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: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 59x^{7} - 12x^{6} + 1144x^{5} + 345x^{4} - 7888x^{3} - 2245x^{2} + 9710x - 2988 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 143) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.765277\) of defining polynomial | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.765277 | −0.270566 | −0.135283 | − | 0.990807i | \(-0.543194\pi\) | ||||
−0.135283 | + | 0.990807i | \(0.543194\pi\) | |||||||
\(3\) | −9.54214 | −1.83639 | −0.918193 | − | 0.396133i | \(-0.870352\pi\) | ||||
−0.918193 | + | 0.396133i | \(0.870352\pi\) | |||||||
\(4\) | −7.41435 | −0.926794 | ||||||||
\(5\) | 17.1562 | 1.53450 | 0.767249 | − | 0.641350i | \(-0.221625\pi\) | ||||
0.767249 | + | 0.641350i | \(0.221625\pi\) | |||||||
\(6\) | 7.30238 | 0.496864 | ||||||||
\(7\) | 4.60754 | 0.248784 | 0.124392 | − | 0.992233i | \(-0.460302\pi\) | ||||
0.124392 | + | 0.992233i | \(0.460302\pi\) | |||||||
\(8\) | 11.7962 | 0.521326 | ||||||||
\(9\) | 64.0525 | 2.37231 | ||||||||
\(10\) | −13.1292 | −0.415183 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | 70.7488 | 1.70195 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −3.52604 | −0.0673125 | ||||||||
\(15\) | −163.707 | −2.81793 | ||||||||
\(16\) | 50.2874 | 0.785741 | ||||||||
\(17\) | −27.1592 | −0.387475 | −0.193738 | − | 0.981053i | \(-0.562061\pi\) | ||||
−0.193738 | + | 0.981053i | \(0.562061\pi\) | |||||||
\(18\) | −49.0179 | −0.641868 | ||||||||
\(19\) | 120.619 | 1.45641 | 0.728207 | − | 0.685357i | \(-0.240354\pi\) | ||||
0.728207 | + | 0.685357i | \(0.240354\pi\) | |||||||
\(20\) | −127.202 | −1.42216 | ||||||||
\(21\) | −43.9658 | −0.456863 | ||||||||
\(22\) | −8.41805 | −0.0815788 | ||||||||
\(23\) | −6.70134 | −0.0607533 | −0.0303766 | − | 0.999539i | \(-0.509671\pi\) | ||||
−0.0303766 | + | 0.999539i | \(0.509671\pi\) | |||||||
\(24\) | −112.562 | −0.957355 | ||||||||
\(25\) | 169.335 | 1.35468 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −353.560 | −2.52010 | ||||||||
\(28\) | −34.1619 | −0.230571 | ||||||||
\(29\) | −257.148 | −1.64659 | −0.823297 | − | 0.567610i | \(-0.807868\pi\) | ||||
−0.823297 | + | 0.567610i | \(0.807868\pi\) | |||||||
\(30\) | 125.281 | 0.762437 | ||||||||
\(31\) | −78.1221 | −0.452617 | −0.226309 | − | 0.974056i | \(-0.572666\pi\) | ||||
−0.226309 | + | 0.974056i | \(0.572666\pi\) | |||||||
\(32\) | −132.854 | −0.733920 | ||||||||
\(33\) | −104.964 | −0.553691 | ||||||||
\(34\) | 20.7843 | 0.104838 | ||||||||
\(35\) | 79.0479 | 0.381758 | ||||||||
\(36\) | −474.908 | −2.19865 | ||||||||
\(37\) | −348.558 | −1.54872 | −0.774359 | − | 0.632746i | \(-0.781928\pi\) | ||||
−0.774359 | + | 0.632746i | \(0.781928\pi\) | |||||||
\(38\) | −92.3069 | −0.394057 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 202.379 | 0.799973 | ||||||||
\(41\) | 66.6085 | 0.253720 | 0.126860 | − | 0.991921i | \(-0.459510\pi\) | ||||
0.126860 | + | 0.991921i | \(0.459510\pi\) | |||||||
\(42\) | 33.6460 | 0.123612 | ||||||||
\(43\) | −139.541 | −0.494878 | −0.247439 | − | 0.968903i | \(-0.579589\pi\) | ||||
−0.247439 | + | 0.968903i | \(0.579589\pi\) | |||||||
\(44\) | −81.5579 | −0.279439 | ||||||||
\(45\) | 1098.90 | 3.64031 | ||||||||
\(46\) | 5.12838 | 0.0164378 | ||||||||
\(47\) | −56.5721 | −0.175572 | −0.0877860 | − | 0.996139i | \(-0.527979\pi\) | ||||
−0.0877860 | + | 0.996139i | \(0.527979\pi\) | |||||||
\(48\) | −479.850 | −1.44292 | ||||||||
\(49\) | −321.771 | −0.938107 | ||||||||
\(50\) | −129.588 | −0.366531 | ||||||||
\(51\) | 259.157 | 0.711554 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 527.757 | 1.36779 | 0.683896 | − | 0.729580i | \(-0.260284\pi\) | ||||
0.683896 | + | 0.729580i | \(0.260284\pi\) | |||||||
\(54\) | 270.572 | 0.681854 | ||||||||
\(55\) | 188.718 | 0.462668 | ||||||||
\(56\) | 54.3517 | 0.129697 | ||||||||
\(57\) | −1150.96 | −2.67454 | ||||||||
\(58\) | 196.790 | 0.445513 | ||||||||
\(59\) | 333.407 | 0.735694 | 0.367847 | − | 0.929886i | \(-0.380095\pi\) | ||||
0.367847 | + | 0.929886i | \(0.380095\pi\) | |||||||
\(60\) | 1213.78 | 2.61164 | ||||||||
\(61\) | 548.859 | 1.15204 | 0.576018 | − | 0.817437i | \(-0.304606\pi\) | ||||
0.576018 | + | 0.817437i | \(0.304606\pi\) | |||||||
\(62\) | 59.7850 | 0.122463 | ||||||||
\(63\) | 295.124 | 0.590193 | ||||||||
\(64\) | −300.629 | −0.587167 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 80.3262 | 0.149810 | ||||||||
\(67\) | 211.547 | 0.385740 | 0.192870 | − | 0.981224i | \(-0.438220\pi\) | ||||
0.192870 | + | 0.981224i | \(0.438220\pi\) | |||||||
\(68\) | 201.368 | 0.359110 | ||||||||
\(69\) | 63.9451 | 0.111567 | ||||||||
\(70\) | −60.4935 | −0.103291 | ||||||||
\(71\) | −846.848 | −1.41553 | −0.707763 | − | 0.706450i | \(-0.750296\pi\) | ||||
−0.707763 | + | 0.706450i | \(0.750296\pi\) | |||||||
\(72\) | 755.579 | 1.23675 | ||||||||
\(73\) | −540.090 | −0.865928 | −0.432964 | − | 0.901411i | \(-0.642532\pi\) | ||||
−0.432964 | + | 0.901411i | \(0.642532\pi\) | |||||||
\(74\) | 266.744 | 0.419031 | ||||||||
\(75\) | −1615.82 | −2.48772 | ||||||||
\(76\) | −894.311 | −1.34980 | ||||||||
\(77\) | 50.6829 | 0.0750111 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1294.67 | −1.84382 | −0.921909 | − | 0.387406i | \(-0.873371\pi\) | ||||
−0.921909 | + | 0.387406i | \(0.873371\pi\) | |||||||
\(80\) | 862.741 | 1.20572 | ||||||||
\(81\) | 1644.30 | 2.25556 | ||||||||
\(82\) | −50.9740 | −0.0686480 | ||||||||
\(83\) | 1460.55 | 1.93153 | 0.965763 | − | 0.259425i | \(-0.0835330\pi\) | ||||
0.965763 | + | 0.259425i | \(0.0835330\pi\) | |||||||
\(84\) | 325.978 | 0.423418 | ||||||||
\(85\) | −465.949 | −0.594580 | ||||||||
\(86\) | 106.787 | 0.133897 | ||||||||
\(87\) | 2453.75 | 3.02378 | ||||||||
\(88\) | 129.759 | 0.157186 | ||||||||
\(89\) | 393.293 | 0.468415 | 0.234208 | − | 0.972187i | \(-0.424750\pi\) | ||||
0.234208 | + | 0.972187i | \(0.424750\pi\) | |||||||
\(90\) | −840.961 | −0.984946 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 49.6861 | 0.0563058 | ||||||||
\(93\) | 745.452 | 0.831180 | ||||||||
\(94\) | 43.2933 | 0.0475039 | ||||||||
\(95\) | 2069.36 | 2.23487 | ||||||||
\(96\) | 1267.71 | 1.34776 | ||||||||
\(97\) | 51.8927 | 0.0543186 | 0.0271593 | − | 0.999631i | \(-0.491354\pi\) | ||||
0.0271593 | + | 0.999631i | \(0.491354\pi\) | |||||||
\(98\) | 246.244 | 0.253820 | ||||||||
\(99\) | 704.577 | 0.715280 | ||||||||
\(100\) | −1255.51 | −1.25551 | ||||||||
\(101\) | −1608.92 | −1.58508 | −0.792542 | − | 0.609817i | \(-0.791243\pi\) | ||||
−0.792542 | + | 0.609817i | \(0.791243\pi\) | |||||||
\(102\) | −198.327 | −0.192523 | ||||||||
\(103\) | 1279.86 | 1.22435 | 0.612176 | − | 0.790721i | \(-0.290294\pi\) | ||||
0.612176 | + | 0.790721i | \(0.290294\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −754.286 | −0.701055 | ||||||||
\(106\) | −403.880 | −0.370078 | ||||||||
\(107\) | 195.933 | 0.177024 | 0.0885121 | − | 0.996075i | \(-0.471789\pi\) | ||||
0.0885121 | + | 0.996075i | \(0.471789\pi\) | |||||||
\(108\) | 2621.42 | 2.33561 | ||||||||
\(109\) | −1301.97 | −1.14409 | −0.572046 | − | 0.820222i | \(-0.693850\pi\) | ||||
−0.572046 | + | 0.820222i | \(0.693850\pi\) | |||||||
\(110\) | −144.422 | −0.125182 | ||||||||
\(111\) | 3325.99 | 2.84405 | ||||||||
\(112\) | 231.701 | 0.195479 | ||||||||
\(113\) | 455.508 | 0.379209 | 0.189604 | − | 0.981861i | \(-0.439279\pi\) | ||||
0.189604 | + | 0.981861i | \(0.439279\pi\) | |||||||
\(114\) | 880.806 | 0.723641 | ||||||||
\(115\) | −114.970 | −0.0932258 | ||||||||
\(116\) | 1906.59 | 1.52605 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −255.149 | −0.199054 | ||||||||
\(119\) | −125.137 | −0.0963975 | ||||||||
\(120\) | −1931.13 | −1.46906 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | −420.029 | −0.311702 | ||||||||
\(123\) | −635.588 | −0.465927 | ||||||||
\(124\) | 579.224 | 0.419483 | ||||||||
\(125\) | 760.626 | 0.544260 | ||||||||
\(126\) | −225.852 | −0.159686 | ||||||||
\(127\) | −92.1973 | −0.0644188 | −0.0322094 | − | 0.999481i | \(-0.510254\pi\) | ||||
−0.0322094 | + | 0.999481i | \(0.510254\pi\) | |||||||
\(128\) | 1292.90 | 0.892788 | ||||||||
\(129\) | 1331.52 | 0.908788 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 270.704 | 0.180546 | 0.0902731 | − | 0.995917i | \(-0.471226\pi\) | ||||
0.0902731 | + | 0.995917i | \(0.471226\pi\) | |||||||
\(132\) | 778.237 | 0.513158 | ||||||||
\(133\) | 555.756 | 0.362332 | ||||||||
\(134\) | −161.892 | −0.104368 | ||||||||
\(135\) | −6065.75 | −3.86709 | ||||||||
\(136\) | −320.377 | −0.202001 | ||||||||
\(137\) | −2631.89 | −1.64129 | −0.820646 | − | 0.571436i | \(-0.806386\pi\) | ||||
−0.820646 | + | 0.571436i | \(0.806386\pi\) | |||||||
\(138\) | −48.9357 | −0.0301861 | ||||||||
\(139\) | 1986.23 | 1.21201 | 0.606006 | − | 0.795460i | \(-0.292771\pi\) | ||||
0.606006 | + | 0.795460i | \(0.292771\pi\) | |||||||
\(140\) | −586.089 | −0.353811 | ||||||||
\(141\) | 539.819 | 0.322418 | ||||||||
\(142\) | 648.073 | 0.382994 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 3221.03 | 1.86402 | ||||||||
\(145\) | −4411.69 | −2.52670 | ||||||||
\(146\) | 413.318 | 0.234291 | ||||||||
\(147\) | 3070.38 | 1.72273 | ||||||||
\(148\) | 2584.33 | 1.43534 | ||||||||
\(149\) | −817.443 | −0.449446 | −0.224723 | − | 0.974423i | \(-0.572148\pi\) | ||||
−0.224723 | + | 0.974423i | \(0.572148\pi\) | |||||||
\(150\) | 1236.55 | 0.673093 | ||||||||
\(151\) | 1584.77 | 0.854082 | 0.427041 | − | 0.904232i | \(-0.359556\pi\) | ||||
0.427041 | + | 0.904232i | \(0.359556\pi\) | |||||||
\(152\) | 1422.85 | 0.759266 | ||||||||
\(153\) | −1739.62 | −0.919213 | ||||||||
\(154\) | −38.7865 | −0.0202955 | ||||||||
\(155\) | −1340.28 | −0.694540 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 300.034 | 0.152518 | 0.0762589 | − | 0.997088i | \(-0.475702\pi\) | ||||
0.0762589 | + | 0.997088i | \(0.475702\pi\) | |||||||
\(158\) | 990.781 | 0.498875 | ||||||||
\(159\) | −5035.93 | −2.51179 | ||||||||
\(160\) | −2279.27 | −1.12620 | ||||||||
\(161\) | −30.8767 | −0.0151144 | ||||||||
\(162\) | −1258.35 | −0.610279 | ||||||||
\(163\) | −1764.24 | −0.847766 | −0.423883 | − | 0.905717i | \(-0.639333\pi\) | ||||
−0.423883 | + | 0.905717i | \(0.639333\pi\) | |||||||
\(164\) | −493.859 | −0.235146 | ||||||||
\(165\) | −1800.78 | −0.849638 | ||||||||
\(166\) | −1117.73 | −0.522606 | ||||||||
\(167\) | 2262.97 | 1.04858 | 0.524292 | − | 0.851538i | \(-0.324330\pi\) | ||||
0.524292 | + | 0.851538i | \(0.324330\pi\) | |||||||
\(168\) | −518.631 | −0.238174 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 356.580 | 0.160873 | ||||||||
\(171\) | 7725.94 | 3.45507 | ||||||||
\(172\) | 1034.60 | 0.458650 | ||||||||
\(173\) | −3704.00 | −1.62780 | −0.813901 | − | 0.581003i | \(-0.802660\pi\) | ||||
−0.813901 | + | 0.581003i | \(0.802660\pi\) | |||||||
\(174\) | −1877.80 | −0.818134 | ||||||||
\(175\) | 780.219 | 0.337023 | ||||||||
\(176\) | 553.161 | 0.236910 | ||||||||
\(177\) | −3181.42 | −1.35102 | ||||||||
\(178\) | −300.978 | −0.126737 | ||||||||
\(179\) | −1024.05 | −0.427604 | −0.213802 | − | 0.976877i | \(-0.568585\pi\) | ||||
−0.213802 | + | 0.976877i | \(0.568585\pi\) | |||||||
\(180\) | −8147.61 | −3.37382 | ||||||||
\(181\) | 3561.20 | 1.46244 | 0.731221 | − | 0.682141i | \(-0.238951\pi\) | ||||
0.731221 | + | 0.682141i | \(0.238951\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5237.29 | −2.11558 | ||||||||
\(184\) | −79.0507 | −0.0316722 | ||||||||
\(185\) | −5979.93 | −2.37651 | ||||||||
\(186\) | −570.477 | −0.224889 | ||||||||
\(187\) | −298.751 | −0.116828 | ||||||||
\(188\) | 419.445 | 0.162719 | ||||||||
\(189\) | −1629.04 | −0.626960 | ||||||||
\(190\) | −1583.64 | −0.604679 | ||||||||
\(191\) | −4947.45 | −1.87427 | −0.937134 | − | 0.348971i | \(-0.886531\pi\) | ||||
−0.937134 | + | 0.348971i | \(0.886531\pi\) | |||||||
\(192\) | 2868.65 | 1.07826 | ||||||||
\(193\) | −4032.80 | −1.50408 | −0.752039 | − | 0.659118i | \(-0.770930\pi\) | ||||
−0.752039 | + | 0.659118i | \(0.770930\pi\) | |||||||
\(194\) | −39.7123 | −0.0146968 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2385.72 | 0.869432 | ||||||||
\(197\) | 3930.21 | 1.42140 | 0.710700 | − | 0.703495i | \(-0.248378\pi\) | ||||
0.710700 | + | 0.703495i | \(0.248378\pi\) | |||||||
\(198\) | −539.197 | −0.193531 | ||||||||
\(199\) | 1404.23 | 0.500217 | 0.250109 | − | 0.968218i | \(-0.419534\pi\) | ||||
0.250109 | + | 0.968218i | \(0.419534\pi\) | |||||||
\(200\) | 1997.52 | 0.706231 | ||||||||
\(201\) | −2018.61 | −0.708368 | ||||||||
\(202\) | 1231.27 | 0.428870 | ||||||||
\(203\) | −1184.82 | −0.409646 | ||||||||
\(204\) | −1921.48 | −0.659464 | ||||||||
\(205\) | 1142.75 | 0.389332 | ||||||||
\(206\) | −979.447 | −0.331268 | ||||||||
\(207\) | −429.238 | −0.144126 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1326.81 | 0.439126 | ||||||||
\(210\) | 577.238 | 0.189682 | ||||||||
\(211\) | −5389.48 | −1.75842 | −0.879211 | − | 0.476432i | \(-0.841930\pi\) | ||||
−0.879211 | + | 0.476432i | \(0.841930\pi\) | |||||||
\(212\) | −3912.97 | −1.26766 | ||||||||
\(213\) | 8080.75 | 2.59945 | ||||||||
\(214\) | −149.943 | −0.0478968 | ||||||||
\(215\) | −2393.99 | −0.759389 | ||||||||
\(216\) | −4170.68 | −1.31379 | ||||||||
\(217\) | −359.950 | −0.112604 | ||||||||
\(218\) | 996.367 | 0.309553 | ||||||||
\(219\) | 5153.61 | 1.59018 | ||||||||
\(220\) | −1399.22 | −0.428798 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −2545.31 | −0.769503 | ||||||||
\(223\) | 4999.29 | 1.50124 | 0.750621 | − | 0.660733i | \(-0.229754\pi\) | ||||
0.750621 | + | 0.660733i | \(0.229754\pi\) | |||||||
\(224\) | −612.129 | −0.182587 | ||||||||
\(225\) | 10846.4 | 3.21373 | ||||||||
\(226\) | −348.590 | −0.102601 | ||||||||
\(227\) | −1621.30 | −0.474051 | −0.237025 | − | 0.971503i | \(-0.576172\pi\) | ||||
−0.237025 | + | 0.971503i | \(0.576172\pi\) | |||||||
\(228\) | 8533.65 | 2.47875 | ||||||||
\(229\) | −1980.22 | −0.571426 | −0.285713 | − | 0.958315i | \(-0.592230\pi\) | ||||
−0.285713 | + | 0.958315i | \(0.592230\pi\) | |||||||
\(230\) | 87.9836 | 0.0252238 | ||||||||
\(231\) | −483.624 | −0.137749 | ||||||||
\(232\) | −3033.39 | −0.858412 | ||||||||
\(233\) | 696.381 | 0.195800 | 0.0979001 | − | 0.995196i | \(-0.468787\pi\) | ||||
0.0979001 | + | 0.995196i | \(0.468787\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −970.562 | −0.269415 | ||||||||
\(236\) | −2472.00 | −0.681836 | ||||||||
\(237\) | 12353.9 | 3.38596 | ||||||||
\(238\) | 95.7646 | 0.0260819 | ||||||||
\(239\) | 1909.56 | 0.516816 | 0.258408 | − | 0.966036i | \(-0.416802\pi\) | ||||
0.258408 | + | 0.966036i | \(0.416802\pi\) | |||||||
\(240\) | −8232.40 | −2.21416 | ||||||||
\(241\) | −4527.84 | −1.21022 | −0.605112 | − | 0.796141i | \(-0.706872\pi\) | ||||
−0.605112 | + | 0.796141i | \(0.706872\pi\) | |||||||
\(242\) | −92.5985 | −0.0245969 | ||||||||
\(243\) | −6144.07 | −1.62198 | ||||||||
\(244\) | −4069.43 | −1.06770 | ||||||||
\(245\) | −5520.36 | −1.43952 | ||||||||
\(246\) | 486.401 | 0.126064 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −921.547 | −0.235961 | ||||||||
\(249\) | −13936.8 | −3.54703 | ||||||||
\(250\) | −582.090 | −0.147258 | ||||||||
\(251\) | −3625.62 | −0.911742 | −0.455871 | − | 0.890046i | \(-0.650672\pi\) | ||||
−0.455871 | + | 0.890046i | \(0.650672\pi\) | |||||||
\(252\) | −2188.16 | −0.546987 | ||||||||
\(253\) | −73.7147 | −0.0183178 | ||||||||
\(254\) | 70.5565 | 0.0174296 | ||||||||
\(255\) | 4446.15 | 1.09188 | ||||||||
\(256\) | 1415.61 | 0.345608 | ||||||||
\(257\) | −33.4012 | −0.00810703 | −0.00405351 | − | 0.999992i | \(-0.501290\pi\) | ||||
−0.00405351 | + | 0.999992i | \(0.501290\pi\) | |||||||
\(258\) | −1018.98 | −0.245887 | ||||||||
\(259\) | −1605.99 | −0.385296 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −16471.0 | −3.90624 | ||||||||
\(262\) | −207.164 | −0.0488497 | ||||||||
\(263\) | 885.980 | 0.207726 | 0.103863 | − | 0.994592i | \(-0.466880\pi\) | ||||
0.103863 | + | 0.994592i | \(0.466880\pi\) | |||||||
\(264\) | −1238.18 | −0.288653 | ||||||||
\(265\) | 9054.30 | 2.09887 | ||||||||
\(266\) | −425.308 | −0.0980349 | ||||||||
\(267\) | −3752.86 | −0.860191 | ||||||||
\(268\) | −1568.48 | −0.357501 | ||||||||
\(269\) | −1464.23 | −0.331881 | −0.165940 | − | 0.986136i | \(-0.553066\pi\) | ||||
−0.165940 | + | 0.986136i | \(0.553066\pi\) | |||||||
\(270\) | 4641.98 | 1.04630 | ||||||||
\(271\) | −1010.25 | −0.226452 | −0.113226 | − | 0.993569i | \(-0.536118\pi\) | ||||
−0.113226 | + | 0.993569i | \(0.536118\pi\) | |||||||
\(272\) | −1365.77 | −0.304455 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2014.12 | 0.444079 | ||||||||
\(275\) | 1862.69 | 0.408452 | ||||||||
\(276\) | −474.112 | −0.103399 | ||||||||
\(277\) | 5869.48 | 1.27315 | 0.636576 | − | 0.771214i | \(-0.280350\pi\) | ||||
0.636576 | + | 0.771214i | \(0.280350\pi\) | |||||||
\(278\) | −1520.01 | −0.327930 | ||||||||
\(279\) | −5003.91 | −1.07375 | ||||||||
\(280\) | 932.468 | 0.199020 | ||||||||
\(281\) | −5296.86 | −1.12450 | −0.562249 | − | 0.826968i | \(-0.690064\pi\) | ||||
−0.562249 | + | 0.826968i | \(0.690064\pi\) | |||||||
\(282\) | −413.111 | −0.0872354 | ||||||||
\(283\) | 9032.41 | 1.89725 | 0.948624 | − | 0.316407i | \(-0.102476\pi\) | ||||
0.948624 | + | 0.316407i | \(0.102476\pi\) | |||||||
\(284\) | 6278.83 | 1.31190 | ||||||||
\(285\) | −19746.2 | −4.10408 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 306.901 | 0.0631213 | ||||||||
\(288\) | −8509.62 | −1.74109 | ||||||||
\(289\) | −4175.38 | −0.849863 | ||||||||
\(290\) | 3376.17 | 0.683639 | ||||||||
\(291\) | −495.168 | −0.0997500 | ||||||||
\(292\) | 4004.41 | 0.802536 | ||||||||
\(293\) | 1016.00 | 0.202578 | 0.101289 | − | 0.994857i | \(-0.467703\pi\) | ||||
0.101289 | + | 0.994857i | \(0.467703\pi\) | |||||||
\(294\) | −2349.69 | −0.466112 | ||||||||
\(295\) | 5720.00 | 1.12892 | ||||||||
\(296\) | −4111.68 | −0.807387 | ||||||||
\(297\) | −3889.16 | −0.759839 | ||||||||
\(298\) | 625.570 | 0.121605 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 11980.3 | 2.30560 | ||||||||
\(301\) | −642.939 | −0.123118 | ||||||||
\(302\) | −1212.78 | −0.231086 | ||||||||
\(303\) | 15352.5 | 2.91083 | ||||||||
\(304\) | 6065.61 | 1.14436 | ||||||||
\(305\) | 9416.33 | 1.76780 | ||||||||
\(306\) | 1331.29 | 0.248708 | ||||||||
\(307\) | −5978.71 | −1.11148 | −0.555738 | − | 0.831357i | \(-0.687564\pi\) | ||||
−0.555738 | + | 0.831357i | \(0.687564\pi\) | |||||||
\(308\) | −375.781 | −0.0695198 | ||||||||
\(309\) | −12212.6 | −2.24838 | ||||||||
\(310\) | 1025.68 | 0.187919 | ||||||||
\(311\) | −7881.59 | −1.43705 | −0.718527 | − | 0.695499i | \(-0.755183\pi\) | ||||
−0.718527 | + | 0.695499i | \(0.755183\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6214.18 | −1.12219 | −0.561096 | − | 0.827751i | \(-0.689620\pi\) | ||||
−0.561096 | + | 0.827751i | \(0.689620\pi\) | |||||||
\(314\) | −229.609 | −0.0412662 | ||||||||
\(315\) | 5063.21 | 0.905650 | ||||||||
\(316\) | 9599.13 | 1.70884 | ||||||||
\(317\) | −7409.37 | −1.31278 | −0.656391 | − | 0.754421i | \(-0.727918\pi\) | ||||
−0.656391 | + | 0.754421i | \(0.727918\pi\) | |||||||
\(318\) | 3853.88 | 0.679607 | ||||||||
\(319\) | −2828.63 | −0.496467 | ||||||||
\(320\) | −5157.66 | −0.901006 | ||||||||
\(321\) | −1869.62 | −0.325085 | ||||||||
\(322\) | 23.6292 | 0.00408945 | ||||||||
\(323\) | −3275.92 | −0.564325 | ||||||||
\(324\) | −12191.5 | −2.09044 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1350.13 | 0.229377 | ||||||||
\(327\) | 12423.6 | 2.10099 | ||||||||
\(328\) | 785.730 | 0.132270 | ||||||||
\(329\) | −260.658 | −0.0436794 | ||||||||
\(330\) | 1378.09 | 0.229883 | ||||||||
\(331\) | −8130.48 | −1.35013 | −0.675063 | − | 0.737760i | \(-0.735883\pi\) | ||||
−0.675063 | + | 0.737760i | \(0.735883\pi\) | |||||||
\(332\) | −10829.1 | −1.79013 | ||||||||
\(333\) | −22326.0 | −3.67405 | ||||||||
\(334\) | −1731.80 | −0.283712 | ||||||||
\(335\) | 3629.34 | 0.591917 | ||||||||
\(336\) | −2210.93 | −0.358976 | ||||||||
\(337\) | 4741.96 | 0.766502 | 0.383251 | − | 0.923644i | \(-0.374805\pi\) | ||||
0.383251 | + | 0.923644i | \(0.374805\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4346.52 | −0.696374 | ||||||||
\(340\) | 3454.71 | 0.551053 | ||||||||
\(341\) | −859.343 | −0.136469 | ||||||||
\(342\) | −5912.49 | −0.934827 | ||||||||
\(343\) | −3062.96 | −0.482169 | ||||||||
\(344\) | −1646.06 | −0.257993 | ||||||||
\(345\) | 1097.06 | 0.171199 | ||||||||
\(346\) | 2834.59 | 0.440429 | ||||||||
\(347\) | 4248.16 | 0.657214 | 0.328607 | − | 0.944467i | \(-0.393421\pi\) | ||||
0.328607 | + | 0.944467i | \(0.393421\pi\) | |||||||
\(348\) | −18192.9 | −2.80242 | ||||||||
\(349\) | 3888.51 | 0.596411 | 0.298205 | − | 0.954502i | \(-0.403612\pi\) | ||||
0.298205 | + | 0.954502i | \(0.403612\pi\) | |||||||
\(350\) | −597.084 | −0.0911870 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1461.39 | −0.221285 | ||||||||
\(353\) | −286.193 | −0.0431516 | −0.0215758 | − | 0.999767i | \(-0.506868\pi\) | ||||
−0.0215758 | + | 0.999767i | \(0.506868\pi\) | |||||||
\(354\) | 2434.67 | 0.365540 | ||||||||
\(355\) | −14528.7 | −2.17212 | ||||||||
\(356\) | −2916.01 | −0.434124 | ||||||||
\(357\) | 1194.08 | 0.177023 | ||||||||
\(358\) | 783.682 | 0.115695 | ||||||||
\(359\) | −2797.34 | −0.411248 | −0.205624 | − | 0.978631i | \(-0.565922\pi\) | ||||
−0.205624 | + | 0.978631i | \(0.565922\pi\) | |||||||
\(360\) | 12962.9 | 1.89779 | ||||||||
\(361\) | 7689.93 | 1.12114 | ||||||||
\(362\) | −2725.31 | −0.395688 | ||||||||
\(363\) | −1154.60 | −0.166944 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9265.89 | −1.32876 | ||||||||
\(366\) | 4007.98 | 0.572405 | ||||||||
\(367\) | 9825.39 | 1.39750 | 0.698748 | − | 0.715367i | \(-0.253741\pi\) | ||||
0.698748 | + | 0.715367i | \(0.253741\pi\) | |||||||
\(368\) | −336.993 | −0.0477363 | ||||||||
\(369\) | 4266.44 | 0.601903 | ||||||||
\(370\) | 4576.31 | 0.643002 | ||||||||
\(371\) | 2431.66 | 0.340284 | ||||||||
\(372\) | −5527.04 | −0.770333 | ||||||||
\(373\) | −7772.12 | −1.07889 | −0.539444 | − | 0.842022i | \(-0.681365\pi\) | ||||
−0.539444 | + | 0.842022i | \(0.681365\pi\) | |||||||
\(374\) | 228.628 | 0.0316098 | ||||||||
\(375\) | −7258.00 | −0.999471 | ||||||||
\(376\) | −667.338 | −0.0915301 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1246.67 | 0.169634 | ||||||||
\(379\) | 4645.18 | 0.629570 | 0.314785 | − | 0.949163i | \(-0.398068\pi\) | ||||
0.314785 | + | 0.949163i | \(0.398068\pi\) | |||||||
\(380\) | −15343.0 | −2.07126 | ||||||||
\(381\) | 879.760 | 0.118298 | ||||||||
\(382\) | 3786.17 | 0.507114 | ||||||||
\(383\) | −5414.13 | −0.722322 | −0.361161 | − | 0.932503i | \(-0.617620\pi\) | ||||
−0.361161 | + | 0.932503i | \(0.617620\pi\) | |||||||
\(384\) | −12337.0 | −1.63950 | ||||||||
\(385\) | 869.526 | 0.115104 | ||||||||
\(386\) | 3086.21 | 0.406953 | ||||||||
\(387\) | −8937.93 | −1.17401 | ||||||||
\(388\) | −384.751 | −0.0503422 | ||||||||
\(389\) | 5464.02 | 0.712176 | 0.356088 | − | 0.934452i | \(-0.384110\pi\) | ||||
0.356088 | + | 0.934452i | \(0.384110\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 182.003 | 0.0235404 | ||||||||
\(392\) | −3795.69 | −0.489059 | ||||||||
\(393\) | −2583.10 | −0.331553 | ||||||||
\(394\) | −3007.70 | −0.384583 | ||||||||
\(395\) | −22211.6 | −2.82934 | ||||||||
\(396\) | −5223.98 | −0.662917 | ||||||||
\(397\) | −761.736 | −0.0962984 | −0.0481492 | − | 0.998840i | \(-0.515332\pi\) | ||||
−0.0481492 | + | 0.998840i | \(0.515332\pi\) | |||||||
\(398\) | −1074.63 | −0.135342 | ||||||||
\(399\) | −5303.11 | −0.665382 | ||||||||
\(400\) | 8515.43 | 1.06443 | ||||||||
\(401\) | −1168.07 | −0.145463 | −0.0727313 | − | 0.997352i | \(-0.523172\pi\) | ||||
−0.0727313 | + | 0.997352i | \(0.523172\pi\) | |||||||
\(402\) | 1544.80 | 0.191660 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 11929.1 | 1.46905 | ||||||||
\(405\) | 28210.0 | 3.46115 | ||||||||
\(406\) | 906.716 | 0.110836 | ||||||||
\(407\) | −3834.14 | −0.466956 | ||||||||
\(408\) | 3057.08 | 0.370951 | ||||||||
\(409\) | 6496.98 | 0.785464 | 0.392732 | − | 0.919653i | \(-0.371530\pi\) | ||||
0.392732 | + | 0.919653i | \(0.371530\pi\) | |||||||
\(410\) | −874.520 | −0.105340 | ||||||||
\(411\) | 25113.8 | 3.01405 | ||||||||
\(412\) | −9489.33 | −1.13472 | ||||||||
\(413\) | 1536.19 | 0.183029 | ||||||||
\(414\) | 328.486 | 0.0389956 | ||||||||
\(415\) | 25057.6 | 2.96392 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −18952.9 | −2.22572 | ||||||||
\(418\) | −1015.38 | −0.118813 | ||||||||
\(419\) | −1130.92 | −0.131859 | −0.0659297 | − | 0.997824i | \(-0.521001\pi\) | ||||
−0.0659297 | + | 0.997824i | \(0.521001\pi\) | |||||||
\(420\) | 5592.54 | 0.649733 | ||||||||
\(421\) | 1999.44 | 0.231465 | 0.115732 | − | 0.993280i | \(-0.463079\pi\) | ||||
0.115732 | + | 0.993280i | \(0.463079\pi\) | |||||||
\(422\) | 4124.45 | 0.475770 | ||||||||
\(423\) | −3623.58 | −0.416512 | ||||||||
\(424\) | 6225.55 | 0.713064 | ||||||||
\(425\) | −4599.02 | −0.524906 | ||||||||
\(426\) | −6184.01 | −0.703324 | ||||||||
\(427\) | 2528.89 | 0.286608 | ||||||||
\(428\) | −1452.72 | −0.164065 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1832.07 | 0.205465 | ||||||||
\(431\) | 7360.14 | 0.822565 | 0.411282 | − | 0.911508i | \(-0.365081\pi\) | ||||
0.411282 | + | 0.911508i | \(0.365081\pi\) | |||||||
\(432\) | −17779.6 | −1.98015 | ||||||||
\(433\) | 6965.19 | 0.773038 | 0.386519 | − | 0.922281i | \(-0.373677\pi\) | ||||
0.386519 | + | 0.922281i | \(0.373677\pi\) | |||||||
\(434\) | 275.462 | 0.0304668 | ||||||||
\(435\) | 42097.0 | 4.63999 | ||||||||
\(436\) | 9653.26 | 1.06034 | ||||||||
\(437\) | −808.308 | −0.0884820 | ||||||||
\(438\) | −3943.94 | −0.430248 | ||||||||
\(439\) | 6034.51 | 0.656063 | 0.328031 | − | 0.944667i | \(-0.393615\pi\) | ||||
0.328031 | + | 0.944667i | \(0.393615\pi\) | |||||||
\(440\) | 2226.17 | 0.241201 | ||||||||
\(441\) | −20610.2 | −2.22548 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8249.55 | 0.884759 | 0.442379 | − | 0.896828i | \(-0.354134\pi\) | ||||
0.442379 | + | 0.896828i | \(0.354134\pi\) | |||||||
\(444\) | −24660.1 | −2.63584 | ||||||||
\(445\) | 6747.41 | 0.718782 | ||||||||
\(446\) | −3825.84 | −0.406186 | ||||||||
\(447\) | 7800.16 | 0.825357 | ||||||||
\(448\) | −1385.16 | −0.146077 | ||||||||
\(449\) | −7293.54 | −0.766600 | −0.383300 | − | 0.923624i | \(-0.625212\pi\) | ||||
−0.383300 | + | 0.923624i | \(0.625212\pi\) | |||||||
\(450\) | −8300.46 | −0.869528 | ||||||||
\(451\) | 732.694 | 0.0764993 | ||||||||
\(452\) | −3377.30 | −0.351448 | ||||||||
\(453\) | −15122.1 | −1.56842 | ||||||||
\(454\) | 1240.74 | 0.128262 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −13577.0 | −1.39431 | ||||||||
\(457\) | 1476.68 | 0.151151 | 0.0755756 | − | 0.997140i | \(-0.475921\pi\) | ||||
0.0755756 | + | 0.997140i | \(0.475921\pi\) | |||||||
\(458\) | 1515.42 | 0.154609 | ||||||||
\(459\) | 9602.42 | 0.976476 | ||||||||
\(460\) | 852.425 | 0.0864011 | ||||||||
\(461\) | 3162.07 | 0.319463 | 0.159731 | − | 0.987161i | \(-0.448937\pi\) | ||||
0.159731 | + | 0.987161i | \(0.448937\pi\) | |||||||
\(462\) | 370.106 | 0.0372703 | ||||||||
\(463\) | 6371.33 | 0.639527 | 0.319763 | − | 0.947497i | \(-0.396397\pi\) | ||||
0.319763 | + | 0.947497i | \(0.396397\pi\) | |||||||
\(464\) | −12931.3 | −1.29380 | ||||||||
\(465\) | 12789.1 | 1.27544 | ||||||||
\(466\) | −532.925 | −0.0529769 | ||||||||
\(467\) | 14599.9 | 1.44668 | 0.723341 | − | 0.690491i | \(-0.242605\pi\) | ||||
0.723341 | + | 0.690491i | \(0.242605\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 974.711 | 0.0959658 | ||||||||
\(470\) | 742.749 | 0.0728945 | ||||||||
\(471\) | −2862.97 | −0.280082 | ||||||||
\(472\) | 3932.95 | 0.383536 | ||||||||
\(473\) | −1534.95 | −0.149211 | ||||||||
\(474\) | −9454.17 | −0.916128 | ||||||||
\(475\) | 20425.0 | 1.97298 | ||||||||
\(476\) | 927.811 | 0.0893406 | ||||||||
\(477\) | 33804.1 | 3.24483 | ||||||||
\(478\) | −1461.34 | −0.139833 | ||||||||
\(479\) | −1662.93 | −0.158624 | −0.0793122 | − | 0.996850i | \(-0.525272\pi\) | ||||
−0.0793122 | + | 0.996850i | \(0.525272\pi\) | |||||||
\(480\) | 21749.1 | 2.06814 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 3465.05 | 0.327446 | ||||||||
\(483\) | 294.630 | 0.0277559 | ||||||||
\(484\) | −897.136 | −0.0842540 | ||||||||
\(485\) | 890.282 | 0.0833518 | ||||||||
\(486\) | 4701.91 | 0.438854 | ||||||||
\(487\) | 924.268 | 0.0860012 | 0.0430006 | − | 0.999075i | \(-0.486308\pi\) | ||||
0.0430006 | + | 0.999075i | \(0.486308\pi\) | |||||||
\(488\) | 6474.48 | 0.600586 | ||||||||
\(489\) | 16834.6 | 1.55683 | ||||||||
\(490\) | 4224.61 | 0.389486 | ||||||||
\(491\) | 5265.07 | 0.483930 | 0.241965 | − | 0.970285i | \(-0.422208\pi\) | ||||
0.241965 | + | 0.970285i | \(0.422208\pi\) | |||||||
\(492\) | 4712.47 | 0.431818 | ||||||||
\(493\) | 6983.95 | 0.638015 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 12087.9 | 1.09760 | ||||||||
\(496\) | −3928.56 | −0.355640 | ||||||||
\(497\) | −3901.88 | −0.352160 | ||||||||
\(498\) | 10665.5 | 0.959707 | ||||||||
\(499\) | −12609.2 | −1.13120 | −0.565598 | − | 0.824681i | \(-0.691354\pi\) | ||||
−0.565598 | + | 0.824681i | \(0.691354\pi\) | |||||||
\(500\) | −5639.55 | −0.504416 | ||||||||
\(501\) | −21593.6 | −1.92561 | ||||||||
\(502\) | 2774.61 | 0.246687 | ||||||||
\(503\) | −491.059 | −0.0435293 | −0.0217647 | − | 0.999763i | \(-0.506928\pi\) | ||||
−0.0217647 | + | 0.999763i | \(0.506928\pi\) | |||||||
\(504\) | 3481.36 | 0.307683 | ||||||||
\(505\) | −27603.0 | −2.43231 | ||||||||
\(506\) | 56.4122 | 0.00495618 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 683.583 | 0.0597030 | ||||||||
\(509\) | 9036.02 | 0.786866 | 0.393433 | − | 0.919353i | \(-0.371287\pi\) | ||||
0.393433 | + | 0.919353i | \(0.371287\pi\) | |||||||
\(510\) | −3402.54 | −0.295425 | ||||||||
\(511\) | −2488.48 | −0.215429 | ||||||||
\(512\) | −11426.5 | −0.986298 | ||||||||
\(513\) | −42646.1 | −3.67031 | ||||||||
\(514\) | 25.5611 | 0.00219349 | ||||||||
\(515\) | 21957.5 | 1.87877 | ||||||||
\(516\) | −9872.34 | −0.842259 | ||||||||
\(517\) | −622.293 | −0.0529369 | ||||||||
\(518\) | 1229.03 | 0.104248 | ||||||||
\(519\) | 35344.1 | 2.98927 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6608.36 | −0.555696 | −0.277848 | − | 0.960625i | \(-0.589621\pi\) | ||||
−0.277848 | + | 0.960625i | \(0.589621\pi\) | |||||||
\(522\) | 12604.9 | 1.05690 | ||||||||
\(523\) | −6437.67 | −0.538240 | −0.269120 | − | 0.963107i | \(-0.586733\pi\) | ||||
−0.269120 | + | 0.963107i | \(0.586733\pi\) | |||||||
\(524\) | −2007.10 | −0.167329 | ||||||||
\(525\) | −7444.96 | −0.618904 | ||||||||
\(526\) | −678.020 | −0.0562036 | ||||||||
\(527\) | 2121.73 | 0.175378 | ||||||||
\(528\) | −5278.35 | −0.435058 | ||||||||
\(529\) | −12122.1 | −0.996309 | ||||||||
\(530\) | −6929.05 | −0.567884 | ||||||||
\(531\) | 21355.6 | 1.74530 | ||||||||
\(532\) | −4120.57 | −0.335807 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 2871.97 | 0.232739 | ||||||||
\(535\) | 3361.47 | 0.271643 | ||||||||
\(536\) | 2495.46 | 0.201096 | ||||||||
\(537\) | 9771.63 | 0.785246 | ||||||||
\(538\) | 1120.55 | 0.0897958 | ||||||||
\(539\) | −3539.48 | −0.282850 | ||||||||
\(540\) | 44973.6 | 3.58399 | ||||||||
\(541\) | −9122.32 | −0.724952 | −0.362476 | − | 0.931993i | \(-0.618069\pi\) | ||||
−0.362476 | + | 0.931993i | \(0.618069\pi\) | |||||||
\(542\) | 773.123 | 0.0612703 | ||||||||
\(543\) | −33981.5 | −2.68561 | ||||||||
\(544\) | 3608.21 | 0.284376 | ||||||||
\(545\) | −22336.8 | −1.75561 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12728.6 | −0.994944 | −0.497472 | − | 0.867480i | \(-0.665738\pi\) | ||||
−0.497472 | + | 0.867480i | \(0.665738\pi\) | |||||||
\(548\) | 19513.7 | 1.52114 | ||||||||
\(549\) | 35155.8 | 2.73299 | ||||||||
\(550\) | −1425.47 | −0.110513 | ||||||||
\(551\) | −31017.0 | −2.39813 | ||||||||
\(552\) | 754.313 | 0.0581625 | ||||||||
\(553\) | −5965.24 | −0.458712 | ||||||||
\(554\) | −4491.78 | −0.344472 | ||||||||
\(555\) | 57061.4 | 4.36418 | ||||||||
\(556\) | −14726.6 | −1.12329 | ||||||||
\(557\) | 9499.03 | 0.722598 | 0.361299 | − | 0.932450i | \(-0.382333\pi\) | ||||
0.361299 | + | 0.932450i | \(0.382333\pi\) | |||||||
\(558\) | 3829.38 | 0.290521 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 3975.11 | 0.299963 | ||||||||
\(561\) | 2850.73 | 0.214542 | ||||||||
\(562\) | 4053.56 | 0.304251 | ||||||||
\(563\) | −6227.76 | −0.466196 | −0.233098 | − | 0.972453i | \(-0.574886\pi\) | ||||
−0.233098 | + | 0.972453i | \(0.574886\pi\) | |||||||
\(564\) | −4002.40 | −0.298815 | ||||||||
\(565\) | 7814.79 | 0.581895 | ||||||||
\(566\) | −6912.30 | −0.513331 | ||||||||
\(567\) | 7576.20 | 0.561147 | ||||||||
\(568\) | −9989.63 | −0.737950 | ||||||||
\(569\) | 17393.6 | 1.28151 | 0.640754 | − | 0.767746i | \(-0.278622\pi\) | ||||
0.640754 | + | 0.767746i | \(0.278622\pi\) | |||||||
\(570\) | 15111.3 | 1.11042 | ||||||||
\(571\) | −7734.09 | −0.566833 | −0.283417 | − | 0.958997i | \(-0.591468\pi\) | ||||
−0.283417 | + | 0.958997i | \(0.591468\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 47209.3 | 3.44188 | ||||||||
\(574\) | −234.864 | −0.0170785 | ||||||||
\(575\) | −1134.77 | −0.0823014 | ||||||||
\(576\) | −19256.1 | −1.39294 | ||||||||
\(577\) | 5598.19 | 0.403909 | 0.201955 | − | 0.979395i | \(-0.435271\pi\) | ||||
0.201955 | + | 0.979395i | \(0.435271\pi\) | |||||||
\(578\) | 3195.32 | 0.229944 | ||||||||
\(579\) | 38481.5 | 2.76207 | ||||||||
\(580\) | 32709.8 | 2.34173 | ||||||||
\(581\) | 6729.56 | 0.480532 | ||||||||
\(582\) | 378.941 | 0.0269890 | ||||||||
\(583\) | 5805.32 | 0.412405 | ||||||||
\(584\) | −6371.03 | −0.451430 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −777.521 | −0.0548108 | ||||||||
\(587\) | −375.821 | −0.0264256 | −0.0132128 | − | 0.999913i | \(-0.504206\pi\) | ||||
−0.0132128 | + | 0.999913i | \(0.504206\pi\) | |||||||
\(588\) | −22764.9 | −1.59661 | ||||||||
\(589\) | −9423.00 | −0.659199 | ||||||||
\(590\) | −4377.39 | −0.305448 | ||||||||
\(591\) | −37502.6 | −2.61024 | ||||||||
\(592\) | −17528.1 | −1.21689 | ||||||||
\(593\) | −5396.41 | −0.373700 | −0.186850 | − | 0.982388i | \(-0.559828\pi\) | ||||
−0.186850 | + | 0.982388i | \(0.559828\pi\) | |||||||
\(594\) | 2976.29 | 0.205587 | ||||||||
\(595\) | −2146.88 | −0.147922 | ||||||||
\(596\) | 6060.81 | 0.416544 | ||||||||
\(597\) | −13399.4 | −0.918592 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 26512.5 | 1.80847 | 0.904234 | − | 0.427038i | \(-0.140443\pi\) | ||||
0.904234 | + | 0.427038i | \(0.140443\pi\) | |||||||
\(600\) | −19060.6 | −1.29691 | ||||||||
\(601\) | −12182.2 | −0.826827 | −0.413413 | − | 0.910543i | \(-0.635664\pi\) | ||||
−0.413413 | + | 0.910543i | \(0.635664\pi\) | |||||||
\(602\) | 492.027 | 0.0333115 | ||||||||
\(603\) | 13550.1 | 0.915096 | ||||||||
\(604\) | −11750.0 | −0.791558 | ||||||||
\(605\) | 2075.90 | 0.139500 | ||||||||
\(606\) | −11749.0 | −0.787572 | ||||||||
\(607\) | −14074.8 | −0.941148 | −0.470574 | − | 0.882360i | \(-0.655953\pi\) | ||||
−0.470574 | + | 0.882360i | \(0.655953\pi\) | |||||||
\(608\) | −16024.7 | −1.06889 | ||||||||
\(609\) | 11305.7 | 0.752268 | ||||||||
\(610\) | −7206.10 | −0.478306 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 12898.1 | 0.851921 | ||||||||
\(613\) | 5247.05 | 0.345720 | 0.172860 | − | 0.984946i | \(-0.444699\pi\) | ||||
0.172860 | + | 0.984946i | \(0.444699\pi\) | |||||||
\(614\) | 4575.37 | 0.300728 | ||||||||
\(615\) | −10904.3 | −0.714964 | ||||||||
\(616\) | 597.868 | 0.0391052 | ||||||||
\(617\) | 13209.6 | 0.861912 | 0.430956 | − | 0.902373i | \(-0.358176\pi\) | ||||
0.430956 | + | 0.902373i | \(0.358176\pi\) | |||||||
\(618\) | 9346.02 | 0.608337 | ||||||||
\(619\) | 20822.3 | 1.35205 | 0.676026 | − | 0.736878i | \(-0.263701\pi\) | ||||
0.676026 | + | 0.736878i | \(0.263701\pi\) | |||||||
\(620\) | 9937.29 | 0.643696 | ||||||||
\(621\) | 2369.33 | 0.153104 | ||||||||
\(622\) | 6031.60 | 0.388818 | ||||||||
\(623\) | 1812.11 | 0.116534 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8117.46 | −0.519518 | ||||||||
\(626\) | 4755.57 | 0.303627 | ||||||||
\(627\) | −12660.6 | −0.806404 | ||||||||
\(628\) | −2224.56 | −0.141353 | ||||||||
\(629\) | 9466.57 | 0.600090 | ||||||||
\(630\) | −3874.76 | −0.245038 | ||||||||
\(631\) | −3455.46 | −0.218003 | −0.109001 | − | 0.994042i | \(-0.534765\pi\) | ||||
−0.109001 | + | 0.994042i | \(0.534765\pi\) | |||||||
\(632\) | −15272.2 | −0.961230 | ||||||||
\(633\) | 51427.2 | 3.22914 | ||||||||
\(634\) | 5670.22 | 0.355194 | ||||||||
\(635\) | −1581.76 | −0.0988505 | ||||||||
\(636\) | 37338.1 | 2.32791 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2164.69 | 0.134327 | ||||||||
\(639\) | −54242.7 | −3.35807 | ||||||||
\(640\) | 22181.2 | 1.36998 | ||||||||
\(641\) | 297.324 | 0.0183207 | 0.00916036 | − | 0.999958i | \(-0.497084\pi\) | ||||
0.00916036 | + | 0.999958i | \(0.497084\pi\) | |||||||
\(642\) | 1430.78 | 0.0879570 | ||||||||
\(643\) | 1512.07 | 0.0927375 | 0.0463687 | − | 0.998924i | \(-0.485235\pi\) | ||||
0.0463687 | + | 0.998924i | \(0.485235\pi\) | |||||||
\(644\) | 228.931 | 0.0140080 | ||||||||
\(645\) | 22843.8 | 1.39453 | ||||||||
\(646\) | 2506.98 | 0.152687 | ||||||||
\(647\) | 13459.8 | 0.817863 | 0.408932 | − | 0.912565i | \(-0.365901\pi\) | ||||
0.408932 | + | 0.912565i | \(0.365901\pi\) | |||||||
\(648\) | 19396.6 | 1.17588 | ||||||||
\(649\) | 3667.48 | 0.221820 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3434.70 | 0.206784 | ||||||||
\(652\) | 13080.7 | 0.785705 | ||||||||
\(653\) | −30509.5 | −1.82838 | −0.914188 | − | 0.405291i | \(-0.867170\pi\) | ||||
−0.914188 | + | 0.405291i | \(0.867170\pi\) | |||||||
\(654\) | −9507.48 | −0.568458 | ||||||||
\(655\) | 4644.26 | 0.277048 | ||||||||
\(656\) | 3349.57 | 0.199358 | ||||||||
\(657\) | −34594.1 | −2.05425 | ||||||||
\(658\) | 199.475 | 0.0118182 | ||||||||
\(659\) | 5574.58 | 0.329522 | 0.164761 | − | 0.986334i | \(-0.447315\pi\) | ||||
0.164761 | + | 0.986334i | \(0.447315\pi\) | |||||||
\(660\) | 13351.6 | 0.787439 | ||||||||
\(661\) | −14283.1 | −0.840467 | −0.420233 | − | 0.907416i | \(-0.638052\pi\) | ||||
−0.420233 | + | 0.907416i | \(0.638052\pi\) | |||||||
\(662\) | 6222.07 | 0.365298 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 17229.1 | 1.00695 | ||||||||
\(665\) | 9534.67 | 0.555998 | ||||||||
\(666\) | 17085.6 | 0.994074 | ||||||||
\(667\) | 1723.24 | 0.100036 | ||||||||
\(668\) | −16778.4 | −0.971822 | ||||||||
\(669\) | −47703.9 | −2.75686 | ||||||||
\(670\) | −2777.45 | −0.160153 | ||||||||
\(671\) | 6037.45 | 0.347352 | ||||||||
\(672\) | 5841.02 | 0.335301 | ||||||||
\(673\) | −10315.3 | −0.590828 | −0.295414 | − | 0.955369i | \(-0.595458\pi\) | ||||
−0.295414 | + | 0.955369i | \(0.595458\pi\) | |||||||
\(674\) | −3628.91 | −0.207389 | ||||||||
\(675\) | −59870.2 | −3.41394 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21225.7 | −1.20498 | −0.602488 | − | 0.798128i | \(-0.705824\pi\) | ||||
−0.602488 | + | 0.798128i | \(0.705824\pi\) | |||||||
\(678\) | 3326.29 | 0.188415 | ||||||||
\(679\) | 239.098 | 0.0135136 | ||||||||
\(680\) | −5496.45 | −0.309970 | ||||||||
\(681\) | 15470.7 | 0.870540 | ||||||||
\(682\) | 657.635 | 0.0369240 | ||||||||
\(683\) | −30133.7 | −1.68819 | −0.844095 | − | 0.536194i | \(-0.819862\pi\) | ||||
−0.844095 | + | 0.536194i | \(0.819862\pi\) | |||||||
\(684\) | −57282.9 | −3.20214 | ||||||||
\(685\) | −45153.2 | −2.51856 | ||||||||
\(686\) | 2344.01 | 0.130459 | ||||||||
\(687\) | 18895.5 | 1.04936 | ||||||||
\(688\) | −7017.14 | −0.388846 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −839.552 | −0.0463206 | ||||||||
\(691\) | −14928.6 | −0.821868 | −0.410934 | − | 0.911665i | \(-0.634797\pi\) | ||||
−0.410934 | + | 0.911665i | \(0.634797\pi\) | |||||||
\(692\) | 27462.8 | 1.50864 | ||||||||
\(693\) | 3246.37 | 0.177950 | ||||||||
\(694\) | −3251.02 | −0.177820 | ||||||||
\(695\) | 34076.1 | 1.85983 | ||||||||
\(696\) | 28945.0 | 1.57638 | ||||||||
\(697\) | −1809.03 | −0.0983100 | ||||||||
\(698\) | −2975.79 | −0.161369 | ||||||||
\(699\) | −6644.97 | −0.359565 | ||||||||
\(700\) | −5784.82 | −0.312351 | ||||||||
\(701\) | −21726.6 | −1.17061 | −0.585307 | − | 0.810812i | \(-0.699026\pi\) | ||||
−0.585307 | + | 0.810812i | \(0.699026\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −42042.7 | −2.25558 | ||||||||
\(704\) | −3306.92 | −0.177037 | ||||||||
\(705\) | 9261.24 | 0.494750 | ||||||||
\(706\) | 219.017 | 0.0116754 | ||||||||
\(707\) | −7413.16 | −0.394343 | ||||||||
\(708\) | 23588.2 | 1.25211 | ||||||||
\(709\) | 23270.5 | 1.23264 | 0.616320 | − | 0.787495i | \(-0.288623\pi\) | ||||
0.616320 | + | 0.787495i | \(0.288623\pi\) | |||||||
\(710\) | 11118.5 | 0.587703 | ||||||||
\(711\) | −82926.8 | −4.37412 | ||||||||
\(712\) | 4639.38 | 0.244197 | ||||||||
\(713\) | 523.523 | 0.0274980 | ||||||||
\(714\) | −913.799 | −0.0478965 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7592.67 | 0.396301 | ||||||||
\(717\) | −18221.3 | −0.949074 | ||||||||
\(718\) | 2140.74 | 0.111270 | ||||||||
\(719\) | −15953.3 | −0.827481 | −0.413740 | − | 0.910395i | \(-0.635778\pi\) | ||||
−0.413740 | + | 0.910395i | \(0.635778\pi\) | |||||||
\(720\) | 55260.7 | 2.86034 | ||||||||
\(721\) | 5897.00 | 0.304599 | ||||||||
\(722\) | −5884.93 | −0.303344 | ||||||||
\(723\) | 43205.3 | 2.22244 | ||||||||
\(724\) | −26404.0 | −1.35538 | ||||||||
\(725\) | −43544.3 | −2.23061 | ||||||||
\(726\) | 883.588 | 0.0451695 | ||||||||
\(727\) | 17892.4 | 0.912783 | 0.456392 | − | 0.889779i | \(-0.349142\pi\) | ||||
0.456392 | + | 0.889779i | \(0.349142\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 14231.3 | 0.723027 | ||||||||
\(730\) | 7090.97 | 0.359519 | ||||||||
\(731\) | 3789.82 | 0.191753 | ||||||||
\(732\) | 38831.1 | 1.96071 | ||||||||
\(733\) | −22696.0 | −1.14365 | −0.571826 | − | 0.820375i | \(-0.693765\pi\) | ||||
−0.571826 | + | 0.820375i | \(0.693765\pi\) | |||||||
\(734\) | −7519.15 | −0.378116 | ||||||||
\(735\) | 52676.1 | 2.64352 | ||||||||
\(736\) | 890.298 | 0.0445881 | ||||||||
\(737\) | 2327.02 | 0.116305 | ||||||||
\(738\) | −3265.01 | −0.162855 | ||||||||
\(739\) | −5274.53 | −0.262553 | −0.131276 | − | 0.991346i | \(-0.541908\pi\) | ||||
−0.131276 | + | 0.991346i | \(0.541908\pi\) | |||||||
\(740\) | 44337.3 | 2.20253 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1860.89 | −0.0920694 | ||||||||
\(743\) | −23897.6 | −1.17997 | −0.589986 | − | 0.807413i | \(-0.700867\pi\) | ||||
−0.589986 | + | 0.807413i | \(0.700867\pi\) | |||||||
\(744\) | 8793.54 | 0.433316 | ||||||||
\(745\) | −14024.2 | −0.689674 | ||||||||
\(746\) | 5947.82 | 0.291911 | ||||||||
\(747\) | 93552.2 | 4.58219 | ||||||||
\(748\) | 2215.05 | 0.108276 | ||||||||
\(749\) | 902.770 | 0.0440407 | ||||||||
\(750\) | 5554.38 | 0.270423 | ||||||||
\(751\) | 10218.3 | 0.496502 | 0.248251 | − | 0.968696i | \(-0.420144\pi\) | ||||
0.248251 | + | 0.968696i | \(0.420144\pi\) | |||||||
\(752\) | −2844.86 | −0.137954 | ||||||||
\(753\) | 34596.2 | 1.67431 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 27188.6 | 1.31059 | ||||||||
\(756\) | 12078.3 | 0.581062 | ||||||||
\(757\) | −24621.5 | −1.18215 | −0.591073 | − | 0.806618i | \(-0.701295\pi\) | ||||
−0.591073 | + | 0.806618i | \(0.701295\pi\) | |||||||
\(758\) | −3554.85 | −0.170340 | ||||||||
\(759\) | 703.397 | 0.0336386 | ||||||||
\(760\) | 24410.7 | 1.16509 | ||||||||
\(761\) | −24507.2 | −1.16739 | −0.583697 | − | 0.811971i | \(-0.698394\pi\) | ||||
−0.583697 | + | 0.811971i | \(0.698394\pi\) | |||||||
\(762\) | −673.260 | −0.0320074 | ||||||||
\(763\) | −5998.87 | −0.284631 | ||||||||
\(764\) | 36682.1 | 1.73706 | ||||||||
\(765\) | −29845.2 | −1.41053 | ||||||||
\(766\) | 4143.31 | 0.195436 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −13508.0 | −0.634670 | ||||||||
\(769\) | −19383.4 | −0.908949 | −0.454474 | − | 0.890760i | \(-0.650173\pi\) | ||||
−0.454474 | + | 0.890760i | \(0.650173\pi\) | |||||||
\(770\) | −665.429 | −0.0311434 | ||||||||
\(771\) | 318.719 | 0.0148876 | ||||||||
\(772\) | 29900.6 | 1.39397 | ||||||||
\(773\) | −23126.6 | −1.07607 | −0.538037 | − | 0.842922i | \(-0.680834\pi\) | ||||
−0.538037 | + | 0.842922i | \(0.680834\pi\) | |||||||
\(774\) | 6840.00 | 0.317647 | ||||||||
\(775\) | −13228.8 | −0.613153 | ||||||||
\(776\) | 612.140 | 0.0283177 | ||||||||
\(777\) | 15324.6 | 0.707552 | ||||||||
\(778\) | −4181.49 | −0.192691 | ||||||||
\(779\) | 8034.25 | 0.369521 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9315.33 | −0.426797 | ||||||||
\(782\) | −139.283 | −0.00636924 | ||||||||
\(783\) | 90917.4 | 4.14958 | ||||||||
\(784\) | −16181.0 | −0.737109 | ||||||||
\(785\) | 5147.44 | 0.234038 | ||||||||
\(786\) | 1976.79 | 0.0897070 | ||||||||
\(787\) | −21746.1 | −0.984962 | −0.492481 | − | 0.870323i | \(-0.663910\pi\) | ||||
−0.492481 | + | 0.870323i | \(0.663910\pi\) | |||||||
\(788\) | −29140.0 | −1.31734 | ||||||||
\(789\) | −8454.15 | −0.381465 | ||||||||
\(790\) | 16998.0 | 0.765523 | ||||||||
\(791\) | 2098.77 | 0.0943410 | ||||||||
\(792\) | 8311.37 | 0.372894 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 582.939 | 0.0260551 | ||||||||
\(795\) | −86397.4 | −3.85434 | ||||||||
\(796\) | −10411.5 | −0.463598 | ||||||||
\(797\) | −22143.6 | −0.984149 | −0.492075 | − | 0.870553i | \(-0.663761\pi\) | ||||
−0.492075 | + | 0.870553i | \(0.663761\pi\) | |||||||
\(798\) | 4058.35 | 0.180030 | ||||||||
\(799\) | 1536.45 | 0.0680298 | ||||||||
\(800\) | −22496.8 | −0.994229 | ||||||||
\(801\) | 25191.4 | 1.11123 | ||||||||
\(802\) | 893.896 | 0.0393573 | ||||||||
\(803\) | −5940.99 | −0.261087 | ||||||||
\(804\) | 14966.7 | 0.656511 | ||||||||
\(805\) | −529.727 | −0.0231931 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13971.9 | 0.609462 | ||||||||
\(808\) | −18979.2 | −0.826345 | ||||||||
\(809\) | −412.718 | −0.0179362 | −0.00896811 | − | 0.999960i | \(-0.502855\pi\) | ||||
−0.00896811 | + | 0.999960i | \(0.502855\pi\) | |||||||
\(810\) | −21588.5 | −0.936472 | ||||||||
\(811\) | 24786.5 | 1.07321 | 0.536604 | − | 0.843834i | \(-0.319707\pi\) | ||||
0.536604 | + | 0.843834i | \(0.319707\pi\) | |||||||
\(812\) | 8784.68 | 0.379657 | ||||||||
\(813\) | 9639.97 | 0.415853 | ||||||||
\(814\) | 2934.18 | 0.126343 | ||||||||
\(815\) | −30267.7 | −1.30090 | ||||||||
\(816\) | 13032.3 | 0.559097 | ||||||||
\(817\) | −16831.3 | −0.720748 | ||||||||
\(818\) | −4971.99 | −0.212520 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8472.74 | −0.360830 | ||||||||
\(821\) | −17895.9 | −0.760745 | −0.380372 | − | 0.924833i | \(-0.624204\pi\) | ||||
−0.380372 | + | 0.924833i | \(0.624204\pi\) | |||||||
\(822\) | −19219.0 | −0.815500 | ||||||||
\(823\) | −29788.0 | −1.26166 | −0.630830 | − | 0.775921i | \(-0.717285\pi\) | ||||
−0.630830 | + | 0.775921i | \(0.717285\pi\) | |||||||
\(824\) | 15097.5 | 0.638286 | ||||||||
\(825\) | −17774.0 | −0.750076 | ||||||||
\(826\) | −1175.61 | −0.0495214 | ||||||||
\(827\) | −4785.93 | −0.201237 | −0.100619 | − | 0.994925i | \(-0.532082\pi\) | ||||
−0.100619 | + | 0.994925i | \(0.532082\pi\) | |||||||
\(828\) | 3182.52 | 0.133575 | ||||||||
\(829\) | −28518.2 | −1.19479 | −0.597393 | − | 0.801948i | \(-0.703797\pi\) | ||||
−0.597393 | + | 0.801948i | \(0.703797\pi\) | |||||||
\(830\) | −19176.0 | −0.801938 | ||||||||
\(831\) | −56007.4 | −2.33800 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8739.04 | 0.363493 | ||||||||
\(834\) | 14504.2 | 0.602205 | ||||||||
\(835\) | 38823.9 | 1.60905 | ||||||||
\(836\) | −9837.42 | −0.406979 | ||||||||
\(837\) | 27620.9 | 1.14064 | ||||||||
\(838\) | 865.468 | 0.0356767 | ||||||||
\(839\) | −2539.34 | −0.104491 | −0.0522454 | − | 0.998634i | \(-0.516638\pi\) | ||||
−0.0522454 | + | 0.998634i | \(0.516638\pi\) | |||||||
\(840\) | −8897.75 | −0.365478 | ||||||||
\(841\) | 41736.3 | 1.71127 | ||||||||
\(842\) | −1530.12 | −0.0626265 | ||||||||
\(843\) | 50543.4 | 2.06501 | ||||||||
\(844\) | 39959.5 | 1.62969 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2773.04 | 0.112694 | ||||||||
\(847\) | 557.512 | 0.0226167 | ||||||||
\(848\) | 26539.5 | 1.07473 | ||||||||
\(849\) | −86188.5 | −3.48408 | ||||||||
\(850\) | 3519.52 | 0.142022 | ||||||||
\(851\) | 2335.81 | 0.0940898 | ||||||||
\(852\) | −59913.5 | −2.40916 | ||||||||
\(853\) | −41815.4 | −1.67847 | −0.839233 | − | 0.543772i | \(-0.816996\pi\) | ||||
−0.839233 | + | 0.543772i | \(0.816996\pi\) | |||||||
\(854\) | −1935.30 | −0.0775464 | ||||||||
\(855\) | 132548. | 5.30180 | ||||||||
\(856\) | 2311.28 | 0.0922873 | ||||||||
\(857\) | 27901.8 | 1.11214 | 0.556071 | − | 0.831135i | \(-0.312308\pi\) | ||||
0.556071 | + | 0.831135i | \(0.312308\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24207.8 | 0.961536 | 0.480768 | − | 0.876848i | \(-0.340358\pi\) | ||||
0.480768 | + | 0.876848i | \(0.340358\pi\) | |||||||
\(860\) | 17749.9 | 0.703797 | ||||||||
\(861\) | −2928.50 | −0.115915 | ||||||||
\(862\) | −5632.55 | −0.222558 | ||||||||
\(863\) | −41886.8 | −1.65220 | −0.826098 | − | 0.563527i | \(-0.809444\pi\) | ||||
−0.826098 | + | 0.563527i | \(0.809444\pi\) | |||||||
\(864\) | 46971.8 | 1.84955 | ||||||||
\(865\) | −63546.6 | −2.49786 | ||||||||
\(866\) | −5330.30 | −0.209158 | ||||||||
\(867\) | 39842.0 | 1.56068 | ||||||||
\(868\) | 2668.80 | 0.104361 | ||||||||
\(869\) | −14241.4 | −0.555932 | ||||||||
\(870\) | −32215.9 | −1.25542 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −15358.4 | −0.596444 | ||||||||
\(873\) | 3323.86 | 0.128861 | ||||||||
\(874\) | 618.580 | 0.0239402 | ||||||||
\(875\) | 3504.61 | 0.135403 | ||||||||
\(876\) | −38210.7 | −1.47377 | ||||||||
\(877\) | 8888.50 | 0.342239 | 0.171119 | − | 0.985250i | \(-0.445262\pi\) | ||||
0.171119 | + | 0.985250i | \(0.445262\pi\) | |||||||
\(878\) | −4618.07 | −0.177508 | ||||||||
\(879\) | −9694.81 | −0.372011 | ||||||||
\(880\) | 9490.15 | 0.363537 | ||||||||
\(881\) | −25780.5 | −0.985889 | −0.492945 | − | 0.870061i | \(-0.664079\pi\) | ||||
−0.492945 | + | 0.870061i | \(0.664079\pi\) | |||||||
\(882\) | 15772.5 | 0.602141 | ||||||||
\(883\) | −2605.05 | −0.0992830 | −0.0496415 | − | 0.998767i | \(-0.515808\pi\) | ||||
−0.0496415 | + | 0.998767i | \(0.515808\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −54581.1 | −2.07313 | ||||||||
\(886\) | −6313.19 | −0.239386 | ||||||||
\(887\) | −28810.6 | −1.09060 | −0.545302 | − | 0.838240i | \(-0.683585\pi\) | ||||
−0.545302 | + | 0.838240i | \(0.683585\pi\) | |||||||
\(888\) | 39234.2 | 1.48267 | ||||||||
\(889\) | −424.803 | −0.0160263 | ||||||||
\(890\) | −5163.64 | −0.194478 | ||||||||
\(891\) | 18087.4 | 0.680078 | ||||||||
\(892\) | −37066.5 | −1.39134 | ||||||||
\(893\) | −6823.66 | −0.255706 | ||||||||
\(894\) | −5969.28 | −0.223314 | ||||||||
\(895\) | −17568.8 | −0.656157 | ||||||||
\(896\) | 5957.06 | 0.222111 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 5581.58 | 0.207416 | ||||||||
\(899\) | 20089.0 | 0.745277 | ||||||||
\(900\) | −80418.7 | −2.97847 | ||||||||
\(901\) | −14333.5 | −0.529985 | ||||||||
\(902\) | −560.714 | −0.0206981 | ||||||||
\(903\) | 6135.02 | 0.226092 | ||||||||
\(904\) | 5373.29 | 0.197691 | ||||||||
\(905\) | 61096.7 | 2.24411 | ||||||||
\(906\) | 11572.6 | 0.424363 | ||||||||
\(907\) | 17259.8 | 0.631867 | 0.315934 | − | 0.948781i | \(-0.397682\pi\) | ||||
0.315934 | + | 0.948781i | \(0.397682\pi\) | |||||||
\(908\) | 12020.9 | 0.439347 | ||||||||
\(909\) | −103055. | −3.76032 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18624.6 | −0.677346 | −0.338673 | − | 0.940904i | \(-0.609978\pi\) | ||||
−0.338673 | + | 0.940904i | \(0.609978\pi\) | |||||||
\(912\) | −57879.0 | −2.10150 | ||||||||
\(913\) | 16066.1 | 0.582377 | ||||||||
\(914\) | −1130.07 | −0.0408964 | ||||||||
\(915\) | −89852.0 | −3.24636 | ||||||||
\(916\) | 14682.0 | 0.529594 | ||||||||
\(917\) | 1247.28 | 0.0449170 | ||||||||
\(918\) | −7348.51 | −0.264202 | ||||||||
\(919\) | −37786.7 | −1.35633 | −0.678166 | − | 0.734909i | \(-0.737225\pi\) | ||||
−0.678166 | + | 0.734909i | \(0.737225\pi\) | |||||||
\(920\) | −1356.21 | −0.0486010 | ||||||||
\(921\) | 57049.7 | 2.04110 | ||||||||
\(922\) | −2419.86 | −0.0864358 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 3585.76 | 0.127665 | ||||||||
\(925\) | −59023.2 | −2.09802 | ||||||||
\(926\) | −4875.83 | −0.173034 | ||||||||
\(927\) | 81978.2 | 2.90455 | ||||||||
\(928\) | 34163.1 | 1.20847 | ||||||||
\(929\) | −802.716 | −0.0283490 | −0.0141745 | − | 0.999900i | \(-0.504512\pi\) | ||||
−0.0141745 | + | 0.999900i | \(0.504512\pi\) | |||||||
\(930\) | −9787.23 | −0.345092 | ||||||||
\(931\) | −38811.6 | −1.36627 | ||||||||
\(932\) | −5163.22 | −0.181466 | ||||||||
\(933\) | 75207.2 | 2.63899 | ||||||||
\(934\) | −11172.9 | −0.391423 | ||||||||
\(935\) | −5125.44 | −0.179273 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9285.83 | −0.323751 | −0.161876 | − | 0.986811i | \(-0.551754\pi\) | ||||
−0.161876 | + | 0.986811i | \(0.551754\pi\) | |||||||
\(938\) | −745.924 | −0.0259651 | ||||||||
\(939\) | 59296.5 | 2.06078 | ||||||||
\(940\) | 7196.08 | 0.249692 | ||||||||
\(941\) | −15587.1 | −0.539984 | −0.269992 | − | 0.962863i | \(-0.587021\pi\) | ||||
−0.269992 | + | 0.962863i | \(0.587021\pi\) | |||||||
\(942\) | 2190.96 | 0.0757807 | ||||||||
\(943\) | −446.366 | −0.0154143 | ||||||||
\(944\) | 16766.2 | 0.578064 | ||||||||
\(945\) | −27948.2 | −0.962068 | ||||||||
\(946\) | 1174.66 | 0.0403716 | ||||||||
\(947\) | −36020.9 | −1.23603 | −0.618016 | − | 0.786166i | \(-0.712063\pi\) | ||||
−0.618016 | + | 0.786166i | \(0.712063\pi\) | |||||||
\(948\) | −91596.3 | −3.13809 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −15630.8 | −0.533822 | ||||||||
\(951\) | 70701.3 | 2.41077 | ||||||||
\(952\) | −1476.15 | −0.0502545 | ||||||||
\(953\) | −12192.9 | −0.414446 | −0.207223 | − | 0.978294i | \(-0.566443\pi\) | ||||
−0.207223 | + | 0.978294i | \(0.566443\pi\) | |||||||
\(954\) | −25869.5 | −0.877942 | ||||||||
\(955\) | −84879.5 | −2.87606 | ||||||||
\(956\) | −14158.1 | −0.478982 | ||||||||
\(957\) | 26991.2 | 0.911705 | ||||||||
\(958\) | 1272.60 | 0.0429184 | ||||||||
\(959\) | −12126.5 | −0.408327 | ||||||||
\(960\) | 49215.1 | 1.65459 | ||||||||
\(961\) | −23687.9 | −0.795138 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12550.0 | 0.419957 | ||||||||
\(964\) | 33571.0 | 1.12163 | ||||||||
\(965\) | −69187.5 | −2.30801 | ||||||||
\(966\) | −225.473 | −0.00750982 | ||||||||
\(967\) | 5307.92 | 0.176516 | 0.0882581 | − | 0.996098i | \(-0.471870\pi\) | ||||
0.0882581 | + | 0.996098i | \(0.471870\pi\) | |||||||
\(968\) | 1427.35 | 0.0473932 | ||||||||
\(969\) | 31259.3 | 1.03632 | ||||||||
\(970\) | −681.313 | −0.0225522 | ||||||||
\(971\) | 41414.0 | 1.36873 | 0.684366 | − | 0.729139i | \(-0.260079\pi\) | ||||
0.684366 | + | 0.729139i | \(0.260079\pi\) | |||||||
\(972\) | 45554.3 | 1.50324 | ||||||||
\(973\) | 9151.62 | 0.301529 | ||||||||
\(974\) | −707.321 | −0.0232690 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 27600.7 | 0.905201 | ||||||||
\(977\) | 32318.8 | 1.05831 | 0.529155 | − | 0.848525i | \(-0.322509\pi\) | ||||
0.529155 | + | 0.848525i | \(0.322509\pi\) | |||||||
\(978\) | −12883.2 | −0.421225 | ||||||||
\(979\) | 4326.22 | 0.141232 | ||||||||
\(980\) | 40929.9 | 1.33414 | ||||||||
\(981\) | −83394.4 | −2.71415 | ||||||||
\(982\) | −4029.24 | −0.130935 | ||||||||
\(983\) | 3000.94 | 0.0973705 | 0.0486852 | − | 0.998814i | \(-0.484497\pi\) | ||||
0.0486852 | + | 0.998814i | \(0.484497\pi\) | |||||||
\(984\) | −7497.55 | −0.242900 | ||||||||
\(985\) | 67427.5 | 2.18114 | ||||||||
\(986\) | −5344.66 | −0.172625 | ||||||||
\(987\) | 2487.23 | 0.0802123 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 935.110 | 0.0300655 | ||||||||
\(990\) | −9250.57 | −0.296972 | ||||||||
\(991\) | 9742.43 | 0.312289 | 0.156144 | − | 0.987734i | \(-0.450093\pi\) | ||||
0.156144 | + | 0.987734i | \(0.450093\pi\) | |||||||
\(992\) | 10378.8 | 0.332185 | ||||||||
\(993\) | 77582.2 | 2.47935 | ||||||||
\(994\) | 2986.02 | 0.0952826 | ||||||||
\(995\) | 24091.3 | 0.767582 | ||||||||
\(996\) | 103332. | 3.28736 | ||||||||
\(997\) | 13288.0 | 0.422100 | 0.211050 | − | 0.977475i | \(-0.432312\pi\) | ||||
0.211050 | + | 0.977475i | \(0.432312\pi\) | |||||||
\(998\) | 9649.55 | 0.306063 | ||||||||
\(999\) | 123236. | 3.90293 |
(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.d.1.4 | 9 | ||
13.12 | even | 2 | 143.4.a.c.1.6 | ✓ | 9 | ||
39.38 | odd | 2 | 1287.4.a.k.1.4 | 9 | |||
52.51 | odd | 2 | 2288.4.a.r.1.9 | 9 | |||
143.142 | odd | 2 | 1573.4.a.e.1.4 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
143.4.a.c.1.6 | ✓ | 9 | 13.12 | even | 2 | ||
1287.4.a.k.1.4 | 9 | 39.38 | odd | 2 | |||
1573.4.a.e.1.4 | 9 | 143.142 | odd | 2 | |||
1859.4.a.d.1.4 | 9 | 1.1 | even | 1 | trivial | ||
2288.4.a.r.1.9 | 9 | 52.51 | odd | 2 |