Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1849,4,Mod(1,1849)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1849, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1849.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1849 = 43^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1849.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: | \(109.094531601\) |
Analytic rank: | \(1\) |
Dimension: | \(50\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 1849.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.53235 | −0.895322 | −0.447661 | − | 0.894203i | \(-0.647743\pi\) | ||||
−0.447661 | + | 0.894203i | \(0.647743\pi\) | |||||||
\(3\) | 8.01322 | 1.54214 | 0.771072 | − | 0.636747i | \(-0.219721\pi\) | ||||
0.771072 | + | 0.636747i | \(0.219721\pi\) | |||||||
\(4\) | −1.58719 | −0.198399 | ||||||||
\(5\) | 20.7136 | 1.85268 | 0.926340 | − | 0.376687i | \(-0.122937\pi\) | ||||
0.926340 | + | 0.376687i | \(0.122937\pi\) | |||||||
\(6\) | −20.2923 | −1.38072 | ||||||||
\(7\) | 3.06093 | 0.165275 | 0.0826374 | − | 0.996580i | \(-0.473666\pi\) | ||||
0.0826374 | + | 0.996580i | \(0.473666\pi\) | |||||||
\(8\) | 24.2781 | 1.07295 | ||||||||
\(9\) | 37.2117 | 1.37821 | ||||||||
\(10\) | −52.4541 | −1.65875 | ||||||||
\(11\) | −50.3240 | −1.37939 | −0.689693 | − | 0.724102i | \(-0.742255\pi\) | ||||
−0.689693 | + | 0.724102i | \(0.742255\pi\) | |||||||
\(12\) | −12.7185 | −0.305961 | ||||||||
\(13\) | −26.3471 | −0.562105 | −0.281053 | − | 0.959692i | \(-0.590684\pi\) | ||||
−0.281053 | + | 0.959692i | \(0.590684\pi\) | |||||||
\(14\) | −7.75136 | −0.147974 | ||||||||
\(15\) | 165.983 | 2.85710 | ||||||||
\(16\) | −48.7833 | −0.762238 | ||||||||
\(17\) | −23.1013 | −0.329582 | −0.164791 | − | 0.986329i | \(-0.552695\pi\) | ||||
−0.164791 | + | 0.986329i | \(0.552695\pi\) | |||||||
\(18\) | −94.2331 | −1.23394 | ||||||||
\(19\) | −135.885 | −1.64075 | −0.820375 | − | 0.571826i | \(-0.806235\pi\) | ||||
−0.820375 | + | 0.571826i | \(0.806235\pi\) | |||||||
\(20\) | −32.8765 | −0.367571 | ||||||||
\(21\) | 24.5279 | 0.254878 | ||||||||
\(22\) | 127.438 | 1.23499 | ||||||||
\(23\) | −91.8712 | −0.832890 | −0.416445 | − | 0.909161i | \(-0.636724\pi\) | ||||
−0.416445 | + | 0.909161i | \(0.636724\pi\) | |||||||
\(24\) | 194.546 | 1.65465 | ||||||||
\(25\) | 304.053 | 2.43243 | ||||||||
\(26\) | 66.7201 | 0.503265 | ||||||||
\(27\) | 81.8285 | 0.583255 | ||||||||
\(28\) | −4.85830 | −0.0327904 | ||||||||
\(29\) | −15.5009 | −0.0992570 | −0.0496285 | − | 0.998768i | \(-0.515804\pi\) | ||||
−0.0496285 | + | 0.998768i | \(0.515804\pi\) | |||||||
\(30\) | −420.326 | −2.55802 | ||||||||
\(31\) | −34.9791 | −0.202659 | −0.101330 | − | 0.994853i | \(-0.532310\pi\) | ||||
−0.101330 | + | 0.994853i | \(0.532310\pi\) | |||||||
\(32\) | −70.6888 | −0.390504 | ||||||||
\(33\) | −403.257 | −2.12721 | ||||||||
\(34\) | 58.5007 | 0.295082 | ||||||||
\(35\) | 63.4029 | 0.306201 | ||||||||
\(36\) | −59.0622 | −0.273436 | ||||||||
\(37\) | −221.246 | −0.983043 | −0.491522 | − | 0.870865i | \(-0.663559\pi\) | ||||
−0.491522 | + | 0.870865i | \(0.663559\pi\) | |||||||
\(38\) | 344.110 | 1.46900 | ||||||||
\(39\) | −211.125 | −0.866848 | ||||||||
\(40\) | 502.888 | 1.98784 | ||||||||
\(41\) | 206.730 | 0.787459 | 0.393729 | − | 0.919226i | \(-0.371185\pi\) | ||||
0.393729 | + | 0.919226i | \(0.371185\pi\) | |||||||
\(42\) | −62.1133 | −0.228197 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | 79.8739 | 0.273669 | ||||||||
\(45\) | 770.788 | 2.55338 | ||||||||
\(46\) | 232.650 | 0.745704 | ||||||||
\(47\) | −600.224 | −1.86280 | −0.931400 | − | 0.363997i | \(-0.881412\pi\) | ||||
−0.931400 | + | 0.363997i | \(0.881412\pi\) | |||||||
\(48\) | −390.911 | −1.17548 | ||||||||
\(49\) | −333.631 | −0.972684 | ||||||||
\(50\) | −769.970 | −2.17780 | ||||||||
\(51\) | −185.116 | −0.508263 | ||||||||
\(52\) | 41.8180 | 0.111521 | ||||||||
\(53\) | 408.162 | 1.05784 | 0.528919 | − | 0.848672i | \(-0.322598\pi\) | ||||
0.528919 | + | 0.848672i | \(0.322598\pi\) | |||||||
\(54\) | −207.218 | −0.522201 | ||||||||
\(55\) | −1042.39 | −2.55556 | ||||||||
\(56\) | 74.3138 | 0.177332 | ||||||||
\(57\) | −1088.88 | −2.53027 | ||||||||
\(58\) | 39.2539 | 0.0888670 | ||||||||
\(59\) | −740.433 | −1.63383 | −0.816916 | − | 0.576756i | \(-0.804318\pi\) | ||||
−0.816916 | + | 0.576756i | \(0.804318\pi\) | |||||||
\(60\) | −263.447 | −0.566847 | ||||||||
\(61\) | 51.7496 | 0.108621 | 0.0543103 | − | 0.998524i | \(-0.482704\pi\) | ||||
0.0543103 | + | 0.998524i | \(0.482704\pi\) | |||||||
\(62\) | 88.5794 | 0.181445 | ||||||||
\(63\) | 113.902 | 0.227783 | ||||||||
\(64\) | 569.275 | 1.11187 | ||||||||
\(65\) | −545.743 | −1.04140 | ||||||||
\(66\) | 1021.19 | 1.90454 | ||||||||
\(67\) | 334.159 | 0.609314 | 0.304657 | − | 0.952462i | \(-0.401458\pi\) | ||||
0.304657 | + | 0.952462i | \(0.401458\pi\) | |||||||
\(68\) | 36.6663 | 0.0653888 | ||||||||
\(69\) | −736.184 | −1.28444 | ||||||||
\(70\) | −160.559 | −0.274149 | ||||||||
\(71\) | −487.740 | −0.815269 | −0.407634 | − | 0.913145i | \(-0.633646\pi\) | ||||
−0.407634 | + | 0.913145i | \(0.633646\pi\) | |||||||
\(72\) | 903.431 | 1.47875 | ||||||||
\(73\) | −722.667 | −1.15865 | −0.579327 | − | 0.815095i | \(-0.696685\pi\) | ||||
−0.579327 | + | 0.815095i | \(0.696685\pi\) | |||||||
\(74\) | 560.272 | 0.880140 | ||||||||
\(75\) | 2436.45 | 3.75115 | ||||||||
\(76\) | 215.677 | 0.325524 | ||||||||
\(77\) | −154.038 | −0.227978 | ||||||||
\(78\) | 534.643 | 0.776107 | ||||||||
\(79\) | −171.428 | −0.244141 | −0.122071 | − | 0.992521i | \(-0.538953\pi\) | ||||
−0.122071 | + | 0.992521i | \(0.538953\pi\) | |||||||
\(80\) | −1010.48 | −1.41218 | ||||||||
\(81\) | −349.006 | −0.478746 | ||||||||
\(82\) | −523.513 | −0.705029 | ||||||||
\(83\) | −241.764 | −0.319724 | −0.159862 | − | 0.987139i | \(-0.551105\pi\) | ||||
−0.159862 | + | 0.987139i | \(0.551105\pi\) | |||||||
\(84\) | −38.9306 | −0.0505676 | ||||||||
\(85\) | −478.511 | −0.610610 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −124.213 | −0.153069 | ||||||||
\(88\) | −1221.77 | −1.48002 | ||||||||
\(89\) | −333.067 | −0.396686 | −0.198343 | − | 0.980133i | \(-0.563556\pi\) | ||||
−0.198343 | + | 0.980133i | \(0.563556\pi\) | |||||||
\(90\) | −1951.91 | −2.28610 | ||||||||
\(91\) | −80.6467 | −0.0929019 | ||||||||
\(92\) | 145.817 | 0.165245 | ||||||||
\(93\) | −280.295 | −0.312530 | ||||||||
\(94\) | 1519.98 | 1.66781 | ||||||||
\(95\) | −2814.68 | −3.03979 | ||||||||
\(96\) | −566.445 | −0.602214 | ||||||||
\(97\) | 687.004 | 0.719120 | 0.359560 | − | 0.933122i | \(-0.382927\pi\) | ||||
0.359560 | + | 0.933122i | \(0.382927\pi\) | |||||||
\(98\) | 844.870 | 0.870865 | ||||||||
\(99\) | −1872.64 | −1.90108 | ||||||||
\(100\) | −482.592 | −0.482592 | ||||||||
\(101\) | 918.164 | 0.904561 | 0.452281 | − | 0.891876i | \(-0.350611\pi\) | ||||
0.452281 | + | 0.891876i | \(0.350611\pi\) | |||||||
\(102\) | 468.779 | 0.455059 | ||||||||
\(103\) | −348.289 | −0.333184 | −0.166592 | − | 0.986026i | \(-0.553276\pi\) | ||||
−0.166592 | + | 0.986026i | \(0.553276\pi\) | |||||||
\(104\) | −639.659 | −0.603112 | ||||||||
\(105\) | 508.062 | 0.472207 | ||||||||
\(106\) | −1033.61 | −0.947105 | ||||||||
\(107\) | 830.251 | 0.750125 | 0.375063 | − | 0.927000i | \(-0.377621\pi\) | ||||
0.375063 | + | 0.927000i | \(0.377621\pi\) | |||||||
\(108\) | −129.878 | −0.115717 | ||||||||
\(109\) | −295.829 | −0.259957 | −0.129979 | − | 0.991517i | \(-0.541491\pi\) | ||||
−0.129979 | + | 0.991517i | \(0.541491\pi\) | |||||||
\(110\) | 2639.70 | 2.28805 | ||||||||
\(111\) | −1772.89 | −1.51599 | ||||||||
\(112\) | −149.322 | −0.125979 | ||||||||
\(113\) | 1631.99 | 1.35862 | 0.679311 | − | 0.733850i | \(-0.262279\pi\) | ||||
0.679311 | + | 0.733850i | \(0.262279\pi\) | |||||||
\(114\) | 2757.43 | 2.26541 | ||||||||
\(115\) | −1902.98 | −1.54308 | ||||||||
\(116\) | 24.6030 | 0.0196925 | ||||||||
\(117\) | −980.420 | −0.774699 | ||||||||
\(118\) | 1875.04 | 1.46281 | ||||||||
\(119\) | −70.7116 | −0.0544716 | ||||||||
\(120\) | 4029.75 | 3.06554 | ||||||||
\(121\) | 1201.50 | 0.902706 | ||||||||
\(122\) | −131.048 | −0.0972503 | ||||||||
\(123\) | 1656.57 | 1.21438 | ||||||||
\(124\) | 55.5186 | 0.0402074 | ||||||||
\(125\) | 3708.84 | 2.65383 | ||||||||
\(126\) | −288.441 | −0.203939 | ||||||||
\(127\) | 243.422 | 0.170080 | 0.0850401 | − | 0.996378i | \(-0.472898\pi\) | ||||
0.0850401 | + | 0.996378i | \(0.472898\pi\) | |||||||
\(128\) | −876.094 | −0.604973 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1382.01 | 0.932389 | ||||||||
\(131\) | −2342.26 | −1.56217 | −0.781083 | − | 0.624427i | \(-0.785333\pi\) | ||||
−0.781083 | + | 0.624427i | \(0.785333\pi\) | |||||||
\(132\) | 640.047 | 0.422038 | ||||||||
\(133\) | −415.936 | −0.271175 | ||||||||
\(134\) | −846.208 | −0.545532 | ||||||||
\(135\) | 1694.96 | 1.08059 | ||||||||
\(136\) | −560.857 | −0.353626 | ||||||||
\(137\) | 1232.79 | 0.768788 | 0.384394 | − | 0.923169i | \(-0.374410\pi\) | ||||
0.384394 | + | 0.923169i | \(0.374410\pi\) | |||||||
\(138\) | 1864.28 | 1.14998 | ||||||||
\(139\) | −310.063 | −0.189203 | −0.0946014 | − | 0.995515i | \(-0.530158\pi\) | ||||
−0.0946014 | + | 0.995515i | \(0.530158\pi\) | |||||||
\(140\) | −100.633 | −0.0607502 | ||||||||
\(141\) | −4809.72 | −2.87271 | ||||||||
\(142\) | 1235.13 | 0.729928 | ||||||||
\(143\) | 1325.89 | 0.775360 | ||||||||
\(144\) | −1815.31 | −1.05052 | ||||||||
\(145\) | −321.080 | −0.183892 | ||||||||
\(146\) | 1830.05 | 1.03737 | ||||||||
\(147\) | −2673.46 | −1.50002 | ||||||||
\(148\) | 351.160 | 0.195035 | ||||||||
\(149\) | 2522.04 | 1.38667 | 0.693334 | − | 0.720616i | \(-0.256141\pi\) | ||||
0.693334 | + | 0.720616i | \(0.256141\pi\) | |||||||
\(150\) | −6169.94 | −3.35849 | ||||||||
\(151\) | −999.113 | −0.538455 | −0.269227 | − | 0.963077i | \(-0.586768\pi\) | ||||
−0.269227 | + | 0.963077i | \(0.586768\pi\) | |||||||
\(152\) | −3299.05 | −1.76045 | ||||||||
\(153\) | −859.639 | −0.454233 | ||||||||
\(154\) | 390.079 | 0.204113 | ||||||||
\(155\) | −724.543 | −0.375462 | ||||||||
\(156\) | 335.097 | 0.171982 | ||||||||
\(157\) | −1192.13 | −0.606002 | −0.303001 | − | 0.952990i | \(-0.597989\pi\) | ||||
−0.303001 | + | 0.952990i | \(0.597989\pi\) | |||||||
\(158\) | 434.116 | 0.218585 | ||||||||
\(159\) | 3270.69 | 1.63134 | ||||||||
\(160\) | −1464.22 | −0.723480 | ||||||||
\(161\) | −281.212 | −0.137656 | ||||||||
\(162\) | 883.806 | 0.428632 | ||||||||
\(163\) | −114.218 | −0.0548847 | −0.0274424 | − | 0.999623i | \(-0.508736\pi\) | ||||
−0.0274424 | + | 0.999623i | \(0.508736\pi\) | |||||||
\(164\) | −328.121 | −0.156231 | ||||||||
\(165\) | −8352.91 | −3.94105 | ||||||||
\(166\) | 612.232 | 0.286256 | ||||||||
\(167\) | 3106.64 | 1.43952 | 0.719758 | − | 0.694225i | \(-0.244253\pi\) | ||||
0.719758 | + | 0.694225i | \(0.244253\pi\) | |||||||
\(168\) | 595.493 | 0.273472 | ||||||||
\(169\) | −1502.83 | −0.684038 | ||||||||
\(170\) | 1211.76 | 0.546692 | ||||||||
\(171\) | −5056.53 | −2.26130 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2342.86 | −1.02962 | −0.514810 | − | 0.857304i | \(-0.672138\pi\) | ||||
−0.514810 | + | 0.857304i | \(0.672138\pi\) | |||||||
\(174\) | 314.550 | 0.137046 | ||||||||
\(175\) | 930.687 | 0.402019 | ||||||||
\(176\) | 2454.97 | 1.05142 | ||||||||
\(177\) | −5933.25 | −2.51961 | ||||||||
\(178\) | 843.442 | 0.355161 | ||||||||
\(179\) | 1671.04 | 0.697762 | 0.348881 | − | 0.937167i | \(-0.386562\pi\) | ||||
0.348881 | + | 0.937167i | \(0.386562\pi\) | |||||||
\(180\) | −1223.39 | −0.506590 | ||||||||
\(181\) | 2195.16 | 0.901465 | 0.450732 | − | 0.892659i | \(-0.351163\pi\) | ||||
0.450732 | + | 0.892659i | \(0.351163\pi\) | |||||||
\(182\) | 204.226 | 0.0831770 | ||||||||
\(183\) | 414.681 | 0.167509 | ||||||||
\(184\) | −2230.46 | −0.893652 | ||||||||
\(185\) | −4582.80 | −1.82127 | ||||||||
\(186\) | 709.806 | 0.279814 | ||||||||
\(187\) | 1162.55 | 0.454621 | ||||||||
\(188\) | 952.672 | 0.369578 | ||||||||
\(189\) | 250.471 | 0.0963974 | ||||||||
\(190\) | 7127.75 | 2.72159 | ||||||||
\(191\) | 79.6602 | 0.0301781 | 0.0150890 | − | 0.999886i | \(-0.495197\pi\) | ||||
0.0150890 | + | 0.999886i | \(0.495197\pi\) | |||||||
\(192\) | 4561.73 | 1.71466 | ||||||||
\(193\) | 1109.31 | 0.413730 | 0.206865 | − | 0.978369i | \(-0.433674\pi\) | ||||
0.206865 | + | 0.978369i | \(0.433674\pi\) | |||||||
\(194\) | −1739.73 | −0.643844 | ||||||||
\(195\) | −4373.16 | −1.60599 | ||||||||
\(196\) | 529.537 | 0.192980 | ||||||||
\(197\) | 2392.69 | 0.865340 | 0.432670 | − | 0.901552i | \(-0.357572\pi\) | ||||
0.432670 | + | 0.901552i | \(0.357572\pi\) | |||||||
\(198\) | 4742.18 | 1.70208 | ||||||||
\(199\) | −210.234 | −0.0748899 | −0.0374450 | − | 0.999299i | \(-0.511922\pi\) | ||||
−0.0374450 | + | 0.999299i | \(0.511922\pi\) | |||||||
\(200\) | 7381.85 | 2.60988 | ||||||||
\(201\) | 2677.69 | 0.939650 | ||||||||
\(202\) | −2325.11 | −0.809873 | ||||||||
\(203\) | −47.4474 | −0.0164047 | ||||||||
\(204\) | 293.815 | 0.100839 | ||||||||
\(205\) | 4282.12 | 1.45891 | ||||||||
\(206\) | 881.991 | 0.298307 | ||||||||
\(207\) | −3418.68 | −1.14790 | ||||||||
\(208\) | 1285.30 | 0.428458 | ||||||||
\(209\) | 6838.29 | 2.26323 | ||||||||
\(210\) | −1286.59 | −0.422777 | ||||||||
\(211\) | −857.579 | −0.279802 | −0.139901 | − | 0.990166i | \(-0.544678\pi\) | ||||
−0.139901 | + | 0.990166i | \(0.544678\pi\) | |||||||
\(212\) | −647.833 | −0.209874 | ||||||||
\(213\) | −3908.37 | −1.25726 | ||||||||
\(214\) | −2102.49 | −0.671603 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1986.64 | 0.625805 | ||||||||
\(217\) | −107.069 | −0.0334944 | ||||||||
\(218\) | 749.144 | 0.232745 | ||||||||
\(219\) | −5790.89 | −1.78681 | ||||||||
\(220\) | 1654.48 | 0.507022 | ||||||||
\(221\) | 608.652 | 0.185260 | ||||||||
\(222\) | 4489.58 | 1.35730 | ||||||||
\(223\) | 3532.28 | 1.06071 | 0.530356 | − | 0.847775i | \(-0.322058\pi\) | ||||
0.530356 | + | 0.847775i | \(0.322058\pi\) | |||||||
\(224\) | −216.374 | −0.0645405 | ||||||||
\(225\) | 11314.3 | 3.35240 | ||||||||
\(226\) | −4132.76 | −1.21640 | ||||||||
\(227\) | 5188.68 | 1.51711 | 0.758557 | − | 0.651607i | \(-0.225905\pi\) | ||||
0.758557 | + | 0.651607i | \(0.225905\pi\) | |||||||
\(228\) | 1728.26 | 0.502005 | ||||||||
\(229\) | 3482.36 | 1.00490 | 0.502448 | − | 0.864607i | \(-0.332433\pi\) | ||||
0.502448 | + | 0.864607i | \(0.332433\pi\) | |||||||
\(230\) | 4819.02 | 1.38155 | ||||||||
\(231\) | −1234.34 | −0.351575 | ||||||||
\(232\) | −376.334 | −0.106498 | ||||||||
\(233\) | −1545.34 | −0.434500 | −0.217250 | − | 0.976116i | \(-0.569709\pi\) | ||||
−0.217250 | + | 0.976116i | \(0.569709\pi\) | |||||||
\(234\) | 2482.77 | 0.693605 | ||||||||
\(235\) | −12432.8 | −3.45117 | ||||||||
\(236\) | 1175.21 | 0.324151 | ||||||||
\(237\) | −1373.69 | −0.376501 | ||||||||
\(238\) | 179.067 | 0.0487696 | ||||||||
\(239\) | −2562.59 | −0.693558 | −0.346779 | − | 0.937947i | \(-0.612725\pi\) | ||||
−0.346779 | + | 0.937947i | \(0.612725\pi\) | |||||||
\(240\) | −8097.17 | −2.17779 | ||||||||
\(241\) | 4941.93 | 1.32090 | 0.660452 | − | 0.750868i | \(-0.270365\pi\) | ||||
0.660452 | + | 0.750868i | \(0.270365\pi\) | |||||||
\(242\) | −3042.63 | −0.808212 | ||||||||
\(243\) | −5006.03 | −1.32155 | ||||||||
\(244\) | −82.1366 | −0.0215502 | ||||||||
\(245\) | −6910.69 | −1.80207 | ||||||||
\(246\) | −4195.03 | −1.08726 | ||||||||
\(247\) | 3580.19 | 0.922274 | ||||||||
\(248\) | −849.228 | −0.217444 | ||||||||
\(249\) | −1937.31 | −0.493060 | ||||||||
\(250\) | −9392.08 | −2.37603 | ||||||||
\(251\) | 4464.77 | 1.12276 | 0.561382 | − | 0.827557i | \(-0.310270\pi\) | ||||
0.561382 | + | 0.827557i | \(0.310270\pi\) | |||||||
\(252\) | −180.785 | −0.0451921 | ||||||||
\(253\) | 4623.32 | 1.14888 | ||||||||
\(254\) | −616.430 | −0.152277 | ||||||||
\(255\) | −3834.42 | −0.941649 | ||||||||
\(256\) | −2335.62 | −0.570220 | ||||||||
\(257\) | 5954.45 | 1.44525 | 0.722624 | − | 0.691242i | \(-0.242936\pi\) | ||||
0.722624 | + | 0.691242i | \(0.242936\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −677.219 | −0.162472 | ||||||||
\(260\) | 866.201 | 0.206613 | ||||||||
\(261\) | −576.816 | −0.136797 | ||||||||
\(262\) | 5931.41 | 1.39864 | ||||||||
\(263\) | −46.0385 | −0.0107941 | −0.00539706 | − | 0.999985i | \(-0.501718\pi\) | ||||
−0.00539706 | + | 0.999985i | \(0.501718\pi\) | |||||||
\(264\) | −9790.33 | −2.28240 | ||||||||
\(265\) | 8454.51 | 1.95984 | ||||||||
\(266\) | 1053.30 | 0.242789 | ||||||||
\(267\) | −2668.94 | −0.611747 | ||||||||
\(268\) | −530.375 | −0.120887 | ||||||||
\(269\) | 924.553 | 0.209558 | 0.104779 | − | 0.994496i | \(-0.466587\pi\) | ||||
0.104779 | + | 0.994496i | \(0.466587\pi\) | |||||||
\(270\) | −4292.24 | −0.967472 | ||||||||
\(271\) | −5175.61 | −1.16013 | −0.580067 | − | 0.814569i | \(-0.696974\pi\) | ||||
−0.580067 | + | 0.814569i | \(0.696974\pi\) | |||||||
\(272\) | 1126.96 | 0.251220 | ||||||||
\(273\) | −646.239 | −0.143268 | ||||||||
\(274\) | −3121.85 | −0.688313 | ||||||||
\(275\) | −15301.2 | −3.35526 | ||||||||
\(276\) | 1168.47 | 0.254831 | ||||||||
\(277\) | −6775.52 | −1.46968 | −0.734840 | − | 0.678240i | \(-0.762743\pi\) | ||||
−0.734840 | + | 0.678240i | \(0.762743\pi\) | |||||||
\(278\) | 785.189 | 0.169397 | ||||||||
\(279\) | −1301.63 | −0.279307 | ||||||||
\(280\) | 1539.31 | 0.328540 | ||||||||
\(281\) | 2921.27 | 0.620172 | 0.310086 | − | 0.950709i | \(-0.399642\pi\) | ||||
0.310086 | + | 0.950709i | \(0.399642\pi\) | |||||||
\(282\) | 12179.9 | 2.57200 | ||||||||
\(283\) | −5154.70 | −1.08274 | −0.541369 | − | 0.840785i | \(-0.682094\pi\) | ||||
−0.541369 | + | 0.840785i | \(0.682094\pi\) | |||||||
\(284\) | 774.138 | 0.161749 | ||||||||
\(285\) | −22554.6 | −4.68779 | ||||||||
\(286\) | −3357.62 | −0.694197 | ||||||||
\(287\) | 632.787 | 0.130147 | ||||||||
\(288\) | −2630.45 | −0.538197 | ||||||||
\(289\) | −4379.33 | −0.891376 | ||||||||
\(290\) | 813.089 | 0.164642 | ||||||||
\(291\) | 5505.11 | 1.10899 | ||||||||
\(292\) | 1147.01 | 0.229876 | ||||||||
\(293\) | −5833.97 | −1.16322 | −0.581611 | − | 0.813467i | \(-0.697578\pi\) | ||||
−0.581611 | + | 0.813467i | \(0.697578\pi\) | |||||||
\(294\) | 6770.13 | 1.34300 | ||||||||
\(295\) | −15337.0 | −3.02697 | ||||||||
\(296\) | −5371.44 | −1.05476 | ||||||||
\(297\) | −4117.93 | −0.804534 | ||||||||
\(298\) | −6386.69 | −1.24151 | ||||||||
\(299\) | 2420.54 | 0.468172 | ||||||||
\(300\) | −3867.11 | −0.744226 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2530.11 | 0.482090 | ||||||||
\(303\) | 7357.45 | 1.39496 | ||||||||
\(304\) | 6628.93 | 1.25064 | ||||||||
\(305\) | 1071.92 | 0.201239 | ||||||||
\(306\) | 2176.91 | 0.406685 | ||||||||
\(307\) | 6732.61 | 1.25163 | 0.625815 | − | 0.779971i | \(-0.284766\pi\) | ||||
0.625815 | + | 0.779971i | \(0.284766\pi\) | |||||||
\(308\) | 244.489 | 0.0452306 | ||||||||
\(309\) | −2790.92 | −0.513818 | ||||||||
\(310\) | 1834.80 | 0.336160 | ||||||||
\(311\) | 8757.73 | 1.59680 | 0.798401 | − | 0.602127i | \(-0.205680\pi\) | ||||
0.798401 | + | 0.602127i | \(0.205680\pi\) | |||||||
\(312\) | −5125.73 | −0.930087 | ||||||||
\(313\) | −6736.28 | −1.21648 | −0.608238 | − | 0.793754i | \(-0.708124\pi\) | ||||
−0.608238 | + | 0.793754i | \(0.708124\pi\) | |||||||
\(314\) | 3018.89 | 0.542567 | ||||||||
\(315\) | 2359.33 | 0.422010 | ||||||||
\(316\) | 272.090 | 0.0484374 | ||||||||
\(317\) | 8651.72 | 1.53290 | 0.766450 | − | 0.642304i | \(-0.222021\pi\) | ||||
0.766450 | + | 0.642304i | \(0.222021\pi\) | |||||||
\(318\) | −8282.55 | −1.46057 | ||||||||
\(319\) | 780.069 | 0.136914 | ||||||||
\(320\) | 11791.7 | 2.05993 | ||||||||
\(321\) | 6652.98 | 1.15680 | ||||||||
\(322\) | 712.127 | 0.123246 | ||||||||
\(323\) | 3139.13 | 0.540762 | ||||||||
\(324\) | 553.941 | 0.0949830 | ||||||||
\(325\) | −8010.92 | −1.36728 | ||||||||
\(326\) | 289.239 | 0.0491395 | ||||||||
\(327\) | −2370.55 | −0.400891 | ||||||||
\(328\) | 5019.02 | 0.844906 | ||||||||
\(329\) | −1837.24 | −0.307874 | ||||||||
\(330\) | 21152.5 | 3.52850 | ||||||||
\(331\) | −5530.88 | −0.918444 | −0.459222 | − | 0.888322i | \(-0.651872\pi\) | ||||
−0.459222 | + | 0.888322i | \(0.651872\pi\) | |||||||
\(332\) | 383.727 | 0.0634330 | ||||||||
\(333\) | −8232.93 | −1.35484 | ||||||||
\(334\) | −7867.11 | −1.28883 | ||||||||
\(335\) | 6921.63 | 1.12886 | ||||||||
\(336\) | −1196.55 | −0.194278 | ||||||||
\(337\) | 2734.73 | 0.442049 | 0.221024 | − | 0.975268i | \(-0.429060\pi\) | ||||
0.221024 | + | 0.975268i | \(0.429060\pi\) | |||||||
\(338\) | 3805.70 | 0.612434 | ||||||||
\(339\) | 13077.5 | 2.09519 | ||||||||
\(340\) | 759.491 | 0.121145 | ||||||||
\(341\) | 1760.29 | 0.279545 | ||||||||
\(342\) | 12804.9 | 2.02459 | ||||||||
\(343\) | −2071.12 | −0.326035 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −15249.0 | −2.37965 | ||||||||
\(346\) | 5932.95 | 0.921842 | ||||||||
\(347\) | −8367.34 | −1.29447 | −0.647237 | − | 0.762289i | \(-0.724076\pi\) | ||||
−0.647237 | + | 0.762289i | \(0.724076\pi\) | |||||||
\(348\) | 197.149 | 0.0303687 | ||||||||
\(349\) | 2243.31 | 0.344074 | 0.172037 | − | 0.985090i | \(-0.444965\pi\) | ||||
0.172037 | + | 0.985090i | \(0.444965\pi\) | |||||||
\(350\) | −2356.83 | −0.359936 | ||||||||
\(351\) | −2155.94 | −0.327851 | ||||||||
\(352\) | 3557.34 | 0.538656 | ||||||||
\(353\) | 1573.11 | 0.237190 | 0.118595 | − | 0.992943i | \(-0.462161\pi\) | ||||
0.118595 | + | 0.992943i | \(0.462161\pi\) | |||||||
\(354\) | 15025.1 | 2.25586 | ||||||||
\(355\) | −10102.8 | −1.51043 | ||||||||
\(356\) | 528.642 | 0.0787022 | ||||||||
\(357\) | −566.627 | −0.0840031 | ||||||||
\(358\) | −4231.66 | −0.624722 | ||||||||
\(359\) | 5107.31 | 0.750846 | 0.375423 | − | 0.926854i | \(-0.377497\pi\) | ||||
0.375423 | + | 0.926854i | \(0.377497\pi\) | |||||||
\(360\) | 18713.3 | 2.73966 | ||||||||
\(361\) | 11605.8 | 1.69206 | ||||||||
\(362\) | −5558.92 | −0.807101 | ||||||||
\(363\) | 9627.90 | 1.39210 | ||||||||
\(364\) | 128.002 | 0.0184317 | ||||||||
\(365\) | −14969.0 | −2.14662 | ||||||||
\(366\) | −1050.12 | −0.149974 | ||||||||
\(367\) | 3195.77 | 0.454545 | 0.227273 | − | 0.973831i | \(-0.427019\pi\) | ||||
0.227273 | + | 0.973831i | \(0.427019\pi\) | |||||||
\(368\) | 4481.78 | 0.634861 | ||||||||
\(369\) | 7692.77 | 1.08528 | ||||||||
\(370\) | 11605.3 | 1.63062 | ||||||||
\(371\) | 1249.36 | 0.174834 | ||||||||
\(372\) | 444.883 | 0.0620057 | ||||||||
\(373\) | −12608.7 | −1.75027 | −0.875136 | − | 0.483876i | \(-0.839228\pi\) | ||||
−0.875136 | + | 0.483876i | \(0.839228\pi\) | |||||||
\(374\) | −2943.99 | −0.407032 | ||||||||
\(375\) | 29719.7 | 4.09259 | ||||||||
\(376\) | −14572.3 | −1.99870 | ||||||||
\(377\) | 408.405 | 0.0557929 | ||||||||
\(378\) | −634.282 | −0.0863067 | ||||||||
\(379\) | 1660.61 | 0.225065 | 0.112532 | − | 0.993648i | \(-0.464104\pi\) | ||||
0.112532 | + | 0.993648i | \(0.464104\pi\) | |||||||
\(380\) | 4467.44 | 0.603092 | ||||||||
\(381\) | 1950.59 | 0.262288 | ||||||||
\(382\) | −201.728 | −0.0270191 | ||||||||
\(383\) | −10824.1 | −1.44409 | −0.722043 | − | 0.691849i | \(-0.756797\pi\) | ||||
−0.722043 | + | 0.691849i | \(0.756797\pi\) | |||||||
\(384\) | −7020.33 | −0.932955 | ||||||||
\(385\) | −3190.69 | −0.422370 | ||||||||
\(386\) | −2809.17 | −0.370422 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1090.41 | −0.142673 | ||||||||
\(389\) | −6272.78 | −0.817590 | −0.408795 | − | 0.912626i | \(-0.634051\pi\) | ||||
−0.408795 | + | 0.912626i | \(0.634051\pi\) | |||||||
\(390\) | 11074.4 | 1.43788 | ||||||||
\(391\) | 2122.35 | 0.274505 | ||||||||
\(392\) | −8099.94 | −1.04364 | ||||||||
\(393\) | −18769.0 | −2.40909 | ||||||||
\(394\) | −6059.13 | −0.774758 | ||||||||
\(395\) | −3550.89 | −0.452316 | ||||||||
\(396\) | 2972.24 | 0.377174 | ||||||||
\(397\) | −2427.36 | −0.306866 | −0.153433 | − | 0.988159i | \(-0.549033\pi\) | ||||
−0.153433 | + | 0.988159i | \(0.549033\pi\) | |||||||
\(398\) | 532.387 | 0.0670506 | ||||||||
\(399\) | −3332.99 | −0.418191 | ||||||||
\(400\) | −14832.7 | −1.85409 | ||||||||
\(401\) | 5002.47 | 0.622971 | 0.311486 | − | 0.950251i | \(-0.399173\pi\) | ||||
0.311486 | + | 0.950251i | \(0.399173\pi\) | |||||||
\(402\) | −6780.85 | −0.841289 | ||||||||
\(403\) | 921.597 | 0.113916 | ||||||||
\(404\) | −1457.30 | −0.179464 | ||||||||
\(405\) | −7229.17 | −0.886964 | ||||||||
\(406\) | 120.153 | 0.0146875 | ||||||||
\(407\) | 11134.0 | 1.35600 | ||||||||
\(408\) | −4494.27 | −0.545342 | ||||||||
\(409\) | 8971.14 | 1.08458 | 0.542292 | − | 0.840190i | \(-0.317557\pi\) | ||||
0.542292 | + | 0.840190i | \(0.317557\pi\) | |||||||
\(410\) | −10843.8 | −1.30619 | ||||||||
\(411\) | 9878.58 | 1.18558 | ||||||||
\(412\) | 552.803 | 0.0661035 | ||||||||
\(413\) | −2266.41 | −0.270031 | ||||||||
\(414\) | 8657.31 | 1.02774 | ||||||||
\(415\) | −5007.81 | −0.592346 | ||||||||
\(416\) | 1862.45 | 0.219505 | ||||||||
\(417\) | −2484.60 | −0.291778 | ||||||||
\(418\) | −17317.0 | −2.02632 | ||||||||
\(419\) | 11112.1 | 1.29561 | 0.647806 | − | 0.761805i | \(-0.275687\pi\) | ||||
0.647806 | + | 0.761805i | \(0.275687\pi\) | |||||||
\(420\) | −806.393 | −0.0936856 | ||||||||
\(421\) | −1138.09 | −0.131751 | −0.0658754 | − | 0.997828i | \(-0.520984\pi\) | ||||
−0.0658754 | + | 0.997828i | \(0.520984\pi\) | |||||||
\(422\) | 2171.69 | 0.250513 | ||||||||
\(423\) | −22335.3 | −2.56733 | ||||||||
\(424\) | 9909.42 | 1.13501 | ||||||||
\(425\) | −7024.03 | −0.801684 | ||||||||
\(426\) | 9897.36 | 1.12565 | ||||||||
\(427\) | 158.402 | 0.0179522 | ||||||||
\(428\) | −1317.77 | −0.148824 | ||||||||
\(429\) | 10624.7 | 1.19572 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7440.65 | −0.831563 | −0.415781 | − | 0.909465i | \(-0.636492\pi\) | ||||
−0.415781 | + | 0.909465i | \(0.636492\pi\) | |||||||
\(432\) | −3991.86 | −0.444580 | ||||||||
\(433\) | −8252.84 | −0.915949 | −0.457975 | − | 0.888965i | \(-0.651425\pi\) | ||||
−0.457975 | + | 0.888965i | \(0.651425\pi\) | |||||||
\(434\) | 271.135 | 0.0299883 | ||||||||
\(435\) | −2572.89 | −0.283587 | ||||||||
\(436\) | 469.539 | 0.0515753 | ||||||||
\(437\) | 12484.0 | 1.36656 | ||||||||
\(438\) | 14664.6 | 1.59977 | ||||||||
\(439\) | −11729.5 | −1.27521 | −0.637605 | − | 0.770364i | \(-0.720075\pi\) | ||||
−0.637605 | + | 0.770364i | \(0.720075\pi\) | |||||||
\(440\) | −25307.3 | −2.74200 | ||||||||
\(441\) | −12415.0 | −1.34056 | ||||||||
\(442\) | −1541.32 | −0.165867 | ||||||||
\(443\) | 1411.13 | 0.151343 | 0.0756714 | − | 0.997133i | \(-0.475890\pi\) | ||||
0.0756714 | + | 0.997133i | \(0.475890\pi\) | |||||||
\(444\) | 2813.92 | 0.300772 | ||||||||
\(445\) | −6899.01 | −0.734932 | ||||||||
\(446\) | −8944.97 | −0.949679 | ||||||||
\(447\) | 20209.7 | 2.13844 | ||||||||
\(448\) | 1742.51 | 0.183763 | ||||||||
\(449\) | −9517.45 | −1.00035 | −0.500174 | − | 0.865925i | \(-0.666731\pi\) | ||||
−0.500174 | + | 0.865925i | \(0.666731\pi\) | |||||||
\(450\) | −28651.9 | −3.00147 | ||||||||
\(451\) | −10403.5 | −1.08621 | ||||||||
\(452\) | −2590.28 | −0.269550 | ||||||||
\(453\) | −8006.11 | −0.830375 | ||||||||
\(454\) | −13139.6 | −1.35830 | ||||||||
\(455\) | −1670.48 | −0.172117 | ||||||||
\(456\) | −26436.0 | −2.71486 | ||||||||
\(457\) | −11178.2 | −1.14419 | −0.572093 | − | 0.820189i | \(-0.693868\pi\) | ||||
−0.572093 | + | 0.820189i | \(0.693868\pi\) | |||||||
\(458\) | −8818.57 | −0.899705 | ||||||||
\(459\) | −1890.34 | −0.192230 | ||||||||
\(460\) | 3020.41 | 0.306146 | ||||||||
\(461\) | −15694.1 | −1.58557 | −0.792786 | − | 0.609500i | \(-0.791370\pi\) | ||||
−0.792786 | + | 0.609500i | \(0.791370\pi\) | |||||||
\(462\) | 3125.79 | 0.314772 | ||||||||
\(463\) | −2547.36 | −0.255693 | −0.127847 | − | 0.991794i | \(-0.540807\pi\) | ||||
−0.127847 | + | 0.991794i | \(0.540807\pi\) | |||||||
\(464\) | 756.187 | 0.0756575 | ||||||||
\(465\) | −5805.92 | −0.579017 | ||||||||
\(466\) | 3913.34 | 0.389017 | ||||||||
\(467\) | −7822.43 | −0.775115 | −0.387558 | − | 0.921845i | \(-0.626681\pi\) | ||||
−0.387558 | + | 0.921845i | \(0.626681\pi\) | |||||||
\(468\) | 1556.12 | 0.153700 | ||||||||
\(469\) | 1022.84 | 0.100704 | ||||||||
\(470\) | 31484.2 | 3.08991 | ||||||||
\(471\) | −9552.80 | −0.934543 | ||||||||
\(472\) | −17976.3 | −1.75302 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 3478.67 | 0.337089 | ||||||||
\(475\) | −41316.4 | −3.99100 | ||||||||
\(476\) | 112.233 | 0.0108071 | ||||||||
\(477\) | 15188.4 | 1.45792 | ||||||||
\(478\) | 6489.39 | 0.620957 | ||||||||
\(479\) | −14772.7 | −1.40915 | −0.704573 | − | 0.709632i | \(-0.748861\pi\) | ||||
−0.704573 | + | 0.709632i | \(0.748861\pi\) | |||||||
\(480\) | −11733.1 | −1.11571 | ||||||||
\(481\) | 5829.19 | 0.552574 | ||||||||
\(482\) | −12514.7 | −1.18263 | ||||||||
\(483\) | −2253.41 | −0.212285 | ||||||||
\(484\) | −1907.02 | −0.179096 | ||||||||
\(485\) | 14230.3 | 1.33230 | ||||||||
\(486\) | 12677.0 | 1.18321 | ||||||||
\(487\) | 5286.95 | 0.491939 | 0.245970 | − | 0.969278i | \(-0.420894\pi\) | ||||
0.245970 | + | 0.969278i | \(0.420894\pi\) | |||||||
\(488\) | 1256.38 | 0.116545 | ||||||||
\(489\) | −915.251 | −0.0846402 | ||||||||
\(490\) | 17500.3 | 1.61344 | ||||||||
\(491\) | −17508.4 | −1.60925 | −0.804624 | − | 0.593784i | \(-0.797633\pi\) | ||||
−0.804624 | + | 0.593784i | \(0.797633\pi\) | |||||||
\(492\) | −2629.30 | −0.240931 | ||||||||
\(493\) | 358.092 | 0.0327133 | ||||||||
\(494\) | −9066.29 | −0.825732 | ||||||||
\(495\) | −38789.1 | −3.52210 | ||||||||
\(496\) | 1706.39 | 0.154474 | ||||||||
\(497\) | −1492.94 | −0.134743 | ||||||||
\(498\) | 4905.95 | 0.441447 | ||||||||
\(499\) | −1560.31 | −0.139978 | −0.0699888 | − | 0.997548i | \(-0.522296\pi\) | ||||
−0.0699888 | + | 0.997548i | \(0.522296\pi\) | |||||||
\(500\) | −5886.65 | −0.526518 | ||||||||
\(501\) | 24894.2 | 2.21994 | ||||||||
\(502\) | −11306.4 | −1.00523 | ||||||||
\(503\) | 7420.52 | 0.657783 | 0.328891 | − | 0.944368i | \(-0.393325\pi\) | ||||
0.328891 | + | 0.944368i | \(0.393325\pi\) | |||||||
\(504\) | 2765.34 | 0.244401 | ||||||||
\(505\) | 19018.5 | 1.67586 | ||||||||
\(506\) | −11707.9 | −1.02861 | ||||||||
\(507\) | −12042.5 | −1.05489 | ||||||||
\(508\) | −386.358 | −0.0337438 | ||||||||
\(509\) | 661.902 | 0.0576390 | 0.0288195 | − | 0.999585i | \(-0.490825\pi\) | ||||
0.0288195 | + | 0.999585i | \(0.490825\pi\) | |||||||
\(510\) | 9710.09 | 0.843079 | ||||||||
\(511\) | −2212.03 | −0.191496 | ||||||||
\(512\) | 12923.4 | 1.11550 | ||||||||
\(513\) | −11119.3 | −0.956976 | ||||||||
\(514\) | −15078.8 | −1.29396 | ||||||||
\(515\) | −7214.33 | −0.617284 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 30205.6 | 2.56952 | ||||||||
\(518\) | 1714.96 | 0.145465 | ||||||||
\(519\) | −18773.9 | −1.58782 | ||||||||
\(520\) | −13249.6 | −1.11737 | ||||||||
\(521\) | 13039.0 | 1.09645 | 0.548225 | − | 0.836331i | \(-0.315304\pi\) | ||||
0.548225 | + | 0.836331i | \(0.315304\pi\) | |||||||
\(522\) | 1460.70 | 0.122477 | ||||||||
\(523\) | −18176.0 | −1.51966 | −0.759829 | − | 0.650123i | \(-0.774717\pi\) | ||||
−0.759829 | + | 0.650123i | \(0.774717\pi\) | |||||||
\(524\) | 3717.62 | 0.309933 | ||||||||
\(525\) | 7457.80 | 0.619971 | ||||||||
\(526\) | 116.586 | 0.00966421 | ||||||||
\(527\) | 808.063 | 0.0667927 | ||||||||
\(528\) | 19672.2 | 1.62144 | ||||||||
\(529\) | −3726.68 | −0.306294 | ||||||||
\(530\) | −21409.8 | −1.75468 | ||||||||
\(531\) | −27552.7 | −2.25176 | ||||||||
\(532\) | 660.172 | 0.0538009 | ||||||||
\(533\) | −5446.74 | −0.442635 | ||||||||
\(534\) | 6758.69 | 0.547710 | ||||||||
\(535\) | 17197.5 | 1.38974 | ||||||||
\(536\) | 8112.76 | 0.653765 | ||||||||
\(537\) | 13390.4 | 1.07605 | ||||||||
\(538\) | −2341.29 | −0.187622 | ||||||||
\(539\) | 16789.6 | 1.34171 | ||||||||
\(540\) | −2690.23 | −0.214388 | ||||||||
\(541\) | 3752.56 | 0.298216 | 0.149108 | − | 0.988821i | \(-0.452360\pi\) | ||||
0.149108 | + | 0.988821i | \(0.452360\pi\) | |||||||
\(542\) | 13106.5 | 1.03869 | ||||||||
\(543\) | 17590.3 | 1.39019 | ||||||||
\(544\) | 1633.00 | 0.128703 | ||||||||
\(545\) | −6127.69 | −0.481617 | ||||||||
\(546\) | 1636.51 | 0.128271 | ||||||||
\(547\) | 7414.69 | 0.579578 | 0.289789 | − | 0.957090i | \(-0.406415\pi\) | ||||
0.289789 | + | 0.957090i | \(0.406415\pi\) | |||||||
\(548\) | −1956.67 | −0.152527 | ||||||||
\(549\) | 1925.69 | 0.149702 | ||||||||
\(550\) | 38747.9 | 3.00403 | ||||||||
\(551\) | 2106.35 | 0.162856 | ||||||||
\(552\) | −17873.2 | −1.37814 | ||||||||
\(553\) | −524.729 | −0.0403504 | ||||||||
\(554\) | 17158.0 | 1.31584 | ||||||||
\(555\) | −36723.0 | −2.80865 | ||||||||
\(556\) | 492.130 | 0.0375377 | ||||||||
\(557\) | −14232.7 | −1.08269 | −0.541345 | − | 0.840801i | \(-0.682085\pi\) | ||||
−0.541345 | + | 0.840801i | \(0.682085\pi\) | |||||||
\(558\) | 3296.19 | 0.250069 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −3093.00 | −0.233399 | ||||||||
\(561\) | 9315.77 | 0.701091 | ||||||||
\(562\) | −7397.68 | −0.555253 | ||||||||
\(563\) | −20932.3 | −1.56695 | −0.783475 | − | 0.621423i | \(-0.786555\pi\) | ||||
−0.783475 | + | 0.621423i | \(0.786555\pi\) | |||||||
\(564\) | 7633.97 | 0.569943 | ||||||||
\(565\) | 33804.3 | 2.51709 | ||||||||
\(566\) | 13053.5 | 0.969399 | ||||||||
\(567\) | −1068.28 | −0.0791247 | ||||||||
\(568\) | −11841.4 | −0.874745 | ||||||||
\(569\) | −3328.84 | −0.245259 | −0.122629 | − | 0.992453i | \(-0.539133\pi\) | ||||
−0.122629 | + | 0.992453i | \(0.539133\pi\) | |||||||
\(570\) | 57116.2 | 4.19708 | ||||||||
\(571\) | −2268.00 | −0.166222 | −0.0831110 | − | 0.996540i | \(-0.526486\pi\) | ||||
−0.0831110 | + | 0.996540i | \(0.526486\pi\) | |||||||
\(572\) | −2104.45 | −0.153831 | ||||||||
\(573\) | 638.335 | 0.0465389 | ||||||||
\(574\) | −1602.44 | −0.116524 | ||||||||
\(575\) | −27933.7 | −2.02594 | ||||||||
\(576\) | 21183.7 | 1.53238 | ||||||||
\(577\) | 11714.3 | 0.845190 | 0.422595 | − | 0.906319i | \(-0.361119\pi\) | ||||
0.422595 | + | 0.906319i | \(0.361119\pi\) | |||||||
\(578\) | 11090.0 | 0.798068 | ||||||||
\(579\) | 8889.16 | 0.638032 | ||||||||
\(580\) | 509.617 | 0.0364840 | ||||||||
\(581\) | −740.024 | −0.0528423 | ||||||||
\(582\) | −13940.9 | −0.992900 | ||||||||
\(583\) | −20540.3 | −1.45917 | ||||||||
\(584\) | −17545.0 | −1.24318 | ||||||||
\(585\) | −20308.0 | −1.43527 | ||||||||
\(586\) | 14773.7 | 1.04146 | ||||||||
\(587\) | −13734.5 | −0.965730 | −0.482865 | − | 0.875695i | \(-0.660404\pi\) | ||||
−0.482865 | + | 0.875695i | \(0.660404\pi\) | |||||||
\(588\) | 4243.30 | 0.297603 | ||||||||
\(589\) | 4753.15 | 0.332513 | ||||||||
\(590\) | 38838.7 | 2.71011 | ||||||||
\(591\) | 19173.1 | 1.33448 | ||||||||
\(592\) | 10793.1 | 0.749313 | ||||||||
\(593\) | −26981.9 | −1.86849 | −0.934244 | − | 0.356634i | \(-0.883924\pi\) | ||||
−0.934244 | + | 0.356634i | \(0.883924\pi\) | |||||||
\(594\) | 10428.1 | 0.720317 | ||||||||
\(595\) | −1464.69 | −0.100918 | ||||||||
\(596\) | −4002.97 | −0.275114 | ||||||||
\(597\) | −1684.65 | −0.115491 | ||||||||
\(598\) | −6129.66 | −0.419164 | ||||||||
\(599\) | 2470.79 | 0.168537 | 0.0842685 | − | 0.996443i | \(-0.473145\pi\) | ||||
0.0842685 | + | 0.996443i | \(0.473145\pi\) | |||||||
\(600\) | 59152.4 | 4.02481 | ||||||||
\(601\) | −20621.9 | −1.39964 | −0.699820 | − | 0.714319i | \(-0.746737\pi\) | ||||
−0.699820 | + | 0.714319i | \(0.746737\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12434.6 | 0.839762 | ||||||||
\(604\) | 1585.79 | 0.106829 | ||||||||
\(605\) | 24887.4 | 1.67243 | ||||||||
\(606\) | −18631.6 | −1.24894 | ||||||||
\(607\) | −4220.90 | −0.282242 | −0.141121 | − | 0.989992i | \(-0.545071\pi\) | ||||
−0.141121 | + | 0.989992i | \(0.545071\pi\) | |||||||
\(608\) | 9605.58 | 0.640720 | ||||||||
\(609\) | −380.206 | −0.0252984 | ||||||||
\(610\) | −2714.48 | −0.180174 | ||||||||
\(611\) | 15814.1 | 1.04709 | ||||||||
\(612\) | 1364.41 | 0.0901196 | ||||||||
\(613\) | 12018.1 | 0.791852 | 0.395926 | − | 0.918282i | \(-0.370424\pi\) | ||||
0.395926 | + | 0.918282i | \(0.370424\pi\) | |||||||
\(614\) | −17049.3 | −1.12061 | ||||||||
\(615\) | 34313.6 | 2.24985 | ||||||||
\(616\) | −3739.76 | −0.244609 | ||||||||
\(617\) | −5171.02 | −0.337403 | −0.168701 | − | 0.985667i | \(-0.553957\pi\) | ||||
−0.168701 | + | 0.985667i | \(0.553957\pi\) | |||||||
\(618\) | 7067.59 | 0.460033 | ||||||||
\(619\) | 5055.56 | 0.328272 | 0.164136 | − | 0.986438i | \(-0.447516\pi\) | ||||
0.164136 | + | 0.986438i | \(0.447516\pi\) | |||||||
\(620\) | 1149.99 | 0.0744915 | ||||||||
\(621\) | −7517.68 | −0.485788 | ||||||||
\(622\) | −22177.6 | −1.42965 | ||||||||
\(623\) | −1019.50 | −0.0655621 | ||||||||
\(624\) | 10299.4 | 0.660745 | ||||||||
\(625\) | 38816.7 | 2.48427 | ||||||||
\(626\) | 17058.6 | 1.08914 | ||||||||
\(627\) | 54796.8 | 3.49023 | ||||||||
\(628\) | 1892.14 | 0.120230 | ||||||||
\(629\) | 5111.07 | 0.323993 | ||||||||
\(630\) | −5974.65 | −0.377835 | ||||||||
\(631\) | 20865.9 | 1.31642 | 0.658209 | − | 0.752835i | \(-0.271314\pi\) | ||||
0.658209 | + | 0.752835i | \(0.271314\pi\) | |||||||
\(632\) | −4161.95 | −0.261952 | ||||||||
\(633\) | −6871.97 | −0.431495 | ||||||||
\(634\) | −21909.2 | −1.37244 | ||||||||
\(635\) | 5042.14 | 0.315105 | ||||||||
\(636\) | −5191.23 | −0.323657 | ||||||||
\(637\) | 8790.20 | 0.546751 | ||||||||
\(638\) | −1975.41 | −0.122582 | ||||||||
\(639\) | −18149.6 | −1.12361 | ||||||||
\(640\) | −18147.1 | −1.12082 | ||||||||
\(641\) | 20942.5 | 1.29045 | 0.645226 | − | 0.763992i | \(-0.276763\pi\) | ||||
0.645226 | + | 0.763992i | \(0.276763\pi\) | |||||||
\(642\) | −16847.7 | −1.03571 | ||||||||
\(643\) | −1235.94 | −0.0758020 | −0.0379010 | − | 0.999281i | \(-0.512067\pi\) | ||||
−0.0379010 | + | 0.999281i | \(0.512067\pi\) | |||||||
\(644\) | 446.337 | 0.0273108 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7949.39 | −0.484155 | ||||||||
\(647\) | 16372.8 | 0.994873 | 0.497437 | − | 0.867500i | \(-0.334275\pi\) | ||||
0.497437 | + | 0.867500i | \(0.334275\pi\) | |||||||
\(648\) | −8473.22 | −0.513672 | ||||||||
\(649\) | 37261.5 | 2.25369 | ||||||||
\(650\) | 20286.5 | 1.22415 | ||||||||
\(651\) | −857.964 | −0.0516533 | ||||||||
\(652\) | 181.286 | 0.0108891 | ||||||||
\(653\) | −3699.21 | −0.221686 | −0.110843 | − | 0.993838i | \(-0.535355\pi\) | ||||
−0.110843 | + | 0.993838i | \(0.535355\pi\) | |||||||
\(654\) | 6003.06 | 0.358927 | ||||||||
\(655\) | −48516.5 | −2.89420 | ||||||||
\(656\) | −10085.0 | −0.600231 | ||||||||
\(657\) | −26891.6 | −1.59687 | ||||||||
\(658\) | 4652.55 | 0.275646 | ||||||||
\(659\) | −27786.0 | −1.64247 | −0.821237 | − | 0.570588i | \(-0.806715\pi\) | ||||
−0.821237 | + | 0.570588i | \(0.806715\pi\) | |||||||
\(660\) | 13257.7 | 0.781901 | ||||||||
\(661\) | 5798.03 | 0.341176 | 0.170588 | − | 0.985342i | \(-0.445433\pi\) | ||||
0.170588 | + | 0.985342i | \(0.445433\pi\) | |||||||
\(662\) | 14006.1 | 0.822302 | ||||||||
\(663\) | 4877.27 | 0.285697 | ||||||||
\(664\) | −5869.59 | −0.343048 | ||||||||
\(665\) | −8615.53 | −0.502400 | ||||||||
\(666\) | 20848.7 | 1.21302 | ||||||||
\(667\) | 1424.09 | 0.0826702 | ||||||||
\(668\) | −4930.85 | −0.285599 | ||||||||
\(669\) | 28304.9 | 1.63577 | ||||||||
\(670\) | −17528.0 | −1.01070 | ||||||||
\(671\) | −2604.24 | −0.149830 | ||||||||
\(672\) | −1733.85 | −0.0995308 | ||||||||
\(673\) | 4577.82 | 0.262202 | 0.131101 | − | 0.991369i | \(-0.458149\pi\) | ||||
0.131101 | + | 0.991369i | \(0.458149\pi\) | |||||||
\(674\) | −6925.30 | −0.395776 | ||||||||
\(675\) | 24880.2 | 1.41873 | ||||||||
\(676\) | 2385.28 | 0.135713 | ||||||||
\(677\) | 12344.6 | 0.700801 | 0.350401 | − | 0.936600i | \(-0.386045\pi\) | ||||
0.350401 | + | 0.936600i | \(0.386045\pi\) | |||||||
\(678\) | −33116.7 | −1.87587 | ||||||||
\(679\) | 2102.87 | 0.118852 | ||||||||
\(680\) | −11617.4 | −0.655156 | ||||||||
\(681\) | 41578.0 | 2.33961 | ||||||||
\(682\) | −4457.66 | −0.250283 | ||||||||
\(683\) | 16504.5 | 0.924635 | 0.462318 | − | 0.886714i | \(-0.347018\pi\) | ||||
0.462318 | + | 0.886714i | \(0.347018\pi\) | |||||||
\(684\) | 8025.69 | 0.448640 | ||||||||
\(685\) | 25535.4 | 1.42432 | ||||||||
\(686\) | 5244.81 | 0.291906 | ||||||||
\(687\) | 27905.0 | 1.54969 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10753.9 | −0.594616 | ||||||||
\(690\) | 38615.9 | 2.13055 | ||||||||
\(691\) | 11094.6 | 0.610791 | 0.305396 | − | 0.952226i | \(-0.401211\pi\) | ||||
0.305396 | + | 0.952226i | \(0.401211\pi\) | |||||||
\(692\) | 3718.58 | 0.204276 | ||||||||
\(693\) | −5732.02 | −0.314201 | ||||||||
\(694\) | 21189.1 | 1.15897 | ||||||||
\(695\) | −6422.52 | −0.350533 | ||||||||
\(696\) | −3015.65 | −0.164236 | ||||||||
\(697\) | −4775.74 | −0.259532 | ||||||||
\(698\) | −5680.86 | −0.308057 | ||||||||
\(699\) | −12383.1 | −0.670061 | ||||||||
\(700\) | −1477.18 | −0.0797603 | ||||||||
\(701\) | 3488.71 | 0.187970 | 0.0939850 | − | 0.995574i | \(-0.470039\pi\) | ||||
0.0939850 | + | 0.995574i | \(0.470039\pi\) | |||||||
\(702\) | 5459.60 | 0.293532 | ||||||||
\(703\) | 30064.1 | 1.61293 | ||||||||
\(704\) | −28648.2 | −1.53369 | ||||||||
\(705\) | −99626.7 | −5.32221 | ||||||||
\(706\) | −3983.66 | −0.212361 | ||||||||
\(707\) | 2810.44 | 0.149501 | ||||||||
\(708\) | 9417.22 | 0.499888 | ||||||||
\(709\) | 11358.7 | 0.601669 | 0.300835 | − | 0.953676i | \(-0.402735\pi\) | ||||
0.300835 | + | 0.953676i | \(0.402735\pi\) | |||||||
\(710\) | 25584.0 | 1.35232 | ||||||||
\(711\) | −6379.12 | −0.336478 | ||||||||
\(712\) | −8086.25 | −0.425625 | ||||||||
\(713\) | 3213.57 | 0.168793 | ||||||||
\(714\) | 1434.90 | 0.0752098 | ||||||||
\(715\) | 27464.0 | 1.43650 | ||||||||
\(716\) | −2652.27 | −0.138436 | ||||||||
\(717\) | −20534.6 | −1.06957 | ||||||||
\(718\) | −12933.5 | −0.672249 | ||||||||
\(719\) | −34524.2 | −1.79073 | −0.895364 | − | 0.445335i | \(-0.853085\pi\) | ||||
−0.895364 | + | 0.445335i | \(0.853085\pi\) | |||||||
\(720\) | −37601.5 | −1.94629 | ||||||||
\(721\) | −1066.09 | −0.0550670 | ||||||||
\(722\) | −29390.1 | −1.51494 | ||||||||
\(723\) | 39600.8 | 2.03703 | ||||||||
\(724\) | −3484.15 | −0.178850 | ||||||||
\(725\) | −4713.11 | −0.241435 | ||||||||
\(726\) | −24381.2 | −1.24638 | ||||||||
\(727\) | 16846.5 | 0.859426 | 0.429713 | − | 0.902966i | \(-0.358615\pi\) | ||||
0.429713 | + | 0.902966i | \(0.358615\pi\) | |||||||
\(728\) | −1957.95 | −0.0996793 | ||||||||
\(729\) | −30691.3 | −1.55928 | ||||||||
\(730\) | 37906.9 | 1.92191 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −658.179 | −0.0332336 | ||||||||
\(733\) | −13917.8 | −0.701317 | −0.350658 | − | 0.936503i | \(-0.614042\pi\) | ||||
−0.350658 | + | 0.936503i | \(0.614042\pi\) | |||||||
\(734\) | −8092.82 | −0.406964 | ||||||||
\(735\) | −55376.9 | −2.77906 | ||||||||
\(736\) | 6494.27 | 0.325247 | ||||||||
\(737\) | −16816.2 | −0.840479 | ||||||||
\(738\) | −19480.8 | −0.971678 | ||||||||
\(739\) | 10001.0 | 0.497825 | 0.248912 | − | 0.968526i | \(-0.419927\pi\) | ||||
0.248912 | + | 0.968526i | \(0.419927\pi\) | |||||||
\(740\) | 7273.79 | 0.361338 | ||||||||
\(741\) | 28688.8 | 1.42228 | ||||||||
\(742\) | −3163.81 | −0.156533 | ||||||||
\(743\) | −5356.46 | −0.264481 | −0.132240 | − | 0.991218i | \(-0.542217\pi\) | ||||
−0.132240 | + | 0.991218i | \(0.542217\pi\) | |||||||
\(744\) | −6805.05 | −0.335329 | ||||||||
\(745\) | 52240.5 | 2.56905 | ||||||||
\(746\) | 31929.6 | 1.56706 | ||||||||
\(747\) | −8996.45 | −0.440647 | ||||||||
\(748\) | −1845.19 | −0.0901964 | ||||||||
\(749\) | 2541.34 | 0.123977 | ||||||||
\(750\) | −75260.8 | −3.66418 | ||||||||
\(751\) | 30162.2 | 1.46556 | 0.732779 | − | 0.680467i | \(-0.238223\pi\) | ||||
0.732779 | + | 0.680467i | \(0.238223\pi\) | |||||||
\(752\) | 29280.9 | 1.41990 | ||||||||
\(753\) | 35777.2 | 1.73146 | ||||||||
\(754\) | −1034.22 | −0.0499526 | ||||||||
\(755\) | −20695.2 | −0.997585 | ||||||||
\(756\) | −397.547 | −0.0191252 | ||||||||
\(757\) | 35857.4 | 1.72161 | 0.860805 | − | 0.508935i | \(-0.169961\pi\) | ||||
0.860805 | + | 0.508935i | \(0.169961\pi\) | |||||||
\(758\) | −4205.24 | −0.201505 | ||||||||
\(759\) | 37047.7 | 1.77173 | ||||||||
\(760\) | −68335.1 | −3.26155 | ||||||||
\(761\) | 3433.69 | 0.163563 | 0.0817814 | − | 0.996650i | \(-0.473939\pi\) | ||||
0.0817814 | + | 0.996650i | \(0.473939\pi\) | |||||||
\(762\) | −4939.59 | −0.234832 | ||||||||
\(763\) | −905.514 | −0.0429644 | ||||||||
\(764\) | −126.436 | −0.00598731 | ||||||||
\(765\) | −17806.2 | −0.841549 | ||||||||
\(766\) | 27410.4 | 1.29292 | ||||||||
\(767\) | 19508.2 | 0.918386 | ||||||||
\(768\) | −18715.9 | −0.879362 | ||||||||
\(769\) | −2028.54 | −0.0951248 | −0.0475624 | − | 0.998868i | \(-0.515145\pi\) | ||||
−0.0475624 | + | 0.998868i | \(0.515145\pi\) | |||||||
\(770\) | 8079.94 | 0.378157 | ||||||||
\(771\) | 47714.3 | 2.22878 | ||||||||
\(772\) | −1760.69 | −0.0820839 | ||||||||
\(773\) | 39469.4 | 1.83650 | 0.918251 | − | 0.395999i | \(-0.129602\pi\) | ||||
0.918251 | + | 0.395999i | \(0.129602\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10635.5 | −0.492953 | ||||||||
\(776\) | 16679.2 | 0.771582 | ||||||||
\(777\) | −5426.70 | −0.250556 | ||||||||
\(778\) | 15884.9 | 0.732006 | ||||||||
\(779\) | −28091.6 | −1.29202 | ||||||||
\(780\) | 6941.06 | 0.318628 | ||||||||
\(781\) | 24545.0 | 1.12457 | ||||||||
\(782\) | −5374.53 | −0.245771 | ||||||||
\(783\) | −1268.42 | −0.0578922 | ||||||||
\(784\) | 16275.6 | 0.741417 | ||||||||
\(785\) | −24693.3 | −1.12273 | ||||||||
\(786\) | 47529.7 | 2.15691 | ||||||||
\(787\) | −39757.2 | −1.80075 | −0.900376 | − | 0.435113i | \(-0.856708\pi\) | ||||
−0.900376 | + | 0.435113i | \(0.856708\pi\) | |||||||
\(788\) | −3797.66 | −0.171683 | ||||||||
\(789\) | −368.916 | −0.0166461 | ||||||||
\(790\) | 8992.10 | 0.404968 | ||||||||
\(791\) | 4995.40 | 0.224546 | ||||||||
\(792\) | −45464.2 | −2.03977 | ||||||||
\(793\) | −1363.45 | −0.0610562 | ||||||||
\(794\) | 6146.94 | 0.274744 | ||||||||
\(795\) | 67747.8 | 3.02235 | ||||||||
\(796\) | 333.682 | 0.0148581 | ||||||||
\(797\) | 9242.68 | 0.410781 | 0.205391 | − | 0.978680i | \(-0.434154\pi\) | ||||
0.205391 | + | 0.978680i | \(0.434154\pi\) | |||||||
\(798\) | 8440.30 | 0.374415 | ||||||||
\(799\) | 13866.0 | 0.613945 | ||||||||
\(800\) | −21493.2 | −0.949873 | ||||||||
\(801\) | −12394.0 | −0.546716 | ||||||||
\(802\) | −12668.0 | −0.557760 | ||||||||
\(803\) | 36367.5 | 1.59823 | ||||||||
\(804\) | −4250.01 | −0.186426 | ||||||||
\(805\) | −5824.90 | −0.255032 | ||||||||
\(806\) | −2333.81 | −0.101991 | ||||||||
\(807\) | 7408.65 | 0.323168 | ||||||||
\(808\) | 22291.3 | 0.970552 | ||||||||
\(809\) | −14493.7 | −0.629877 | −0.314939 | − | 0.949112i | \(-0.601984\pi\) | ||||
−0.314939 | + | 0.949112i | \(0.601984\pi\) | |||||||
\(810\) | 18306.8 | 0.794118 | ||||||||
\(811\) | 36976.4 | 1.60101 | 0.800504 | − | 0.599328i | \(-0.204565\pi\) | ||||
0.800504 | + | 0.599328i | \(0.204565\pi\) | |||||||
\(812\) | 75.3082 | 0.00325468 | ||||||||
\(813\) | −41473.3 | −1.78909 | ||||||||
\(814\) | −28195.1 | −1.21405 | ||||||||
\(815\) | −2365.86 | −0.101684 | ||||||||
\(816\) | 9030.56 | 0.387418 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −22718.1 | −0.971051 | ||||||||
\(819\) | −3001.00 | −0.128038 | ||||||||
\(820\) | −6796.57 | −0.289447 | ||||||||
\(821\) | 41436.7 | 1.76145 | 0.880724 | − | 0.473629i | \(-0.157056\pi\) | ||||
0.880724 | + | 0.473629i | \(0.157056\pi\) | |||||||
\(822\) | −25016.0 | −1.06148 | ||||||||
\(823\) | −29097.3 | −1.23241 | −0.616203 | − | 0.787588i | \(-0.711330\pi\) | ||||
−0.616203 | + | 0.787588i | \(0.711330\pi\) | |||||||
\(824\) | −8455.82 | −0.357491 | ||||||||
\(825\) | −122612. | −5.17429 | ||||||||
\(826\) | 5739.36 | 0.241765 | ||||||||
\(827\) | −16157.9 | −0.679402 | −0.339701 | − | 0.940534i | \(-0.610326\pi\) | ||||
−0.339701 | + | 0.940534i | \(0.610326\pi\) | |||||||
\(828\) | 5426.11 | 0.227742 | ||||||||
\(829\) | 41034.9 | 1.71918 | 0.859591 | − | 0.510983i | \(-0.170718\pi\) | ||||
0.859591 | + | 0.510983i | \(0.170718\pi\) | |||||||
\(830\) | 12681.5 | 0.530340 | ||||||||
\(831\) | −54293.7 | −2.26646 | ||||||||
\(832\) | −14998.7 | −0.624985 | ||||||||
\(833\) | 7707.31 | 0.320579 | ||||||||
\(834\) | 6291.89 | 0.261235 | ||||||||
\(835\) | 64349.7 | 2.66696 | ||||||||
\(836\) | −10853.7 | −0.449023 | ||||||||
\(837\) | −2862.28 | −0.118202 | ||||||||
\(838\) | −28139.7 | −1.15999 | ||||||||
\(839\) | 28367.1 | 1.16727 | 0.583636 | − | 0.812015i | \(-0.301629\pi\) | ||||
0.583636 | + | 0.812015i | \(0.301629\pi\) | |||||||
\(840\) | 12334.8 | 0.506656 | ||||||||
\(841\) | −24148.7 | −0.990148 | ||||||||
\(842\) | 2882.04 | 0.117959 | ||||||||
\(843\) | 23408.8 | 0.956395 | ||||||||
\(844\) | 1361.15 | 0.0555125 | ||||||||
\(845\) | −31129.0 | −1.26730 | ||||||||
\(846\) | 56560.9 | 2.29859 | ||||||||
\(847\) | 3677.72 | 0.149195 | ||||||||
\(848\) | −19911.5 | −0.806324 | ||||||||
\(849\) | −41305.7 | −1.66974 | ||||||||
\(850\) | 17787.3 | 0.717765 | ||||||||
\(851\) | 20326.1 | 0.818767 | ||||||||
\(852\) | 6203.34 | 0.249440 | ||||||||
\(853\) | −18754.4 | −0.752801 | −0.376400 | − | 0.926457i | \(-0.622838\pi\) | ||||
−0.376400 | + | 0.926457i | \(0.622838\pi\) | |||||||
\(854\) | −401.129 | −0.0160730 | ||||||||
\(855\) | −104739. | −4.18947 | ||||||||
\(856\) | 20157.0 | 0.804849 | ||||||||
\(857\) | −12782.0 | −0.509481 | −0.254741 | − | 0.967009i | \(-0.581990\pi\) | ||||
−0.254741 | + | 0.967009i | \(0.581990\pi\) | |||||||
\(858\) | −26905.4 | −1.07055 | ||||||||
\(859\) | 2156.19 | 0.0856442 | 0.0428221 | − | 0.999083i | \(-0.486365\pi\) | ||||
0.0428221 | + | 0.999083i | \(0.486365\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5070.66 | 0.200706 | ||||||||
\(862\) | 18842.3 | 0.744516 | ||||||||
\(863\) | 20877.3 | 0.823489 | 0.411744 | − | 0.911299i | \(-0.364920\pi\) | ||||
0.411744 | + | 0.911299i | \(0.364920\pi\) | |||||||
\(864\) | −5784.36 | −0.227764 | ||||||||
\(865\) | −48529.1 | −1.90756 | ||||||||
\(866\) | 20899.1 | 0.820069 | ||||||||
\(867\) | −35092.5 | −1.37463 | ||||||||
\(868\) | 169.939 | 0.00664527 | ||||||||
\(869\) | 8626.93 | 0.336765 | ||||||||
\(870\) | 6515.46 | 0.253902 | ||||||||
\(871\) | −8804.12 | −0.342498 | ||||||||
\(872\) | −7182.19 | −0.278922 | ||||||||
\(873\) | 25564.6 | 0.991099 | ||||||||
\(874\) | −31613.8 | −1.22351 | ||||||||
\(875\) | 11352.5 | 0.438611 | ||||||||
\(876\) | 9191.27 | 0.354502 | ||||||||
\(877\) | 21747.0 | 0.837336 | 0.418668 | − | 0.908139i | \(-0.362497\pi\) | ||||
0.418668 | + | 0.908139i | \(0.362497\pi\) | |||||||
\(878\) | 29703.1 | 1.14172 | ||||||||
\(879\) | −46748.9 | −1.79386 | ||||||||
\(880\) | 50851.2 | 1.94795 | ||||||||
\(881\) | 39665.9 | 1.51689 | 0.758444 | − | 0.651738i | \(-0.225960\pi\) | ||||
0.758444 | + | 0.651738i | \(0.225960\pi\) | |||||||
\(882\) | 31439.0 | 1.20024 | ||||||||
\(883\) | −32675.0 | −1.24530 | −0.622652 | − | 0.782499i | \(-0.713945\pi\) | ||||
−0.622652 | + | 0.782499i | \(0.713945\pi\) | |||||||
\(884\) | −966.050 | −0.0367554 | ||||||||
\(885\) | −122899. | −4.66803 | ||||||||
\(886\) | −3573.48 | −0.135500 | ||||||||
\(887\) | −1318.70 | −0.0499183 | −0.0249592 | − | 0.999688i | \(-0.507946\pi\) | ||||
−0.0249592 | + | 0.999688i | \(0.507946\pi\) | |||||||
\(888\) | −43042.5 | −1.62659 | ||||||||
\(889\) | 745.098 | 0.0281100 | ||||||||
\(890\) | 17470.7 | 0.658000 | ||||||||
\(891\) | 17563.4 | 0.660376 | ||||||||
\(892\) | −5606.41 | −0.210445 | ||||||||
\(893\) | 81561.6 | 3.05639 | ||||||||
\(894\) | −51178.0 | −1.91459 | ||||||||
\(895\) | 34613.3 | 1.29273 | ||||||||
\(896\) | −2681.66 | −0.0999867 | ||||||||
\(897\) | 19396.3 | 0.721989 | ||||||||
\(898\) | 24101.5 | 0.895634 | ||||||||
\(899\) | 542.209 | 0.0201153 | ||||||||
\(900\) | −17958.1 | −0.665113 | ||||||||
\(901\) | −9429.08 | −0.348644 | ||||||||
\(902\) | 26345.3 | 0.972507 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 39621.6 | 1.45774 | ||||||||
\(905\) | 45469.7 | 1.67013 | ||||||||
\(906\) | 20274.3 | 0.743453 | ||||||||
\(907\) | −2202.10 | −0.0806170 | −0.0403085 | − | 0.999187i | \(-0.512834\pi\) | ||||
−0.0403085 | + | 0.999187i | \(0.512834\pi\) | |||||||
\(908\) | −8235.45 | −0.300994 | ||||||||
\(909\) | 34166.4 | 1.24668 | ||||||||
\(910\) | 4230.25 | 0.154100 | ||||||||
\(911\) | −10427.7 | −0.379237 | −0.189618 | − | 0.981858i | \(-0.560725\pi\) | ||||
−0.189618 | + | 0.981858i | \(0.560725\pi\) | |||||||
\(912\) | 53119.1 | 1.92867 | ||||||||
\(913\) | 12166.5 | 0.441022 | ||||||||
\(914\) | 28307.1 | 1.02441 | ||||||||
\(915\) | 8589.53 | 0.310340 | ||||||||
\(916\) | −5527.19 | −0.199371 | ||||||||
\(917\) | −7169.49 | −0.258187 | ||||||||
\(918\) | 4787.02 | 0.172108 | ||||||||
\(919\) | −4793.05 | −0.172044 | −0.0860218 | − | 0.996293i | \(-0.527415\pi\) | ||||
−0.0860218 | + | 0.996293i | \(0.527415\pi\) | |||||||
\(920\) | −46200.9 | −1.65565 | ||||||||
\(921\) | 53949.9 | 1.93020 | ||||||||
\(922\) | 39743.1 | 1.41960 | ||||||||
\(923\) | 12850.5 | 0.458267 | ||||||||
\(924\) | 1959.14 | 0.0697522 | ||||||||
\(925\) | −67270.5 | −2.39118 | ||||||||
\(926\) | 6450.82 | 0.228928 | ||||||||
\(927\) | −12960.4 | −0.459198 | ||||||||
\(928\) | 1095.74 | 0.0387603 | ||||||||
\(929\) | −42938.0 | −1.51641 | −0.758207 | − | 0.652014i | \(-0.773924\pi\) | ||||
−0.758207 | + | 0.652014i | \(0.773924\pi\) | |||||||
\(930\) | 14702.6 | 0.518407 | ||||||||
\(931\) | 45335.5 | 1.59593 | ||||||||
\(932\) | 2452.75 | 0.0862044 | ||||||||
\(933\) | 70177.6 | 2.46250 | ||||||||
\(934\) | 19809.1 | 0.693977 | ||||||||
\(935\) | 24080.6 | 0.842267 | ||||||||
\(936\) | −23802.8 | −0.831216 | ||||||||
\(937\) | −17961.4 | −0.626224 | −0.313112 | − | 0.949716i | \(-0.601372\pi\) | ||||
−0.313112 | + | 0.949716i | \(0.601372\pi\) | |||||||
\(938\) | −2590.19 | −0.0901626 | ||||||||
\(939\) | −53979.3 | −1.87598 | ||||||||
\(940\) | 19733.3 | 0.684711 | ||||||||
\(941\) | 1417.03 | 0.0490902 | 0.0245451 | − | 0.999699i | \(-0.492186\pi\) | ||||
0.0245451 | + | 0.999699i | \(0.492186\pi\) | |||||||
\(942\) | 24191.0 | 0.836716 | ||||||||
\(943\) | −18992.5 | −0.655867 | ||||||||
\(944\) | 36120.7 | 1.24537 | ||||||||
\(945\) | 5188.16 | 0.178594 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1240.24 | −0.0425579 | −0.0212789 | − | 0.999774i | \(-0.506774\pi\) | ||||
−0.0212789 | + | 0.999774i | \(0.506774\pi\) | |||||||
\(948\) | 2180.31 | 0.0746975 | ||||||||
\(949\) | 19040.2 | 0.651286 | ||||||||
\(950\) | 104628. | 3.57323 | ||||||||
\(951\) | 69328.2 | 2.36395 | ||||||||
\(952\) | −1716.75 | −0.0584454 | ||||||||
\(953\) | −39421.9 | −1.33998 | −0.669989 | − | 0.742371i | \(-0.733701\pi\) | ||||
−0.669989 | + | 0.742371i | \(0.733701\pi\) | |||||||
\(954\) | −38462.4 | −1.30531 | ||||||||
\(955\) | 1650.05 | 0.0559103 | ||||||||
\(956\) | 4067.33 | 0.137601 | ||||||||
\(957\) | 6250.87 | 0.211141 | ||||||||
\(958\) | 37409.6 | 1.26164 | ||||||||
\(959\) | 3773.47 | 0.127061 | ||||||||
\(960\) | 94489.8 | 3.17671 | ||||||||
\(961\) | −28567.5 | −0.958929 | ||||||||
\(962\) | −14761.5 | −0.494731 | ||||||||
\(963\) | 30895.0 | 1.03383 | ||||||||
\(964\) | −7843.81 | −0.262067 | ||||||||
\(965\) | 22977.8 | 0.766511 | ||||||||
\(966\) | 5706.43 | 0.190063 | ||||||||
\(967\) | 13213.8 | 0.439428 | 0.219714 | − | 0.975564i | \(-0.429488\pi\) | ||||
0.219714 | + | 0.975564i | \(0.429488\pi\) | |||||||
\(968\) | 29170.2 | 0.968561 | ||||||||
\(969\) | 25154.6 | 0.833933 | ||||||||
\(970\) | −36036.2 | −1.19284 | ||||||||
\(971\) | 16647.1 | 0.550186 | 0.275093 | − | 0.961418i | \(-0.411291\pi\) | ||||
0.275093 | + | 0.961418i | \(0.411291\pi\) | |||||||
\(972\) | 7945.55 | 0.262195 | ||||||||
\(973\) | −949.082 | −0.0312705 | ||||||||
\(974\) | −13388.4 | −0.440444 | ||||||||
\(975\) | −64193.3 | −2.10854 | ||||||||
\(976\) | −2524.51 | −0.0827948 | ||||||||
\(977\) | −3092.02 | −0.101251 | −0.0506256 | − | 0.998718i | \(-0.516122\pi\) | ||||
−0.0506256 | + | 0.998718i | \(0.516122\pi\) | |||||||
\(978\) | 2317.74 | 0.0757802 | ||||||||
\(979\) | 16761.2 | 0.547183 | ||||||||
\(980\) | 10968.6 | 0.357530 | ||||||||
\(981\) | −11008.3 | −0.358276 | ||||||||
\(982\) | 44337.3 | 1.44079 | ||||||||
\(983\) | −14697.7 | −0.476890 | −0.238445 | − | 0.971156i | \(-0.576638\pi\) | ||||
−0.238445 | + | 0.971156i | \(0.576638\pi\) | |||||||
\(984\) | 40218.5 | 1.30297 | ||||||||
\(985\) | 49561.2 | 1.60320 | ||||||||
\(986\) | −906.816 | −0.0292889 | ||||||||
\(987\) | −14722.2 | −0.474786 | ||||||||
\(988\) | −5682.45 | −0.182979 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 98227.7 | 3.15341 | ||||||||
\(991\) | −43483.8 | −1.39385 | −0.696927 | − | 0.717143i | \(-0.745450\pi\) | ||||
−0.696927 | + | 0.717143i | \(0.745450\pi\) | |||||||
\(992\) | 2472.63 | 0.0791392 | ||||||||
\(993\) | −44320.2 | −1.41637 | ||||||||
\(994\) | 3780.65 | 0.120639 | ||||||||
\(995\) | −4354.70 | −0.138747 | ||||||||
\(996\) | 3074.89 | 0.0978228 | ||||||||
\(997\) | −35710.8 | −1.13437 | −0.567187 | − | 0.823589i | \(-0.691968\pi\) | ||||
−0.567187 | + | 0.823589i | \(0.691968\pi\) | |||||||
\(998\) | 3951.24 | 0.125325 | ||||||||
\(999\) | −18104.2 | −0.573365 |
(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 | 1849.4.a.i.1.17 | ✓ | 50 | |
43.42 | odd | 2 | 1849.4.a.j.1.34 | yes | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1849.4.a.i.1.17 | ✓ | 50 | 1.1 | even | 1 | trivial | |
1849.4.a.j.1.34 | yes | 50 | 43.42 | odd | 2 |