Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1859,4,Mod(1,1859)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1859, 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("1859.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1859 = 11 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1859.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(109.684550701\) |
Analytic rank: | \(0\) |
Dimension: | \(51\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 1859.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.99679 | −1.76663 | −0.883316 | − | 0.468779i | \(-0.844694\pi\) | ||||
−0.883316 | + | 0.468779i | \(0.844694\pi\) | |||||||
\(3\) | 8.59946 | 1.65497 | 0.827483 | − | 0.561491i | \(-0.189772\pi\) | ||||
0.827483 | + | 0.561491i | \(0.189772\pi\) | |||||||
\(4\) | 16.9679 | 2.12099 | ||||||||
\(5\) | −10.1780 | −0.910347 | −0.455173 | − | 0.890403i | \(-0.650423\pi\) | ||||
−0.455173 | + | 0.890403i | \(0.650423\pi\) | |||||||
\(6\) | −42.9697 | −2.92371 | ||||||||
\(7\) | −9.94954 | −0.537225 | −0.268612 | − | 0.963248i | \(-0.586565\pi\) | ||||
−0.268612 | + | 0.963248i | \(0.586565\pi\) | |||||||
\(8\) | −44.8107 | −1.98037 | ||||||||
\(9\) | 46.9506 | 1.73891 | ||||||||
\(10\) | 50.8572 | 1.60825 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | 145.915 | 3.51016 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 49.7157 | 0.949078 | ||||||||
\(15\) | −87.5251 | −1.50659 | ||||||||
\(16\) | 88.1662 | 1.37760 | ||||||||
\(17\) | −85.1519 | −1.21485 | −0.607423 | − | 0.794379i | \(-0.707797\pi\) | ||||
−0.607423 | + | 0.794379i | \(0.707797\pi\) | |||||||
\(18\) | −234.602 | −3.07202 | ||||||||
\(19\) | 118.078 | 1.42574 | 0.712870 | − | 0.701296i | \(-0.247395\pi\) | ||||
0.712870 | + | 0.701296i | \(0.247395\pi\) | |||||||
\(20\) | −172.699 | −1.93083 | ||||||||
\(21\) | −85.5606 | −0.889088 | ||||||||
\(22\) | 54.9647 | 0.532659 | ||||||||
\(23\) | −61.9873 | −0.561967 | −0.280983 | − | 0.959713i | \(-0.590661\pi\) | ||||
−0.280983 | + | 0.959713i | \(0.590661\pi\) | |||||||
\(24\) | −385.347 | −3.27744 | ||||||||
\(25\) | −21.4086 | −0.171269 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 171.565 | 1.22287 | ||||||||
\(28\) | −168.823 | −1.13945 | ||||||||
\(29\) | 202.832 | 1.29879 | 0.649396 | − | 0.760450i | \(-0.275022\pi\) | ||||
0.649396 | + | 0.760450i | \(0.275022\pi\) | |||||||
\(30\) | 437.345 | 2.66159 | ||||||||
\(31\) | −290.047 | −1.68045 | −0.840224 | − | 0.542239i | \(-0.817577\pi\) | ||||
−0.840224 | + | 0.542239i | \(0.817577\pi\) | |||||||
\(32\) | −82.0626 | −0.453336 | ||||||||
\(33\) | −94.5940 | −0.498991 | ||||||||
\(34\) | 425.486 | 2.14618 | ||||||||
\(35\) | 101.266 | 0.489061 | ||||||||
\(36\) | 796.653 | 3.68821 | ||||||||
\(37\) | 390.052 | 1.73308 | 0.866542 | − | 0.499104i | \(-0.166337\pi\) | ||||
0.866542 | + | 0.499104i | \(0.166337\pi\) | |||||||
\(38\) | −590.013 | −2.51876 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 456.082 | 1.80282 | ||||||||
\(41\) | −148.007 | −0.563775 | −0.281887 | − | 0.959448i | \(-0.590960\pi\) | ||||
−0.281887 | + | 0.959448i | \(0.590960\pi\) | |||||||
\(42\) | 427.528 | 1.57069 | ||||||||
\(43\) | 326.948 | 1.15951 | 0.579757 | − | 0.814789i | \(-0.303147\pi\) | ||||
0.579757 | + | 0.814789i | \(0.303147\pi\) | |||||||
\(44\) | −186.647 | −0.639501 | ||||||||
\(45\) | −477.863 | −1.58301 | ||||||||
\(46\) | 309.737 | 0.992788 | ||||||||
\(47\) | 96.8534 | 0.300586 | 0.150293 | − | 0.988642i | \(-0.451978\pi\) | ||||
0.150293 | + | 0.988642i | \(0.451978\pi\) | |||||||
\(48\) | 758.181 | 2.27988 | ||||||||
\(49\) | −244.007 | −0.711390 | ||||||||
\(50\) | 106.974 | 0.302569 | ||||||||
\(51\) | −732.260 | −2.01053 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −26.3159 | −0.0682031 | −0.0341015 | − | 0.999418i | \(-0.510857\pi\) | ||||
−0.0341015 | + | 0.999418i | \(0.510857\pi\) | |||||||
\(54\) | −857.272 | −2.16037 | ||||||||
\(55\) | 111.958 | 0.274480 | ||||||||
\(56\) | 445.845 | 1.06390 | ||||||||
\(57\) | 1015.41 | 2.35955 | ||||||||
\(58\) | −1013.51 | −2.29449 | ||||||||
\(59\) | −798.970 | −1.76300 | −0.881501 | − | 0.472183i | \(-0.843466\pi\) | ||||
−0.881501 | + | 0.472183i | \(0.843466\pi\) | |||||||
\(60\) | −1485.12 | −3.19546 | ||||||||
\(61\) | 259.628 | 0.544949 | 0.272475 | − | 0.962163i | \(-0.412158\pi\) | ||||
0.272475 | + | 0.962163i | \(0.412158\pi\) | |||||||
\(62\) | 1449.30 | 2.96873 | ||||||||
\(63\) | −467.137 | −0.934187 | ||||||||
\(64\) | −295.280 | −0.576719 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 472.666 | 0.881533 | ||||||||
\(67\) | −560.359 | −1.02177 | −0.510887 | − | 0.859648i | \(-0.670683\pi\) | ||||
−0.510887 | + | 0.859648i | \(0.670683\pi\) | |||||||
\(68\) | −1444.85 | −2.57667 | ||||||||
\(69\) | −533.057 | −0.930036 | ||||||||
\(70\) | −506.006 | −0.863990 | ||||||||
\(71\) | −343.779 | −0.574635 | −0.287317 | − | 0.957835i | \(-0.592763\pi\) | ||||
−0.287317 | + | 0.957835i | \(0.592763\pi\) | |||||||
\(72\) | −2103.89 | −3.44369 | ||||||||
\(73\) | 898.545 | 1.44064 | 0.720320 | − | 0.693642i | \(-0.243995\pi\) | ||||
0.720320 | + | 0.693642i | \(0.243995\pi\) | |||||||
\(74\) | −1949.01 | −3.06172 | ||||||||
\(75\) | −184.102 | −0.283444 | ||||||||
\(76\) | 2003.54 | 3.02398 | ||||||||
\(77\) | 109.445 | 0.161979 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −618.949 | −0.881483 | −0.440742 | − | 0.897634i | \(-0.645284\pi\) | ||||
−0.440742 | + | 0.897634i | \(0.645284\pi\) | |||||||
\(80\) | −897.354 | −1.25409 | ||||||||
\(81\) | 207.695 | 0.284904 | ||||||||
\(82\) | 739.558 | 0.995982 | ||||||||
\(83\) | 312.605 | 0.413408 | 0.206704 | − | 0.978404i | \(-0.433726\pi\) | ||||
0.206704 | + | 0.978404i | \(0.433726\pi\) | |||||||
\(84\) | −1451.78 | −1.88574 | ||||||||
\(85\) | 866.675 | 1.10593 | ||||||||
\(86\) | −1633.69 | −2.04843 | ||||||||
\(87\) | 1744.25 | 2.14946 | ||||||||
\(88\) | 492.917 | 0.597104 | ||||||||
\(89\) | 1484.66 | 1.76824 | 0.884121 | − | 0.467258i | \(-0.154758\pi\) | ||||
0.884121 | + | 0.467258i | \(0.154758\pi\) | |||||||
\(90\) | 2387.78 | 2.79660 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1051.79 | −1.19192 | ||||||||
\(93\) | −2494.24 | −2.78109 | ||||||||
\(94\) | −483.956 | −0.531024 | ||||||||
\(95\) | −1201.80 | −1.29792 | ||||||||
\(96\) | −705.694 | −0.750256 | ||||||||
\(97\) | 1163.87 | 1.21828 | 0.609140 | − | 0.793063i | \(-0.291515\pi\) | ||||
0.609140 | + | 0.793063i | \(0.291515\pi\) | |||||||
\(98\) | 1219.25 | 1.25676 | ||||||||
\(99\) | −516.457 | −0.524302 | ||||||||
\(100\) | −363.259 | −0.363259 | ||||||||
\(101\) | −1208.60 | −1.19069 | −0.595347 | − | 0.803468i | \(-0.702986\pi\) | ||||
−0.595347 | + | 0.803468i | \(0.702986\pi\) | |||||||
\(102\) | 3658.95 | 3.55186 | ||||||||
\(103\) | −307.769 | −0.294421 | −0.147211 | − | 0.989105i | \(-0.547029\pi\) | ||||
−0.147211 | + | 0.989105i | \(0.547029\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 870.835 | 0.809379 | ||||||||
\(106\) | 131.495 | 0.120490 | ||||||||
\(107\) | −34.9235 | −0.0315531 | −0.0157765 | − | 0.999876i | \(-0.505022\pi\) | ||||
−0.0157765 | + | 0.999876i | \(0.505022\pi\) | |||||||
\(108\) | 2911.09 | 2.59370 | ||||||||
\(109\) | 1831.40 | 1.60932 | 0.804662 | − | 0.593734i | \(-0.202347\pi\) | ||||
0.804662 | + | 0.593734i | \(0.202347\pi\) | |||||||
\(110\) | −559.430 | −0.484905 | ||||||||
\(111\) | 3354.23 | 2.86820 | ||||||||
\(112\) | −877.213 | −0.740079 | ||||||||
\(113\) | 625.296 | 0.520557 | 0.260278 | − | 0.965534i | \(-0.416186\pi\) | ||||
0.260278 | + | 0.965534i | \(0.416186\pi\) | |||||||
\(114\) | −5073.79 | −4.16846 | ||||||||
\(115\) | 630.905 | 0.511585 | ||||||||
\(116\) | 3441.63 | 2.75472 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3992.29 | 3.11457 | ||||||||
\(119\) | 847.222 | 0.652645 | ||||||||
\(120\) | 3922.06 | 2.98361 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | −1297.30 | −0.962724 | ||||||||
\(123\) | −1272.78 | −0.933028 | ||||||||
\(124\) | −4921.48 | −3.56421 | ||||||||
\(125\) | 1490.14 | 1.06626 | ||||||||
\(126\) | 2334.19 | 1.65036 | ||||||||
\(127\) | 1447.57 | 1.01143 | 0.505714 | − | 0.862701i | \(-0.331229\pi\) | ||||
0.505714 | + | 0.862701i | \(0.331229\pi\) | |||||||
\(128\) | 2131.95 | 1.47219 | ||||||||
\(129\) | 2811.57 | 1.91896 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1971.98 | 1.31521 | 0.657604 | − | 0.753364i | \(-0.271570\pi\) | ||||
0.657604 | + | 0.753364i | \(0.271570\pi\) | |||||||
\(132\) | −1605.06 | −1.05835 | ||||||||
\(133\) | −1174.83 | −0.765943 | ||||||||
\(134\) | 2800.00 | 1.80510 | ||||||||
\(135\) | −1746.18 | −1.11324 | ||||||||
\(136\) | 3815.71 | 2.40584 | ||||||||
\(137\) | −2007.87 | −1.25215 | −0.626073 | − | 0.779765i | \(-0.715339\pi\) | ||||
−0.626073 | + | 0.779765i | \(0.715339\pi\) | |||||||
\(138\) | 2663.57 | 1.64303 | ||||||||
\(139\) | −271.756 | −0.165828 | −0.0829138 | − | 0.996557i | \(-0.526423\pi\) | ||||
−0.0829138 | + | 0.996557i | \(0.526423\pi\) | |||||||
\(140\) | 1718.27 | 1.03729 | ||||||||
\(141\) | 832.886 | 0.497459 | ||||||||
\(142\) | 1717.79 | 1.01517 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 4139.46 | 2.39552 | ||||||||
\(145\) | −2064.42 | −1.18235 | ||||||||
\(146\) | −4489.84 | −2.54508 | ||||||||
\(147\) | −2098.32 | −1.17733 | ||||||||
\(148\) | 6618.36 | 3.67585 | ||||||||
\(149\) | −335.937 | −0.184705 | −0.0923524 | − | 0.995726i | \(-0.529439\pi\) | ||||
−0.0923524 | + | 0.995726i | \(0.529439\pi\) | |||||||
\(150\) | 919.921 | 0.500741 | ||||||||
\(151\) | 2819.45 | 1.51950 | 0.759748 | − | 0.650217i | \(-0.225322\pi\) | ||||
0.759748 | + | 0.650217i | \(0.225322\pi\) | |||||||
\(152\) | −5291.17 | −2.82349 | ||||||||
\(153\) | −3997.94 | −2.11251 | ||||||||
\(154\) | −546.873 | −0.286158 | ||||||||
\(155\) | 2952.09 | 1.52979 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2087.34 | 1.06107 | 0.530534 | − | 0.847664i | \(-0.321992\pi\) | ||||
0.530534 | + | 0.847664i | \(0.321992\pi\) | |||||||
\(158\) | 3092.75 | 1.55726 | ||||||||
\(159\) | −226.302 | −0.112874 | ||||||||
\(160\) | 835.232 | 0.412693 | ||||||||
\(161\) | 616.745 | 0.301902 | ||||||||
\(162\) | −1037.81 | −0.503320 | ||||||||
\(163\) | −1070.88 | −0.514588 | −0.257294 | − | 0.966333i | \(-0.582831\pi\) | ||||
−0.257294 | + | 0.966333i | \(0.582831\pi\) | |||||||
\(164\) | −2511.36 | −1.19576 | ||||||||
\(165\) | 962.776 | 0.454255 | ||||||||
\(166\) | −1562.02 | −0.730340 | ||||||||
\(167\) | −3711.75 | −1.71991 | −0.859953 | − | 0.510374i | \(-0.829507\pi\) | ||||
−0.859953 | + | 0.510374i | \(0.829507\pi\) | |||||||
\(168\) | 3834.03 | 1.76072 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −4330.59 | −1.95377 | ||||||||
\(171\) | 5543.86 | 2.47924 | ||||||||
\(172\) | 5547.62 | 2.45931 | ||||||||
\(173\) | −40.5410 | −0.0178166 | −0.00890831 | − | 0.999960i | \(-0.502836\pi\) | ||||
−0.00890831 | + | 0.999960i | \(0.502836\pi\) | |||||||
\(174\) | −8715.63 | −3.79730 | ||||||||
\(175\) | 213.006 | 0.0920099 | ||||||||
\(176\) | −969.828 | −0.415361 | ||||||||
\(177\) | −6870.71 | −2.91771 | ||||||||
\(178\) | −7418.53 | −3.12383 | ||||||||
\(179\) | 288.006 | 0.120260 | 0.0601301 | − | 0.998191i | \(-0.480848\pi\) | ||||
0.0601301 | + | 0.998191i | \(0.480848\pi\) | |||||||
\(180\) | −8108.33 | −3.35755 | ||||||||
\(181\) | 3327.39 | 1.36643 | 0.683213 | − | 0.730219i | \(-0.260582\pi\) | ||||
0.683213 | + | 0.730219i | \(0.260582\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2232.66 | 0.901872 | ||||||||
\(184\) | 2777.69 | 1.11290 | ||||||||
\(185\) | −3969.94 | −1.57771 | ||||||||
\(186\) | 12463.2 | 4.91315 | ||||||||
\(187\) | 936.671 | 0.366290 | ||||||||
\(188\) | 1643.40 | 0.637538 | ||||||||
\(189\) | −1706.99 | −0.656959 | ||||||||
\(190\) | 6005.14 | 2.29294 | ||||||||
\(191\) | 2851.33 | 1.08018 | 0.540091 | − | 0.841607i | \(-0.318390\pi\) | ||||
0.540091 | + | 0.841607i | \(0.318390\pi\) | |||||||
\(192\) | −2539.25 | −0.954450 | ||||||||
\(193\) | −890.551 | −0.332141 | −0.166071 | − | 0.986114i | \(-0.553108\pi\) | ||||
−0.166071 | + | 0.986114i | \(0.553108\pi\) | |||||||
\(194\) | −5815.61 | −2.15225 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4140.28 | −1.50885 | ||||||||
\(197\) | 3291.09 | 1.19026 | 0.595129 | − | 0.803630i | \(-0.297101\pi\) | ||||
0.595129 | + | 0.803630i | \(0.297101\pi\) | |||||||
\(198\) | 2580.63 | 0.926248 | ||||||||
\(199\) | −1146.44 | −0.408387 | −0.204193 | − | 0.978931i | \(-0.565457\pi\) | ||||
−0.204193 | + | 0.978931i | \(0.565457\pi\) | |||||||
\(200\) | 959.334 | 0.339176 | ||||||||
\(201\) | −4818.79 | −1.69100 | ||||||||
\(202\) | 6039.12 | 2.10352 | ||||||||
\(203\) | −2018.09 | −0.697743 | ||||||||
\(204\) | −12424.9 | −4.26430 | ||||||||
\(205\) | 1506.41 | 0.513230 | ||||||||
\(206\) | 1537.86 | 0.520134 | ||||||||
\(207\) | −2910.34 | −0.977211 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1298.86 | −0.429877 | ||||||||
\(210\) | −4351.38 | −1.42987 | ||||||||
\(211\) | 3675.73 | 1.19928 | 0.599639 | − | 0.800270i | \(-0.295311\pi\) | ||||
0.599639 | + | 0.800270i | \(0.295311\pi\) | |||||||
\(212\) | −446.525 | −0.144658 | ||||||||
\(213\) | −2956.31 | −0.951001 | ||||||||
\(214\) | 174.505 | 0.0557427 | ||||||||
\(215\) | −3327.67 | −1.05556 | ||||||||
\(216\) | −7687.92 | −2.42174 | ||||||||
\(217\) | 2885.83 | 0.902779 | ||||||||
\(218\) | −9151.11 | −2.84308 | ||||||||
\(219\) | 7727.00 | 2.38421 | ||||||||
\(220\) | 1899.69 | 0.582168 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −16760.4 | −5.06704 | ||||||||
\(223\) | −3171.24 | −0.952294 | −0.476147 | − | 0.879366i | \(-0.657967\pi\) | ||||
−0.476147 | + | 0.879366i | \(0.657967\pi\) | |||||||
\(224\) | 816.485 | 0.243543 | ||||||||
\(225\) | −1005.15 | −0.297822 | ||||||||
\(226\) | −3124.47 | −0.919632 | ||||||||
\(227\) | −3526.96 | −1.03125 | −0.515623 | − | 0.856816i | \(-0.672439\pi\) | ||||
−0.515623 | + | 0.856816i | \(0.672439\pi\) | |||||||
\(228\) | 17229.4 | 5.00458 | ||||||||
\(229\) | 6076.99 | 1.75362 | 0.876810 | − | 0.480837i | \(-0.159667\pi\) | ||||
0.876810 | + | 0.480837i | \(0.159667\pi\) | |||||||
\(230\) | −3152.50 | −0.903782 | ||||||||
\(231\) | 941.167 | 0.268070 | ||||||||
\(232\) | −9089.04 | −2.57209 | ||||||||
\(233\) | 244.038 | 0.0686157 | 0.0343078 | − | 0.999411i | \(-0.489077\pi\) | ||||
0.0343078 | + | 0.999411i | \(0.489077\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −985.772 | −0.273637 | ||||||||
\(236\) | −13556.8 | −3.73930 | ||||||||
\(237\) | −5322.62 | −1.45882 | ||||||||
\(238\) | −4233.39 | −1.15298 | ||||||||
\(239\) | −2163.92 | −0.585657 | −0.292829 | − | 0.956165i | \(-0.594597\pi\) | ||||
−0.292829 | + | 0.956165i | \(0.594597\pi\) | |||||||
\(240\) | −7716.76 | −2.07548 | ||||||||
\(241\) | −2150.23 | −0.574723 | −0.287361 | − | 0.957822i | \(-0.592778\pi\) | ||||
−0.287361 | + | 0.957822i | \(0.592778\pi\) | |||||||
\(242\) | −604.611 | −0.160603 | ||||||||
\(243\) | −2846.18 | −0.751369 | ||||||||
\(244\) | 4405.33 | 1.15583 | ||||||||
\(245\) | 2483.50 | 0.647611 | ||||||||
\(246\) | 6359.80 | 1.64832 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 12997.2 | 3.32791 | ||||||||
\(249\) | 2688.23 | 0.684177 | ||||||||
\(250\) | −7445.94 | −1.88369 | ||||||||
\(251\) | 502.969 | 0.126483 | 0.0632413 | − | 0.997998i | \(-0.479856\pi\) | ||||
0.0632413 | + | 0.997998i | \(0.479856\pi\) | |||||||
\(252\) | −7926.33 | −1.98140 | ||||||||
\(253\) | 681.860 | 0.169439 | ||||||||
\(254\) | −7233.22 | −1.78682 | ||||||||
\(255\) | 7452.93 | 1.83028 | ||||||||
\(256\) | −8290.68 | −2.02409 | ||||||||
\(257\) | 5172.87 | 1.25554 | 0.627772 | − | 0.778398i | \(-0.283967\pi\) | ||||
0.627772 | + | 0.778398i | \(0.283967\pi\) | |||||||
\(258\) | −14048.8 | −3.39009 | ||||||||
\(259\) | −3880.83 | −0.931055 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9523.10 | 2.25849 | ||||||||
\(262\) | −9853.54 | −2.32349 | ||||||||
\(263\) | −2695.62 | −0.632011 | −0.316005 | − | 0.948757i | \(-0.602342\pi\) | ||||
−0.316005 | + | 0.948757i | \(0.602342\pi\) | |||||||
\(264\) | 4238.82 | 0.988187 | ||||||||
\(265\) | 267.843 | 0.0620884 | ||||||||
\(266\) | 5870.36 | 1.35314 | ||||||||
\(267\) | 12767.3 | 2.92638 | ||||||||
\(268\) | −9508.12 | −2.16717 | ||||||||
\(269\) | 3727.17 | 0.844793 | 0.422397 | − | 0.906411i | \(-0.361189\pi\) | ||||
0.422397 | + | 0.906411i | \(0.361189\pi\) | |||||||
\(270\) | 8725.30 | 1.96668 | ||||||||
\(271\) | 3317.84 | 0.743707 | 0.371854 | − | 0.928291i | \(-0.378722\pi\) | ||||
0.371854 | + | 0.928291i | \(0.378722\pi\) | |||||||
\(272\) | −7507.52 | −1.67357 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10032.9 | 2.21208 | ||||||||
\(275\) | 235.495 | 0.0516395 | ||||||||
\(276\) | −9044.85 | −1.97259 | ||||||||
\(277\) | 4520.71 | 0.980589 | 0.490294 | − | 0.871557i | \(-0.336889\pi\) | ||||
0.490294 | + | 0.871557i | \(0.336889\pi\) | |||||||
\(278\) | 1357.91 | 0.292956 | ||||||||
\(279\) | −13617.9 | −2.92215 | ||||||||
\(280\) | −4537.81 | −0.968521 | ||||||||
\(281\) | 3526.53 | 0.748667 | 0.374333 | − | 0.927294i | \(-0.377872\pi\) | ||||
0.374333 | + | 0.927294i | \(0.377872\pi\) | |||||||
\(282\) | −4161.76 | −0.878826 | ||||||||
\(283\) | −3367.83 | −0.707409 | −0.353705 | − | 0.935357i | \(-0.615078\pi\) | ||||
−0.353705 | + | 0.935357i | \(0.615078\pi\) | |||||||
\(284\) | −5833.21 | −1.21879 | ||||||||
\(285\) | −10334.8 | −2.14801 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1472.60 | 0.302874 | ||||||||
\(288\) | −3852.89 | −0.788312 | ||||||||
\(289\) | 2337.85 | 0.475849 | ||||||||
\(290\) | 10315.5 | 2.08878 | ||||||||
\(291\) | 10008.6 | 2.01621 | ||||||||
\(292\) | 15246.4 | 3.05558 | ||||||||
\(293\) | 5144.64 | 1.02578 | 0.512889 | − | 0.858455i | \(-0.328575\pi\) | ||||
0.512889 | + | 0.858455i | \(0.328575\pi\) | |||||||
\(294\) | 10484.9 | 2.07990 | ||||||||
\(295\) | 8131.91 | 1.60494 | ||||||||
\(296\) | −17478.5 | −3.43215 | ||||||||
\(297\) | −1887.21 | −0.368711 | ||||||||
\(298\) | 1678.61 | 0.326305 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −3123.83 | −0.601181 | ||||||||
\(301\) | −3252.98 | −0.622919 | ||||||||
\(302\) | −14088.2 | −2.68439 | ||||||||
\(303\) | −10393.3 | −1.97056 | ||||||||
\(304\) | 10410.5 | 1.96410 | ||||||||
\(305\) | −2642.49 | −0.496093 | ||||||||
\(306\) | 19976.8 | 3.73203 | ||||||||
\(307\) | −8322.60 | −1.54722 | −0.773609 | − | 0.633663i | \(-0.781551\pi\) | ||||
−0.773609 | + | 0.633663i | \(0.781551\pi\) | |||||||
\(308\) | 1857.05 | 0.343556 | ||||||||
\(309\) | −2646.65 | −0.487257 | ||||||||
\(310\) | −14751.0 | −2.70258 | ||||||||
\(311\) | 6866.90 | 1.25205 | 0.626023 | − | 0.779805i | \(-0.284682\pi\) | ||||
0.626023 | + | 0.779805i | \(0.284682\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1954.64 | −0.352979 | −0.176490 | − | 0.984302i | \(-0.556474\pi\) | ||||
−0.176490 | + | 0.984302i | \(0.556474\pi\) | |||||||
\(314\) | −10430.0 | −1.87452 | ||||||||
\(315\) | 4754.52 | 0.850434 | ||||||||
\(316\) | −10502.3 | −1.86961 | ||||||||
\(317\) | 3097.55 | 0.548820 | 0.274410 | − | 0.961613i | \(-0.411517\pi\) | ||||
0.274410 | + | 0.961613i | \(0.411517\pi\) | |||||||
\(318\) | 1130.78 | 0.199406 | ||||||||
\(319\) | −2231.15 | −0.391601 | ||||||||
\(320\) | 3005.36 | 0.525014 | ||||||||
\(321\) | −300.323 | −0.0522193 | ||||||||
\(322\) | −3081.74 | −0.533350 | ||||||||
\(323\) | −10054.6 | −1.73205 | ||||||||
\(324\) | 3524.15 | 0.604277 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5350.96 | 0.909087 | ||||||||
\(327\) | 15749.0 | 2.66338 | ||||||||
\(328\) | 6632.28 | 1.11648 | ||||||||
\(329\) | −963.647 | −0.161482 | ||||||||
\(330\) | −4810.79 | −0.802501 | ||||||||
\(331\) | 2904.59 | 0.482329 | 0.241164 | − | 0.970484i | \(-0.422471\pi\) | ||||
0.241164 | + | 0.970484i | \(0.422471\pi\) | |||||||
\(332\) | 5304.25 | 0.876833 | ||||||||
\(333\) | 18313.2 | 3.01368 | ||||||||
\(334\) | 18546.9 | 3.03844 | ||||||||
\(335\) | 5703.33 | 0.930168 | ||||||||
\(336\) | −7543.56 | −1.22481 | ||||||||
\(337\) | −3911.44 | −0.632254 | −0.316127 | − | 0.948717i | \(-0.602383\pi\) | ||||
−0.316127 | + | 0.948717i | \(0.602383\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5377.21 | 0.861504 | ||||||||
\(340\) | 14705.6 | 2.34566 | ||||||||
\(341\) | 3190.51 | 0.506674 | ||||||||
\(342\) | −27701.5 | −4.37990 | ||||||||
\(343\) | 5840.45 | 0.919401 | ||||||||
\(344\) | −14650.8 | −2.29627 | ||||||||
\(345\) | 5425.44 | 0.846655 | ||||||||
\(346\) | 202.575 | 0.0314754 | ||||||||
\(347\) | −6199.11 | −0.959036 | −0.479518 | − | 0.877532i | \(-0.659188\pi\) | ||||
−0.479518 | + | 0.877532i | \(0.659188\pi\) | |||||||
\(348\) | 29596.2 | 4.55897 | ||||||||
\(349\) | 9339.47 | 1.43247 | 0.716233 | − | 0.697862i | \(-0.245865\pi\) | ||||
0.716233 | + | 0.697862i | \(0.245865\pi\) | |||||||
\(350\) | −1064.35 | −0.162548 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 902.689 | 0.136686 | ||||||||
\(353\) | −1538.08 | −0.231909 | −0.115954 | − | 0.993255i | \(-0.536993\pi\) | ||||
−0.115954 | + | 0.993255i | \(0.536993\pi\) | |||||||
\(354\) | 34331.5 | 5.15451 | ||||||||
\(355\) | 3498.98 | 0.523117 | ||||||||
\(356\) | 25191.5 | 3.75042 | ||||||||
\(357\) | 7285.65 | 1.08011 | ||||||||
\(358\) | −1439.11 | −0.212456 | ||||||||
\(359\) | 3856.14 | 0.566906 | 0.283453 | − | 0.958986i | \(-0.408520\pi\) | ||||
0.283453 | + | 0.958986i | \(0.408520\pi\) | |||||||
\(360\) | 21413.3 | 3.13495 | ||||||||
\(361\) | 7083.53 | 1.03273 | ||||||||
\(362\) | −16626.3 | −2.41397 | ||||||||
\(363\) | 1040.53 | 0.150451 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9145.38 | −1.31148 | ||||||||
\(366\) | −11156.1 | −1.59328 | ||||||||
\(367\) | 7807.63 | 1.11050 | 0.555252 | − | 0.831682i | \(-0.312622\pi\) | ||||
0.555252 | + | 0.831682i | \(0.312622\pi\) | |||||||
\(368\) | −5465.18 | −0.774164 | ||||||||
\(369\) | −6949.01 | −0.980355 | ||||||||
\(370\) | 19837.0 | 2.78723 | ||||||||
\(371\) | 261.831 | 0.0366404 | ||||||||
\(372\) | −42322.0 | −5.89865 | ||||||||
\(373\) | 1707.02 | 0.236960 | 0.118480 | − | 0.992956i | \(-0.462198\pi\) | ||||
0.118480 | + | 0.992956i | \(0.462198\pi\) | |||||||
\(374\) | −4680.35 | −0.647099 | ||||||||
\(375\) | 12814.4 | 1.76463 | ||||||||
\(376\) | −4340.06 | −0.595270 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 8529.46 | 1.16060 | ||||||||
\(379\) | −7494.31 | −1.01572 | −0.507858 | − | 0.861441i | \(-0.669563\pi\) | ||||
−0.507858 | + | 0.861441i | \(0.669563\pi\) | |||||||
\(380\) | −20392.0 | −2.75287 | ||||||||
\(381\) | 12448.3 | 1.67388 | ||||||||
\(382\) | −14247.5 | −1.90828 | ||||||||
\(383\) | 1912.26 | 0.255123 | 0.127562 | − | 0.991831i | \(-0.459285\pi\) | ||||
0.127562 | + | 0.991831i | \(0.459285\pi\) | |||||||
\(384\) | 18333.6 | 2.43642 | ||||||||
\(385\) | −1113.93 | −0.147457 | ||||||||
\(386\) | 4449.90 | 0.586771 | ||||||||
\(387\) | 15350.4 | 2.01629 | ||||||||
\(388\) | 19748.4 | 2.58395 | ||||||||
\(389\) | 1802.21 | 0.234899 | 0.117449 | − | 0.993079i | \(-0.462528\pi\) | ||||
0.117449 | + | 0.993079i | \(0.462528\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5278.33 | 0.682703 | ||||||||
\(392\) | 10934.1 | 1.40881 | ||||||||
\(393\) | 16957.9 | 2.17663 | ||||||||
\(394\) | −16444.9 | −2.10275 | ||||||||
\(395\) | 6299.65 | 0.802455 | ||||||||
\(396\) | −8763.19 | −1.11204 | ||||||||
\(397\) | −8612.12 | −1.08874 | −0.544370 | − | 0.838845i | \(-0.683231\pi\) | ||||
−0.544370 | + | 0.838845i | \(0.683231\pi\) | |||||||
\(398\) | 5728.51 | 0.721468 | ||||||||
\(399\) | −10102.9 | −1.26761 | ||||||||
\(400\) | −1887.52 | −0.235940 | ||||||||
\(401\) | 6830.18 | 0.850581 | 0.425290 | − | 0.905057i | \(-0.360172\pi\) | ||||
0.425290 | + | 0.905057i | \(0.360172\pi\) | |||||||
\(402\) | 24078.5 | 2.98737 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −20507.4 | −2.52545 | ||||||||
\(405\) | −2113.92 | −0.259361 | ||||||||
\(406\) | 10084.0 | 1.23266 | ||||||||
\(407\) | −4290.57 | −0.522544 | ||||||||
\(408\) | 32813.1 | 3.98159 | ||||||||
\(409\) | 13767.3 | 1.66443 | 0.832213 | − | 0.554457i | \(-0.187074\pi\) | ||||
0.832213 | + | 0.554457i | \(0.187074\pi\) | |||||||
\(410\) | −7527.21 | −0.906689 | ||||||||
\(411\) | −17266.6 | −2.07226 | ||||||||
\(412\) | −5222.19 | −0.624463 | ||||||||
\(413\) | 7949.39 | 0.947128 | ||||||||
\(414\) | 14542.4 | 1.72637 | ||||||||
\(415\) | −3181.69 | −0.376345 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2336.95 | −0.274439 | ||||||||
\(418\) | 6490.14 | 0.759434 | ||||||||
\(419\) | −6227.23 | −0.726063 | −0.363031 | − | 0.931777i | \(-0.618258\pi\) | ||||
−0.363031 | + | 0.931777i | \(0.618258\pi\) | |||||||
\(420\) | 14776.2 | 1.71668 | ||||||||
\(421\) | 10023.7 | 1.16039 | 0.580194 | − | 0.814478i | \(-0.302977\pi\) | ||||
0.580194 | + | 0.814478i | \(0.302977\pi\) | |||||||
\(422\) | −18366.8 | −2.11868 | ||||||||
\(423\) | 4547.33 | 0.522692 | ||||||||
\(424\) | 1179.23 | 0.135067 | ||||||||
\(425\) | 1822.98 | 0.208065 | ||||||||
\(426\) | 14772.1 | 1.68007 | ||||||||
\(427\) | −2583.17 | −0.292760 | ||||||||
\(428\) | −592.578 | −0.0669237 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 16627.7 | 1.86478 | ||||||||
\(431\) | 9244.20 | 1.03313 | 0.516563 | − | 0.856249i | \(-0.327211\pi\) | ||||
0.516563 | + | 0.856249i | \(0.327211\pi\) | |||||||
\(432\) | 15126.2 | 1.68463 | ||||||||
\(433\) | 15672.7 | 1.73945 | 0.869726 | − | 0.493535i | \(-0.164295\pi\) | ||||
0.869726 | + | 0.493535i | \(0.164295\pi\) | |||||||
\(434\) | −14419.9 | −1.59488 | ||||||||
\(435\) | −17752.9 | −1.95675 | ||||||||
\(436\) | 31075.0 | 3.41335 | ||||||||
\(437\) | −7319.36 | −0.801219 | ||||||||
\(438\) | −38610.2 | −4.21202 | ||||||||
\(439\) | −10815.1 | −1.17580 | −0.587902 | − | 0.808932i | \(-0.700046\pi\) | ||||
−0.587902 | + | 0.808932i | \(0.700046\pi\) | |||||||
\(440\) | −5016.90 | −0.543572 | ||||||||
\(441\) | −11456.3 | −1.23704 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5596.30 | 0.600199 | 0.300100 | − | 0.953908i | \(-0.402980\pi\) | ||||
0.300100 | + | 0.953908i | \(0.402980\pi\) | |||||||
\(444\) | 56914.3 | 6.08340 | ||||||||
\(445\) | −15110.8 | −1.60971 | ||||||||
\(446\) | 15846.0 | 1.68235 | ||||||||
\(447\) | −2888.87 | −0.305680 | ||||||||
\(448\) | 2937.90 | 0.309828 | ||||||||
\(449\) | −16603.1 | −1.74510 | −0.872549 | − | 0.488527i | \(-0.837535\pi\) | ||||
−0.872549 | + | 0.488527i | \(0.837535\pi\) | |||||||
\(450\) | 5022.51 | 0.526141 | ||||||||
\(451\) | 1628.07 | 0.169984 | ||||||||
\(452\) | 10610.0 | 1.10409 | ||||||||
\(453\) | 24245.8 | 2.51471 | ||||||||
\(454\) | 17623.5 | 1.82183 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −45501.2 | −4.67278 | ||||||||
\(457\) | 15233.1 | 1.55925 | 0.779624 | − | 0.626248i | \(-0.215410\pi\) | ||||
0.779624 | + | 0.626248i | \(0.215410\pi\) | |||||||
\(458\) | −30365.4 | −3.09800 | ||||||||
\(459\) | −14609.1 | −1.48560 | ||||||||
\(460\) | 10705.1 | 1.08506 | ||||||||
\(461\) | −15626.2 | −1.57871 | −0.789355 | − | 0.613937i | \(-0.789585\pi\) | ||||
−0.789355 | + | 0.613937i | \(0.789585\pi\) | |||||||
\(462\) | −4702.81 | −0.473581 | ||||||||
\(463\) | −4820.16 | −0.483827 | −0.241914 | − | 0.970298i | \(-0.577775\pi\) | ||||
−0.241914 | + | 0.970298i | \(0.577775\pi\) | |||||||
\(464\) | 17882.9 | 1.78921 | ||||||||
\(465\) | 25386.4 | 2.53175 | ||||||||
\(466\) | −1219.41 | −0.121219 | ||||||||
\(467\) | −1382.23 | −0.136964 | −0.0684818 | − | 0.997652i | \(-0.521815\pi\) | ||||
−0.0684818 | + | 0.997652i | \(0.521815\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5575.32 | 0.548922 | ||||||||
\(470\) | 4925.70 | 0.483416 | ||||||||
\(471\) | 17950.0 | 1.75603 | ||||||||
\(472\) | 35802.4 | 3.49139 | ||||||||
\(473\) | −3596.43 | −0.349607 | ||||||||
\(474\) | 26596.0 | 2.57720 | ||||||||
\(475\) | −2527.90 | −0.244185 | ||||||||
\(476\) | 14375.6 | 1.38425 | ||||||||
\(477\) | −1235.55 | −0.118599 | ||||||||
\(478\) | 10812.6 | 1.03464 | ||||||||
\(479\) | −5537.16 | −0.528183 | −0.264091 | − | 0.964498i | \(-0.585072\pi\) | ||||
−0.264091 | + | 0.964498i | \(0.585072\pi\) | |||||||
\(480\) | 7182.54 | 0.682993 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 10744.2 | 1.01532 | ||||||||
\(483\) | 5303.67 | 0.499638 | ||||||||
\(484\) | 2053.11 | 0.192817 | ||||||||
\(485\) | −11845.9 | −1.10906 | ||||||||
\(486\) | 14221.8 | 1.32739 | ||||||||
\(487\) | 2985.52 | 0.277796 | 0.138898 | − | 0.990307i | \(-0.455644\pi\) | ||||
0.138898 | + | 0.990307i | \(0.455644\pi\) | |||||||
\(488\) | −11634.1 | −1.07920 | ||||||||
\(489\) | −9208.98 | −0.851625 | ||||||||
\(490\) | −12409.5 | −1.14409 | ||||||||
\(491\) | −14284.6 | −1.31295 | −0.656474 | − | 0.754349i | \(-0.727953\pi\) | ||||
−0.656474 | + | 0.754349i | \(0.727953\pi\) | |||||||
\(492\) | −21596.3 | −1.97894 | ||||||||
\(493\) | −17271.5 | −1.57783 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5256.49 | 0.477296 | ||||||||
\(496\) | −25572.3 | −2.31498 | ||||||||
\(497\) | 3420.44 | 0.308708 | ||||||||
\(498\) | −13432.5 | −1.20869 | ||||||||
\(499\) | −6738.75 | −0.604545 | −0.302272 | − | 0.953222i | \(-0.597745\pi\) | ||||
−0.302272 | + | 0.953222i | \(0.597745\pi\) | |||||||
\(500\) | 25284.6 | 2.26152 | ||||||||
\(501\) | −31919.1 | −2.84638 | ||||||||
\(502\) | −2513.23 | −0.223448 | ||||||||
\(503\) | −2629.88 | −0.233123 | −0.116561 | − | 0.993183i | \(-0.537187\pi\) | ||||
−0.116561 | + | 0.993183i | \(0.537187\pi\) | |||||||
\(504\) | 20932.7 | 1.85003 | ||||||||
\(505\) | 12301.1 | 1.08395 | ||||||||
\(506\) | −3407.11 | −0.299337 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 24562.3 | 2.14523 | ||||||||
\(509\) | 5693.59 | 0.495803 | 0.247902 | − | 0.968785i | \(-0.420259\pi\) | ||||
0.247902 | + | 0.968785i | \(0.420259\pi\) | |||||||
\(510\) | −37240.7 | −3.23343 | ||||||||
\(511\) | −8940.11 | −0.773948 | ||||||||
\(512\) | 24371.1 | 2.10364 | ||||||||
\(513\) | 20258.1 | 1.74350 | ||||||||
\(514\) | −25847.7 | −2.21808 | ||||||||
\(515\) | 3132.47 | 0.268025 | ||||||||
\(516\) | 47706.5 | 4.07008 | ||||||||
\(517\) | −1065.39 | −0.0906299 | ||||||||
\(518\) | 19391.7 | 1.64483 | ||||||||
\(519\) | −348.631 | −0.0294859 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17275.8 | 1.45272 | 0.726358 | − | 0.687316i | \(-0.241211\pi\) | ||||
0.726358 | + | 0.687316i | \(0.241211\pi\) | |||||||
\(522\) | −47584.9 | −3.98991 | ||||||||
\(523\) | −2205.46 | −0.184394 | −0.0921969 | − | 0.995741i | \(-0.529389\pi\) | ||||
−0.0921969 | + | 0.995741i | \(0.529389\pi\) | |||||||
\(524\) | 33460.3 | 2.78954 | ||||||||
\(525\) | 1831.73 | 0.152273 | ||||||||
\(526\) | 13469.4 | 1.11653 | ||||||||
\(527\) | 24698.0 | 2.04149 | ||||||||
\(528\) | −8340.00 | −0.687409 | ||||||||
\(529\) | −8324.58 | −0.684193 | ||||||||
\(530\) | −1338.35 | −0.109687 | ||||||||
\(531\) | −37512.2 | −3.06571 | ||||||||
\(532\) | −19934.3 | −1.62455 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −63795.3 | −5.16983 | ||||||||
\(535\) | 355.451 | 0.0287242 | ||||||||
\(536\) | 25110.1 | 2.02349 | ||||||||
\(537\) | 2476.70 | 0.199027 | ||||||||
\(538\) | −18623.9 | −1.49244 | ||||||||
\(539\) | 2684.07 | 0.214492 | ||||||||
\(540\) | −29629.0 | −2.36117 | ||||||||
\(541\) | 16236.4 | 1.29031 | 0.645153 | − | 0.764054i | \(-0.276794\pi\) | ||||
0.645153 | + | 0.764054i | \(0.276794\pi\) | |||||||
\(542\) | −16578.6 | −1.31386 | ||||||||
\(543\) | 28613.7 | 2.26139 | ||||||||
\(544\) | 6987.79 | 0.550733 | ||||||||
\(545\) | −18640.0 | −1.46504 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18132.1 | 1.41732 | 0.708660 | − | 0.705551i | \(-0.249300\pi\) | ||||
0.708660 | + | 0.705551i | \(0.249300\pi\) | |||||||
\(548\) | −34069.3 | −2.65578 | ||||||||
\(549\) | 12189.7 | 0.947619 | ||||||||
\(550\) | −1176.72 | −0.0912280 | ||||||||
\(551\) | 23950.1 | 1.85174 | ||||||||
\(552\) | 23886.6 | 1.84182 | ||||||||
\(553\) | 6158.25 | 0.473554 | ||||||||
\(554\) | −22589.0 | −1.73234 | ||||||||
\(555\) | −34139.3 | −2.61105 | ||||||||
\(556\) | −4611.13 | −0.351718 | ||||||||
\(557\) | −1588.05 | −0.120804 | −0.0604019 | − | 0.998174i | \(-0.519238\pi\) | ||||
−0.0604019 | + | 0.998174i | \(0.519238\pi\) | |||||||
\(558\) | 68045.6 | 5.16237 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 8928.26 | 0.673728 | ||||||||
\(561\) | 8054.86 | 0.606197 | ||||||||
\(562\) | −17621.3 | −1.32262 | ||||||||
\(563\) | 7948.65 | 0.595019 | 0.297509 | − | 0.954719i | \(-0.403844\pi\) | ||||
0.297509 | + | 0.954719i | \(0.403844\pi\) | |||||||
\(564\) | 14132.3 | 1.05510 | ||||||||
\(565\) | −6364.26 | −0.473887 | ||||||||
\(566\) | 16828.3 | 1.24973 | ||||||||
\(567\) | −2066.47 | −0.153057 | ||||||||
\(568\) | 15405.0 | 1.13799 | ||||||||
\(569\) | 14065.1 | 1.03627 | 0.518135 | − | 0.855299i | \(-0.326626\pi\) | ||||
0.518135 | + | 0.855299i | \(0.326626\pi\) | |||||||
\(570\) | 51641.0 | 3.79474 | ||||||||
\(571\) | 8812.31 | 0.645856 | 0.322928 | − | 0.946424i | \(-0.395333\pi\) | ||||
0.322928 | + | 0.946424i | \(0.395333\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 24519.8 | 1.78766 | ||||||||
\(574\) | −7358.26 | −0.535066 | ||||||||
\(575\) | 1327.06 | 0.0962475 | ||||||||
\(576\) | −13863.6 | −1.00286 | ||||||||
\(577\) | −23605.9 | −1.70316 | −0.851582 | − | 0.524222i | \(-0.824356\pi\) | ||||
−0.851582 | + | 0.524222i | \(0.824356\pi\) | |||||||
\(578\) | −11681.7 | −0.840650 | ||||||||
\(579\) | −7658.26 | −0.549683 | ||||||||
\(580\) | −35028.9 | −2.50775 | ||||||||
\(581\) | −3110.28 | −0.222093 | ||||||||
\(582\) | −50011.1 | −3.56190 | ||||||||
\(583\) | 289.475 | 0.0205640 | ||||||||
\(584\) | −40264.4 | −2.85300 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −25706.7 | −1.81217 | ||||||||
\(587\) | 17011.1 | 1.19612 | 0.598060 | − | 0.801451i | \(-0.295938\pi\) | ||||
0.598060 | + | 0.801451i | \(0.295938\pi\) | |||||||
\(588\) | −35604.1 | −2.49709 | ||||||||
\(589\) | −34248.3 | −2.39588 | ||||||||
\(590\) | −40633.4 | −2.83534 | ||||||||
\(591\) | 28301.6 | 1.96984 | ||||||||
\(592\) | 34389.4 | 2.38749 | ||||||||
\(593\) | 2224.19 | 0.154025 | 0.0770123 | − | 0.997030i | \(-0.475462\pi\) | ||||
0.0770123 | + | 0.997030i | \(0.475462\pi\) | |||||||
\(594\) | 9429.99 | 0.651376 | ||||||||
\(595\) | −8623.02 | −0.594133 | ||||||||
\(596\) | −5700.14 | −0.391756 | ||||||||
\(597\) | −9858.75 | −0.675866 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19673.7 | 1.34198 | 0.670991 | − | 0.741465i | \(-0.265869\pi\) | ||||
0.670991 | + | 0.741465i | \(0.265869\pi\) | |||||||
\(600\) | 8249.75 | 0.561324 | ||||||||
\(601\) | 11698.6 | 0.794004 | 0.397002 | − | 0.917818i | \(-0.370051\pi\) | ||||
0.397002 | + | 0.917818i | \(0.370051\pi\) | |||||||
\(602\) | 16254.5 | 1.10047 | ||||||||
\(603\) | −26309.2 | −1.77677 | ||||||||
\(604\) | 47840.2 | 3.22283 | ||||||||
\(605\) | −1231.54 | −0.0827588 | ||||||||
\(606\) | 51933.1 | 3.48125 | ||||||||
\(607\) | 6836.66 | 0.457152 | 0.228576 | − | 0.973526i | \(-0.426593\pi\) | ||||
0.228576 | + | 0.973526i | \(0.426593\pi\) | |||||||
\(608\) | −9689.83 | −0.646340 | ||||||||
\(609\) | −17354.4 | −1.15474 | ||||||||
\(610\) | 13203.9 | 0.876413 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −67836.5 | −4.48060 | ||||||||
\(613\) | −249.182 | −0.0164182 | −0.00820910 | − | 0.999966i | \(-0.502613\pi\) | ||||
−0.00820910 | + | 0.999966i | \(0.502613\pi\) | |||||||
\(614\) | 41586.3 | 2.73336 | ||||||||
\(615\) | 12954.3 | 0.849379 | ||||||||
\(616\) | −4904.30 | −0.320779 | ||||||||
\(617\) | −10289.6 | −0.671383 | −0.335691 | − | 0.941972i | \(-0.608970\pi\) | ||||
−0.335691 | + | 0.941972i | \(0.608970\pi\) | |||||||
\(618\) | 13224.7 | 0.860803 | ||||||||
\(619\) | −1258.08 | −0.0816906 | −0.0408453 | − | 0.999165i | \(-0.513005\pi\) | ||||
−0.0408453 | + | 0.999165i | \(0.513005\pi\) | |||||||
\(620\) | 50090.8 | 3.24467 | ||||||||
\(621\) | −10634.8 | −0.687215 | ||||||||
\(622\) | −34312.4 | −2.21190 | ||||||||
\(623\) | −14771.7 | −0.949943 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12490.6 | −0.799398 | ||||||||
\(626\) | 9766.90 | 0.623585 | ||||||||
\(627\) | −11169.5 | −0.711431 | ||||||||
\(628\) | 35417.7 | 2.25051 | ||||||||
\(629\) | −33213.6 | −2.10543 | ||||||||
\(630\) | −23757.3 | −1.50240 | ||||||||
\(631\) | −5559.42 | −0.350740 | −0.175370 | − | 0.984503i | \(-0.556112\pi\) | ||||
−0.175370 | + | 0.984503i | \(0.556112\pi\) | |||||||
\(632\) | 27735.5 | 1.74566 | ||||||||
\(633\) | 31609.3 | 1.98477 | ||||||||
\(634\) | −15477.8 | −0.969563 | ||||||||
\(635\) | −14733.4 | −0.920751 | ||||||||
\(636\) | −3839.87 | −0.239404 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 11148.6 | 0.691814 | ||||||||
\(639\) | −16140.6 | −0.999239 | ||||||||
\(640\) | −21699.0 | −1.34020 | ||||||||
\(641\) | 27189.2 | 1.67536 | 0.837681 | − | 0.546160i | \(-0.183911\pi\) | ||||
0.837681 | + | 0.546160i | \(0.183911\pi\) | |||||||
\(642\) | 1500.65 | 0.0922522 | ||||||||
\(643\) | 11158.3 | 0.684357 | 0.342179 | − | 0.939635i | \(-0.388835\pi\) | ||||
0.342179 | + | 0.939635i | \(0.388835\pi\) | |||||||
\(644\) | 10464.9 | 0.640331 | ||||||||
\(645\) | −28616.2 | −1.74692 | ||||||||
\(646\) | 50240.7 | 3.05990 | ||||||||
\(647\) | −29322.4 | −1.78173 | −0.890866 | − | 0.454266i | \(-0.849902\pi\) | ||||
−0.890866 | + | 0.454266i | \(0.849902\pi\) | |||||||
\(648\) | −9306.95 | −0.564215 | ||||||||
\(649\) | 8788.67 | 0.531565 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 24816.6 | 1.49407 | ||||||||
\(652\) | −18170.6 | −1.09143 | ||||||||
\(653\) | −25517.5 | −1.52922 | −0.764608 | − | 0.644495i | \(-0.777068\pi\) | ||||
−0.764608 | + | 0.644495i | \(0.777068\pi\) | |||||||
\(654\) | −78694.6 | −4.70520 | ||||||||
\(655\) | −20070.7 | −1.19730 | ||||||||
\(656\) | −13049.2 | −0.776654 | ||||||||
\(657\) | 42187.3 | 2.50515 | ||||||||
\(658\) | 4815.14 | 0.285279 | ||||||||
\(659\) | −5612.95 | −0.331790 | −0.165895 | − | 0.986143i | \(-0.553051\pi\) | ||||
−0.165895 | + | 0.986143i | \(0.553051\pi\) | |||||||
\(660\) | 16336.3 | 0.963468 | ||||||||
\(661\) | −27212.7 | −1.60129 | −0.800643 | − | 0.599141i | \(-0.795509\pi\) | ||||
−0.800643 | + | 0.599141i | \(0.795509\pi\) | |||||||
\(662\) | −14513.6 | −0.852097 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −14008.0 | −0.818701 | ||||||||
\(665\) | 11957.4 | 0.697273 | ||||||||
\(666\) | −91507.1 | −5.32406 | ||||||||
\(667\) | −12573.0 | −0.729879 | ||||||||
\(668\) | −62980.7 | −3.64790 | ||||||||
\(669\) | −27270.9 | −1.57601 | ||||||||
\(670\) | −28498.3 | −1.64326 | ||||||||
\(671\) | −2855.90 | −0.164308 | ||||||||
\(672\) | 7021.33 | 0.403056 | ||||||||
\(673\) | 9591.29 | 0.549357 | 0.274678 | − | 0.961536i | \(-0.411429\pi\) | ||||
0.274678 | + | 0.961536i | \(0.411429\pi\) | |||||||
\(674\) | 19544.6 | 1.11696 | ||||||||
\(675\) | −3672.96 | −0.209440 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −736.743 | −0.0418247 | −0.0209124 | − | 0.999781i | \(-0.506657\pi\) | ||||
−0.0209124 | + | 0.999781i | \(0.506657\pi\) | |||||||
\(678\) | −26868.8 | −1.52196 | ||||||||
\(679\) | −11580.0 | −0.654490 | ||||||||
\(680\) | −38836.3 | −2.19015 | ||||||||
\(681\) | −30330.0 | −1.70668 | ||||||||
\(682\) | −15942.3 | −0.895107 | ||||||||
\(683\) | 5276.86 | 0.295627 | 0.147814 | − | 0.989015i | \(-0.452776\pi\) | ||||
0.147814 | + | 0.989015i | \(0.452776\pi\) | |||||||
\(684\) | 94067.6 | 5.25843 | ||||||||
\(685\) | 20436.1 | 1.13989 | ||||||||
\(686\) | −29183.5 | −1.62424 | ||||||||
\(687\) | 52258.8 | 2.90218 | ||||||||
\(688\) | 28825.8 | 1.59734 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −27109.8 | −1.49573 | ||||||||
\(691\) | 20497.2 | 1.12844 | 0.564219 | − | 0.825625i | \(-0.309177\pi\) | ||||
0.564219 | + | 0.825625i | \(0.309177\pi\) | |||||||
\(692\) | −687.896 | −0.0377888 | ||||||||
\(693\) | 5138.51 | 0.281668 | ||||||||
\(694\) | 30975.6 | 1.69426 | ||||||||
\(695\) | 2765.93 | 0.150961 | ||||||||
\(696\) | −78160.8 | −4.25672 | ||||||||
\(697\) | 12603.1 | 0.684899 | ||||||||
\(698\) | −46667.3 | −2.53064 | ||||||||
\(699\) | 2098.59 | 0.113557 | ||||||||
\(700\) | 3614.26 | 0.195152 | ||||||||
\(701\) | 9115.38 | 0.491132 | 0.245566 | − | 0.969380i | \(-0.421026\pi\) | ||||
0.245566 | + | 0.969380i | \(0.421026\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 46056.7 | 2.47093 | ||||||||
\(704\) | 3248.08 | 0.173887 | ||||||||
\(705\) | −8477.11 | −0.452860 | ||||||||
\(706\) | 7685.46 | 0.409697 | ||||||||
\(707\) | 12025.0 | 0.639671 | ||||||||
\(708\) | −116581. | −6.18842 | ||||||||
\(709\) | 16439.1 | 0.870781 | 0.435390 | − | 0.900242i | \(-0.356610\pi\) | ||||
0.435390 | + | 0.900242i | \(0.356610\pi\) | |||||||
\(710\) | −17483.7 | −0.924155 | ||||||||
\(711\) | −29060.0 | −1.53282 | ||||||||
\(712\) | −66528.5 | −3.50177 | ||||||||
\(713\) | 17979.2 | 0.944357 | ||||||||
\(714\) | −36404.8 | −1.90815 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4886.86 | 0.255070 | ||||||||
\(717\) | −18608.5 | −0.969243 | ||||||||
\(718\) | −19268.3 | −1.00151 | ||||||||
\(719\) | 27336.5 | 1.41791 | 0.708956 | − | 0.705253i | \(-0.249167\pi\) | ||||
0.708956 | + | 0.705253i | \(0.249167\pi\) | |||||||
\(720\) | −42131.4 | −2.18075 | ||||||||
\(721\) | 3062.16 | 0.158170 | ||||||||
\(722\) | −35394.9 | −1.82446 | ||||||||
\(723\) | −18490.8 | −0.951147 | ||||||||
\(724\) | 56458.8 | 2.89817 | ||||||||
\(725\) | −4342.36 | −0.222443 | ||||||||
\(726\) | −5199.33 | −0.265792 | ||||||||
\(727\) | 31683.6 | 1.61634 | 0.808170 | − | 0.588950i | \(-0.200458\pi\) | ||||
0.808170 | + | 0.588950i | \(0.200458\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −30083.4 | −1.52839 | ||||||||
\(730\) | 45697.5 | 2.31691 | ||||||||
\(731\) | −27840.2 | −1.40863 | ||||||||
\(732\) | 37883.5 | 1.91286 | ||||||||
\(733\) | 8125.89 | 0.409463 | 0.204732 | − | 0.978818i | \(-0.434368\pi\) | ||||
0.204732 | + | 0.978818i | \(0.434368\pi\) | |||||||
\(734\) | −39013.1 | −1.96185 | ||||||||
\(735\) | 21356.7 | 1.07177 | ||||||||
\(736\) | 5086.84 | 0.254760 | ||||||||
\(737\) | 6163.95 | 0.308076 | ||||||||
\(738\) | 34722.7 | 1.73193 | ||||||||
\(739\) | 7426.81 | 0.369688 | 0.184844 | − | 0.982768i | \(-0.440822\pi\) | ||||
0.184844 | + | 0.982768i | \(0.440822\pi\) | |||||||
\(740\) | −67361.5 | −3.34630 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1308.31 | −0.0647300 | ||||||||
\(743\) | −7474.38 | −0.369056 | −0.184528 | − | 0.982827i | \(-0.559076\pi\) | ||||
−0.184528 | + | 0.982827i | \(0.559076\pi\) | |||||||
\(744\) | 111769. | 5.50758 | ||||||||
\(745\) | 3419.16 | 0.168145 | ||||||||
\(746\) | −8529.61 | −0.418621 | ||||||||
\(747\) | 14677.0 | 0.718881 | ||||||||
\(748\) | 15893.3 | 0.776895 | ||||||||
\(749\) | 347.472 | 0.0169511 | ||||||||
\(750\) | −64031.0 | −3.11744 | ||||||||
\(751\) | −3881.02 | −0.188576 | −0.0942879 | − | 0.995545i | \(-0.530057\pi\) | ||||
−0.0942879 | + | 0.995545i | \(0.530057\pi\) | |||||||
\(752\) | 8539.20 | 0.414086 | ||||||||
\(753\) | 4325.26 | 0.209324 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −28696.4 | −1.38327 | ||||||||
\(756\) | −28964.0 | −1.39340 | ||||||||
\(757\) | 13052.4 | 0.626682 | 0.313341 | − | 0.949641i | \(-0.398552\pi\) | ||||
0.313341 | + | 0.949641i | \(0.398552\pi\) | |||||||
\(758\) | 37447.5 | 1.79440 | ||||||||
\(759\) | 5863.62 | 0.280416 | ||||||||
\(760\) | 53853.5 | 2.57036 | ||||||||
\(761\) | 25895.4 | 1.23352 | 0.616760 | − | 0.787152i | \(-0.288445\pi\) | ||||
0.616760 | + | 0.787152i | \(0.288445\pi\) | |||||||
\(762\) | −62201.8 | −2.95713 | ||||||||
\(763\) | −18221.6 | −0.864568 | ||||||||
\(764\) | 48381.0 | 2.29105 | ||||||||
\(765\) | 40690.9 | 1.92312 | ||||||||
\(766\) | −9555.18 | −0.450709 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −71295.3 | −3.34980 | ||||||||
\(769\) | 23302.8 | 1.09275 | 0.546373 | − | 0.837542i | \(-0.316008\pi\) | ||||
0.546373 | + | 0.837542i | \(0.316008\pi\) | |||||||
\(770\) | 5566.07 | 0.260503 | ||||||||
\(771\) | 44483.8 | 2.07788 | ||||||||
\(772\) | −15110.8 | −0.704467 | ||||||||
\(773\) | 10182.0 | 0.473768 | 0.236884 | − | 0.971538i | \(-0.423874\pi\) | ||||
0.236884 | + | 0.971538i | \(0.423874\pi\) | |||||||
\(774\) | −76702.8 | −3.56205 | ||||||||
\(775\) | 6209.50 | 0.287809 | ||||||||
\(776\) | −52153.8 | −2.41264 | ||||||||
\(777\) | −33373.1 | −1.54087 | ||||||||
\(778\) | −9005.25 | −0.414979 | ||||||||
\(779\) | −17476.4 | −0.803796 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3781.57 | 0.173259 | ||||||||
\(782\) | −26374.7 | −1.20608 | ||||||||
\(783\) | 34798.8 | 1.58826 | ||||||||
\(784\) | −21513.1 | −0.980008 | ||||||||
\(785\) | −21244.9 | −0.965939 | ||||||||
\(786\) | −84735.1 | −3.84529 | ||||||||
\(787\) | −26826.2 | −1.21506 | −0.607530 | − | 0.794297i | \(-0.707840\pi\) | ||||
−0.607530 | + | 0.794297i | \(0.707840\pi\) | |||||||
\(788\) | 55842.9 | 2.52452 | ||||||||
\(789\) | −23180.8 | −1.04596 | ||||||||
\(790\) | −31478.0 | −1.41764 | ||||||||
\(791\) | −6221.41 | −0.279656 | ||||||||
\(792\) | 23142.8 | 1.03831 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 43033.0 | 1.92340 | ||||||||
\(795\) | 2303.30 | 0.102754 | ||||||||
\(796\) | −19452.7 | −0.866182 | ||||||||
\(797\) | −502.155 | −0.0223177 | −0.0111589 | − | 0.999938i | \(-0.503552\pi\) | ||||
−0.0111589 | + | 0.999938i | \(0.503552\pi\) | |||||||
\(798\) | 50481.9 | 2.23940 | ||||||||
\(799\) | −8247.25 | −0.365165 | ||||||||
\(800\) | 1756.85 | 0.0776424 | ||||||||
\(801\) | 69705.7 | 3.07482 | ||||||||
\(802\) | −34129.0 | −1.50266 | ||||||||
\(803\) | −9884.00 | −0.434369 | ||||||||
\(804\) | −81764.6 | −3.58659 | ||||||||
\(805\) | −6277.22 | −0.274836 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 32051.6 | 1.39810 | ||||||||
\(808\) | 54158.2 | 2.35802 | ||||||||
\(809\) | 19896.8 | 0.864691 | 0.432345 | − | 0.901708i | \(-0.357686\pi\) | ||||
0.432345 | + | 0.901708i | \(0.357686\pi\) | |||||||
\(810\) | 10562.8 | 0.458196 | ||||||||
\(811\) | 29534.8 | 1.27880 | 0.639401 | − | 0.768874i | \(-0.279182\pi\) | ||||
0.639401 | + | 0.768874i | \(0.279182\pi\) | |||||||
\(812\) | −34242.7 | −1.47990 | ||||||||
\(813\) | 28531.6 | 1.23081 | ||||||||
\(814\) | 21439.1 | 0.923144 | ||||||||
\(815\) | 10899.4 | 0.468453 | ||||||||
\(816\) | −64560.6 | −2.76970 | ||||||||
\(817\) | 38605.5 | 1.65317 | ||||||||
\(818\) | −68792.4 | −2.94043 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 25560.6 | 1.08855 | ||||||||
\(821\) | −2221.45 | −0.0944327 | −0.0472164 | − | 0.998885i | \(-0.515035\pi\) | ||||
−0.0472164 | + | 0.998885i | \(0.515035\pi\) | |||||||
\(822\) | 86277.5 | 3.66092 | ||||||||
\(823\) | −17096.9 | −0.724131 | −0.362066 | − | 0.932153i | \(-0.617928\pi\) | ||||
−0.362066 | + | 0.932153i | \(0.617928\pi\) | |||||||
\(824\) | 13791.3 | 0.583063 | ||||||||
\(825\) | 2025.13 | 0.0854616 | ||||||||
\(826\) | −39721.4 | −1.67323 | ||||||||
\(827\) | −4093.79 | −0.172134 | −0.0860672 | − | 0.996289i | \(-0.527430\pi\) | ||||
−0.0860672 | + | 0.996289i | \(0.527430\pi\) | |||||||
\(828\) | −49382.4 | −2.07265 | ||||||||
\(829\) | −15871.1 | −0.664927 | −0.332464 | − | 0.943116i | \(-0.607880\pi\) | ||||
−0.332464 | + | 0.943116i | \(0.607880\pi\) | |||||||
\(830\) | 15898.2 | 0.664863 | ||||||||
\(831\) | 38875.6 | 1.62284 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 20777.6 | 0.864229 | ||||||||
\(834\) | 11677.3 | 0.484833 | ||||||||
\(835\) | 37778.2 | 1.56571 | ||||||||
\(836\) | −22039.0 | −0.911763 | ||||||||
\(837\) | −49761.7 | −2.05498 | ||||||||
\(838\) | 31116.2 | 1.28269 | ||||||||
\(839\) | −1830.35 | −0.0753167 | −0.0376584 | − | 0.999291i | \(-0.511990\pi\) | ||||
−0.0376584 | + | 0.999291i | \(0.511990\pi\) | |||||||
\(840\) | −39022.7 | −1.60287 | ||||||||
\(841\) | 16751.9 | 0.686863 | ||||||||
\(842\) | −50086.1 | −2.04998 | ||||||||
\(843\) | 30326.3 | 1.23902 | ||||||||
\(844\) | 62369.4 | 2.54365 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −22722.0 | −0.923404 | ||||||||
\(847\) | −1203.89 | −0.0488386 | ||||||||
\(848\) | −2320.17 | −0.0939563 | ||||||||
\(849\) | −28961.5 | −1.17074 | ||||||||
\(850\) | −9109.07 | −0.367575 | ||||||||
\(851\) | −24178.2 | −0.973936 | ||||||||
\(852\) | −50162.4 | −2.01706 | ||||||||
\(853\) | 3596.23 | 0.144352 | 0.0721761 | − | 0.997392i | \(-0.477006\pi\) | ||||
0.0721761 | + | 0.997392i | \(0.477006\pi\) | |||||||
\(854\) | 12907.6 | 0.517199 | ||||||||
\(855\) | −56425.3 | −2.25697 | ||||||||
\(856\) | 1564.94 | 0.0624868 | ||||||||
\(857\) | −14566.2 | −0.580595 | −0.290298 | − | 0.956936i | \(-0.593754\pi\) | ||||
−0.290298 | + | 0.956936i | \(0.593754\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18351.6 | −0.728926 | −0.364463 | − | 0.931218i | \(-0.618747\pi\) | ||||
−0.364463 | + | 0.931218i | \(0.618747\pi\) | |||||||
\(860\) | −56463.6 | −2.23883 | ||||||||
\(861\) | 12663.5 | 0.501246 | ||||||||
\(862\) | −46191.3 | −1.82515 | ||||||||
\(863\) | −9255.00 | −0.365057 | −0.182528 | − | 0.983201i | \(-0.558428\pi\) | ||||
−0.182528 | + | 0.983201i | \(0.558428\pi\) | |||||||
\(864\) | −14079.0 | −0.554374 | ||||||||
\(865\) | 412.626 | 0.0162193 | ||||||||
\(866\) | −78313.3 | −3.07297 | ||||||||
\(867\) | 20104.2 | 0.787514 | ||||||||
\(868\) | 48966.5 | 1.91478 | ||||||||
\(869\) | 6808.43 | 0.265777 | ||||||||
\(870\) | 88707.5 | 3.45686 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −82066.2 | −3.18706 | ||||||||
\(873\) | 54644.4 | 2.11848 | ||||||||
\(874\) | 36573.3 | 1.41546 | ||||||||
\(875\) | −14826.3 | −0.572822 | ||||||||
\(876\) | 131111. | 5.05688 | ||||||||
\(877\) | 17153.7 | 0.660476 | 0.330238 | − | 0.943898i | \(-0.392871\pi\) | ||||
0.330238 | + | 0.943898i | \(0.392871\pi\) | |||||||
\(878\) | 54040.9 | 2.07721 | ||||||||
\(879\) | 44241.1 | 1.69763 | ||||||||
\(880\) | 9870.90 | 0.378123 | ||||||||
\(881\) | −19571.0 | −0.748428 | −0.374214 | − | 0.927342i | \(-0.622088\pi\) | ||||
−0.374214 | + | 0.927342i | \(0.622088\pi\) | |||||||
\(882\) | 57244.5 | 2.18540 | ||||||||
\(883\) | 37138.6 | 1.41542 | 0.707709 | − | 0.706505i | \(-0.249729\pi\) | ||||
0.707709 | + | 0.706505i | \(0.249729\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 69930.0 | 2.65613 | ||||||||
\(886\) | −27963.5 | −1.06033 | ||||||||
\(887\) | 11738.9 | 0.444366 | 0.222183 | − | 0.975005i | \(-0.428682\pi\) | ||||
0.222183 | + | 0.975005i | \(0.428682\pi\) | |||||||
\(888\) | −150305. | −5.68009 | ||||||||
\(889\) | −14402.7 | −0.543364 | ||||||||
\(890\) | 75505.6 | 2.84377 | ||||||||
\(891\) | −2284.65 | −0.0859018 | ||||||||
\(892\) | −53809.2 | −2.01980 | ||||||||
\(893\) | 11436.3 | 0.428557 | ||||||||
\(894\) | 14435.1 | 0.540024 | ||||||||
\(895\) | −2931.32 | −0.109479 | ||||||||
\(896\) | −21211.9 | −0.790895 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 82962.2 | 3.08294 | ||||||||
\(899\) | −58830.8 | −2.18255 | ||||||||
\(900\) | −17055.2 | −0.631676 | ||||||||
\(901\) | 2240.85 | 0.0828562 | ||||||||
\(902\) | −8135.14 | −0.300300 | ||||||||
\(903\) | −27973.9 | −1.03091 | ||||||||
\(904\) | −28019.9 | −1.03090 | ||||||||
\(905\) | −33866.1 | −1.24392 | ||||||||
\(906\) | −121151. | −4.44257 | ||||||||
\(907\) | 32379.7 | 1.18539 | 0.592696 | − | 0.805426i | \(-0.298064\pi\) | ||||
0.592696 | + | 0.805426i | \(0.298064\pi\) | |||||||
\(908\) | −59845.1 | −2.18726 | ||||||||
\(909\) | −56744.5 | −2.07051 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −39029.9 | −1.41945 | −0.709725 | − | 0.704479i | \(-0.751181\pi\) | ||||
−0.709725 | + | 0.704479i | \(0.751181\pi\) | |||||||
\(912\) | 89524.9 | 3.25051 | ||||||||
\(913\) | −3438.66 | −0.124647 | ||||||||
\(914\) | −76116.8 | −2.75462 | ||||||||
\(915\) | −22723.9 | −0.821017 | ||||||||
\(916\) | 103114. | 3.71940 | ||||||||
\(917\) | −19620.2 | −0.706562 | ||||||||
\(918\) | 72998.3 | 2.62451 | ||||||||
\(919\) | −18246.4 | −0.654944 | −0.327472 | − | 0.944861i | \(-0.606197\pi\) | ||||
−0.327472 | + | 0.944861i | \(0.606197\pi\) | |||||||
\(920\) | −28271.3 | −1.01313 | ||||||||
\(921\) | −71569.9 | −2.56059 | ||||||||
\(922\) | 78080.9 | 2.78900 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 15969.6 | 0.568573 | ||||||||
\(925\) | −8350.47 | −0.296823 | ||||||||
\(926\) | 24085.3 | 0.854744 | ||||||||
\(927\) | −14449.9 | −0.511973 | ||||||||
\(928\) | −16644.9 | −0.588790 | ||||||||
\(929\) | −21810.4 | −0.770263 | −0.385132 | − | 0.922862i | \(-0.625844\pi\) | ||||
−0.385132 | + | 0.922862i | \(0.625844\pi\) | |||||||
\(930\) | −126850. | −4.47267 | ||||||||
\(931\) | −28811.9 | −1.01426 | ||||||||
\(932\) | 4140.81 | 0.145533 | ||||||||
\(933\) | 59051.6 | 2.07209 | ||||||||
\(934\) | 6906.71 | 0.241964 | ||||||||
\(935\) | −9533.42 | −0.333451 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −42280.6 | −1.47412 | −0.737058 | − | 0.675830i | \(-0.763785\pi\) | ||||
−0.737058 | + | 0.675830i | \(0.763785\pi\) | |||||||
\(938\) | −27858.7 | −0.969742 | ||||||||
\(939\) | −16808.8 | −0.584169 | ||||||||
\(940\) | −16726.5 | −0.580380 | ||||||||
\(941\) | 29896.5 | 1.03571 | 0.517853 | − | 0.855470i | \(-0.326732\pi\) | ||||
0.517853 | + | 0.855470i | \(0.326732\pi\) | |||||||
\(942\) | −89692.1 | −3.10226 | ||||||||
\(943\) | 9174.53 | 0.316823 | ||||||||
\(944\) | −70442.2 | −2.42871 | ||||||||
\(945\) | 17373.7 | 0.598060 | ||||||||
\(946\) | 17970.6 | 0.617626 | ||||||||
\(947\) | −43408.9 | −1.48954 | −0.744772 | − | 0.667318i | \(-0.767442\pi\) | ||||
−0.744772 | + | 0.667318i | \(0.767442\pi\) | |||||||
\(948\) | −90313.7 | −3.09415 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 12631.4 | 0.431385 | ||||||||
\(951\) | 26637.3 | 0.908279 | ||||||||
\(952\) | −37964.6 | −1.29248 | ||||||||
\(953\) | −56267.7 | −1.91258 | −0.956291 | − | 0.292416i | \(-0.905541\pi\) | ||||
−0.956291 | + | 0.292416i | \(0.905541\pi\) | |||||||
\(954\) | 6173.77 | 0.209521 | ||||||||
\(955\) | −29020.7 | −0.983340 | ||||||||
\(956\) | −36717.1 | −1.24217 | ||||||||
\(957\) | −19186.7 | −0.648086 | ||||||||
\(958\) | 27668.0 | 0.933104 | ||||||||
\(959\) | 19977.4 | 0.672683 | ||||||||
\(960\) | 25844.4 | 0.868881 | ||||||||
\(961\) | 54336.1 | 1.82391 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1639.68 | −0.0548680 | ||||||||
\(964\) | −36484.8 | −1.21898 | ||||||||
\(965\) | 9064.02 | 0.302364 | ||||||||
\(966\) | −26501.3 | −0.882677 | ||||||||
\(967\) | −4785.60 | −0.159146 | −0.0795732 | − | 0.996829i | \(-0.525356\pi\) | ||||
−0.0795732 | + | 0.996829i | \(0.525356\pi\) | |||||||
\(968\) | −5422.09 | −0.180034 | ||||||||
\(969\) | −86464.2 | −2.86649 | ||||||||
\(970\) | 59191.2 | 1.95929 | ||||||||
\(971\) | 2162.54 | 0.0714720 | 0.0357360 | − | 0.999361i | \(-0.488622\pi\) | ||||
0.0357360 | + | 0.999361i | \(0.488622\pi\) | |||||||
\(972\) | −48293.7 | −1.59364 | ||||||||
\(973\) | 2703.85 | 0.0890867 | ||||||||
\(974\) | −14918.0 | −0.490763 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 22890.4 | 0.750720 | ||||||||
\(977\) | −5430.36 | −0.177822 | −0.0889112 | − | 0.996040i | \(-0.528339\pi\) | ||||
−0.0889112 | + | 0.996040i | \(0.528339\pi\) | |||||||
\(978\) | 46015.3 | 1.50451 | ||||||||
\(979\) | −16331.2 | −0.533145 | ||||||||
\(980\) | 42139.7 | 1.37357 | ||||||||
\(981\) | 85985.4 | 2.79847 | ||||||||
\(982\) | 71377.4 | 2.31949 | ||||||||
\(983\) | 18109.5 | 0.587594 | 0.293797 | − | 0.955868i | \(-0.405081\pi\) | ||||
0.293797 | + | 0.955868i | \(0.405081\pi\) | |||||||
\(984\) | 57034.0 | 1.84774 | ||||||||
\(985\) | −33496.7 | −1.08355 | ||||||||
\(986\) | 86302.3 | 2.78745 | ||||||||
\(987\) | −8286.84 | −0.267247 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −20266.6 | −0.651608 | ||||||||
\(990\) | −26265.6 | −0.843207 | ||||||||
\(991\) | 33767.4 | 1.08240 | 0.541200 | − | 0.840894i | \(-0.317970\pi\) | ||||
0.541200 | + | 0.840894i | \(0.317970\pi\) | |||||||
\(992\) | 23802.0 | 0.761808 | ||||||||
\(993\) | 24977.9 | 0.798238 | ||||||||
\(994\) | −17091.2 | −0.545373 | ||||||||
\(995\) | 11668.4 | 0.371773 | ||||||||
\(996\) | 45613.7 | 1.45113 | ||||||||
\(997\) | 36561.6 | 1.16140 | 0.580701 | − | 0.814117i | \(-0.302779\pi\) | ||||
0.580701 | + | 0.814117i | \(0.302779\pi\) | |||||||
\(998\) | 33672.1 | 1.06801 | ||||||||
\(999\) | 66919.1 | 2.11935 |
(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 | 1859.4.a.p.1.5 | ✓ | 51 | |
13.12 | even | 2 | 1859.4.a.q.1.47 | yes | 51 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1859.4.a.p.1.5 | ✓ | 51 | 1.1 | even | 1 | trivial | |
1859.4.a.q.1.47 | yes | 51 | 13.12 | even | 2 |