Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [435,4,Mod(1,435)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(435, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("435.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 435 = 3 \cdot 5 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 435.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: | \(25.6658308525\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 2x^{6} - 37x^{5} + 55x^{4} + 336x^{3} - 227x^{2} - 824x - 166 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.57720\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 435.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.57720 | −1.26473 | −0.632366 | − | 0.774670i | \(-0.717916\pi\) | ||||
−0.632366 | + | 0.774670i | \(0.717916\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 4.79637 | 0.599546 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 10.7316 | 0.730193 | ||||||||
\(7\) | 15.0281 | 0.811443 | 0.405721 | − | 0.913997i | \(-0.367020\pi\) | ||||
0.405721 | + | 0.913997i | \(0.367020\pi\) | |||||||
\(8\) | 11.4600 | 0.506467 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −17.8860 | −0.565605 | ||||||||
\(11\) | 70.8260 | 1.94135 | 0.970674 | − | 0.240399i | \(-0.0772781\pi\) | ||||
0.970674 | + | 0.240399i | \(0.0772781\pi\) | |||||||
\(12\) | −14.3891 | −0.346148 | ||||||||
\(13\) | 62.2117 | 1.32726 | 0.663632 | − | 0.748059i | \(-0.269014\pi\) | ||||
0.663632 | + | 0.748059i | \(0.269014\pi\) | |||||||
\(14\) | −53.7587 | −1.02626 | ||||||||
\(15\) | −15.0000 | −0.258199 | ||||||||
\(16\) | −79.3658 | −1.24009 | ||||||||
\(17\) | −67.1848 | −0.958513 | −0.479256 | − | 0.877675i | \(-0.659094\pi\) | ||||
−0.479256 | + | 0.877675i | \(0.659094\pi\) | |||||||
\(18\) | −32.1948 | −0.421577 | ||||||||
\(19\) | 118.988 | 1.43673 | 0.718364 | − | 0.695667i | \(-0.244891\pi\) | ||||
0.718364 | + | 0.695667i | \(0.244891\pi\) | |||||||
\(20\) | 23.9818 | 0.268125 | ||||||||
\(21\) | −45.0844 | −0.468487 | ||||||||
\(22\) | −253.359 | −2.45528 | ||||||||
\(23\) | 72.5383 | 0.657621 | 0.328810 | − | 0.944396i | \(-0.393352\pi\) | ||||
0.328810 | + | 0.944396i | \(0.393352\pi\) | |||||||
\(24\) | −34.3801 | −0.292409 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −222.544 | −1.67863 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 72.0804 | 0.486497 | ||||||||
\(29\) | 29.0000 | 0.185695 | ||||||||
\(30\) | 53.6580 | 0.326552 | ||||||||
\(31\) | −180.227 | −1.04418 | −0.522092 | − | 0.852889i | \(-0.674848\pi\) | ||||
−0.522092 | + | 0.852889i | \(0.674848\pi\) | |||||||
\(32\) | 192.227 | 1.06191 | ||||||||
\(33\) | −212.478 | −1.12084 | ||||||||
\(34\) | 240.334 | 1.21226 | ||||||||
\(35\) | 75.1407 | 0.362888 | ||||||||
\(36\) | 43.1673 | 0.199849 | ||||||||
\(37\) | −47.8439 | −0.212581 | −0.106290 | − | 0.994335i | \(-0.533897\pi\) | ||||
−0.106290 | + | 0.994335i | \(0.533897\pi\) | |||||||
\(38\) | −425.646 | −1.81708 | ||||||||
\(39\) | −186.635 | −0.766296 | ||||||||
\(40\) | 57.3002 | 0.226499 | ||||||||
\(41\) | 371.956 | 1.41682 | 0.708411 | − | 0.705800i | \(-0.249412\pi\) | ||||
0.708411 | + | 0.705800i | \(0.249412\pi\) | |||||||
\(42\) | 161.276 | 0.592510 | ||||||||
\(43\) | −409.069 | −1.45075 | −0.725377 | − | 0.688352i | \(-0.758334\pi\) | ||||
−0.725377 | + | 0.688352i | \(0.758334\pi\) | |||||||
\(44\) | 339.707 | 1.16393 | ||||||||
\(45\) | 45.0000 | 0.149071 | ||||||||
\(46\) | −259.484 | −0.831714 | ||||||||
\(47\) | 125.891 | 0.390705 | 0.195353 | − | 0.980733i | \(-0.437415\pi\) | ||||
0.195353 | + | 0.980733i | \(0.437415\pi\) | |||||||
\(48\) | 238.097 | 0.715967 | ||||||||
\(49\) | −117.155 | −0.341560 | ||||||||
\(50\) | −89.4300 | −0.252946 | ||||||||
\(51\) | 201.555 | 0.553398 | ||||||||
\(52\) | 298.390 | 0.795755 | ||||||||
\(53\) | −215.764 | −0.559198 | −0.279599 | − | 0.960117i | \(-0.590202\pi\) | ||||
−0.279599 | + | 0.960117i | \(0.590202\pi\) | |||||||
\(54\) | 96.5844 | 0.243398 | ||||||||
\(55\) | 354.130 | 0.868197 | ||||||||
\(56\) | 172.223 | 0.410969 | ||||||||
\(57\) | −356.965 | −0.829495 | ||||||||
\(58\) | −103.739 | −0.234855 | ||||||||
\(59\) | 356.919 | 0.787575 | 0.393788 | − | 0.919201i | \(-0.371165\pi\) | ||||
0.393788 | + | 0.919201i | \(0.371165\pi\) | |||||||
\(60\) | −71.9455 | −0.154802 | ||||||||
\(61\) | −466.115 | −0.978358 | −0.489179 | − | 0.872183i | \(-0.662704\pi\) | ||||
−0.489179 | + | 0.872183i | \(0.662704\pi\) | |||||||
\(62\) | 644.707 | 1.32061 | ||||||||
\(63\) | 135.253 | 0.270481 | ||||||||
\(64\) | −52.7086 | −0.102946 | ||||||||
\(65\) | 311.059 | 0.593570 | ||||||||
\(66\) | 760.076 | 1.41756 | ||||||||
\(67\) | −578.359 | −1.05459 | −0.527297 | − | 0.849681i | \(-0.676794\pi\) | ||||
−0.527297 | + | 0.849681i | \(0.676794\pi\) | |||||||
\(68\) | −322.243 | −0.574672 | ||||||||
\(69\) | −217.615 | −0.379678 | ||||||||
\(70\) | −268.793 | −0.458956 | ||||||||
\(71\) | 870.924 | 1.45577 | 0.727885 | − | 0.685699i | \(-0.240503\pi\) | ||||
0.727885 | + | 0.685699i | \(0.240503\pi\) | |||||||
\(72\) | 103.140 | 0.168822 | ||||||||
\(73\) | 411.904 | 0.660407 | 0.330204 | − | 0.943910i | \(-0.392883\pi\) | ||||
0.330204 | + | 0.943910i | \(0.392883\pi\) | |||||||
\(74\) | 171.147 | 0.268857 | ||||||||
\(75\) | −75.0000 | −0.115470 | ||||||||
\(76\) | 570.712 | 0.861384 | ||||||||
\(77\) | 1064.38 | 1.57529 | ||||||||
\(78\) | 667.631 | 0.969159 | ||||||||
\(79\) | 1120.23 | 1.59538 | 0.797692 | − | 0.603065i | \(-0.206054\pi\) | ||||
0.797692 | + | 0.603065i | \(0.206054\pi\) | |||||||
\(80\) | −396.829 | −0.554585 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −1330.56 | −1.79190 | ||||||||
\(83\) | 1079.28 | 1.42730 | 0.713652 | − | 0.700501i | \(-0.247040\pi\) | ||||
0.713652 | + | 0.700501i | \(0.247040\pi\) | |||||||
\(84\) | −216.241 | −0.280879 | ||||||||
\(85\) | −335.924 | −0.428660 | ||||||||
\(86\) | 1463.32 | 1.83481 | ||||||||
\(87\) | −87.0000 | −0.107211 | ||||||||
\(88\) | 811.668 | 0.983229 | ||||||||
\(89\) | 388.993 | 0.463294 | 0.231647 | − | 0.972800i | \(-0.425589\pi\) | ||||
0.231647 | + | 0.972800i | \(0.425589\pi\) | |||||||
\(90\) | −160.974 | −0.188535 | ||||||||
\(91\) | 934.926 | 1.07700 | ||||||||
\(92\) | 347.920 | 0.394274 | ||||||||
\(93\) | 540.680 | 0.602859 | ||||||||
\(94\) | −450.339 | −0.494137 | ||||||||
\(95\) | 594.942 | 0.642524 | ||||||||
\(96\) | −576.681 | −0.613097 | ||||||||
\(97\) | −1528.82 | −1.60029 | −0.800147 | − | 0.599803i | \(-0.795245\pi\) | ||||
−0.800147 | + | 0.599803i | \(0.795245\pi\) | |||||||
\(98\) | 419.088 | 0.431982 | ||||||||
\(99\) | 637.434 | 0.647116 | ||||||||
\(100\) | 119.909 | 0.119909 | ||||||||
\(101\) | −1425.50 | −1.40439 | −0.702193 | − | 0.711987i | \(-0.747796\pi\) | ||||
−0.702193 | + | 0.711987i | \(0.747796\pi\) | |||||||
\(102\) | −721.001 | −0.699899 | ||||||||
\(103\) | −1595.68 | −1.52648 | −0.763240 | − | 0.646116i | \(-0.776392\pi\) | ||||
−0.763240 | + | 0.646116i | \(0.776392\pi\) | |||||||
\(104\) | 712.949 | 0.672215 | ||||||||
\(105\) | −225.422 | −0.209514 | ||||||||
\(106\) | 771.832 | 0.707236 | ||||||||
\(107\) | −155.104 | −0.140135 | −0.0700675 | − | 0.997542i | \(-0.522321\pi\) | ||||
−0.0700675 | + | 0.997542i | \(0.522321\pi\) | |||||||
\(108\) | −129.502 | −0.115383 | ||||||||
\(109\) | 1212.23 | 1.06524 | 0.532618 | − | 0.846356i | \(-0.321208\pi\) | ||||
0.532618 | + | 0.846356i | \(0.321208\pi\) | |||||||
\(110\) | −1266.79 | −1.09804 | ||||||||
\(111\) | 143.532 | 0.122733 | ||||||||
\(112\) | −1192.72 | −1.00626 | ||||||||
\(113\) | −1152.01 | −0.959043 | −0.479521 | − | 0.877530i | \(-0.659190\pi\) | ||||
−0.479521 | + | 0.877530i | \(0.659190\pi\) | |||||||
\(114\) | 1276.94 | 1.04909 | ||||||||
\(115\) | 362.691 | 0.294097 | ||||||||
\(116\) | 139.095 | 0.111333 | ||||||||
\(117\) | 559.905 | 0.442421 | ||||||||
\(118\) | −1276.77 | −0.996072 | ||||||||
\(119\) | −1009.66 | −0.777778 | ||||||||
\(120\) | −171.901 | −0.130769 | ||||||||
\(121\) | 3685.32 | 2.76883 | ||||||||
\(122\) | 1667.39 | 1.23736 | ||||||||
\(123\) | −1115.87 | −0.818003 | ||||||||
\(124\) | −864.434 | −0.626036 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | −483.828 | −0.342086 | ||||||||
\(127\) | 398.743 | 0.278604 | 0.139302 | − | 0.990250i | \(-0.455514\pi\) | ||||
0.139302 | + | 0.990250i | \(0.455514\pi\) | |||||||
\(128\) | −1349.27 | −0.931715 | ||||||||
\(129\) | 1227.21 | 0.837593 | ||||||||
\(130\) | −1112.72 | −0.750707 | ||||||||
\(131\) | −385.241 | −0.256937 | −0.128468 | − | 0.991714i | \(-0.541006\pi\) | ||||
−0.128468 | + | 0.991714i | \(0.541006\pi\) | |||||||
\(132\) | −1019.12 | −0.671994 | ||||||||
\(133\) | 1788.17 | 1.16582 | ||||||||
\(134\) | 2068.90 | 1.33378 | ||||||||
\(135\) | −135.000 | −0.0860663 | ||||||||
\(136\) | −769.941 | −0.485455 | ||||||||
\(137\) | −351.877 | −0.219437 | −0.109719 | − | 0.993963i | \(-0.534995\pi\) | ||||
−0.109719 | + | 0.993963i | \(0.534995\pi\) | |||||||
\(138\) | 778.452 | 0.480190 | ||||||||
\(139\) | 1138.48 | 0.694711 | 0.347355 | − | 0.937734i | \(-0.387080\pi\) | ||||
0.347355 | + | 0.937734i | \(0.387080\pi\) | |||||||
\(140\) | 360.402 | 0.217568 | ||||||||
\(141\) | −377.674 | −0.225574 | ||||||||
\(142\) | −3115.47 | −1.84116 | ||||||||
\(143\) | 4406.21 | 2.57668 | ||||||||
\(144\) | −714.292 | −0.413364 | ||||||||
\(145\) | 145.000 | 0.0830455 | ||||||||
\(146\) | −1473.46 | −0.835238 | ||||||||
\(147\) | 351.466 | 0.197200 | ||||||||
\(148\) | −229.477 | −0.127452 | ||||||||
\(149\) | 1200.59 | 0.660107 | 0.330053 | − | 0.943962i | \(-0.392933\pi\) | ||||
0.330053 | + | 0.943962i | \(0.392933\pi\) | |||||||
\(150\) | 268.290 | 0.146039 | ||||||||
\(151\) | −1539.35 | −0.829605 | −0.414802 | − | 0.909911i | \(-0.636149\pi\) | ||||
−0.414802 | + | 0.909911i | \(0.636149\pi\) | |||||||
\(152\) | 1363.61 | 0.727655 | ||||||||
\(153\) | −604.664 | −0.319504 | ||||||||
\(154\) | −3807.51 | −1.99232 | ||||||||
\(155\) | −901.134 | −0.466973 | ||||||||
\(156\) | −895.171 | −0.459430 | ||||||||
\(157\) | 223.134 | 0.113427 | 0.0567136 | − | 0.998390i | \(-0.481938\pi\) | ||||
0.0567136 | + | 0.998390i | \(0.481938\pi\) | |||||||
\(158\) | −4007.28 | −2.01773 | ||||||||
\(159\) | 647.293 | 0.322853 | ||||||||
\(160\) | 961.136 | 0.474903 | ||||||||
\(161\) | 1090.11 | 0.533622 | ||||||||
\(162\) | −289.753 | −0.140526 | ||||||||
\(163\) | −3114.71 | −1.49671 | −0.748353 | − | 0.663301i | \(-0.769155\pi\) | ||||
−0.748353 | + | 0.663301i | \(0.769155\pi\) | |||||||
\(164\) | 1784.04 | 0.849450 | ||||||||
\(165\) | −1062.39 | −0.501254 | ||||||||
\(166\) | −3860.79 | −1.80516 | ||||||||
\(167\) | −1720.78 | −0.797351 | −0.398676 | − | 0.917092i | \(-0.630530\pi\) | ||||
−0.398676 | + | 0.917092i | \(0.630530\pi\) | |||||||
\(168\) | −516.669 | −0.237273 | ||||||||
\(169\) | 1673.30 | 0.761629 | ||||||||
\(170\) | 1201.67 | 0.542140 | ||||||||
\(171\) | 1070.90 | 0.478909 | ||||||||
\(172\) | −1962.04 | −0.869793 | ||||||||
\(173\) | 2438.70 | 1.07174 | 0.535870 | − | 0.844301i | \(-0.319984\pi\) | ||||
0.535870 | + | 0.844301i | \(0.319984\pi\) | |||||||
\(174\) | 311.216 | 0.135593 | ||||||||
\(175\) | 375.703 | 0.162289 | ||||||||
\(176\) | −5621.16 | −2.40745 | ||||||||
\(177\) | −1070.76 | −0.454707 | ||||||||
\(178\) | −1391.50 | −0.585942 | ||||||||
\(179\) | −2248.00 | −0.938676 | −0.469338 | − | 0.883018i | \(-0.655507\pi\) | ||||
−0.469338 | + | 0.883018i | \(0.655507\pi\) | |||||||
\(180\) | 215.837 | 0.0893750 | ||||||||
\(181\) | −2357.13 | −0.967977 | −0.483989 | − | 0.875074i | \(-0.660812\pi\) | ||||
−0.483989 | + | 0.875074i | \(0.660812\pi\) | |||||||
\(182\) | −3344.42 | −1.36211 | ||||||||
\(183\) | 1398.34 | 0.564855 | ||||||||
\(184\) | 831.292 | 0.333063 | ||||||||
\(185\) | −239.219 | −0.0950689 | ||||||||
\(186\) | −1934.12 | −0.762455 | ||||||||
\(187\) | −4758.43 | −1.86081 | ||||||||
\(188\) | 603.821 | 0.234246 | ||||||||
\(189\) | −405.760 | −0.156162 | ||||||||
\(190\) | −2128.23 | −0.812621 | ||||||||
\(191\) | 1922.56 | 0.728331 | 0.364166 | − | 0.931334i | \(-0.381354\pi\) | ||||
0.364166 | + | 0.931334i | \(0.381354\pi\) | |||||||
\(192\) | 158.126 | 0.0594362 | ||||||||
\(193\) | 1840.68 | 0.686504 | 0.343252 | − | 0.939243i | \(-0.388472\pi\) | ||||
0.343252 | + | 0.939243i | \(0.388472\pi\) | |||||||
\(194\) | 5468.91 | 2.02394 | ||||||||
\(195\) | −933.176 | −0.342698 | ||||||||
\(196\) | −561.919 | −0.204781 | ||||||||
\(197\) | −2712.79 | −0.981109 | −0.490555 | − | 0.871410i | \(-0.663206\pi\) | ||||
−0.490555 | + | 0.871410i | \(0.663206\pi\) | |||||||
\(198\) | −2280.23 | −0.818428 | ||||||||
\(199\) | 224.631 | 0.0800185 | 0.0400093 | − | 0.999199i | \(-0.487261\pi\) | ||||
0.0400093 | + | 0.999199i | \(0.487261\pi\) | |||||||
\(200\) | 286.501 | 0.101293 | ||||||||
\(201\) | 1735.08 | 0.608870 | ||||||||
\(202\) | 5099.31 | 1.77617 | ||||||||
\(203\) | 435.816 | 0.150681 | ||||||||
\(204\) | 966.729 | 0.331787 | ||||||||
\(205\) | 1859.78 | 0.633622 | ||||||||
\(206\) | 5708.08 | 1.93059 | ||||||||
\(207\) | 652.845 | 0.219207 | ||||||||
\(208\) | −4937.48 | −1.64593 | ||||||||
\(209\) | 8427.48 | 2.78919 | ||||||||
\(210\) | 806.380 | 0.264979 | ||||||||
\(211\) | −4160.10 | −1.35731 | −0.678656 | − | 0.734456i | \(-0.737437\pi\) | ||||
−0.678656 | + | 0.734456i | \(0.737437\pi\) | |||||||
\(212\) | −1034.88 | −0.335265 | ||||||||
\(213\) | −2612.77 | −0.840489 | ||||||||
\(214\) | 554.837 | 0.177233 | ||||||||
\(215\) | −2045.34 | −0.648797 | ||||||||
\(216\) | −309.421 | −0.0974696 | ||||||||
\(217\) | −2708.47 | −0.847295 | ||||||||
\(218\) | −4336.40 | −1.34724 | ||||||||
\(219\) | −1235.71 | −0.381286 | ||||||||
\(220\) | 1698.54 | 0.520524 | ||||||||
\(221\) | −4179.68 | −1.27220 | ||||||||
\(222\) | −513.441 | −0.155225 | ||||||||
\(223\) | −1746.41 | −0.524432 | −0.262216 | − | 0.965009i | \(-0.584453\pi\) | ||||
−0.262216 | + | 0.965009i | \(0.584453\pi\) | |||||||
\(224\) | 2888.81 | 0.861683 | ||||||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | 4120.97 | 1.21293 | ||||||||
\(227\) | 129.508 | 0.0378666 | 0.0189333 | − | 0.999821i | \(-0.493973\pi\) | ||||
0.0189333 | + | 0.999821i | \(0.493973\pi\) | |||||||
\(228\) | −1712.14 | −0.497320 | ||||||||
\(229\) | −682.166 | −0.196851 | −0.0984253 | − | 0.995144i | \(-0.531381\pi\) | ||||
−0.0984253 | + | 0.995144i | \(0.531381\pi\) | |||||||
\(230\) | −1297.42 | −0.371954 | ||||||||
\(231\) | −3193.15 | −0.909496 | ||||||||
\(232\) | 332.341 | 0.0940486 | ||||||||
\(233\) | 1731.11 | 0.486732 | 0.243366 | − | 0.969935i | \(-0.421748\pi\) | ||||
0.243366 | + | 0.969935i | \(0.421748\pi\) | |||||||
\(234\) | −2002.89 | −0.559544 | ||||||||
\(235\) | 629.457 | 0.174729 | ||||||||
\(236\) | 1711.92 | 0.472188 | ||||||||
\(237\) | −3360.68 | −0.921095 | ||||||||
\(238\) | 3611.77 | 0.983681 | ||||||||
\(239\) | 3308.38 | 0.895402 | 0.447701 | − | 0.894183i | \(-0.352243\pi\) | ||||
0.447701 | + | 0.894183i | \(0.352243\pi\) | |||||||
\(240\) | 1190.49 | 0.320190 | ||||||||
\(241\) | 3586.39 | 0.958588 | 0.479294 | − | 0.877654i | \(-0.340893\pi\) | ||||
0.479294 | + | 0.877654i | \(0.340893\pi\) | |||||||
\(242\) | −13183.1 | −3.50183 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | −2235.66 | −0.586571 | ||||||||
\(245\) | −585.776 | −0.152750 | ||||||||
\(246\) | 3991.68 | 1.03455 | ||||||||
\(247\) | 7402.48 | 1.90692 | ||||||||
\(248\) | −2065.41 | −0.528844 | ||||||||
\(249\) | −3237.83 | −0.824054 | ||||||||
\(250\) | −447.150 | −0.113121 | ||||||||
\(251\) | −2956.22 | −0.743406 | −0.371703 | − | 0.928352i | \(-0.621226\pi\) | ||||
−0.371703 | + | 0.928352i | \(0.621226\pi\) | |||||||
\(252\) | 648.724 | 0.162166 | ||||||||
\(253\) | 5137.59 | 1.27667 | ||||||||
\(254\) | −1426.39 | −0.352360 | ||||||||
\(255\) | 1007.77 | 0.247487 | ||||||||
\(256\) | 5248.27 | 1.28132 | ||||||||
\(257\) | 2258.12 | 0.548084 | 0.274042 | − | 0.961718i | \(-0.411639\pi\) | ||||
0.274042 | + | 0.961718i | \(0.411639\pi\) | |||||||
\(258\) | −4389.96 | −1.05933 | ||||||||
\(259\) | −719.004 | −0.172497 | ||||||||
\(260\) | 1491.95 | 0.355873 | ||||||||
\(261\) | 261.000 | 0.0618984 | ||||||||
\(262\) | 1378.09 | 0.324956 | ||||||||
\(263\) | 2908.67 | 0.681963 | 0.340981 | − | 0.940070i | \(-0.389241\pi\) | ||||
0.340981 | + | 0.940070i | \(0.389241\pi\) | |||||||
\(264\) | −2435.01 | −0.567667 | ||||||||
\(265\) | −1078.82 | −0.250081 | ||||||||
\(266\) | −6396.66 | −1.47445 | ||||||||
\(267\) | −1166.98 | −0.267483 | ||||||||
\(268\) | −2774.02 | −0.632277 | ||||||||
\(269\) | −297.910 | −0.0675238 | −0.0337619 | − | 0.999430i | \(-0.510749\pi\) | ||||
−0.0337619 | + | 0.999430i | \(0.510749\pi\) | |||||||
\(270\) | 482.922 | 0.108851 | ||||||||
\(271\) | 6993.04 | 1.56752 | 0.783758 | − | 0.621067i | \(-0.213300\pi\) | ||||
0.783758 | + | 0.621067i | \(0.213300\pi\) | |||||||
\(272\) | 5332.18 | 1.18864 | ||||||||
\(273\) | −2804.78 | −0.621805 | ||||||||
\(274\) | 1258.73 | 0.277529 | ||||||||
\(275\) | 1770.65 | 0.388270 | ||||||||
\(276\) | −1043.76 | −0.227634 | ||||||||
\(277\) | 5701.84 | 1.23679 | 0.618394 | − | 0.785868i | \(-0.287784\pi\) | ||||
0.618394 | + | 0.785868i | \(0.287784\pi\) | |||||||
\(278\) | −4072.58 | −0.878622 | ||||||||
\(279\) | −1622.04 | −0.348061 | ||||||||
\(280\) | 861.115 | 0.183791 | ||||||||
\(281\) | −1216.34 | −0.258223 | −0.129112 | − | 0.991630i | \(-0.541213\pi\) | ||||
−0.129112 | + | 0.991630i | \(0.541213\pi\) | |||||||
\(282\) | 1351.02 | 0.285290 | ||||||||
\(283\) | 4096.17 | 0.860396 | 0.430198 | − | 0.902735i | \(-0.358444\pi\) | ||||
0.430198 | + | 0.902735i | \(0.358444\pi\) | |||||||
\(284\) | 4177.27 | 0.872801 | ||||||||
\(285\) | −1784.83 | −0.370962 | ||||||||
\(286\) | −15761.9 | −3.25881 | ||||||||
\(287\) | 5589.80 | 1.14967 | ||||||||
\(288\) | 1730.04 | 0.353972 | ||||||||
\(289\) | −399.197 | −0.0812532 | ||||||||
\(290\) | −518.694 | −0.105030 | ||||||||
\(291\) | 4586.47 | 0.923931 | ||||||||
\(292\) | 1975.64 | 0.395944 | ||||||||
\(293\) | 5854.29 | 1.16727 | 0.583637 | − | 0.812015i | \(-0.301629\pi\) | ||||
0.583637 | + | 0.812015i | \(0.301629\pi\) | |||||||
\(294\) | −1257.26 | −0.249405 | ||||||||
\(295\) | 1784.60 | 0.352214 | ||||||||
\(296\) | −548.292 | −0.107665 | ||||||||
\(297\) | −1912.30 | −0.373613 | ||||||||
\(298\) | −4294.74 | −0.834858 | ||||||||
\(299\) | 4512.73 | 0.872836 | ||||||||
\(300\) | −359.728 | −0.0692296 | ||||||||
\(301\) | −6147.54 | −1.17720 | ||||||||
\(302\) | 5506.56 | 1.04923 | ||||||||
\(303\) | 4276.51 | 0.810822 | ||||||||
\(304\) | −9443.62 | −1.78167 | ||||||||
\(305\) | −2330.57 | −0.437535 | ||||||||
\(306\) | 2163.00 | 0.404087 | ||||||||
\(307\) | −2748.38 | −0.510940 | −0.255470 | − | 0.966817i | \(-0.582230\pi\) | ||||
−0.255470 | + | 0.966817i | \(0.582230\pi\) | |||||||
\(308\) | 5105.17 | 0.944461 | ||||||||
\(309\) | 4787.05 | 0.881313 | ||||||||
\(310\) | 3223.54 | 0.590595 | ||||||||
\(311\) | −10289.0 | −1.87600 | −0.938000 | − | 0.346634i | \(-0.887325\pi\) | ||||
−0.938000 | + | 0.346634i | \(0.887325\pi\) | |||||||
\(312\) | −2138.85 | −0.388104 | ||||||||
\(313\) | 8540.93 | 1.54237 | 0.771185 | − | 0.636611i | \(-0.219664\pi\) | ||||
0.771185 | + | 0.636611i | \(0.219664\pi\) | |||||||
\(314\) | −798.196 | −0.143455 | ||||||||
\(315\) | 676.266 | 0.120963 | ||||||||
\(316\) | 5373.02 | 0.956506 | ||||||||
\(317\) | −131.153 | −0.0232375 | −0.0116187 | − | 0.999933i | \(-0.503698\pi\) | ||||
−0.0116187 | + | 0.999933i | \(0.503698\pi\) | |||||||
\(318\) | −2315.50 | −0.408323 | ||||||||
\(319\) | 2053.95 | 0.360499 | ||||||||
\(320\) | −263.543 | −0.0460391 | ||||||||
\(321\) | 465.311 | 0.0809070 | ||||||||
\(322\) | −3899.56 | −0.674888 | ||||||||
\(323\) | −7994.22 | −1.37712 | ||||||||
\(324\) | 388.506 | 0.0666162 | ||||||||
\(325\) | 1555.29 | 0.265453 | ||||||||
\(326\) | 11142.0 | 1.89293 | ||||||||
\(327\) | −3636.70 | −0.615014 | ||||||||
\(328\) | 4262.63 | 0.717574 | ||||||||
\(329\) | 1891.91 | 0.317035 | ||||||||
\(330\) | 3800.38 | 0.633952 | ||||||||
\(331\) | −7274.79 | −1.20803 | −0.604016 | − | 0.796972i | \(-0.706434\pi\) | ||||
−0.604016 | + | 0.796972i | \(0.706434\pi\) | |||||||
\(332\) | 5176.61 | 0.855734 | ||||||||
\(333\) | −430.595 | −0.0708602 | ||||||||
\(334\) | 6155.56 | 1.00844 | ||||||||
\(335\) | −2891.79 | −0.471628 | ||||||||
\(336\) | 3578.16 | 0.580966 | ||||||||
\(337\) | 4663.56 | 0.753830 | 0.376915 | − | 0.926248i | \(-0.376985\pi\) | ||||
0.376915 | + | 0.926248i | \(0.376985\pi\) | |||||||
\(338\) | −5985.72 | −0.963256 | ||||||||
\(339\) | 3456.03 | 0.553704 | ||||||||
\(340\) | −1611.22 | −0.257001 | ||||||||
\(341\) | −12764.7 | −2.02712 | ||||||||
\(342\) | −3830.81 | −0.605692 | ||||||||
\(343\) | −6915.27 | −1.08860 | ||||||||
\(344\) | −4687.94 | −0.734759 | ||||||||
\(345\) | −1088.07 | −0.169797 | ||||||||
\(346\) | −8723.72 | −1.35546 | ||||||||
\(347\) | 6050.81 | 0.936093 | 0.468046 | − | 0.883704i | \(-0.344958\pi\) | ||||
0.468046 | + | 0.883704i | \(0.344958\pi\) | |||||||
\(348\) | −417.284 | −0.0642781 | ||||||||
\(349\) | 12824.0 | 1.96691 | 0.983455 | − | 0.181152i | \(-0.0579825\pi\) | ||||
0.983455 | + | 0.181152i | \(0.0579825\pi\) | |||||||
\(350\) | −1343.97 | −0.205251 | ||||||||
\(351\) | −1679.72 | −0.255432 | ||||||||
\(352\) | 13614.7 | 2.06155 | ||||||||
\(353\) | 12514.5 | 1.88691 | 0.943457 | − | 0.331494i | \(-0.107553\pi\) | ||||
0.943457 | + | 0.331494i | \(0.107553\pi\) | |||||||
\(354\) | 3830.32 | 0.575082 | ||||||||
\(355\) | 4354.62 | 0.651040 | ||||||||
\(356\) | 1865.75 | 0.277766 | ||||||||
\(357\) | 3028.99 | 0.449051 | ||||||||
\(358\) | 8041.53 | 1.18717 | ||||||||
\(359\) | 3394.70 | 0.499068 | 0.249534 | − | 0.968366i | \(-0.419723\pi\) | ||||
0.249534 | + | 0.968366i | \(0.419723\pi\) | |||||||
\(360\) | 515.702 | 0.0754996 | ||||||||
\(361\) | 7299.26 | 1.06419 | ||||||||
\(362\) | 8431.92 | 1.22423 | ||||||||
\(363\) | −11056.0 | −1.59859 | ||||||||
\(364\) | 4484.25 | 0.645710 | ||||||||
\(365\) | 2059.52 | 0.295343 | ||||||||
\(366\) | −5002.16 | −0.714391 | ||||||||
\(367\) | −9991.93 | −1.42118 | −0.710592 | − | 0.703604i | \(-0.751573\pi\) | ||||
−0.710592 | + | 0.703604i | \(0.751573\pi\) | |||||||
\(368\) | −5757.06 | −0.815509 | ||||||||
\(369\) | 3347.60 | 0.472274 | ||||||||
\(370\) | 855.735 | 0.120237 | ||||||||
\(371\) | −3242.54 | −0.453758 | ||||||||
\(372\) | 2593.30 | 0.361442 | ||||||||
\(373\) | 7219.40 | 1.00216 | 0.501081 | − | 0.865400i | \(-0.332936\pi\) | ||||
0.501081 | + | 0.865400i | \(0.332936\pi\) | |||||||
\(374\) | 17021.9 | 2.35342 | ||||||||
\(375\) | −375.000 | −0.0516398 | ||||||||
\(376\) | 1442.72 | 0.197879 | ||||||||
\(377\) | 1804.14 | 0.246467 | ||||||||
\(378\) | 1451.48 | 0.197503 | ||||||||
\(379\) | 10797.8 | 1.46345 | 0.731724 | − | 0.681601i | \(-0.238716\pi\) | ||||
0.731724 | + | 0.681601i | \(0.238716\pi\) | |||||||
\(380\) | 2853.56 | 0.385223 | ||||||||
\(381\) | −1196.23 | −0.160852 | ||||||||
\(382\) | −6877.37 | −0.921144 | ||||||||
\(383\) | −3396.75 | −0.453174 | −0.226587 | − | 0.973991i | \(-0.572757\pi\) | ||||
−0.226587 | + | 0.973991i | \(0.572757\pi\) | |||||||
\(384\) | 4047.80 | 0.537926 | ||||||||
\(385\) | 5321.91 | 0.704493 | ||||||||
\(386\) | −6584.49 | −0.868243 | ||||||||
\(387\) | −3681.62 | −0.483585 | ||||||||
\(388\) | −7332.80 | −0.959450 | ||||||||
\(389\) | −4927.07 | −0.642192 | −0.321096 | − | 0.947047i | \(-0.604051\pi\) | ||||
−0.321096 | + | 0.947047i | \(0.604051\pi\) | |||||||
\(390\) | 3338.16 | 0.433421 | ||||||||
\(391\) | −4873.47 | −0.630338 | ||||||||
\(392\) | −1342.60 | −0.172989 | ||||||||
\(393\) | 1155.72 | 0.148342 | ||||||||
\(394\) | 9704.21 | 1.24084 | ||||||||
\(395\) | 5601.13 | 0.713477 | ||||||||
\(396\) | 3057.37 | 0.387976 | ||||||||
\(397\) | −7777.55 | −0.983234 | −0.491617 | − | 0.870812i | \(-0.663594\pi\) | ||||
−0.491617 | + | 0.870812i | \(0.663594\pi\) | |||||||
\(398\) | −803.551 | −0.101202 | ||||||||
\(399\) | −5364.52 | −0.673088 | ||||||||
\(400\) | −1984.14 | −0.248018 | ||||||||
\(401\) | 6058.22 | 0.754446 | 0.377223 | − | 0.926122i | \(-0.376879\pi\) | ||||
0.377223 | + | 0.926122i | \(0.376879\pi\) | |||||||
\(402\) | −6206.71 | −0.770057 | ||||||||
\(403\) | −11212.2 | −1.38591 | ||||||||
\(404\) | −6837.24 | −0.841994 | ||||||||
\(405\) | 405.000 | 0.0496904 | ||||||||
\(406\) | −1559.00 | −0.190571 | ||||||||
\(407\) | −3388.59 | −0.412693 | ||||||||
\(408\) | 2309.82 | 0.280278 | ||||||||
\(409\) | −15078.2 | −1.82291 | −0.911454 | − | 0.411403i | \(-0.865039\pi\) | ||||
−0.911454 | + | 0.411403i | \(0.865039\pi\) | |||||||
\(410\) | −6652.80 | −0.801362 | ||||||||
\(411\) | 1055.63 | 0.126692 | ||||||||
\(412\) | −7653.48 | −0.915194 | ||||||||
\(413\) | 5363.83 | 0.639073 | ||||||||
\(414\) | −2335.36 | −0.277238 | ||||||||
\(415\) | 5396.39 | 0.638309 | ||||||||
\(416\) | 11958.8 | 1.40944 | ||||||||
\(417\) | −3415.45 | −0.401091 | ||||||||
\(418\) | −30146.8 | −3.52758 | ||||||||
\(419\) | 5698.22 | 0.664383 | 0.332192 | − | 0.943212i | \(-0.392212\pi\) | ||||
0.332192 | + | 0.943212i | \(0.392212\pi\) | |||||||
\(420\) | −1081.21 | −0.125613 | ||||||||
\(421\) | 846.838 | 0.0980341 | 0.0490171 | − | 0.998798i | \(-0.484391\pi\) | ||||
0.0490171 | + | 0.998798i | \(0.484391\pi\) | |||||||
\(422\) | 14881.5 | 1.71664 | ||||||||
\(423\) | 1133.02 | 0.130235 | ||||||||
\(424\) | −2472.67 | −0.283215 | ||||||||
\(425\) | −1679.62 | −0.191703 | ||||||||
\(426\) | 9346.41 | 1.06299 | ||||||||
\(427\) | −7004.83 | −0.793882 | ||||||||
\(428\) | −743.934 | −0.0840173 | ||||||||
\(429\) | −13218.6 | −1.48765 | ||||||||
\(430\) | 7316.61 | 0.820554 | ||||||||
\(431\) | −7518.27 | −0.840237 | −0.420119 | − | 0.907469i | \(-0.638012\pi\) | ||||
−0.420119 | + | 0.907469i | \(0.638012\pi\) | |||||||
\(432\) | 2142.88 | 0.238656 | ||||||||
\(433\) | 12686.0 | 1.40797 | 0.703987 | − | 0.710213i | \(-0.251401\pi\) | ||||
0.703987 | + | 0.710213i | \(0.251401\pi\) | |||||||
\(434\) | 9688.75 | 1.07160 | ||||||||
\(435\) | −435.000 | −0.0479463 | ||||||||
\(436\) | 5814.31 | 0.638658 | ||||||||
\(437\) | 8631.22 | 0.944822 | ||||||||
\(438\) | 4420.39 | 0.482225 | ||||||||
\(439\) | 10530.4 | 1.14485 | 0.572424 | − | 0.819958i | \(-0.306003\pi\) | ||||
0.572424 | + | 0.819958i | \(0.306003\pi\) | |||||||
\(440\) | 4058.34 | 0.439713 | ||||||||
\(441\) | −1054.40 | −0.113853 | ||||||||
\(442\) | 14951.6 | 1.60899 | ||||||||
\(443\) | −5199.17 | −0.557608 | −0.278804 | − | 0.960348i | \(-0.589938\pi\) | ||||
−0.278804 | + | 0.960348i | \(0.589938\pi\) | |||||||
\(444\) | 688.430 | 0.0735843 | ||||||||
\(445\) | 1944.96 | 0.207191 | ||||||||
\(446\) | 6247.27 | 0.663266 | ||||||||
\(447\) | −3601.76 | −0.381113 | ||||||||
\(448\) | −792.112 | −0.0835352 | ||||||||
\(449\) | −11836.7 | −1.24412 | −0.622058 | − | 0.782971i | \(-0.713703\pi\) | ||||
−0.622058 | + | 0.782971i | \(0.713703\pi\) | |||||||
\(450\) | −804.870 | −0.0843154 | ||||||||
\(451\) | 26344.1 | 2.75055 | ||||||||
\(452\) | −5525.46 | −0.574990 | ||||||||
\(453\) | 4618.04 | 0.478973 | ||||||||
\(454\) | −463.274 | −0.0478911 | ||||||||
\(455\) | 4674.63 | 0.481648 | ||||||||
\(456\) | −4090.84 | −0.420112 | ||||||||
\(457\) | 404.451 | 0.0413992 | 0.0206996 | − | 0.999786i | \(-0.493411\pi\) | ||||
0.0206996 | + | 0.999786i | \(0.493411\pi\) | |||||||
\(458\) | 2440.24 | 0.248963 | ||||||||
\(459\) | 1813.99 | 0.184466 | ||||||||
\(460\) | 1739.60 | 0.176325 | ||||||||
\(461\) | 7072.59 | 0.714541 | 0.357270 | − | 0.934001i | \(-0.383707\pi\) | ||||
0.357270 | + | 0.934001i | \(0.383707\pi\) | |||||||
\(462\) | 11422.5 | 1.15027 | ||||||||
\(463\) | −6500.22 | −0.652464 | −0.326232 | − | 0.945290i | \(-0.605779\pi\) | ||||
−0.326232 | + | 0.945290i | \(0.605779\pi\) | |||||||
\(464\) | −2301.61 | −0.230279 | ||||||||
\(465\) | 2703.40 | 0.269607 | ||||||||
\(466\) | −6192.51 | −0.615585 | ||||||||
\(467\) | −8850.61 | −0.876997 | −0.438498 | − | 0.898732i | \(-0.644489\pi\) | ||||
−0.438498 | + | 0.898732i | \(0.644489\pi\) | |||||||
\(468\) | 2685.51 | 0.265252 | ||||||||
\(469\) | −8691.65 | −0.855742 | ||||||||
\(470\) | −2251.69 | −0.220985 | ||||||||
\(471\) | −669.403 | −0.0654872 | ||||||||
\(472\) | 4090.31 | 0.398881 | ||||||||
\(473\) | −28972.7 | −2.81642 | ||||||||
\(474\) | 12021.8 | 1.16494 | ||||||||
\(475\) | 2974.71 | 0.287346 | ||||||||
\(476\) | −4842.71 | −0.466314 | ||||||||
\(477\) | −1941.88 | −0.186399 | ||||||||
\(478\) | −11834.7 | −1.13244 | ||||||||
\(479\) | −8582.91 | −0.818712 | −0.409356 | − | 0.912375i | \(-0.634247\pi\) | ||||
−0.409356 | + | 0.912375i | \(0.634247\pi\) | |||||||
\(480\) | −2883.41 | −0.274185 | ||||||||
\(481\) | −2976.45 | −0.282150 | ||||||||
\(482\) | −12829.2 | −1.21236 | ||||||||
\(483\) | −3270.34 | −0.308087 | ||||||||
\(484\) | 17676.1 | 1.66004 | ||||||||
\(485\) | −7644.12 | −0.715674 | ||||||||
\(486\) | 869.260 | 0.0811326 | ||||||||
\(487\) | −2823.62 | −0.262732 | −0.131366 | − | 0.991334i | \(-0.541936\pi\) | ||||
−0.131366 | + | 0.991334i | \(0.541936\pi\) | |||||||
\(488\) | −5341.69 | −0.495506 | ||||||||
\(489\) | 9344.14 | 0.864124 | ||||||||
\(490\) | 2095.44 | 0.193188 | ||||||||
\(491\) | −13116.2 | −1.20555 | −0.602776 | − | 0.797911i | \(-0.705939\pi\) | ||||
−0.602776 | + | 0.797911i | \(0.705939\pi\) | |||||||
\(492\) | −5352.11 | −0.490430 | ||||||||
\(493\) | −1948.36 | −0.177991 | ||||||||
\(494\) | −26480.2 | −2.41174 | ||||||||
\(495\) | 3187.17 | 0.289399 | ||||||||
\(496\) | 14303.8 | 1.29488 | ||||||||
\(497\) | 13088.4 | 1.18127 | ||||||||
\(498\) | 11582.4 | 1.04221 | ||||||||
\(499\) | −16495.4 | −1.47983 | −0.739916 | − | 0.672699i | \(-0.765135\pi\) | ||||
−0.739916 | + | 0.672699i | \(0.765135\pi\) | |||||||
\(500\) | 599.546 | 0.0536250 | ||||||||
\(501\) | 5162.33 | 0.460351 | ||||||||
\(502\) | 10575.0 | 0.940209 | ||||||||
\(503\) | −16677.3 | −1.47834 | −0.739169 | − | 0.673520i | \(-0.764781\pi\) | ||||
−0.739169 | + | 0.673520i | \(0.764781\pi\) | |||||||
\(504\) | 1550.01 | 0.136990 | ||||||||
\(505\) | −7127.52 | −0.628060 | ||||||||
\(506\) | −18378.2 | −1.61465 | ||||||||
\(507\) | −5019.89 | −0.439726 | ||||||||
\(508\) | 1912.52 | 0.167036 | ||||||||
\(509\) | 9386.35 | 0.817373 | 0.408686 | − | 0.912675i | \(-0.365987\pi\) | ||||
0.408686 | + | 0.912675i | \(0.365987\pi\) | |||||||
\(510\) | −3605.01 | −0.313005 | ||||||||
\(511\) | 6190.15 | 0.535883 | ||||||||
\(512\) | −7979.98 | −0.688806 | ||||||||
\(513\) | −3212.69 | −0.276498 | ||||||||
\(514\) | −8077.75 | −0.693180 | ||||||||
\(515\) | −7978.42 | −0.682662 | ||||||||
\(516\) | 5886.13 | 0.502175 | ||||||||
\(517\) | 8916.37 | 0.758495 | ||||||||
\(518\) | 2572.02 | 0.218162 | ||||||||
\(519\) | −7316.10 | −0.618769 | ||||||||
\(520\) | 3564.74 | 0.300624 | ||||||||
\(521\) | −16530.2 | −1.39002 | −0.695009 | − | 0.719001i | \(-0.744600\pi\) | ||||
−0.695009 | + | 0.719001i | \(0.744600\pi\) | |||||||
\(522\) | −933.649 | −0.0782849 | ||||||||
\(523\) | −18295.9 | −1.52968 | −0.764842 | − | 0.644217i | \(-0.777183\pi\) | ||||
−0.764842 | + | 0.644217i | \(0.777183\pi\) | |||||||
\(524\) | −1847.76 | −0.154045 | ||||||||
\(525\) | −1127.11 | −0.0936974 | ||||||||
\(526\) | −10404.9 | −0.862500 | ||||||||
\(527\) | 12108.5 | 1.00086 | ||||||||
\(528\) | 16863.5 | 1.38994 | ||||||||
\(529\) | −6905.20 | −0.567535 | ||||||||
\(530\) | 3859.16 | 0.316285 | ||||||||
\(531\) | 3212.27 | 0.262525 | ||||||||
\(532\) | 8576.74 | 0.698964 | ||||||||
\(533\) | 23140.0 | 1.88050 | ||||||||
\(534\) | 4174.51 | 0.338294 | ||||||||
\(535\) | −775.518 | −0.0626703 | ||||||||
\(536\) | −6628.01 | −0.534117 | ||||||||
\(537\) | 6743.99 | 0.541945 | ||||||||
\(538\) | 1065.68 | 0.0853994 | ||||||||
\(539\) | −8297.63 | −0.663088 | ||||||||
\(540\) | −647.510 | −0.0516007 | ||||||||
\(541\) | −949.695 | −0.0754724 | −0.0377362 | − | 0.999288i | \(-0.512015\pi\) | ||||
−0.0377362 | + | 0.999288i | \(0.512015\pi\) | |||||||
\(542\) | −25015.5 | −1.98249 | ||||||||
\(543\) | 7071.38 | 0.558862 | ||||||||
\(544\) | −12914.7 | −1.01786 | ||||||||
\(545\) | 6061.16 | 0.476388 | ||||||||
\(546\) | 10033.3 | 0.786417 | ||||||||
\(547\) | 18017.4 | 1.40835 | 0.704177 | − | 0.710024i | \(-0.251316\pi\) | ||||
0.704177 | + | 0.710024i | \(0.251316\pi\) | |||||||
\(548\) | −1687.73 | −0.131563 | ||||||||
\(549\) | −4195.03 | −0.326119 | ||||||||
\(550\) | −6333.97 | −0.491057 | ||||||||
\(551\) | 3450.67 | 0.266794 | ||||||||
\(552\) | −2493.87 | −0.192294 | ||||||||
\(553\) | 16834.9 | 1.29456 | ||||||||
\(554\) | −20396.6 | −1.56420 | ||||||||
\(555\) | 717.658 | 0.0548881 | ||||||||
\(556\) | 5460.58 | 0.416511 | ||||||||
\(557\) | −11387.6 | −0.866263 | −0.433131 | − | 0.901331i | \(-0.642591\pi\) | ||||
−0.433131 | + | 0.901331i | \(0.642591\pi\) | |||||||
\(558\) | 5802.37 | 0.440204 | ||||||||
\(559\) | −25448.9 | −1.92553 | ||||||||
\(560\) | −5963.60 | −0.450014 | ||||||||
\(561\) | 14275.3 | 1.07434 | ||||||||
\(562\) | 4351.09 | 0.326583 | ||||||||
\(563\) | −277.822 | −0.0207971 | −0.0103986 | − | 0.999946i | \(-0.503310\pi\) | ||||
−0.0103986 | + | 0.999946i | \(0.503310\pi\) | |||||||
\(564\) | −1811.46 | −0.135242 | ||||||||
\(565\) | −5760.04 | −0.428897 | ||||||||
\(566\) | −14652.8 | −1.08817 | ||||||||
\(567\) | 1217.28 | 0.0901603 | ||||||||
\(568\) | 9980.82 | 0.737299 | ||||||||
\(569\) | 15475.5 | 1.14019 | 0.570093 | − | 0.821580i | \(-0.306907\pi\) | ||||
0.570093 | + | 0.821580i | \(0.306907\pi\) | |||||||
\(570\) | 6384.69 | 0.469167 | ||||||||
\(571\) | −3245.82 | −0.237887 | −0.118944 | − | 0.992901i | \(-0.537951\pi\) | ||||
−0.118944 | + | 0.992901i | \(0.537951\pi\) | |||||||
\(572\) | 21133.8 | 1.54484 | ||||||||
\(573\) | −5767.67 | −0.420502 | ||||||||
\(574\) | −19995.8 | −1.45402 | ||||||||
\(575\) | 1813.46 | 0.131524 | ||||||||
\(576\) | −474.377 | −0.0343155 | ||||||||
\(577\) | −23087.9 | −1.66579 | −0.832895 | − | 0.553430i | \(-0.813318\pi\) | ||||
−0.832895 | + | 0.553430i | \(0.813318\pi\) | |||||||
\(578\) | 1428.01 | 0.102764 | ||||||||
\(579\) | −5522.05 | −0.396353 | ||||||||
\(580\) | 695.473 | 0.0497896 | ||||||||
\(581\) | 16219.5 | 1.15818 | ||||||||
\(582\) | −16406.7 | −1.16852 | ||||||||
\(583\) | −15281.7 | −1.08560 | ||||||||
\(584\) | 4720.44 | 0.334474 | ||||||||
\(585\) | 2799.53 | 0.197857 | ||||||||
\(586\) | −20942.0 | −1.47629 | ||||||||
\(587\) | 13526.1 | 0.951075 | 0.475537 | − | 0.879696i | \(-0.342254\pi\) | ||||
0.475537 | + | 0.879696i | \(0.342254\pi\) | |||||||
\(588\) | 1685.76 | 0.118230 | ||||||||
\(589\) | −21444.9 | −1.50021 | ||||||||
\(590\) | −6383.86 | −0.445457 | ||||||||
\(591\) | 8138.38 | 0.566444 | ||||||||
\(592\) | 3797.17 | 0.263619 | ||||||||
\(593\) | 15964.6 | 1.10554 | 0.552770 | − | 0.833334i | \(-0.313571\pi\) | ||||
0.552770 | + | 0.833334i | \(0.313571\pi\) | |||||||
\(594\) | 6840.69 | 0.472520 | ||||||||
\(595\) | −5048.31 | −0.347833 | ||||||||
\(596\) | 5758.46 | 0.395764 | ||||||||
\(597\) | −673.894 | −0.0461987 | ||||||||
\(598\) | −16142.9 | −1.10390 | ||||||||
\(599\) | 22.9584 | 0.00156603 | 0.000783017 | − | 1.00000i | \(-0.499751\pi\) | ||||
0.000783017 | 1.00000i | \(0.499751\pi\) | ||||||||
\(600\) | −859.503 | −0.0584818 | ||||||||
\(601\) | −7471.32 | −0.507090 | −0.253545 | − | 0.967324i | \(-0.581597\pi\) | ||||
−0.253545 | + | 0.967324i | \(0.581597\pi\) | |||||||
\(602\) | 21991.0 | 1.48885 | ||||||||
\(603\) | −5205.23 | −0.351531 | ||||||||
\(604\) | −7383.28 | −0.497386 | ||||||||
\(605\) | 18426.6 | 1.23826 | ||||||||
\(606\) | −15297.9 | −1.02547 | ||||||||
\(607\) | 23036.9 | 1.54042 | 0.770212 | − | 0.637788i | \(-0.220151\pi\) | ||||
0.770212 | + | 0.637788i | \(0.220151\pi\) | |||||||
\(608\) | 22872.8 | 1.52568 | ||||||||
\(609\) | −1307.45 | −0.0869958 | ||||||||
\(610\) | 8336.93 | 0.553365 | ||||||||
\(611\) | 7831.91 | 0.518569 | ||||||||
\(612\) | −2900.19 | −0.191557 | ||||||||
\(613\) | −20040.0 | −1.32040 | −0.660202 | − | 0.751088i | \(-0.729530\pi\) | ||||
−0.660202 | + | 0.751088i | \(0.729530\pi\) | |||||||
\(614\) | 9831.52 | 0.646202 | ||||||||
\(615\) | −5579.34 | −0.365822 | ||||||||
\(616\) | 12197.9 | 0.797834 | ||||||||
\(617\) | −27464.4 | −1.79202 | −0.896010 | − | 0.444035i | \(-0.853547\pi\) | ||||
−0.896010 | + | 0.444035i | \(0.853547\pi\) | |||||||
\(618\) | −17124.2 | −1.11462 | ||||||||
\(619\) | 3585.29 | 0.232803 | 0.116402 | − | 0.993202i | \(-0.462864\pi\) | ||||
0.116402 | + | 0.993202i | \(0.462864\pi\) | |||||||
\(620\) | −4322.17 | −0.279972 | ||||||||
\(621\) | −1958.53 | −0.126559 | ||||||||
\(622\) | 36805.9 | 2.37264 | ||||||||
\(623\) | 5845.83 | 0.375936 | ||||||||
\(624\) | 14812.4 | 0.950276 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −30552.6 | −1.95069 | ||||||||
\(627\) | −25282.4 | −1.61034 | ||||||||
\(628\) | 1070.23 | 0.0680048 | ||||||||
\(629\) | 3214.38 | 0.203761 | ||||||||
\(630\) | −2419.14 | −0.152985 | ||||||||
\(631\) | −27135.3 | −1.71195 | −0.855973 | − | 0.517020i | \(-0.827041\pi\) | ||||
−0.855973 | + | 0.517020i | \(0.827041\pi\) | |||||||
\(632\) | 12837.8 | 0.808009 | ||||||||
\(633\) | 12480.3 | 0.783645 | ||||||||
\(634\) | 469.160 | 0.0293892 | ||||||||
\(635\) | 1993.72 | 0.124596 | ||||||||
\(636\) | 3104.65 | 0.193565 | ||||||||
\(637\) | −7288.43 | −0.453341 | ||||||||
\(638\) | −7347.40 | −0.455935 | ||||||||
\(639\) | 7838.32 | 0.485257 | ||||||||
\(640\) | −6746.34 | −0.416676 | ||||||||
\(641\) | 23443.5 | 1.44456 | 0.722278 | − | 0.691603i | \(-0.243095\pi\) | ||||
0.722278 | + | 0.691603i | \(0.243095\pi\) | |||||||
\(642\) | −1664.51 | −0.102326 | ||||||||
\(643\) | −9339.29 | −0.572792 | −0.286396 | − | 0.958111i | \(-0.592457\pi\) | ||||
−0.286396 | + | 0.958111i | \(0.592457\pi\) | |||||||
\(644\) | 5228.59 | 0.319931 | ||||||||
\(645\) | 6136.03 | 0.374583 | ||||||||
\(646\) | 28596.9 | 1.74169 | ||||||||
\(647\) | 1103.56 | 0.0670562 | 0.0335281 | − | 0.999438i | \(-0.489326\pi\) | ||||
0.0335281 | + | 0.999438i | \(0.489326\pi\) | |||||||
\(648\) | 928.263 | 0.0562741 | ||||||||
\(649\) | 25279.2 | 1.52896 | ||||||||
\(650\) | −5563.60 | −0.335726 | ||||||||
\(651\) | 8125.41 | 0.489186 | ||||||||
\(652\) | −14939.3 | −0.897344 | ||||||||
\(653\) | −3127.51 | −0.187425 | −0.0937127 | − | 0.995599i | \(-0.529874\pi\) | ||||
−0.0937127 | + | 0.995599i | \(0.529874\pi\) | |||||||
\(654\) | 13009.2 | 0.777828 | ||||||||
\(655\) | −1926.21 | −0.114906 | ||||||||
\(656\) | −29520.6 | −1.75699 | ||||||||
\(657\) | 3707.14 | 0.220136 | ||||||||
\(658\) | −6767.75 | −0.400964 | ||||||||
\(659\) | 16004.5 | 0.946050 | 0.473025 | − | 0.881049i | \(-0.343162\pi\) | ||||
0.473025 | + | 0.881049i | \(0.343162\pi\) | |||||||
\(660\) | −5095.61 | −0.300525 | ||||||||
\(661\) | 10807.3 | 0.635939 | 0.317970 | − | 0.948101i | \(-0.396999\pi\) | ||||
0.317970 | + | 0.948101i | \(0.396999\pi\) | |||||||
\(662\) | 26023.4 | 1.52784 | ||||||||
\(663\) | 12539.1 | 0.734504 | ||||||||
\(664\) | 12368.6 | 0.722882 | ||||||||
\(665\) | 8940.87 | 0.521372 | ||||||||
\(666\) | 1540.32 | 0.0896191 | ||||||||
\(667\) | 2103.61 | 0.122117 | ||||||||
\(668\) | −8253.47 | −0.478049 | ||||||||
\(669\) | 5239.24 | 0.302781 | ||||||||
\(670\) | 10344.5 | 0.596483 | ||||||||
\(671\) | −33013.0 | −1.89933 | ||||||||
\(672\) | −8666.44 | −0.497493 | ||||||||
\(673\) | 23835.6 | 1.36522 | 0.682612 | − | 0.730781i | \(-0.260844\pi\) | ||||
0.682612 | + | 0.730781i | \(0.260844\pi\) | |||||||
\(674\) | −16682.5 | −0.953392 | ||||||||
\(675\) | −675.000 | −0.0384900 | ||||||||
\(676\) | 8025.75 | 0.456631 | ||||||||
\(677\) | 5081.10 | 0.288453 | 0.144227 | − | 0.989545i | \(-0.453931\pi\) | ||||
0.144227 | + | 0.989545i | \(0.453931\pi\) | |||||||
\(678\) | −12362.9 | −0.700286 | ||||||||
\(679\) | −22975.4 | −1.29855 | ||||||||
\(680\) | −3849.70 | −0.217102 | ||||||||
\(681\) | −388.523 | −0.0218623 | ||||||||
\(682\) | 45662.0 | 2.56377 | ||||||||
\(683\) | 7815.19 | 0.437833 | 0.218917 | − | 0.975744i | \(-0.429748\pi\) | ||||
0.218917 | + | 0.975744i | \(0.429748\pi\) | |||||||
\(684\) | 5136.41 | 0.287128 | ||||||||
\(685\) | −1759.38 | −0.0981352 | ||||||||
\(686\) | 24737.3 | 1.37679 | ||||||||
\(687\) | 2046.50 | 0.113652 | ||||||||
\(688\) | 32466.1 | 1.79907 | ||||||||
\(689\) | −13423.1 | −0.742204 | ||||||||
\(690\) | 3892.26 | 0.214748 | ||||||||
\(691\) | 8815.96 | 0.485347 | 0.242674 | − | 0.970108i | \(-0.421976\pi\) | ||||
0.242674 | + | 0.970108i | \(0.421976\pi\) | |||||||
\(692\) | 11696.9 | 0.642557 | ||||||||
\(693\) | 9579.44 | 0.525098 | ||||||||
\(694\) | −21644.9 | −1.18391 | ||||||||
\(695\) | 5692.41 | 0.310684 | ||||||||
\(696\) | −997.023 | −0.0542990 | ||||||||
\(697\) | −24989.8 | −1.35804 | ||||||||
\(698\) | −45873.9 | −2.48761 | ||||||||
\(699\) | −5193.32 | −0.281015 | ||||||||
\(700\) | 1802.01 | 0.0972994 | ||||||||
\(701\) | −4100.40 | −0.220927 | −0.110464 | − | 0.993880i | \(-0.535234\pi\) | ||||
−0.110464 | + | 0.993880i | \(0.535234\pi\) | |||||||
\(702\) | 6008.68 | 0.323053 | ||||||||
\(703\) | −5692.87 | −0.305420 | ||||||||
\(704\) | −3733.14 | −0.199855 | ||||||||
\(705\) | −1888.37 | −0.100880 | ||||||||
\(706\) | −44767.0 | −2.38644 | ||||||||
\(707\) | −21422.7 | −1.13958 | ||||||||
\(708\) | −5135.75 | −0.272618 | ||||||||
\(709\) | −17803.3 | −0.943042 | −0.471521 | − | 0.881855i | \(-0.656295\pi\) | ||||
−0.471521 | + | 0.881855i | \(0.656295\pi\) | |||||||
\(710\) | −15577.4 | −0.823391 | ||||||||
\(711\) | 10082.0 | 0.531795 | ||||||||
\(712\) | 4457.87 | 0.234643 | ||||||||
\(713\) | −13073.3 | −0.686677 | ||||||||
\(714\) | −10835.3 | −0.567928 | ||||||||
\(715\) | 22031.0 | 1.15233 | ||||||||
\(716\) | −10782.2 | −0.562780 | ||||||||
\(717\) | −9925.13 | −0.516961 | ||||||||
\(718\) | −12143.5 | −0.631187 | ||||||||
\(719\) | −4213.37 | −0.218543 | −0.109271 | − | 0.994012i | \(-0.534852\pi\) | ||||
−0.109271 | + | 0.994012i | \(0.534852\pi\) | |||||||
\(720\) | −3571.46 | −0.184862 | ||||||||
\(721\) | −23980.1 | −1.23865 | ||||||||
\(722\) | −26110.9 | −1.34591 | ||||||||
\(723\) | −10759.2 | −0.553441 | ||||||||
\(724\) | −11305.6 | −0.580347 | ||||||||
\(725\) | 725.000 | 0.0371391 | ||||||||
\(726\) | 39549.4 | 2.02178 | ||||||||
\(727\) | 29559.3 | 1.50797 | 0.753984 | − | 0.656893i | \(-0.228130\pi\) | ||||
0.753984 | + | 0.656893i | \(0.228130\pi\) | |||||||
\(728\) | 10714.3 | 0.545464 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −7367.32 | −0.373530 | ||||||||
\(731\) | 27483.2 | 1.39057 | ||||||||
\(732\) | 6706.97 | 0.338657 | ||||||||
\(733\) | 23312.9 | 1.17474 | 0.587369 | − | 0.809319i | \(-0.300164\pi\) | ||||
0.587369 | + | 0.809319i | \(0.300164\pi\) | |||||||
\(734\) | 35743.1 | 1.79742 | ||||||||
\(735\) | 1757.33 | 0.0881905 | ||||||||
\(736\) | 13943.8 | 0.698337 | ||||||||
\(737\) | −40962.8 | −2.04733 | ||||||||
\(738\) | −11975.0 | −0.597300 | ||||||||
\(739\) | 27985.2 | 1.39303 | 0.696517 | − | 0.717540i | \(-0.254732\pi\) | ||||
0.696517 | + | 0.717540i | \(0.254732\pi\) | |||||||
\(740\) | −1147.38 | −0.0569982 | ||||||||
\(741\) | −22207.4 | −1.10096 | ||||||||
\(742\) | 11599.2 | 0.573881 | ||||||||
\(743\) | −2542.48 | −0.125538 | −0.0627690 | − | 0.998028i | \(-0.519993\pi\) | ||||
−0.0627690 | + | 0.998028i | \(0.519993\pi\) | |||||||
\(744\) | 6196.22 | 0.305328 | ||||||||
\(745\) | 6002.94 | 0.295209 | ||||||||
\(746\) | −25825.3 | −1.26747 | ||||||||
\(747\) | 9713.50 | 0.475768 | ||||||||
\(748\) | −22823.2 | −1.11564 | ||||||||
\(749\) | −2330.92 | −0.113712 | ||||||||
\(750\) | 1341.45 | 0.0653105 | ||||||||
\(751\) | 33600.2 | 1.63261 | 0.816305 | − | 0.577622i | \(-0.196019\pi\) | ||||
0.816305 | + | 0.577622i | \(0.196019\pi\) | |||||||
\(752\) | −9991.46 | −0.484510 | ||||||||
\(753\) | 8868.65 | 0.429206 | ||||||||
\(754\) | −6453.77 | −0.311714 | ||||||||
\(755\) | −7696.74 | −0.371011 | ||||||||
\(756\) | −1946.17 | −0.0936264 | ||||||||
\(757\) | −34022.4 | −1.63351 | −0.816754 | − | 0.576986i | \(-0.804229\pi\) | ||||
−0.816754 | + | 0.576986i | \(0.804229\pi\) | |||||||
\(758\) | −38626.0 | −1.85087 | ||||||||
\(759\) | −15412.8 | −0.737086 | ||||||||
\(760\) | 6818.06 | 0.325417 | ||||||||
\(761\) | 15032.8 | 0.716084 | 0.358042 | − | 0.933705i | \(-0.383444\pi\) | ||||
0.358042 | + | 0.933705i | \(0.383444\pi\) | |||||||
\(762\) | 4279.16 | 0.203435 | ||||||||
\(763\) | 18217.6 | 0.864378 | ||||||||
\(764\) | 9221.28 | 0.436668 | ||||||||
\(765\) | −3023.32 | −0.142887 | ||||||||
\(766\) | 12150.8 | 0.573144 | ||||||||
\(767\) | 22204.6 | 1.04532 | ||||||||
\(768\) | −15744.8 | −0.739768 | ||||||||
\(769\) | −24042.9 | −1.12745 | −0.563725 | − | 0.825963i | \(-0.690632\pi\) | ||||
−0.563725 | + | 0.825963i | \(0.690632\pi\) | |||||||
\(770\) | −19037.5 | −0.890994 | ||||||||
\(771\) | −6774.36 | −0.316437 | ||||||||
\(772\) | 8828.59 | 0.411590 | ||||||||
\(773\) | 17441.1 | 0.811530 | 0.405765 | − | 0.913977i | \(-0.367005\pi\) | ||||
0.405765 | + | 0.913977i | \(0.367005\pi\) | |||||||
\(774\) | 13169.9 | 0.611605 | ||||||||
\(775\) | −4505.67 | −0.208837 | ||||||||
\(776\) | −17520.4 | −0.810496 | ||||||||
\(777\) | 2157.01 | 0.0995912 | ||||||||
\(778\) | 17625.1 | 0.812200 | ||||||||
\(779\) | 44258.5 | 2.03559 | ||||||||
\(780\) | −4475.85 | −0.205463 | ||||||||
\(781\) | 61684.0 | 2.82616 | ||||||||
\(782\) | 17433.4 | 0.797208 | ||||||||
\(783\) | −783.000 | −0.0357371 | ||||||||
\(784\) | 9298.12 | 0.423566 | ||||||||
\(785\) | 1115.67 | 0.0507262 | ||||||||
\(786\) | −4134.26 | −0.187613 | ||||||||
\(787\) | −38211.9 | −1.73076 | −0.865379 | − | 0.501119i | \(-0.832922\pi\) | ||||
−0.865379 | + | 0.501119i | \(0.832922\pi\) | |||||||
\(788\) | −13011.6 | −0.588220 | ||||||||
\(789\) | −8726.00 | −0.393731 | ||||||||
\(790\) | −20036.4 | −0.902357 | ||||||||
\(791\) | −17312.5 | −0.778208 | ||||||||
\(792\) | 7305.02 | 0.327743 | ||||||||
\(793\) | −28997.8 | −1.29854 | ||||||||
\(794\) | 27821.8 | 1.24353 | ||||||||
\(795\) | 3236.47 | 0.144384 | ||||||||
\(796\) | 1077.41 | 0.0479748 | ||||||||
\(797\) | 18149.9 | 0.806655 | 0.403327 | − | 0.915056i | \(-0.367854\pi\) | ||||
0.403327 | + | 0.915056i | \(0.367854\pi\) | |||||||
\(798\) | 19190.0 | 0.851276 | ||||||||
\(799\) | −8457.99 | −0.374496 | ||||||||
\(800\) | 4805.68 | 0.212383 | ||||||||
\(801\) | 3500.93 | 0.154431 | ||||||||
\(802\) | −21671.5 | −0.954172 | ||||||||
\(803\) | 29173.5 | 1.28208 | ||||||||
\(804\) | 8322.06 | 0.365045 | ||||||||
\(805\) | 5450.57 | 0.238643 | ||||||||
\(806\) | 40108.3 | 1.75280 | ||||||||
\(807\) | 893.730 | 0.0389849 | ||||||||
\(808\) | −16336.3 | −0.711275 | ||||||||
\(809\) | −339.522 | −0.0147552 | −0.00737759 | − | 0.999973i | \(-0.502348\pi\) | ||||
−0.00737759 | + | 0.999973i | \(0.502348\pi\) | |||||||
\(810\) | −1448.77 | −0.0628450 | ||||||||
\(811\) | 26295.4 | 1.13854 | 0.569270 | − | 0.822151i | \(-0.307226\pi\) | ||||
0.569270 | + | 0.822151i | \(0.307226\pi\) | |||||||
\(812\) | 2090.33 | 0.0903403 | ||||||||
\(813\) | −20979.1 | −0.905005 | ||||||||
\(814\) | 12121.7 | 0.521946 | ||||||||
\(815\) | −15573.6 | −0.669347 | ||||||||
\(816\) | −15996.5 | −0.686263 | ||||||||
\(817\) | −48674.5 | −2.08434 | ||||||||
\(818\) | 53937.8 | 2.30549 | ||||||||
\(819\) | 8414.33 | 0.359000 | ||||||||
\(820\) | 8920.18 | 0.379886 | ||||||||
\(821\) | −46289.6 | −1.96775 | −0.983873 | − | 0.178867i | \(-0.942757\pi\) | ||||
−0.983873 | + | 0.178867i | \(0.942757\pi\) | |||||||
\(822\) | −3776.20 | −0.160231 | ||||||||
\(823\) | −28099.3 | −1.19013 | −0.595067 | − | 0.803676i | \(-0.702874\pi\) | ||||
−0.595067 | + | 0.803676i | \(0.702874\pi\) | |||||||
\(824\) | −18286.6 | −0.773111 | ||||||||
\(825\) | −5311.95 | −0.224168 | ||||||||
\(826\) | −19187.5 | −0.808255 | ||||||||
\(827\) | −38732.3 | −1.62860 | −0.814301 | − | 0.580443i | \(-0.802879\pi\) | ||||
−0.814301 | + | 0.580443i | \(0.802879\pi\) | |||||||
\(828\) | 3131.28 | 0.131425 | ||||||||
\(829\) | −9334.33 | −0.391067 | −0.195534 | − | 0.980697i | \(-0.562644\pi\) | ||||
−0.195534 | + | 0.980697i | \(0.562644\pi\) | |||||||
\(830\) | −19304.0 | −0.807290 | ||||||||
\(831\) | −17105.5 | −0.714060 | ||||||||
\(832\) | −3279.09 | −0.136637 | ||||||||
\(833\) | 7871.06 | 0.327390 | ||||||||
\(834\) | 12217.7 | 0.507273 | ||||||||
\(835\) | −8603.88 | −0.356586 | ||||||||
\(836\) | 40421.3 | 1.67225 | ||||||||
\(837\) | 4866.12 | 0.200953 | ||||||||
\(838\) | −20383.7 | −0.840266 | ||||||||
\(839\) | −40742.1 | −1.67649 | −0.838245 | − | 0.545294i | \(-0.816418\pi\) | ||||
−0.838245 | + | 0.545294i | \(0.816418\pi\) | |||||||
\(840\) | −2583.34 | −0.106112 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | −3029.31 | −0.123987 | ||||||||
\(843\) | 3649.02 | 0.149085 | ||||||||
\(844\) | −19953.4 | −0.813771 | ||||||||
\(845\) | 8366.49 | 0.340611 | ||||||||
\(846\) | −4053.05 | −0.164712 | ||||||||
\(847\) | 55383.5 | 2.24675 | ||||||||
\(848\) | 17124.3 | 0.693457 | ||||||||
\(849\) | −12288.5 | −0.496750 | ||||||||
\(850\) | 6008.34 | 0.242452 | ||||||||
\(851\) | −3470.51 | −0.139797 | ||||||||
\(852\) | −12531.8 | −0.503912 | ||||||||
\(853\) | −29088.9 | −1.16762 | −0.583812 | − | 0.811889i | \(-0.698440\pi\) | ||||
−0.583812 | + | 0.811889i | \(0.698440\pi\) | |||||||
\(854\) | 25057.7 | 1.00405 | ||||||||
\(855\) | 5354.48 | 0.214175 | ||||||||
\(856\) | −1777.49 | −0.0709737 | ||||||||
\(857\) | 31564.0 | 1.25812 | 0.629059 | − | 0.777357i | \(-0.283440\pi\) | ||||
0.629059 | + | 0.777357i | \(0.283440\pi\) | |||||||
\(858\) | 47285.6 | 1.88147 | ||||||||
\(859\) | 21654.5 | 0.860120 | 0.430060 | − | 0.902800i | \(-0.358492\pi\) | ||||
0.430060 | + | 0.902800i | \(0.358492\pi\) | |||||||
\(860\) | −9810.22 | −0.388983 | ||||||||
\(861\) | −16769.4 | −0.663763 | ||||||||
\(862\) | 26894.4 | 1.06267 | ||||||||
\(863\) | 2304.51 | 0.0908996 | 0.0454498 | − | 0.998967i | \(-0.485528\pi\) | ||||
0.0454498 | + | 0.998967i | \(0.485528\pi\) | |||||||
\(864\) | −5190.13 | −0.204366 | ||||||||
\(865\) | 12193.5 | 0.479297 | ||||||||
\(866\) | −45380.5 | −1.78071 | ||||||||
\(867\) | 1197.59 | 0.0469116 | ||||||||
\(868\) | −12990.8 | −0.507992 | ||||||||
\(869\) | 79341.1 | 3.09720 | ||||||||
\(870\) | 1556.08 | 0.0606392 | ||||||||
\(871\) | −35980.7 | −1.39972 | ||||||||
\(872\) | 13892.2 | 0.539507 | ||||||||
\(873\) | −13759.4 | −0.533432 | ||||||||
\(874\) | −30875.6 | −1.19495 | ||||||||
\(875\) | 1878.52 | 0.0725777 | ||||||||
\(876\) | −5926.93 | −0.228599 | ||||||||
\(877\) | 42141.0 | 1.62258 | 0.811289 | − | 0.584645i | \(-0.198766\pi\) | ||||
0.811289 | + | 0.584645i | \(0.198766\pi\) | |||||||
\(878\) | −37669.4 | −1.44793 | ||||||||
\(879\) | −17562.9 | −0.673926 | ||||||||
\(880\) | −28105.8 | −1.07664 | ||||||||
\(881\) | 3482.39 | 0.133172 | 0.0665861 | − | 0.997781i | \(-0.478789\pi\) | ||||
0.0665861 | + | 0.997781i | \(0.478789\pi\) | |||||||
\(882\) | 3771.79 | 0.143994 | ||||||||
\(883\) | 28559.6 | 1.08846 | 0.544229 | − | 0.838937i | \(-0.316822\pi\) | ||||
0.544229 | + | 0.838937i | \(0.316822\pi\) | |||||||
\(884\) | −20047.3 | −0.762742 | ||||||||
\(885\) | −5353.79 | −0.203351 | ||||||||
\(886\) | 18598.5 | 0.705224 | ||||||||
\(887\) | −42485.5 | −1.60826 | −0.804128 | − | 0.594456i | \(-0.797367\pi\) | ||||
−0.804128 | + | 0.594456i | \(0.797367\pi\) | |||||||
\(888\) | 1644.88 | 0.0621604 | ||||||||
\(889\) | 5992.37 | 0.226072 | ||||||||
\(890\) | −6957.52 | −0.262041 | ||||||||
\(891\) | 5736.90 | 0.215705 | ||||||||
\(892\) | −8376.43 | −0.314421 | ||||||||
\(893\) | 14979.6 | 0.561337 | ||||||||
\(894\) | 12884.2 | 0.482005 | ||||||||
\(895\) | −11240.0 | −0.419789 | ||||||||
\(896\) | −20277.0 | −0.756034 | ||||||||
\(897\) | −13538.2 | −0.503932 | ||||||||
\(898\) | 42342.3 | 1.57347 | ||||||||
\(899\) | −5226.58 | −0.193900 | ||||||||
\(900\) | 1079.18 | 0.0399697 | ||||||||
\(901\) | 14496.1 | 0.535999 | ||||||||
\(902\) | −94238.2 | −3.47870 | ||||||||
\(903\) | 18442.6 | 0.679659 | ||||||||
\(904\) | −13202.1 | −0.485724 | ||||||||
\(905\) | −11785.6 | −0.432893 | ||||||||
\(906\) | −16519.7 | −0.605772 | ||||||||
\(907\) | −22359.4 | −0.818559 | −0.409280 | − | 0.912409i | \(-0.634220\pi\) | ||||
−0.409280 | + | 0.912409i | \(0.634220\pi\) | |||||||
\(908\) | 621.166 | 0.0227028 | ||||||||
\(909\) | −12829.5 | −0.468128 | ||||||||
\(910\) | −16722.1 | −0.609156 | ||||||||
\(911\) | −14833.6 | −0.539471 | −0.269735 | − | 0.962934i | \(-0.586936\pi\) | ||||
−0.269735 | + | 0.962934i | \(0.586936\pi\) | |||||||
\(912\) | 28330.9 | 1.02865 | ||||||||
\(913\) | 76440.9 | 2.77089 | ||||||||
\(914\) | −1446.80 | −0.0523588 | ||||||||
\(915\) | 6991.72 | 0.252611 | ||||||||
\(916\) | −3271.92 | −0.118021 | ||||||||
\(917\) | −5789.46 | −0.208489 | ||||||||
\(918\) | −6489.01 | −0.233300 | ||||||||
\(919\) | −41161.8 | −1.47748 | −0.738740 | − | 0.673991i | \(-0.764579\pi\) | ||||
−0.738740 | + | 0.673991i | \(0.764579\pi\) | |||||||
\(920\) | 4156.46 | 0.148950 | ||||||||
\(921\) | 8245.15 | 0.294991 | ||||||||
\(922\) | −25300.1 | −0.903702 | ||||||||
\(923\) | 54181.7 | 1.93219 | ||||||||
\(924\) | −15315.5 | −0.545285 | ||||||||
\(925\) | −1196.10 | −0.0425161 | ||||||||
\(926\) | 23252.6 | 0.825192 | ||||||||
\(927\) | −14361.2 | −0.508826 | ||||||||
\(928\) | 5574.59 | 0.197193 | ||||||||
\(929\) | 29321.8 | 1.03554 | 0.517771 | − | 0.855519i | \(-0.326762\pi\) | ||||
0.517771 | + | 0.855519i | \(0.326762\pi\) | |||||||
\(930\) | −9670.61 | −0.340980 | ||||||||
\(931\) | −13940.1 | −0.490729 | ||||||||
\(932\) | 8303.02 | 0.291818 | ||||||||
\(933\) | 30867.0 | 1.08311 | ||||||||
\(934\) | 31660.4 | 1.10917 | ||||||||
\(935\) | −23792.2 | −0.832178 | ||||||||
\(936\) | 6416.54 | 0.224072 | ||||||||
\(937\) | −42922.5 | −1.49650 | −0.748249 | − | 0.663418i | \(-0.769105\pi\) | ||||
−0.748249 | + | 0.663418i | \(0.769105\pi\) | |||||||
\(938\) | 31091.8 | 1.08228 | ||||||||
\(939\) | −25622.8 | −0.890488 | ||||||||
\(940\) | 3019.10 | 0.104758 | ||||||||
\(941\) | −13239.3 | −0.458650 | −0.229325 | − | 0.973350i | \(-0.573652\pi\) | ||||
−0.229325 | + | 0.973350i | \(0.573652\pi\) | |||||||
\(942\) | 2394.59 | 0.0828237 | ||||||||
\(943\) | 26981.0 | 0.931732 | ||||||||
\(944\) | −28327.2 | −0.976665 | ||||||||
\(945\) | −2028.80 | −0.0698379 | ||||||||
\(946\) | 103641. | 3.56201 | ||||||||
\(947\) | −19266.8 | −0.661126 | −0.330563 | − | 0.943784i | \(-0.607239\pi\) | ||||
−0.330563 | + | 0.943784i | \(0.607239\pi\) | |||||||
\(948\) | −16119.1 | −0.552239 | ||||||||
\(949\) | 25625.3 | 0.876534 | ||||||||
\(950\) | −10641.1 | −0.363415 | ||||||||
\(951\) | 393.459 | 0.0134162 | ||||||||
\(952\) | −11570.8 | −0.393919 | ||||||||
\(953\) | −14816.2 | −0.503615 | −0.251807 | − | 0.967777i | \(-0.581025\pi\) | ||||
−0.251807 | + | 0.967777i | \(0.581025\pi\) | |||||||
\(954\) | 6946.49 | 0.235745 | ||||||||
\(955\) | 9612.78 | 0.325720 | ||||||||
\(956\) | 15868.2 | 0.536835 | ||||||||
\(957\) | −6161.86 | −0.208134 | ||||||||
\(958\) | 30702.8 | 1.03545 | ||||||||
\(959\) | −5288.05 | −0.178061 | ||||||||
\(960\) | 790.629 | 0.0265807 | ||||||||
\(961\) | 2690.68 | 0.0903185 | ||||||||
\(962\) | 10647.4 | 0.356845 | ||||||||
\(963\) | −1395.93 | −0.0467117 | ||||||||
\(964\) | 17201.6 | 0.574717 | ||||||||
\(965\) | 9203.41 | 0.307014 | ||||||||
\(966\) | 11698.7 | 0.389647 | ||||||||
\(967\) | 1342.65 | 0.0446502 | 0.0223251 | − | 0.999751i | \(-0.492893\pi\) | ||||
0.0223251 | + | 0.999751i | \(0.492893\pi\) | |||||||
\(968\) | 42233.9 | 1.40232 | ||||||||
\(969\) | 23982.7 | 0.795082 | ||||||||
\(970\) | 27344.6 | 0.905135 | ||||||||
\(971\) | −11211.1 | −0.370526 | −0.185263 | − | 0.982689i | \(-0.559314\pi\) | ||||
−0.185263 | + | 0.982689i | \(0.559314\pi\) | |||||||
\(972\) | −1165.52 | −0.0384609 | ||||||||
\(973\) | 17109.3 | 0.563718 | ||||||||
\(974\) | 10100.7 | 0.332285 | ||||||||
\(975\) | −4665.88 | −0.153259 | ||||||||
\(976\) | 36993.6 | 1.21325 | ||||||||
\(977\) | 30870.2 | 1.01088 | 0.505438 | − | 0.862863i | \(-0.331331\pi\) | ||||
0.505438 | + | 0.862863i | \(0.331331\pi\) | |||||||
\(978\) | −33425.9 | −1.09288 | ||||||||
\(979\) | 27550.8 | 0.899414 | ||||||||
\(980\) | −2809.60 | −0.0915809 | ||||||||
\(981\) | 10910.1 | 0.355079 | ||||||||
\(982\) | 46919.3 | 1.52470 | ||||||||
\(983\) | 28549.4 | 0.926332 | 0.463166 | − | 0.886272i | \(-0.346713\pi\) | ||||
0.463166 | + | 0.886272i | \(0.346713\pi\) | |||||||
\(984\) | −12787.9 | −0.414292 | ||||||||
\(985\) | −13564.0 | −0.438765 | ||||||||
\(986\) | 6969.68 | 0.225111 | ||||||||
\(987\) | −5675.73 | −0.183040 | ||||||||
\(988\) | 35505.0 | 1.14328 | ||||||||
\(989\) | −29673.1 | −0.954046 | ||||||||
\(990\) | −11401.1 | −0.366012 | ||||||||
\(991\) | −20806.0 | −0.666927 | −0.333464 | − | 0.942763i | \(-0.608217\pi\) | ||||
−0.333464 | + | 0.942763i | \(0.608217\pi\) | |||||||
\(992\) | −34644.5 | −1.10883 | ||||||||
\(993\) | 21824.4 | 0.697458 | ||||||||
\(994\) | −46819.7 | −1.49399 | ||||||||
\(995\) | 1123.16 | 0.0357854 | ||||||||
\(996\) | −15529.8 | −0.494058 | ||||||||
\(997\) | 57999.9 | 1.84240 | 0.921201 | − | 0.389088i | \(-0.127210\pi\) | ||||
0.921201 | + | 0.389088i | \(0.127210\pi\) | |||||||
\(998\) | 59007.4 | 1.87159 | ||||||||
\(999\) | 1291.78 | 0.0409112 |
(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 | 435.4.a.i.1.2 | ✓ | 7 | |
3.2 | odd | 2 | 1305.4.a.n.1.6 | 7 | |||
5.4 | even | 2 | 2175.4.a.n.1.6 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
435.4.a.i.1.2 | ✓ | 7 | 1.1 | even | 1 | trivial | |
1305.4.a.n.1.6 | 7 | 3.2 | odd | 2 | |||
2175.4.a.n.1.6 | 7 | 5.4 | even | 2 |