Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2166,4,Mod(1,2166)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2166, 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("2166.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2166 = 2 \cdot 3 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2166.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: | \(127.798137072\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2166.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | 0.707107 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | −0.909830 | −0.0813777 | −0.0406888 | − | 0.999172i | \(-0.512955\pi\) | ||||
−0.0406888 | + | 0.999172i | \(0.512955\pi\) | |||||||
\(6\) | 6.00000 | 0.408248 | ||||||||
\(7\) | −16.3262 | −0.881534 | −0.440767 | − | 0.897622i | \(-0.645293\pi\) | ||||
−0.440767 | + | 0.897622i | \(0.645293\pi\) | |||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −1.81966 | −0.0575427 | ||||||||
\(11\) | −1.94427 | −0.0532927 | −0.0266464 | − | 0.999645i | \(-0.508483\pi\) | ||||
−0.0266464 | + | 0.999645i | \(0.508483\pi\) | |||||||
\(12\) | 12.0000 | 0.288675 | ||||||||
\(13\) | 15.0902 | 0.321943 | 0.160972 | − | 0.986959i | \(-0.448537\pi\) | ||||
0.160972 | + | 0.986959i | \(0.448537\pi\) | |||||||
\(14\) | −32.6525 | −0.623339 | ||||||||
\(15\) | −2.72949 | −0.0469834 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 32.0132 | 0.456725 | 0.228363 | − | 0.973576i | \(-0.426663\pi\) | ||||
0.228363 | + | 0.973576i | \(0.426663\pi\) | |||||||
\(18\) | 18.0000 | 0.235702 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −3.63932 | −0.0406888 | ||||||||
\(21\) | −48.9787 | −0.508954 | ||||||||
\(22\) | −3.88854 | −0.0376837 | ||||||||
\(23\) | −44.8885 | −0.406953 | −0.203476 | − | 0.979080i | \(-0.565224\pi\) | ||||
−0.203476 | + | 0.979080i | \(0.565224\pi\) | |||||||
\(24\) | 24.0000 | 0.204124 | ||||||||
\(25\) | −124.172 | −0.993378 | ||||||||
\(26\) | 30.1803 | 0.227648 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | −65.3050 | −0.440767 | ||||||||
\(29\) | 31.1509 | 0.199468 | 0.0997342 | − | 0.995014i | \(-0.468201\pi\) | ||||
0.0997342 | + | 0.995014i | \(0.468201\pi\) | |||||||
\(30\) | −5.45898 | −0.0332223 | ||||||||
\(31\) | −299.503 | −1.73524 | −0.867620 | − | 0.497229i | \(-0.834351\pi\) | ||||
−0.867620 | + | 0.497229i | \(0.834351\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | −5.83282 | −0.0307686 | ||||||||
\(34\) | 64.0263 | 0.322954 | ||||||||
\(35\) | 14.8541 | 0.0717372 | ||||||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | −252.885 | −1.12362 | −0.561812 | − | 0.827265i | \(-0.689896\pi\) | ||||
−0.561812 | + | 0.827265i | \(0.689896\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 45.2705 | 0.185874 | ||||||||
\(40\) | −7.27864 | −0.0287714 | ||||||||
\(41\) | 81.6475 | 0.311005 | 0.155502 | − | 0.987836i | \(-0.450300\pi\) | ||||
0.155502 | + | 0.987836i | \(0.450300\pi\) | |||||||
\(42\) | −97.9574 | −0.359885 | ||||||||
\(43\) | −217.095 | −0.769923 | −0.384962 | − | 0.922933i | \(-0.625785\pi\) | ||||
−0.384962 | + | 0.922933i | \(0.625785\pi\) | |||||||
\(44\) | −7.77709 | −0.0266464 | ||||||||
\(45\) | −8.18847 | −0.0271259 | ||||||||
\(46\) | −89.7771 | −0.287759 | ||||||||
\(47\) | 187.743 | 0.582661 | 0.291331 | − | 0.956622i | \(-0.405902\pi\) | ||||
0.291331 | + | 0.956622i | \(0.405902\pi\) | |||||||
\(48\) | 48.0000 | 0.144338 | ||||||||
\(49\) | −76.4540 | −0.222898 | ||||||||
\(50\) | −248.344 | −0.702424 | ||||||||
\(51\) | 96.0395 | 0.263690 | ||||||||
\(52\) | 60.3607 | 0.160972 | ||||||||
\(53\) | −11.8127 | −0.0306151 | −0.0153076 | − | 0.999883i | \(-0.504873\pi\) | ||||
−0.0153076 | + | 0.999883i | \(0.504873\pi\) | |||||||
\(54\) | 54.0000 | 0.136083 | ||||||||
\(55\) | 1.76896 | 0.00433684 | ||||||||
\(56\) | −130.610 | −0.311669 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 62.3018 | 0.141045 | ||||||||
\(59\) | 244.046 | 0.538511 | 0.269255 | − | 0.963069i | \(-0.413222\pi\) | ||||
0.269255 | + | 0.963069i | \(0.413222\pi\) | |||||||
\(60\) | −10.9180 | −0.0234917 | ||||||||
\(61\) | 526.508 | 1.10512 | 0.552562 | − | 0.833472i | \(-0.313650\pi\) | ||||
0.552562 | + | 0.833472i | \(0.313650\pi\) | |||||||
\(62\) | −599.007 | −1.22700 | ||||||||
\(63\) | −146.936 | −0.293845 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −13.7295 | −0.0261990 | ||||||||
\(66\) | −11.6656 | −0.0217567 | ||||||||
\(67\) | −210.726 | −0.384244 | −0.192122 | − | 0.981371i | \(-0.561537\pi\) | ||||
−0.192122 | + | 0.981371i | \(0.561537\pi\) | |||||||
\(68\) | 128.053 | 0.228363 | ||||||||
\(69\) | −134.666 | −0.234954 | ||||||||
\(70\) | 29.7082 | 0.0507259 | ||||||||
\(71\) | −503.418 | −0.841476 | −0.420738 | − | 0.907182i | \(-0.638229\pi\) | ||||
−0.420738 | + | 0.907182i | \(0.638229\pi\) | |||||||
\(72\) | 72.0000 | 0.117851 | ||||||||
\(73\) | 115.265 | 0.184806 | 0.0924028 | − | 0.995722i | \(-0.470545\pi\) | ||||
0.0924028 | + | 0.995722i | \(0.470545\pi\) | |||||||
\(74\) | −505.771 | −0.794523 | ||||||||
\(75\) | −372.517 | −0.573527 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 31.7426 | 0.0469794 | ||||||||
\(78\) | 90.5410 | 0.131433 | ||||||||
\(79\) | 220.492 | 0.314016 | 0.157008 | − | 0.987597i | \(-0.449815\pi\) | ||||
0.157008 | + | 0.987597i | \(0.449815\pi\) | |||||||
\(80\) | −14.5573 | −0.0203444 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 163.295 | 0.219913 | ||||||||
\(83\) | 200.023 | 0.264523 | 0.132261 | − | 0.991215i | \(-0.457776\pi\) | ||||
0.132261 | + | 0.991215i | \(0.457776\pi\) | |||||||
\(84\) | −195.915 | −0.254477 | ||||||||
\(85\) | −29.1265 | −0.0371672 | ||||||||
\(86\) | −434.190 | −0.544418 | ||||||||
\(87\) | 93.4528 | 0.115163 | ||||||||
\(88\) | −15.5542 | −0.0188418 | ||||||||
\(89\) | −174.091 | −0.207344 | −0.103672 | − | 0.994612i | \(-0.533059\pi\) | ||||
−0.103672 | + | 0.994612i | \(0.533059\pi\) | |||||||
\(90\) | −16.3769 | −0.0191809 | ||||||||
\(91\) | −246.366 | −0.283804 | ||||||||
\(92\) | −179.554 | −0.203476 | ||||||||
\(93\) | −898.510 | −1.00184 | ||||||||
\(94\) | 375.485 | 0.412004 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 96.0000 | 0.102062 | ||||||||
\(97\) | −1105.40 | −1.15708 | −0.578538 | − | 0.815655i | \(-0.696377\pi\) | ||||
−0.578538 | + | 0.815655i | \(0.696377\pi\) | |||||||
\(98\) | −152.908 | −0.157613 | ||||||||
\(99\) | −17.4984 | −0.0177642 | ||||||||
\(100\) | −496.689 | −0.496689 | ||||||||
\(101\) | −896.371 | −0.883092 | −0.441546 | − | 0.897239i | \(-0.645570\pi\) | ||||
−0.441546 | + | 0.897239i | \(0.645570\pi\) | |||||||
\(102\) | 192.079 | 0.186457 | ||||||||
\(103\) | 161.160 | 0.154170 | 0.0770852 | − | 0.997025i | \(-0.475439\pi\) | ||||
0.0770852 | + | 0.997025i | \(0.475439\pi\) | |||||||
\(104\) | 120.721 | 0.113824 | ||||||||
\(105\) | 44.5623 | 0.0414175 | ||||||||
\(106\) | −23.6254 | −0.0216482 | ||||||||
\(107\) | −1121.56 | −1.01333 | −0.506663 | − | 0.862144i | \(-0.669121\pi\) | ||||
−0.506663 | + | 0.862144i | \(0.669121\pi\) | |||||||
\(108\) | 108.000 | 0.0962250 | ||||||||
\(109\) | 983.166 | 0.863947 | 0.431973 | − | 0.901886i | \(-0.357817\pi\) | ||||
0.431973 | + | 0.901886i | \(0.357817\pi\) | |||||||
\(110\) | 3.53791 | 0.00306661 | ||||||||
\(111\) | −758.656 | −0.648725 | ||||||||
\(112\) | −261.220 | −0.220383 | ||||||||
\(113\) | −500.349 | −0.416539 | −0.208270 | − | 0.978071i | \(-0.566783\pi\) | ||||
−0.208270 | + | 0.978071i | \(0.566783\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 40.8409 | 0.0331169 | ||||||||
\(116\) | 124.604 | 0.0997342 | ||||||||
\(117\) | 135.812 | 0.107314 | ||||||||
\(118\) | 488.093 | 0.380785 | ||||||||
\(119\) | −522.654 | −0.402619 | ||||||||
\(120\) | −21.8359 | −0.0166111 | ||||||||
\(121\) | −1327.22 | −0.997160 | ||||||||
\(122\) | 1053.02 | 0.781440 | ||||||||
\(123\) | 244.942 | 0.179559 | ||||||||
\(124\) | −1198.01 | −0.867620 | ||||||||
\(125\) | 226.704 | 0.162216 | ||||||||
\(126\) | −293.872 | −0.207780 | ||||||||
\(127\) | −865.459 | −0.604701 | −0.302351 | − | 0.953197i | \(-0.597771\pi\) | ||||
−0.302351 | + | 0.953197i | \(0.597771\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | −651.286 | −0.444515 | ||||||||
\(130\) | −27.4590 | −0.0185255 | ||||||||
\(131\) | −2344.79 | −1.56386 | −0.781930 | − | 0.623366i | \(-0.785765\pi\) | ||||
−0.781930 | + | 0.623366i | \(0.785765\pi\) | |||||||
\(132\) | −23.3313 | −0.0153843 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −421.453 | −0.271701 | ||||||||
\(135\) | −24.5654 | −0.0156611 | ||||||||
\(136\) | 256.105 | 0.161477 | ||||||||
\(137\) | 2071.28 | 1.29169 | 0.645843 | − | 0.763470i | \(-0.276506\pi\) | ||||
0.645843 | + | 0.763470i | \(0.276506\pi\) | |||||||
\(138\) | −269.331 | −0.166138 | ||||||||
\(139\) | −1467.54 | −0.895507 | −0.447753 | − | 0.894157i | \(-0.647776\pi\) | ||||
−0.447753 | + | 0.894157i | \(0.647776\pi\) | |||||||
\(140\) | 59.4164 | 0.0358686 | ||||||||
\(141\) | 563.228 | 0.336400 | ||||||||
\(142\) | −1006.84 | −0.595013 | ||||||||
\(143\) | −29.3394 | −0.0171572 | ||||||||
\(144\) | 144.000 | 0.0833333 | ||||||||
\(145\) | −28.3420 | −0.0162323 | ||||||||
\(146\) | 230.531 | 0.130677 | ||||||||
\(147\) | −229.362 | −0.128690 | ||||||||
\(148\) | −1011.54 | −0.561812 | ||||||||
\(149\) | −176.948 | −0.0972895 | −0.0486447 | − | 0.998816i | \(-0.515490\pi\) | ||||
−0.0486447 | + | 0.998816i | \(0.515490\pi\) | |||||||
\(150\) | −745.033 | −0.405545 | ||||||||
\(151\) | −1138.74 | −0.613706 | −0.306853 | − | 0.951757i | \(-0.599276\pi\) | ||||
−0.306853 | + | 0.951757i | \(0.599276\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 288.118 | 0.152242 | ||||||||
\(154\) | 63.4853 | 0.0332194 | ||||||||
\(155\) | 272.497 | 0.141210 | ||||||||
\(156\) | 181.082 | 0.0929370 | ||||||||
\(157\) | −1952.19 | −0.992366 | −0.496183 | − | 0.868218i | \(-0.665266\pi\) | ||||
−0.496183 | + | 0.868218i | \(0.665266\pi\) | |||||||
\(158\) | 440.983 | 0.222043 | ||||||||
\(159\) | −35.4381 | −0.0176756 | ||||||||
\(160\) | −29.1146 | −0.0143857 | ||||||||
\(161\) | 732.861 | 0.358742 | ||||||||
\(162\) | 162.000 | 0.0785674 | ||||||||
\(163\) | 385.974 | 0.185471 | 0.0927357 | − | 0.995691i | \(-0.470439\pi\) | ||||
0.0927357 | + | 0.995691i | \(0.470439\pi\) | |||||||
\(164\) | 326.590 | 0.155502 | ||||||||
\(165\) | 5.30687 | 0.00250387 | ||||||||
\(166\) | 400.046 | 0.187046 | ||||||||
\(167\) | −3206.11 | −1.48561 | −0.742803 | − | 0.669510i | \(-0.766504\pi\) | ||||
−0.742803 | + | 0.669510i | \(0.766504\pi\) | |||||||
\(168\) | −391.830 | −0.179942 | ||||||||
\(169\) | −1969.29 | −0.896353 | ||||||||
\(170\) | −58.2531 | −0.0262812 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −868.381 | −0.384962 | ||||||||
\(173\) | −3194.72 | −1.40399 | −0.701993 | − | 0.712184i | \(-0.747706\pi\) | ||||
−0.701993 | + | 0.712184i | \(0.747706\pi\) | |||||||
\(174\) | 186.906 | 0.0814326 | ||||||||
\(175\) | 2027.27 | 0.875696 | ||||||||
\(176\) | −31.1084 | −0.0133232 | ||||||||
\(177\) | 732.139 | 0.310909 | ||||||||
\(178\) | −348.183 | −0.146615 | ||||||||
\(179\) | 2449.26 | 1.02272 | 0.511358 | − | 0.859368i | \(-0.329142\pi\) | ||||
0.511358 | + | 0.859368i | \(0.329142\pi\) | |||||||
\(180\) | −32.7539 | −0.0135629 | ||||||||
\(181\) | −2002.67 | −0.822415 | −0.411207 | − | 0.911542i | \(-0.634893\pi\) | ||||
−0.411207 | + | 0.911542i | \(0.634893\pi\) | |||||||
\(182\) | −492.731 | −0.200680 | ||||||||
\(183\) | 1579.53 | 0.638043 | ||||||||
\(184\) | −359.108 | −0.143879 | ||||||||
\(185\) | 230.083 | 0.0914380 | ||||||||
\(186\) | −1797.02 | −0.708408 | ||||||||
\(187\) | −62.2423 | −0.0243401 | ||||||||
\(188\) | 750.971 | 0.291331 | ||||||||
\(189\) | −440.808 | −0.169651 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4101.97 | 1.55397 | 0.776984 | − | 0.629520i | \(-0.216749\pi\) | ||||
0.776984 | + | 0.629520i | \(0.216749\pi\) | |||||||
\(192\) | 192.000 | 0.0721688 | ||||||||
\(193\) | 1756.55 | 0.655126 | 0.327563 | − | 0.944829i | \(-0.393773\pi\) | ||||
0.327563 | + | 0.944829i | \(0.393773\pi\) | |||||||
\(194\) | −2210.80 | −0.818176 | ||||||||
\(195\) | −41.1885 | −0.0151260 | ||||||||
\(196\) | −305.816 | −0.111449 | ||||||||
\(197\) | 3670.57 | 1.32750 | 0.663750 | − | 0.747955i | \(-0.268964\pi\) | ||||
0.663750 | + | 0.747955i | \(0.268964\pi\) | |||||||
\(198\) | −34.9969 | −0.0125612 | ||||||||
\(199\) | −2610.75 | −0.930007 | −0.465004 | − | 0.885309i | \(-0.653947\pi\) | ||||
−0.465004 | + | 0.885309i | \(0.653947\pi\) | |||||||
\(200\) | −993.378 | −0.351212 | ||||||||
\(201\) | −632.179 | −0.221843 | ||||||||
\(202\) | −1792.74 | −0.624440 | ||||||||
\(203\) | −508.577 | −0.175838 | ||||||||
\(204\) | 384.158 | 0.131845 | ||||||||
\(205\) | −74.2853 | −0.0253088 | ||||||||
\(206\) | 322.320 | 0.109015 | ||||||||
\(207\) | −403.997 | −0.135651 | ||||||||
\(208\) | 241.443 | 0.0804858 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 89.1246 | 0.0292866 | ||||||||
\(211\) | −3473.35 | −1.13325 | −0.566624 | − | 0.823976i | \(-0.691751\pi\) | ||||
−0.566624 | + | 0.823976i | \(0.691751\pi\) | |||||||
\(212\) | −47.2509 | −0.0153076 | ||||||||
\(213\) | −1510.25 | −0.485826 | ||||||||
\(214\) | −2243.13 | −0.716529 | ||||||||
\(215\) | 197.520 | 0.0626546 | ||||||||
\(216\) | 216.000 | 0.0680414 | ||||||||
\(217\) | 4889.76 | 1.52967 | ||||||||
\(218\) | 1966.33 | 0.610903 | ||||||||
\(219\) | 345.796 | 0.106698 | ||||||||
\(220\) | 7.07583 | 0.00216842 | ||||||||
\(221\) | 483.084 | 0.147040 | ||||||||
\(222\) | −1517.31 | −0.458718 | ||||||||
\(223\) | 2530.49 | 0.759885 | 0.379942 | − | 0.925010i | \(-0.375944\pi\) | ||||
0.379942 | + | 0.925010i | \(0.375944\pi\) | |||||||
\(224\) | −522.440 | −0.155835 | ||||||||
\(225\) | −1117.55 | −0.331126 | ||||||||
\(226\) | −1000.70 | −0.294538 | ||||||||
\(227\) | −6734.59 | −1.96912 | −0.984560 | − | 0.175046i | \(-0.943993\pi\) | ||||
−0.984560 | + | 0.175046i | \(0.943993\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −337.719 | −0.0974546 | −0.0487273 | − | 0.998812i | \(-0.515517\pi\) | ||||
−0.0487273 | + | 0.998812i | \(0.515517\pi\) | |||||||
\(230\) | 81.6819 | 0.0234172 | ||||||||
\(231\) | 95.2279 | 0.0271235 | ||||||||
\(232\) | 249.207 | 0.0705227 | ||||||||
\(233\) | −6311.26 | −1.77452 | −0.887262 | − | 0.461265i | \(-0.847396\pi\) | ||||
−0.887262 | + | 0.461265i | \(0.847396\pi\) | |||||||
\(234\) | 271.623 | 0.0758827 | ||||||||
\(235\) | −170.814 | −0.0474156 | ||||||||
\(236\) | 976.186 | 0.269255 | ||||||||
\(237\) | 661.475 | 0.181297 | ||||||||
\(238\) | −1045.31 | −0.284695 | ||||||||
\(239\) | −3275.56 | −0.886519 | −0.443260 | − | 0.896393i | \(-0.646178\pi\) | ||||
−0.443260 | + | 0.896393i | \(0.646178\pi\) | |||||||
\(240\) | −43.6718 | −0.0117459 | ||||||||
\(241\) | 1668.27 | 0.445904 | 0.222952 | − | 0.974829i | \(-0.428431\pi\) | ||||
0.222952 | + | 0.974829i | \(0.428431\pi\) | |||||||
\(242\) | −2654.44 | −0.705099 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 2106.03 | 0.552562 | ||||||||
\(245\) | 69.5601 | 0.0181389 | ||||||||
\(246\) | 489.885 | 0.126967 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −2396.03 | −0.613500 | ||||||||
\(249\) | 600.070 | 0.152722 | ||||||||
\(250\) | 453.409 | 0.114704 | ||||||||
\(251\) | −2044.39 | −0.514106 | −0.257053 | − | 0.966397i | \(-0.582751\pi\) | ||||
−0.257053 | + | 0.966397i | \(0.582751\pi\) | |||||||
\(252\) | −587.745 | −0.146922 | ||||||||
\(253\) | 87.2755 | 0.0216876 | ||||||||
\(254\) | −1730.92 | −0.427588 | ||||||||
\(255\) | −87.3796 | −0.0214585 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 5181.31 | 1.25759 | 0.628797 | − | 0.777570i | \(-0.283548\pi\) | ||||
0.628797 | + | 0.777570i | \(0.283548\pi\) | |||||||
\(258\) | −1302.57 | −0.314320 | ||||||||
\(259\) | 4128.67 | 0.990513 | ||||||||
\(260\) | −54.9180 | −0.0130995 | ||||||||
\(261\) | 280.358 | 0.0664894 | ||||||||
\(262\) | −4689.59 | −1.10582 | ||||||||
\(263\) | 7137.93 | 1.67355 | 0.836774 | − | 0.547548i | \(-0.184439\pi\) | ||||
0.836774 | + | 0.547548i | \(0.184439\pi\) | |||||||
\(264\) | −46.6625 | −0.0108783 | ||||||||
\(265\) | 10.7476 | 0.00249139 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −522.274 | −0.119710 | ||||||||
\(268\) | −842.906 | −0.192122 | ||||||||
\(269\) | 6395.52 | 1.44960 | 0.724798 | − | 0.688961i | \(-0.241933\pi\) | ||||
0.724798 | + | 0.688961i | \(0.241933\pi\) | |||||||
\(270\) | −49.1308 | −0.0110741 | ||||||||
\(271\) | −6478.86 | −1.45226 | −0.726131 | − | 0.687556i | \(-0.758683\pi\) | ||||
−0.726131 | + | 0.687556i | \(0.758683\pi\) | |||||||
\(272\) | 512.210 | 0.114181 | ||||||||
\(273\) | −739.097 | −0.163854 | ||||||||
\(274\) | 4142.55 | 0.913360 | ||||||||
\(275\) | 241.425 | 0.0529398 | ||||||||
\(276\) | −538.663 | −0.117477 | ||||||||
\(277\) | 3501.93 | 0.759606 | 0.379803 | − | 0.925067i | \(-0.375992\pi\) | ||||
0.379803 | + | 0.925067i | \(0.375992\pi\) | |||||||
\(278\) | −2935.09 | −0.633219 | ||||||||
\(279\) | −2695.53 | −0.578413 | ||||||||
\(280\) | 118.833 | 0.0253629 | ||||||||
\(281\) | 1722.75 | 0.365731 | 0.182865 | − | 0.983138i | \(-0.441463\pi\) | ||||
0.182865 | + | 0.983138i | \(0.441463\pi\) | |||||||
\(282\) | 1126.46 | 0.237870 | ||||||||
\(283\) | −905.945 | −0.190293 | −0.0951464 | − | 0.995463i | \(-0.530332\pi\) | ||||
−0.0951464 | + | 0.995463i | \(0.530332\pi\) | |||||||
\(284\) | −2013.67 | −0.420738 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −58.6788 | −0.0121320 | ||||||||
\(287\) | −1333.00 | −0.274161 | ||||||||
\(288\) | 288.000 | 0.0589256 | ||||||||
\(289\) | −3888.16 | −0.791402 | ||||||||
\(290\) | −56.6841 | −0.0114779 | ||||||||
\(291\) | −3316.20 | −0.668038 | ||||||||
\(292\) | 461.062 | 0.0924028 | ||||||||
\(293\) | 6570.56 | 1.31009 | 0.655045 | − | 0.755590i | \(-0.272650\pi\) | ||||
0.655045 | + | 0.755590i | \(0.272650\pi\) | |||||||
\(294\) | −458.724 | −0.0909977 | ||||||||
\(295\) | −222.041 | −0.0438228 | ||||||||
\(296\) | −2023.08 | −0.397261 | ||||||||
\(297\) | −52.4953 | −0.0102562 | ||||||||
\(298\) | −353.896 | −0.0687940 | ||||||||
\(299\) | −677.376 | −0.131016 | ||||||||
\(300\) | −1490.07 | −0.286763 | ||||||||
\(301\) | 3544.35 | 0.678714 | ||||||||
\(302\) | −2277.49 | −0.433956 | ||||||||
\(303\) | −2689.11 | −0.509853 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −479.033 | −0.0899323 | ||||||||
\(306\) | 576.237 | 0.107651 | ||||||||
\(307\) | 566.581 | 0.105331 | 0.0526653 | − | 0.998612i | \(-0.483228\pi\) | ||||
0.0526653 | + | 0.998612i | \(0.483228\pi\) | |||||||
\(308\) | 126.971 | 0.0234897 | ||||||||
\(309\) | 483.479 | 0.0890103 | ||||||||
\(310\) | 544.995 | 0.0998504 | ||||||||
\(311\) | 3507.55 | 0.639534 | 0.319767 | − | 0.947496i | \(-0.396395\pi\) | ||||
0.319767 | + | 0.947496i | \(0.396395\pi\) | |||||||
\(312\) | 362.164 | 0.0657164 | ||||||||
\(313\) | −321.768 | −0.0581067 | −0.0290534 | − | 0.999578i | \(-0.509249\pi\) | ||||
−0.0290534 | + | 0.999578i | \(0.509249\pi\) | |||||||
\(314\) | −3904.37 | −0.701709 | ||||||||
\(315\) | 133.687 | 0.0239124 | ||||||||
\(316\) | 881.966 | 0.157008 | ||||||||
\(317\) | −3797.03 | −0.672752 | −0.336376 | − | 0.941728i | \(-0.609201\pi\) | ||||
−0.336376 | + | 0.941728i | \(0.609201\pi\) | |||||||
\(318\) | −70.8763 | −0.0124986 | ||||||||
\(319\) | −60.5659 | −0.0106302 | ||||||||
\(320\) | −58.2291 | −0.0101722 | ||||||||
\(321\) | −3364.69 | −0.585043 | ||||||||
\(322\) | 1465.72 | 0.253669 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 324.000 | 0.0555556 | ||||||||
\(325\) | −1873.78 | −0.319811 | ||||||||
\(326\) | 771.948 | 0.131148 | ||||||||
\(327\) | 2949.50 | 0.498800 | ||||||||
\(328\) | 653.180 | 0.109957 | ||||||||
\(329\) | −3065.13 | −0.513636 | ||||||||
\(330\) | 10.6137 | 0.00177051 | ||||||||
\(331\) | 9588.45 | 1.59223 | 0.796116 | − | 0.605144i | \(-0.206885\pi\) | ||||
0.796116 | + | 0.605144i | \(0.206885\pi\) | |||||||
\(332\) | 800.093 | 0.132261 | ||||||||
\(333\) | −2275.97 | −0.374542 | ||||||||
\(334\) | −6412.22 | −1.05048 | ||||||||
\(335\) | 191.725 | 0.0312689 | ||||||||
\(336\) | −783.659 | −0.127238 | ||||||||
\(337\) | 9263.59 | 1.49739 | 0.748694 | − | 0.662916i | \(-0.230681\pi\) | ||||
0.748694 | + | 0.662916i | \(0.230681\pi\) | |||||||
\(338\) | −3938.57 | −0.633817 | ||||||||
\(339\) | −1501.05 | −0.240489 | ||||||||
\(340\) | −116.506 | −0.0185836 | ||||||||
\(341\) | 582.316 | 0.0924756 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6848.11 | 1.07803 | ||||||||
\(344\) | −1736.76 | −0.272209 | ||||||||
\(345\) | 122.523 | 0.0191200 | ||||||||
\(346\) | −6389.43 | −0.992768 | ||||||||
\(347\) | −3603.50 | −0.557481 | −0.278740 | − | 0.960367i | \(-0.589917\pi\) | ||||
−0.278740 | + | 0.960367i | \(0.589917\pi\) | |||||||
\(348\) | 373.811 | 0.0575815 | ||||||||
\(349\) | 3751.60 | 0.575411 | 0.287706 | − | 0.957719i | \(-0.407108\pi\) | ||||
0.287706 | + | 0.957719i | \(0.407108\pi\) | |||||||
\(350\) | 4054.53 | 0.619211 | ||||||||
\(351\) | 407.435 | 0.0619580 | ||||||||
\(352\) | −62.2167 | −0.00942091 | ||||||||
\(353\) | −8836.39 | −1.33233 | −0.666166 | − | 0.745803i | \(-0.732066\pi\) | ||||
−0.666166 | + | 0.745803i | \(0.732066\pi\) | |||||||
\(354\) | 1464.28 | 0.219846 | ||||||||
\(355\) | 458.025 | 0.0684773 | ||||||||
\(356\) | −696.365 | −0.103672 | ||||||||
\(357\) | −1567.96 | −0.232452 | ||||||||
\(358\) | 4898.52 | 0.723170 | ||||||||
\(359\) | 7348.14 | 1.08028 | 0.540139 | − | 0.841576i | \(-0.318371\pi\) | ||||
0.540139 | + | 0.841576i | \(0.318371\pi\) | |||||||
\(360\) | −65.5078 | −0.00959045 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −4005.33 | −0.581535 | ||||||||
\(363\) | −3981.66 | −0.575711 | ||||||||
\(364\) | −985.463 | −0.141902 | ||||||||
\(365\) | −104.872 | −0.0150390 | ||||||||
\(366\) | 3159.05 | 0.451165 | ||||||||
\(367\) | −10829.4 | −1.54030 | −0.770150 | − | 0.637862i | \(-0.779819\pi\) | ||||
−0.770150 | + | 0.637862i | \(0.779819\pi\) | |||||||
\(368\) | −718.217 | −0.101738 | ||||||||
\(369\) | 734.827 | 0.103668 | ||||||||
\(370\) | 460.166 | 0.0646564 | ||||||||
\(371\) | 192.857 | 0.0269883 | ||||||||
\(372\) | −3594.04 | −0.500920 | ||||||||
\(373\) | 10614.6 | 1.47347 | 0.736734 | − | 0.676183i | \(-0.236367\pi\) | ||||
0.736734 | + | 0.676183i | \(0.236367\pi\) | |||||||
\(374\) | −124.485 | −0.0172111 | ||||||||
\(375\) | 680.113 | 0.0936557 | ||||||||
\(376\) | 1501.94 | 0.206002 | ||||||||
\(377\) | 470.073 | 0.0642174 | ||||||||
\(378\) | −881.617 | −0.119962 | ||||||||
\(379\) | 3538.17 | 0.479535 | 0.239767 | − | 0.970830i | \(-0.422929\pi\) | ||||
0.239767 | + | 0.970830i | \(0.422929\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2596.38 | −0.349124 | ||||||||
\(382\) | 8203.93 | 1.09882 | ||||||||
\(383\) | 13138.1 | 1.75280 | 0.876402 | − | 0.481581i | \(-0.159937\pi\) | ||||
0.876402 | + | 0.481581i | \(0.159937\pi\) | |||||||
\(384\) | 384.000 | 0.0510310 | ||||||||
\(385\) | −28.8804 | −0.00382307 | ||||||||
\(386\) | 3513.10 | 0.463244 | ||||||||
\(387\) | −1953.86 | −0.256641 | ||||||||
\(388\) | −4421.60 | −0.578538 | ||||||||
\(389\) | 1058.46 | 0.137958 | 0.0689792 | − | 0.997618i | \(-0.478026\pi\) | ||||
0.0689792 | + | 0.997618i | \(0.478026\pi\) | |||||||
\(390\) | −82.3769 | −0.0106957 | ||||||||
\(391\) | −1437.02 | −0.185866 | ||||||||
\(392\) | −611.632 | −0.0788063 | ||||||||
\(393\) | −7034.38 | −0.902895 | ||||||||
\(394\) | 7341.14 | 0.938684 | ||||||||
\(395\) | −200.610 | −0.0255539 | ||||||||
\(396\) | −69.9938 | −0.00888212 | ||||||||
\(397\) | −15180.8 | −1.91915 | −0.959573 | − | 0.281461i | \(-0.909181\pi\) | ||||
−0.959573 | + | 0.281461i | \(0.909181\pi\) | |||||||
\(398\) | −5221.51 | −0.657615 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1986.76 | −0.248344 | ||||||||
\(401\) | −1336.20 | −0.166400 | −0.0832002 | − | 0.996533i | \(-0.526514\pi\) | ||||
−0.0832002 | + | 0.996533i | \(0.526514\pi\) | |||||||
\(402\) | −1264.36 | −0.156867 | ||||||||
\(403\) | −4519.56 | −0.558648 | ||||||||
\(404\) | −3585.49 | −0.441546 | ||||||||
\(405\) | −73.6962 | −0.00904196 | ||||||||
\(406\) | −1017.15 | −0.124336 | ||||||||
\(407\) | 491.678 | 0.0598810 | ||||||||
\(408\) | 768.316 | 0.0932287 | ||||||||
\(409\) | −1976.03 | −0.238896 | −0.119448 | − | 0.992840i | \(-0.538112\pi\) | ||||
−0.119448 | + | 0.992840i | \(0.538112\pi\) | |||||||
\(410\) | −148.571 | −0.0178960 | ||||||||
\(411\) | 6213.83 | 0.745755 | ||||||||
\(412\) | 644.639 | 0.0770852 | ||||||||
\(413\) | −3984.36 | −0.474716 | ||||||||
\(414\) | −807.994 | −0.0959196 | ||||||||
\(415\) | −181.987 | −0.0215263 | ||||||||
\(416\) | 482.885 | 0.0569120 | ||||||||
\(417\) | −4402.63 | −0.517021 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3242.90 | 0.378105 | 0.189052 | − | 0.981967i | \(-0.439458\pi\) | ||||
0.189052 | + | 0.981967i | \(0.439458\pi\) | |||||||
\(420\) | 178.249 | 0.0207087 | ||||||||
\(421\) | 11959.4 | 1.38448 | 0.692241 | − | 0.721667i | \(-0.256624\pi\) | ||||
0.692241 | + | 0.721667i | \(0.256624\pi\) | |||||||
\(422\) | −6946.71 | −0.801328 | ||||||||
\(423\) | 1689.68 | 0.194220 | ||||||||
\(424\) | −94.5017 | −0.0108241 | ||||||||
\(425\) | −3975.14 | −0.453701 | ||||||||
\(426\) | −3020.51 | −0.343531 | ||||||||
\(427\) | −8595.90 | −0.974204 | ||||||||
\(428\) | −4486.26 | −0.506663 | ||||||||
\(429\) | −88.0182 | −0.00990573 | ||||||||
\(430\) | 395.039 | 0.0443035 | ||||||||
\(431\) | −7226.13 | −0.807589 | −0.403794 | − | 0.914850i | \(-0.632309\pi\) | ||||
−0.403794 | + | 0.914850i | \(0.632309\pi\) | |||||||
\(432\) | 432.000 | 0.0481125 | ||||||||
\(433\) | 9903.01 | 1.09909 | 0.549547 | − | 0.835462i | \(-0.314800\pi\) | ||||
0.549547 | + | 0.835462i | \(0.314800\pi\) | |||||||
\(434\) | 9779.53 | 1.08164 | ||||||||
\(435\) | −85.0261 | −0.00937170 | ||||||||
\(436\) | 3932.66 | 0.431973 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 691.593 | 0.0754465 | ||||||||
\(439\) | 7077.97 | 0.769506 | 0.384753 | − | 0.923020i | \(-0.374287\pi\) | ||||
0.384753 | + | 0.923020i | \(0.374287\pi\) | |||||||
\(440\) | 14.1517 | 0.00153330 | ||||||||
\(441\) | −688.086 | −0.0742993 | ||||||||
\(442\) | 966.168 | 0.103973 | ||||||||
\(443\) | −7730.58 | −0.829099 | −0.414550 | − | 0.910027i | \(-0.636061\pi\) | ||||
−0.414550 | + | 0.910027i | \(0.636061\pi\) | |||||||
\(444\) | −3034.63 | −0.324362 | ||||||||
\(445\) | 158.394 | 0.0168732 | ||||||||
\(446\) | 5060.98 | 0.537320 | ||||||||
\(447\) | −530.843 | −0.0561701 | ||||||||
\(448\) | −1044.88 | −0.110192 | ||||||||
\(449\) | 2353.41 | 0.247359 | 0.123679 | − | 0.992322i | \(-0.460531\pi\) | ||||
0.123679 | + | 0.992322i | \(0.460531\pi\) | |||||||
\(450\) | −2235.10 | −0.234141 | ||||||||
\(451\) | −158.745 | −0.0165743 | ||||||||
\(452\) | −2001.40 | −0.208270 | ||||||||
\(453\) | −3416.23 | −0.354323 | ||||||||
\(454\) | −13469.2 | −1.39238 | ||||||||
\(455\) | 224.151 | 0.0230953 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8420.95 | 0.861959 | 0.430980 | − | 0.902362i | \(-0.358168\pi\) | ||||
0.430980 | + | 0.902362i | \(0.358168\pi\) | |||||||
\(458\) | −675.438 | −0.0689108 | ||||||||
\(459\) | 864.355 | 0.0878968 | ||||||||
\(460\) | 163.364 | 0.0165584 | ||||||||
\(461\) | −669.622 | −0.0676517 | −0.0338258 | − | 0.999428i | \(-0.510769\pi\) | ||||
−0.0338258 | + | 0.999428i | \(0.510769\pi\) | |||||||
\(462\) | 190.456 | 0.0191792 | ||||||||
\(463\) | 5570.89 | 0.559182 | 0.279591 | − | 0.960119i | \(-0.409801\pi\) | ||||
0.279591 | + | 0.960119i | \(0.409801\pi\) | |||||||
\(464\) | 498.415 | 0.0498671 | ||||||||
\(465\) | 817.492 | 0.0815275 | ||||||||
\(466\) | −12622.5 | −1.25478 | ||||||||
\(467\) | −10869.8 | −1.07707 | −0.538537 | − | 0.842602i | \(-0.681023\pi\) | ||||
−0.538537 | + | 0.842602i | \(0.681023\pi\) | |||||||
\(468\) | 543.246 | 0.0536572 | ||||||||
\(469\) | 3440.37 | 0.338724 | ||||||||
\(470\) | −341.628 | −0.0335279 | ||||||||
\(471\) | −5856.56 | −0.572943 | ||||||||
\(472\) | 1952.37 | 0.190392 | ||||||||
\(473\) | 422.092 | 0.0410313 | ||||||||
\(474\) | 1322.95 | 0.128196 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2090.62 | −0.201309 | ||||||||
\(477\) | −106.314 | −0.0102050 | ||||||||
\(478\) | −6551.11 | −0.626864 | ||||||||
\(479\) | −2435.33 | −0.232303 | −0.116151 | − | 0.993232i | \(-0.537056\pi\) | ||||
−0.116151 | + | 0.993232i | \(0.537056\pi\) | |||||||
\(480\) | −87.3437 | −0.00830557 | ||||||||
\(481\) | −3816.08 | −0.361743 | ||||||||
\(482\) | 3336.55 | 0.315302 | ||||||||
\(483\) | 2198.58 | 0.207120 | ||||||||
\(484\) | −5308.88 | −0.498580 | ||||||||
\(485\) | 1005.73 | 0.0941602 | ||||||||
\(486\) | 486.000 | 0.0453609 | ||||||||
\(487\) | 10685.2 | 0.994233 | 0.497116 | − | 0.867684i | \(-0.334392\pi\) | ||||
0.497116 | + | 0.867684i | \(0.334392\pi\) | |||||||
\(488\) | 4212.07 | 0.390720 | ||||||||
\(489\) | 1157.92 | 0.107082 | ||||||||
\(490\) | 139.120 | 0.0128261 | ||||||||
\(491\) | −9068.91 | −0.833552 | −0.416776 | − | 0.909009i | \(-0.636840\pi\) | ||||
−0.416776 | + | 0.909009i | \(0.636840\pi\) | |||||||
\(492\) | 979.769 | 0.0897793 | ||||||||
\(493\) | 997.239 | 0.0911022 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 15.9206 | 0.00144561 | ||||||||
\(496\) | −4792.06 | −0.433810 | ||||||||
\(497\) | 8218.93 | 0.741789 | ||||||||
\(498\) | 1200.14 | 0.107991 | ||||||||
\(499\) | −9085.54 | −0.815080 | −0.407540 | − | 0.913187i | \(-0.633613\pi\) | ||||
−0.407540 | + | 0.913187i | \(0.633613\pi\) | |||||||
\(500\) | 906.817 | 0.0811082 | ||||||||
\(501\) | −9618.33 | −0.857716 | ||||||||
\(502\) | −4088.77 | −0.363528 | ||||||||
\(503\) | −229.914 | −0.0203804 | −0.0101902 | − | 0.999948i | \(-0.503244\pi\) | ||||
−0.0101902 | + | 0.999948i | \(0.503244\pi\) | |||||||
\(504\) | −1175.49 | −0.103890 | ||||||||
\(505\) | 815.546 | 0.0718640 | ||||||||
\(506\) | 174.551 | 0.0153355 | ||||||||
\(507\) | −5907.86 | −0.517509 | ||||||||
\(508\) | −3461.84 | −0.302351 | ||||||||
\(509\) | 9812.78 | 0.854507 | 0.427253 | − | 0.904132i | \(-0.359481\pi\) | ||||
0.427253 | + | 0.904132i | \(0.359481\pi\) | |||||||
\(510\) | −174.759 | −0.0151735 | ||||||||
\(511\) | −1881.85 | −0.162912 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 10362.6 | 0.889253 | ||||||||
\(515\) | −146.628 | −0.0125460 | ||||||||
\(516\) | −2605.14 | −0.222258 | ||||||||
\(517\) | −365.023 | −0.0310516 | ||||||||
\(518\) | 8257.34 | 0.700399 | ||||||||
\(519\) | −9584.15 | −0.810592 | ||||||||
\(520\) | −109.836 | −0.00926274 | ||||||||
\(521\) | 8772.27 | 0.737658 | 0.368829 | − | 0.929497i | \(-0.379759\pi\) | ||||
0.368829 | + | 0.929497i | \(0.379759\pi\) | |||||||
\(522\) | 560.717 | 0.0470151 | ||||||||
\(523\) | −4563.38 | −0.381535 | −0.190767 | − | 0.981635i | \(-0.561098\pi\) | ||||
−0.190767 | + | 0.981635i | \(0.561098\pi\) | |||||||
\(524\) | −9379.18 | −0.781930 | ||||||||
\(525\) | 6081.80 | 0.505583 | ||||||||
\(526\) | 14275.9 | 1.18338 | ||||||||
\(527\) | −9588.05 | −0.792528 | ||||||||
\(528\) | −93.3251 | −0.00769214 | ||||||||
\(529\) | −10152.0 | −0.834390 | ||||||||
\(530\) | 21.4951 | 0.00176168 | ||||||||
\(531\) | 2196.42 | 0.179504 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1232.07 | 0.100126 | ||||||||
\(534\) | −1044.55 | −0.0846480 | ||||||||
\(535\) | 1020.43 | 0.0824620 | ||||||||
\(536\) | −1685.81 | −0.135851 | ||||||||
\(537\) | 7347.78 | 0.590466 | ||||||||
\(538\) | 12791.0 | 1.02502 | ||||||||
\(539\) | 148.647 | 0.0118788 | ||||||||
\(540\) | −98.2616 | −0.00783057 | ||||||||
\(541\) | −5541.69 | −0.440399 | −0.220200 | − | 0.975455i | \(-0.570671\pi\) | ||||
−0.220200 | + | 0.975455i | \(0.570671\pi\) | |||||||
\(542\) | −12957.7 | −1.02690 | ||||||||
\(543\) | −6008.00 | −0.474821 | ||||||||
\(544\) | 1024.42 | 0.0807384 | ||||||||
\(545\) | −894.514 | −0.0703060 | ||||||||
\(546\) | −1478.19 | −0.115862 | ||||||||
\(547\) | 482.902 | 0.0377466 | 0.0188733 | − | 0.999822i | \(-0.493992\pi\) | ||||
0.0188733 | + | 0.999822i | \(0.493992\pi\) | |||||||
\(548\) | 8285.10 | 0.645843 | ||||||||
\(549\) | 4738.58 | 0.368374 | ||||||||
\(550\) | 482.849 | 0.0374341 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −1077.33 | −0.0830688 | ||||||||
\(553\) | −3599.80 | −0.276815 | ||||||||
\(554\) | 7003.87 | 0.537123 | ||||||||
\(555\) | 690.248 | 0.0527917 | ||||||||
\(556\) | −5870.18 | −0.447753 | ||||||||
\(557\) | −9850.15 | −0.749308 | −0.374654 | − | 0.927165i | \(-0.622238\pi\) | ||||
−0.374654 | + | 0.927165i | \(0.622238\pi\) | |||||||
\(558\) | −5391.06 | −0.409000 | ||||||||
\(559\) | −3276.00 | −0.247872 | ||||||||
\(560\) | 237.666 | 0.0179343 | ||||||||
\(561\) | −186.727 | −0.0140528 | ||||||||
\(562\) | 3445.49 | 0.258611 | ||||||||
\(563\) | −15083.7 | −1.12913 | −0.564567 | − | 0.825387i | \(-0.690957\pi\) | ||||
−0.564567 | + | 0.825387i | \(0.690957\pi\) | |||||||
\(564\) | 2252.91 | 0.168200 | ||||||||
\(565\) | 455.233 | 0.0338970 | ||||||||
\(566\) | −1811.89 | −0.134557 | ||||||||
\(567\) | −1322.43 | −0.0979482 | ||||||||
\(568\) | −4027.35 | −0.297507 | ||||||||
\(569\) | 354.846 | 0.0261439 | 0.0130720 | − | 0.999915i | \(-0.495839\pi\) | ||||
0.0130720 | + | 0.999915i | \(0.495839\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10394.6 | 0.761821 | 0.380910 | − | 0.924612i | \(-0.375611\pi\) | ||||
0.380910 | + | 0.924612i | \(0.375611\pi\) | |||||||
\(572\) | −117.358 | −0.00857861 | ||||||||
\(573\) | 12305.9 | 0.897184 | ||||||||
\(574\) | −2665.99 | −0.193861 | ||||||||
\(575\) | 5573.91 | 0.404258 | ||||||||
\(576\) | 576.000 | 0.0416667 | ||||||||
\(577\) | 1289.40 | 0.0930303 | 0.0465151 | − | 0.998918i | \(-0.485188\pi\) | ||||
0.0465151 | + | 0.998918i | \(0.485188\pi\) | |||||||
\(578\) | −7776.32 | −0.559606 | ||||||||
\(579\) | 5269.65 | 0.378237 | ||||||||
\(580\) | −113.368 | −0.00811613 | ||||||||
\(581\) | −3265.63 | −0.233186 | ||||||||
\(582\) | −6632.40 | −0.472374 | ||||||||
\(583\) | 22.9671 | 0.00163156 | ||||||||
\(584\) | 922.124 | 0.0653386 | ||||||||
\(585\) | −123.565 | −0.00873299 | ||||||||
\(586\) | 13141.1 | 0.926373 | ||||||||
\(587\) | 19612.9 | 1.37906 | 0.689531 | − | 0.724256i | \(-0.257817\pi\) | ||||
0.689531 | + | 0.724256i | \(0.257817\pi\) | |||||||
\(588\) | −917.447 | −0.0643451 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −444.082 | −0.0309874 | ||||||||
\(591\) | 11011.7 | 0.766432 | ||||||||
\(592\) | −4046.17 | −0.280906 | ||||||||
\(593\) | 7358.41 | 0.509568 | 0.254784 | − | 0.966998i | \(-0.417996\pi\) | ||||
0.254784 | + | 0.966998i | \(0.417996\pi\) | |||||||
\(594\) | −104.991 | −0.00725222 | ||||||||
\(595\) | 475.527 | 0.0327642 | ||||||||
\(596\) | −707.791 | −0.0486447 | ||||||||
\(597\) | −7832.26 | −0.536940 | ||||||||
\(598\) | −1354.75 | −0.0926420 | ||||||||
\(599\) | 16712.6 | 1.13999 | 0.569997 | − | 0.821647i | \(-0.306944\pi\) | ||||
0.569997 | + | 0.821647i | \(0.306944\pi\) | |||||||
\(600\) | −2980.13 | −0.202772 | ||||||||
\(601\) | 8181.83 | 0.555314 | 0.277657 | − | 0.960680i | \(-0.410442\pi\) | ||||
0.277657 | + | 0.960680i | \(0.410442\pi\) | |||||||
\(602\) | 7088.70 | 0.479923 | ||||||||
\(603\) | −1896.54 | −0.128081 | ||||||||
\(604\) | −4554.97 | −0.306853 | ||||||||
\(605\) | 1207.54 | 0.0811466 | ||||||||
\(606\) | −5378.23 | −0.360521 | ||||||||
\(607\) | 19171.1 | 1.28193 | 0.640966 | − | 0.767569i | \(-0.278534\pi\) | ||||
0.640966 | + | 0.767569i | \(0.278534\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1525.73 | −0.101520 | ||||||||
\(610\) | −958.067 | −0.0635918 | ||||||||
\(611\) | 2833.07 | 0.187584 | ||||||||
\(612\) | 1152.47 | 0.0761209 | ||||||||
\(613\) | −23387.4 | −1.54096 | −0.770481 | − | 0.637463i | \(-0.779984\pi\) | ||||
−0.770481 | + | 0.637463i | \(0.779984\pi\) | |||||||
\(614\) | 1133.16 | 0.0744800 | ||||||||
\(615\) | −222.856 | −0.0146121 | ||||||||
\(616\) | 253.941 | 0.0166097 | ||||||||
\(617\) | 29646.2 | 1.93438 | 0.967189 | − | 0.254056i | \(-0.0817649\pi\) | ||||
0.967189 | + | 0.254056i | \(0.0817649\pi\) | |||||||
\(618\) | 966.959 | 0.0629398 | ||||||||
\(619\) | 17042.8 | 1.10663 | 0.553317 | − | 0.832971i | \(-0.313362\pi\) | ||||
0.553317 | + | 0.832971i | \(0.313362\pi\) | |||||||
\(620\) | 1089.99 | 0.0706049 | ||||||||
\(621\) | −1211.99 | −0.0783181 | ||||||||
\(622\) | 7015.11 | 0.452219 | ||||||||
\(623\) | 2842.26 | 0.182781 | ||||||||
\(624\) | 724.328 | 0.0464685 | ||||||||
\(625\) | 15315.3 | 0.980177 | ||||||||
\(626\) | −643.536 | −0.0410876 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −7808.75 | −0.496183 | ||||||||
\(629\) | −8095.66 | −0.513188 | ||||||||
\(630\) | 267.374 | 0.0169086 | ||||||||
\(631\) | −12936.7 | −0.816170 | −0.408085 | − | 0.912944i | \(-0.633803\pi\) | ||||
−0.408085 | + | 0.912944i | \(0.633803\pi\) | |||||||
\(632\) | 1763.93 | 0.111021 | ||||||||
\(633\) | −10420.1 | −0.654282 | ||||||||
\(634\) | −7594.05 | −0.475707 | ||||||||
\(635\) | 787.421 | 0.0492092 | ||||||||
\(636\) | −141.753 | −0.00883782 | ||||||||
\(637\) | −1153.70 | −0.0717604 | ||||||||
\(638\) | −121.132 | −0.00751669 | ||||||||
\(639\) | −4530.76 | −0.280492 | ||||||||
\(640\) | −116.458 | −0.00719284 | ||||||||
\(641\) | −30925.1 | −1.90557 | −0.952783 | − | 0.303650i | \(-0.901794\pi\) | ||||
−0.952783 | + | 0.303650i | \(0.901794\pi\) | |||||||
\(642\) | −6729.39 | −0.413688 | ||||||||
\(643\) | −2848.23 | −0.174686 | −0.0873430 | − | 0.996178i | \(-0.527838\pi\) | ||||
−0.0873430 | + | 0.996178i | \(0.527838\pi\) | |||||||
\(644\) | 2931.44 | 0.179371 | ||||||||
\(645\) | 592.559 | 0.0361736 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 14856.5 | 0.902733 | 0.451367 | − | 0.892339i | \(-0.350937\pi\) | ||||
0.451367 | + | 0.892339i | \(0.350937\pi\) | |||||||
\(648\) | 648.000 | 0.0392837 | ||||||||
\(649\) | −474.493 | −0.0286987 | ||||||||
\(650\) | −3747.56 | −0.226141 | ||||||||
\(651\) | 14669.3 | 0.883157 | ||||||||
\(652\) | 1543.90 | 0.0927357 | ||||||||
\(653\) | −697.326 | −0.0417894 | −0.0208947 | − | 0.999782i | \(-0.506651\pi\) | ||||
−0.0208947 | + | 0.999782i | \(0.506651\pi\) | |||||||
\(654\) | 5898.99 | 0.352705 | ||||||||
\(655\) | 2133.36 | 0.127263 | ||||||||
\(656\) | 1306.36 | 0.0777512 | ||||||||
\(657\) | 1037.39 | 0.0616018 | ||||||||
\(658\) | −6130.26 | −0.363195 | ||||||||
\(659\) | −2792.41 | −0.165064 | −0.0825319 | − | 0.996588i | \(-0.526301\pi\) | ||||
−0.0825319 | + | 0.996588i | \(0.526301\pi\) | |||||||
\(660\) | 21.2275 | 0.00125194 | ||||||||
\(661\) | 28297.2 | 1.66510 | 0.832551 | − | 0.553949i | \(-0.186880\pi\) | ||||
0.832551 | + | 0.553949i | \(0.186880\pi\) | |||||||
\(662\) | 19176.9 | 1.12588 | ||||||||
\(663\) | 1449.25 | 0.0848933 | ||||||||
\(664\) | 1600.19 | 0.0935230 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4551.94 | −0.264841 | ||||||||
\(667\) | −1398.32 | −0.0811741 | ||||||||
\(668\) | −12824.4 | −0.742803 | ||||||||
\(669\) | 7591.48 | 0.438720 | ||||||||
\(670\) | 383.450 | 0.0221104 | ||||||||
\(671\) | −1023.68 | −0.0588950 | ||||||||
\(672\) | −1567.32 | −0.0899712 | ||||||||
\(673\) | −19162.8 | −1.09758 | −0.548790 | − | 0.835960i | \(-0.684911\pi\) | ||||
−0.548790 | + | 0.835960i | \(0.684911\pi\) | |||||||
\(674\) | 18527.2 | 1.05881 | ||||||||
\(675\) | −3352.65 | −0.191176 | ||||||||
\(676\) | −7877.15 | −0.448176 | ||||||||
\(677\) | −14029.7 | −0.796463 | −0.398232 | − | 0.917285i | \(-0.630376\pi\) | ||||
−0.398232 | + | 0.917285i | \(0.630376\pi\) | |||||||
\(678\) | −3002.10 | −0.170051 | ||||||||
\(679\) | 18047.0 | 1.02000 | ||||||||
\(680\) | −233.012 | −0.0131406 | ||||||||
\(681\) | −20203.8 | −1.13687 | ||||||||
\(682\) | 1164.63 | 0.0653901 | ||||||||
\(683\) | −6578.33 | −0.368540 | −0.184270 | − | 0.982876i | \(-0.558992\pi\) | ||||
−0.184270 | + | 0.982876i | \(0.558992\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1884.51 | −0.105114 | ||||||||
\(686\) | 13696.2 | 0.762279 | ||||||||
\(687\) | −1013.16 | −0.0562654 | ||||||||
\(688\) | −3473.52 | −0.192481 | ||||||||
\(689\) | −178.256 | −0.00985633 | ||||||||
\(690\) | 245.046 | 0.0135199 | ||||||||
\(691\) | 28001.9 | 1.54159 | 0.770797 | − | 0.637080i | \(-0.219858\pi\) | ||||
0.770797 | + | 0.637080i | \(0.219858\pi\) | |||||||
\(692\) | −12778.9 | −0.701993 | ||||||||
\(693\) | 285.684 | 0.0156598 | ||||||||
\(694\) | −7206.99 | −0.394198 | ||||||||
\(695\) | 1335.22 | 0.0728743 | ||||||||
\(696\) | 747.622 | 0.0407163 | ||||||||
\(697\) | 2613.79 | 0.142044 | ||||||||
\(698\) | 7503.20 | 0.406877 | ||||||||
\(699\) | −18933.8 | −1.02452 | ||||||||
\(700\) | 8109.06 | 0.437848 | ||||||||
\(701\) | 1649.54 | 0.0888762 | 0.0444381 | − | 0.999012i | \(-0.485850\pi\) | ||||
0.0444381 | + | 0.999012i | \(0.485850\pi\) | |||||||
\(702\) | 814.869 | 0.0438109 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −124.433 | −0.00666159 | ||||||||
\(705\) | −512.442 | −0.0273754 | ||||||||
\(706\) | −17672.8 | −0.942102 | ||||||||
\(707\) | 14634.4 | 0.778476 | ||||||||
\(708\) | 2928.56 | 0.155455 | ||||||||
\(709\) | 12138.8 | 0.642993 | 0.321496 | − | 0.946911i | \(-0.395814\pi\) | ||||
0.321496 | + | 0.946911i | \(0.395814\pi\) | |||||||
\(710\) | 916.050 | 0.0484208 | ||||||||
\(711\) | 1984.42 | 0.104672 | ||||||||
\(712\) | −1392.73 | −0.0733073 | ||||||||
\(713\) | 13444.3 | 0.706160 | ||||||||
\(714\) | −3135.93 | −0.164368 | ||||||||
\(715\) | 26.6939 | 0.00139622 | ||||||||
\(716\) | 9797.04 | 0.511358 | ||||||||
\(717\) | −9826.67 | −0.511832 | ||||||||
\(718\) | 14696.3 | 0.763872 | ||||||||
\(719\) | −17081.4 | −0.885994 | −0.442997 | − | 0.896523i | \(-0.646085\pi\) | ||||
−0.442997 | + | 0.896523i | \(0.646085\pi\) | |||||||
\(720\) | −131.016 | −0.00678147 | ||||||||
\(721\) | −2631.13 | −0.135906 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5004.82 | 0.257443 | ||||||||
\(724\) | −8010.67 | −0.411207 | ||||||||
\(725\) | −3868.08 | −0.198147 | ||||||||
\(726\) | −7963.32 | −0.407089 | ||||||||
\(727\) | −8523.48 | −0.434826 | −0.217413 | − | 0.976080i | \(-0.569762\pi\) | ||||
−0.217413 | + | 0.976080i | \(0.569762\pi\) | |||||||
\(728\) | −1970.93 | −0.100340 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −209.744 | −0.0106342 | ||||||||
\(731\) | −6949.90 | −0.351644 | ||||||||
\(732\) | 6318.10 | 0.319022 | ||||||||
\(733\) | 19655.2 | 0.990425 | 0.495212 | − | 0.868772i | \(-0.335090\pi\) | ||||
0.495212 | + | 0.868772i | \(0.335090\pi\) | |||||||
\(734\) | −21658.8 | −1.08916 | ||||||||
\(735\) | 208.680 | 0.0104725 | ||||||||
\(736\) | −1436.43 | −0.0719397 | ||||||||
\(737\) | 409.709 | 0.0204774 | ||||||||
\(738\) | 1469.65 | 0.0733045 | ||||||||
\(739\) | −844.721 | −0.0420481 | −0.0210241 | − | 0.999779i | \(-0.506693\pi\) | ||||
−0.0210241 | + | 0.999779i | \(0.506693\pi\) | |||||||
\(740\) | 920.331 | 0.0457190 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 385.714 | 0.0190836 | ||||||||
\(743\) | −23692.3 | −1.16983 | −0.584916 | − | 0.811094i | \(-0.698873\pi\) | ||||
−0.584916 | + | 0.811094i | \(0.698873\pi\) | |||||||
\(744\) | −7188.08 | −0.354204 | ||||||||
\(745\) | 160.992 | 0.00791719 | ||||||||
\(746\) | 21229.2 | 1.04190 | ||||||||
\(747\) | 1800.21 | 0.0881743 | ||||||||
\(748\) | −248.969 | −0.0121701 | ||||||||
\(749\) | 18310.9 | 0.893280 | ||||||||
\(750\) | 1360.23 | 0.0662246 | ||||||||
\(751\) | −8581.33 | −0.416960 | −0.208480 | − | 0.978027i | \(-0.566852\pi\) | ||||
−0.208480 | + | 0.978027i | \(0.566852\pi\) | |||||||
\(752\) | 3003.88 | 0.145665 | ||||||||
\(753\) | −6133.16 | −0.296819 | ||||||||
\(754\) | 940.145 | 0.0454086 | ||||||||
\(755\) | 1036.06 | 0.0499420 | ||||||||
\(756\) | −1763.23 | −0.0848256 | ||||||||
\(757\) | −19326.7 | −0.927926 | −0.463963 | − | 0.885855i | \(-0.653573\pi\) | ||||
−0.463963 | + | 0.885855i | \(0.653573\pi\) | |||||||
\(758\) | 7076.34 | 0.339082 | ||||||||
\(759\) | 261.827 | 0.0125213 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26601.6 | −1.26716 | −0.633580 | − | 0.773677i | \(-0.718415\pi\) | ||||
−0.633580 | + | 0.773677i | \(0.718415\pi\) | |||||||
\(762\) | −5192.75 | −0.246868 | ||||||||
\(763\) | −16051.4 | −0.761598 | ||||||||
\(764\) | 16407.9 | 0.776984 | ||||||||
\(765\) | −262.139 | −0.0123891 | ||||||||
\(766\) | 26276.1 | 1.23942 | ||||||||
\(767\) | 3682.70 | 0.173370 | ||||||||
\(768\) | 768.000 | 0.0360844 | ||||||||
\(769\) | −24235.8 | −1.13650 | −0.568248 | − | 0.822857i | \(-0.692379\pi\) | ||||
−0.568248 | + | 0.822857i | \(0.692379\pi\) | |||||||
\(770\) | −57.7608 | −0.00270332 | ||||||||
\(771\) | 15543.9 | 0.726072 | ||||||||
\(772\) | 7026.20 | 0.327563 | ||||||||
\(773\) | −11054.8 | −0.514377 | −0.257188 | − | 0.966361i | \(-0.582796\pi\) | ||||
−0.257188 | + | 0.966361i | \(0.582796\pi\) | |||||||
\(774\) | −3907.71 | −0.181473 | ||||||||
\(775\) | 37190.0 | 1.72375 | ||||||||
\(776\) | −8843.20 | −0.409088 | ||||||||
\(777\) | 12386.0 | 0.571873 | ||||||||
\(778\) | 2116.91 | 0.0975514 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −164.754 | −0.00756299 | ||||||||
\(781\) | 978.782 | 0.0448445 | ||||||||
\(782\) | −2874.05 | −0.131427 | ||||||||
\(783\) | 841.075 | 0.0383877 | ||||||||
\(784\) | −1223.26 | −0.0557245 | ||||||||
\(785\) | 1776.16 | 0.0807565 | ||||||||
\(786\) | −14068.8 | −0.638443 | ||||||||
\(787\) | −34632.5 | −1.56863 | −0.784316 | − | 0.620361i | \(-0.786986\pi\) | ||||
−0.784316 | + | 0.620361i | \(0.786986\pi\) | |||||||
\(788\) | 14682.3 | 0.663750 | ||||||||
\(789\) | 21413.8 | 0.966224 | ||||||||
\(790\) | −401.220 | −0.0180693 | ||||||||
\(791\) | 8168.82 | 0.367193 | ||||||||
\(792\) | −139.988 | −0.00628061 | ||||||||
\(793\) | 7945.10 | 0.355787 | ||||||||
\(794\) | −30361.5 | −1.35704 | ||||||||
\(795\) | 32.2427 | 0.00143840 | ||||||||
\(796\) | −10443.0 | −0.465004 | ||||||||
\(797\) | 21904.6 | 0.973526 | 0.486763 | − | 0.873534i | \(-0.338178\pi\) | ||||
0.486763 | + | 0.873534i | \(0.338178\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6010.23 | 0.266116 | ||||||||
\(800\) | −3973.51 | −0.175606 | ||||||||
\(801\) | −1566.82 | −0.0691148 | ||||||||
\(802\) | −2672.40 | −0.117663 | ||||||||
\(803\) | −224.107 | −0.00984879 | ||||||||
\(804\) | −2528.72 | −0.110922 | ||||||||
\(805\) | −666.779 | −0.0291936 | ||||||||
\(806\) | −9039.12 | −0.395024 | ||||||||
\(807\) | 19186.6 | 0.836925 | ||||||||
\(808\) | −7170.97 | −0.312220 | ||||||||
\(809\) | 33327.8 | 1.44838 | 0.724192 | − | 0.689598i | \(-0.242213\pi\) | ||||
0.724192 | + | 0.689598i | \(0.242213\pi\) | |||||||
\(810\) | −147.392 | −0.00639363 | ||||||||
\(811\) | 1389.76 | 0.0601738 | 0.0300869 | − | 0.999547i | \(-0.490422\pi\) | ||||
0.0300869 | + | 0.999547i | \(0.490422\pi\) | |||||||
\(812\) | −2034.31 | −0.0879191 | ||||||||
\(813\) | −19436.6 | −0.838464 | ||||||||
\(814\) | 983.356 | 0.0423423 | ||||||||
\(815\) | −351.171 | −0.0150932 | ||||||||
\(816\) | 1536.63 | 0.0659226 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −3952.06 | −0.168925 | ||||||||
\(819\) | −2217.29 | −0.0946013 | ||||||||
\(820\) | −297.141 | −0.0126544 | ||||||||
\(821\) | −11572.6 | −0.491943 | −0.245972 | − | 0.969277i | \(-0.579107\pi\) | ||||
−0.245972 | + | 0.969277i | \(0.579107\pi\) | |||||||
\(822\) | 12427.7 | 0.527329 | ||||||||
\(823\) | 26073.3 | 1.10432 | 0.552162 | − | 0.833737i | \(-0.313803\pi\) | ||||
0.552162 | + | 0.833737i | \(0.313803\pi\) | |||||||
\(824\) | 1289.28 | 0.0545074 | ||||||||
\(825\) | 724.274 | 0.0305648 | ||||||||
\(826\) | −7968.72 | −0.335675 | ||||||||
\(827\) | 44795.6 | 1.88355 | 0.941775 | − | 0.336245i | \(-0.109157\pi\) | ||||
0.941775 | + | 0.336245i | \(0.109157\pi\) | |||||||
\(828\) | −1615.99 | −0.0678254 | ||||||||
\(829\) | 12346.2 | 0.517250 | 0.258625 | − | 0.965978i | \(-0.416731\pi\) | ||||
0.258625 | + | 0.965978i | \(0.416731\pi\) | |||||||
\(830\) | −363.974 | −0.0152214 | ||||||||
\(831\) | 10505.8 | 0.438559 | ||||||||
\(832\) | 965.771 | 0.0402429 | ||||||||
\(833\) | −2447.53 | −0.101803 | ||||||||
\(834\) | −8805.26 | −0.365589 | ||||||||
\(835\) | 2917.02 | 0.120895 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8086.59 | −0.333947 | ||||||||
\(838\) | 6485.79 | 0.267360 | ||||||||
\(839\) | −7050.38 | −0.290115 | −0.145057 | − | 0.989423i | \(-0.546337\pi\) | ||||
−0.145057 | + | 0.989423i | \(0.546337\pi\) | |||||||
\(840\) | 356.498 | 0.0146433 | ||||||||
\(841\) | −23418.6 | −0.960212 | ||||||||
\(842\) | 23918.8 | 0.978976 | ||||||||
\(843\) | 5168.24 | 0.211155 | ||||||||
\(844\) | −13893.4 | −0.566624 | ||||||||
\(845\) | 1791.72 | 0.0729431 | ||||||||
\(846\) | 3379.37 | 0.137335 | ||||||||
\(847\) | 21668.5 | 0.879030 | ||||||||
\(848\) | −189.003 | −0.00765378 | ||||||||
\(849\) | −2717.84 | −0.109866 | ||||||||
\(850\) | −7950.29 | −0.320815 | ||||||||
\(851\) | 11351.7 | 0.457262 | ||||||||
\(852\) | −6041.02 | −0.242913 | ||||||||
\(853\) | 6590.63 | 0.264547 | 0.132274 | − | 0.991213i | \(-0.457772\pi\) | ||||
0.132274 | + | 0.991213i | \(0.457772\pi\) | |||||||
\(854\) | −17191.8 | −0.688866 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8972.52 | −0.358264 | ||||||||
\(857\) | 41470.4 | 1.65298 | 0.826489 | − | 0.562954i | \(-0.190335\pi\) | ||||
0.826489 | + | 0.562954i | \(0.190335\pi\) | |||||||
\(858\) | −176.036 | −0.00700441 | ||||||||
\(859\) | 33928.2 | 1.34763 | 0.673816 | − | 0.738899i | \(-0.264654\pi\) | ||||
0.673816 | + | 0.738899i | \(0.264654\pi\) | |||||||
\(860\) | 790.079 | 0.0313273 | ||||||||
\(861\) | −3998.99 | −0.158287 | ||||||||
\(862\) | −14452.3 | −0.571051 | ||||||||
\(863\) | −6042.42 | −0.238339 | −0.119169 | − | 0.992874i | \(-0.538023\pi\) | ||||
−0.119169 | + | 0.992874i | \(0.538023\pi\) | |||||||
\(864\) | 864.000 | 0.0340207 | ||||||||
\(865\) | 2906.65 | 0.114253 | ||||||||
\(866\) | 19806.0 | 0.777177 | ||||||||
\(867\) | −11664.5 | −0.456916 | ||||||||
\(868\) | 19559.1 | 0.764836 | ||||||||
\(869\) | −428.695 | −0.0167347 | ||||||||
\(870\) | −170.052 | −0.00662680 | ||||||||
\(871\) | −3179.90 | −0.123705 | ||||||||
\(872\) | 7865.32 | 0.305451 | ||||||||
\(873\) | −9948.60 | −0.385692 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3701.23 | −0.142999 | ||||||||
\(876\) | 1383.19 | 0.0533488 | ||||||||
\(877\) | −23546.2 | −0.906611 | −0.453306 | − | 0.891355i | \(-0.649755\pi\) | ||||
−0.453306 | + | 0.891355i | \(0.649755\pi\) | |||||||
\(878\) | 14155.9 | 0.544123 | ||||||||
\(879\) | 19711.7 | 0.756381 | ||||||||
\(880\) | 28.3033 | 0.00108421 | ||||||||
\(881\) | −39700.3 | −1.51820 | −0.759101 | − | 0.650973i | \(-0.774361\pi\) | ||||
−0.759101 | + | 0.650973i | \(0.774361\pi\) | |||||||
\(882\) | −1376.17 | −0.0525375 | ||||||||
\(883\) | −41792.3 | −1.59278 | −0.796389 | − | 0.604785i | \(-0.793259\pi\) | ||||
−0.796389 | + | 0.604785i | \(0.793259\pi\) | |||||||
\(884\) | 1932.34 | 0.0735198 | ||||||||
\(885\) | −666.122 | −0.0253011 | ||||||||
\(886\) | −15461.2 | −0.586262 | ||||||||
\(887\) | −3207.98 | −0.121435 | −0.0607177 | − | 0.998155i | \(-0.519339\pi\) | ||||
−0.0607177 | + | 0.998155i | \(0.519339\pi\) | |||||||
\(888\) | −6069.25 | −0.229359 | ||||||||
\(889\) | 14129.7 | 0.533065 | ||||||||
\(890\) | 316.787 | 0.0119312 | ||||||||
\(891\) | −157.486 | −0.00592141 | ||||||||
\(892\) | 10122.0 | 0.379942 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −1061.69 | −0.0397183 | ||||||||
\(895\) | −2228.41 | −0.0832263 | ||||||||
\(896\) | −2089.76 | −0.0779173 | ||||||||
\(897\) | −2032.13 | −0.0756419 | ||||||||
\(898\) | 4706.81 | 0.174909 | ||||||||
\(899\) | −9329.81 | −0.346125 | ||||||||
\(900\) | −4470.20 | −0.165563 | ||||||||
\(901\) | −378.162 | −0.0139827 | ||||||||
\(902\) | −317.490 | −0.0117198 | ||||||||
\(903\) | 10633.0 | 0.391856 | ||||||||
\(904\) | −4002.80 | −0.147269 | ||||||||
\(905\) | 1822.09 | 0.0669262 | ||||||||
\(906\) | −6832.46 | −0.250544 | ||||||||
\(907\) | 51184.8 | 1.87383 | 0.936915 | − | 0.349558i | \(-0.113668\pi\) | ||||
0.936915 | + | 0.349558i | \(0.113668\pi\) | |||||||
\(908\) | −26938.4 | −0.984560 | ||||||||
\(909\) | −8067.34 | −0.294364 | ||||||||
\(910\) | 448.302 | 0.0163308 | ||||||||
\(911\) | 15160.8 | 0.551372 | 0.275686 | − | 0.961248i | \(-0.411095\pi\) | ||||
0.275686 | + | 0.961248i | \(0.411095\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −388.900 | −0.0140971 | ||||||||
\(914\) | 16841.9 | 0.609497 | ||||||||
\(915\) | −1437.10 | −0.0519225 | ||||||||
\(916\) | −1350.88 | −0.0487273 | ||||||||
\(917\) | 38281.7 | 1.37860 | ||||||||
\(918\) | 1728.71 | 0.0621524 | ||||||||
\(919\) | 33318.2 | 1.19594 | 0.597969 | − | 0.801519i | \(-0.295974\pi\) | ||||
0.597969 | + | 0.801519i | \(0.295974\pi\) | |||||||
\(920\) | 326.728 | 0.0117086 | ||||||||
\(921\) | 1699.74 | 0.0608127 | ||||||||
\(922\) | −1339.24 | −0.0478369 | ||||||||
\(923\) | −7596.67 | −0.270907 | ||||||||
\(924\) | 380.912 | 0.0135618 | ||||||||
\(925\) | 31401.3 | 1.11618 | ||||||||
\(926\) | 11141.8 | 0.395401 | ||||||||
\(927\) | 1450.44 | 0.0513901 | ||||||||
\(928\) | 996.830 | 0.0352613 | ||||||||
\(929\) | 14464.8 | 0.510843 | 0.255421 | − | 0.966830i | \(-0.417786\pi\) | ||||
0.255421 | + | 0.966830i | \(0.417786\pi\) | |||||||
\(930\) | 1634.98 | 0.0576486 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −25245.0 | −0.887262 | ||||||||
\(933\) | 10522.7 | 0.369235 | ||||||||
\(934\) | −21739.6 | −0.761606 | ||||||||
\(935\) | 56.6299 | 0.00198074 | ||||||||
\(936\) | 1086.49 | 0.0379414 | ||||||||
\(937\) | 16046.8 | 0.559475 | 0.279737 | − | 0.960077i | \(-0.409753\pi\) | ||||
0.279737 | + | 0.960077i | \(0.409753\pi\) | |||||||
\(938\) | 6880.74 | 0.239514 | ||||||||
\(939\) | −965.304 | −0.0335479 | ||||||||
\(940\) | −683.256 | −0.0237078 | ||||||||
\(941\) | 19129.4 | 0.662700 | 0.331350 | − | 0.943508i | \(-0.392496\pi\) | ||||
0.331350 | + | 0.943508i | \(0.392496\pi\) | |||||||
\(942\) | −11713.1 | −0.405132 | ||||||||
\(943\) | −3665.04 | −0.126564 | ||||||||
\(944\) | 3904.74 | 0.134628 | ||||||||
\(945\) | 401.061 | 0.0138058 | ||||||||
\(946\) | 844.184 | 0.0290135 | ||||||||
\(947\) | −41617.7 | −1.42808 | −0.714041 | − | 0.700104i | \(-0.753137\pi\) | ||||
−0.714041 | + | 0.700104i | \(0.753137\pi\) | |||||||
\(948\) | 2645.90 | 0.0906485 | ||||||||
\(949\) | 1739.38 | 0.0594969 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11391.1 | −0.388413 | ||||||||
\(952\) | −4181.24 | −0.142347 | ||||||||
\(953\) | −36269.8 | −1.23284 | −0.616419 | − | 0.787419i | \(-0.711417\pi\) | ||||
−0.616419 | + | 0.787419i | \(0.711417\pi\) | |||||||
\(954\) | −212.629 | −0.00721605 | ||||||||
\(955\) | −3732.09 | −0.126458 | ||||||||
\(956\) | −13102.2 | −0.443260 | ||||||||
\(957\) | −181.698 | −0.00613736 | ||||||||
\(958\) | −4870.66 | −0.164263 | ||||||||
\(959\) | −33816.1 | −1.13867 | ||||||||
\(960\) | −174.687 | −0.00587293 | ||||||||
\(961\) | 59911.3 | 2.01105 | ||||||||
\(962\) | −7632.17 | −0.255791 | ||||||||
\(963\) | −10094.1 | −0.337775 | ||||||||
\(964\) | 6673.09 | 0.222952 | ||||||||
\(965\) | −1598.16 | −0.0533126 | ||||||||
\(966\) | 4397.17 | 0.146456 | ||||||||
\(967\) | 28249.4 | 0.939442 | 0.469721 | − | 0.882815i | \(-0.344354\pi\) | ||||
0.469721 | + | 0.882815i | \(0.344354\pi\) | |||||||
\(968\) | −10617.8 | −0.352549 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2011.45 | 0.0665813 | ||||||||
\(971\) | −11234.1 | −0.371285 | −0.185643 | − | 0.982617i | \(-0.559437\pi\) | ||||
−0.185643 | + | 0.982617i | \(0.559437\pi\) | |||||||
\(972\) | 972.000 | 0.0320750 | ||||||||
\(973\) | 23959.5 | 0.789420 | ||||||||
\(974\) | 21370.3 | 0.703029 | ||||||||
\(975\) | −5621.34 | −0.184643 | ||||||||
\(976\) | 8424.14 | 0.276281 | ||||||||
\(977\) | −10338.6 | −0.338547 | −0.169273 | − | 0.985569i | \(-0.554142\pi\) | ||||
−0.169273 | + | 0.985569i | \(0.554142\pi\) | |||||||
\(978\) | 2315.84 | 0.0757184 | ||||||||
\(979\) | 338.481 | 0.0110499 | ||||||||
\(980\) | 278.240 | 0.00906945 | ||||||||
\(981\) | 8848.49 | 0.287982 | ||||||||
\(982\) | −18137.8 | −0.589410 | ||||||||
\(983\) | −35054.0 | −1.13739 | −0.568693 | − | 0.822550i | \(-0.692551\pi\) | ||||
−0.568693 | + | 0.822550i | \(0.692551\pi\) | |||||||
\(984\) | 1959.54 | 0.0634836 | ||||||||
\(985\) | −3339.60 | −0.108029 | ||||||||
\(986\) | 1994.48 | 0.0644190 | ||||||||
\(987\) | −9195.39 | −0.296548 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9745.09 | 0.313322 | ||||||||
\(990\) | 31.8412 | 0.00102220 | ||||||||
\(991\) | −25256.8 | −0.809595 | −0.404798 | − | 0.914406i | \(-0.632658\pi\) | ||||
−0.404798 | + | 0.914406i | \(0.632658\pi\) | |||||||
\(992\) | −9584.11 | −0.306750 | ||||||||
\(993\) | 28765.3 | 0.919275 | ||||||||
\(994\) | 16437.9 | 0.524524 | ||||||||
\(995\) | 2375.34 | 0.0756818 | ||||||||
\(996\) | 2400.28 | 0.0763612 | ||||||||
\(997\) | −39035.2 | −1.23998 | −0.619989 | − | 0.784611i | \(-0.712863\pi\) | ||||
−0.619989 | + | 0.784611i | \(0.712863\pi\) | |||||||
\(998\) | −18171.1 | −0.576348 | ||||||||
\(999\) | −6827.91 | −0.216242 |
(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 | 2166.4.a.p.1.2 | yes | 2 | |
19.18 | odd | 2 | 2166.4.a.j.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2166.4.a.j.1.2 | ✓ | 2 | 19.18 | odd | 2 | ||
2166.4.a.p.1.2 | yes | 2 | 1.1 | even | 1 | trivial |