||
\(856\) | 23766.5 | 0.948977 | ||||||||
\(857\) | 26097.6 | 1.04023 | 0.520115 | − | 0.854096i | \(-0.325889\pi\) | ||||
0.520115 | + | 0.854096i | \(0.325889\pi\) | |||||||
\(858\) | 1535.65 | 0.0611027 | ||||||||
\(859\) | 13130.6 | 0.521548 | 0.260774 | − | 0.965400i | \(-0.416022\pi\) | ||||
0.260774 | + | 0.965400i | \(0.416022\pi\) | |||||||
\(860\) | −10174.2 | −0.403415 | ||||||||
\(861\) | 1096.16 | 0.0433881 | ||||||||
\(862\) | −12989.8 | −0.513263 | ||||||||
\(863\) | 6736.45 | 0.265714 | 0.132857 | − | 0.991135i | \(-0.457585\pi\) | ||||
0.132857 | + | 0.991135i | \(0.457585\pi\) | |||||||
\(864\) | −23832.2 | −0.938411 | ||||||||
\(865\) | 19359.1 | 0.760960 | ||||||||
\(866\) | 4221.76 | 0.165660 | ||||||||
\(867\) | −14193.8 | −0.555994 | ||||||||
\(868\) | 6989.90 | 0.273333 | ||||||||
\(869\) | 179.979 | 0.00702575 | ||||||||
\(870\) | 4390.72 | 0.171103 | ||||||||
\(871\) | −4806.79 | −0.186994 | ||||||||
\(872\) | −9978.43 | −0.387514 | ||||||||
\(873\) | 3246.50 | 0.125862 | ||||||||
\(874\) | 2899.75 | 0.112226 | ||||||||
\(875\) | −681.815 | −0.0263423 | ||||||||
\(876\) | 9288.94 | 0.358270 | ||||||||
\(877\) | −10543.4 | −0.405959 | −0.202979 | − | 0.979183i | \(-0.565062\pi\) | ||||
−0.202979 | + | 0.979183i | \(0.565062\pi\) | |||||||
\(878\) | 3560.73 | 0.136867 | ||||||||
\(879\) | 31978.2 | 1.22707 | ||||||||
\(880\) | −2258.73 | −0.0865246 | ||||||||
\(881\) | 44371.6 | 1.69684 | 0.848420 | − | 0.529323i | \(-0.177554\pi\) | ||||
0.848420 | + | 0.529323i | \(0.177554\pi\) | |||||||
\(882\) | 1153.48 | 0.0440359 | ||||||||
\(883\) | −6983.35 | −0.266148 | −0.133074 | − | 0.991106i | \(-0.542485\pi\) | ||||
−0.133074 | + | 0.991106i | \(0.542485\pi\) | |||||||
\(884\) | −9008.66 | −0.342753 | ||||||||
\(885\) | 3042.56 | 0.115565 | ||||||||
\(886\) | −1677.45 | −0.0636062 | ||||||||
\(887\) | 58.6566 | 0.00222040 | 0.00111020 | − | 0.999999i | \(-0.499647\pi\) | ||||
0.00111020 | + | 0.999999i | \(0.499647\pi\) | |||||||
\(888\) | −20194.3 | −0.763150 | ||||||||
\(889\) | −12882.9 | −0.486028 | ||||||||
\(890\) | 2441.29 | 0.0919465 | ||||||||
\(891\) | 6774.05 | 0.254702 | ||||||||
\(892\) | −30482.9 | −1.14422 | ||||||||
\(893\) | 734.418 | 0.0275211 | ||||||||
\(894\) | 3161.72 | 0.118281 | ||||||||
\(895\) | −16670.8 | −0.622619 | ||||||||
\(896\) | 7933.27 | 0.295795 | ||||||||
\(897\) | −21372.0 | −0.795530 | ||||||||
\(898\) | −13684.1 | −0.508514 | ||||||||
\(899\) | 33332.8 | 1.23661 | ||||||||
\(900\) | 645.684 | 0.0239142 | ||||||||
\(901\) | −23181.2 | −0.857132 | ||||||||
\(902\) | 457.143 | 0.0168750 | ||||||||
\(903\) | −7652.20 | −0.282004 | ||||||||
\(904\) | −35159.9 | −1.29359 | ||||||||
\(905\) | 15624.2 | 0.573886 | ||||||||
\(906\) | −5894.84 | −0.216162 | ||||||||
\(907\) | −8790.86 | −0.321825 | −0.160913 | − | 0.986969i | \(-0.551444\pi\) | ||||
−0.160913 | + | 0.986969i | \(0.551444\pi\) | |||||||
\(908\) | 6207.36 | 0.226871 | ||||||||
\(909\) | 2233.75 | 0.0815057 | ||||||||
\(910\) | 788.561 | 0.0287259 | ||||||||
\(911\) | 11883.6 | 0.432188 | 0.216094 | − | 0.976373i | \(-0.430668\pi\) | ||||
0.216094 | + | 0.976373i | \(0.430668\pi\) | |||||||
\(912\) | 3767.42 | 0.136789 | ||||||||
\(913\) | 4100.10 | 0.148624 | ||||||||
\(914\) | −16048.7 | −0.580791 | ||||||||
\(915\) | 7143.00 | 0.258077 | ||||||||
\(916\) | −30420.6 | −1.09730 | ||||||||
\(917\) | 5383.46 | 0.193869 | ||||||||
\(918\) | 6571.74 | 0.236274 | ||||||||
\(919\) | −45359.0 | −1.62813 | −0.814067 | − | 0.580770i | \(-0.802751\pi\) | ||||
−0.814067 | + | 0.580770i | \(0.802751\pi\) | |||||||
\(920\) | −11448.7 | −0.410275 | ||||||||
\(921\) | 33443.1 | 1.19651 | ||||||||
\(922\) | −1553.57 | −0.0554924 | ||||||||
\(923\) | −6478.67 | −0.231038 | ||||||||
\(924\) | −2028.75 | −0.0722304 | ||||||||
\(925\) | 6980.21 | 0.248117 | ||||||||
\(926\) | −9634.44 | −0.341909 | ||||||||
\(927\) | 826.294 | 0.0292762 | ||||||||
\(928\) | 29298.9 | 1.03640 | ||||||||
\(929\) | 11907.7 | 0.420536 | 0.210268 | − | 0.977644i | \(-0.432566\pi\) | ||||
0.210268 | + | 0.977644i | \(0.432566\pi\) | |||||||
\(930\) | 4410.78 | 0.155522 | ||||||||
\(931\) | −5951.72 | −0.209516 | ||||||||
\(932\) | 23086.9 | 0.811413 | ||||||||
\(933\) | −18636.9 | −0.653960 | ||||||||
\(934\) | 13872.7 | 0.486003 | ||||||||
\(935\) | 2443.18 | 0.0854550 | ||||||||
\(936\) | −1599.85 | −0.0558684 | ||||||||
\(937\) | 10362.9 | 0.361303 | 0.180651 | − | 0.983547i | \(-0.442179\pi\) | ||||
0.180651 | + | 0.983547i | \(0.442179\pi\) | |||||||
\(938\) | −903.988 | −0.0314672 | ||||||||
\(939\) | 12179.9 | 0.423295 | ||||||||
\(940\) | −1353.47 | −0.0469631 | ||||||||
\(941\) | −39616.2 | −1.37243 | −0.686213 | − | 0.727401i | \(-0.740728\pi\) | ||||
−0.686213 | + | 0.727401i | \(0.740728\pi\) | |||||||
\(942\) | −4150.62 | −0.143561 | ||||||||
\(943\) | −6362.18 | −0.219704 | ||||||||
\(944\) | 5175.84 | 0.178453 | ||||||||
\(945\) | 4040.96 | 0.139103 | ||||||||
\(946\) | −3191.27 | −0.109680 | ||||||||
\(947\) | −40101.9 | −1.37607 | −0.688034 | − | 0.725678i | \(-0.741526\pi\) | ||||
−0.688034 | + | 0.725678i | \(0.741526\pi\) | |||||||
\(948\) | 553.234 | 0.0189538 | ||||||||
\(949\) | 7955.48 | 0.272124 | ||||||||
\(950\) | 474.268 | 0.0161971 | ||||||||
\(951\) | −41196.0 | −1.40470 | ||||||||
\(952\) | −3629.60 | −0.123567 | ||||||||
\(953\) | 43628.0 | 1.48295 | 0.741475 | − | 0.670981i | \(-0.234127\pi\) | ||||
0.741475 | + | 0.670981i | \(0.234127\pi\) | |||||||
\(954\) | −1921.60 | −0.0652141 | ||||||||
\(955\) | 24786.4 | 0.839862 | ||||||||
\(956\) | −42557.1 | −1.43974 | ||||||||
\(957\) | −9674.50 | −0.326784 | ||||||||
\(958\) | −17238.7 | −0.581375 | ||||||||
\(959\) | −14463.0 | −0.487001 | ||||||||
\(960\) | −4054.42 | −0.136308 | ||||||||
\(961\) | 3694.06 | 0.123999 | ||||||||
\(962\) | −8073.06 | −0.270567 | ||||||||
\(963\) | 5851.22 | 0.195797 | ||||||||
\(964\) | −1999.87 | −0.0668170 | ||||||||
\(965\) | 1680.69 | 0.0560657 | ||||||||
\(966\) | −4019.32 | −0.133871 | ||||||||
\(967\) | 38617.4 | 1.28423 | 0.642116 | − | 0.766607i | \(-0.278057\pi\) | ||||
0.642116 | + | 0.766607i | \(0.278057\pi\) | |||||||
\(968\) | −1812.57 | −0.0601843 | ||||||||
\(969\) | −4075.07 | −0.135098 | ||||||||
\(970\) | −4394.66 | −0.145468 | ||||||||
\(971\) | 18200.4 | 0.601521 | 0.300761 | − | 0.953700i | \(-0.402759\pi\) | ||||
0.300761 | + | 0.953700i | \(0.402759\pi\) | |||||||
\(972\) | −7193.74 | −0.237386 | ||||||||
\(973\) | −12873.8 | −0.424168 | ||||||||
\(974\) | −17504.9 | −0.575864 | ||||||||
\(975\) | −3495.50 | −0.114816 | ||||||||
\(976\) | 12151.3 | 0.398517 | ||||||||
\(977\) | 30881.1 | 1.01123 | 0.505617 | − | 0.862758i | \(-0.331265\pi\) | ||||
0.505617 | + | 0.862758i | \(0.331265\pi\) | |||||||
\(978\) | −8232.44 | −0.269166 | ||||||||
\(979\) | −5379.14 | −0.175606 | ||||||||
\(980\) | 10968.5 | 0.357527 | ||||||||
\(981\) | −2456.64 | −0.0799537 | ||||||||
\(982\) | −5689.14 | −0.184876 | ||||||||
\(983\) | 54916.6 | 1.78186 | 0.890929 | − | 0.454143i | \(-0.150054\pi\) | ||||
0.890929 | + | 0.454143i | \(0.150054\pi\) | |||||||
\(984\) | 3010.44 | 0.0975298 | ||||||||
\(985\) | −19061.6 | −0.616603 | ||||||||
\(986\) | −8079.20 | −0.260947 | ||||||||
\(987\) | −1017.97 | −0.0328292 | ||||||||
\(988\) | 3853.20 | 0.124076 | ||||||||
\(989\) | 44413.7 | 1.42798 | ||||||||
\(990\) | 202.527 | 0.00650176 | ||||||||
\(991\) | 52780.6 | 1.69186 | 0.845929 | − | 0.533296i | \(-0.179047\pi\) | ||||
0.845929 | + | 0.533296i | \(0.179047\pi\) | |||||||
\(992\) | 29432.7 | 0.942027 | ||||||||
\(993\) | −34883.0 | −1.11478 | ||||||||
\(994\) | −1218.41 | −0.0388789 | ||||||||
\(995\) | −1662.70 | −0.0529760 | ||||||||
\(996\) | 12603.2 | 0.400951 | ||||||||
\(997\) | −54096.9 | −1.71842 | −0.859211 | − | 0.511622i | \(-0.829045\pi\) | ||||
−0.859211 | + | 0.511622i | \(0.829045\pi\) | |||||||
\(998\) | −1511.02 | −0.0479263 | ||||||||
\(999\) | −41370.2 | −1.31020 |
(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 | 1045.4.a.h.1.14 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.4.a.h.1.14 | ✓ | 24 | 1.1 | even | 1 | trivial |