Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,4,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, 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("177.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(10.4433380710\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 45x^{6} + 47x^{5} + 654x^{4} - 157x^{3} - 2898x^{2} + 96x + 2432 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-3.06139\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.06139 | 1.43592 | 0.717958 | − | 0.696086i | \(-0.245077\pi\) | ||||
0.717958 | + | 0.696086i | \(0.245077\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 8.49485 | 1.06186 | ||||||||
\(5\) | 16.2722 | 1.45543 | 0.727713 | − | 0.685882i | \(-0.240583\pi\) | ||||
0.727713 | + | 0.685882i | \(0.240583\pi\) | |||||||
\(6\) | 12.1842 | 0.829027 | ||||||||
\(7\) | 6.77038 | 0.365566 | 0.182783 | − | 0.983153i | \(-0.441489\pi\) | ||||
0.182783 | + | 0.983153i | \(0.441489\pi\) | |||||||
\(8\) | 2.00979 | 0.0888212 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 66.0875 | 2.08987 | ||||||||
\(11\) | −16.5845 | −0.454583 | −0.227292 | − | 0.973827i | \(-0.572987\pi\) | ||||
−0.227292 | + | 0.973827i | \(0.572987\pi\) | |||||||
\(12\) | 25.4846 | 0.613063 | ||||||||
\(13\) | −82.3410 | −1.75672 | −0.878358 | − | 0.478004i | \(-0.841360\pi\) | ||||
−0.878358 | + | 0.478004i | \(0.841360\pi\) | |||||||
\(14\) | 27.4971 | 0.524923 | ||||||||
\(15\) | 48.8165 | 0.840291 | ||||||||
\(16\) | −59.7963 | −0.934317 | ||||||||
\(17\) | 6.48327 | 0.0924956 | 0.0462478 | − | 0.998930i | \(-0.485274\pi\) | ||||
0.0462478 | + | 0.998930i | \(0.485274\pi\) | |||||||
\(18\) | 36.5525 | 0.478639 | ||||||||
\(19\) | 151.026 | 1.82356 | 0.911782 | − | 0.410674i | \(-0.134706\pi\) | ||||
0.911782 | + | 0.410674i | \(0.134706\pi\) | |||||||
\(20\) | 138.230 | 1.54545 | ||||||||
\(21\) | 20.3111 | 0.211060 | ||||||||
\(22\) | −67.3561 | −0.652744 | ||||||||
\(23\) | −154.283 | −1.39871 | −0.699353 | − | 0.714777i | \(-0.746528\pi\) | ||||
−0.699353 | + | 0.714777i | \(0.746528\pi\) | |||||||
\(24\) | 6.02938 | 0.0512809 | ||||||||
\(25\) | 139.783 | 1.11827 | ||||||||
\(26\) | −334.419 | −2.52250 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 57.5134 | 0.388179 | ||||||||
\(29\) | 220.887 | 1.41440 | 0.707201 | − | 0.707012i | \(-0.249958\pi\) | ||||
0.707201 | + | 0.707012i | \(0.249958\pi\) | |||||||
\(30\) | 198.263 | 1.20659 | ||||||||
\(31\) | −79.4162 | −0.460115 | −0.230058 | − | 0.973177i | \(-0.573891\pi\) | ||||
−0.230058 | + | 0.973177i | \(0.573891\pi\) | |||||||
\(32\) | −258.934 | −1.43042 | ||||||||
\(33\) | −49.7535 | −0.262454 | ||||||||
\(34\) | 26.3311 | 0.132816 | ||||||||
\(35\) | 110.169 | 0.532055 | ||||||||
\(36\) | 76.4537 | 0.353952 | ||||||||
\(37\) | 414.092 | 1.83990 | 0.919949 | − | 0.392038i | \(-0.128230\pi\) | ||||
0.919949 | + | 0.392038i | \(0.128230\pi\) | |||||||
\(38\) | 613.375 | 2.61849 | ||||||||
\(39\) | −247.023 | −1.01424 | ||||||||
\(40\) | 32.7037 | 0.129273 | ||||||||
\(41\) | −521.903 | −1.98799 | −0.993995 | − | 0.109423i | \(-0.965100\pi\) | ||||
−0.993995 | + | 0.109423i | \(0.965100\pi\) | |||||||
\(42\) | 82.4914 | 0.303064 | ||||||||
\(43\) | −265.009 | −0.939848 | −0.469924 | − | 0.882707i | \(-0.655719\pi\) | ||||
−0.469924 | + | 0.882707i | \(0.655719\pi\) | |||||||
\(44\) | −140.883 | −0.482702 | ||||||||
\(45\) | 146.449 | 0.485142 | ||||||||
\(46\) | −626.603 | −2.00843 | ||||||||
\(47\) | 31.6419 | 0.0982011 | 0.0491005 | − | 0.998794i | \(-0.484365\pi\) | ||||
0.0491005 | + | 0.998794i | \(0.484365\pi\) | |||||||
\(48\) | −179.389 | −0.539428 | ||||||||
\(49\) | −297.162 | −0.866361 | ||||||||
\(50\) | 567.714 | 1.60574 | ||||||||
\(51\) | 19.4498 | 0.0534023 | ||||||||
\(52\) | −699.475 | −1.86538 | ||||||||
\(53\) | −256.788 | −0.665519 | −0.332760 | − | 0.943012i | \(-0.607980\pi\) | ||||
−0.332760 | + | 0.943012i | \(0.607980\pi\) | |||||||
\(54\) | 109.657 | 0.276342 | ||||||||
\(55\) | −269.866 | −0.661613 | ||||||||
\(56\) | 13.6071 | 0.0324700 | ||||||||
\(57\) | 453.078 | 1.05284 | ||||||||
\(58\) | 897.107 | 2.03096 | ||||||||
\(59\) | 59.0000 | 0.130189 | ||||||||
\(60\) | 414.689 | 0.892268 | ||||||||
\(61\) | −68.7236 | −0.144248 | −0.0721242 | − | 0.997396i | \(-0.522978\pi\) | ||||
−0.0721242 | + | 0.997396i | \(0.522978\pi\) | |||||||
\(62\) | −322.540 | −0.660687 | ||||||||
\(63\) | 60.9334 | 0.121855 | ||||||||
\(64\) | −573.261 | −1.11965 | ||||||||
\(65\) | −1339.87 | −2.55677 | ||||||||
\(66\) | −202.068 | −0.376862 | ||||||||
\(67\) | 198.971 | 0.362808 | 0.181404 | − | 0.983409i | \(-0.441936\pi\) | ||||
0.181404 | + | 0.983409i | \(0.441936\pi\) | |||||||
\(68\) | 55.0745 | 0.0982170 | ||||||||
\(69\) | −462.849 | −0.807543 | ||||||||
\(70\) | 447.438 | 0.763986 | ||||||||
\(71\) | 725.821 | 1.21323 | 0.606613 | − | 0.794997i | \(-0.292528\pi\) | ||||
0.606613 | + | 0.794997i | \(0.292528\pi\) | |||||||
\(72\) | 18.0882 | 0.0296071 | ||||||||
\(73\) | 571.563 | 0.916388 | 0.458194 | − | 0.888852i | \(-0.348496\pi\) | ||||
0.458194 | + | 0.888852i | \(0.348496\pi\) | |||||||
\(74\) | 1681.79 | 2.64194 | ||||||||
\(75\) | 419.350 | 0.645631 | ||||||||
\(76\) | 1282.94 | 1.93636 | ||||||||
\(77\) | −112.283 | −0.166180 | ||||||||
\(78\) | −1003.26 | −1.45636 | ||||||||
\(79\) | −304.888 | −0.434209 | −0.217105 | − | 0.976148i | \(-0.569661\pi\) | ||||
−0.217105 | + | 0.976148i | \(0.569661\pi\) | |||||||
\(80\) | −973.015 | −1.35983 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −2119.65 | −2.85459 | ||||||||
\(83\) | 731.213 | 0.967001 | 0.483500 | − | 0.875344i | \(-0.339365\pi\) | ||||
0.483500 | + | 0.875344i | \(0.339365\pi\) | |||||||
\(84\) | 172.540 | 0.224115 | ||||||||
\(85\) | 105.497 | 0.134620 | ||||||||
\(86\) | −1076.30 | −1.34954 | ||||||||
\(87\) | 662.661 | 0.816606 | ||||||||
\(88\) | −33.3315 | −0.0403766 | ||||||||
\(89\) | −694.016 | −0.826580 | −0.413290 | − | 0.910600i | \(-0.635620\pi\) | ||||
−0.413290 | + | 0.910600i | \(0.635620\pi\) | |||||||
\(90\) | 594.788 | 0.696624 | ||||||||
\(91\) | −557.480 | −0.642196 | ||||||||
\(92\) | −1310.61 | −1.48523 | ||||||||
\(93\) | −238.249 | −0.265648 | ||||||||
\(94\) | 128.510 | 0.141009 | ||||||||
\(95\) | 2457.52 | 2.65406 | ||||||||
\(96\) | −776.802 | −0.825855 | ||||||||
\(97\) | −597.160 | −0.625076 | −0.312538 | − | 0.949905i | \(-0.601179\pi\) | ||||
−0.312538 | + | 0.949905i | \(0.601179\pi\) | |||||||
\(98\) | −1206.89 | −1.24402 | ||||||||
\(99\) | −149.261 | −0.151528 | ||||||||
\(100\) | 1187.44 | 1.18744 | ||||||||
\(101\) | 1186.90 | 1.16932 | 0.584659 | − | 0.811279i | \(-0.301228\pi\) | ||||
0.584659 | + | 0.811279i | \(0.301228\pi\) | |||||||
\(102\) | 78.9932 | 0.0766813 | ||||||||
\(103\) | −1037.17 | −0.992190 | −0.496095 | − | 0.868268i | \(-0.665233\pi\) | ||||
−0.496095 | + | 0.868268i | \(0.665233\pi\) | |||||||
\(104\) | −165.489 | −0.156034 | ||||||||
\(105\) | 330.506 | 0.307182 | ||||||||
\(106\) | −1042.91 | −0.955630 | ||||||||
\(107\) | 1786.99 | 1.61453 | 0.807266 | − | 0.590188i | \(-0.200946\pi\) | ||||
0.807266 | + | 0.590188i | \(0.200946\pi\) | |||||||
\(108\) | 229.361 | 0.204354 | ||||||||
\(109\) | −1548.23 | −1.36050 | −0.680248 | − | 0.732982i | \(-0.738128\pi\) | ||||
−0.680248 | + | 0.732982i | \(0.738128\pi\) | |||||||
\(110\) | −1096.03 | −0.950021 | ||||||||
\(111\) | 1242.27 | 1.06227 | ||||||||
\(112\) | −404.844 | −0.341555 | ||||||||
\(113\) | 1414.84 | 1.17785 | 0.588924 | − | 0.808189i | \(-0.299552\pi\) | ||||
0.588924 | + | 0.808189i | \(0.299552\pi\) | |||||||
\(114\) | 1840.12 | 1.51178 | ||||||||
\(115\) | −2510.52 | −2.03571 | ||||||||
\(116\) | 1876.40 | 1.50189 | ||||||||
\(117\) | −741.069 | −0.585572 | ||||||||
\(118\) | 239.622 | 0.186940 | ||||||||
\(119\) | 43.8942 | 0.0338133 | ||||||||
\(120\) | 98.1111 | 0.0746356 | ||||||||
\(121\) | −1055.95 | −0.793354 | ||||||||
\(122\) | −279.113 | −0.207129 | ||||||||
\(123\) | −1565.71 | −1.14777 | ||||||||
\(124\) | −674.629 | −0.488576 | ||||||||
\(125\) | 240.555 | 0.172127 | ||||||||
\(126\) | 247.474 | 0.174974 | ||||||||
\(127\) | 1389.63 | 0.970942 | 0.485471 | − | 0.874253i | \(-0.338648\pi\) | ||||
0.485471 | + | 0.874253i | \(0.338648\pi\) | |||||||
\(128\) | −256.762 | −0.177303 | ||||||||
\(129\) | −795.026 | −0.542621 | ||||||||
\(130\) | −5441.72 | −3.67131 | ||||||||
\(131\) | −398.137 | −0.265537 | −0.132769 | − | 0.991147i | \(-0.542387\pi\) | ||||
−0.132769 | + | 0.991147i | \(0.542387\pi\) | |||||||
\(132\) | −422.649 | −0.278688 | ||||||||
\(133\) | 1022.50 | 0.666634 | ||||||||
\(134\) | 808.096 | 0.520962 | ||||||||
\(135\) | 439.348 | 0.280097 | ||||||||
\(136\) | 13.0300 | 0.00821557 | ||||||||
\(137\) | −42.8475 | −0.0267205 | −0.0133603 | − | 0.999911i | \(-0.504253\pi\) | ||||
−0.0133603 | + | 0.999911i | \(0.504253\pi\) | |||||||
\(138\) | −1879.81 | −1.15956 | ||||||||
\(139\) | −245.792 | −0.149984 | −0.0749922 | − | 0.997184i | \(-0.523893\pi\) | ||||
−0.0749922 | + | 0.997184i | \(0.523893\pi\) | |||||||
\(140\) | 935.868 | 0.564966 | ||||||||
\(141\) | 94.9258 | 0.0566964 | ||||||||
\(142\) | 2947.84 | 1.74209 | ||||||||
\(143\) | 1365.59 | 0.798574 | ||||||||
\(144\) | −538.167 | −0.311439 | ||||||||
\(145\) | 3594.31 | 2.05856 | ||||||||
\(146\) | 2321.34 | 1.31586 | ||||||||
\(147\) | −891.486 | −0.500194 | ||||||||
\(148\) | 3517.65 | 1.95371 | ||||||||
\(149\) | 1492.30 | 0.820495 | 0.410247 | − | 0.911974i | \(-0.365442\pi\) | ||||
0.410247 | + | 0.911974i | \(0.365442\pi\) | |||||||
\(150\) | 1703.14 | 0.927072 | ||||||||
\(151\) | −917.443 | −0.494440 | −0.247220 | − | 0.968959i | \(-0.579517\pi\) | ||||
−0.247220 | + | 0.968959i | \(0.579517\pi\) | |||||||
\(152\) | 303.531 | 0.161971 | ||||||||
\(153\) | 58.3495 | 0.0308319 | ||||||||
\(154\) | −456.027 | −0.238621 | ||||||||
\(155\) | −1292.27 | −0.669664 | ||||||||
\(156\) | −2098.43 | −1.07698 | ||||||||
\(157\) | 2338.93 | 1.18896 | 0.594479 | − | 0.804111i | \(-0.297358\pi\) | ||||
0.594479 | + | 0.804111i | \(0.297358\pi\) | |||||||
\(158\) | −1238.27 | −0.623489 | ||||||||
\(159\) | −770.364 | −0.384238 | ||||||||
\(160\) | −4213.42 | −2.08187 | ||||||||
\(161\) | −1044.56 | −0.511320 | ||||||||
\(162\) | 328.972 | 0.159546 | ||||||||
\(163\) | 1425.51 | 0.684995 | 0.342498 | − | 0.939519i | \(-0.388727\pi\) | ||||
0.342498 | + | 0.939519i | \(0.388727\pi\) | |||||||
\(164\) | −4433.49 | −2.11096 | ||||||||
\(165\) | −809.597 | −0.381982 | ||||||||
\(166\) | 2969.74 | 1.38853 | ||||||||
\(167\) | 1937.97 | 0.897993 | 0.448996 | − | 0.893534i | \(-0.351782\pi\) | ||||
0.448996 | + | 0.893534i | \(0.351782\pi\) | |||||||
\(168\) | 40.8212 | 0.0187466 | ||||||||
\(169\) | 4583.05 | 2.08605 | ||||||||
\(170\) | 428.463 | 0.193304 | ||||||||
\(171\) | 1359.23 | 0.607855 | ||||||||
\(172\) | −2251.21 | −0.997984 | ||||||||
\(173\) | 925.049 | 0.406533 | 0.203266 | − | 0.979123i | \(-0.434844\pi\) | ||||
0.203266 | + | 0.979123i | \(0.434844\pi\) | |||||||
\(174\) | 2691.32 | 1.17258 | ||||||||
\(175\) | 946.386 | 0.408800 | ||||||||
\(176\) | 991.692 | 0.424725 | ||||||||
\(177\) | 177.000 | 0.0751646 | ||||||||
\(178\) | −2818.67 | −1.18690 | ||||||||
\(179\) | 2245.15 | 0.937490 | 0.468745 | − | 0.883334i | \(-0.344706\pi\) | ||||
0.468745 | + | 0.883334i | \(0.344706\pi\) | |||||||
\(180\) | 1244.07 | 0.515151 | ||||||||
\(181\) | −1772.98 | −0.728090 | −0.364045 | − | 0.931381i | \(-0.618605\pi\) | ||||
−0.364045 | + | 0.931381i | \(0.618605\pi\) | |||||||
\(182\) | −2264.14 | −0.922140 | ||||||||
\(183\) | −206.171 | −0.0832819 | ||||||||
\(184\) | −310.077 | −0.124235 | ||||||||
\(185\) | 6738.17 | 2.67784 | ||||||||
\(186\) | −967.619 | −0.381448 | ||||||||
\(187\) | −107.522 | −0.0420469 | ||||||||
\(188\) | 268.794 | 0.104276 | ||||||||
\(189\) | 182.800 | 0.0703533 | ||||||||
\(190\) | 9980.93 | 3.81102 | ||||||||
\(191\) | −620.457 | −0.235051 | −0.117525 | − | 0.993070i | \(-0.537496\pi\) | ||||
−0.117525 | + | 0.993070i | \(0.537496\pi\) | |||||||
\(192\) | −1719.78 | −0.646431 | ||||||||
\(193\) | −2381.92 | −0.888366 | −0.444183 | − | 0.895936i | \(-0.646506\pi\) | ||||
−0.444183 | + | 0.895936i | \(0.646506\pi\) | |||||||
\(194\) | −2425.30 | −0.897557 | ||||||||
\(195\) | −4019.60 | −1.47615 | ||||||||
\(196\) | −2524.35 | −0.919952 | ||||||||
\(197\) | 2044.21 | 0.739311 | 0.369655 | − | 0.929169i | \(-0.379476\pi\) | ||||
0.369655 | + | 0.929169i | \(0.379476\pi\) | |||||||
\(198\) | −606.205 | −0.217581 | ||||||||
\(199\) | 986.827 | 0.351529 | 0.175765 | − | 0.984432i | \(-0.443760\pi\) | ||||
0.175765 | + | 0.984432i | \(0.443760\pi\) | |||||||
\(200\) | 280.936 | 0.0993257 | ||||||||
\(201\) | 596.912 | 0.209467 | ||||||||
\(202\) | 4820.46 | 1.67904 | ||||||||
\(203\) | 1495.49 | 0.517058 | ||||||||
\(204\) | 165.223 | 0.0567056 | ||||||||
\(205\) | −8492.50 | −2.89337 | ||||||||
\(206\) | −4212.35 | −1.42470 | ||||||||
\(207\) | −1388.55 | −0.466235 | ||||||||
\(208\) | 4923.69 | 1.64133 | ||||||||
\(209\) | −2504.69 | −0.828962 | ||||||||
\(210\) | 1342.31 | 0.441088 | ||||||||
\(211\) | 2539.95 | 0.828706 | 0.414353 | − | 0.910116i | \(-0.364008\pi\) | ||||
0.414353 | + | 0.910116i | \(0.364008\pi\) | |||||||
\(212\) | −2181.38 | −0.706686 | ||||||||
\(213\) | 2177.46 | 0.700457 | ||||||||
\(214\) | 7257.66 | 2.31833 | ||||||||
\(215\) | −4312.27 | −1.36788 | ||||||||
\(216\) | 54.2645 | 0.0170936 | ||||||||
\(217\) | −537.678 | −0.168203 | ||||||||
\(218\) | −6287.98 | −1.95356 | ||||||||
\(219\) | 1714.69 | 0.529077 | ||||||||
\(220\) | −2292.47 | −0.702538 | ||||||||
\(221\) | −533.839 | −0.162488 | ||||||||
\(222\) | 5045.36 | 1.52533 | ||||||||
\(223\) | 5064.96 | 1.52096 | 0.760482 | − | 0.649359i | \(-0.224963\pi\) | ||||
0.760482 | + | 0.649359i | \(0.224963\pi\) | |||||||
\(224\) | −1753.08 | −0.522914 | ||||||||
\(225\) | 1258.05 | 0.372755 | ||||||||
\(226\) | 5746.20 | 1.69129 | ||||||||
\(227\) | −875.416 | −0.255962 | −0.127981 | − | 0.991777i | \(-0.540850\pi\) | ||||
−0.127981 | + | 0.991777i | \(0.540850\pi\) | |||||||
\(228\) | 3848.83 | 1.11796 | ||||||||
\(229\) | −4519.88 | −1.30429 | −0.652145 | − | 0.758095i | \(-0.726131\pi\) | ||||
−0.652145 | + | 0.758095i | \(0.726131\pi\) | |||||||
\(230\) | −10196.2 | −2.92311 | ||||||||
\(231\) | −336.850 | −0.0959443 | ||||||||
\(232\) | 443.937 | 0.125629 | ||||||||
\(233\) | −3300.46 | −0.927983 | −0.463992 | − | 0.885840i | \(-0.653583\pi\) | ||||
−0.463992 | + | 0.885840i | \(0.653583\pi\) | |||||||
\(234\) | −3009.77 | −0.840832 | ||||||||
\(235\) | 514.883 | 0.142924 | ||||||||
\(236\) | 501.196 | 0.138242 | ||||||||
\(237\) | −914.663 | −0.250691 | ||||||||
\(238\) | 178.271 | 0.0485530 | ||||||||
\(239\) | 2036.15 | 0.551079 | 0.275539 | − | 0.961290i | \(-0.411144\pi\) | ||||
0.275539 | + | 0.961290i | \(0.411144\pi\) | |||||||
\(240\) | −2919.04 | −0.785098 | ||||||||
\(241\) | 1135.42 | 0.303480 | 0.151740 | − | 0.988420i | \(-0.451512\pi\) | ||||
0.151740 | + | 0.988420i | \(0.451512\pi\) | |||||||
\(242\) | −4288.64 | −1.13919 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | −583.797 | −0.153171 | ||||||||
\(245\) | −4835.47 | −1.26092 | ||||||||
\(246\) | −6358.95 | −1.64810 | ||||||||
\(247\) | −12435.6 | −3.20348 | ||||||||
\(248\) | −159.610 | −0.0408680 | ||||||||
\(249\) | 2193.64 | 0.558298 | ||||||||
\(250\) | 976.987 | 0.247160 | ||||||||
\(251\) | 6147.42 | 1.54590 | 0.772952 | − | 0.634465i | \(-0.218780\pi\) | ||||
0.772952 | + | 0.634465i | \(0.218780\pi\) | |||||||
\(252\) | 517.621 | 0.129393 | ||||||||
\(253\) | 2558.71 | 0.635828 | ||||||||
\(254\) | 5643.82 | 1.39419 | ||||||||
\(255\) | 316.491 | 0.0777232 | ||||||||
\(256\) | 3543.28 | 0.865059 | ||||||||
\(257\) | 866.093 | 0.210216 | 0.105108 | − | 0.994461i | \(-0.466481\pi\) | ||||
0.105108 | + | 0.994461i | \(0.466481\pi\) | |||||||
\(258\) | −3228.91 | −0.779159 | ||||||||
\(259\) | 2803.56 | 0.672605 | ||||||||
\(260\) | −11382.0 | −2.71492 | ||||||||
\(261\) | 1987.98 | 0.471467 | ||||||||
\(262\) | −1616.99 | −0.381289 | ||||||||
\(263\) | −4743.67 | −1.11220 | −0.556098 | − | 0.831117i | \(-0.687702\pi\) | ||||
−0.556098 | + | 0.831117i | \(0.687702\pi\) | |||||||
\(264\) | −99.9944 | −0.0233115 | ||||||||
\(265\) | −4178.49 | −0.968615 | ||||||||
\(266\) | 4152.78 | 0.957231 | ||||||||
\(267\) | −2082.05 | −0.477226 | ||||||||
\(268\) | 1690.23 | 0.385250 | ||||||||
\(269\) | −5845.97 | −1.32504 | −0.662519 | − | 0.749045i | \(-0.730513\pi\) | ||||
−0.662519 | + | 0.749045i | \(0.730513\pi\) | |||||||
\(270\) | 1784.36 | 0.402196 | ||||||||
\(271\) | −4680.05 | −1.04905 | −0.524525 | − | 0.851395i | \(-0.675757\pi\) | ||||
−0.524525 | + | 0.851395i | \(0.675757\pi\) | |||||||
\(272\) | −387.676 | −0.0864202 | ||||||||
\(273\) | −1672.44 | −0.370772 | ||||||||
\(274\) | −174.020 | −0.0383684 | ||||||||
\(275\) | −2318.24 | −0.508345 | ||||||||
\(276\) | −3931.84 | −0.857495 | ||||||||
\(277\) | −3885.21 | −0.842742 | −0.421371 | − | 0.906888i | \(-0.638451\pi\) | ||||
−0.421371 | + | 0.906888i | \(0.638451\pi\) | |||||||
\(278\) | −998.257 | −0.215365 | ||||||||
\(279\) | −714.746 | −0.153372 | ||||||||
\(280\) | 221.417 | 0.0472578 | ||||||||
\(281\) | −7580.94 | −1.60940 | −0.804700 | − | 0.593682i | \(-0.797674\pi\) | ||||
−0.804700 | + | 0.593682i | \(0.797674\pi\) | |||||||
\(282\) | 385.530 | 0.0814113 | ||||||||
\(283\) | 947.742 | 0.199072 | 0.0995361 | − | 0.995034i | \(-0.468264\pi\) | ||||
0.0995361 | + | 0.995034i | \(0.468264\pi\) | |||||||
\(284\) | 6165.74 | 1.28827 | ||||||||
\(285\) | 7372.56 | 1.53232 | ||||||||
\(286\) | 5546.17 | 1.14669 | ||||||||
\(287\) | −3533.49 | −0.726742 | ||||||||
\(288\) | −2330.41 | −0.476808 | ||||||||
\(289\) | −4870.97 | −0.991445 | ||||||||
\(290\) | 14597.9 | 2.95592 | ||||||||
\(291\) | −1791.48 | −0.360888 | ||||||||
\(292\) | 4855.34 | 0.973073 | ||||||||
\(293\) | −2612.95 | −0.520990 | −0.260495 | − | 0.965475i | \(-0.583886\pi\) | ||||
−0.260495 | + | 0.965475i | \(0.583886\pi\) | |||||||
\(294\) | −3620.67 | −0.718237 | ||||||||
\(295\) | 960.058 | 0.189480 | ||||||||
\(296\) | 832.239 | 0.163422 | ||||||||
\(297\) | −447.782 | −0.0874846 | ||||||||
\(298\) | 6060.79 | 1.17816 | ||||||||
\(299\) | 12703.8 | 2.45713 | ||||||||
\(300\) | 3562.31 | 0.685568 | ||||||||
\(301\) | −1794.21 | −0.343577 | ||||||||
\(302\) | −3726.09 | −0.709975 | ||||||||
\(303\) | 3560.70 | 0.675106 | ||||||||
\(304\) | −9030.79 | −1.70379 | ||||||||
\(305\) | −1118.28 | −0.209943 | ||||||||
\(306\) | 236.980 | 0.0442720 | ||||||||
\(307\) | 6751.14 | 1.25507 | 0.627537 | − | 0.778587i | \(-0.284063\pi\) | ||||
0.627537 | + | 0.778587i | \(0.284063\pi\) | |||||||
\(308\) | −953.832 | −0.176460 | ||||||||
\(309\) | −3111.51 | −0.572841 | ||||||||
\(310\) | −5248.42 | −0.961581 | ||||||||
\(311\) | 1176.93 | 0.214591 | 0.107295 | − | 0.994227i | \(-0.465781\pi\) | ||||
0.107295 | + | 0.994227i | \(0.465781\pi\) | |||||||
\(312\) | −496.466 | −0.0900860 | ||||||||
\(313\) | 2059.81 | 0.371972 | 0.185986 | − | 0.982552i | \(-0.440452\pi\) | ||||
0.185986 | + | 0.982552i | \(0.440452\pi\) | |||||||
\(314\) | 9499.28 | 1.70725 | ||||||||
\(315\) | 991.519 | 0.177352 | ||||||||
\(316\) | −2589.98 | −0.461068 | ||||||||
\(317\) | 5322.47 | 0.943027 | 0.471513 | − | 0.881859i | \(-0.343708\pi\) | ||||
0.471513 | + | 0.881859i | \(0.343708\pi\) | |||||||
\(318\) | −3128.74 | −0.551734 | ||||||||
\(319\) | −3663.30 | −0.642964 | ||||||||
\(320\) | −9328.20 | −1.62957 | ||||||||
\(321\) | 5360.97 | 0.932151 | ||||||||
\(322\) | −4242.34 | −0.734213 | ||||||||
\(323\) | 979.142 | 0.168672 | ||||||||
\(324\) | 688.083 | 0.117984 | ||||||||
\(325\) | −11509.9 | −1.96447 | ||||||||
\(326\) | 5789.53 | 0.983596 | ||||||||
\(327\) | −4644.70 | −0.785482 | ||||||||
\(328\) | −1048.92 | −0.176576 | ||||||||
\(329\) | 214.228 | 0.0358990 | ||||||||
\(330\) | −3288.09 | −0.548495 | ||||||||
\(331\) | −10946.3 | −1.81772 | −0.908860 | − | 0.417101i | \(-0.863046\pi\) | ||||
−0.908860 | + | 0.417101i | \(0.863046\pi\) | |||||||
\(332\) | 6211.55 | 1.02682 | ||||||||
\(333\) | 3726.82 | 0.613299 | ||||||||
\(334\) | 7870.85 | 1.28944 | ||||||||
\(335\) | 3237.68 | 0.528040 | ||||||||
\(336\) | −1214.53 | −0.197197 | ||||||||
\(337\) | 333.243 | 0.0538661 | 0.0269331 | − | 0.999637i | \(-0.491426\pi\) | ||||
0.0269331 | + | 0.999637i | \(0.491426\pi\) | |||||||
\(338\) | 18613.5 | 2.99539 | ||||||||
\(339\) | 4244.51 | 0.680030 | ||||||||
\(340\) | 896.180 | 0.142948 | ||||||||
\(341\) | 1317.08 | 0.209161 | ||||||||
\(342\) | 5520.37 | 0.872829 | ||||||||
\(343\) | −4334.14 | −0.682279 | ||||||||
\(344\) | −532.613 | −0.0834784 | ||||||||
\(345\) | −7531.55 | −1.17532 | ||||||||
\(346\) | 3756.98 | 0.583747 | ||||||||
\(347\) | −2054.05 | −0.317773 | −0.158886 | − | 0.987297i | \(-0.550790\pi\) | ||||
−0.158886 | + | 0.987297i | \(0.550790\pi\) | |||||||
\(348\) | 5629.21 | 0.867118 | ||||||||
\(349\) | 6861.41 | 1.05239 | 0.526193 | − | 0.850365i | \(-0.323619\pi\) | ||||
0.526193 | + | 0.850365i | \(0.323619\pi\) | |||||||
\(350\) | 3843.64 | 0.587003 | ||||||||
\(351\) | −2223.21 | −0.338080 | ||||||||
\(352\) | 4294.30 | 0.650246 | ||||||||
\(353\) | −3523.31 | −0.531237 | −0.265618 | − | 0.964078i | \(-0.585576\pi\) | ||||
−0.265618 | + | 0.964078i | \(0.585576\pi\) | |||||||
\(354\) | 718.865 | 0.107930 | ||||||||
\(355\) | 11810.7 | 1.76576 | ||||||||
\(356\) | −5895.57 | −0.877709 | ||||||||
\(357\) | 131.683 | 0.0195221 | ||||||||
\(358\) | 9118.44 | 1.34616 | ||||||||
\(359\) | 1692.91 | 0.248882 | 0.124441 | − | 0.992227i | \(-0.460286\pi\) | ||||
0.124441 | + | 0.992227i | \(0.460286\pi\) | |||||||
\(360\) | 294.333 | 0.0430909 | ||||||||
\(361\) | 15949.8 | 2.32539 | ||||||||
\(362\) | −7200.74 | −1.04548 | ||||||||
\(363\) | −3167.86 | −0.458043 | ||||||||
\(364\) | −4735.72 | −0.681920 | ||||||||
\(365\) | 9300.56 | 1.33374 | ||||||||
\(366\) | −837.339 | −0.119586 | ||||||||
\(367\) | −3865.33 | −0.549778 | −0.274889 | − | 0.961476i | \(-0.588641\pi\) | ||||
−0.274889 | + | 0.961476i | \(0.588641\pi\) | |||||||
\(368\) | 9225.55 | 1.30683 | ||||||||
\(369\) | −4697.13 | −0.662664 | ||||||||
\(370\) | 27366.3 | 3.84515 | ||||||||
\(371\) | −1738.55 | −0.243292 | ||||||||
\(372\) | −2023.89 | −0.282080 | ||||||||
\(373\) | −6121.11 | −0.849703 | −0.424851 | − | 0.905263i | \(-0.639674\pi\) | ||||
−0.424851 | + | 0.905263i | \(0.639674\pi\) | |||||||
\(374\) | −436.688 | −0.0603759 | ||||||||
\(375\) | 721.665 | 0.0993777 | ||||||||
\(376\) | 63.5938 | 0.00872234 | ||||||||
\(377\) | −18188.1 | −2.48470 | ||||||||
\(378\) | 742.423 | 0.101021 | ||||||||
\(379\) | −2939.20 | −0.398356 | −0.199178 | − | 0.979963i | \(-0.563827\pi\) | ||||
−0.199178 | + | 0.979963i | \(0.563827\pi\) | |||||||
\(380\) | 20876.3 | 2.81824 | ||||||||
\(381\) | 4168.89 | 0.560573 | ||||||||
\(382\) | −2519.92 | −0.337513 | ||||||||
\(383\) | 8175.22 | 1.09069 | 0.545345 | − | 0.838212i | \(-0.316399\pi\) | ||||
0.545345 | + | 0.838212i | \(0.316399\pi\) | |||||||
\(384\) | −770.285 | −0.102366 | ||||||||
\(385\) | −1827.09 | −0.241863 | ||||||||
\(386\) | −9673.91 | −1.27562 | ||||||||
\(387\) | −2385.08 | −0.313283 | ||||||||
\(388\) | −5072.78 | −0.663741 | ||||||||
\(389\) | 7355.93 | 0.958768 | 0.479384 | − | 0.877605i | \(-0.340860\pi\) | ||||
0.479384 | + | 0.877605i | \(0.340860\pi\) | |||||||
\(390\) | −16325.1 | −2.11963 | ||||||||
\(391\) | −1000.26 | −0.129374 | ||||||||
\(392\) | −597.234 | −0.0769513 | ||||||||
\(393\) | −1194.41 | −0.153308 | ||||||||
\(394\) | 8302.34 | 1.06159 | ||||||||
\(395\) | −4961.18 | −0.631960 | ||||||||
\(396\) | −1267.95 | −0.160901 | ||||||||
\(397\) | −7487.16 | −0.946523 | −0.473261 | − | 0.880922i | \(-0.656923\pi\) | ||||
−0.473261 | + | 0.880922i | \(0.656923\pi\) | |||||||
\(398\) | 4007.89 | 0.504767 | ||||||||
\(399\) | 3067.51 | 0.384881 | ||||||||
\(400\) | −8358.52 | −1.04481 | ||||||||
\(401\) | −9700.71 | −1.20806 | −0.604028 | − | 0.796963i | \(-0.706438\pi\) | ||||
−0.604028 | + | 0.796963i | \(0.706438\pi\) | |||||||
\(402\) | 2424.29 | 0.300777 | ||||||||
\(403\) | 6539.21 | 0.808291 | ||||||||
\(404\) | 10082.6 | 1.24165 | ||||||||
\(405\) | 1318.05 | 0.161714 | ||||||||
\(406\) | 6073.76 | 0.742452 | ||||||||
\(407\) | −6867.51 | −0.836387 | ||||||||
\(408\) | 39.0901 | 0.00474326 | ||||||||
\(409\) | −1378.30 | −0.166632 | −0.0833160 | − | 0.996523i | \(-0.526551\pi\) | ||||
−0.0833160 | + | 0.996523i | \(0.526551\pi\) | |||||||
\(410\) | −34491.3 | −4.15464 | ||||||||
\(411\) | −128.543 | −0.0154271 | ||||||||
\(412\) | −8810.62 | −1.05356 | ||||||||
\(413\) | 399.453 | 0.0475927 | ||||||||
\(414\) | −5639.43 | −0.669475 | ||||||||
\(415\) | 11898.4 | 1.40740 | ||||||||
\(416\) | 21320.9 | 2.51285 | ||||||||
\(417\) | −737.377 | −0.0865935 | ||||||||
\(418\) | −10172.5 | −1.19032 | ||||||||
\(419\) | −6367.90 | −0.742463 | −0.371232 | − | 0.928540i | \(-0.621064\pi\) | ||||
−0.371232 | + | 0.928540i | \(0.621064\pi\) | |||||||
\(420\) | 2807.60 | 0.326183 | ||||||||
\(421\) | 4730.02 | 0.547570 | 0.273785 | − | 0.961791i | \(-0.411724\pi\) | ||||
0.273785 | + | 0.961791i | \(0.411724\pi\) | |||||||
\(422\) | 10315.7 | 1.18995 | ||||||||
\(423\) | 284.777 | 0.0327337 | ||||||||
\(424\) | −516.091 | −0.0591122 | ||||||||
\(425\) | 906.253 | 0.103435 | ||||||||
\(426\) | 8843.52 | 1.00580 | ||||||||
\(427\) | −465.285 | −0.0527324 | ||||||||
\(428\) | 15180.2 | 1.71440 | ||||||||
\(429\) | 4096.76 | 0.461057 | ||||||||
\(430\) | −17513.8 | −1.96416 | ||||||||
\(431\) | 12035.5 | 1.34509 | 0.672543 | − | 0.740058i | \(-0.265202\pi\) | ||||
0.672543 | + | 0.740058i | \(0.265202\pi\) | |||||||
\(432\) | −1614.50 | −0.179809 | ||||||||
\(433\) | −16014.7 | −1.77741 | −0.888705 | − | 0.458479i | \(-0.848395\pi\) | ||||
−0.888705 | + | 0.458479i | \(0.848395\pi\) | |||||||
\(434\) | −2183.72 | −0.241525 | ||||||||
\(435\) | 10782.9 | 1.18851 | ||||||||
\(436\) | −13152.0 | −1.44465 | ||||||||
\(437\) | −23300.7 | −2.55063 | ||||||||
\(438\) | 6964.01 | 0.759711 | ||||||||
\(439\) | 3032.82 | 0.329724 | 0.164862 | − | 0.986317i | \(-0.447282\pi\) | ||||
0.164862 | + | 0.986317i | \(0.447282\pi\) | |||||||
\(440\) | −542.375 | −0.0587652 | ||||||||
\(441\) | −2674.46 | −0.288787 | ||||||||
\(442\) | −2168.13 | −0.233320 | ||||||||
\(443\) | −1755.79 | −0.188308 | −0.0941538 | − | 0.995558i | \(-0.530015\pi\) | ||||
−0.0941538 | + | 0.995558i | \(0.530015\pi\) | |||||||
\(444\) | 10552.9 | 1.12797 | ||||||||
\(445\) | −11293.1 | −1.20303 | ||||||||
\(446\) | 20570.8 | 2.18398 | ||||||||
\(447\) | 4476.89 | 0.473713 | ||||||||
\(448\) | −3881.20 | −0.409307 | ||||||||
\(449\) | −11467.7 | −1.20533 | −0.602666 | − | 0.797994i | \(-0.705895\pi\) | ||||
−0.602666 | + | 0.797994i | \(0.705895\pi\) | |||||||
\(450\) | 5109.42 | 0.535246 | ||||||||
\(451\) | 8655.51 | 0.903708 | ||||||||
\(452\) | 12018.8 | 1.25071 | ||||||||
\(453\) | −2752.33 | −0.285465 | ||||||||
\(454\) | −3555.40 | −0.367540 | ||||||||
\(455\) | −9071.41 | −0.934669 | ||||||||
\(456\) | 910.593 | 0.0935141 | ||||||||
\(457\) | 920.816 | 0.0942537 | 0.0471268 | − | 0.998889i | \(-0.484993\pi\) | ||||
0.0471268 | + | 0.998889i | \(0.484993\pi\) | |||||||
\(458\) | −18357.0 | −1.87285 | ||||||||
\(459\) | 175.048 | 0.0178008 | ||||||||
\(460\) | −21326.5 | −2.16164 | ||||||||
\(461\) | 18808.7 | 1.90023 | 0.950117 | − | 0.311895i | \(-0.100964\pi\) | ||||
0.950117 | + | 0.311895i | \(0.100964\pi\) | |||||||
\(462\) | −1368.08 | −0.137768 | ||||||||
\(463\) | −4494.12 | −0.451101 | −0.225550 | − | 0.974232i | \(-0.572418\pi\) | ||||
−0.225550 | + | 0.974232i | \(0.572418\pi\) | |||||||
\(464\) | −13208.2 | −1.32150 | ||||||||
\(465\) | −3876.82 | −0.386630 | ||||||||
\(466\) | −13404.4 | −1.33251 | ||||||||
\(467\) | 608.207 | 0.0602665 | 0.0301332 | − | 0.999546i | \(-0.490407\pi\) | ||||
0.0301332 | + | 0.999546i | \(0.490407\pi\) | |||||||
\(468\) | −6295.28 | −0.621793 | ||||||||
\(469\) | 1347.11 | 0.132630 | ||||||||
\(470\) | 2091.14 | 0.205228 | ||||||||
\(471\) | 7016.78 | 0.686446 | ||||||||
\(472\) | 118.578 | 0.0115635 | ||||||||
\(473\) | 4395.04 | 0.427239 | ||||||||
\(474\) | −3714.80 | −0.359971 | ||||||||
\(475\) | 21110.9 | 2.03923 | ||||||||
\(476\) | 372.875 | 0.0359048 | ||||||||
\(477\) | −2311.09 | −0.221840 | ||||||||
\(478\) | 8269.60 | 0.791303 | ||||||||
\(479\) | −4182.01 | −0.398916 | −0.199458 | − | 0.979906i | \(-0.563918\pi\) | ||||
−0.199458 | + | 0.979906i | \(0.563918\pi\) | |||||||
\(480\) | −12640.3 | −1.20197 | ||||||||
\(481\) | −34096.7 | −3.23218 | ||||||||
\(482\) | 4611.37 | 0.435772 | ||||||||
\(483\) | −3133.67 | −0.295211 | ||||||||
\(484\) | −8970.18 | −0.842428 | ||||||||
\(485\) | −9717.08 | −0.909752 | ||||||||
\(486\) | 986.917 | 0.0921141 | ||||||||
\(487\) | −18578.4 | −1.72868 | −0.864340 | − | 0.502908i | \(-0.832264\pi\) | ||||
−0.864340 | + | 0.502908i | \(0.832264\pi\) | |||||||
\(488\) | −138.120 | −0.0128123 | ||||||||
\(489\) | 4276.52 | 0.395482 | ||||||||
\(490\) | −19638.7 | −1.81058 | ||||||||
\(491\) | 14967.0 | 1.37567 | 0.687833 | − | 0.725869i | \(-0.258562\pi\) | ||||
0.687833 | + | 0.725869i | \(0.258562\pi\) | |||||||
\(492\) | −13300.5 | −1.21876 | ||||||||
\(493\) | 1432.07 | 0.130826 | ||||||||
\(494\) | −50505.9 | −4.59994 | ||||||||
\(495\) | −2428.79 | −0.220538 | ||||||||
\(496\) | 4748.79 | 0.429893 | ||||||||
\(497\) | 4914.09 | 0.443515 | ||||||||
\(498\) | 8909.22 | 0.801670 | ||||||||
\(499\) | −14608.3 | −1.31053 | −0.655266 | − | 0.755398i | \(-0.727444\pi\) | ||||
−0.655266 | + | 0.755398i | \(0.727444\pi\) | |||||||
\(500\) | 2043.48 | 0.182774 | ||||||||
\(501\) | 5813.92 | 0.518456 | ||||||||
\(502\) | 24967.0 | 2.21979 | ||||||||
\(503\) | 11306.5 | 1.00225 | 0.501127 | − | 0.865374i | \(-0.332919\pi\) | ||||
0.501127 | + | 0.865374i | \(0.332919\pi\) | |||||||
\(504\) | 122.464 | 0.0108233 | ||||||||
\(505\) | 19313.4 | 1.70186 | ||||||||
\(506\) | 10391.9 | 0.912997 | ||||||||
\(507\) | 13749.1 | 1.20438 | ||||||||
\(508\) | 11804.7 | 1.03100 | ||||||||
\(509\) | 6037.40 | 0.525743 | 0.262871 | − | 0.964831i | \(-0.415330\pi\) | ||||
0.262871 | + | 0.964831i | \(0.415330\pi\) | |||||||
\(510\) | 1285.39 | 0.111604 | ||||||||
\(511\) | 3869.70 | 0.335001 | ||||||||
\(512\) | 16444.7 | 1.41946 | ||||||||
\(513\) | 4077.70 | 0.350945 | ||||||||
\(514\) | 3517.54 | 0.301852 | ||||||||
\(515\) | −16877.0 | −1.44406 | ||||||||
\(516\) | −6753.63 | −0.576186 | ||||||||
\(517\) | −524.766 | −0.0446406 | ||||||||
\(518\) | 11386.3 | 0.965805 | ||||||||
\(519\) | 2775.15 | 0.234712 | ||||||||
\(520\) | −2692.86 | −0.227095 | ||||||||
\(521\) | 12456.9 | 1.04750 | 0.523750 | − | 0.851872i | \(-0.324532\pi\) | ||||
0.523750 | + | 0.851872i | \(0.324532\pi\) | |||||||
\(522\) | 8073.96 | 0.676988 | ||||||||
\(523\) | 17565.0 | 1.46858 | 0.734288 | − | 0.678838i | \(-0.237516\pi\) | ||||
0.734288 | + | 0.678838i | \(0.237516\pi\) | |||||||
\(524\) | −3382.11 | −0.281962 | ||||||||
\(525\) | 2839.16 | 0.236021 | ||||||||
\(526\) | −19265.9 | −1.59702 | ||||||||
\(527\) | −514.877 | −0.0425586 | ||||||||
\(528\) | 2975.08 | 0.245215 | ||||||||
\(529\) | 11636.3 | 0.956378 | ||||||||
\(530\) | −16970.5 | −1.39085 | ||||||||
\(531\) | 531.000 | 0.0433963 | ||||||||
\(532\) | 8686.02 | 0.707870 | ||||||||
\(533\) | 42974.1 | 3.49233 | ||||||||
\(534\) | −8456.00 | −0.685257 | ||||||||
\(535\) | 29078.2 | 2.34983 | ||||||||
\(536\) | 399.890 | 0.0322250 | ||||||||
\(537\) | 6735.46 | 0.541260 | ||||||||
\(538\) | −23742.8 | −1.90264 | ||||||||
\(539\) | 4928.28 | 0.393833 | ||||||||
\(540\) | 3732.20 | 0.297423 | ||||||||
\(541\) | −12600.3 | −1.00135 | −0.500674 | − | 0.865636i | \(-0.666914\pi\) | ||||
−0.500674 | + | 0.865636i | \(0.666914\pi\) | |||||||
\(542\) | −19007.5 | −1.50635 | ||||||||
\(543\) | −5318.93 | −0.420363 | ||||||||
\(544\) | −1678.74 | −0.132308 | ||||||||
\(545\) | −25193.1 | −1.98010 | ||||||||
\(546\) | −6792.43 | −0.532398 | ||||||||
\(547\) | 18529.7 | 1.44840 | 0.724198 | − | 0.689592i | \(-0.242210\pi\) | ||||
0.724198 | + | 0.689592i | \(0.242210\pi\) | |||||||
\(548\) | −363.983 | −0.0283734 | ||||||||
\(549\) | −618.512 | −0.0480828 | ||||||||
\(550\) | −9415.25 | −0.729941 | ||||||||
\(551\) | 33359.7 | 2.57925 | ||||||||
\(552\) | −930.232 | −0.0717270 | ||||||||
\(553\) | −2064.21 | −0.158732 | ||||||||
\(554\) | −15779.3 | −1.21011 | ||||||||
\(555\) | 20214.5 | 1.54605 | ||||||||
\(556\) | −2087.97 | −0.159262 | ||||||||
\(557\) | −17686.0 | −1.34538 | −0.672691 | − | 0.739923i | \(-0.734862\pi\) | ||||
−0.672691 | + | 0.739923i | \(0.734862\pi\) | |||||||
\(558\) | −2902.86 | −0.220229 | ||||||||
\(559\) | 21821.1 | 1.65105 | ||||||||
\(560\) | −6587.68 | −0.497108 | ||||||||
\(561\) | −322.566 | −0.0242758 | ||||||||
\(562\) | −30789.1 | −2.31096 | ||||||||
\(563\) | 1719.56 | 0.128723 | 0.0643614 | − | 0.997927i | \(-0.479499\pi\) | ||||
0.0643614 | + | 0.997927i | \(0.479499\pi\) | |||||||
\(564\) | 806.381 | 0.0602035 | ||||||||
\(565\) | 23022.5 | 1.71427 | ||||||||
\(566\) | 3849.15 | 0.285851 | ||||||||
\(567\) | 548.401 | 0.0406185 | ||||||||
\(568\) | 1458.75 | 0.107760 | ||||||||
\(569\) | 4196.95 | 0.309218 | 0.154609 | − | 0.987976i | \(-0.450588\pi\) | ||||
0.154609 | + | 0.987976i | \(0.450588\pi\) | |||||||
\(570\) | 29942.8 | 2.20029 | ||||||||
\(571\) | −16717.6 | −1.22523 | −0.612616 | − | 0.790380i | \(-0.709883\pi\) | ||||
−0.612616 | + | 0.790380i | \(0.709883\pi\) | |||||||
\(572\) | 11600.5 | 0.847971 | ||||||||
\(573\) | −1861.37 | −0.135707 | ||||||||
\(574\) | −14350.8 | −1.04354 | ||||||||
\(575\) | −21566.2 | −1.56412 | ||||||||
\(576\) | −5159.35 | −0.373217 | ||||||||
\(577\) | 4687.41 | 0.338196 | 0.169098 | − | 0.985599i | \(-0.445915\pi\) | ||||
0.169098 | + | 0.985599i | \(0.445915\pi\) | |||||||
\(578\) | −19782.9 | −1.42363 | ||||||||
\(579\) | −7145.77 | −0.512898 | ||||||||
\(580\) | 30533.1 | 2.18589 | ||||||||
\(581\) | 4950.59 | 0.353503 | ||||||||
\(582\) | −7275.89 | −0.518205 | ||||||||
\(583\) | 4258.70 | 0.302534 | ||||||||
\(584\) | 1148.72 | 0.0813947 | ||||||||
\(585\) | −12058.8 | −0.852257 | ||||||||
\(586\) | −10612.2 | −0.748098 | ||||||||
\(587\) | 15750.6 | 1.10749 | 0.553745 | − | 0.832686i | \(-0.313198\pi\) | ||||
0.553745 | + | 0.832686i | \(0.313198\pi\) | |||||||
\(588\) | −7573.04 | −0.531134 | ||||||||
\(589\) | −11993.9 | −0.839050 | ||||||||
\(590\) | 3899.16 | 0.272078 | ||||||||
\(591\) | 6132.64 | 0.426841 | ||||||||
\(592\) | −24761.1 | −1.71905 | ||||||||
\(593\) | −3706.55 | −0.256677 | −0.128339 | − | 0.991730i | \(-0.540964\pi\) | ||||
−0.128339 | + | 0.991730i | \(0.540964\pi\) | |||||||
\(594\) | −1818.61 | −0.125621 | ||||||||
\(595\) | 714.254 | 0.0492127 | ||||||||
\(596\) | 12676.8 | 0.871248 | ||||||||
\(597\) | 2960.48 | 0.202956 | ||||||||
\(598\) | 51595.1 | 3.52823 | ||||||||
\(599\) | 263.566 | 0.0179783 | 0.00898917 | − | 0.999960i | \(-0.497139\pi\) | ||||
0.00898917 | + | 0.999960i | \(0.497139\pi\) | |||||||
\(600\) | 842.807 | 0.0573457 | ||||||||
\(601\) | −11714.8 | −0.795101 | −0.397550 | − | 0.917580i | \(-0.630140\pi\) | ||||
−0.397550 | + | 0.917580i | \(0.630140\pi\) | |||||||
\(602\) | −7286.98 | −0.493348 | ||||||||
\(603\) | 1790.74 | 0.120936 | ||||||||
\(604\) | −7793.55 | −0.525025 | ||||||||
\(605\) | −17182.7 | −1.15467 | ||||||||
\(606\) | 14461.4 | 0.969396 | ||||||||
\(607\) | 7579.45 | 0.506821 | 0.253410 | − | 0.967359i | \(-0.418448\pi\) | ||||
0.253410 | + | 0.967359i | \(0.418448\pi\) | |||||||
\(608\) | −39105.8 | −2.60847 | ||||||||
\(609\) | 4486.47 | 0.298523 | ||||||||
\(610\) | −4541.77 | −0.301461 | ||||||||
\(611\) | −2605.43 | −0.172511 | ||||||||
\(612\) | 495.670 | 0.0327390 | ||||||||
\(613\) | −15090.5 | −0.994291 | −0.497146 | − | 0.867667i | \(-0.665619\pi\) | ||||
−0.497146 | + | 0.867667i | \(0.665619\pi\) | |||||||
\(614\) | 27419.0 | 1.80218 | ||||||||
\(615\) | −25477.5 | −1.67049 | ||||||||
\(616\) | −225.667 | −0.0147603 | ||||||||
\(617\) | −19397.1 | −1.26564 | −0.632819 | − | 0.774300i | \(-0.718102\pi\) | ||||
−0.632819 | + | 0.774300i | \(0.718102\pi\) | |||||||
\(618\) | −12637.1 | −0.822552 | ||||||||
\(619\) | −14955.2 | −0.971082 | −0.485541 | − | 0.874214i | \(-0.661377\pi\) | ||||
−0.485541 | + | 0.874214i | \(0.661377\pi\) | |||||||
\(620\) | −10977.7 | −0.711087 | ||||||||
\(621\) | −4165.64 | −0.269181 | ||||||||
\(622\) | 4779.97 | 0.308134 | ||||||||
\(623\) | −4698.76 | −0.302170 | ||||||||
\(624\) | 14771.1 | 0.947622 | ||||||||
\(625\) | −13558.6 | −0.867747 | ||||||||
\(626\) | 8365.68 | 0.534121 | ||||||||
\(627\) | −7514.07 | −0.478602 | ||||||||
\(628\) | 19868.8 | 1.26250 | ||||||||
\(629\) | 2684.67 | 0.170182 | ||||||||
\(630\) | 4026.94 | 0.254662 | ||||||||
\(631\) | −2751.59 | −0.173596 | −0.0867979 | − | 0.996226i | \(-0.527663\pi\) | ||||
−0.0867979 | + | 0.996226i | \(0.527663\pi\) | |||||||
\(632\) | −612.762 | −0.0385670 | ||||||||
\(633\) | 7619.84 | 0.478454 | ||||||||
\(634\) | 21616.6 | 1.35411 | ||||||||
\(635\) | 22612.3 | 1.41313 | ||||||||
\(636\) | −6544.13 | −0.408006 | ||||||||
\(637\) | 24468.6 | 1.52195 | ||||||||
\(638\) | −14878.1 | −0.923242 | ||||||||
\(639\) | 6532.39 | 0.404409 | ||||||||
\(640\) | −4178.07 | −0.258051 | ||||||||
\(641\) | −16315.9 | −1.00536 | −0.502682 | − | 0.864471i | \(-0.667653\pi\) | ||||
−0.502682 | + | 0.864471i | \(0.667653\pi\) | |||||||
\(642\) | 21773.0 | 1.33849 | ||||||||
\(643\) | 24947.6 | 1.53007 | 0.765037 | − | 0.643987i | \(-0.222721\pi\) | ||||
0.765037 | + | 0.643987i | \(0.222721\pi\) | |||||||
\(644\) | −8873.34 | −0.542948 | ||||||||
\(645\) | −12936.8 | −0.789745 | ||||||||
\(646\) | 3976.68 | 0.242198 | ||||||||
\(647\) | −9286.05 | −0.564254 | −0.282127 | − | 0.959377i | \(-0.591040\pi\) | ||||
−0.282127 | + | 0.959377i | \(0.591040\pi\) | |||||||
\(648\) | 162.793 | 0.00986902 | ||||||||
\(649\) | −978.486 | −0.0591817 | ||||||||
\(650\) | −46746.1 | −2.82082 | ||||||||
\(651\) | −1613.03 | −0.0971118 | ||||||||
\(652\) | 12109.5 | 0.727367 | ||||||||
\(653\) | −7806.02 | −0.467800 | −0.233900 | − | 0.972261i | \(-0.575149\pi\) | ||||
−0.233900 | + | 0.972261i | \(0.575149\pi\) | |||||||
\(654\) | −18863.9 | −1.12789 | ||||||||
\(655\) | −6478.54 | −0.386470 | ||||||||
\(656\) | 31207.9 | 1.85741 | ||||||||
\(657\) | 5144.06 | 0.305463 | ||||||||
\(658\) | 870.063 | 0.0515480 | ||||||||
\(659\) | −30652.4 | −1.81191 | −0.905955 | − | 0.423374i | \(-0.860846\pi\) | ||||
−0.905955 | + | 0.423374i | \(0.860846\pi\) | |||||||
\(660\) | −6877.41 | −0.405610 | ||||||||
\(661\) | −1119.99 | −0.0659041 | −0.0329520 | − | 0.999457i | \(-0.510491\pi\) | ||||
−0.0329520 | + | 0.999457i | \(0.510491\pi\) | |||||||
\(662\) | −44457.3 | −2.61010 | ||||||||
\(663\) | −1601.52 | −0.0938127 | ||||||||
\(664\) | 1469.59 | 0.0858902 | ||||||||
\(665\) | 16638.3 | 0.970237 | ||||||||
\(666\) | 15136.1 | 0.880647 | ||||||||
\(667\) | −34079.1 | −1.97833 | ||||||||
\(668\) | 16462.8 | 0.953540 | ||||||||
\(669\) | 15194.9 | 0.878129 | ||||||||
\(670\) | 13149.5 | 0.758222 | ||||||||
\(671\) | 1139.75 | 0.0655730 | ||||||||
\(672\) | −5259.25 | −0.301905 | ||||||||
\(673\) | −20636.6 | −1.18199 | −0.590996 | − | 0.806675i | \(-0.701265\pi\) | ||||
−0.590996 | + | 0.806675i | \(0.701265\pi\) | |||||||
\(674\) | 1353.43 | 0.0773473 | ||||||||
\(675\) | 3774.15 | 0.215210 | ||||||||
\(676\) | 38932.3 | 2.21508 | ||||||||
\(677\) | −24871.6 | −1.41195 | −0.705976 | − | 0.708236i | \(-0.749491\pi\) | ||||
−0.705976 | + | 0.708236i | \(0.749491\pi\) | |||||||
\(678\) | 17238.6 | 0.976467 | ||||||||
\(679\) | −4043.00 | −0.228507 | ||||||||
\(680\) | 212.027 | 0.0119572 | ||||||||
\(681\) | −2626.25 | −0.147780 | ||||||||
\(682\) | 5349.16 | 0.300337 | ||||||||
\(683\) | 17124.9 | 0.959392 | 0.479696 | − | 0.877435i | \(-0.340747\pi\) | ||||
0.479696 | + | 0.877435i | \(0.340747\pi\) | |||||||
\(684\) | 11546.5 | 0.645455 | ||||||||
\(685\) | −697.222 | −0.0388897 | ||||||||
\(686\) | −17602.6 | −0.979696 | ||||||||
\(687\) | −13559.6 | −0.753032 | ||||||||
\(688\) | 15846.5 | 0.878116 | ||||||||
\(689\) | 21144.2 | 1.16913 | ||||||||
\(690\) | −30588.5 | −1.68766 | ||||||||
\(691\) | −15624.6 | −0.860183 | −0.430092 | − | 0.902785i | \(-0.641519\pi\) | ||||
−0.430092 | + | 0.902785i | \(0.641519\pi\) | |||||||
\(692\) | 7858.16 | 0.431680 | ||||||||
\(693\) | −1010.55 | −0.0553935 | ||||||||
\(694\) | −8342.29 | −0.456295 | ||||||||
\(695\) | −3999.57 | −0.218291 | ||||||||
\(696\) | 1331.81 | 0.0725319 | ||||||||
\(697\) | −3383.64 | −0.183880 | ||||||||
\(698\) | 27866.8 | 1.51114 | ||||||||
\(699\) | −9901.37 | −0.535771 | ||||||||
\(700\) | 8039.41 | 0.434087 | ||||||||
\(701\) | 21519.2 | 1.15944 | 0.579722 | − | 0.814814i | \(-0.303161\pi\) | ||||
0.579722 | + | 0.814814i | \(0.303161\pi\) | |||||||
\(702\) | −9029.31 | −0.485455 | ||||||||
\(703\) | 62538.6 | 3.35517 | ||||||||
\(704\) | 9507.25 | 0.508975 | ||||||||
\(705\) | 1544.65 | 0.0825175 | ||||||||
\(706\) | −14309.5 | −0.762812 | ||||||||
\(707\) | 8035.77 | 0.427463 | ||||||||
\(708\) | 1503.59 | 0.0798140 | ||||||||
\(709\) | −28820.4 | −1.52662 | −0.763309 | − | 0.646034i | \(-0.776426\pi\) | ||||
−0.763309 | + | 0.646034i | \(0.776426\pi\) | |||||||
\(710\) | 47967.7 | 2.53549 | ||||||||
\(711\) | −2743.99 | −0.144736 | ||||||||
\(712\) | −1394.83 | −0.0734178 | ||||||||
\(713\) | 12252.6 | 0.643566 | ||||||||
\(714\) | 534.814 | 0.0280321 | ||||||||
\(715\) | 22221.0 | 1.16227 | ||||||||
\(716\) | 19072.3 | 0.995480 | ||||||||
\(717\) | 6108.46 | 0.318165 | ||||||||
\(718\) | 6875.57 | 0.357373 | ||||||||
\(719\) | −4082.36 | −0.211747 | −0.105874 | − | 0.994380i | \(-0.533764\pi\) | ||||
−0.105874 | + | 0.994380i | \(0.533764\pi\) | |||||||
\(720\) | −8757.13 | −0.453276 | ||||||||
\(721\) | −7022.05 | −0.362711 | ||||||||
\(722\) | 64778.5 | 3.33906 | ||||||||
\(723\) | 3406.26 | 0.175214 | ||||||||
\(724\) | −15061.2 | −0.773127 | ||||||||
\(725\) | 30876.3 | 1.58168 | ||||||||
\(726\) | −12865.9 | −0.657712 | ||||||||
\(727\) | 34069.5 | 1.73806 | 0.869028 | − | 0.494763i | \(-0.164745\pi\) | ||||
0.869028 | + | 0.494763i | \(0.164745\pi\) | |||||||
\(728\) | −1120.42 | −0.0570406 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 37773.2 | 1.91513 | ||||||||
\(731\) | −1718.12 | −0.0869318 | ||||||||
\(732\) | −1751.39 | −0.0884334 | ||||||||
\(733\) | 23108.8 | 1.16445 | 0.582226 | − | 0.813027i | \(-0.302182\pi\) | ||||
0.582226 | + | 0.813027i | \(0.302182\pi\) | |||||||
\(734\) | −15698.6 | −0.789435 | ||||||||
\(735\) | −14506.4 | −0.727995 | ||||||||
\(736\) | 39949.1 | 2.00074 | ||||||||
\(737\) | −3299.83 | −0.164926 | ||||||||
\(738\) | −19076.9 | −0.951530 | ||||||||
\(739\) | −22291.4 | −1.10961 | −0.554805 | − | 0.831981i | \(-0.687207\pi\) | ||||
−0.554805 | + | 0.831981i | \(0.687207\pi\) | |||||||
\(740\) | 57239.7 | 2.84348 | ||||||||
\(741\) | −37306.9 | −1.84953 | ||||||||
\(742\) | −7060.93 | −0.349346 | ||||||||
\(743\) | 2619.28 | 0.129330 | 0.0646648 | − | 0.997907i | \(-0.479402\pi\) | ||||
0.0646648 | + | 0.997907i | \(0.479402\pi\) | |||||||
\(744\) | −478.831 | −0.0235951 | ||||||||
\(745\) | 24282.9 | 1.19417 | ||||||||
\(746\) | −24860.2 | −1.22010 | ||||||||
\(747\) | 6580.92 | 0.322334 | ||||||||
\(748\) | −913.383 | −0.0446478 | ||||||||
\(749\) | 12098.6 | 0.590219 | ||||||||
\(750\) | 2930.96 | 0.142698 | ||||||||
\(751\) | −16907.8 | −0.821538 | −0.410769 | − | 0.911739i | \(-0.634740\pi\) | ||||
−0.410769 | + | 0.911739i | \(0.634740\pi\) | |||||||
\(752\) | −1892.07 | −0.0917509 | ||||||||
\(753\) | 18442.3 | 0.892528 | ||||||||
\(754\) | −73868.7 | −3.56783 | ||||||||
\(755\) | −14928.8 | −0.719621 | ||||||||
\(756\) | 1552.86 | 0.0747051 | ||||||||
\(757\) | 3540.46 | 0.169987 | 0.0849936 | − | 0.996382i | \(-0.472913\pi\) | ||||
0.0849936 | + | 0.996382i | \(0.472913\pi\) | |||||||
\(758\) | −11937.2 | −0.572005 | ||||||||
\(759\) | 7676.12 | 0.367096 | ||||||||
\(760\) | 4939.11 | 0.235737 | ||||||||
\(761\) | −23640.9 | −1.12613 | −0.563063 | − | 0.826414i | \(-0.690377\pi\) | ||||
−0.563063 | + | 0.826414i | \(0.690377\pi\) | |||||||
\(762\) | 16931.5 | 0.804937 | ||||||||
\(763\) | −10482.1 | −0.497351 | ||||||||
\(764\) | −5270.69 | −0.249590 | ||||||||
\(765\) | 949.472 | 0.0448735 | ||||||||
\(766\) | 33202.7 | 1.56614 | ||||||||
\(767\) | −4858.12 | −0.228705 | ||||||||
\(768\) | 10629.8 | 0.499442 | ||||||||
\(769\) | 7631.43 | 0.357863 | 0.178931 | − | 0.983862i | \(-0.442736\pi\) | ||||
0.178931 | + | 0.983862i | \(0.442736\pi\) | |||||||
\(770\) | −7420.54 | −0.347296 | ||||||||
\(771\) | 2598.28 | 0.121368 | ||||||||
\(772\) | −20234.1 | −0.943318 | ||||||||
\(773\) | −18739.3 | −0.871936 | −0.435968 | − | 0.899962i | \(-0.643594\pi\) | ||||
−0.435968 | + | 0.899962i | \(0.643594\pi\) | |||||||
\(774\) | −9686.73 | −0.449848 | ||||||||
\(775\) | −11101.0 | −0.514531 | ||||||||
\(776\) | −1200.17 | −0.0555200 | ||||||||
\(777\) | 8410.68 | 0.388329 | ||||||||
\(778\) | 29875.3 | 1.37671 | ||||||||
\(779\) | −78821.0 | −3.62523 | ||||||||
\(780\) | −34145.9 | −1.56746 | ||||||||
\(781\) | −12037.4 | −0.551513 | ||||||||
\(782\) | −4062.44 | −0.185770 | ||||||||
\(783\) | 5963.95 | 0.272202 | ||||||||
\(784\) | 17769.2 | 0.809456 | ||||||||
\(785\) | 38059.4 | 1.73044 | ||||||||
\(786\) | −4850.96 | −0.220137 | ||||||||
\(787\) | 11942.8 | 0.540933 | 0.270467 | − | 0.962729i | \(-0.412822\pi\) | ||||
0.270467 | + | 0.962729i | \(0.412822\pi\) | |||||||
\(788\) | 17365.3 | 0.785042 | ||||||||
\(789\) | −14231.0 | −0.642126 | ||||||||
\(790\) | −20149.3 | −0.907442 | ||||||||
\(791\) | 9578.99 | 0.430581 | ||||||||
\(792\) | −299.983 | −0.0134589 | ||||||||
\(793\) | 5658.77 | 0.253403 | ||||||||
\(794\) | −30408.2 | −1.35913 | ||||||||
\(795\) | −12535.5 | −0.559230 | ||||||||
\(796\) | 8382.96 | 0.373274 | ||||||||
\(797\) | 11411.4 | 0.507167 | 0.253583 | − | 0.967314i | \(-0.418391\pi\) | ||||
0.253583 | + | 0.967314i | \(0.418391\pi\) | |||||||
\(798\) | 12458.3 | 0.552657 | ||||||||
\(799\) | 205.143 | 0.00908317 | ||||||||
\(800\) | −36194.6 | −1.59959 | ||||||||
\(801\) | −6246.15 | −0.275527 | ||||||||
\(802\) | −39398.3 | −1.73467 | ||||||||
\(803\) | −9479.09 | −0.416575 | ||||||||
\(804\) | 5070.68 | 0.222424 | ||||||||
\(805\) | −16997.2 | −0.744188 | ||||||||
\(806\) | 26558.3 | 1.16064 | ||||||||
\(807\) | −17537.9 | −0.765011 | ||||||||
\(808\) | 2385.43 | 0.103860 | ||||||||
\(809\) | 30559.4 | 1.32808 | 0.664038 | − | 0.747699i | \(-0.268841\pi\) | ||||
0.664038 | + | 0.747699i | \(0.268841\pi\) | |||||||
\(810\) | 5353.09 | 0.232208 | ||||||||
\(811\) | −38485.1 | −1.66633 | −0.833165 | − | 0.553025i | \(-0.813473\pi\) | ||||
−0.833165 | + | 0.553025i | \(0.813473\pi\) | |||||||
\(812\) | 12704.0 | 0.549041 | ||||||||
\(813\) | −14040.1 | −0.605669 | ||||||||
\(814\) | −27891.6 | −1.20098 | ||||||||
\(815\) | 23196.1 | 0.996960 | ||||||||
\(816\) | −1163.03 | −0.0498947 | ||||||||
\(817\) | −40023.2 | −1.71387 | ||||||||
\(818\) | −5597.80 | −0.239270 | ||||||||
\(819\) | −5017.32 | −0.214065 | ||||||||
\(820\) | −72142.5 | −3.07235 | ||||||||
\(821\) | 34212.3 | 1.45434 | 0.727172 | − | 0.686455i | \(-0.240834\pi\) | ||||
0.727172 | + | 0.686455i | \(0.240834\pi\) | |||||||
\(822\) | −522.061 | −0.0221520 | ||||||||
\(823\) | 24648.8 | 1.04399 | 0.521995 | − | 0.852949i | \(-0.325188\pi\) | ||||
0.521995 | + | 0.852949i | \(0.325188\pi\) | |||||||
\(824\) | −2084.50 | −0.0881275 | ||||||||
\(825\) | −6954.71 | −0.293493 | ||||||||
\(826\) | 1622.33 | 0.0683391 | ||||||||
\(827\) | −20204.0 | −0.849532 | −0.424766 | − | 0.905303i | \(-0.639644\pi\) | ||||
−0.424766 | + | 0.905303i | \(0.639644\pi\) | |||||||
\(828\) | −11795.5 | −0.495075 | ||||||||
\(829\) | −12267.7 | −0.513964 | −0.256982 | − | 0.966416i | \(-0.582728\pi\) | ||||
−0.256982 | + | 0.966416i | \(0.582728\pi\) | |||||||
\(830\) | 48324.1 | 2.02091 | ||||||||
\(831\) | −11655.6 | −0.486557 | ||||||||
\(832\) | 47202.9 | 1.96691 | ||||||||
\(833\) | −1926.58 | −0.0801346 | ||||||||
\(834\) | −2994.77 | −0.124341 | ||||||||
\(835\) | 31535.0 | 1.30696 | ||||||||
\(836\) | −21277.0 | −0.880239 | ||||||||
\(837\) | −2144.24 | −0.0885492 | ||||||||
\(838\) | −25862.5 | −1.06612 | ||||||||
\(839\) | −8916.91 | −0.366920 | −0.183460 | − | 0.983027i | \(-0.558730\pi\) | ||||
−0.183460 | + | 0.983027i | \(0.558730\pi\) | |||||||
\(840\) | 664.250 | 0.0272843 | ||||||||
\(841\) | 24402.0 | 1.00053 | ||||||||
\(842\) | 19210.4 | 0.786265 | ||||||||
\(843\) | −22742.8 | −0.929187 | ||||||||
\(844\) | 21576.5 | 0.879968 | ||||||||
\(845\) | 74576.1 | 3.03609 | ||||||||
\(846\) | 1156.59 | 0.0470029 | ||||||||
\(847\) | −7149.21 | −0.290023 | ||||||||
\(848\) | 15355.0 | 0.621806 | ||||||||
\(849\) | 2843.23 | 0.114934 | ||||||||
\(850\) | 3680.64 | 0.148524 | ||||||||
\(851\) | −63887.3 | −2.57348 | ||||||||
\(852\) | 18497.2 | 0.743785 | ||||||||
\(853\) | 5454.65 | 0.218949 | 0.109475 | − | 0.993990i | \(-0.465083\pi\) | ||||
0.109475 | + | 0.993990i | \(0.465083\pi\) | |||||||
\(854\) | −1889.70 | −0.0757193 | ||||||||
\(855\) | 22117.7 | 0.884688 | ||||||||
\(856\) | 3591.48 | 0.143405 | ||||||||
\(857\) | 30739.7 | 1.22526 | 0.612630 | − | 0.790370i | \(-0.290112\pi\) | ||||
0.612630 | + | 0.790370i | \(0.290112\pi\) | |||||||
\(858\) | 16638.5 | 0.662039 | ||||||||
\(859\) | −9450.34 | −0.375368 | −0.187684 | − | 0.982229i | \(-0.560098\pi\) | ||||
−0.187684 | + | 0.982229i | \(0.560098\pi\) | |||||||
\(860\) | −36632.1 | −1.45249 | ||||||||
\(861\) | −10600.5 | −0.419585 | ||||||||
\(862\) | 48881.0 | 1.93143 | ||||||||
\(863\) | 20494.1 | 0.808373 | 0.404186 | − | 0.914677i | \(-0.367555\pi\) | ||||
0.404186 | + | 0.914677i | \(0.367555\pi\) | |||||||
\(864\) | −6991.22 | −0.275285 | ||||||||
\(865\) | 15052.5 | 0.591678 | ||||||||
\(866\) | −65042.0 | −2.55221 | ||||||||
\(867\) | −14612.9 | −0.572411 | ||||||||
\(868\) | −4567.50 | −0.178607 | ||||||||
\(869\) | 5056.41 | 0.197384 | ||||||||
\(870\) | 43793.6 | 1.70660 | ||||||||
\(871\) | −16383.4 | −0.637350 | ||||||||
\(872\) | −3111.63 | −0.120841 | ||||||||
\(873\) | −5374.44 | −0.208359 | ||||||||
\(874\) | −94633.3 | −3.66249 | ||||||||
\(875\) | 1628.65 | 0.0629239 | ||||||||
\(876\) | 14566.0 | 0.561804 | ||||||||
\(877\) | 9745.52 | 0.375237 | 0.187618 | − | 0.982242i | \(-0.439923\pi\) | ||||
0.187618 | + | 0.982242i | \(0.439923\pi\) | |||||||
\(878\) | 12317.5 | 0.473456 | ||||||||
\(879\) | −7838.84 | −0.300794 | ||||||||
\(880\) | 16137.0 | 0.618156 | ||||||||
\(881\) | −15386.5 | −0.588405 | −0.294203 | − | 0.955743i | \(-0.595054\pi\) | ||||
−0.294203 | + | 0.955743i | \(0.595054\pi\) | |||||||
\(882\) | −10862.0 | −0.414674 | ||||||||
\(883\) | −38659.6 | −1.47339 | −0.736693 | − | 0.676227i | \(-0.763614\pi\) | ||||
−0.736693 | + | 0.676227i | \(0.763614\pi\) | |||||||
\(884\) | −4534.89 | −0.172539 | ||||||||
\(885\) | 2880.17 | 0.109397 | ||||||||
\(886\) | −7130.96 | −0.270394 | ||||||||
\(887\) | −2987.34 | −0.113083 | −0.0565417 | − | 0.998400i | \(-0.518007\pi\) | ||||
−0.0565417 | + | 0.998400i | \(0.518007\pi\) | |||||||
\(888\) | 2496.72 | 0.0943517 | ||||||||
\(889\) | 9408.32 | 0.354944 | ||||||||
\(890\) | −45865.8 | −1.72744 | ||||||||
\(891\) | −1343.35 | −0.0505093 | ||||||||
\(892\) | 43026.1 | 1.61505 | ||||||||
\(893\) | 4778.75 | 0.179076 | ||||||||
\(894\) | 18182.4 | 0.680212 | ||||||||
\(895\) | 36533.5 | 1.36445 | ||||||||
\(896\) | −1738.37 | −0.0648158 | ||||||||
\(897\) | 38111.5 | 1.41862 | ||||||||
\(898\) | −46574.7 | −1.73076 | ||||||||
\(899\) | −17542.0 | −0.650788 | ||||||||
\(900\) | 10686.9 | 0.395813 | ||||||||
\(901\) | −1664.83 | −0.0615576 | ||||||||
\(902\) | 35153.4 | 1.29765 | ||||||||
\(903\) | −5382.63 | −0.198364 | ||||||||
\(904\) | 2843.53 | 0.104618 | ||||||||
\(905\) | −28850.2 | −1.05968 | ||||||||
\(906\) | −11178.3 | −0.409904 | ||||||||
\(907\) | −8601.67 | −0.314899 | −0.157450 | − | 0.987527i | \(-0.550327\pi\) | ||||
−0.157450 | + | 0.987527i | \(0.550327\pi\) | |||||||
\(908\) | −7436.53 | −0.271795 | ||||||||
\(909\) | 10682.1 | 0.389772 | ||||||||
\(910\) | −36842.5 | −1.34211 | ||||||||
\(911\) | −6239.74 | −0.226928 | −0.113464 | − | 0.993542i | \(-0.536195\pi\) | ||||
−0.113464 | + | 0.993542i | \(0.536195\pi\) | |||||||
\(912\) | −27092.4 | −0.983682 | ||||||||
\(913\) | −12126.8 | −0.439583 | ||||||||
\(914\) | 3739.79 | 0.135340 | ||||||||
\(915\) | −3354.84 | −0.121211 | ||||||||
\(916\) | −38395.7 | −1.38497 | ||||||||
\(917\) | −2695.54 | −0.0970714 | ||||||||
\(918\) | 710.939 | 0.0255604 | ||||||||
\(919\) | 44905.0 | 1.61184 | 0.805918 | − | 0.592027i | \(-0.201672\pi\) | ||||
0.805918 | + | 0.592027i | \(0.201672\pi\) | |||||||
\(920\) | −5045.63 | −0.180815 | ||||||||
\(921\) | 20253.4 | 0.724617 | ||||||||
\(922\) | 76389.3 | 2.72858 | ||||||||
\(923\) | −59764.9 | −2.13129 | ||||||||
\(924\) | −2861.50 | −0.101879 | ||||||||
\(925\) | 57883.1 | 2.05750 | ||||||||
\(926\) | −18252.4 | −0.647743 | ||||||||
\(927\) | −9334.54 | −0.330730 | ||||||||
\(928\) | −57195.2 | −2.02319 | ||||||||
\(929\) | −20966.7 | −0.740470 | −0.370235 | − | 0.928938i | \(-0.620723\pi\) | ||||
−0.370235 | + | 0.928938i | \(0.620723\pi\) | |||||||
\(930\) | −15745.3 | −0.555169 | ||||||||
\(931\) | −44879.2 | −1.57987 | ||||||||
\(932\) | −28036.9 | −0.985385 | ||||||||
\(933\) | 3530.80 | 0.123894 | ||||||||
\(934\) | 2470.16 | 0.0865377 | ||||||||
\(935\) | −1749.61 | −0.0611962 | ||||||||
\(936\) | −1489.40 | −0.0520112 | ||||||||
\(937\) | 42889.9 | 1.49536 | 0.747679 | − | 0.664060i | \(-0.231168\pi\) | ||||
0.747679 | + | 0.664060i | \(0.231168\pi\) | |||||||
\(938\) | 5471.12 | 0.190446 | ||||||||
\(939\) | 6179.43 | 0.214758 | ||||||||
\(940\) | 4373.85 | 0.151765 | ||||||||
\(941\) | 17830.3 | 0.617697 | 0.308848 | − | 0.951111i | \(-0.400056\pi\) | ||||
0.308848 | + | 0.951111i | \(0.400056\pi\) | |||||||
\(942\) | 28497.8 | 0.985679 | ||||||||
\(943\) | 80520.8 | 2.78061 | ||||||||
\(944\) | −3527.98 | −0.121638 | ||||||||
\(945\) | 2974.56 | 0.102394 | ||||||||
\(946\) | 17850.0 | 0.613480 | ||||||||
\(947\) | −20658.3 | −0.708874 | −0.354437 | − | 0.935080i | \(-0.615328\pi\) | ||||
−0.354437 | + | 0.935080i | \(0.615328\pi\) | |||||||
\(948\) | −7769.93 | −0.266198 | ||||||||
\(949\) | −47063.1 | −1.60983 | ||||||||
\(950\) | 85739.5 | 2.92816 | ||||||||
\(951\) | 15967.4 | 0.544457 | ||||||||
\(952\) | 88.2184 | 0.00300333 | ||||||||
\(953\) | −44095.2 | −1.49883 | −0.749415 | − | 0.662101i | \(-0.769665\pi\) | ||||
−0.749415 | + | 0.662101i | \(0.769665\pi\) | |||||||
\(954\) | −9386.23 | −0.318543 | ||||||||
\(955\) | −10096.2 | −0.342099 | ||||||||
\(956\) | 17296.8 | 0.585167 | ||||||||
\(957\) | −10989.9 | −0.371215 | ||||||||
\(958\) | −16984.8 | −0.572810 | ||||||||
\(959\) | −290.094 | −0.00976812 | ||||||||
\(960\) | −27984.6 | −0.940832 | ||||||||
\(961\) | −23484.1 | −0.788294 | ||||||||
\(962\) | −138480. | −4.64114 | ||||||||
\(963\) | 16082.9 | 0.538177 | ||||||||
\(964\) | 9645.22 | 0.322253 | ||||||||
\(965\) | −38759.1 | −1.29295 | ||||||||
\(966\) | −12727.0 | −0.423898 | ||||||||
\(967\) | 45160.1 | 1.50181 | 0.750906 | − | 0.660409i | \(-0.229617\pi\) | ||||
0.750906 | + | 0.660409i | \(0.229617\pi\) | |||||||
\(968\) | −2122.25 | −0.0704667 | ||||||||
\(969\) | 2937.43 | 0.0973826 | ||||||||
\(970\) | −39464.8 | −1.30633 | ||||||||
\(971\) | 49299.5 | 1.62935 | 0.814673 | − | 0.579920i | \(-0.196916\pi\) | ||||
0.814673 | + | 0.579920i | \(0.196916\pi\) | |||||||
\(972\) | 2064.25 | 0.0681181 | ||||||||
\(973\) | −1664.11 | −0.0548292 | ||||||||
\(974\) | −75454.0 | −2.48224 | ||||||||
\(975\) | −34529.7 | −1.13419 | ||||||||
\(976\) | 4109.42 | 0.134774 | ||||||||
\(977\) | 27045.5 | 0.885632 | 0.442816 | − | 0.896613i | \(-0.353980\pi\) | ||||
0.442816 | + | 0.896613i | \(0.353980\pi\) | |||||||
\(978\) | 17368.6 | 0.567880 | ||||||||
\(979\) | 11509.9 | 0.375749 | ||||||||
\(980\) | −41076.6 | −1.33892 | ||||||||
\(981\) | −13934.1 | −0.453498 | ||||||||
\(982\) | 60786.8 | 1.97534 | ||||||||
\(983\) | −23169.0 | −0.751757 | −0.375878 | − | 0.926669i | \(-0.622659\pi\) | ||||
−0.375878 | + | 0.926669i | \(0.622659\pi\) | |||||||
\(984\) | −3146.76 | −0.101946 | ||||||||
\(985\) | 33263.8 | 1.07601 | ||||||||
\(986\) | 5816.19 | 0.187855 | ||||||||
\(987\) | 642.684 | 0.0207263 | ||||||||
\(988\) | −105639. | −3.40164 | ||||||||
\(989\) | 40886.4 | 1.31457 | ||||||||
\(990\) | −9864.26 | −0.316674 | ||||||||
\(991\) | −58402.5 | −1.87206 | −0.936032 | − | 0.351915i | \(-0.885531\pi\) | ||||
−0.936032 | + | 0.351915i | \(0.885531\pi\) | |||||||
\(992\) | 20563.6 | 0.658159 | ||||||||
\(993\) | −32839.0 | −1.04946 | ||||||||
\(994\) | 19958.0 | 0.636851 | ||||||||
\(995\) | 16057.8 | 0.511625 | ||||||||
\(996\) | 18634.6 | 0.592833 | ||||||||
\(997\) | −3853.02 | −0.122394 | −0.0611968 | − | 0.998126i | \(-0.519492\pi\) | ||||
−0.0611968 | + | 0.998126i | \(0.519492\pi\) | |||||||
\(998\) | −59329.8 | −1.88182 | ||||||||
\(999\) | 11180.5 | 0.354089 |
(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 | 177.4.a.d.1.6 | ✓ | 8 | |
3.2 | odd | 2 | 531.4.a.e.1.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.4.a.d.1.6 | ✓ | 8 | 1.1 | even | 1 | trivial | |
531.4.a.e.1.3 | 8 | 3.2 | odd | 2 |