Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,4,Mod(1,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, 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("507.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.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: | \(29.9139683729\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 70x^{8} + 1645x^{6} - 14700x^{4} + 44100x^{2} - 27648 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 39) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(3.27897\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.27897 | 1.15929 | 0.579646 | − | 0.814868i | \(-0.303191\pi\) | ||||
0.579646 | + | 0.814868i | \(0.303191\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 2.75167 | 0.343959 | ||||||||
\(5\) | −17.5414 | −1.56895 | −0.784476 | − | 0.620160i | \(-0.787068\pi\) | ||||
−0.784476 | + | 0.620160i | \(0.787068\pi\) | |||||||
\(6\) | 9.83692 | 0.669318 | ||||||||
\(7\) | 26.6999 | 1.44166 | 0.720829 | − | 0.693112i | \(-0.243761\pi\) | ||||
0.720829 | + | 0.693112i | \(0.243761\pi\) | |||||||
\(8\) | −17.2091 | −0.760544 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −57.5178 | −1.81887 | ||||||||
\(11\) | 21.4026 | 0.586647 | 0.293324 | − | 0.956013i | \(-0.405239\pi\) | ||||
0.293324 | + | 0.956013i | \(0.405239\pi\) | |||||||
\(12\) | 8.25501 | 0.198585 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 87.5483 | 1.67130 | ||||||||
\(15\) | −52.6242 | −0.905834 | ||||||||
\(16\) | −78.4417 | −1.22565 | ||||||||
\(17\) | 83.9630 | 1.19788 | 0.598942 | − | 0.800793i | \(-0.295588\pi\) | ||||
0.598942 | + | 0.800793i | \(0.295588\pi\) | |||||||
\(18\) | 29.5108 | 0.386431 | ||||||||
\(19\) | 77.1142 | 0.931116 | 0.465558 | − | 0.885017i | \(-0.345854\pi\) | ||||
0.465558 | + | 0.885017i | \(0.345854\pi\) | |||||||
\(20\) | −48.2682 | −0.539654 | ||||||||
\(21\) | 80.0997 | 0.832342 | ||||||||
\(22\) | 70.1785 | 0.680096 | ||||||||
\(23\) | 142.119 | 1.28843 | 0.644216 | − | 0.764844i | \(-0.277184\pi\) | ||||
0.644216 | + | 0.764844i | \(0.277184\pi\) | |||||||
\(24\) | −51.6274 | −0.439100 | ||||||||
\(25\) | 182.701 | 1.46161 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 73.4693 | 0.495871 | ||||||||
\(29\) | 134.223 | 0.859469 | 0.429734 | − | 0.902955i | \(-0.358607\pi\) | ||||
0.429734 | + | 0.902955i | \(0.358607\pi\) | |||||||
\(30\) | −172.553 | −1.05013 | ||||||||
\(31\) | −122.559 | −0.710074 | −0.355037 | − | 0.934852i | \(-0.615532\pi\) | ||||
−0.355037 | + | 0.934852i | \(0.615532\pi\) | |||||||
\(32\) | −119.535 | −0.660344 | ||||||||
\(33\) | 64.2077 | 0.338701 | ||||||||
\(34\) | 275.312 | 1.38870 | ||||||||
\(35\) | −468.354 | −2.26189 | ||||||||
\(36\) | 24.7650 | 0.114653 | ||||||||
\(37\) | 222.587 | 0.989003 | 0.494502 | − | 0.869177i | \(-0.335351\pi\) | ||||
0.494502 | + | 0.869177i | \(0.335351\pi\) | |||||||
\(38\) | 252.855 | 1.07944 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 301.873 | 1.19326 | ||||||||
\(41\) | −198.321 | −0.755427 | −0.377713 | − | 0.925923i | \(-0.623290\pi\) | ||||
−0.377713 | + | 0.925923i | \(0.623290\pi\) | |||||||
\(42\) | 262.645 | 0.964928 | ||||||||
\(43\) | 154.656 | 0.548483 | 0.274242 | − | 0.961661i | \(-0.411573\pi\) | ||||
0.274242 | + | 0.961661i | \(0.411573\pi\) | |||||||
\(44\) | 58.8928 | 0.201782 | ||||||||
\(45\) | −157.873 | −0.522984 | ||||||||
\(46\) | 466.006 | 1.49367 | ||||||||
\(47\) | 78.7956 | 0.244543 | 0.122271 | − | 0.992497i | \(-0.460982\pi\) | ||||
0.122271 | + | 0.992497i | \(0.460982\pi\) | |||||||
\(48\) | −235.325 | −0.707630 | ||||||||
\(49\) | 369.884 | 1.07838 | ||||||||
\(50\) | 599.072 | 1.69443 | ||||||||
\(51\) | 251.889 | 0.691598 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −477.088 | −1.23647 | −0.618237 | − | 0.785992i | \(-0.712153\pi\) | ||||
−0.618237 | + | 0.785992i | \(0.712153\pi\) | |||||||
\(54\) | 88.5323 | 0.223106 | ||||||||
\(55\) | −375.431 | −0.920421 | ||||||||
\(56\) | −459.482 | −1.09644 | ||||||||
\(57\) | 231.342 | 0.537580 | ||||||||
\(58\) | 440.114 | 0.996376 | ||||||||
\(59\) | 42.9282 | 0.0947249 | 0.0473625 | − | 0.998878i | \(-0.484918\pi\) | ||||
0.0473625 | + | 0.998878i | \(0.484918\pi\) | |||||||
\(60\) | −144.804 | −0.311570 | ||||||||
\(61\) | 496.539 | 1.04222 | 0.521109 | − | 0.853490i | \(-0.325519\pi\) | ||||
0.521109 | + | 0.853490i | \(0.325519\pi\) | |||||||
\(62\) | −401.869 | −0.823183 | ||||||||
\(63\) | 240.299 | 0.480553 | ||||||||
\(64\) | 235.581 | 0.460119 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 210.535 | 0.392653 | ||||||||
\(67\) | 484.659 | 0.883739 | 0.441869 | − | 0.897079i | \(-0.354315\pi\) | ||||
0.441869 | + | 0.897079i | \(0.354315\pi\) | |||||||
\(68\) | 231.038 | 0.412022 | ||||||||
\(69\) | 426.358 | 0.743876 | ||||||||
\(70\) | −1535.72 | −2.62219 | ||||||||
\(71\) | −382.432 | −0.639245 | −0.319622 | − | 0.947545i | \(-0.603556\pi\) | ||||
−0.319622 | + | 0.947545i | \(0.603556\pi\) | |||||||
\(72\) | −154.882 | −0.253515 | ||||||||
\(73\) | −193.622 | −0.310435 | −0.155217 | − | 0.987880i | \(-0.549608\pi\) | ||||
−0.155217 | + | 0.987880i | \(0.549608\pi\) | |||||||
\(74\) | 729.858 | 1.14654 | ||||||||
\(75\) | 548.103 | 0.843860 | ||||||||
\(76\) | 212.193 | 0.320265 | ||||||||
\(77\) | 571.447 | 0.845745 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1049.60 | 1.49480 | 0.747399 | − | 0.664375i | \(-0.231302\pi\) | ||||
0.747399 | + | 0.664375i | \(0.231302\pi\) | |||||||
\(80\) | 1375.98 | 1.92299 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −650.289 | −0.875761 | ||||||||
\(83\) | −861.900 | −1.13983 | −0.569914 | − | 0.821704i | \(-0.693024\pi\) | ||||
−0.569914 | + | 0.821704i | \(0.693024\pi\) | |||||||
\(84\) | 220.408 | 0.286291 | ||||||||
\(85\) | −1472.83 | −1.87942 | ||||||||
\(86\) | 507.112 | 0.635853 | ||||||||
\(87\) | 402.669 | 0.496215 | ||||||||
\(88\) | −368.320 | −0.446171 | ||||||||
\(89\) | −967.645 | −1.15247 | −0.576237 | − | 0.817283i | \(-0.695479\pi\) | ||||
−0.576237 | + | 0.817283i | \(0.695479\pi\) | |||||||
\(90\) | −517.660 | −0.606291 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 391.065 | 0.443167 | ||||||||
\(93\) | −367.678 | −0.409961 | ||||||||
\(94\) | 258.369 | 0.283497 | ||||||||
\(95\) | −1352.69 | −1.46088 | ||||||||
\(96\) | −358.605 | −0.381250 | ||||||||
\(97\) | −591.470 | −0.619120 | −0.309560 | − | 0.950880i | \(-0.600182\pi\) | ||||
−0.309560 | + | 0.950880i | \(0.600182\pi\) | |||||||
\(98\) | 1212.84 | 1.25016 | ||||||||
\(99\) | 192.623 | 0.195549 | ||||||||
\(100\) | 502.733 | 0.502733 | ||||||||
\(101\) | 255.110 | 0.251331 | 0.125665 | − | 0.992073i | \(-0.459893\pi\) | ||||
0.125665 | + | 0.992073i | \(0.459893\pi\) | |||||||
\(102\) | 825.937 | 0.801764 | ||||||||
\(103\) | −247.355 | −0.236627 | −0.118313 | − | 0.992976i | \(-0.537749\pi\) | ||||
−0.118313 | + | 0.992976i | \(0.537749\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1405.06 | −1.30590 | ||||||||
\(106\) | −1564.36 | −1.43343 | ||||||||
\(107\) | 683.484 | 0.617522 | 0.308761 | − | 0.951140i | \(-0.400086\pi\) | ||||
0.308761 | + | 0.951140i | \(0.400086\pi\) | |||||||
\(108\) | 74.2951 | 0.0661949 | ||||||||
\(109\) | −1697.76 | −1.49189 | −0.745946 | − | 0.666006i | \(-0.768002\pi\) | ||||
−0.745946 | + | 0.666006i | \(0.768002\pi\) | |||||||
\(110\) | −1231.03 | −1.06704 | ||||||||
\(111\) | 667.762 | 0.571001 | ||||||||
\(112\) | −2094.38 | −1.76697 | ||||||||
\(113\) | −380.709 | −0.316939 | −0.158469 | − | 0.987364i | \(-0.550656\pi\) | ||||
−0.158469 | + | 0.987364i | \(0.550656\pi\) | |||||||
\(114\) | 758.566 | 0.623212 | ||||||||
\(115\) | −2492.97 | −2.02149 | ||||||||
\(116\) | 369.337 | 0.295622 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 140.760 | 0.109814 | ||||||||
\(119\) | 2241.80 | 1.72694 | ||||||||
\(120\) | 905.618 | 0.688927 | ||||||||
\(121\) | −872.930 | −0.655845 | ||||||||
\(122\) | 1628.14 | 1.20824 | ||||||||
\(123\) | −594.962 | −0.436146 | ||||||||
\(124\) | −337.243 | −0.244236 | ||||||||
\(125\) | −1012.16 | −0.724241 | ||||||||
\(126\) | 787.934 | 0.557101 | ||||||||
\(127\) | 123.231 | 0.0861025 | 0.0430513 | − | 0.999073i | \(-0.486292\pi\) | ||||
0.0430513 | + | 0.999073i | \(0.486292\pi\) | |||||||
\(128\) | 1728.74 | 1.19376 | ||||||||
\(129\) | 463.967 | 0.316667 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1218.41 | −0.812616 | −0.406308 | − | 0.913736i | \(-0.633184\pi\) | ||||
−0.406308 | + | 0.913736i | \(0.633184\pi\) | |||||||
\(132\) | 176.678 | 0.116499 | ||||||||
\(133\) | 2058.94 | 1.34235 | ||||||||
\(134\) | 1589.18 | 1.02451 | ||||||||
\(135\) | −473.618 | −0.301945 | ||||||||
\(136\) | −1444.93 | −0.911042 | ||||||||
\(137\) | −2728.83 | −1.70175 | −0.850875 | − | 0.525369i | \(-0.823927\pi\) | ||||
−0.850875 | + | 0.525369i | \(0.823927\pi\) | |||||||
\(138\) | 1398.02 | 0.862370 | ||||||||
\(139\) | 3112.78 | 1.89944 | 0.949722 | − | 0.313094i | \(-0.101366\pi\) | ||||
0.949722 | + | 0.313094i | \(0.101366\pi\) | |||||||
\(140\) | −1288.75 | −0.777998 | ||||||||
\(141\) | 236.387 | 0.141187 | ||||||||
\(142\) | −1253.99 | −0.741071 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −705.975 | −0.408550 | ||||||||
\(145\) | −2354.46 | −1.34846 | ||||||||
\(146\) | −634.881 | −0.359885 | ||||||||
\(147\) | 1109.65 | 0.622603 | ||||||||
\(148\) | 612.487 | 0.340176 | ||||||||
\(149\) | −1370.57 | −0.753567 | −0.376784 | − | 0.926301i | \(-0.622970\pi\) | ||||
−0.376784 | + | 0.926301i | \(0.622970\pi\) | |||||||
\(150\) | 1797.22 | 0.978280 | ||||||||
\(151\) | 2847.56 | 1.53464 | 0.767321 | − | 0.641263i | \(-0.221589\pi\) | ||||
0.767321 | + | 0.641263i | \(0.221589\pi\) | |||||||
\(152\) | −1327.07 | −0.708154 | ||||||||
\(153\) | 755.667 | 0.399294 | ||||||||
\(154\) | 1873.76 | 0.980466 | ||||||||
\(155\) | 2149.86 | 1.11407 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3354.00 | 1.70496 | 0.852479 | − | 0.522761i | \(-0.175098\pi\) | ||||
0.852479 | + | 0.522761i | \(0.175098\pi\) | |||||||
\(158\) | 3441.61 | 1.73291 | ||||||||
\(159\) | −1431.26 | −0.713878 | ||||||||
\(160\) | 2096.81 | 1.03605 | ||||||||
\(161\) | 3794.57 | 1.85748 | ||||||||
\(162\) | 265.597 | 0.128810 | ||||||||
\(163\) | 2196.18 | 1.05533 | 0.527664 | − | 0.849453i | \(-0.323068\pi\) | ||||
0.527664 | + | 0.849453i | \(0.323068\pi\) | |||||||
\(164\) | −545.713 | −0.259836 | ||||||||
\(165\) | −1126.29 | −0.531405 | ||||||||
\(166\) | −2826.15 | −1.32139 | ||||||||
\(167\) | −912.535 | −0.422839 | −0.211419 | − | 0.977395i | \(-0.567809\pi\) | ||||
−0.211419 | + | 0.977395i | \(0.567809\pi\) | |||||||
\(168\) | −1378.45 | −0.633033 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −4829.37 | −2.17880 | ||||||||
\(171\) | 694.027 | 0.310372 | ||||||||
\(172\) | 425.562 | 0.188656 | ||||||||
\(173\) | 899.636 | 0.395364 | 0.197682 | − | 0.980266i | \(-0.436659\pi\) | ||||
0.197682 | + | 0.980266i | \(0.436659\pi\) | |||||||
\(174\) | 1320.34 | 0.575258 | ||||||||
\(175\) | 4878.10 | 2.10714 | ||||||||
\(176\) | −1678.85 | −0.719025 | ||||||||
\(177\) | 128.784 | 0.0546895 | ||||||||
\(178\) | −3172.88 | −1.33605 | ||||||||
\(179\) | 313.278 | 0.130813 | 0.0654064 | − | 0.997859i | \(-0.479166\pi\) | ||||
0.0654064 | + | 0.997859i | \(0.479166\pi\) | |||||||
\(180\) | −434.413 | −0.179885 | ||||||||
\(181\) | −2745.06 | −1.12728 | −0.563642 | − | 0.826019i | \(-0.690600\pi\) | ||||
−0.563642 | + | 0.826019i | \(0.690600\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1489.62 | 0.601725 | ||||||||
\(184\) | −2445.75 | −0.979909 | ||||||||
\(185\) | −3904.50 | −1.55170 | ||||||||
\(186\) | −1205.61 | −0.475265 | ||||||||
\(187\) | 1797.02 | 0.702735 | ||||||||
\(188\) | 216.819 | 0.0841126 | ||||||||
\(189\) | 720.897 | 0.277447 | ||||||||
\(190\) | −4435.44 | −1.69358 | ||||||||
\(191\) | 89.8679 | 0.0340451 | 0.0170226 | − | 0.999855i | \(-0.494581\pi\) | ||||
0.0170226 | + | 0.999855i | \(0.494581\pi\) | |||||||
\(192\) | 706.743 | 0.265650 | ||||||||
\(193\) | −848.954 | −0.316627 | −0.158314 | − | 0.987389i | \(-0.550606\pi\) | ||||
−0.158314 | + | 0.987389i | \(0.550606\pi\) | |||||||
\(194\) | −1939.41 | −0.717741 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1017.80 | 0.370918 | ||||||||
\(197\) | −4343.86 | −1.57100 | −0.785501 | − | 0.618860i | \(-0.787595\pi\) | ||||
−0.785501 | + | 0.618860i | \(0.787595\pi\) | |||||||
\(198\) | 631.606 | 0.226699 | ||||||||
\(199\) | −3328.41 | −1.18565 | −0.592825 | − | 0.805331i | \(-0.701988\pi\) | ||||
−0.592825 | + | 0.805331i | \(0.701988\pi\) | |||||||
\(200\) | −3144.13 | −1.11162 | ||||||||
\(201\) | 1453.98 | 0.510227 | ||||||||
\(202\) | 836.499 | 0.291366 | ||||||||
\(203\) | 3583.74 | 1.23906 | ||||||||
\(204\) | 693.115 | 0.237881 | ||||||||
\(205\) | 3478.83 | 1.18523 | ||||||||
\(206\) | −811.069 | −0.274320 | ||||||||
\(207\) | 1279.07 | 0.429477 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1650.44 | 0.546236 | ||||||||
\(210\) | −4607.16 | −1.51392 | ||||||||
\(211\) | −4599.88 | −1.50080 | −0.750401 | − | 0.660983i | \(-0.770139\pi\) | ||||
−0.750401 | + | 0.660983i | \(0.770139\pi\) | |||||||
\(212\) | −1312.79 | −0.425296 | ||||||||
\(213\) | −1147.30 | −0.369068 | ||||||||
\(214\) | 2241.13 | 0.715889 | ||||||||
\(215\) | −2712.88 | −0.860544 | ||||||||
\(216\) | −464.647 | −0.146367 | ||||||||
\(217\) | −3272.32 | −1.02368 | ||||||||
\(218\) | −5566.92 | −1.72954 | ||||||||
\(219\) | −580.866 | −0.179230 | ||||||||
\(220\) | −1033.06 | −0.316587 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 2189.57 | 0.661958 | ||||||||
\(223\) | 2529.58 | 0.759611 | 0.379806 | − | 0.925066i | \(-0.375991\pi\) | ||||
0.379806 | + | 0.925066i | \(0.375991\pi\) | |||||||
\(224\) | −3191.57 | −0.951991 | ||||||||
\(225\) | 1644.31 | 0.487203 | ||||||||
\(226\) | −1248.33 | −0.367425 | ||||||||
\(227\) | −37.2670 | −0.0108965 | −0.00544823 | − | 0.999985i | \(-0.501734\pi\) | ||||
−0.00544823 | + | 0.999985i | \(0.501734\pi\) | |||||||
\(228\) | 636.578 | 0.184905 | ||||||||
\(229\) | 4094.45 | 1.18152 | 0.590762 | − | 0.806846i | \(-0.298827\pi\) | ||||
0.590762 | + | 0.806846i | \(0.298827\pi\) | |||||||
\(230\) | −8174.40 | −2.34349 | ||||||||
\(231\) | 1714.34 | 0.488291 | ||||||||
\(232\) | −2309.86 | −0.653664 | ||||||||
\(233\) | 1466.04 | 0.412205 | 0.206103 | − | 0.978530i | \(-0.433922\pi\) | ||||
0.206103 | + | 0.978530i | \(0.433922\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1382.19 | −0.383676 | ||||||||
\(236\) | 118.124 | 0.0325815 | ||||||||
\(237\) | 3148.80 | 0.863023 | ||||||||
\(238\) | 7350.81 | 2.00203 | ||||||||
\(239\) | 5520.53 | 1.49412 | 0.747058 | − | 0.664759i | \(-0.231466\pi\) | ||||
0.747058 | + | 0.664759i | \(0.231466\pi\) | |||||||
\(240\) | 4127.93 | 1.11024 | ||||||||
\(241\) | −2665.63 | −0.712483 | −0.356241 | − | 0.934394i | \(-0.615942\pi\) | ||||
−0.356241 | + | 0.934394i | \(0.615942\pi\) | |||||||
\(242\) | −2862.31 | −0.760316 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 1366.31 | 0.358480 | ||||||||
\(245\) | −6488.30 | −1.69193 | ||||||||
\(246\) | −1950.87 | −0.505621 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 2109.14 | 0.540042 | ||||||||
\(249\) | −2585.70 | −0.658080 | ||||||||
\(250\) | −3318.84 | −0.839607 | ||||||||
\(251\) | 1579.21 | 0.397127 | 0.198564 | − | 0.980088i | \(-0.436372\pi\) | ||||
0.198564 | + | 0.980088i | \(0.436372\pi\) | |||||||
\(252\) | 661.224 | 0.165290 | ||||||||
\(253\) | 3041.72 | 0.755855 | ||||||||
\(254\) | 404.073 | 0.0998180 | ||||||||
\(255\) | −4418.49 | −1.08508 | ||||||||
\(256\) | 3783.86 | 0.923794 | ||||||||
\(257\) | −2663.91 | −0.646577 | −0.323288 | − | 0.946300i | \(-0.604788\pi\) | ||||
−0.323288 | + | 0.946300i | \(0.604788\pi\) | |||||||
\(258\) | 1521.34 | 0.367110 | ||||||||
\(259\) | 5943.06 | 1.42581 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1208.01 | 0.286490 | ||||||||
\(262\) | −3995.12 | −0.942059 | ||||||||
\(263\) | −2436.93 | −0.571360 | −0.285680 | − | 0.958325i | \(-0.592219\pi\) | ||||
−0.285680 | + | 0.958325i | \(0.592219\pi\) | |||||||
\(264\) | −1104.96 | −0.257597 | ||||||||
\(265\) | 8368.80 | 1.93997 | ||||||||
\(266\) | 6751.21 | 1.55618 | ||||||||
\(267\) | −2902.94 | −0.665381 | ||||||||
\(268\) | 1333.62 | 0.303970 | ||||||||
\(269\) | −2683.18 | −0.608165 | −0.304083 | − | 0.952646i | \(-0.598350\pi\) | ||||
−0.304083 | + | 0.952646i | \(0.598350\pi\) | |||||||
\(270\) | −1552.98 | −0.350042 | ||||||||
\(271\) | 3857.14 | 0.864592 | 0.432296 | − | 0.901732i | \(-0.357704\pi\) | ||||
0.432296 | + | 0.901732i | \(0.357704\pi\) | |||||||
\(272\) | −6586.20 | −1.46819 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8947.76 | −1.97282 | ||||||||
\(275\) | 3910.27 | 0.857448 | ||||||||
\(276\) | 1173.20 | 0.255863 | ||||||||
\(277\) | 1104.91 | 0.239666 | 0.119833 | − | 0.992794i | \(-0.461764\pi\) | ||||
0.119833 | + | 0.992794i | \(0.461764\pi\) | |||||||
\(278\) | 10206.7 | 2.20201 | ||||||||
\(279\) | −1103.03 | −0.236691 | ||||||||
\(280\) | 8059.97 | 1.72027 | ||||||||
\(281\) | −4982.58 | −1.05778 | −0.528890 | − | 0.848691i | \(-0.677391\pi\) | ||||
−0.528890 | + | 0.848691i | \(0.677391\pi\) | |||||||
\(282\) | 775.106 | 0.163677 | ||||||||
\(283\) | 2584.86 | 0.542947 | 0.271473 | − | 0.962446i | \(-0.412489\pi\) | ||||
0.271473 | + | 0.962446i | \(0.412489\pi\) | |||||||
\(284\) | −1052.33 | −0.219874 | ||||||||
\(285\) | −4058.07 | −0.843437 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5295.14 | −1.08907 | ||||||||
\(288\) | −1075.82 | −0.220115 | ||||||||
\(289\) | 2136.78 | 0.434924 | ||||||||
\(290\) | −7720.22 | −1.56326 | ||||||||
\(291\) | −1774.41 | −0.357449 | ||||||||
\(292\) | −532.784 | −0.106777 | ||||||||
\(293\) | 92.5482 | 0.0184530 | 0.00922649 | − | 0.999957i | \(-0.497063\pi\) | ||||
0.00922649 | + | 0.999957i | \(0.497063\pi\) | |||||||
\(294\) | 3638.52 | 0.721779 | ||||||||
\(295\) | −753.020 | −0.148619 | ||||||||
\(296\) | −3830.54 | −0.752180 | ||||||||
\(297\) | 577.870 | 0.112900 | ||||||||
\(298\) | −4494.07 | −0.873605 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1508.20 | 0.290253 | ||||||||
\(301\) | 4129.29 | 0.790726 | ||||||||
\(302\) | 9337.07 | 1.77910 | ||||||||
\(303\) | 765.330 | 0.145106 | ||||||||
\(304\) | −6048.96 | −1.14122 | ||||||||
\(305\) | −8709.99 | −1.63519 | ||||||||
\(306\) | 2477.81 | 0.462899 | ||||||||
\(307\) | 3979.46 | 0.739803 | 0.369901 | − | 0.929071i | \(-0.379391\pi\) | ||||
0.369901 | + | 0.929071i | \(0.379391\pi\) | |||||||
\(308\) | 1572.43 | 0.290901 | ||||||||
\(309\) | −742.064 | −0.136617 | ||||||||
\(310\) | 7049.34 | 1.29153 | ||||||||
\(311\) | 3450.91 | 0.629207 | 0.314604 | − | 0.949223i | \(-0.398128\pi\) | ||||
0.314604 | + | 0.949223i | \(0.398128\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6189.03 | −1.11765 | −0.558825 | − | 0.829285i | \(-0.688748\pi\) | ||||
−0.558825 | + | 0.829285i | \(0.688748\pi\) | |||||||
\(314\) | 10997.7 | 1.97654 | ||||||||
\(315\) | −4215.18 | −0.753964 | ||||||||
\(316\) | 2888.15 | 0.514149 | ||||||||
\(317\) | −5437.78 | −0.963459 | −0.481729 | − | 0.876320i | \(-0.659991\pi\) | ||||
−0.481729 | + | 0.876320i | \(0.659991\pi\) | |||||||
\(318\) | −4693.08 | −0.827593 | ||||||||
\(319\) | 2872.72 | 0.504205 | ||||||||
\(320\) | −4132.42 | −0.721904 | ||||||||
\(321\) | 2050.45 | 0.356527 | ||||||||
\(322\) | 12442.3 | 2.15336 | ||||||||
\(323\) | 6474.73 | 1.11537 | ||||||||
\(324\) | 222.885 | 0.0382176 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 7201.23 | 1.22343 | ||||||||
\(327\) | −5093.29 | −0.861344 | ||||||||
\(328\) | 3412.93 | 0.574535 | ||||||||
\(329\) | 2103.83 | 0.352547 | ||||||||
\(330\) | −3693.09 | −0.616054 | ||||||||
\(331\) | −6626.64 | −1.10040 | −0.550201 | − | 0.835032i | \(-0.685449\pi\) | ||||
−0.550201 | + | 0.835032i | \(0.685449\pi\) | |||||||
\(332\) | −2371.66 | −0.392054 | ||||||||
\(333\) | 2003.29 | 0.329668 | ||||||||
\(334\) | −2992.18 | −0.490194 | ||||||||
\(335\) | −8501.60 | −1.38654 | ||||||||
\(336\) | −6283.15 | −1.02016 | ||||||||
\(337\) | −5538.63 | −0.895277 | −0.447638 | − | 0.894215i | \(-0.647735\pi\) | ||||
−0.447638 | + | 0.894215i | \(0.647735\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1142.13 | −0.182985 | ||||||||
\(340\) | −4052.74 | −0.646443 | ||||||||
\(341\) | −2623.08 | −0.416563 | ||||||||
\(342\) | 2275.70 | 0.359812 | ||||||||
\(343\) | 717.813 | 0.112998 | ||||||||
\(344\) | −2661.49 | −0.417146 | ||||||||
\(345\) | −7478.92 | −1.16711 | ||||||||
\(346\) | 2949.88 | 0.458343 | ||||||||
\(347\) | 9398.94 | 1.45407 | 0.727034 | − | 0.686602i | \(-0.240898\pi\) | ||||
0.727034 | + | 0.686602i | \(0.240898\pi\) | |||||||
\(348\) | 1108.01 | 0.170677 | ||||||||
\(349\) | −5757.33 | −0.883045 | −0.441522 | − | 0.897250i | \(-0.645561\pi\) | ||||
−0.441522 | + | 0.897250i | \(0.645561\pi\) | |||||||
\(350\) | 15995.2 | 2.44279 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2558.36 | −0.387389 | ||||||||
\(353\) | −3457.82 | −0.521364 | −0.260682 | − | 0.965425i | \(-0.583947\pi\) | ||||
−0.260682 | + | 0.965425i | \(0.583947\pi\) | |||||||
\(354\) | 422.281 | 0.0634011 | ||||||||
\(355\) | 6708.40 | 1.00294 | ||||||||
\(356\) | −2662.64 | −0.396403 | ||||||||
\(357\) | 6725.41 | 0.997049 | ||||||||
\(358\) | 1027.23 | 0.151650 | ||||||||
\(359\) | 7168.96 | 1.05394 | 0.526968 | − | 0.849885i | \(-0.323329\pi\) | ||||
0.526968 | + | 0.849885i | \(0.323329\pi\) | |||||||
\(360\) | 2716.85 | 0.397752 | ||||||||
\(361\) | −912.407 | −0.133023 | ||||||||
\(362\) | −9000.97 | −1.30685 | ||||||||
\(363\) | −2618.79 | −0.378652 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3396.40 | 0.487057 | ||||||||
\(366\) | 4884.41 | 0.697575 | ||||||||
\(367\) | 3910.11 | 0.556147 | 0.278073 | − | 0.960560i | \(-0.410304\pi\) | ||||
0.278073 | + | 0.960560i | \(0.410304\pi\) | |||||||
\(368\) | −11148.1 | −1.57917 | ||||||||
\(369\) | −1784.89 | −0.251809 | ||||||||
\(370\) | −12802.7 | −1.79887 | ||||||||
\(371\) | −12738.2 | −1.78257 | ||||||||
\(372\) | −1011.73 | −0.141010 | ||||||||
\(373\) | 11377.6 | 1.57938 | 0.789691 | − | 0.613505i | \(-0.210241\pi\) | ||||
0.789691 | + | 0.613505i | \(0.210241\pi\) | |||||||
\(374\) | 5892.39 | 0.814675 | ||||||||
\(375\) | −3036.47 | −0.418141 | ||||||||
\(376\) | −1356.00 | −0.185986 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 2363.80 | 0.321643 | ||||||||
\(379\) | 4032.22 | 0.546494 | 0.273247 | − | 0.961944i | \(-0.411902\pi\) | ||||
0.273247 | + | 0.961944i | \(0.411902\pi\) | |||||||
\(380\) | −3722.16 | −0.502481 | ||||||||
\(381\) | 369.694 | 0.0497113 | ||||||||
\(382\) | 294.675 | 0.0394682 | ||||||||
\(383\) | 1990.96 | 0.265622 | 0.132811 | − | 0.991141i | \(-0.457600\pi\) | ||||
0.132811 | + | 0.991141i | \(0.457600\pi\) | |||||||
\(384\) | 5186.23 | 0.689216 | ||||||||
\(385\) | −10024.0 | −1.32693 | ||||||||
\(386\) | −2783.70 | −0.367063 | ||||||||
\(387\) | 1391.90 | 0.182828 | ||||||||
\(388\) | −1627.53 | −0.212952 | ||||||||
\(389\) | −11122.4 | −1.44969 | −0.724846 | − | 0.688911i | \(-0.758089\pi\) | ||||
−0.724846 | + | 0.688911i | \(0.758089\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11932.8 | 1.54339 | ||||||||
\(392\) | −6365.39 | −0.820155 | ||||||||
\(393\) | −3655.22 | −0.469164 | ||||||||
\(394\) | −14243.4 | −1.82125 | ||||||||
\(395\) | −18411.4 | −2.34527 | ||||||||
\(396\) | 530.035 | 0.0672608 | ||||||||
\(397\) | −10778.1 | −1.36256 | −0.681282 | − | 0.732021i | \(-0.738577\pi\) | ||||
−0.681282 | + | 0.732021i | \(0.738577\pi\) | |||||||
\(398\) | −10913.8 | −1.37452 | ||||||||
\(399\) | 6176.82 | 0.775007 | ||||||||
\(400\) | −14331.4 | −1.79142 | ||||||||
\(401\) | 4711.58 | 0.586746 | 0.293373 | − | 0.955998i | \(-0.405222\pi\) | ||||
0.293373 | + | 0.955998i | \(0.405222\pi\) | |||||||
\(402\) | 4767.55 | 0.591502 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 701.978 | 0.0864473 | ||||||||
\(405\) | −1420.85 | −0.174328 | ||||||||
\(406\) | 11751.0 | 1.43643 | ||||||||
\(407\) | 4763.94 | 0.580196 | ||||||||
\(408\) | −4334.79 | −0.525991 | ||||||||
\(409\) | −1184.78 | −0.143236 | −0.0716179 | − | 0.997432i | \(-0.522816\pi\) | ||||
−0.0716179 | + | 0.997432i | \(0.522816\pi\) | |||||||
\(410\) | 11407.0 | 1.37403 | ||||||||
\(411\) | −8186.49 | −0.982505 | ||||||||
\(412\) | −680.638 | −0.0813899 | ||||||||
\(413\) | 1146.18 | 0.136561 | ||||||||
\(414\) | 4194.05 | 0.497890 | ||||||||
\(415\) | 15118.9 | 1.78834 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9338.35 | 1.09664 | ||||||||
\(418\) | 5411.75 | 0.633248 | ||||||||
\(419\) | −6168.30 | −0.719191 | −0.359596 | − | 0.933108i | \(-0.617085\pi\) | ||||
−0.359596 | + | 0.933108i | \(0.617085\pi\) | |||||||
\(420\) | −3866.26 | −0.449177 | ||||||||
\(421\) | 10328.8 | 1.19571 | 0.597857 | − | 0.801603i | \(-0.296019\pi\) | ||||
0.597857 | + | 0.801603i | \(0.296019\pi\) | |||||||
\(422\) | −15082.9 | −1.73987 | ||||||||
\(423\) | 709.160 | 0.0815143 | ||||||||
\(424\) | 8210.27 | 0.940392 | ||||||||
\(425\) | 15340.1 | 1.75084 | ||||||||
\(426\) | −3761.96 | −0.427858 | ||||||||
\(427\) | 13257.5 | 1.50252 | ||||||||
\(428\) | 1880.72 | 0.212402 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8895.46 | −0.997622 | ||||||||
\(431\) | 11312.5 | 1.26427 | 0.632137 | − | 0.774857i | \(-0.282178\pi\) | ||||
0.632137 | + | 0.774857i | \(0.282178\pi\) | |||||||
\(432\) | −2117.93 | −0.235877 | ||||||||
\(433\) | −10475.7 | −1.16266 | −0.581331 | − | 0.813667i | \(-0.697468\pi\) | ||||
−0.581331 | + | 0.813667i | \(0.697468\pi\) | |||||||
\(434\) | −10729.8 | −1.18675 | ||||||||
\(435\) | −7063.38 | −0.778536 | ||||||||
\(436\) | −4671.68 | −0.513149 | ||||||||
\(437\) | 10959.4 | 1.19968 | ||||||||
\(438\) | −1904.64 | −0.207779 | ||||||||
\(439\) | −2040.62 | −0.221853 | −0.110926 | − | 0.993829i | \(-0.535382\pi\) | ||||
−0.110926 | + | 0.993829i | \(0.535382\pi\) | |||||||
\(440\) | 6460.85 | 0.700020 | ||||||||
\(441\) | 3328.96 | 0.359460 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4089.28 | −0.438572 | −0.219286 | − | 0.975661i | \(-0.570373\pi\) | ||||
−0.219286 | + | 0.975661i | \(0.570373\pi\) | |||||||
\(444\) | 1837.46 | 0.196401 | ||||||||
\(445\) | 16973.9 | 1.80818 | ||||||||
\(446\) | 8294.43 | 0.880611 | ||||||||
\(447\) | −4111.71 | −0.435072 | ||||||||
\(448\) | 6289.99 | 0.663335 | ||||||||
\(449\) | 15217.9 | 1.59951 | 0.799753 | − | 0.600330i | \(-0.204964\pi\) | ||||
0.799753 | + | 0.600330i | \(0.204964\pi\) | |||||||
\(450\) | 5391.65 | 0.564810 | ||||||||
\(451\) | −4244.58 | −0.443169 | ||||||||
\(452\) | −1047.58 | −0.109014 | ||||||||
\(453\) | 8542.67 | 0.886026 | ||||||||
\(454\) | −122.197 | −0.0126322 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3981.20 | −0.408853 | ||||||||
\(457\) | −876.316 | −0.0896988 | −0.0448494 | − | 0.998994i | \(-0.514281\pi\) | ||||
−0.0448494 | + | 0.998994i | \(0.514281\pi\) | |||||||
\(458\) | 13425.6 | 1.36973 | ||||||||
\(459\) | 2267.00 | 0.230533 | ||||||||
\(460\) | −6859.84 | −0.695308 | ||||||||
\(461\) | 16293.4 | 1.64611 | 0.823057 | − | 0.567959i | \(-0.192267\pi\) | ||||
0.823057 | + | 0.567959i | \(0.192267\pi\) | |||||||
\(462\) | 5621.27 | 0.566072 | ||||||||
\(463\) | −11704.8 | −1.17488 | −0.587438 | − | 0.809269i | \(-0.699863\pi\) | ||||
−0.587438 | + | 0.809269i | \(0.699863\pi\) | |||||||
\(464\) | −10528.7 | −1.05341 | ||||||||
\(465\) | 6449.59 | 0.643209 | ||||||||
\(466\) | 4807.12 | 0.477866 | ||||||||
\(467\) | −15616.1 | −1.54738 | −0.773688 | − | 0.633567i | \(-0.781590\pi\) | ||||
−0.773688 | + | 0.633567i | \(0.781590\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12940.3 | 1.27405 | ||||||||
\(470\) | −4532.15 | −0.444792 | ||||||||
\(471\) | 10062.0 | 0.984358 | ||||||||
\(472\) | −738.757 | −0.0720424 | ||||||||
\(473\) | 3310.03 | 0.321766 | ||||||||
\(474\) | 10324.8 | 1.00050 | ||||||||
\(475\) | 14088.8 | 1.36093 | ||||||||
\(476\) | 6168.70 | 0.593996 | ||||||||
\(477\) | −4293.79 | −0.412158 | ||||||||
\(478\) | 18101.7 | 1.73212 | ||||||||
\(479\) | −10376.0 | −0.989755 | −0.494877 | − | 0.868963i | \(-0.664787\pi\) | ||||
−0.494877 | + | 0.868963i | \(0.664787\pi\) | |||||||
\(480\) | 6290.44 | 0.598163 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −8740.53 | −0.825976 | ||||||||
\(483\) | 11383.7 | 1.07242 | ||||||||
\(484\) | −2402.01 | −0.225584 | ||||||||
\(485\) | 10375.2 | 0.971369 | ||||||||
\(486\) | 796.791 | 0.0743686 | ||||||||
\(487\) | 3994.27 | 0.371658 | 0.185829 | − | 0.982582i | \(-0.440503\pi\) | ||||
0.185829 | + | 0.982582i | \(0.440503\pi\) | |||||||
\(488\) | −8545.01 | −0.792652 | ||||||||
\(489\) | 6588.55 | 0.609294 | ||||||||
\(490\) | −21275.0 | −1.96144 | ||||||||
\(491\) | 12267.3 | 1.12753 | 0.563763 | − | 0.825936i | \(-0.309353\pi\) | ||||
0.563763 | + | 0.825936i | \(0.309353\pi\) | |||||||
\(492\) | −1637.14 | −0.150016 | ||||||||
\(493\) | 11269.8 | 1.02954 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3378.88 | −0.306807 | ||||||||
\(496\) | 9613.75 | 0.870303 | ||||||||
\(497\) | −10210.9 | −0.921573 | ||||||||
\(498\) | −8478.44 | −0.762907 | ||||||||
\(499\) | 3578.76 | 0.321056 | 0.160528 | − | 0.987031i | \(-0.448680\pi\) | ||||
0.160528 | + | 0.987031i | \(0.448680\pi\) | |||||||
\(500\) | −2785.12 | −0.249109 | ||||||||
\(501\) | −2737.61 | −0.244126 | ||||||||
\(502\) | 5178.19 | 0.460386 | ||||||||
\(503\) | −1296.82 | −0.114955 | −0.0574774 | − | 0.998347i | \(-0.518306\pi\) | ||||
−0.0574774 | + | 0.998347i | \(0.518306\pi\) | |||||||
\(504\) | −4135.34 | −0.365482 | ||||||||
\(505\) | −4474.99 | −0.394325 | ||||||||
\(506\) | 9973.72 | 0.876257 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 339.092 | 0.0296157 | ||||||||
\(509\) | −4728.60 | −0.411771 | −0.205886 | − | 0.978576i | \(-0.566007\pi\) | ||||
−0.205886 | + | 0.978576i | \(0.566007\pi\) | |||||||
\(510\) | −14488.1 | −1.25793 | ||||||||
\(511\) | −5169.69 | −0.447541 | ||||||||
\(512\) | −1422.78 | −0.122810 | ||||||||
\(513\) | 2082.08 | 0.179193 | ||||||||
\(514\) | −8734.90 | −0.749571 | ||||||||
\(515\) | 4338.95 | 0.371256 | ||||||||
\(516\) | 1276.68 | 0.108920 | ||||||||
\(517\) | 1686.43 | 0.143460 | ||||||||
\(518\) | 19487.1 | 1.65293 | ||||||||
\(519\) | 2698.91 | 0.228264 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9220.74 | −0.775370 | −0.387685 | − | 0.921792i | \(-0.626725\pi\) | ||||
−0.387685 | + | 0.921792i | \(0.626725\pi\) | |||||||
\(522\) | 3961.03 | 0.332125 | ||||||||
\(523\) | −12102.7 | −1.01188 | −0.505939 | − | 0.862569i | \(-0.668854\pi\) | ||||
−0.505939 | + | 0.862569i | \(0.668854\pi\) | |||||||
\(524\) | −3352.65 | −0.279506 | ||||||||
\(525\) | 14634.3 | 1.21656 | ||||||||
\(526\) | −7990.64 | −0.662373 | ||||||||
\(527\) | −10290.4 | −0.850585 | ||||||||
\(528\) | −5036.56 | −0.415129 | ||||||||
\(529\) | 8030.91 | 0.660057 | ||||||||
\(530\) | 27441.1 | 2.24899 | ||||||||
\(531\) | 386.353 | 0.0315750 | ||||||||
\(532\) | 5665.52 | 0.461713 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −9518.65 | −0.771371 | ||||||||
\(535\) | −11989.3 | −0.968862 | ||||||||
\(536\) | −8340.56 | −0.672122 | ||||||||
\(537\) | 939.833 | 0.0755248 | ||||||||
\(538\) | −8798.08 | −0.705041 | ||||||||
\(539\) | 7916.48 | 0.632629 | ||||||||
\(540\) | −1303.24 | −0.103857 | ||||||||
\(541\) | 12801.3 | 1.01732 | 0.508659 | − | 0.860968i | \(-0.330141\pi\) | ||||
0.508659 | + | 0.860968i | \(0.330141\pi\) | |||||||
\(542\) | 12647.5 | 1.00231 | ||||||||
\(543\) | −8235.17 | −0.650838 | ||||||||
\(544\) | −10036.5 | −0.791015 | ||||||||
\(545\) | 29781.2 | 2.34071 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 400.693 | 0.0313207 | 0.0156603 | − | 0.999877i | \(-0.495015\pi\) | ||||
0.0156603 | + | 0.999877i | \(0.495015\pi\) | |||||||
\(548\) | −7508.84 | −0.585331 | ||||||||
\(549\) | 4468.85 | 0.347406 | ||||||||
\(550\) | 12821.7 | 0.994033 | ||||||||
\(551\) | 10350.5 | 0.800265 | ||||||||
\(552\) | −7337.25 | −0.565751 | ||||||||
\(553\) | 28024.2 | 2.15499 | ||||||||
\(554\) | 3622.96 | 0.277843 | ||||||||
\(555\) | −11713.5 | −0.895873 | ||||||||
\(556\) | 8565.35 | 0.653330 | ||||||||
\(557\) | 14475.5 | 1.10116 | 0.550582 | − | 0.834781i | \(-0.314406\pi\) | ||||
0.550582 | + | 0.834781i | \(0.314406\pi\) | |||||||
\(558\) | −3616.82 | −0.274394 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 36738.5 | 2.77229 | ||||||||
\(561\) | 5391.07 | 0.405724 | ||||||||
\(562\) | −16337.8 | −1.22628 | ||||||||
\(563\) | −14776.4 | −1.10613 | −0.553063 | − | 0.833139i | \(-0.686541\pi\) | ||||
−0.553063 | + | 0.833139i | \(0.686541\pi\) | |||||||
\(564\) | 650.458 | 0.0485625 | ||||||||
\(565\) | 6678.17 | 0.497261 | ||||||||
\(566\) | 8475.68 | 0.629434 | ||||||||
\(567\) | 2162.69 | 0.160184 | ||||||||
\(568\) | 6581.33 | 0.486173 | ||||||||
\(569\) | −6868.88 | −0.506078 | −0.253039 | − | 0.967456i | \(-0.581430\pi\) | ||||
−0.253039 | + | 0.967456i | \(0.581430\pi\) | |||||||
\(570\) | −13306.3 | −0.977790 | ||||||||
\(571\) | 3011.00 | 0.220677 | 0.110338 | − | 0.993894i | \(-0.464807\pi\) | ||||
0.110338 | + | 0.993894i | \(0.464807\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 269.604 | 0.0196559 | ||||||||
\(574\) | −17362.6 | −1.26255 | ||||||||
\(575\) | 25965.4 | 1.88318 | ||||||||
\(576\) | 2120.23 | 0.153373 | ||||||||
\(577\) | −23106.6 | −1.66714 | −0.833572 | − | 0.552411i | \(-0.813708\pi\) | ||||
−0.833572 | + | 0.552411i | \(0.813708\pi\) | |||||||
\(578\) | 7006.45 | 0.504204 | ||||||||
\(579\) | −2546.86 | −0.182805 | ||||||||
\(580\) | −6478.70 | −0.463816 | ||||||||
\(581\) | −23012.6 | −1.64324 | ||||||||
\(582\) | −5818.24 | −0.414388 | ||||||||
\(583\) | −10210.9 | −0.725374 | ||||||||
\(584\) | 3332.07 | 0.236099 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 303.463 | 0.0213924 | ||||||||
\(587\) | 3024.81 | 0.212687 | 0.106343 | − | 0.994329i | \(-0.466086\pi\) | ||||
0.106343 | + | 0.994329i | \(0.466086\pi\) | |||||||
\(588\) | 3053.40 | 0.214150 | ||||||||
\(589\) | −9451.05 | −0.661161 | ||||||||
\(590\) | −2469.13 | −0.172293 | ||||||||
\(591\) | −13031.6 | −0.907019 | ||||||||
\(592\) | −17460.1 | −1.21217 | ||||||||
\(593\) | −6396.07 | −0.442926 | −0.221463 | − | 0.975169i | \(-0.571083\pi\) | ||||
−0.221463 | + | 0.975169i | \(0.571083\pi\) | |||||||
\(594\) | 1894.82 | 0.130884 | ||||||||
\(595\) | −39324.4 | −2.70948 | ||||||||
\(596\) | −3771.36 | −0.259196 | ||||||||
\(597\) | −9985.22 | −0.684536 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12095.9 | 0.825084 | 0.412542 | − | 0.910939i | \(-0.364641\pi\) | ||||
0.412542 | + | 0.910939i | \(0.364641\pi\) | |||||||
\(600\) | −9432.38 | −0.641792 | ||||||||
\(601\) | −11816.5 | −0.802005 | −0.401003 | − | 0.916077i | \(-0.631338\pi\) | ||||
−0.401003 | + | 0.916077i | \(0.631338\pi\) | |||||||
\(602\) | 13539.8 | 0.916682 | ||||||||
\(603\) | 4361.93 | 0.294580 | ||||||||
\(604\) | 7835.54 | 0.527853 | ||||||||
\(605\) | 15312.4 | 1.02899 | ||||||||
\(606\) | 2509.50 | 0.168220 | ||||||||
\(607\) | −25164.0 | −1.68266 | −0.841329 | − | 0.540523i | \(-0.818226\pi\) | ||||
−0.841329 | + | 0.540523i | \(0.818226\pi\) | |||||||
\(608\) | −9217.85 | −0.614857 | ||||||||
\(609\) | 10751.2 | 0.715372 | ||||||||
\(610\) | −28559.8 | −1.89566 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 2079.35 | 0.137341 | ||||||||
\(613\) | 19583.0 | 1.29030 | 0.645148 | − | 0.764058i | \(-0.276796\pi\) | ||||
0.645148 | + | 0.764058i | \(0.276796\pi\) | |||||||
\(614\) | 13048.5 | 0.857648 | ||||||||
\(615\) | 10436.5 | 0.684292 | ||||||||
\(616\) | −9834.10 | −0.643226 | ||||||||
\(617\) | 19677.1 | 1.28390 | 0.641952 | − | 0.766745i | \(-0.278125\pi\) | ||||
0.641952 | + | 0.766745i | \(0.278125\pi\) | |||||||
\(618\) | −2433.21 | −0.158379 | ||||||||
\(619\) | −4394.05 | −0.285318 | −0.142659 | − | 0.989772i | \(-0.545565\pi\) | ||||
−0.142659 | + | 0.989772i | \(0.545565\pi\) | |||||||
\(620\) | 5915.71 | 0.383194 | ||||||||
\(621\) | 3837.22 | 0.247959 | ||||||||
\(622\) | 11315.5 | 0.729435 | ||||||||
\(623\) | −25836.0 | −1.66147 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5082.96 | −0.325310 | ||||||||
\(626\) | −20293.7 | −1.29568 | ||||||||
\(627\) | 4951.32 | 0.315370 | ||||||||
\(628\) | 9229.10 | 0.586435 | ||||||||
\(629\) | 18689.1 | 1.18471 | ||||||||
\(630\) | −13821.5 | −0.874065 | ||||||||
\(631\) | −23887.7 | −1.50706 | −0.753529 | − | 0.657415i | \(-0.771650\pi\) | ||||
−0.753529 | + | 0.657415i | \(0.771650\pi\) | |||||||
\(632\) | −18062.7 | −1.13686 | ||||||||
\(633\) | −13799.7 | −0.866488 | ||||||||
\(634\) | −17830.4 | −1.11693 | ||||||||
\(635\) | −2161.65 | −0.135091 | ||||||||
\(636\) | −3938.37 | −0.245545 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 9419.57 | 0.584521 | ||||||||
\(639\) | −3441.89 | −0.213082 | ||||||||
\(640\) | −30324.6 | −1.87295 | ||||||||
\(641\) | −5443.62 | −0.335429 | −0.167714 | − | 0.985836i | \(-0.553639\pi\) | ||||
−0.167714 | + | 0.985836i | \(0.553639\pi\) | |||||||
\(642\) | 6723.38 | 0.413318 | ||||||||
\(643\) | 5839.00 | 0.358115 | 0.179057 | − | 0.983839i | \(-0.442695\pi\) | ||||
0.179057 | + | 0.983839i | \(0.442695\pi\) | |||||||
\(644\) | 10441.4 | 0.638896 | ||||||||
\(645\) | −8138.64 | −0.496835 | ||||||||
\(646\) | 21230.5 | 1.29304 | ||||||||
\(647\) | 8708.86 | 0.529182 | 0.264591 | − | 0.964361i | \(-0.414763\pi\) | ||||
0.264591 | + | 0.964361i | \(0.414763\pi\) | |||||||
\(648\) | −1393.94 | −0.0845049 | ||||||||
\(649\) | 918.773 | 0.0555701 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9816.96 | −0.591024 | ||||||||
\(652\) | 6043.17 | 0.362989 | ||||||||
\(653\) | 2794.93 | 0.167495 | 0.0837475 | − | 0.996487i | \(-0.473311\pi\) | ||||
0.0837475 | + | 0.996487i | \(0.473311\pi\) | |||||||
\(654\) | −16700.8 | −0.998550 | ||||||||
\(655\) | 21372.6 | 1.27495 | ||||||||
\(656\) | 15556.6 | 0.925890 | ||||||||
\(657\) | −1742.60 | −0.103478 | ||||||||
\(658\) | 6898.41 | 0.408705 | ||||||||
\(659\) | 31389.9 | 1.85550 | 0.927752 | − | 0.373197i | \(-0.121738\pi\) | ||||
0.927752 | + | 0.373197i | \(0.121738\pi\) | |||||||
\(660\) | −3099.19 | −0.182781 | ||||||||
\(661\) | −20597.2 | −1.21201 | −0.606005 | − | 0.795461i | \(-0.707229\pi\) | ||||
−0.606005 | + | 0.795461i | \(0.707229\pi\) | |||||||
\(662\) | −21728.6 | −1.27569 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 14832.5 | 0.866889 | ||||||||
\(665\) | −36116.7 | −2.10608 | ||||||||
\(666\) | 6568.72 | 0.382181 | ||||||||
\(667\) | 19075.7 | 1.10737 | ||||||||
\(668\) | −2511.00 | −0.145439 | ||||||||
\(669\) | 7588.74 | 0.438562 | ||||||||
\(670\) | −27876.5 | −1.60741 | ||||||||
\(671\) | 10627.2 | 0.611414 | ||||||||
\(672\) | −9574.72 | −0.549632 | ||||||||
\(673\) | −17935.8 | −1.02730 | −0.513651 | − | 0.857999i | \(-0.671707\pi\) | ||||
−0.513651 | + | 0.857999i | \(0.671707\pi\) | |||||||
\(674\) | −18161.0 | −1.03789 | ||||||||
\(675\) | 4932.93 | 0.281287 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −24104.0 | −1.36838 | −0.684188 | − | 0.729305i | \(-0.739843\pi\) | ||||
−0.684188 | + | 0.729305i | \(0.739843\pi\) | |||||||
\(678\) | −3745.00 | −0.212133 | ||||||||
\(679\) | −15792.2 | −0.892560 | ||||||||
\(680\) | 25346.1 | 1.42938 | ||||||||
\(681\) | −111.801 | −0.00629107 | ||||||||
\(682\) | −8601.02 | −0.482918 | ||||||||
\(683\) | 6744.25 | 0.377835 | 0.188918 | − | 0.981993i | \(-0.439502\pi\) | ||||
0.188918 | + | 0.981993i | \(0.439502\pi\) | |||||||
\(684\) | 1909.73 | 0.106755 | ||||||||
\(685\) | 47867.5 | 2.66996 | ||||||||
\(686\) | 2353.69 | 0.130998 | ||||||||
\(687\) | 12283.3 | 0.682153 | ||||||||
\(688\) | −12131.5 | −0.672249 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −24523.2 | −1.35302 | ||||||||
\(691\) | 30844.4 | 1.69809 | 0.849043 | − | 0.528323i | \(-0.177179\pi\) | ||||
0.849043 | + | 0.528323i | \(0.177179\pi\) | |||||||
\(692\) | 2475.50 | 0.135989 | ||||||||
\(693\) | 5143.02 | 0.281915 | ||||||||
\(694\) | 30818.9 | 1.68569 | ||||||||
\(695\) | −54602.6 | −2.98014 | ||||||||
\(696\) | −6929.59 | −0.377393 | ||||||||
\(697\) | −16651.6 | −0.904913 | ||||||||
\(698\) | −18878.1 | −1.02371 | ||||||||
\(699\) | 4398.13 | 0.237987 | ||||||||
\(700\) | 13422.9 | 0.724769 | ||||||||
\(701\) | −21007.6 | −1.13188 | −0.565940 | − | 0.824447i | \(-0.691486\pi\) | ||||
−0.565940 | + | 0.824447i | \(0.691486\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17164.6 | 0.920877 | ||||||||
\(704\) | 5042.04 | 0.269928 | ||||||||
\(705\) | −4146.56 | −0.221515 | ||||||||
\(706\) | −11338.1 | −0.604413 | ||||||||
\(707\) | 6811.41 | 0.362333 | ||||||||
\(708\) | 354.372 | 0.0188109 | ||||||||
\(709\) | 14763.4 | 0.782017 | 0.391008 | − | 0.920387i | \(-0.372126\pi\) | ||||
0.391008 | + | 0.920387i | \(0.372126\pi\) | |||||||
\(710\) | 21996.7 | 1.16271 | ||||||||
\(711\) | 9446.39 | 0.498266 | ||||||||
\(712\) | 16652.3 | 0.876507 | ||||||||
\(713\) | −17418.0 | −0.914882 | ||||||||
\(714\) | 22052.4 | 1.15587 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 862.037 | 0.0449942 | ||||||||
\(717\) | 16561.6 | 0.862628 | ||||||||
\(718\) | 23506.8 | 1.22182 | ||||||||
\(719\) | −26186.3 | −1.35825 | −0.679126 | − | 0.734022i | \(-0.737641\pi\) | ||||
−0.679126 | + | 0.734022i | \(0.737641\pi\) | |||||||
\(720\) | 12383.8 | 0.640996 | ||||||||
\(721\) | −6604.34 | −0.341135 | ||||||||
\(722\) | −2991.76 | −0.154213 | ||||||||
\(723\) | −7996.89 | −0.411352 | ||||||||
\(724\) | −7553.49 | −0.387739 | ||||||||
\(725\) | 24522.7 | 1.25621 | ||||||||
\(726\) | −8586.94 | −0.438969 | ||||||||
\(727\) | 20044.0 | 1.02254 | 0.511272 | − | 0.859419i | \(-0.329175\pi\) | ||||
0.511272 | + | 0.859419i | \(0.329175\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 11136.7 | 0.564641 | ||||||||
\(731\) | 12985.4 | 0.657019 | ||||||||
\(732\) | 4098.93 | 0.206968 | ||||||||
\(733\) | −25555.5 | −1.28774 | −0.643871 | − | 0.765134i | \(-0.722673\pi\) | ||||
−0.643871 | + | 0.765134i | \(0.722673\pi\) | |||||||
\(734\) | 12821.1 | 0.644737 | ||||||||
\(735\) | −19464.9 | −0.976834 | ||||||||
\(736\) | −16988.2 | −0.850809 | ||||||||
\(737\) | 10372.9 | 0.518443 | ||||||||
\(738\) | −5852.60 | −0.291920 | ||||||||
\(739\) | −11108.5 | −0.552953 | −0.276477 | − | 0.961021i | \(-0.589167\pi\) | ||||
−0.276477 | + | 0.961021i | \(0.589167\pi\) | |||||||
\(740\) | −10743.9 | −0.533720 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −41768.2 | −2.06652 | ||||||||
\(743\) | −28188.2 | −1.39182 | −0.695911 | − | 0.718128i | \(-0.744999\pi\) | ||||
−0.695911 | + | 0.718128i | \(0.744999\pi\) | |||||||
\(744\) | 6327.42 | 0.311793 | ||||||||
\(745\) | 24041.7 | 1.18231 | ||||||||
\(746\) | 37306.8 | 1.83096 | ||||||||
\(747\) | −7757.10 | −0.379943 | ||||||||
\(748\) | 4944.82 | 0.241712 | ||||||||
\(749\) | 18248.9 | 0.890256 | ||||||||
\(750\) | −9956.51 | −0.484747 | ||||||||
\(751\) | 17176.6 | 0.834596 | 0.417298 | − | 0.908770i | \(-0.362977\pi\) | ||||
0.417298 | + | 0.908770i | \(0.362977\pi\) | |||||||
\(752\) | −6180.86 | −0.299724 | ||||||||
\(753\) | 4737.63 | 0.229281 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −49950.2 | −2.40778 | ||||||||
\(756\) | 1983.67 | 0.0954304 | ||||||||
\(757\) | −4409.96 | −0.211734 | −0.105867 | − | 0.994380i | \(-0.533762\pi\) | ||||
−0.105867 | + | 0.994380i | \(0.533762\pi\) | |||||||
\(758\) | 13221.5 | 0.633546 | ||||||||
\(759\) | 9125.16 | 0.436393 | ||||||||
\(760\) | 23278.6 | 1.11106 | ||||||||
\(761\) | 32443.6 | 1.54544 | 0.772721 | − | 0.634746i | \(-0.218895\pi\) | ||||
0.772721 | + | 0.634746i | \(0.218895\pi\) | |||||||
\(762\) | 1212.22 | 0.0576300 | ||||||||
\(763\) | −45330.1 | −2.15080 | ||||||||
\(764\) | 247.287 | 0.0117101 | ||||||||
\(765\) | −13255.5 | −0.626473 | ||||||||
\(766\) | 6528.30 | 0.307934 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 11351.6 | 0.533353 | ||||||||
\(769\) | −31994.1 | −1.50031 | −0.750155 | − | 0.661263i | \(-0.770021\pi\) | ||||
−0.750155 | + | 0.661263i | \(0.770021\pi\) | |||||||
\(770\) | −32868.4 | −1.53830 | ||||||||
\(771\) | −7991.73 | −0.373301 | ||||||||
\(772\) | −2336.04 | −0.108907 | ||||||||
\(773\) | −8979.39 | −0.417809 | −0.208904 | − | 0.977936i | \(-0.566990\pi\) | ||||
−0.208904 | + | 0.977936i | \(0.566990\pi\) | |||||||
\(774\) | 4564.01 | 0.211951 | ||||||||
\(775\) | −22391.7 | −1.03785 | ||||||||
\(776\) | 10178.7 | 0.470868 | ||||||||
\(777\) | 17829.2 | 0.823189 | ||||||||
\(778\) | −36470.2 | −1.68062 | ||||||||
\(779\) | −15293.3 | −0.703390 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8185.04 | −0.375011 | ||||||||
\(782\) | 39127.2 | 1.78924 | ||||||||
\(783\) | 3624.02 | 0.165405 | ||||||||
\(784\) | −29014.4 | −1.32172 | ||||||||
\(785\) | −58833.9 | −2.67500 | ||||||||
\(786\) | −11985.4 | −0.543898 | ||||||||
\(787\) | −12570.5 | −0.569366 | −0.284683 | − | 0.958622i | \(-0.591888\pi\) | ||||
−0.284683 | + | 0.958622i | \(0.591888\pi\) | |||||||
\(788\) | −11952.9 | −0.540360 | ||||||||
\(789\) | −7310.80 | −0.329875 | ||||||||
\(790\) | −60370.6 | −2.71885 | ||||||||
\(791\) | −10164.9 | −0.456917 | ||||||||
\(792\) | −3314.88 | −0.148724 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −35341.2 | −1.57961 | ||||||||
\(795\) | 25106.4 | 1.12004 | ||||||||
\(796\) | −9158.67 | −0.407815 | ||||||||
\(797\) | 37863.3 | 1.68280 | 0.841398 | − | 0.540416i | \(-0.181733\pi\) | ||||
0.841398 | + | 0.540416i | \(0.181733\pi\) | |||||||
\(798\) | 20253.6 | 0.898460 | ||||||||
\(799\) | 6615.91 | 0.292934 | ||||||||
\(800\) | −21839.2 | −0.965165 | ||||||||
\(801\) | −8708.81 | −0.384158 | ||||||||
\(802\) | 15449.2 | 0.680210 | ||||||||
\(803\) | −4144.01 | −0.182116 | ||||||||
\(804\) | 4000.86 | 0.175497 | ||||||||
\(805\) | −66562.1 | −2.91429 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8049.54 | −0.351124 | ||||||||
\(808\) | −4390.22 | −0.191148 | ||||||||
\(809\) | 2503.79 | 0.108812 | 0.0544058 | − | 0.998519i | \(-0.482674\pi\) | ||||
0.0544058 | + | 0.998519i | \(0.482674\pi\) | |||||||
\(810\) | −4658.94 | −0.202097 | ||||||||
\(811\) | −5409.55 | −0.234223 | −0.117112 | − | 0.993119i | \(-0.537364\pi\) | ||||
−0.117112 | + | 0.993119i | \(0.537364\pi\) | |||||||
\(812\) | 9861.27 | 0.426186 | ||||||||
\(813\) | 11571.4 | 0.499172 | ||||||||
\(814\) | 15620.8 | 0.672617 | ||||||||
\(815\) | −38524.2 | −1.65576 | ||||||||
\(816\) | −19758.6 | −0.847658 | ||||||||
\(817\) | 11926.1 | 0.510702 | ||||||||
\(818\) | −3884.85 | −0.166052 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9572.58 | 0.407669 | ||||||||
\(821\) | −31381.6 | −1.33401 | −0.667007 | − | 0.745051i | \(-0.732425\pi\) | ||||
−0.667007 | + | 0.745051i | \(0.732425\pi\) | |||||||
\(822\) | −26843.3 | −1.13901 | ||||||||
\(823\) | −33046.1 | −1.39965 | −0.699827 | − | 0.714312i | \(-0.746740\pi\) | ||||
−0.699827 | + | 0.714312i | \(0.746740\pi\) | |||||||
\(824\) | 4256.76 | 0.179965 | ||||||||
\(825\) | 11730.8 | 0.495048 | ||||||||
\(826\) | 3758.29 | 0.158314 | ||||||||
\(827\) | −33653.7 | −1.41506 | −0.707529 | − | 0.706684i | \(-0.750190\pi\) | ||||
−0.707529 | + | 0.706684i | \(0.750190\pi\) | |||||||
\(828\) | 3519.59 | 0.147722 | ||||||||
\(829\) | 12898.5 | 0.540390 | 0.270195 | − | 0.962806i | \(-0.412912\pi\) | ||||
0.270195 | + | 0.962806i | \(0.412912\pi\) | |||||||
\(830\) | 49574.6 | 2.07320 | ||||||||
\(831\) | 3314.72 | 0.138371 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 31056.6 | 1.29177 | ||||||||
\(834\) | 30620.2 | 1.27133 | ||||||||
\(835\) | 16007.2 | 0.663414 | ||||||||
\(836\) | 4541.47 | 0.187883 | ||||||||
\(837\) | −3309.10 | −0.136654 | ||||||||
\(838\) | −20225.7 | −0.833753 | ||||||||
\(839\) | −395.829 | −0.0162879 | −0.00814395 | − | 0.999967i | \(-0.502592\pi\) | ||||
−0.00814395 | + | 0.999967i | \(0.502592\pi\) | |||||||
\(840\) | 24179.9 | 0.993197 | ||||||||
\(841\) | −6373.17 | −0.261313 | ||||||||
\(842\) | 33867.9 | 1.38618 | ||||||||
\(843\) | −14947.7 | −0.610709 | ||||||||
\(844\) | −12657.4 | −0.516214 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2325.32 | 0.0944989 | ||||||||
\(847\) | −23307.1 | −0.945505 | ||||||||
\(848\) | 37423.6 | 1.51548 | ||||||||
\(849\) | 7754.57 | 0.313470 | ||||||||
\(850\) | 50299.9 | 2.02973 | ||||||||
\(851\) | 31634.0 | 1.27426 | ||||||||
\(852\) | −3156.98 | −0.126944 | ||||||||
\(853\) | −21248.9 | −0.852930 | −0.426465 | − | 0.904504i | \(-0.640241\pi\) | ||||
−0.426465 | + | 0.904504i | \(0.640241\pi\) | |||||||
\(854\) | 43471.1 | 1.74186 | ||||||||
\(855\) | −12174.2 | −0.486958 | ||||||||
\(856\) | −11762.2 | −0.469653 | ||||||||
\(857\) | −9920.37 | −0.395418 | −0.197709 | − | 0.980261i | \(-0.563350\pi\) | ||||
−0.197709 | + | 0.980261i | \(0.563350\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20946.3 | 0.831990 | 0.415995 | − | 0.909367i | \(-0.363433\pi\) | ||||
0.415995 | + | 0.909367i | \(0.363433\pi\) | |||||||
\(860\) | −7464.95 | −0.295991 | ||||||||
\(861\) | −15885.4 | −0.628774 | ||||||||
\(862\) | 37093.2 | 1.46566 | ||||||||
\(863\) | −11271.4 | −0.444594 | −0.222297 | − | 0.974979i | \(-0.571355\pi\) | ||||
−0.222297 | + | 0.974979i | \(0.571355\pi\) | |||||||
\(864\) | −3227.45 | −0.127083 | ||||||||
\(865\) | −15780.9 | −0.620308 | ||||||||
\(866\) | −34349.7 | −1.34786 | ||||||||
\(867\) | 6410.34 | 0.251103 | ||||||||
\(868\) | −9004.34 | −0.352105 | ||||||||
\(869\) | 22464.1 | 0.876920 | ||||||||
\(870\) | −23160.7 | −0.902551 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 29217.0 | 1.13465 | ||||||||
\(873\) | −5323.23 | −0.206373 | ||||||||
\(874\) | 35935.6 | 1.39078 | ||||||||
\(875\) | −27024.5 | −1.04411 | ||||||||
\(876\) | −1598.35 | −0.0616476 | ||||||||
\(877\) | −9436.36 | −0.363333 | −0.181667 | − | 0.983360i | \(-0.558149\pi\) | ||||
−0.181667 | + | 0.983360i | \(0.558149\pi\) | |||||||
\(878\) | −6691.13 | −0.257192 | ||||||||
\(879\) | 277.645 | 0.0106538 | ||||||||
\(880\) | 29449.5 | 1.12811 | ||||||||
\(881\) | −20343.0 | −0.777949 | −0.388974 | − | 0.921249i | \(-0.627171\pi\) | ||||
−0.388974 | + | 0.921249i | \(0.627171\pi\) | |||||||
\(882\) | 10915.6 | 0.416719 | ||||||||
\(883\) | 46521.9 | 1.77303 | 0.886515 | − | 0.462699i | \(-0.153119\pi\) | ||||
0.886515 | + | 0.462699i | \(0.153119\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2259.06 | −0.0858051 | ||||||||
\(886\) | −13408.6 | −0.508433 | ||||||||
\(887\) | −19955.1 | −0.755384 | −0.377692 | − | 0.925931i | \(-0.623282\pi\) | ||||
−0.377692 | + | 0.925931i | \(0.623282\pi\) | |||||||
\(888\) | −11491.6 | −0.434272 | ||||||||
\(889\) | 3290.27 | 0.124130 | ||||||||
\(890\) | 55656.8 | 2.09620 | ||||||||
\(891\) | 1733.61 | 0.0651830 | ||||||||
\(892\) | 6960.57 | 0.261275 | ||||||||
\(893\) | 6076.25 | 0.227698 | ||||||||
\(894\) | −13482.2 | −0.504376 | ||||||||
\(895\) | −5495.33 | −0.205239 | ||||||||
\(896\) | 46157.3 | 1.72099 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 49899.1 | 1.85429 | ||||||||
\(899\) | −16450.3 | −0.610286 | ||||||||
\(900\) | 4524.60 | 0.167578 | ||||||||
\(901\) | −40057.7 | −1.48115 | ||||||||
\(902\) | −13917.9 | −0.513762 | ||||||||
\(903\) | 12387.9 | 0.456526 | ||||||||
\(904\) | 6551.67 | 0.241046 | ||||||||
\(905\) | 48152.2 | 1.76866 | ||||||||
\(906\) | 28011.2 | 1.02716 | ||||||||
\(907\) | −2653.95 | −0.0971587 | −0.0485793 | − | 0.998819i | \(-0.515469\pi\) | ||||
−0.0485793 | + | 0.998819i | \(0.515469\pi\) | |||||||
\(908\) | −102.546 | −0.00374793 | ||||||||
\(909\) | 2295.99 | 0.0837769 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1797.50 | 0.0653720 | 0.0326860 | − | 0.999466i | \(-0.489594\pi\) | ||||
0.0326860 | + | 0.999466i | \(0.489594\pi\) | |||||||
\(912\) | −18146.9 | −0.658885 | ||||||||
\(913\) | −18446.9 | −0.668677 | ||||||||
\(914\) | −2873.42 | −0.103987 | ||||||||
\(915\) | −26130.0 | −0.944077 | ||||||||
\(916\) | 11266.6 | 0.406395 | ||||||||
\(917\) | −32531.3 | −1.17151 | ||||||||
\(918\) | 7433.43 | 0.267255 | ||||||||
\(919\) | −48642.0 | −1.74597 | −0.872987 | − | 0.487743i | \(-0.837820\pi\) | ||||
−0.872987 | + | 0.487743i | \(0.837820\pi\) | |||||||
\(920\) | 42901.9 | 1.53743 | ||||||||
\(921\) | 11938.4 | 0.427125 | ||||||||
\(922\) | 53425.6 | 1.90833 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 4717.30 | 0.167952 | ||||||||
\(925\) | 40666.9 | 1.44554 | ||||||||
\(926\) | −38379.7 | −1.36202 | ||||||||
\(927\) | −2226.19 | −0.0788756 | ||||||||
\(928\) | −16044.4 | −0.567545 | ||||||||
\(929\) | −37745.3 | −1.33303 | −0.666513 | − | 0.745493i | \(-0.732214\pi\) | ||||
−0.666513 | + | 0.745493i | \(0.732214\pi\) | |||||||
\(930\) | 21148.0 | 0.745668 | ||||||||
\(931\) | 28523.3 | 1.00410 | ||||||||
\(932\) | 4034.07 | 0.141782 | ||||||||
\(933\) | 10352.7 | 0.363273 | ||||||||
\(934\) | −51204.6 | −1.79386 | ||||||||
\(935\) | −31522.3 | −1.10256 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2705.50 | 0.0943273 | 0.0471637 | − | 0.998887i | \(-0.484982\pi\) | ||||
0.0471637 | + | 0.998887i | \(0.484982\pi\) | |||||||
\(938\) | 42431.0 | 1.47700 | ||||||||
\(939\) | −18567.1 | −0.645276 | ||||||||
\(940\) | −3803.32 | −0.131969 | ||||||||
\(941\) | −5189.27 | −0.179772 | −0.0898860 | − | 0.995952i | \(-0.528650\pi\) | ||||
−0.0898860 | + | 0.995952i | \(0.528650\pi\) | |||||||
\(942\) | 32993.0 | 1.14116 | ||||||||
\(943\) | −28185.2 | −0.973316 | ||||||||
\(944\) | −3367.36 | −0.116100 | ||||||||
\(945\) | −12645.6 | −0.435301 | ||||||||
\(946\) | 10853.5 | 0.373021 | ||||||||
\(947\) | 72.2711 | 0.00247993 | 0.00123997 | − | 0.999999i | \(-0.499605\pi\) | ||||
0.00123997 | + | 0.999999i | \(0.499605\pi\) | |||||||
\(948\) | 8664.45 | 0.296844 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 46196.9 | 1.57771 | ||||||||
\(951\) | −16313.4 | −0.556253 | ||||||||
\(952\) | −38579.5 | −1.31341 | ||||||||
\(953\) | 44695.1 | 1.51922 | 0.759609 | − | 0.650380i | \(-0.225390\pi\) | ||||
0.759609 | + | 0.650380i | \(0.225390\pi\) | |||||||
\(954\) | −14079.2 | −0.477811 | ||||||||
\(955\) | −1576.41 | −0.0534151 | ||||||||
\(956\) | 15190.7 | 0.513914 | ||||||||
\(957\) | 8618.16 | 0.291103 | ||||||||
\(958\) | −34022.7 | −1.14742 | ||||||||
\(959\) | −72859.5 | −2.45334 | ||||||||
\(960\) | −12397.3 | −0.416792 | ||||||||
\(961\) | −14770.2 | −0.495795 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6151.35 | 0.205841 | ||||||||
\(964\) | −7334.93 | −0.245065 | ||||||||
\(965\) | 14891.8 | 0.496772 | ||||||||
\(966\) | 37326.9 | 1.24324 | ||||||||
\(967\) | 17936.9 | 0.596496 | 0.298248 | − | 0.954488i | \(-0.403598\pi\) | ||||
0.298248 | + | 0.954488i | \(0.403598\pi\) | |||||||
\(968\) | 15022.4 | 0.498799 | ||||||||
\(969\) | 19424.2 | 0.643958 | ||||||||
\(970\) | 34020.1 | 1.12610 | ||||||||
\(971\) | −40914.6 | −1.35223 | −0.676113 | − | 0.736798i | \(-0.736337\pi\) | ||||
−0.676113 | + | 0.736798i | \(0.736337\pi\) | |||||||
\(972\) | 668.656 | 0.0220650 | ||||||||
\(973\) | 83111.0 | 2.73835 | ||||||||
\(974\) | 13097.1 | 0.430860 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −38949.3 | −1.27740 | ||||||||
\(977\) | −24118.1 | −0.789770 | −0.394885 | − | 0.918731i | \(-0.629216\pi\) | ||||
−0.394885 | + | 0.918731i | \(0.629216\pi\) | |||||||
\(978\) | 21603.7 | 0.706350 | ||||||||
\(979\) | −20710.1 | −0.676096 | ||||||||
\(980\) | −17853.6 | −0.581953 | ||||||||
\(981\) | −15279.9 | −0.497297 | ||||||||
\(982\) | 40224.2 | 1.30713 | ||||||||
\(983\) | 2928.61 | 0.0950235 | 0.0475118 | − | 0.998871i | \(-0.484871\pi\) | ||||
0.0475118 | + | 0.998871i | \(0.484871\pi\) | |||||||
\(984\) | 10238.8 | 0.331708 | ||||||||
\(985\) | 76197.5 | 2.46483 | ||||||||
\(986\) | 36953.3 | 1.19354 | ||||||||
\(987\) | 6311.50 | 0.203543 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 21979.6 | 0.706683 | ||||||||
\(990\) | −11079.3 | −0.355679 | ||||||||
\(991\) | 49809.9 | 1.59663 | 0.798317 | − | 0.602238i | \(-0.205724\pi\) | ||||
0.798317 | + | 0.602238i | \(0.205724\pi\) | |||||||
\(992\) | 14650.1 | 0.468893 | ||||||||
\(993\) | −19879.9 | −0.635318 | ||||||||
\(994\) | −33481.3 | −1.06837 | ||||||||
\(995\) | 58384.9 | 1.86023 | ||||||||
\(996\) | −7114.99 | −0.226352 | ||||||||
\(997\) | −41151.7 | −1.30721 | −0.653604 | − | 0.756837i | \(-0.726744\pi\) | ||||
−0.653604 | + | 0.756837i | \(0.726744\pi\) | |||||||
\(998\) | 11734.7 | 0.372198 | ||||||||
\(999\) | 6009.86 | 0.190334 |
(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 | 507.4.a.r.1.8 | 10 | ||
3.2 | odd | 2 | 1521.4.a.bk.1.3 | 10 | |||
13.2 | odd | 12 | 39.4.j.c.4.4 | ✓ | 10 | ||
13.5 | odd | 4 | 507.4.b.i.337.3 | 10 | |||
13.7 | odd | 12 | 39.4.j.c.10.4 | yes | 10 | ||
13.8 | odd | 4 | 507.4.b.i.337.8 | 10 | |||
13.12 | even | 2 | inner | 507.4.a.r.1.3 | 10 | ||
39.2 | even | 12 | 117.4.q.e.82.2 | 10 | |||
39.20 | even | 12 | 117.4.q.e.10.2 | 10 | |||
39.38 | odd | 2 | 1521.4.a.bk.1.8 | 10 | |||
52.7 | even | 12 | 624.4.bv.h.49.1 | 10 | |||
52.15 | even | 12 | 624.4.bv.h.433.5 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.j.c.4.4 | ✓ | 10 | 13.2 | odd | 12 | ||
39.4.j.c.10.4 | yes | 10 | 13.7 | odd | 12 | ||
117.4.q.e.10.2 | 10 | 39.20 | even | 12 | |||
117.4.q.e.82.2 | 10 | 39.2 | even | 12 | |||
507.4.a.r.1.3 | 10 | 13.12 | even | 2 | inner | ||
507.4.a.r.1.8 | 10 | 1.1 | even | 1 | trivial | ||
507.4.b.i.337.3 | 10 | 13.5 | odd | 4 | |||
507.4.b.i.337.8 | 10 | 13.8 | odd | 4 | |||
624.4.bv.h.49.1 | 10 | 52.7 | even | 12 | |||
624.4.bv.h.433.5 | 10 | 52.15 | even | 12 | |||
1521.4.a.bk.1.3 | 10 | 3.2 | odd | 2 | |||
1521.4.a.bk.1.8 | 10 | 39.38 | odd | 2 |