Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,4,Mod(1,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, 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("441.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.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: | \(26.0198423125\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 147) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.41421 | −0.853553 | −0.426777 | − | 0.904357i | \(-0.640351\pi\) | ||||
−0.426777 | + | 0.904357i | \(0.640351\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.17157 | −0.271447 | ||||||||
\(5\) | 19.8995 | 1.77986 | 0.889932 | − | 0.456092i | \(-0.150751\pi\) | ||||
0.889932 | + | 0.456092i | \(0.150751\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 24.5563 | 1.08525 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −48.0416 | −1.51921 | ||||||||
\(11\) | −23.9411 | −0.656229 | −0.328115 | − | 0.944638i | \(-0.606413\pi\) | ||||
−0.328115 | + | 0.944638i | \(0.606413\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −87.3553 | −1.86369 | −0.931847 | − | 0.362852i | \(-0.881803\pi\) | ||||
−0.931847 | + | 0.362852i | \(0.881803\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −41.9117 | −0.654870 | ||||||||
\(17\) | −5.63961 | −0.0804592 | −0.0402296 | − | 0.999190i | \(-0.512809\pi\) | ||||
−0.0402296 | + | 0.999190i | \(0.512809\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −64.8873 | −0.783483 | −0.391741 | − | 0.920075i | \(-0.628127\pi\) | ||||
−0.391741 | + | 0.920075i | \(0.628127\pi\) | |||||||
\(20\) | −43.2132 | −0.483138 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 57.7990 | 0.560127 | ||||||||
\(23\) | 25.5980 | 0.232067 | 0.116034 | − | 0.993245i | \(-0.462982\pi\) | ||||
0.116034 | + | 0.993245i | \(0.462982\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 270.990 | 2.16792 | ||||||||
\(26\) | 210.894 | 1.59076 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −60.3188 | −0.386238 | −0.193119 | − | 0.981175i | \(-0.561860\pi\) | ||||
−0.193119 | + | 0.981175i | \(0.561860\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 122.711 | 0.710951 | 0.355476 | − | 0.934686i | \(-0.384319\pi\) | ||||
0.355476 | + | 0.934686i | \(0.384319\pi\) | |||||||
\(32\) | −95.2670 | −0.526281 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 13.6152 | 0.0686762 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −56.1177 | −0.249343 | −0.124672 | − | 0.992198i | \(-0.539788\pi\) | ||||
−0.124672 | + | 0.992198i | \(0.539788\pi\) | |||||||
\(38\) | 156.652 | 0.668744 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 488.659 | 1.93159 | ||||||||
\(41\) | −299.713 | −1.14164 | −0.570820 | − | 0.821075i | \(-0.693375\pi\) | ||||
−0.570820 | + | 0.821075i | \(0.693375\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −501.421 | −1.77828 | −0.889140 | − | 0.457635i | \(-0.848697\pi\) | ||||
−0.889140 | + | 0.457635i | \(0.848697\pi\) | |||||||
\(44\) | 51.9899 | 0.178131 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −61.7990 | −0.198082 | ||||||||
\(47\) | 305.553 | 0.948288 | 0.474144 | − | 0.880447i | \(-0.342758\pi\) | ||||
0.474144 | + | 0.880447i | \(0.342758\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −654.227 | −1.85043 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 189.698 | 0.505893 | ||||||||
\(53\) | 375.117 | 0.972194 | 0.486097 | − | 0.873905i | \(-0.338420\pi\) | ||||
0.486097 | + | 0.873905i | \(0.338420\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −476.416 | −1.16800 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 145.622 | 0.329675 | ||||||||
\(59\) | −627.612 | −1.38488 | −0.692442 | − | 0.721474i | \(-0.743465\pi\) | ||||
−0.692442 | + | 0.721474i | \(0.743465\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.75736 | −0.00788657 | −0.00394328 | − | 0.999992i | \(-0.501255\pi\) | ||||
−0.00394328 | + | 0.999992i | \(0.501255\pi\) | |||||||
\(62\) | −296.250 | −0.606835 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 565.288 | 1.10408 | ||||||||
\(65\) | −1738.33 | −3.31712 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −813.048 | −1.48253 | −0.741266 | − | 0.671212i | \(-0.765774\pi\) | ||||
−0.741266 | + | 0.671212i | \(0.765774\pi\) | |||||||
\(68\) | 12.2468 | 0.0218404 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −165.902 | −0.277310 | −0.138655 | − | 0.990341i | \(-0.544278\pi\) | ||||
−0.138655 | + | 0.990341i | \(0.544278\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −619.100 | −0.992605 | −0.496302 | − | 0.868150i | \(-0.665309\pi\) | ||||
−0.496302 | + | 0.868150i | \(0.665309\pi\) | |||||||
\(74\) | 135.480 | 0.212828 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 140.908 | 0.212674 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −138.246 | −0.196884 | −0.0984421 | − | 0.995143i | \(-0.531386\pi\) | ||||
−0.0984421 | + | 0.995143i | \(0.531386\pi\) | |||||||
\(80\) | −834.021 | −1.16558 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 723.571 | 0.974451 | ||||||||
\(83\) | 621.137 | 0.821430 | 0.410715 | − | 0.911764i | \(-0.365279\pi\) | ||||
0.410715 | + | 0.911764i | \(0.365279\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −112.225 | −0.143207 | ||||||||
\(86\) | 1210.54 | 1.51786 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −587.907 | −0.712171 | ||||||||
\(89\) | 285.418 | 0.339936 | 0.169968 | − | 0.985450i | \(-0.445634\pi\) | ||||
0.169968 | + | 0.985450i | \(0.445634\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −55.5879 | −0.0629939 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −737.671 | −0.809415 | ||||||||
\(95\) | −1291.22 | −1.39449 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 603.114 | 0.631309 | 0.315654 | − | 0.948874i | \(-0.397776\pi\) | ||||
0.315654 | + | 0.948874i | \(0.397776\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −588.474 | −0.588474 | ||||||||
\(101\) | 457.209 | 0.450436 | 0.225218 | − | 0.974308i | \(-0.427691\pi\) | ||||
0.225218 | + | 0.974308i | \(0.427691\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −786.045 | −0.751954 | −0.375977 | − | 0.926629i | \(-0.622693\pi\) | ||||
−0.375977 | + | 0.926629i | \(0.622693\pi\) | |||||||
\(104\) | −2145.13 | −2.02257 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −905.612 | −0.829819 | ||||||||
\(107\) | 196.461 | 0.177501 | 0.0887504 | − | 0.996054i | \(-0.471713\pi\) | ||||
0.0887504 | + | 0.996054i | \(0.471713\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −306.343 | −0.269196 | −0.134598 | − | 0.990900i | \(-0.542974\pi\) | ||||
−0.134598 | + | 0.990900i | \(0.542974\pi\) | |||||||
\(110\) | 1150.17 | 0.996950 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1997.63 | −1.66302 | −0.831508 | − | 0.555512i | \(-0.812522\pi\) | ||||
−0.831508 | + | 0.555512i | \(0.812522\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 509.387 | 0.413048 | ||||||||
\(116\) | 130.987 | 0.104843 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1515.19 | 1.18207 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −757.823 | −0.569363 | ||||||||
\(122\) | 9.07107 | 0.00673161 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −266.475 | −0.192985 | ||||||||
\(125\) | 2905.13 | 2.07874 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2311.40 | −1.61499 | −0.807494 | − | 0.589875i | \(-0.799177\pi\) | ||||
−0.807494 | + | 0.589875i | \(0.799177\pi\) | |||||||
\(128\) | −602.591 | −0.416109 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4196.69 | 2.83134 | ||||||||
\(131\) | −155.018 | −0.103389 | −0.0516945 | − | 0.998663i | \(-0.516462\pi\) | ||||
−0.0516945 | + | 0.998663i | \(0.516462\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1962.87 | 1.26542 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −138.488 | −0.0873182 | ||||||||
\(137\) | −516.936 | −0.322371 | −0.161186 | − | 0.986924i | \(-0.551532\pi\) | ||||
−0.161186 | + | 0.986924i | \(0.551532\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −958.067 | −0.584620 | −0.292310 | − | 0.956324i | \(-0.594424\pi\) | ||||
−0.292310 | + | 0.956324i | \(0.594424\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 400.524 | 0.236699 | ||||||||
\(143\) | 2091.39 | 1.22301 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1200.31 | −0.687452 | ||||||||
\(146\) | 1494.64 | 0.847241 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 121.864 | 0.0676834 | ||||||||
\(149\) | 1770.63 | 0.973526 | 0.486763 | − | 0.873534i | \(-0.338178\pi\) | ||||
0.486763 | + | 0.873534i | \(0.338178\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2540.24 | −1.36902 | −0.684508 | − | 0.729005i | \(-0.739983\pi\) | ||||
−0.684508 | + | 0.729005i | \(0.739983\pi\) | |||||||
\(152\) | −1593.40 | −0.850272 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2441.88 | 1.26540 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1083.34 | 0.550702 | 0.275351 | − | 0.961344i | \(-0.411206\pi\) | ||||
0.275351 | + | 0.961344i | \(0.411206\pi\) | |||||||
\(158\) | 333.754 | 0.168051 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1895.77 | −0.936709 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2968.72 | 1.42655 | 0.713277 | − | 0.700882i | \(-0.247210\pi\) | ||||
0.713277 | + | 0.700882i | \(0.247210\pi\) | |||||||
\(164\) | 650.848 | 0.309895 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1499.56 | −0.701134 | ||||||||
\(167\) | −2091.53 | −0.969149 | −0.484574 | − | 0.874750i | \(-0.661025\pi\) | ||||
−0.484574 | + | 0.874750i | \(0.661025\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5433.96 | 2.47335 | ||||||||
\(170\) | 270.936 | 0.122234 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1088.87 | 0.482708 | ||||||||
\(173\) | −470.148 | −0.206617 | −0.103308 | − | 0.994649i | \(-0.532943\pi\) | ||||
−0.103308 | + | 0.994649i | \(0.532943\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1003.41 | 0.429745 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −689.061 | −0.290153 | ||||||||
\(179\) | −1056.46 | −0.441137 | −0.220569 | − | 0.975371i | \(-0.570791\pi\) | ||||
−0.220569 | + | 0.975371i | \(0.570791\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 406.470 | 0.166921 | 0.0834605 | − | 0.996511i | \(-0.473403\pi\) | ||||
0.0834605 | + | 0.996511i | \(0.473403\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 628.593 | 0.251850 | ||||||||
\(185\) | −1116.71 | −0.443797 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 135.019 | 0.0527997 | ||||||||
\(188\) | −663.531 | −0.257410 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3117.29 | 1.19027 | ||||||||
\(191\) | −179.410 | −0.0679666 | −0.0339833 | − | 0.999422i | \(-0.510819\pi\) | ||||
−0.0339833 | + | 0.999422i | \(0.510819\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2388.37 | −0.890769 | −0.445385 | − | 0.895339i | \(-0.646933\pi\) | ||||
−0.445385 | + | 0.895339i | \(0.646933\pi\) | |||||||
\(194\) | −1456.05 | −0.538856 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2665.35 | 0.963952 | 0.481976 | − | 0.876184i | \(-0.339919\pi\) | ||||
0.481976 | + | 0.876184i | \(0.339919\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1342.31 | 0.478159 | 0.239079 | − | 0.971000i | \(-0.423154\pi\) | ||||
0.239079 | + | 0.971000i | \(0.423154\pi\) | |||||||
\(200\) | 6654.52 | 2.35273 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1103.80 | −0.384471 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5964.13 | −2.03197 | ||||||||
\(206\) | 1897.68 | 0.641833 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3661.21 | 1.22048 | ||||||||
\(209\) | 1553.48 | 0.514144 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 628.442 | 0.205042 | 0.102521 | − | 0.994731i | \(-0.467309\pi\) | ||||
0.102521 | + | 0.994731i | \(0.467309\pi\) | |||||||
\(212\) | −814.594 | −0.263899 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −474.299 | −0.151506 | ||||||||
\(215\) | −9978.03 | −3.16510 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 739.578 | 0.229773 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1034.57 | 0.317049 | ||||||||
\(221\) | 492.650 | 0.149951 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 969.970 | 0.291273 | 0.145637 | − | 0.989338i | \(-0.453477\pi\) | ||||
0.145637 | + | 0.989338i | \(0.453477\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4822.70 | 1.41947 | ||||||||
\(227\) | −4748.64 | −1.38845 | −0.694225 | − | 0.719758i | \(-0.744253\pi\) | ||||
−0.694225 | + | 0.719758i | \(0.744253\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4801.99 | 1.38570 | 0.692848 | − | 0.721083i | \(-0.256356\pi\) | ||||
0.692848 | + | 0.721083i | \(0.256356\pi\) | |||||||
\(230\) | −1229.77 | −0.352559 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1481.21 | −0.419164 | ||||||||
\(233\) | 3155.29 | 0.887166 | 0.443583 | − | 0.896233i | \(-0.353707\pi\) | ||||
0.443583 | + | 0.896233i | \(0.353707\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6080.36 | 1.68782 | ||||||||
\(236\) | 1362.91 | 0.375922 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4241.93 | −1.14806 | −0.574032 | − | 0.818833i | \(-0.694622\pi\) | ||||
−0.574032 | + | 0.818833i | \(0.694622\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4342.99 | 1.16081 | 0.580407 | − | 0.814326i | \(-0.302893\pi\) | ||||
0.580407 | + | 0.814326i | \(0.302893\pi\) | |||||||
\(242\) | 1829.55 | 0.485982 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 8.15938 | 0.00214078 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5668.25 | 1.46017 | ||||||||
\(248\) | 3013.33 | 0.771558 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −7013.59 | −1.77431 | ||||||||
\(251\) | 3003.01 | 0.755172 | 0.377586 | − | 0.925974i | \(-0.376754\pi\) | ||||
0.377586 | + | 0.925974i | \(0.376754\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −612.844 | −0.152289 | ||||||||
\(254\) | 5580.21 | 1.37848 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3067.52 | −0.748907 | ||||||||
\(257\) | 4468.84 | 1.08466 | 0.542332 | − | 0.840164i | \(-0.317541\pi\) | ||||
0.542332 | + | 0.840164i | \(0.317541\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 3774.90 | 0.900422 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 374.246 | 0.0882480 | ||||||||
\(263\) | −6160.13 | −1.44430 | −0.722148 | − | 0.691738i | \(-0.756845\pi\) | ||||
−0.722148 | + | 0.691738i | \(0.756845\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7464.64 | 1.73037 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1765.59 | 0.402428 | ||||||||
\(269\) | 4988.90 | 1.13078 | 0.565388 | − | 0.824825i | \(-0.308726\pi\) | ||||
0.565388 | + | 0.824825i | \(0.308726\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4433.73 | −0.993837 | −0.496918 | − | 0.867797i | \(-0.665535\pi\) | ||||
−0.496918 | + | 0.867797i | \(0.665535\pi\) | |||||||
\(272\) | 236.366 | 0.0526903 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1247.99 | 0.275161 | ||||||||
\(275\) | −6487.80 | −1.42265 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1112.37 | 0.241284 | 0.120642 | − | 0.992696i | \(-0.461505\pi\) | ||||
0.120642 | + | 0.992696i | \(0.461505\pi\) | |||||||
\(278\) | 2312.98 | 0.499005 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2813.22 | −0.597233 | −0.298616 | − | 0.954373i | \(-0.596525\pi\) | ||||
−0.298616 | + | 0.954373i | \(0.596525\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3147.54 | −0.661137 | −0.330569 | − | 0.943782i | \(-0.607241\pi\) | ||||
−0.330569 | + | 0.943782i | \(0.607241\pi\) | |||||||
\(284\) | 360.269 | 0.0752748 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5049.05 | −1.04390 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4881.19 | −0.993526 | ||||||||
\(290\) | 2897.81 | 0.586777 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1344.42 | 0.269439 | ||||||||
\(293\) | 9143.04 | 1.82301 | 0.911505 | − | 0.411289i | \(-0.134921\pi\) | ||||
0.911505 | + | 0.411289i | \(0.134921\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12489.2 | −2.46491 | ||||||||
\(296\) | −1378.05 | −0.270599 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4274.67 | −0.830956 | ||||||||
\(299\) | −2236.12 | −0.432502 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 6132.67 | 1.16853 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2719.54 | 0.513079 | ||||||||
\(305\) | −74.7696 | −0.0140370 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4648.90 | 0.864257 | 0.432129 | − | 0.901812i | \(-0.357763\pi\) | ||||
0.432129 | + | 0.901812i | \(0.357763\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5895.22 | −1.08008 | ||||||||
\(311\) | −6417.18 | −1.17005 | −0.585024 | − | 0.811016i | \(-0.698915\pi\) | ||||
−0.585024 | + | 0.811016i | \(0.698915\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5868.22 | −1.05972 | −0.529858 | − | 0.848086i | \(-0.677755\pi\) | ||||
−0.529858 | + | 0.848086i | \(0.677755\pi\) | |||||||
\(314\) | −2615.42 | −0.470054 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 300.210 | 0.0534435 | ||||||||
\(317\) | 3974.52 | 0.704200 | 0.352100 | − | 0.935962i | \(-0.385468\pi\) | ||||
0.352100 | + | 0.935962i | \(0.385468\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1444.10 | 0.253461 | ||||||||
\(320\) | 11249.0 | 1.96511 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 365.939 | 0.0630384 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −23672.4 | −4.04034 | ||||||||
\(326\) | −7167.13 | −1.21764 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −7359.85 | −1.23896 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8912.82 | −1.48004 | −0.740020 | − | 0.672585i | \(-0.765184\pi\) | ||||
−0.740020 | + | 0.672585i | \(0.765184\pi\) | |||||||
\(332\) | −1348.84 | −0.222974 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5049.41 | 0.827220 | ||||||||
\(335\) | −16179.2 | −2.63871 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3977.06 | 0.642862 | 0.321431 | − | 0.946933i | \(-0.395836\pi\) | ||||
0.321431 | + | 0.946933i | \(0.395836\pi\) | |||||||
\(338\) | −13118.7 | −2.11114 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 243.706 | 0.0388729 | ||||||||
\(341\) | −2937.83 | −0.466547 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −12313.1 | −1.92987 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1135.04 | 0.176358 | ||||||||
\(347\) | −6826.43 | −1.05609 | −0.528043 | − | 0.849218i | \(-0.677074\pi\) | ||||
−0.528043 | + | 0.849218i | \(0.677074\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 807.342 | 0.123828 | 0.0619141 | − | 0.998081i | \(-0.480280\pi\) | ||||
0.0619141 | + | 0.998081i | \(0.480280\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2280.80 | 0.345361 | ||||||||
\(353\) | −7919.20 | −1.19404 | −0.597020 | − | 0.802226i | \(-0.703649\pi\) | ||||
−0.597020 | + | 0.802226i | \(0.703649\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3301.38 | −0.493574 | ||||||||
\(356\) | −619.807 | −0.0922744 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2550.52 | 0.376534 | ||||||||
\(359\) | 8819.21 | 1.29655 | 0.648273 | − | 0.761408i | \(-0.275491\pi\) | ||||
0.648273 | + | 0.761408i | \(0.275491\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2648.64 | −0.386155 | ||||||||
\(362\) | −981.307 | −0.142476 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12319.8 | −1.76670 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11161.8 | 1.58758 | 0.793788 | − | 0.608194i | \(-0.208106\pi\) | ||||
0.793788 | + | 0.608194i | \(0.208106\pi\) | |||||||
\(368\) | −1072.85 | −0.151974 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2695.99 | 0.378805 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2727.86 | 0.378668 | 0.189334 | − | 0.981913i | \(-0.439367\pi\) | ||||
0.189334 | + | 0.981913i | \(0.439367\pi\) | |||||||
\(374\) | −325.964 | −0.0450673 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7503.28 | 1.02913 | ||||||||
\(377\) | 5269.17 | 0.719830 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4086.49 | 0.553849 | 0.276924 | − | 0.960892i | \(-0.410685\pi\) | ||||
0.276924 | + | 0.960892i | \(0.410685\pi\) | |||||||
\(380\) | 2803.99 | 0.378530 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 433.133 | 0.0580131 | ||||||||
\(383\) | 13032.9 | 1.73878 | 0.869389 | − | 0.494129i | \(-0.164513\pi\) | ||||
0.869389 | + | 0.494129i | \(0.164513\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5766.03 | 0.760319 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1309.71 | −0.171367 | ||||||||
\(389\) | 194.991 | 0.0254151 | 0.0127075 | − | 0.999919i | \(-0.495955\pi\) | ||||
0.0127075 | + | 0.999919i | \(0.495955\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −144.363 | −0.0186719 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6434.73 | −0.822785 | ||||||||
\(395\) | −2751.02 | −0.350427 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14183.0 | 1.79300 | 0.896501 | − | 0.443042i | \(-0.146101\pi\) | ||||
0.896501 | + | 0.443042i | \(0.146101\pi\) | |||||||
\(398\) | −3240.61 | −0.408134 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −11357.6 | −1.41971 | ||||||||
\(401\) | −10005.0 | −1.24596 | −0.622978 | − | 0.782239i | \(-0.714077\pi\) | ||||
−0.622978 | + | 0.782239i | \(0.714077\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10719.4 | −1.32500 | ||||||||
\(404\) | −992.863 | −0.122269 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1343.52 | 0.163626 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4634.93 | −0.560349 | −0.280174 | − | 0.959949i | \(-0.590392\pi\) | ||||
−0.280174 | + | 0.959949i | \(0.590392\pi\) | |||||||
\(410\) | 14398.7 | 1.73439 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1706.95 | 0.204115 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12360.3 | 1.46203 | ||||||||
\(416\) | 8322.08 | 0.980826 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3750.42 | −0.438849 | ||||||||
\(419\) | 4998.31 | 0.582777 | 0.291388 | − | 0.956605i | \(-0.405883\pi\) | ||||
0.291388 | + | 0.956605i | \(0.405883\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −704.160 | −0.0815170 | −0.0407585 | − | 0.999169i | \(-0.512977\pi\) | ||||
−0.0407585 | + | 0.999169i | \(0.512977\pi\) | |||||||
\(422\) | −1517.19 | −0.175014 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 9211.50 | 1.05507 | ||||||||
\(425\) | −1528.28 | −0.174429 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −426.629 | −0.0481820 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 24089.1 | 2.70158 | ||||||||
\(431\) | 10332.8 | 1.15479 | 0.577393 | − | 0.816466i | \(-0.304070\pi\) | ||||
0.577393 | + | 0.816466i | \(0.304070\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11106.8 | −1.23270 | −0.616348 | − | 0.787474i | \(-0.711389\pi\) | ||||
−0.616348 | + | 0.787474i | \(0.711389\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 665.246 | 0.0730723 | ||||||||
\(437\) | −1660.98 | −0.181821 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7299.28 | 0.793566 | 0.396783 | − | 0.917912i | \(-0.370126\pi\) | ||||
0.396783 | + | 0.917912i | \(0.370126\pi\) | |||||||
\(440\) | −11699.0 | −1.26757 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1189.36 | −0.127991 | ||||||||
\(443\) | −16089.7 | −1.72560 | −0.862802 | − | 0.505542i | \(-0.831293\pi\) | ||||
−0.862802 | + | 0.505542i | \(0.831293\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5679.68 | 0.605040 | ||||||||
\(446\) | −2341.71 | −0.248617 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13561.7 | −1.42543 | −0.712715 | − | 0.701454i | \(-0.752534\pi\) | ||||
−0.712715 | + | 0.701454i | \(0.752534\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7175.46 | 0.749178 | ||||||||
\(452\) | 4337.99 | 0.451420 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 11464.2 | 1.18512 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10848.6 | 1.11045 | 0.555224 | − | 0.831701i | \(-0.312633\pi\) | ||||
0.555224 | + | 0.831701i | \(0.312633\pi\) | |||||||
\(458\) | −11593.0 | −1.18277 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1106.17 | −0.112121 | ||||||||
\(461\) | −1758.69 | −0.177679 | −0.0888397 | − | 0.996046i | \(-0.528316\pi\) | ||||
−0.0888397 | + | 0.996046i | \(0.528316\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5411.95 | −0.543228 | −0.271614 | − | 0.962406i | \(-0.587557\pi\) | ||||
−0.271614 | + | 0.962406i | \(0.587557\pi\) | |||||||
\(464\) | 2528.06 | 0.252936 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7617.54 | −0.757244 | ||||||||
\(467\) | 8111.34 | 0.803744 | 0.401872 | − | 0.915696i | \(-0.368360\pi\) | ||||
0.401872 | + | 0.915696i | \(0.368360\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −14679.3 | −1.44065 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −15411.9 | −1.50294 | ||||||||
\(473\) | 12004.6 | 1.16696 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −17583.8 | −1.69853 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 10240.9 | 0.979935 | ||||||||
\(479\) | 2095.76 | 0.199912 | 0.0999559 | − | 0.994992i | \(-0.468130\pi\) | ||||
0.0999559 | + | 0.994992i | \(0.468130\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4902.18 | 0.464699 | ||||||||
\(482\) | −10484.9 | −0.990817 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1645.67 | 0.154552 | ||||||||
\(485\) | 12001.7 | 1.12364 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9610.08 | 0.894197 | 0.447099 | − | 0.894485i | \(-0.352457\pi\) | ||||
0.447099 | + | 0.894485i | \(0.352457\pi\) | |||||||
\(488\) | −92.2670 | −0.00855888 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11717.3 | 1.07698 | 0.538488 | − | 0.842633i | \(-0.318996\pi\) | ||||
0.538488 | + | 0.842633i | \(0.318996\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 340.174 | 0.0310764 | ||||||||
\(494\) | −13684.4 | −1.24633 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5143.01 | −0.465581 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9195.19 | −0.824916 | −0.412458 | − | 0.910977i | \(-0.635330\pi\) | ||||
−0.412458 | + | 0.910977i | \(0.635330\pi\) | |||||||
\(500\) | −6308.69 | −0.564266 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −7249.90 | −0.644580 | ||||||||
\(503\) | 16118.8 | 1.42883 | 0.714414 | − | 0.699724i | \(-0.246693\pi\) | ||||
0.714414 | + | 0.699724i | \(0.246693\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9098.23 | 0.801715 | ||||||||
\(506\) | 1479.54 | 0.129987 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5019.37 | 0.438383 | ||||||||
\(509\) | 4918.78 | 0.428333 | 0.214166 | − | 0.976797i | \(-0.431297\pi\) | ||||
0.214166 | + | 0.976797i | \(0.431297\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 12226.4 | 1.05534 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −10788.7 | −0.925819 | ||||||||
\(515\) | −15641.9 | −1.33838 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7315.29 | −0.622294 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −42687.0 | −3.59990 | ||||||||
\(521\) | 13963.4 | 1.17418 | 0.587089 | − | 0.809522i | \(-0.300274\pi\) | ||||
0.587089 | + | 0.809522i | \(0.300274\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13755.3 | 1.15005 | 0.575024 | − | 0.818136i | \(-0.304993\pi\) | ||||
0.575024 | + | 0.818136i | \(0.304993\pi\) | |||||||
\(524\) | 336.632 | 0.0280646 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 14871.9 | 1.23278 | ||||||||
\(527\) | −692.040 | −0.0572026 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11511.7 | −0.946145 | ||||||||
\(530\) | −18021.2 | −1.47697 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 26181.5 | 2.12767 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3909.47 | 0.315928 | ||||||||
\(536\) | −19965.5 | −1.60891 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −12044.3 | −0.965178 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14462.7 | 1.14935 | 0.574676 | − | 0.818381i | \(-0.305128\pi\) | ||||
0.574676 | + | 0.818381i | \(0.305128\pi\) | |||||||
\(542\) | 10704.0 | 0.848293 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 537.269 | 0.0423441 | ||||||||
\(545\) | −6096.07 | −0.479132 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13682.5 | 1.06951 | 0.534755 | − | 0.845007i | \(-0.320404\pi\) | ||||
0.534755 | + | 0.845007i | \(0.320404\pi\) | |||||||
\(548\) | 1122.56 | 0.0875065 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 15662.9 | 1.21431 | ||||||||
\(551\) | 3913.92 | 0.302611 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −2685.49 | −0.205949 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2080.51 | 0.158693 | ||||||||
\(557\) | 7663.13 | 0.582939 | 0.291470 | − | 0.956580i | \(-0.405856\pi\) | ||||
0.291470 | + | 0.956580i | \(0.405856\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 43801.8 | 3.31417 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6791.71 | 0.509770 | ||||||||
\(563\) | 17470.5 | 1.30780 | 0.653902 | − | 0.756580i | \(-0.273131\pi\) | ||||
0.653902 | + | 0.756580i | \(0.273131\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −39751.8 | −2.95995 | ||||||||
\(566\) | 7598.83 | 0.564316 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4073.96 | −0.300950 | ||||||||
\(569\) | 13873.9 | 1.02219 | 0.511094 | − | 0.859525i | \(-0.329240\pi\) | ||||
0.511094 | + | 0.859525i | \(0.329240\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3777.52 | −0.276855 | −0.138428 | − | 0.990373i | \(-0.544205\pi\) | ||||
−0.138428 | + | 0.990373i | \(0.544205\pi\) | |||||||
\(572\) | −4541.60 | −0.331982 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6936.79 | 0.503103 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13880.5 | −1.00148 | −0.500738 | − | 0.865599i | \(-0.666938\pi\) | ||||
−0.500738 | + | 0.865599i | \(0.666938\pi\) | |||||||
\(578\) | 11784.2 | 0.848028 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2606.57 | 0.186607 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8980.72 | −0.637982 | ||||||||
\(584\) | −15202.8 | −1.07722 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −22073.2 | −1.55604 | ||||||||
\(587\) | −2395.61 | −0.168445 | −0.0842227 | − | 0.996447i | \(-0.526841\pi\) | ||||
−0.0842227 | + | 0.996447i | \(0.526841\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7962.36 | −0.557018 | ||||||||
\(590\) | 30151.5 | 2.10393 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2351.99 | 0.163287 | ||||||||
\(593\) | 6603.50 | 0.457290 | 0.228645 | − | 0.973510i | \(-0.426570\pi\) | ||||
0.228645 | + | 0.973510i | \(0.426570\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3845.04 | −0.264260 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5398.47 | 0.369164 | ||||||||
\(599\) | −17252.1 | −1.17680 | −0.588399 | − | 0.808571i | \(-0.700241\pi\) | ||||
−0.588399 | + | 0.808571i | \(0.700241\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12833.1 | −0.871005 | −0.435503 | − | 0.900187i | \(-0.643429\pi\) | ||||
−0.435503 | + | 0.900187i | \(0.643429\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5516.31 | 0.371615 | ||||||||
\(605\) | −15080.3 | −1.01339 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8620.16 | −0.576411 | −0.288206 | − | 0.957569i | \(-0.593059\pi\) | ||||
−0.288206 | + | 0.957569i | \(0.593059\pi\) | |||||||
\(608\) | 6181.62 | 0.412332 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 180.510 | 0.0119813 | ||||||||
\(611\) | −26691.7 | −1.76732 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5136.73 | 0.338451 | 0.169226 | − | 0.985577i | \(-0.445873\pi\) | ||||
0.169226 | + | 0.985577i | \(0.445873\pi\) | |||||||
\(614\) | −11223.4 | −0.737690 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1759.82 | 0.114826 | 0.0574131 | − | 0.998351i | \(-0.481715\pi\) | ||||
0.0574131 | + | 0.998351i | \(0.481715\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3560.24 | 0.231176 | 0.115588 | − | 0.993297i | \(-0.463125\pi\) | ||||
0.115588 | + | 0.993297i | \(0.463125\pi\) | |||||||
\(620\) | −5302.72 | −0.343488 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 15492.4 | 0.998698 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23936.8 | 1.53195 | ||||||||
\(626\) | 14167.1 | 0.904524 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2352.56 | −0.149486 | ||||||||
\(629\) | 316.482 | 0.0200620 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27321.4 | −1.72369 | −0.861845 | − | 0.507172i | \(-0.830691\pi\) | ||||
−0.861845 | + | 0.507172i | \(0.830691\pi\) | |||||||
\(632\) | −3394.81 | −0.213668 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −9595.34 | −0.601072 | ||||||||
\(635\) | −45995.7 | −2.87446 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −3486.36 | −0.216342 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −11991.3 | −0.740619 | ||||||||
\(641\) | 21927.0 | 1.35112 | 0.675558 | − | 0.737307i | \(-0.263903\pi\) | ||||
0.675558 | + | 0.737307i | \(0.263903\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5826.04 | 0.357320 | 0.178660 | − | 0.983911i | \(-0.442824\pi\) | ||||
0.178660 | + | 0.983911i | \(0.442824\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −883.455 | −0.0538066 | ||||||||
\(647\) | 24210.7 | 1.47113 | 0.735565 | − | 0.677454i | \(-0.236917\pi\) | ||||
0.735565 | + | 0.677454i | \(0.236917\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15025.7 | 0.908801 | ||||||||
\(650\) | 57150.3 | 3.44864 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6446.80 | −0.387233 | ||||||||
\(653\) | 25623.3 | 1.53556 | 0.767778 | − | 0.640716i | \(-0.221363\pi\) | ||||
0.767778 | + | 0.640716i | \(0.221363\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3084.77 | −0.184018 | ||||||||
\(656\) | 12561.5 | 0.747626 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23273.7 | 1.37574 | 0.687871 | − | 0.725833i | \(-0.258545\pi\) | ||||
0.687871 | + | 0.725833i | \(0.258545\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20036.5 | 1.17902 | 0.589508 | − | 0.807763i | \(-0.299322\pi\) | ||||
0.589508 | + | 0.807763i | \(0.299322\pi\) | |||||||
\(662\) | 21517.5 | 1.26329 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 15252.9 | 0.891454 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1544.04 | −0.0896333 | ||||||||
\(668\) | 4541.92 | 0.263072 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 39060.1 | 2.25228 | ||||||||
\(671\) | 89.9554 | 0.00517540 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18127.8 | −1.03830 | −0.519149 | − | 0.854684i | \(-0.673751\pi\) | ||||
−0.519149 | + | 0.854684i | \(0.673751\pi\) | |||||||
\(674\) | −9601.48 | −0.548717 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11800.2 | −0.671383 | ||||||||
\(677\) | 13815.5 | 0.784301 | 0.392150 | − | 0.919901i | \(-0.371731\pi\) | ||||
0.392150 | + | 0.919901i | \(0.371731\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −2755.85 | −0.155415 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 7092.55 | 0.398223 | ||||||||
\(683\) | 4604.23 | 0.257944 | 0.128972 | − | 0.991648i | \(-0.458832\pi\) | ||||
0.128972 | + | 0.991648i | \(0.458832\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10286.8 | −0.573777 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 21015.4 | 1.16454 | ||||||||
\(689\) | −32768.5 | −1.81187 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17913.7 | −0.986205 | −0.493103 | − | 0.869971i | \(-0.664137\pi\) | ||||
−0.493103 | + | 0.869971i | \(0.664137\pi\) | |||||||
\(692\) | 1020.96 | 0.0560854 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 16480.5 | 0.901426 | ||||||||
\(695\) | −19065.1 | −1.04054 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1690.26 | 0.0918555 | ||||||||
\(698\) | −1949.10 | −0.105694 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11303.7 | −0.609035 | −0.304518 | − | 0.952507i | \(-0.598495\pi\) | ||||
−0.304518 | + | 0.952507i | \(0.598495\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3641.33 | 0.195356 | ||||||||
\(704\) | −13533.6 | −0.724529 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 19118.6 | 1.01918 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16046.3 | −0.849973 | −0.424987 | − | 0.905200i | \(-0.639721\pi\) | ||||
−0.424987 | + | 0.905200i | \(0.639721\pi\) | |||||||
\(710\) | 7970.22 | 0.421292 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7008.83 | 0.368915 | ||||||||
\(713\) | 3141.15 | 0.164989 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 41617.5 | 2.17679 | ||||||||
\(716\) | 2294.18 | 0.119745 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −21291.5 | −1.10667 | ||||||||
\(719\) | −25190.5 | −1.30660 | −0.653300 | − | 0.757099i | \(-0.726616\pi\) | ||||
−0.653300 | + | 0.757099i | \(0.726616\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 6394.38 | 0.329604 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −882.680 | −0.0453102 | ||||||||
\(725\) | −16345.8 | −0.837334 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11277.2 | −0.575307 | −0.287653 | − | 0.957735i | \(-0.592875\pi\) | ||||
−0.287653 | + | 0.957735i | \(0.592875\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 29742.6 | 1.50797 | ||||||||
\(731\) | 2827.82 | 0.143079 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23720.0 | −1.19525 | −0.597626 | − | 0.801775i | \(-0.703889\pi\) | ||||
−0.597626 | + | 0.801775i | \(0.703889\pi\) | |||||||
\(734\) | −26946.9 | −1.35508 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2438.64 | −0.122133 | ||||||||
\(737\) | 19465.3 | 0.972880 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8124.72 | 0.404428 | 0.202214 | − | 0.979341i | \(-0.435186\pi\) | ||||
0.202214 | + | 0.979341i | \(0.435186\pi\) | |||||||
\(740\) | 2425.03 | 0.120467 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20955.3 | −1.03469 | −0.517346 | − | 0.855777i | \(-0.673080\pi\) | ||||
−0.517346 | + | 0.855777i | \(0.673080\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 35234.6 | 1.73274 | ||||||||
\(746\) | −6585.63 | −0.323213 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −293.203 | −0.0143323 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −38208.1 | −1.85650 | −0.928251 | − | 0.371954i | \(-0.878688\pi\) | ||||
−0.928251 | + | 0.371954i | \(0.878688\pi\) | |||||||
\(752\) | −12806.3 | −0.621006 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −12720.9 | −0.614413 | ||||||||
\(755\) | −50549.4 | −2.43666 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30958.1 | 1.48638 | 0.743191 | − | 0.669079i | \(-0.233311\pi\) | ||||
0.743191 | + | 0.669079i | \(0.233311\pi\) | |||||||
\(758\) | −9865.65 | −0.472740 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −31707.8 | −1.51337 | ||||||||
\(761\) | −40049.4 | −1.90774 | −0.953871 | − | 0.300218i | \(-0.902941\pi\) | ||||
−0.953871 | + | 0.300218i | \(0.902941\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 389.601 | 0.0184493 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −31464.3 | −1.48414 | ||||||||
\(767\) | 54825.3 | 2.58100 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8002.01 | 0.375240 | 0.187620 | − | 0.982242i | \(-0.439923\pi\) | ||||
0.187620 | + | 0.982242i | \(0.439923\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5186.52 | 0.241796 | ||||||||
\(773\) | −13933.4 | −0.648316 | −0.324158 | − | 0.946003i | \(-0.605081\pi\) | ||||
−0.324158 | + | 0.946003i | \(0.605081\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 33253.4 | 1.54128 | ||||||||
\(776\) | 14810.3 | 0.685126 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −470.751 | −0.0216931 | ||||||||
\(779\) | 19447.6 | 0.894456 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3971.89 | 0.181979 | ||||||||
\(782\) | 348.522 | 0.0159375 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 21558.0 | 0.980175 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −37581.7 | −1.70222 | −0.851108 | − | 0.524991i | \(-0.824069\pi\) | ||||
−0.851108 | + | 0.524991i | \(0.824069\pi\) | |||||||
\(788\) | −5788.01 | −0.261662 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6641.54 | 0.299108 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 328.225 | 0.0146981 | ||||||||
\(794\) | −34240.7 | −1.53042 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2914.92 | −0.129795 | ||||||||
\(797\) | −9458.78 | −0.420385 | −0.210193 | − | 0.977660i | \(-0.567409\pi\) | ||||
−0.210193 | + | 0.977660i | \(0.567409\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1723.20 | −0.0762985 | ||||||||
\(800\) | −25816.4 | −1.14093 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 24154.3 | 1.06349 | ||||||||
\(803\) | 14821.9 | 0.651376 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 25879.0 | 1.13095 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 11227.4 | 0.488834 | ||||||||
\(809\) | 1909.94 | 0.0830034 | 0.0415017 | − | 0.999138i | \(-0.486786\pi\) | ||||
0.0415017 | + | 0.999138i | \(0.486786\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −43110.6 | −1.86661 | −0.933303 | − | 0.359091i | \(-0.883087\pi\) | ||||
−0.933303 | + | 0.359091i | \(0.883087\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3243.55 | −0.139664 | ||||||||
\(815\) | 59076.1 | 2.53907 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 32535.9 | 1.39325 | ||||||||
\(818\) | 11189.7 | 0.478287 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 12951.5 | 0.551570 | ||||||||
\(821\) | −4026.56 | −0.171167 | −0.0855834 | − | 0.996331i | \(-0.527275\pi\) | ||||
−0.0855834 | + | 0.996331i | \(0.527275\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 39668.1 | 1.68012 | 0.840062 | − | 0.542491i | \(-0.182519\pi\) | ||||
0.840062 | + | 0.542491i | \(0.182519\pi\) | |||||||
\(824\) | −19302.4 | −0.816056 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −30137.7 | −1.26722 | −0.633611 | − | 0.773652i | \(-0.718428\pi\) | ||||
−0.633611 | + | 0.773652i | \(0.718428\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23278.0 | −0.975245 | −0.487622 | − | 0.873055i | \(-0.662136\pi\) | ||||
−0.487622 | + | 0.873055i | \(0.662136\pi\) | |||||||
\(830\) | −29840.4 | −1.24792 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −49381.0 | −2.05766 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −41620.5 | −1.72495 | ||||||||
\(836\) | −3373.48 | −0.139563 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −12067.0 | −0.497431 | ||||||||
\(839\) | −9494.43 | −0.390684 | −0.195342 | − | 0.980735i | \(-0.562582\pi\) | ||||
−0.195342 | + | 0.980735i | \(0.562582\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20750.6 | −0.850820 | ||||||||
\(842\) | 1699.99 | 0.0695791 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1364.71 | −0.0556578 | ||||||||
\(845\) | 108133. | 4.40223 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −15721.8 | −0.636661 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3689.59 | 0.148885 | ||||||||
\(851\) | −1436.50 | −0.0578644 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12692.4 | 0.509471 | 0.254736 | − | 0.967011i | \(-0.418012\pi\) | ||||
0.254736 | + | 0.967011i | \(0.418012\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4824.36 | 0.192632 | ||||||||
\(857\) | 22206.0 | 0.885114 | 0.442557 | − | 0.896740i | \(-0.354071\pi\) | ||||
0.442557 | + | 0.896740i | \(0.354071\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19820.5 | −0.787271 | −0.393636 | − | 0.919267i | \(-0.628783\pi\) | ||||
−0.393636 | + | 0.919267i | \(0.628783\pi\) | |||||||
\(860\) | 21668.0 | 0.859155 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −24945.5 | −0.985671 | ||||||||
\(863\) | −36413.8 | −1.43631 | −0.718157 | − | 0.695881i | \(-0.755014\pi\) | ||||
−0.718157 | + | 0.695881i | \(0.755014\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9355.70 | −0.367749 | ||||||||
\(866\) | 26814.1 | 1.05217 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3309.76 | 0.129201 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 71024.1 | 2.76298 | ||||||||
\(872\) | −7522.67 | −0.292144 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4009.97 | 0.155194 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19442.6 | 0.748609 | 0.374305 | − | 0.927306i | \(-0.377881\pi\) | ||||
0.374305 | + | 0.927306i | \(0.377881\pi\) | |||||||
\(878\) | −17622.0 | −0.677351 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 19967.4 | 0.764888 | ||||||||
\(881\) | −25184.2 | −0.963082 | −0.481541 | − | 0.876423i | \(-0.659923\pi\) | ||||
−0.481541 | + | 0.876423i | \(0.659923\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4050.03 | −0.154354 | −0.0771769 | − | 0.997017i | \(-0.524591\pi\) | ||||
−0.0771769 | + | 0.997017i | \(0.524591\pi\) | |||||||
\(884\) | −1069.83 | −0.0407038 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 38843.9 | 1.47290 | ||||||||
\(887\) | 41604.2 | 1.57489 | 0.787447 | − | 0.616383i | \(-0.211402\pi\) | ||||
0.787447 | + | 0.616383i | \(0.211402\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −13712.0 | −0.516434 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2106.36 | −0.0790652 | ||||||||
\(893\) | −19826.5 | −0.742967 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −21023.0 | −0.785165 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 32740.9 | 1.21668 | ||||||||
\(899\) | −7401.76 | −0.274597 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2115.51 | −0.0782219 | ||||||||
\(902\) | −17323.1 | −0.639463 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −49054.4 | −1.80478 | ||||||||
\(905\) | 8088.56 | 0.297097 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3572.60 | −0.130790 | −0.0653949 | − | 0.997859i | \(-0.520831\pi\) | ||||
−0.0653949 | + | 0.997859i | \(0.520831\pi\) | |||||||
\(908\) | 10312.0 | 0.376890 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29457.7 | −1.07133 | −0.535663 | − | 0.844432i | \(-0.679938\pi\) | ||||
−0.535663 | + | 0.844432i | \(0.679938\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14870.7 | −0.539046 | ||||||||
\(914\) | −26190.8 | −0.947827 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10427.9 | −0.376143 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3310.65 | −0.118834 | −0.0594168 | − | 0.998233i | \(-0.518924\pi\) | ||||
−0.0594168 | + | 0.998233i | \(0.518924\pi\) | |||||||
\(920\) | 12508.7 | 0.448260 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 4245.85 | 0.151659 | ||||||||
\(923\) | 14492.5 | 0.516820 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15207.3 | −0.540556 | ||||||||
\(926\) | 13065.6 | 0.463674 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5746.39 | 0.203270 | ||||||||
\(929\) | −31467.5 | −1.11132 | −0.555660 | − | 0.831410i | \(-0.687534\pi\) | ||||
−0.555660 | + | 0.831410i | \(0.687534\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −6851.94 | −0.240818 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −19582.5 | −0.686038 | ||||||||
\(935\) | 2686.80 | 0.0939763 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17363.4 | 0.605375 | 0.302688 | − | 0.953090i | \(-0.402116\pi\) | ||||
0.302688 | + | 0.953090i | \(0.402116\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −13203.9 | −0.458154 | ||||||||
\(941\) | −5547.77 | −0.192192 | −0.0960958 | − | 0.995372i | \(-0.530636\pi\) | ||||
−0.0960958 | + | 0.995372i | \(0.530636\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7672.04 | −0.264937 | ||||||||
\(944\) | 26304.3 | 0.906919 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −28981.6 | −0.996062 | ||||||||
\(947\) | 37960.3 | 1.30258 | 0.651290 | − | 0.758829i | \(-0.274228\pi\) | ||||
0.651290 | + | 0.758829i | \(0.274228\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 54081.7 | 1.84991 | ||||||||
\(950\) | 42451.1 | 1.44978 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10019.3 | 0.340563 | 0.170282 | − | 0.985395i | \(-0.445532\pi\) | ||||
0.170282 | + | 0.985395i | \(0.445532\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3570.16 | −0.120971 | ||||||||
\(956\) | 9211.65 | 0.311638 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −5059.61 | −0.170635 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14733.1 | −0.494548 | ||||||||
\(962\) | −11834.9 | −0.396646 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −9431.11 | −0.315099 | ||||||||
\(965\) | −47527.3 | −1.58545 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27834.4 | 0.925641 | 0.462820 | − | 0.886452i | \(-0.346837\pi\) | ||||
0.462820 | + | 0.886452i | \(0.346837\pi\) | |||||||
\(968\) | −18609.4 | −0.617900 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −28974.6 | −0.959090 | ||||||||
\(971\) | −18275.3 | −0.604000 | −0.302000 | − | 0.953308i | \(-0.597654\pi\) | ||||
−0.302000 | + | 0.953308i | \(0.597654\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −23200.8 | −0.763245 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 157.477 | 0.00516468 | ||||||||
\(977\) | 43028.9 | 1.40903 | 0.704513 | − | 0.709691i | \(-0.251166\pi\) | ||||
0.704513 | + | 0.709691i | \(0.251166\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6833.24 | −0.223076 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −28288.1 | −0.919256 | ||||||||
\(983\) | 30559.2 | 0.991544 | 0.495772 | − | 0.868453i | \(-0.334885\pi\) | ||||
0.495772 | + | 0.868453i | \(0.334885\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 53039.2 | 1.71571 | ||||||||
\(986\) | −821.253 | −0.0265254 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −12309.0 | −0.396358 | ||||||||
\(989\) | −12835.4 | −0.412681 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −44945.9 | −1.44072 | −0.720360 | − | 0.693600i | \(-0.756024\pi\) | ||||
−0.720360 | + | 0.693600i | \(0.756024\pi\) | |||||||
\(992\) | −11690.3 | −0.374160 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 26711.2 | 0.851058 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29006.1 | −0.921397 | −0.460698 | − | 0.887557i | \(-0.652401\pi\) | ||||
−0.460698 | + | 0.887557i | \(0.652401\pi\) | |||||||
\(998\) | 22199.1 | 0.704110 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 441.4.a.o.1.1 | 2 | ||
3.2 | odd | 2 | 147.4.a.k.1.2 | yes | 2 | ||
7.2 | even | 3 | 441.4.e.u.361.2 | 4 | |||
7.3 | odd | 6 | 441.4.e.v.226.2 | 4 | |||
7.4 | even | 3 | 441.4.e.u.226.2 | 4 | |||
7.5 | odd | 6 | 441.4.e.v.361.2 | 4 | |||
7.6 | odd | 2 | 441.4.a.n.1.1 | 2 | |||
12.11 | even | 2 | 2352.4.a.bl.1.1 | 2 | |||
21.2 | odd | 6 | 147.4.e.j.67.1 | 4 | |||
21.5 | even | 6 | 147.4.e.k.67.1 | 4 | |||
21.11 | odd | 6 | 147.4.e.j.79.1 | 4 | |||
21.17 | even | 6 | 147.4.e.k.79.1 | 4 | |||
21.20 | even | 2 | 147.4.a.j.1.2 | ✓ | 2 | ||
84.83 | odd | 2 | 2352.4.a.cf.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
147.4.a.j.1.2 | ✓ | 2 | 21.20 | even | 2 | ||
147.4.a.k.1.2 | yes | 2 | 3.2 | odd | 2 | ||
147.4.e.j.67.1 | 4 | 21.2 | odd | 6 | |||
147.4.e.j.79.1 | 4 | 21.11 | odd | 6 | |||
147.4.e.k.67.1 | 4 | 21.5 | even | 6 | |||
147.4.e.k.79.1 | 4 | 21.17 | even | 6 | |||
441.4.a.n.1.1 | 2 | 7.6 | odd | 2 | |||
441.4.a.o.1.1 | 2 | 1.1 | even | 1 | trivial | ||
441.4.e.u.226.2 | 4 | 7.4 | even | 3 | |||
441.4.e.u.361.2 | 4 | 7.2 | even | 3 | |||
441.4.e.v.226.2 | 4 | 7.3 | odd | 6 | |||
441.4.e.v.361.2 | 4 | 7.5 | odd | 6 | |||
2352.4.a.bl.1.1 | 2 | 12.11 | even | 2 | |||
2352.4.a.cf.1.2 | 2 | 84.83 | odd | 2 |