Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [37,4,Mod(1,37)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(37, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("37.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 37 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 37.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: | \(2.18307067021\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.21208.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 8x^{2} + 13x - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-3.07664\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 37.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.389055 | 0.137552 | 0.0687759 | − | 0.997632i | \(-0.478091\pi\) | ||||
0.0687759 | + | 0.997632i | \(0.478091\pi\) | |||||||
\(3\) | −4.19207 | −0.806765 | −0.403383 | − | 0.915031i | \(-0.632166\pi\) | ||||
−0.403383 | + | 0.915031i | \(0.632166\pi\) | |||||||
\(4\) | −7.84864 | −0.981080 | ||||||||
\(5\) | −19.1145 | −1.70965 | −0.854825 | − | 0.518916i | \(-0.826336\pi\) | ||||
−0.854825 | + | 0.518916i | \(0.826336\pi\) | |||||||
\(6\) | −1.63095 | −0.110972 | ||||||||
\(7\) | 34.7993 | 1.87899 | 0.939493 | − | 0.342569i | \(-0.111297\pi\) | ||||
0.939493 | + | 0.342569i | \(0.111297\pi\) | |||||||
\(8\) | −6.16599 | −0.272501 | ||||||||
\(9\) | −9.42651 | −0.349130 | ||||||||
\(10\) | −7.43658 | −0.235165 | ||||||||
\(11\) | −21.7796 | −0.596983 | −0.298491 | − | 0.954412i | \(-0.596483\pi\) | ||||
−0.298491 | + | 0.954412i | \(0.596483\pi\) | |||||||
\(12\) | 32.9021 | 0.791501 | ||||||||
\(13\) | −28.9327 | −0.617269 | −0.308634 | − | 0.951181i | \(-0.599872\pi\) | ||||
−0.308634 | + | 0.951181i | \(0.599872\pi\) | |||||||
\(14\) | 13.5388 | 0.258458 | ||||||||
\(15\) | 80.1293 | 1.37929 | ||||||||
\(16\) | 60.3902 | 0.943597 | ||||||||
\(17\) | 9.03724 | 0.128933 | 0.0644663 | − | 0.997920i | \(-0.479466\pi\) | ||||
0.0644663 | + | 0.997920i | \(0.479466\pi\) | |||||||
\(18\) | −3.66743 | −0.0480235 | ||||||||
\(19\) | −106.253 | −1.28296 | −0.641479 | − | 0.767140i | \(-0.721679\pi\) | ||||
−0.641479 | + | 0.767140i | \(0.721679\pi\) | |||||||
\(20\) | 150.023 | 1.67730 | ||||||||
\(21\) | −145.881 | −1.51590 | ||||||||
\(22\) | −8.47348 | −0.0821160 | ||||||||
\(23\) | −64.0322 | −0.580506 | −0.290253 | − | 0.956950i | \(-0.593739\pi\) | ||||
−0.290253 | + | 0.956950i | \(0.593739\pi\) | |||||||
\(24\) | 25.8483 | 0.219844 | ||||||||
\(25\) | 240.363 | 1.92290 | ||||||||
\(26\) | −11.2564 | −0.0849064 | ||||||||
\(27\) | 152.703 | 1.08843 | ||||||||
\(28\) | −273.127 | −1.84343 | ||||||||
\(29\) | −123.010 | −0.787667 | −0.393833 | − | 0.919182i | \(-0.628851\pi\) | ||||
−0.393833 | + | 0.919182i | \(0.628851\pi\) | |||||||
\(30\) | 31.1747 | 0.189723 | ||||||||
\(31\) | −141.150 | −0.817784 | −0.408892 | − | 0.912583i | \(-0.634085\pi\) | ||||
−0.408892 | + | 0.912583i | \(0.634085\pi\) | |||||||
\(32\) | 72.8230 | 0.402294 | ||||||||
\(33\) | 91.3019 | 0.481625 | ||||||||
\(34\) | 3.51599 | 0.0177349 | ||||||||
\(35\) | −665.170 | −3.21241 | ||||||||
\(36\) | 73.9853 | 0.342524 | ||||||||
\(37\) | 37.0000 | 0.164399 | ||||||||
\(38\) | −41.3384 | −0.176473 | ||||||||
\(39\) | 121.288 | 0.497991 | ||||||||
\(40\) | 117.860 | 0.465881 | ||||||||
\(41\) | 47.1693 | 0.179673 | 0.0898367 | − | 0.995957i | \(-0.471365\pi\) | ||||
0.0898367 | + | 0.995957i | \(0.471365\pi\) | |||||||
\(42\) | −56.7558 | −0.208515 | ||||||||
\(43\) | 141.839 | 0.503028 | 0.251514 | − | 0.967854i | \(-0.419072\pi\) | ||||
0.251514 | + | 0.967854i | \(0.419072\pi\) | |||||||
\(44\) | 170.940 | 0.585687 | ||||||||
\(45\) | 180.183 | 0.596890 | ||||||||
\(46\) | −24.9120 | −0.0798496 | ||||||||
\(47\) | −546.877 | −1.69724 | −0.848619 | − | 0.529004i | \(-0.822565\pi\) | ||||
−0.848619 | + | 0.529004i | \(0.822565\pi\) | |||||||
\(48\) | −253.160 | −0.761261 | ||||||||
\(49\) | 867.991 | 2.53059 | ||||||||
\(50\) | 93.5144 | 0.264499 | ||||||||
\(51\) | −37.8848 | −0.104018 | ||||||||
\(52\) | 227.082 | 0.605590 | ||||||||
\(53\) | −22.9484 | −0.0594757 | −0.0297378 | − | 0.999558i | \(-0.509467\pi\) | ||||
−0.0297378 | + | 0.999558i | \(0.509467\pi\) | |||||||
\(54\) | 59.4097 | 0.149716 | ||||||||
\(55\) | 416.306 | 1.02063 | ||||||||
\(56\) | −214.572 | −0.512025 | ||||||||
\(57\) | 445.422 | 1.03505 | ||||||||
\(58\) | −47.8576 | −0.108345 | ||||||||
\(59\) | 125.564 | 0.277069 | 0.138535 | − | 0.990358i | \(-0.455761\pi\) | ||||
0.138535 | + | 0.990358i | \(0.455761\pi\) | |||||||
\(60\) | −628.906 | −1.35319 | ||||||||
\(61\) | 30.9403 | 0.0649426 | 0.0324713 | − | 0.999473i | \(-0.489662\pi\) | ||||
0.0324713 | + | 0.999473i | \(0.489662\pi\) | |||||||
\(62\) | −54.9151 | −0.112488 | ||||||||
\(63\) | −328.036 | −0.656010 | ||||||||
\(64\) | −454.789 | −0.888260 | ||||||||
\(65\) | 553.034 | 1.05531 | ||||||||
\(66\) | 35.5215 | 0.0662483 | ||||||||
\(67\) | −306.101 | −0.558153 | −0.279076 | − | 0.960269i | \(-0.590028\pi\) | ||||
−0.279076 | + | 0.960269i | \(0.590028\pi\) | |||||||
\(68\) | −70.9300 | −0.126493 | ||||||||
\(69\) | 268.428 | 0.468332 | ||||||||
\(70\) | −258.788 | −0.441872 | ||||||||
\(71\) | 768.020 | 1.28376 | 0.641882 | − | 0.766804i | \(-0.278154\pi\) | ||||
0.641882 | + | 0.766804i | \(0.278154\pi\) | |||||||
\(72\) | 58.1238 | 0.0951383 | ||||||||
\(73\) | −758.203 | −1.21563 | −0.607814 | − | 0.794079i | \(-0.707954\pi\) | ||||
−0.607814 | + | 0.794079i | \(0.707954\pi\) | |||||||
\(74\) | 14.3950 | 0.0226134 | ||||||||
\(75\) | −1007.62 | −1.55133 | ||||||||
\(76\) | 833.945 | 1.25868 | ||||||||
\(77\) | −757.916 | −1.12172 | ||||||||
\(78\) | 47.1878 | 0.0684995 | ||||||||
\(79\) | 488.538 | 0.695757 | 0.347878 | − | 0.937540i | \(-0.386902\pi\) | ||||
0.347878 | + | 0.937540i | \(0.386902\pi\) | |||||||
\(80\) | −1154.33 | −1.61322 | ||||||||
\(81\) | −385.625 | −0.528978 | ||||||||
\(82\) | 18.3515 | 0.0247144 | ||||||||
\(83\) | 126.187 | 0.166877 | 0.0834385 | − | 0.996513i | \(-0.473410\pi\) | ||||
0.0834385 | + | 0.996513i | \(0.473410\pi\) | |||||||
\(84\) | 1144.97 | 1.48722 | ||||||||
\(85\) | −172.742 | −0.220430 | ||||||||
\(86\) | 55.1830 | 0.0691923 | ||||||||
\(87\) | 515.666 | 0.635462 | ||||||||
\(88\) | 134.293 | 0.162678 | ||||||||
\(89\) | −1506.07 | −1.79374 | −0.896869 | − | 0.442296i | \(-0.854164\pi\) | ||||
−0.896869 | + | 0.442296i | \(0.854164\pi\) | |||||||
\(90\) | 70.1010 | 0.0821033 | ||||||||
\(91\) | −1006.84 | −1.15984 | ||||||||
\(92\) | 502.565 | 0.569522 | ||||||||
\(93\) | 591.711 | 0.659759 | ||||||||
\(94\) | −212.765 | −0.233458 | ||||||||
\(95\) | 2030.98 | 2.19341 | ||||||||
\(96\) | −305.280 | −0.324557 | ||||||||
\(97\) | −7.19091 | −0.00752708 | −0.00376354 | − | 0.999993i | \(-0.501198\pi\) | ||||
−0.00376354 | + | 0.999993i | \(0.501198\pi\) | |||||||
\(98\) | 337.696 | 0.348086 | ||||||||
\(99\) | 205.306 | 0.208425 | ||||||||
\(100\) | −1886.52 | −1.88652 | ||||||||
\(101\) | 40.8841 | 0.0402784 | 0.0201392 | − | 0.999797i | \(-0.493589\pi\) | ||||
0.0201392 | + | 0.999797i | \(0.493589\pi\) | |||||||
\(102\) | −14.7393 | −0.0143079 | ||||||||
\(103\) | −662.427 | −0.633698 | −0.316849 | − | 0.948476i | \(-0.602625\pi\) | ||||
−0.316849 | + | 0.948476i | \(0.602625\pi\) | |||||||
\(104\) | 178.399 | 0.168206 | ||||||||
\(105\) | 2788.44 | 2.59166 | ||||||||
\(106\) | −8.92821 | −0.00818098 | ||||||||
\(107\) | −1510.98 | −1.36516 | −0.682579 | − | 0.730812i | \(-0.739141\pi\) | ||||
−0.682579 | + | 0.730812i | \(0.739141\pi\) | |||||||
\(108\) | −1198.51 | −1.06784 | ||||||||
\(109\) | 1583.87 | 1.39181 | 0.695903 | − | 0.718136i | \(-0.255004\pi\) | ||||
0.695903 | + | 0.718136i | \(0.255004\pi\) | |||||||
\(110\) | 161.966 | 0.140390 | ||||||||
\(111\) | −155.107 | −0.132631 | ||||||||
\(112\) | 2101.54 | 1.77300 | ||||||||
\(113\) | 648.893 | 0.540201 | 0.270100 | − | 0.962832i | \(-0.412943\pi\) | ||||
0.270100 | + | 0.962832i | \(0.412943\pi\) | |||||||
\(114\) | 173.294 | 0.142372 | ||||||||
\(115\) | 1223.94 | 0.992462 | ||||||||
\(116\) | 965.459 | 0.772764 | ||||||||
\(117\) | 272.735 | 0.215507 | ||||||||
\(118\) | 48.8514 | 0.0381114 | ||||||||
\(119\) | 314.490 | 0.242262 | ||||||||
\(120\) | −494.076 | −0.375857 | ||||||||
\(121\) | −856.647 | −0.643612 | ||||||||
\(122\) | 12.0375 | 0.00893297 | ||||||||
\(123\) | −197.737 | −0.144954 | ||||||||
\(124\) | 1107.84 | 0.802311 | ||||||||
\(125\) | −2205.10 | −1.57784 | ||||||||
\(126\) | −127.624 | −0.0902354 | ||||||||
\(127\) | −1362.53 | −0.952009 | −0.476004 | − | 0.879443i | \(-0.657915\pi\) | ||||
−0.476004 | + | 0.879443i | \(0.657915\pi\) | |||||||
\(128\) | −759.522 | −0.524476 | ||||||||
\(129\) | −594.598 | −0.405825 | ||||||||
\(130\) | 215.161 | 0.145160 | ||||||||
\(131\) | −1790.42 | −1.19412 | −0.597061 | − | 0.802196i | \(-0.703665\pi\) | ||||
−0.597061 | + | 0.802196i | \(0.703665\pi\) | |||||||
\(132\) | −716.595 | −0.472512 | ||||||||
\(133\) | −3697.54 | −2.41066 | ||||||||
\(134\) | −119.090 | −0.0767748 | ||||||||
\(135\) | −2918.83 | −1.86084 | ||||||||
\(136\) | −55.7236 | −0.0351342 | ||||||||
\(137\) | 1752.27 | 1.09275 | 0.546374 | − | 0.837541i | \(-0.316008\pi\) | ||||
0.546374 | + | 0.837541i | \(0.316008\pi\) | |||||||
\(138\) | 104.433 | 0.0644198 | ||||||||
\(139\) | 243.061 | 0.148318 | 0.0741588 | − | 0.997246i | \(-0.476373\pi\) | ||||
0.0741588 | + | 0.997246i | \(0.476373\pi\) | |||||||
\(140\) | 5220.68 | 3.15163 | ||||||||
\(141\) | 2292.55 | 1.36927 | ||||||||
\(142\) | 298.802 | 0.176584 | ||||||||
\(143\) | 630.145 | 0.368499 | ||||||||
\(144\) | −569.269 | −0.329438 | ||||||||
\(145\) | 2351.27 | 1.34663 | ||||||||
\(146\) | −294.983 | −0.167212 | ||||||||
\(147\) | −3638.68 | −2.04159 | ||||||||
\(148\) | −290.400 | −0.161288 | ||||||||
\(149\) | 617.182 | 0.339339 | 0.169670 | − | 0.985501i | \(-0.445730\pi\) | ||||
0.169670 | + | 0.985501i | \(0.445730\pi\) | |||||||
\(150\) | −392.019 | −0.213388 | ||||||||
\(151\) | −1070.97 | −0.577182 | −0.288591 | − | 0.957452i | \(-0.593187\pi\) | ||||
−0.288591 | + | 0.957452i | \(0.593187\pi\) | |||||||
\(152\) | 655.158 | 0.349607 | ||||||||
\(153\) | −85.1897 | −0.0450142 | ||||||||
\(154\) | −294.871 | −0.154295 | ||||||||
\(155\) | 2698.01 | 1.39812 | ||||||||
\(156\) | −951.947 | −0.488569 | ||||||||
\(157\) | −501.788 | −0.255077 | −0.127538 | − | 0.991834i | \(-0.540708\pi\) | ||||
−0.127538 | + | 0.991834i | \(0.540708\pi\) | |||||||
\(158\) | 190.068 | 0.0957025 | ||||||||
\(159\) | 96.2016 | 0.0479829 | ||||||||
\(160\) | −1391.97 | −0.687782 | ||||||||
\(161\) | −2228.27 | −1.09076 | ||||||||
\(162\) | −150.029 | −0.0727618 | ||||||||
\(163\) | −776.453 | −0.373107 | −0.186554 | − | 0.982445i | \(-0.559732\pi\) | ||||
−0.186554 | + | 0.982445i | \(0.559732\pi\) | |||||||
\(164\) | −370.215 | −0.176274 | ||||||||
\(165\) | −1745.19 | −0.823410 | ||||||||
\(166\) | 49.0936 | 0.0229542 | ||||||||
\(167\) | −1531.43 | −0.709613 | −0.354806 | − | 0.934940i | \(-0.615453\pi\) | ||||
−0.354806 | + | 0.934940i | \(0.615453\pi\) | |||||||
\(168\) | 899.502 | 0.413084 | ||||||||
\(169\) | −1359.90 | −0.618979 | ||||||||
\(170\) | −67.2062 | −0.0303205 | ||||||||
\(171\) | 1001.60 | 0.447919 | ||||||||
\(172\) | −1113.24 | −0.493510 | ||||||||
\(173\) | 3647.28 | 1.60288 | 0.801438 | − | 0.598078i | \(-0.204069\pi\) | ||||
0.801438 | + | 0.598078i | \(0.204069\pi\) | |||||||
\(174\) | 200.622 | 0.0874089 | ||||||||
\(175\) | 8364.46 | 3.61311 | ||||||||
\(176\) | −1315.28 | −0.563311 | ||||||||
\(177\) | −526.375 | −0.223530 | ||||||||
\(178\) | −585.943 | −0.246732 | ||||||||
\(179\) | 3008.97 | 1.25643 | 0.628216 | − | 0.778039i | \(-0.283785\pi\) | ||||
0.628216 | + | 0.778039i | \(0.283785\pi\) | |||||||
\(180\) | −1414.19 | −0.585597 | ||||||||
\(181\) | 822.932 | 0.337945 | 0.168973 | − | 0.985621i | \(-0.445955\pi\) | ||||
0.168973 | + | 0.985621i | \(0.445955\pi\) | |||||||
\(182\) | −391.716 | −0.159538 | ||||||||
\(183\) | −129.704 | −0.0523934 | ||||||||
\(184\) | 394.822 | 0.158188 | ||||||||
\(185\) | −707.235 | −0.281065 | ||||||||
\(186\) | 230.208 | 0.0907510 | ||||||||
\(187\) | −196.828 | −0.0769705 | ||||||||
\(188\) | 4292.24 | 1.66513 | ||||||||
\(189\) | 5313.94 | 2.04515 | ||||||||
\(190\) | 790.162 | 0.301707 | ||||||||
\(191\) | −2432.13 | −0.921375 | −0.460687 | − | 0.887562i | \(-0.652397\pi\) | ||||
−0.460687 | + | 0.887562i | \(0.652397\pi\) | |||||||
\(192\) | 1906.51 | 0.716617 | ||||||||
\(193\) | −1252.89 | −0.467281 | −0.233641 | − | 0.972323i | \(-0.575064\pi\) | ||||
−0.233641 | + | 0.972323i | \(0.575064\pi\) | |||||||
\(194\) | −2.79766 | −0.00103536 | ||||||||
\(195\) | −2318.36 | −0.851390 | ||||||||
\(196\) | −6812.54 | −2.48271 | ||||||||
\(197\) | 4445.85 | 1.60789 | 0.803944 | − | 0.594705i | \(-0.202731\pi\) | ||||
0.803944 | + | 0.594705i | \(0.202731\pi\) | |||||||
\(198\) | 79.8754 | 0.0286692 | ||||||||
\(199\) | −45.5237 | −0.0162165 | −0.00810827 | − | 0.999967i | \(-0.502581\pi\) | ||||
−0.00810827 | + | 0.999967i | \(0.502581\pi\) | |||||||
\(200\) | −1482.08 | −0.523993 | ||||||||
\(201\) | 1283.20 | 0.450298 | ||||||||
\(202\) | 15.9062 | 0.00554036 | ||||||||
\(203\) | −4280.65 | −1.48001 | ||||||||
\(204\) | 297.344 | 0.102050 | ||||||||
\(205\) | −901.616 | −0.307179 | ||||||||
\(206\) | −257.720 | −0.0871662 | ||||||||
\(207\) | 603.600 | 0.202672 | ||||||||
\(208\) | −1747.25 | −0.582453 | ||||||||
\(209\) | 2314.16 | 0.765904 | ||||||||
\(210\) | 1084.86 | 0.356487 | ||||||||
\(211\) | 1904.01 | 0.621220 | 0.310610 | − | 0.950538i | \(-0.399467\pi\) | ||||
0.310610 | + | 0.950538i | \(0.399467\pi\) | |||||||
\(212\) | 180.114 | 0.0583504 | ||||||||
\(213\) | −3219.60 | −1.03570 | ||||||||
\(214\) | −587.854 | −0.187780 | ||||||||
\(215\) | −2711.17 | −0.860001 | ||||||||
\(216\) | −941.563 | −0.296598 | ||||||||
\(217\) | −4911.92 | −1.53660 | ||||||||
\(218\) | 616.211 | 0.191445 | ||||||||
\(219\) | 3178.44 | 0.980727 | ||||||||
\(220\) | −3267.44 | −1.00132 | ||||||||
\(221\) | −261.472 | −0.0795861 | ||||||||
\(222\) | −60.3451 | −0.0182437 | ||||||||
\(223\) | −82.2973 | −0.0247132 | −0.0123566 | − | 0.999924i | \(-0.503933\pi\) | ||||
−0.0123566 | + | 0.999924i | \(0.503933\pi\) | |||||||
\(224\) | 2534.19 | 0.755905 | ||||||||
\(225\) | −2265.79 | −0.671344 | ||||||||
\(226\) | 252.455 | 0.0743056 | ||||||||
\(227\) | −4601.52 | −1.34543 | −0.672717 | − | 0.739900i | \(-0.734873\pi\) | ||||
−0.672717 | + | 0.739900i | \(0.734873\pi\) | |||||||
\(228\) | −3495.96 | −1.01546 | ||||||||
\(229\) | 1051.40 | 0.303399 | 0.151699 | − | 0.988427i | \(-0.451525\pi\) | ||||
0.151699 | + | 0.988427i | \(0.451525\pi\) | |||||||
\(230\) | 476.181 | 0.136515 | ||||||||
\(231\) | 3177.24 | 0.904966 | ||||||||
\(232\) | 758.477 | 0.214640 | ||||||||
\(233\) | 1555.50 | 0.437356 | 0.218678 | − | 0.975797i | \(-0.429826\pi\) | ||||
0.218678 | + | 0.975797i | \(0.429826\pi\) | |||||||
\(234\) | 106.109 | 0.0296434 | ||||||||
\(235\) | 10453.3 | 2.90168 | ||||||||
\(236\) | −985.509 | −0.271827 | ||||||||
\(237\) | −2047.99 | −0.561312 | ||||||||
\(238\) | 122.354 | 0.0333236 | ||||||||
\(239\) | −1662.79 | −0.450028 | −0.225014 | − | 0.974356i | \(-0.572243\pi\) | ||||
−0.225014 | + | 0.974356i | \(0.572243\pi\) | |||||||
\(240\) | 4839.02 | 1.30149 | ||||||||
\(241\) | −2759.31 | −0.737521 | −0.368760 | − | 0.929524i | \(-0.620218\pi\) | ||||
−0.368760 | + | 0.929524i | \(0.620218\pi\) | |||||||
\(242\) | −333.283 | −0.0885299 | ||||||||
\(243\) | −2506.40 | −0.661670 | ||||||||
\(244\) | −242.839 | −0.0637139 | ||||||||
\(245\) | −16591.2 | −4.32642 | ||||||||
\(246\) | −76.9307 | −0.0199387 | ||||||||
\(247\) | 3074.20 | 0.791930 | ||||||||
\(248\) | 870.330 | 0.222847 | ||||||||
\(249\) | −528.984 | −0.134631 | ||||||||
\(250\) | −857.906 | −0.217035 | ||||||||
\(251\) | 4538.25 | 1.14124 | 0.570621 | − | 0.821214i | \(-0.306703\pi\) | ||||
0.570621 | + | 0.821214i | \(0.306703\pi\) | |||||||
\(252\) | 2574.64 | 0.643598 | ||||||||
\(253\) | 1394.60 | 0.346552 | ||||||||
\(254\) | −530.100 | −0.130950 | ||||||||
\(255\) | 724.148 | 0.177835 | ||||||||
\(256\) | 3342.82 | 0.816118 | ||||||||
\(257\) | 5143.48 | 1.24841 | 0.624206 | − | 0.781260i | \(-0.285423\pi\) | ||||
0.624206 | + | 0.781260i | \(0.285423\pi\) | |||||||
\(258\) | −231.331 | −0.0558219 | ||||||||
\(259\) | 1287.57 | 0.308903 | ||||||||
\(260\) | −4340.56 | −1.03535 | ||||||||
\(261\) | 1159.55 | 0.274998 | ||||||||
\(262\) | −696.573 | −0.164254 | ||||||||
\(263\) | 2336.54 | 0.547822 | 0.273911 | − | 0.961755i | \(-0.411683\pi\) | ||||
0.273911 | + | 0.961755i | \(0.411683\pi\) | |||||||
\(264\) | −562.967 | −0.131243 | ||||||||
\(265\) | 438.647 | 0.101683 | ||||||||
\(266\) | −1438.55 | −0.331590 | ||||||||
\(267\) | 6313.54 | 1.44713 | ||||||||
\(268\) | 2402.48 | 0.547592 | ||||||||
\(269\) | −5041.06 | −1.14260 | −0.571298 | − | 0.820742i | \(-0.693560\pi\) | ||||
−0.571298 | + | 0.820742i | \(0.693560\pi\) | |||||||
\(270\) | −1135.59 | −0.255961 | ||||||||
\(271\) | 7193.38 | 1.61242 | 0.806212 | − | 0.591627i | \(-0.201514\pi\) | ||||
0.806212 | + | 0.591627i | \(0.201514\pi\) | |||||||
\(272\) | 545.761 | 0.121660 | ||||||||
\(273\) | 4220.74 | 0.935718 | ||||||||
\(274\) | 681.729 | 0.150309 | ||||||||
\(275\) | −5235.02 | −1.14794 | ||||||||
\(276\) | −2106.79 | −0.459471 | ||||||||
\(277\) | 6189.38 | 1.34254 | 0.671271 | − | 0.741212i | \(-0.265749\pi\) | ||||
0.671271 | + | 0.741212i | \(0.265749\pi\) | |||||||
\(278\) | 94.5640 | 0.0204013 | ||||||||
\(279\) | 1330.55 | 0.285513 | ||||||||
\(280\) | 4101.43 | 0.875384 | ||||||||
\(281\) | 6288.34 | 1.33498 | 0.667492 | − | 0.744617i | \(-0.267368\pi\) | ||||
0.667492 | + | 0.744617i | \(0.267368\pi\) | |||||||
\(282\) | 891.928 | 0.188346 | ||||||||
\(283\) | −6655.88 | −1.39806 | −0.699030 | − | 0.715093i | \(-0.746384\pi\) | ||||
−0.699030 | + | 0.715093i | \(0.746384\pi\) | |||||||
\(284\) | −6027.91 | −1.25947 | ||||||||
\(285\) | −8514.01 | −1.76957 | ||||||||
\(286\) | 245.161 | 0.0506877 | ||||||||
\(287\) | 1641.46 | 0.337604 | ||||||||
\(288\) | −686.467 | −0.140453 | ||||||||
\(289\) | −4831.33 | −0.983376 | ||||||||
\(290\) | 914.772 | 0.185232 | ||||||||
\(291\) | 30.1448 | 0.00607258 | ||||||||
\(292\) | 5950.86 | 1.19263 | ||||||||
\(293\) | −4690.70 | −0.935269 | −0.467634 | − | 0.883922i | \(-0.654894\pi\) | ||||
−0.467634 | + | 0.883922i | \(0.654894\pi\) | |||||||
\(294\) | −1415.65 | −0.280824 | ||||||||
\(295\) | −2400.10 | −0.473692 | ||||||||
\(296\) | −228.142 | −0.0447989 | ||||||||
\(297\) | −3325.81 | −0.649774 | ||||||||
\(298\) | 240.118 | 0.0466767 | ||||||||
\(299\) | 1852.63 | 0.358328 | ||||||||
\(300\) | 7908.44 | 1.52198 | ||||||||
\(301\) | 4935.88 | 0.945181 | ||||||||
\(302\) | −416.667 | −0.0793924 | ||||||||
\(303\) | −171.389 | −0.0324952 | ||||||||
\(304\) | −6416.66 | −1.21060 | ||||||||
\(305\) | −591.408 | −0.111029 | ||||||||
\(306\) | −33.1435 | −0.00619179 | ||||||||
\(307\) | −4131.48 | −0.768066 | −0.384033 | − | 0.923319i | \(-0.625465\pi\) | ||||
−0.384033 | + | 0.923319i | \(0.625465\pi\) | |||||||
\(308\) | 5948.61 | 1.10050 | ||||||||
\(309\) | 2776.94 | 0.511245 | ||||||||
\(310\) | 1049.67 | 0.192314 | ||||||||
\(311\) | −3013.89 | −0.549524 | −0.274762 | − | 0.961512i | \(-0.588599\pi\) | ||||
−0.274762 | + | 0.961512i | \(0.588599\pi\) | |||||||
\(312\) | −747.862 | −0.135703 | ||||||||
\(313\) | −8766.62 | −1.58313 | −0.791563 | − | 0.611087i | \(-0.790733\pi\) | ||||
−0.791563 | + | 0.611087i | \(0.790733\pi\) | |||||||
\(314\) | −195.223 | −0.0350862 | ||||||||
\(315\) | 6270.23 | 1.12155 | ||||||||
\(316\) | −3834.35 | −0.682592 | ||||||||
\(317\) | 2364.98 | 0.419023 | 0.209511 | − | 0.977806i | \(-0.432813\pi\) | ||||
0.209511 | + | 0.977806i | \(0.432813\pi\) | |||||||
\(318\) | 37.4277 | 0.00660013 | ||||||||
\(319\) | 2679.11 | 0.470223 | ||||||||
\(320\) | 8693.06 | 1.51861 | ||||||||
\(321\) | 6334.13 | 1.10136 | ||||||||
\(322\) | −866.921 | −0.150036 | ||||||||
\(323\) | −960.238 | −0.165415 | ||||||||
\(324\) | 3026.63 | 0.518969 | ||||||||
\(325\) | −6954.36 | −1.18695 | ||||||||
\(326\) | −302.083 | −0.0513216 | ||||||||
\(327\) | −6639.68 | −1.12286 | ||||||||
\(328\) | −290.846 | −0.0489612 | ||||||||
\(329\) | −19030.9 | −3.18909 | ||||||||
\(330\) | −678.974 | −0.113261 | ||||||||
\(331\) | −3898.71 | −0.647409 | −0.323705 | − | 0.946158i | \(-0.604928\pi\) | ||||
−0.323705 | + | 0.946158i | \(0.604928\pi\) | |||||||
\(332\) | −990.393 | −0.163720 | ||||||||
\(333\) | −348.781 | −0.0573966 | ||||||||
\(334\) | −595.809 | −0.0976085 | ||||||||
\(335\) | 5850.96 | 0.954246 | ||||||||
\(336\) | −8809.79 | −1.43040 | ||||||||
\(337\) | −5630.51 | −0.910129 | −0.455065 | − | 0.890458i | \(-0.650384\pi\) | ||||
−0.455065 | + | 0.890458i | \(0.650384\pi\) | |||||||
\(338\) | −529.075 | −0.0851416 | ||||||||
\(339\) | −2720.21 | −0.435815 | ||||||||
\(340\) | 1355.79 | 0.216259 | ||||||||
\(341\) | 3074.20 | 0.488203 | ||||||||
\(342\) | 389.677 | 0.0616121 | ||||||||
\(343\) | 18269.3 | 2.87595 | ||||||||
\(344\) | −874.576 | −0.137075 | ||||||||
\(345\) | −5130.85 | −0.800684 | ||||||||
\(346\) | 1418.99 | 0.220478 | ||||||||
\(347\) | −8239.07 | −1.27463 | −0.637314 | − | 0.770604i | \(-0.719955\pi\) | ||||
−0.637314 | + | 0.770604i | \(0.719955\pi\) | |||||||
\(348\) | −4047.27 | −0.623439 | ||||||||
\(349\) | 783.432 | 0.120161 | 0.0600804 | − | 0.998194i | \(-0.480864\pi\) | ||||
0.0600804 | + | 0.998194i | \(0.480864\pi\) | |||||||
\(350\) | 3254.24 | 0.496989 | ||||||||
\(351\) | −4418.10 | −0.671855 | ||||||||
\(352\) | −1586.06 | −0.240163 | ||||||||
\(353\) | 10756.4 | 1.62183 | 0.810913 | − | 0.585166i | \(-0.198971\pi\) | ||||
0.810913 | + | 0.585166i | \(0.198971\pi\) | |||||||
\(354\) | −204.789 | −0.0307469 | ||||||||
\(355\) | −14680.3 | −2.19479 | ||||||||
\(356\) | 11820.6 | 1.75980 | ||||||||
\(357\) | −1318.36 | −0.195449 | ||||||||
\(358\) | 1170.66 | 0.172824 | ||||||||
\(359\) | 6689.50 | 0.983449 | 0.491725 | − | 0.870751i | \(-0.336367\pi\) | ||||
0.491725 | + | 0.870751i | \(0.336367\pi\) | |||||||
\(360\) | −1111.01 | −0.162653 | ||||||||
\(361\) | 4430.79 | 0.645982 | ||||||||
\(362\) | 320.166 | 0.0464849 | ||||||||
\(363\) | 3591.13 | 0.519243 | ||||||||
\(364\) | 7902.31 | 1.13789 | ||||||||
\(365\) | 14492.6 | 2.07830 | ||||||||
\(366\) | −50.4620 | −0.00720681 | ||||||||
\(367\) | −1801.03 | −0.256166 | −0.128083 | − | 0.991763i | \(-0.540882\pi\) | ||||
−0.128083 | + | 0.991763i | \(0.540882\pi\) | |||||||
\(368\) | −3866.92 | −0.547763 | ||||||||
\(369\) | −444.642 | −0.0627294 | ||||||||
\(370\) | −275.153 | −0.0386609 | ||||||||
\(371\) | −798.590 | −0.111754 | ||||||||
\(372\) | −4644.13 | −0.647276 | ||||||||
\(373\) | 3055.25 | 0.424114 | 0.212057 | − | 0.977257i | \(-0.431984\pi\) | ||||
0.212057 | + | 0.977257i | \(0.431984\pi\) | |||||||
\(374\) | −76.5769 | −0.0105874 | ||||||||
\(375\) | 9243.96 | 1.27295 | ||||||||
\(376\) | 3372.04 | 0.462499 | ||||||||
\(377\) | 3559.01 | 0.486202 | ||||||||
\(378\) | 2067.42 | 0.281313 | ||||||||
\(379\) | −8569.97 | −1.16150 | −0.580752 | − | 0.814081i | \(-0.697241\pi\) | ||||
−0.580752 | + | 0.814081i | \(0.697241\pi\) | |||||||
\(380\) | −15940.4 | −2.15191 | ||||||||
\(381\) | 5711.83 | 0.768048 | ||||||||
\(382\) | −946.232 | −0.126737 | ||||||||
\(383\) | −6442.32 | −0.859496 | −0.429748 | − | 0.902949i | \(-0.641398\pi\) | ||||
−0.429748 | + | 0.902949i | \(0.641398\pi\) | |||||||
\(384\) | 3183.97 | 0.423129 | ||||||||
\(385\) | 14487.2 | 1.91775 | ||||||||
\(386\) | −487.445 | −0.0642753 | ||||||||
\(387\) | −1337.04 | −0.175622 | ||||||||
\(388\) | 56.4389 | 0.00738466 | ||||||||
\(389\) | −13088.7 | −1.70598 | −0.852988 | − | 0.521930i | \(-0.825212\pi\) | ||||
−0.852988 | + | 0.521930i | \(0.825212\pi\) | |||||||
\(390\) | −901.969 | −0.117110 | ||||||||
\(391\) | −578.675 | −0.0748461 | ||||||||
\(392\) | −5352.02 | −0.689587 | ||||||||
\(393\) | 7505.59 | 0.963376 | ||||||||
\(394\) | 1729.68 | 0.221168 | ||||||||
\(395\) | −9338.14 | −1.18950 | ||||||||
\(396\) | −1611.37 | −0.204481 | ||||||||
\(397\) | −2752.59 | −0.347981 | −0.173991 | − | 0.984747i | \(-0.555666\pi\) | ||||
−0.173991 | + | 0.984747i | \(0.555666\pi\) | |||||||
\(398\) | −17.7112 | −0.00223061 | ||||||||
\(399\) | 15500.4 | 1.94484 | ||||||||
\(400\) | 14515.6 | 1.81445 | ||||||||
\(401\) | 8507.27 | 1.05943 | 0.529716 | − | 0.848175i | \(-0.322298\pi\) | ||||
0.529716 | + | 0.848175i | \(0.322298\pi\) | |||||||
\(402\) | 499.235 | 0.0619393 | ||||||||
\(403\) | 4083.86 | 0.504792 | ||||||||
\(404\) | −320.884 | −0.0395163 | ||||||||
\(405\) | 7371.02 | 0.904367 | ||||||||
\(406\) | −1665.41 | −0.203579 | ||||||||
\(407\) | −805.847 | −0.0981433 | ||||||||
\(408\) | 233.597 | 0.0283451 | ||||||||
\(409\) | −7857.22 | −0.949913 | −0.474956 | − | 0.880009i | \(-0.657536\pi\) | ||||
−0.474956 | + | 0.880009i | \(0.657536\pi\) | |||||||
\(410\) | −350.778 | −0.0422529 | ||||||||
\(411\) | −7345.64 | −0.881590 | ||||||||
\(412\) | 5199.15 | 0.621708 | ||||||||
\(413\) | 4369.55 | 0.520609 | ||||||||
\(414\) | 234.834 | 0.0278779 | ||||||||
\(415\) | −2411.99 | −0.285301 | ||||||||
\(416\) | −2106.97 | −0.248324 | ||||||||
\(417\) | −1018.93 | −0.119657 | ||||||||
\(418\) | 900.336 | 0.105351 | ||||||||
\(419\) | −11112.9 | −1.29571 | −0.647853 | − | 0.761766i | \(-0.724333\pi\) | ||||
−0.647853 | + | 0.761766i | \(0.724333\pi\) | |||||||
\(420\) | −21885.5 | −2.54262 | ||||||||
\(421\) | −10448.4 | −1.20955 | −0.604777 | − | 0.796395i | \(-0.706738\pi\) | ||||
−0.604777 | + | 0.796395i | \(0.706738\pi\) | |||||||
\(422\) | 740.764 | 0.0854498 | ||||||||
\(423\) | 5155.14 | 0.592557 | ||||||||
\(424\) | 141.500 | 0.0162072 | ||||||||
\(425\) | 2172.22 | 0.247925 | ||||||||
\(426\) | −1252.60 | −0.142462 | ||||||||
\(427\) | 1076.70 | 0.122026 | ||||||||
\(428\) | 11859.1 | 1.33933 | ||||||||
\(429\) | −2641.61 | −0.297292 | ||||||||
\(430\) | −1054.79 | −0.118295 | ||||||||
\(431\) | −1885.68 | −0.210743 | −0.105371 | − | 0.994433i | \(-0.533603\pi\) | ||||
−0.105371 | + | 0.994433i | \(0.533603\pi\) | |||||||
\(432\) | 9221.74 | 1.02704 | ||||||||
\(433\) | −9819.97 | −1.08988 | −0.544939 | − | 0.838475i | \(-0.683447\pi\) | ||||
−0.544939 | + | 0.838475i | \(0.683447\pi\) | |||||||
\(434\) | −1911.01 | −0.211362 | ||||||||
\(435\) | −9856.68 | −1.08642 | ||||||||
\(436\) | −12431.2 | −1.36547 | ||||||||
\(437\) | 6803.64 | 0.744765 | ||||||||
\(438\) | 1236.59 | 0.134901 | ||||||||
\(439\) | 6488.41 | 0.705410 | 0.352705 | − | 0.935735i | \(-0.385262\pi\) | ||||
0.352705 | + | 0.935735i | \(0.385262\pi\) | |||||||
\(440\) | −2566.94 | −0.278123 | ||||||||
\(441\) | −8182.13 | −0.883504 | ||||||||
\(442\) | −101.727 | −0.0109472 | ||||||||
\(443\) | 6.08995 | 0.000653143 0 | 0.000326571 | − | 1.00000i | \(-0.499896\pi\) | ||||
0.000326571 | 1.00000i | \(0.499896\pi\) | ||||||||
\(444\) | 1217.38 | 0.130122 | ||||||||
\(445\) | 28787.7 | 3.06667 | ||||||||
\(446\) | −32.0182 | −0.00339934 | ||||||||
\(447\) | −2587.27 | −0.273767 | ||||||||
\(448\) | −15826.3 | −1.66903 | ||||||||
\(449\) | −12026.4 | −1.26405 | −0.632026 | − | 0.774947i | \(-0.717776\pi\) | ||||
−0.632026 | + | 0.774947i | \(0.717776\pi\) | |||||||
\(450\) | −881.515 | −0.0923445 | ||||||||
\(451\) | −1027.33 | −0.107262 | ||||||||
\(452\) | −5092.92 | −0.529980 | ||||||||
\(453\) | 4489.60 | 0.465650 | ||||||||
\(454\) | −1790.24 | −0.185067 | ||||||||
\(455\) | 19245.2 | 1.98292 | ||||||||
\(456\) | −2746.47 | −0.282051 | ||||||||
\(457\) | 1789.36 | 0.183157 | 0.0915783 | − | 0.995798i | \(-0.470809\pi\) | ||||
0.0915783 | + | 0.995798i | \(0.470809\pi\) | |||||||
\(458\) | 409.051 | 0.0417330 | ||||||||
\(459\) | 1380.01 | 0.140334 | ||||||||
\(460\) | −9606.27 | −0.973684 | ||||||||
\(461\) | 15554.5 | 1.57147 | 0.785733 | − | 0.618566i | \(-0.212286\pi\) | ||||
0.785733 | + | 0.618566i | \(0.212286\pi\) | |||||||
\(462\) | 1236.12 | 0.124480 | ||||||||
\(463\) | 13327.1 | 1.33772 | 0.668858 | − | 0.743391i | \(-0.266784\pi\) | ||||
0.668858 | + | 0.743391i | \(0.266784\pi\) | |||||||
\(464\) | −7428.58 | −0.743240 | ||||||||
\(465\) | −11310.3 | −1.12796 | ||||||||
\(466\) | 605.174 | 0.0601591 | ||||||||
\(467\) | 4291.69 | 0.425259 | 0.212629 | − | 0.977133i | \(-0.431797\pi\) | ||||
0.212629 | + | 0.977133i | \(0.431797\pi\) | |||||||
\(468\) | −2140.60 | −0.211430 | ||||||||
\(469\) | −10652.1 | −1.04876 | ||||||||
\(470\) | 4066.89 | 0.399132 | ||||||||
\(471\) | 2103.53 | 0.205787 | ||||||||
\(472\) | −774.229 | −0.0755016 | ||||||||
\(473\) | −3089.19 | −0.300299 | ||||||||
\(474\) | −796.779 | −0.0772094 | ||||||||
\(475\) | −25539.4 | −2.46701 | ||||||||
\(476\) | −2468.32 | −0.237679 | ||||||||
\(477\) | 216.324 | 0.0207648 | ||||||||
\(478\) | −646.915 | −0.0619021 | ||||||||
\(479\) | −10186.0 | −0.971632 | −0.485816 | − | 0.874061i | \(-0.661478\pi\) | ||||
−0.485816 | + | 0.874061i | \(0.661478\pi\) | |||||||
\(480\) | 5835.26 | 0.554879 | ||||||||
\(481\) | −1070.51 | −0.101478 | ||||||||
\(482\) | −1073.52 | −0.101447 | ||||||||
\(483\) | 9341.09 | 0.879989 | ||||||||
\(484\) | 6723.51 | 0.631434 | ||||||||
\(485\) | 137.451 | 0.0128687 | ||||||||
\(486\) | −975.129 | −0.0910139 | ||||||||
\(487\) | −7054.92 | −0.656446 | −0.328223 | − | 0.944600i | \(-0.606450\pi\) | ||||
−0.328223 | + | 0.944600i | \(0.606450\pi\) | |||||||
\(488\) | −190.778 | −0.0176969 | ||||||||
\(489\) | 3254.95 | 0.301010 | ||||||||
\(490\) | −6454.88 | −0.595106 | ||||||||
\(491\) | 12783.3 | 1.17495 | 0.587476 | − | 0.809241i | \(-0.300122\pi\) | ||||
0.587476 | + | 0.809241i | \(0.300122\pi\) | |||||||
\(492\) | 1551.97 | 0.142212 | ||||||||
\(493\) | −1111.67 | −0.101556 | ||||||||
\(494\) | 1196.03 | 0.108931 | ||||||||
\(495\) | −3924.32 | −0.356333 | ||||||||
\(496\) | −8524.08 | −0.771658 | ||||||||
\(497\) | 26726.5 | 2.41217 | ||||||||
\(498\) | −205.804 | −0.0185187 | ||||||||
\(499\) | −11825.1 | −1.06085 | −0.530425 | − | 0.847732i | \(-0.677968\pi\) | ||||
−0.530425 | + | 0.847732i | \(0.677968\pi\) | |||||||
\(500\) | 17307.1 | 1.54799 | ||||||||
\(501\) | 6419.85 | 0.572491 | ||||||||
\(502\) | 1765.63 | 0.156980 | ||||||||
\(503\) | 5670.57 | 0.502661 | 0.251330 | − | 0.967901i | \(-0.419132\pi\) | ||||
0.251330 | + | 0.967901i | \(0.419132\pi\) | |||||||
\(504\) | 2022.67 | 0.178763 | ||||||||
\(505\) | −781.478 | −0.0688620 | ||||||||
\(506\) | 542.575 | 0.0476688 | ||||||||
\(507\) | 5700.79 | 0.499371 | ||||||||
\(508\) | 10694.0 | 0.933997 | ||||||||
\(509\) | 15815.2 | 1.37720 | 0.688600 | − | 0.725141i | \(-0.258226\pi\) | ||||
0.688600 | + | 0.725141i | \(0.258226\pi\) | |||||||
\(510\) | 281.733 | 0.0244615 | ||||||||
\(511\) | −26384.9 | −2.28415 | ||||||||
\(512\) | 7376.72 | 0.636734 | ||||||||
\(513\) | −16225.2 | −1.39641 | ||||||||
\(514\) | 2001.10 | 0.171721 | ||||||||
\(515\) | 12661.9 | 1.08340 | ||||||||
\(516\) | 4666.78 | 0.398147 | ||||||||
\(517\) | 11910.8 | 1.01322 | ||||||||
\(518\) | 500.937 | 0.0424902 | ||||||||
\(519\) | −15289.7 | −1.29314 | ||||||||
\(520\) | −3410.00 | −0.287574 | ||||||||
\(521\) | 15351.1 | 1.29087 | 0.645435 | − | 0.763815i | \(-0.276676\pi\) | ||||
0.645435 | + | 0.763815i | \(0.276676\pi\) | |||||||
\(522\) | 451.130 | 0.0378265 | ||||||||
\(523\) | 16011.6 | 1.33870 | 0.669349 | − | 0.742948i | \(-0.266573\pi\) | ||||
0.669349 | + | 0.742948i | \(0.266573\pi\) | |||||||
\(524\) | 14052.4 | 1.17153 | ||||||||
\(525\) | −35064.4 | −2.91493 | ||||||||
\(526\) | 909.043 | 0.0753539 | ||||||||
\(527\) | −1275.61 | −0.105439 | ||||||||
\(528\) | 5513.74 | 0.454459 | ||||||||
\(529\) | −8066.88 | −0.663013 | ||||||||
\(530\) | 170.658 | 0.0139866 | ||||||||
\(531\) | −1183.63 | −0.0967332 | ||||||||
\(532\) | 29020.7 | 2.36505 | ||||||||
\(533\) | −1364.74 | −0.110907 | ||||||||
\(534\) | 2456.32 | 0.199055 | ||||||||
\(535\) | 28881.6 | 2.33394 | ||||||||
\(536\) | 1887.42 | 0.152097 | ||||||||
\(537\) | −12613.8 | −1.01365 | ||||||||
\(538\) | −1961.25 | −0.157166 | ||||||||
\(539\) | −18904.5 | −1.51072 | ||||||||
\(540\) | 22908.8 | 1.82563 | ||||||||
\(541\) | −6395.21 | −0.508228 | −0.254114 | − | 0.967174i | \(-0.581784\pi\) | ||||
−0.254114 | + | 0.967174i | \(0.581784\pi\) | |||||||
\(542\) | 2798.62 | 0.221792 | ||||||||
\(543\) | −3449.79 | −0.272642 | ||||||||
\(544\) | 658.120 | 0.0518688 | ||||||||
\(545\) | −30274.8 | −2.37950 | ||||||||
\(546\) | 1642.10 | 0.128710 | ||||||||
\(547\) | −18429.7 | −1.44058 | −0.720289 | − | 0.693675i | \(-0.755991\pi\) | ||||
−0.720289 | + | 0.693675i | \(0.755991\pi\) | |||||||
\(548\) | −13752.9 | −1.07207 | ||||||||
\(549\) | −291.659 | −0.0226734 | ||||||||
\(550\) | −2036.71 | −0.157901 | ||||||||
\(551\) | 13070.2 | 1.01054 | ||||||||
\(552\) | −1655.12 | −0.127621 | ||||||||
\(553\) | 17000.8 | 1.30732 | ||||||||
\(554\) | 2408.01 | 0.184669 | ||||||||
\(555\) | 2964.78 | 0.226753 | ||||||||
\(556\) | −1907.70 | −0.145511 | ||||||||
\(557\) | −10082.3 | −0.766970 | −0.383485 | − | 0.923547i | \(-0.625276\pi\) | ||||
−0.383485 | + | 0.923547i | \(0.625276\pi\) | |||||||
\(558\) | 517.658 | 0.0392728 | ||||||||
\(559\) | −4103.78 | −0.310503 | ||||||||
\(560\) | −40169.7 | −3.03122 | ||||||||
\(561\) | 825.117 | 0.0620971 | ||||||||
\(562\) | 2446.51 | 0.183629 | ||||||||
\(563\) | 6890.96 | 0.515843 | 0.257921 | − | 0.966166i | \(-0.416962\pi\) | ||||
0.257921 | + | 0.966166i | \(0.416962\pi\) | |||||||
\(564\) | −17993.4 | −1.34337 | ||||||||
\(565\) | −12403.2 | −0.923555 | ||||||||
\(566\) | −2589.50 | −0.192305 | ||||||||
\(567\) | −13419.5 | −0.993942 | ||||||||
\(568\) | −4735.60 | −0.349827 | ||||||||
\(569\) | 15563.8 | 1.14670 | 0.573348 | − | 0.819312i | \(-0.305644\pi\) | ||||
0.573348 | + | 0.819312i | \(0.305644\pi\) | |||||||
\(570\) | −3312.42 | −0.243407 | ||||||||
\(571\) | −2209.76 | −0.161954 | −0.0809768 | − | 0.996716i | \(-0.525804\pi\) | ||||
−0.0809768 | + | 0.996716i | \(0.525804\pi\) | |||||||
\(572\) | −4945.78 | −0.361527 | ||||||||
\(573\) | 10195.7 | 0.743333 | ||||||||
\(574\) | 638.618 | 0.0464380 | ||||||||
\(575\) | −15391.0 | −1.11626 | ||||||||
\(576\) | 4287.08 | 0.310118 | ||||||||
\(577\) | 24459.1 | 1.76472 | 0.882362 | − | 0.470571i | \(-0.155952\pi\) | ||||
0.882362 | + | 0.470571i | \(0.155952\pi\) | |||||||
\(578\) | −1879.65 | −0.135265 | ||||||||
\(579\) | 5252.22 | 0.376986 | ||||||||
\(580\) | −18454.2 | −1.32116 | ||||||||
\(581\) | 4391.21 | 0.313559 | ||||||||
\(582\) | 11.7280 | 0.000835294 0 | ||||||||
\(583\) | 499.809 | 0.0355060 | ||||||||
\(584\) | 4675.07 | 0.331260 | ||||||||
\(585\) | −5213.18 | −0.368442 | ||||||||
\(586\) | −1824.94 | −0.128648 | ||||||||
\(587\) | −21429.1 | −1.50677 | −0.753386 | − | 0.657579i | \(-0.771581\pi\) | ||||
−0.753386 | + | 0.657579i | \(0.771581\pi\) | |||||||
\(588\) | 28558.7 | 2.00296 | ||||||||
\(589\) | 14997.7 | 1.04918 | ||||||||
\(590\) | −933.770 | −0.0651571 | ||||||||
\(591\) | −18637.3 | −1.29719 | ||||||||
\(592\) | 2234.44 | 0.155126 | ||||||||
\(593\) | −18608.9 | −1.28866 | −0.644332 | − | 0.764746i | \(-0.722864\pi\) | ||||
−0.644332 | + | 0.764746i | \(0.722864\pi\) | |||||||
\(594\) | −1293.92 | −0.0893776 | ||||||||
\(595\) | −6011.30 | −0.414184 | ||||||||
\(596\) | −4844.04 | −0.332919 | ||||||||
\(597\) | 190.839 | 0.0130829 | ||||||||
\(598\) | 720.773 | 0.0492887 | ||||||||
\(599\) | 20758.6 | 1.41598 | 0.707990 | − | 0.706222i | \(-0.249602\pi\) | ||||
0.707990 | + | 0.706222i | \(0.249602\pi\) | |||||||
\(600\) | 6212.97 | 0.422739 | ||||||||
\(601\) | 27590.6 | 1.87262 | 0.936309 | − | 0.351177i | \(-0.114218\pi\) | ||||
0.936309 | + | 0.351177i | \(0.114218\pi\) | |||||||
\(602\) | 1920.33 | 0.130011 | ||||||||
\(603\) | 2885.47 | 0.194868 | ||||||||
\(604\) | 8405.67 | 0.566261 | ||||||||
\(605\) | 16374.4 | 1.10035 | ||||||||
\(606\) | −66.6798 | −0.00446977 | ||||||||
\(607\) | 5116.79 | 0.342148 | 0.171074 | − | 0.985258i | \(-0.445276\pi\) | ||||
0.171074 | + | 0.985258i | \(0.445276\pi\) | |||||||
\(608\) | −7737.70 | −0.516127 | ||||||||
\(609\) | 17944.8 | 1.19402 | ||||||||
\(610\) | −230.090 | −0.0152723 | ||||||||
\(611\) | 15822.6 | 1.04765 | ||||||||
\(612\) | 668.623 | 0.0441626 | ||||||||
\(613\) | 358.961 | 0.0236514 | 0.0118257 | − | 0.999930i | \(-0.496236\pi\) | ||||
0.0118257 | + | 0.999930i | \(0.496236\pi\) | |||||||
\(614\) | −1607.37 | −0.105649 | ||||||||
\(615\) | 3779.64 | 0.247821 | ||||||||
\(616\) | 4673.30 | 0.305670 | ||||||||
\(617\) | −11395.0 | −0.743512 | −0.371756 | − | 0.928331i | \(-0.621244\pi\) | ||||
−0.371756 | + | 0.928331i | \(0.621244\pi\) | |||||||
\(618\) | 1080.38 | 0.0703226 | ||||||||
\(619\) | −21799.3 | −1.41549 | −0.707745 | − | 0.706468i | \(-0.750287\pi\) | ||||
−0.707745 | + | 0.706468i | \(0.750287\pi\) | |||||||
\(620\) | −21175.7 | −1.37167 | ||||||||
\(621\) | −9777.88 | −0.631841 | ||||||||
\(622\) | −1172.57 | −0.0755879 | ||||||||
\(623\) | −52410.1 | −3.37041 | ||||||||
\(624\) | 7324.61 | 0.469903 | ||||||||
\(625\) | 12104.0 | 0.774656 | ||||||||
\(626\) | −3410.70 | −0.217762 | ||||||||
\(627\) | −9701.14 | −0.617905 | ||||||||
\(628\) | 3938.35 | 0.250250 | ||||||||
\(629\) | 334.378 | 0.0211964 | ||||||||
\(630\) | 2439.47 | 0.154271 | ||||||||
\(631\) | −5222.86 | −0.329506 | −0.164753 | − | 0.986335i | \(-0.552683\pi\) | ||||
−0.164753 | + | 0.986335i | \(0.552683\pi\) | |||||||
\(632\) | −3012.32 | −0.189594 | ||||||||
\(633\) | −7981.74 | −0.501178 | ||||||||
\(634\) | 920.106 | 0.0576373 | ||||||||
\(635\) | 26044.1 | 1.62760 | ||||||||
\(636\) | −755.051 | −0.0470750 | ||||||||
\(637\) | −25113.3 | −1.56205 | ||||||||
\(638\) | 1042.32 | 0.0646800 | ||||||||
\(639\) | −7239.75 | −0.448200 | ||||||||
\(640\) | 14517.9 | 0.896670 | ||||||||
\(641\) | −9141.52 | −0.563289 | −0.281645 | − | 0.959519i | \(-0.590880\pi\) | ||||
−0.281645 | + | 0.959519i | \(0.590880\pi\) | |||||||
\(642\) | 2464.33 | 0.151494 | ||||||||
\(643\) | −16323.8 | −1.00116 | −0.500582 | − | 0.865689i | \(-0.666881\pi\) | ||||
−0.500582 | + | 0.865689i | \(0.666881\pi\) | |||||||
\(644\) | 17488.9 | 1.07012 | ||||||||
\(645\) | 11365.4 | 0.693819 | ||||||||
\(646\) | −373.585 | −0.0227531 | ||||||||
\(647\) | −11823.8 | −0.718457 | −0.359228 | − | 0.933250i | \(-0.616960\pi\) | ||||
−0.359228 | + | 0.933250i | \(0.616960\pi\) | |||||||
\(648\) | 2377.76 | 0.144147 | ||||||||
\(649\) | −2734.75 | −0.165406 | ||||||||
\(650\) | −2705.63 | −0.163267 | ||||||||
\(651\) | 20591.1 | 1.23968 | ||||||||
\(652\) | 6094.10 | 0.366048 | ||||||||
\(653\) | −8377.85 | −0.502068 | −0.251034 | − | 0.967978i | \(-0.580771\pi\) | ||||
−0.251034 | + | 0.967978i | \(0.580771\pi\) | |||||||
\(654\) | −2583.20 | −0.154451 | ||||||||
\(655\) | 34223.0 | 2.04153 | ||||||||
\(656\) | 2848.56 | 0.169539 | ||||||||
\(657\) | 7147.21 | 0.424413 | ||||||||
\(658\) | −7404.08 | −0.438664 | ||||||||
\(659\) | 15544.6 | 0.918867 | 0.459434 | − | 0.888212i | \(-0.348052\pi\) | ||||
0.459434 | + | 0.888212i | \(0.348052\pi\) | |||||||
\(660\) | 13697.3 | 0.807831 | ||||||||
\(661\) | −6693.63 | −0.393876 | −0.196938 | − | 0.980416i | \(-0.563100\pi\) | ||||
−0.196938 | + | 0.980416i | \(0.563100\pi\) | |||||||
\(662\) | −1516.81 | −0.0890523 | ||||||||
\(663\) | 1096.11 | 0.0642073 | ||||||||
\(664\) | −778.066 | −0.0454741 | ||||||||
\(665\) | 70676.6 | 4.12138 | ||||||||
\(666\) | −135.695 | −0.00789501 | ||||||||
\(667\) | 7876.58 | 0.457245 | ||||||||
\(668\) | 12019.6 | 0.696187 | ||||||||
\(669\) | 344.996 | 0.0199377 | ||||||||
\(670\) | 2276.35 | 0.131258 | ||||||||
\(671\) | −673.869 | −0.0387696 | ||||||||
\(672\) | −10623.5 | −0.609838 | ||||||||
\(673\) | −29921.2 | −1.71379 | −0.856893 | − | 0.515494i | \(-0.827609\pi\) | ||||
−0.856893 | + | 0.515494i | \(0.827609\pi\) | |||||||
\(674\) | −2190.58 | −0.125190 | ||||||||
\(675\) | 36704.1 | 2.09295 | ||||||||
\(676\) | 10673.3 | 0.607268 | ||||||||
\(677\) | −6660.32 | −0.378105 | −0.189052 | − | 0.981967i | \(-0.560542\pi\) | ||||
−0.189052 | + | 0.981967i | \(0.560542\pi\) | |||||||
\(678\) | −1058.31 | −0.0599471 | ||||||||
\(679\) | −250.239 | −0.0141433 | ||||||||
\(680\) | 1065.13 | 0.0600673 | ||||||||
\(681\) | 19289.9 | 1.08545 | ||||||||
\(682\) | 1196.03 | 0.0671531 | ||||||||
\(683\) | −20913.9 | −1.17167 | −0.585834 | − | 0.810431i | \(-0.699233\pi\) | ||||
−0.585834 | + | 0.810431i | \(0.699233\pi\) | |||||||
\(684\) | −7861.19 | −0.439445 | ||||||||
\(685\) | −33493.7 | −1.86822 | ||||||||
\(686\) | 7107.77 | 0.395591 | ||||||||
\(687\) | −4407.53 | −0.244771 | ||||||||
\(688\) | 8565.66 | 0.474655 | ||||||||
\(689\) | 663.961 | 0.0367125 | ||||||||
\(690\) | −1996.18 | −0.110135 | ||||||||
\(691\) | 26125.3 | 1.43828 | 0.719140 | − | 0.694865i | \(-0.244536\pi\) | ||||
0.719140 | + | 0.694865i | \(0.244536\pi\) | |||||||
\(692\) | −28626.2 | −1.57255 | ||||||||
\(693\) | 7144.51 | 0.391627 | ||||||||
\(694\) | −3205.45 | −0.175327 | ||||||||
\(695\) | −4645.98 | −0.253571 | ||||||||
\(696\) | −3179.59 | −0.173164 | ||||||||
\(697\) | 426.281 | 0.0231657 | ||||||||
\(698\) | 304.798 | 0.0165283 | ||||||||
\(699\) | −6520.76 | −0.352844 | ||||||||
\(700\) | −65649.6 | −3.54475 | ||||||||
\(701\) | 7182.29 | 0.386978 | 0.193489 | − | 0.981102i | \(-0.438020\pi\) | ||||
0.193489 | + | 0.981102i | \(0.438020\pi\) | |||||||
\(702\) | −1718.89 | −0.0924148 | ||||||||
\(703\) | −3931.38 | −0.210917 | ||||||||
\(704\) | 9905.15 | 0.530276 | ||||||||
\(705\) | −43820.9 | −2.34098 | ||||||||
\(706\) | 4184.83 | 0.223085 | ||||||||
\(707\) | 1422.74 | 0.0756825 | ||||||||
\(708\) | 4131.33 | 0.219301 | ||||||||
\(709\) | 29154.3 | 1.54431 | 0.772153 | − | 0.635437i | \(-0.219180\pi\) | ||||
0.772153 | + | 0.635437i | \(0.219180\pi\) | |||||||
\(710\) | −5711.44 | −0.301897 | ||||||||
\(711\) | −4605.21 | −0.242910 | ||||||||
\(712\) | 9286.39 | 0.488795 | ||||||||
\(713\) | 9038.14 | 0.474728 | ||||||||
\(714\) | −512.916 | −0.0268843 | ||||||||
\(715\) | −12044.9 | −0.630004 | ||||||||
\(716\) | −23616.3 | −1.23266 | ||||||||
\(717\) | 6970.52 | 0.363067 | ||||||||
\(718\) | 2602.58 | 0.135275 | ||||||||
\(719\) | −9542.01 | −0.494933 | −0.247466 | − | 0.968896i | \(-0.579598\pi\) | ||||
−0.247466 | + | 0.968896i | \(0.579598\pi\) | |||||||
\(720\) | 10881.3 | 0.563224 | ||||||||
\(721\) | −23052.0 | −1.19071 | ||||||||
\(722\) | 1723.82 | 0.0888559 | ||||||||
\(723\) | 11567.2 | 0.595006 | ||||||||
\(724\) | −6458.90 | −0.331551 | ||||||||
\(725\) | −29567.0 | −1.51461 | ||||||||
\(726\) | 1397.15 | 0.0714228 | ||||||||
\(727\) | 22584.8 | 1.15216 | 0.576082 | − | 0.817392i | \(-0.304581\pi\) | ||||
0.576082 | + | 0.817392i | \(0.304581\pi\) | |||||||
\(728\) | 6208.16 | 0.316057 | ||||||||
\(729\) | 20918.9 | 1.06279 | ||||||||
\(730\) | 5638.44 | 0.285874 | ||||||||
\(731\) | 1281.83 | 0.0648566 | ||||||||
\(732\) | 1018.00 | 0.0514021 | ||||||||
\(733\) | 701.056 | 0.0353262 | 0.0176631 | − | 0.999844i | \(-0.494377\pi\) | ||||
0.0176631 | + | 0.999844i | \(0.494377\pi\) | |||||||
\(734\) | −700.700 | −0.0352361 | ||||||||
\(735\) | 69551.5 | 3.49040 | ||||||||
\(736\) | −4663.02 | −0.233534 | ||||||||
\(737\) | 6666.78 | 0.333207 | ||||||||
\(738\) | −172.990 | −0.00862853 | ||||||||
\(739\) | −5160.98 | −0.256901 | −0.128450 | − | 0.991716i | \(-0.541000\pi\) | ||||
−0.128450 | + | 0.991716i | \(0.541000\pi\) | |||||||
\(740\) | 5550.83 | 0.275747 | ||||||||
\(741\) | −12887.3 | −0.638902 | ||||||||
\(742\) | −310.695 | −0.0153719 | ||||||||
\(743\) | −34307.3 | −1.69396 | −0.846979 | − | 0.531626i | \(-0.821581\pi\) | ||||
−0.846979 | + | 0.531626i | \(0.821581\pi\) | |||||||
\(744\) | −3648.49 | −0.179785 | ||||||||
\(745\) | −11797.1 | −0.580151 | ||||||||
\(746\) | 1188.66 | 0.0583376 | ||||||||
\(747\) | −1189.50 | −0.0582618 | ||||||||
\(748\) | 1544.83 | 0.0755142 | ||||||||
\(749\) | −52581.0 | −2.56511 | ||||||||
\(750\) | 3596.41 | 0.175096 | ||||||||
\(751\) | 21101.1 | 1.02528 | 0.512642 | − | 0.858602i | \(-0.328667\pi\) | ||||
0.512642 | + | 0.858602i | \(0.328667\pi\) | |||||||
\(752\) | −33026.0 | −1.60151 | ||||||||
\(753\) | −19024.7 | −0.920713 | ||||||||
\(754\) | 1384.65 | 0.0668780 | ||||||||
\(755\) | 20471.1 | 0.986779 | ||||||||
\(756\) | −41707.2 | −2.00645 | ||||||||
\(757\) | −14495.1 | −0.695948 | −0.347974 | − | 0.937504i | \(-0.613130\pi\) | ||||
−0.347974 | + | 0.937504i | \(0.613130\pi\) | |||||||
\(758\) | −3334.19 | −0.159767 | ||||||||
\(759\) | −5846.26 | −0.279586 | ||||||||
\(760\) | −12523.0 | −0.597706 | ||||||||
\(761\) | 7577.93 | 0.360972 | 0.180486 | − | 0.983578i | \(-0.442233\pi\) | ||||
0.180486 | + | 0.983578i | \(0.442233\pi\) | |||||||
\(762\) | 2222.22 | 0.105646 | ||||||||
\(763\) | 55117.4 | 2.61518 | ||||||||
\(764\) | 19088.9 | 0.903942 | ||||||||
\(765\) | 1628.36 | 0.0769586 | ||||||||
\(766\) | −2506.42 | −0.118225 | ||||||||
\(767\) | −3632.92 | −0.171026 | ||||||||
\(768\) | −14013.3 | −0.658415 | ||||||||
\(769\) | 38841.9 | 1.82142 | 0.910711 | − | 0.413045i | \(-0.135535\pi\) | ||||
0.910711 | + | 0.413045i | \(0.135535\pi\) | |||||||
\(770\) | 5636.30 | 0.263790 | ||||||||
\(771\) | −21561.9 | −1.00717 | ||||||||
\(772\) | 9833.51 | 0.458440 | ||||||||
\(773\) | −17094.7 | −0.795414 | −0.397707 | − | 0.917512i | \(-0.630194\pi\) | ||||
−0.397707 | + | 0.917512i | \(0.630194\pi\) | |||||||
\(774\) | −520.184 | −0.0241571 | ||||||||
\(775\) | −33927.2 | −1.57252 | ||||||||
\(776\) | 44.3391 | 0.00205114 | ||||||||
\(777\) | −5397.60 | −0.249212 | ||||||||
\(778\) | −5092.24 | −0.234660 | ||||||||
\(779\) | −5011.90 | −0.230513 | ||||||||
\(780\) | 18196.0 | 0.835282 | ||||||||
\(781\) | −16727.2 | −0.766384 | ||||||||
\(782\) | −225.136 | −0.0102952 | ||||||||
\(783\) | −18783.9 | −0.857321 | ||||||||
\(784\) | 52418.1 | 2.38785 | ||||||||
\(785\) | 9591.41 | 0.436092 | ||||||||
\(786\) | 2920.09 | 0.132514 | ||||||||
\(787\) | 7931.12 | 0.359230 | 0.179615 | − | 0.983737i | \(-0.442515\pi\) | ||||
0.179615 | + | 0.983737i | \(0.442515\pi\) | |||||||
\(788\) | −34893.9 | −1.57747 | ||||||||
\(789\) | −9794.95 | −0.441964 | ||||||||
\(790\) | −3633.05 | −0.163618 | ||||||||
\(791\) | 22581.0 | 1.01503 | ||||||||
\(792\) | −1265.92 | −0.0567959 | ||||||||
\(793\) | −895.188 | −0.0400871 | ||||||||
\(794\) | −1070.91 | −0.0478654 | ||||||||
\(795\) | −1838.84 | −0.0820340 | ||||||||
\(796\) | 357.299 | 0.0159097 | ||||||||
\(797\) | 17835.5 | 0.792679 | 0.396339 | − | 0.918104i | \(-0.370280\pi\) | ||||
0.396339 | + | 0.918104i | \(0.370280\pi\) | |||||||
\(798\) | 6030.50 | 0.267516 | ||||||||
\(799\) | −4942.26 | −0.218829 | ||||||||
\(800\) | 17504.0 | 0.773573 | ||||||||
\(801\) | 14197.0 | 0.626248 | ||||||||
\(802\) | 3309.79 | 0.145727 | ||||||||
\(803\) | 16513.4 | 0.725709 | ||||||||
\(804\) | −10071.4 | −0.441778 | ||||||||
\(805\) | 42592.3 | 1.86482 | ||||||||
\(806\) | 1588.84 | 0.0694351 | ||||||||
\(807\) | 21132.5 | 0.921807 | ||||||||
\(808\) | −252.091 | −0.0109759 | ||||||||
\(809\) | −3069.78 | −0.133409 | −0.0667044 | − | 0.997773i | \(-0.521248\pi\) | ||||
−0.0667044 | + | 0.997773i | \(0.521248\pi\) | |||||||
\(810\) | 2867.73 | 0.124397 | ||||||||
\(811\) | −11589.5 | −0.501802 | −0.250901 | − | 0.968013i | \(-0.580727\pi\) | ||||
−0.250901 | + | 0.968013i | \(0.580727\pi\) | |||||||
\(812\) | 33597.3 | 1.45201 | ||||||||
\(813\) | −30155.2 | −1.30085 | ||||||||
\(814\) | −313.519 | −0.0134998 | ||||||||
\(815\) | 14841.5 | 0.637883 | ||||||||
\(816\) | −2287.87 | −0.0981513 | ||||||||
\(817\) | −15070.8 | −0.645363 | ||||||||
\(818\) | −3056.89 | −0.130662 | ||||||||
\(819\) | 9490.98 | 0.404935 | ||||||||
\(820\) | 7076.46 | 0.301367 | ||||||||
\(821\) | 3165.51 | 0.134564 | 0.0672820 | − | 0.997734i | \(-0.478567\pi\) | ||||
0.0672820 | + | 0.997734i | \(0.478567\pi\) | |||||||
\(822\) | −2857.86 | −0.121264 | ||||||||
\(823\) | 61.4767 | 0.00260382 | 0.00130191 | − | 0.999999i | \(-0.499586\pi\) | ||||
0.00130191 | + | 0.999999i | \(0.499586\pi\) | |||||||
\(824\) | 4084.52 | 0.172683 | ||||||||
\(825\) | 21945.6 | 0.926118 | ||||||||
\(826\) | 1700.00 | 0.0716107 | ||||||||
\(827\) | 5341.84 | 0.224612 | 0.112306 | − | 0.993674i | \(-0.464176\pi\) | ||||
0.112306 | + | 0.993674i | \(0.464176\pi\) | |||||||
\(828\) | −4737.44 | −0.198837 | ||||||||
\(829\) | 24525.9 | 1.02753 | 0.513763 | − | 0.857932i | \(-0.328251\pi\) | ||||
0.513763 | + | 0.857932i | \(0.328251\pi\) | |||||||
\(830\) | −938.398 | −0.0392437 | ||||||||
\(831\) | −25946.3 | −1.08312 | ||||||||
\(832\) | 13158.3 | 0.548295 | ||||||||
\(833\) | 7844.24 | 0.326275 | ||||||||
\(834\) | −396.419 | −0.0164591 | ||||||||
\(835\) | 29272.4 | 1.21319 | ||||||||
\(836\) | −18163.0 | −0.751413 | ||||||||
\(837\) | −21554.0 | −0.890101 | ||||||||
\(838\) | −4323.53 | −0.178226 | ||||||||
\(839\) | −37364.7 | −1.53751 | −0.768757 | − | 0.639541i | \(-0.779124\pi\) | ||||
−0.768757 | + | 0.639541i | \(0.779124\pi\) | |||||||
\(840\) | −17193.5 | −0.706229 | ||||||||
\(841\) | −9257.60 | −0.379581 | ||||||||
\(842\) | −4064.99 | −0.166376 | ||||||||
\(843\) | −26361.2 | −1.07702 | ||||||||
\(844\) | −14943.9 | −0.609466 | ||||||||
\(845\) | 25993.7 | 1.05824 | ||||||||
\(846\) | 2005.63 | 0.0815072 | ||||||||
\(847\) | −29810.7 | −1.20934 | ||||||||
\(848\) | −1385.86 | −0.0561210 | ||||||||
\(849\) | 27901.9 | 1.12791 | ||||||||
\(850\) | 845.113 | 0.0341025 | ||||||||
\(851\) | −2369.19 | −0.0954346 | ||||||||
\(852\) | 25269.4 | 1.01610 | ||||||||
\(853\) | 9667.56 | 0.388055 | 0.194028 | − | 0.980996i | \(-0.437845\pi\) | ||||
0.194028 | + | 0.980996i | \(0.437845\pi\) | |||||||
\(854\) | 418.896 | 0.0167849 | ||||||||
\(855\) | −19145.0 | −0.765786 | ||||||||
\(856\) | 9316.68 | 0.372007 | ||||||||
\(857\) | 41823.6 | 1.66706 | 0.833528 | − | 0.552478i | \(-0.186318\pi\) | ||||
0.833528 | + | 0.552478i | \(0.186318\pi\) | |||||||
\(858\) | −1027.73 | −0.0408930 | ||||||||
\(859\) | 28840.1 | 1.14553 | 0.572766 | − | 0.819719i | \(-0.305870\pi\) | ||||
0.572766 | + | 0.819719i | \(0.305870\pi\) | |||||||
\(860\) | 21279.0 | 0.843730 | ||||||||
\(861\) | −6881.12 | −0.272367 | ||||||||
\(862\) | −733.635 | −0.0289881 | ||||||||
\(863\) | 19646.5 | 0.774943 | 0.387471 | − | 0.921882i | \(-0.373349\pi\) | ||||
0.387471 | + | 0.921882i | \(0.373349\pi\) | |||||||
\(864\) | 11120.3 | 0.437870 | ||||||||
\(865\) | −69715.8 | −2.74036 | ||||||||
\(866\) | −3820.51 | −0.149915 | ||||||||
\(867\) | 20253.3 | 0.793354 | ||||||||
\(868\) | 38551.9 | 1.50753 | ||||||||
\(869\) | −10640.2 | −0.415355 | ||||||||
\(870\) | −3834.79 | −0.149439 | ||||||||
\(871\) | 8856.35 | 0.344530 | ||||||||
\(872\) | −9766.10 | −0.379268 | ||||||||
\(873\) | 67.7853 | 0.00262793 | ||||||||
\(874\) | 2646.99 | 0.102444 | ||||||||
\(875\) | −76736.0 | −2.96474 | ||||||||
\(876\) | −24946.4 | −0.962171 | ||||||||
\(877\) | −30530.3 | −1.17552 | −0.587762 | − | 0.809034i | \(-0.699991\pi\) | ||||
−0.587762 | + | 0.809034i | \(0.699991\pi\) | |||||||
\(878\) | 2524.35 | 0.0970303 | ||||||||
\(879\) | 19663.8 | 0.754542 | ||||||||
\(880\) | 25140.8 | 0.963064 | ||||||||
\(881\) | −1599.92 | −0.0611835 | −0.0305918 | − | 0.999532i | \(-0.509739\pi\) | ||||
−0.0305918 | + | 0.999532i | \(0.509739\pi\) | |||||||
\(882\) | −3183.30 | −0.121527 | ||||||||
\(883\) | −31200.1 | −1.18909 | −0.594545 | − | 0.804062i | \(-0.702668\pi\) | ||||
−0.594545 | + | 0.804062i | \(0.702668\pi\) | |||||||
\(884\) | 2052.20 | 0.0780803 | ||||||||
\(885\) | 10061.4 | 0.382158 | ||||||||
\(886\) | 2.36933 | 8.98409e−5 0 | ||||||||
\(887\) | 12134.9 | 0.459357 | 0.229679 | − | 0.973267i | \(-0.426233\pi\) | ||||
0.229679 | + | 0.973267i | \(0.426233\pi\) | |||||||
\(888\) | 956.387 | 0.0361422 | ||||||||
\(889\) | −47415.1 | −1.78881 | ||||||||
\(890\) | 11200.0 | 0.421825 | ||||||||
\(891\) | 8398.77 | 0.315791 | ||||||||
\(892\) | 645.922 | 0.0242456 | ||||||||
\(893\) | 58107.5 | 2.17749 | ||||||||
\(894\) | −1006.59 | −0.0376571 | ||||||||
\(895\) | −57515.0 | −2.14806 | ||||||||
\(896\) | −26430.8 | −0.985483 | ||||||||
\(897\) | −7766.35 | −0.289087 | ||||||||
\(898\) | −4678.92 | −0.173873 | ||||||||
\(899\) | 17362.8 | 0.644141 | ||||||||
\(900\) | 17783.3 | 0.658642 | ||||||||
\(901\) | −207.391 | −0.00766835 | ||||||||
\(902\) | −399.688 | −0.0147541 | ||||||||
\(903\) | −20691.6 | −0.762539 | ||||||||
\(904\) | −4001.07 | −0.147205 | ||||||||
\(905\) | −15729.9 | −0.577768 | ||||||||
\(906\) | 1746.70 | 0.0640510 | ||||||||
\(907\) | 47562.7 | 1.74123 | 0.870613 | − | 0.491969i | \(-0.163723\pi\) | ||||
0.870613 | + | 0.491969i | \(0.163723\pi\) | |||||||
\(908\) | 36115.7 | 1.31998 | ||||||||
\(909\) | −385.394 | −0.0140624 | ||||||||
\(910\) | 7487.44 | 0.272754 | ||||||||
\(911\) | −9657.49 | −0.351226 | −0.175613 | − | 0.984459i | \(-0.556191\pi\) | ||||
−0.175613 | + | 0.984459i | \(0.556191\pi\) | |||||||
\(912\) | 26899.1 | 0.976666 | ||||||||
\(913\) | −2748.30 | −0.0996227 | ||||||||
\(914\) | 696.158 | 0.0251935 | ||||||||
\(915\) | 2479.22 | 0.0895745 | ||||||||
\(916\) | −8252.03 | −0.297658 | ||||||||
\(917\) | −62305.5 | −2.24374 | ||||||||
\(918\) | 536.900 | 0.0193032 | ||||||||
\(919\) | 18388.2 | 0.660034 | 0.330017 | − | 0.943975i | \(-0.392945\pi\) | ||||
0.330017 | + | 0.943975i | \(0.392945\pi\) | |||||||
\(920\) | −7546.81 | −0.270447 | ||||||||
\(921\) | 17319.5 | 0.619649 | ||||||||
\(922\) | 6051.56 | 0.216158 | ||||||||
\(923\) | −22220.9 | −0.792427 | ||||||||
\(924\) | −24937.0 | −0.887843 | ||||||||
\(925\) | 8893.43 | 0.316123 | ||||||||
\(926\) | 5184.97 | 0.184005 | ||||||||
\(927\) | 6244.38 | 0.221243 | ||||||||
\(928\) | −8957.94 | −0.316874 | ||||||||
\(929\) | 40380.1 | 1.42608 | 0.713041 | − | 0.701123i | \(-0.247318\pi\) | ||||
0.713041 | + | 0.701123i | \(0.247318\pi\) | |||||||
\(930\) | −4400.31 | −0.155153 | ||||||||
\(931\) | −92227.0 | −3.24664 | ||||||||
\(932\) | −12208.5 | −0.429081 | ||||||||
\(933\) | 12634.4 | 0.443336 | ||||||||
\(934\) | 1669.71 | 0.0584951 | ||||||||
\(935\) | 3762.26 | 0.131593 | ||||||||
\(936\) | −1681.68 | −0.0587259 | ||||||||
\(937\) | 10056.4 | 0.350616 | 0.175308 | − | 0.984514i | \(-0.443908\pi\) | ||||
0.175308 | + | 0.984514i | \(0.443908\pi\) | |||||||
\(938\) | −4144.26 | −0.144259 | ||||||||
\(939\) | 36750.3 | 1.27721 | ||||||||
\(940\) | −82043.9 | −2.84678 | ||||||||
\(941\) | 25842.2 | 0.895253 | 0.447626 | − | 0.894221i | \(-0.352269\pi\) | ||||
0.447626 | + | 0.894221i | \(0.352269\pi\) | |||||||
\(942\) | 818.390 | 0.0283063 | ||||||||
\(943\) | −3020.35 | −0.104301 | ||||||||
\(944\) | 7582.85 | 0.261442 | ||||||||
\(945\) | −101573. | −3.49648 | ||||||||
\(946\) | −1201.87 | −0.0413066 | ||||||||
\(947\) | −28722.3 | −0.985585 | −0.492793 | − | 0.870147i | \(-0.664024\pi\) | ||||
−0.492793 | + | 0.870147i | \(0.664024\pi\) | |||||||
\(948\) | 16073.9 | 0.550692 | ||||||||
\(949\) | 21936.9 | 0.750370 | ||||||||
\(950\) | −9936.23 | −0.339341 | ||||||||
\(951\) | −9914.15 | −0.338053 | ||||||||
\(952\) | −1939.14 | −0.0660167 | ||||||||
\(953\) | −19844.1 | −0.674514 | −0.337257 | − | 0.941413i | \(-0.609499\pi\) | ||||
−0.337257 | + | 0.941413i | \(0.609499\pi\) | |||||||
\(954\) | 84.1619 | 0.00285623 | ||||||||
\(955\) | 46488.8 | 1.57523 | ||||||||
\(956\) | 13050.6 | 0.441513 | ||||||||
\(957\) | −11231.0 | −0.379360 | ||||||||
\(958\) | −3962.93 | −0.133650 | ||||||||
\(959\) | 60977.7 | 2.05326 | ||||||||
\(960\) | −36441.9 | −1.22517 | ||||||||
\(961\) | −9867.67 | −0.331230 | ||||||||
\(962\) | −416.488 | −0.0139585 | ||||||||
\(963\) | 14243.3 | 0.476617 | ||||||||
\(964\) | 21656.8 | 0.723567 | ||||||||
\(965\) | 23948.4 | 0.798887 | ||||||||
\(966\) | 3634.20 | 0.121044 | ||||||||
\(967\) | −39599.1 | −1.31688 | −0.658438 | − | 0.752635i | \(-0.728783\pi\) | ||||
−0.658438 | + | 0.752635i | \(0.728783\pi\) | |||||||
\(968\) | 5282.08 | 0.175385 | ||||||||
\(969\) | 4025.39 | 0.133451 | ||||||||
\(970\) | 53.4758 | 0.00177011 | ||||||||
\(971\) | −13977.1 | −0.461942 | −0.230971 | − | 0.972961i | \(-0.574190\pi\) | ||||
−0.230971 | + | 0.972961i | \(0.574190\pi\) | |||||||
\(972\) | 19671.8 | 0.649151 | ||||||||
\(973\) | 8458.34 | 0.278687 | ||||||||
\(974\) | −2744.75 | −0.0902953 | ||||||||
\(975\) | 29153.2 | 0.957589 | ||||||||
\(976\) | 1868.49 | 0.0612796 | ||||||||
\(977\) | −40368.7 | −1.32191 | −0.660956 | − | 0.750425i | \(-0.729849\pi\) | ||||
−0.660956 | + | 0.750425i | \(0.729849\pi\) | |||||||
\(978\) | 1266.35 | 0.0414044 | ||||||||
\(979\) | 32801.6 | 1.07083 | ||||||||
\(980\) | 130218. | 4.24456 | ||||||||
\(981\) | −14930.3 | −0.485921 | ||||||||
\(982\) | 4973.40 | 0.161617 | ||||||||
\(983\) | 22848.3 | 0.741351 | 0.370675 | − | 0.928763i | \(-0.379126\pi\) | ||||
0.370675 | + | 0.928763i | \(0.379126\pi\) | |||||||
\(984\) | 1219.25 | 0.0395001 | ||||||||
\(985\) | −84980.1 | −2.74893 | ||||||||
\(986\) | −432.500 | −0.0139692 | ||||||||
\(987\) | 79779.1 | 2.57284 | ||||||||
\(988\) | −24128.3 | −0.776947 | ||||||||
\(989\) | −9082.24 | −0.292010 | ||||||||
\(990\) | −1526.78 | −0.0490143 | ||||||||
\(991\) | 35035.8 | 1.12306 | 0.561529 | − | 0.827457i | \(-0.310213\pi\) | ||||
0.561529 | + | 0.827457i | \(0.310213\pi\) | |||||||
\(992\) | −10279.0 | −0.328990 | ||||||||
\(993\) | 16343.7 | 0.522307 | ||||||||
\(994\) | 10398.1 | 0.331798 | ||||||||
\(995\) | 870.162 | 0.0277246 | ||||||||
\(996\) | 4151.80 | 0.132083 | ||||||||
\(997\) | 34408.6 | 1.09301 | 0.546505 | − | 0.837456i | \(-0.315958\pi\) | ||||
0.546505 | + | 0.837456i | \(0.315958\pi\) | |||||||
\(998\) | −4600.62 | −0.145922 | ||||||||
\(999\) | 5650.00 | 0.178937 |
(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 | 37.4.a.a.1.3 | ✓ | 4 | |
3.2 | odd | 2 | 333.4.a.e.1.2 | 4 | |||
4.3 | odd | 2 | 592.4.a.f.1.3 | 4 | |||
5.4 | even | 2 | 925.4.a.a.1.2 | 4 | |||
7.6 | odd | 2 | 1813.4.a.b.1.3 | 4 | |||
8.3 | odd | 2 | 2368.4.a.g.1.2 | 4 | |||
8.5 | even | 2 | 2368.4.a.l.1.3 | 4 | |||
37.36 | even | 2 | 1369.4.a.c.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
37.4.a.a.1.3 | ✓ | 4 | 1.1 | even | 1 | trivial | |
333.4.a.e.1.2 | 4 | 3.2 | odd | 2 | |||
592.4.a.f.1.3 | 4 | 4.3 | odd | 2 | |||
925.4.a.a.1.2 | 4 | 5.4 | even | 2 | |||
1369.4.a.c.1.2 | 4 | 37.36 | even | 2 | |||
1813.4.a.b.1.3 | 4 | 7.6 | odd | 2 | |||
2368.4.a.g.1.2 | 4 | 8.3 | odd | 2 | |||
2368.4.a.l.1.3 | 4 | 8.5 | even | 2 |