Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1849,4,Mod(1,1849)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1849, 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("1849.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1849 = 43^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1849.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(109.094531601\) |
Analytic rank: | \(1\) |
Dimension: | \(30\) |
Twist minimal: | no (minimal twist has level 43) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.24 | ||
Character | \(\chi\) | \(=\) | 1849.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.68353 | 1.30233 | 0.651163 | − | 0.758938i | \(-0.274282\pi\) | ||||
0.651163 | + | 0.758938i | \(0.274282\pi\) | |||||||
\(3\) | 8.25521 | 1.58872 | 0.794358 | − | 0.607450i | \(-0.207807\pi\) | ||||
0.794358 | + | 0.607450i | \(0.207807\pi\) | |||||||
\(4\) | 5.56841 | 0.696051 | ||||||||
\(5\) | 12.2925 | 1.09948 | 0.549738 | − | 0.835337i | \(-0.314728\pi\) | ||||
0.549738 | + | 0.835337i | \(0.314728\pi\) | |||||||
\(6\) | 30.4083 | 2.06903 | ||||||||
\(7\) | −28.5576 | −1.54196 | −0.770981 | − | 0.636858i | \(-0.780234\pi\) | ||||
−0.770981 | + | 0.636858i | \(0.780234\pi\) | |||||||
\(8\) | −8.95684 | −0.395840 | ||||||||
\(9\) | 41.1485 | 1.52402 | ||||||||
\(10\) | 45.2798 | 1.43187 | ||||||||
\(11\) | −55.8522 | −1.53092 | −0.765458 | − | 0.643486i | \(-0.777488\pi\) | ||||
−0.765458 | + | 0.643486i | \(0.777488\pi\) | |||||||
\(12\) | 45.9684 | 1.10583 | ||||||||
\(13\) | −70.9474 | −1.51364 | −0.756818 | − | 0.653626i | \(-0.773247\pi\) | ||||
−0.756818 | + | 0.653626i | \(0.773247\pi\) | |||||||
\(14\) | −105.193 | −2.00814 | ||||||||
\(15\) | 101.477 | 1.74675 | ||||||||
\(16\) | −77.5401 | −1.21156 | ||||||||
\(17\) | 20.9256 | 0.298541 | 0.149271 | − | 0.988796i | \(-0.452307\pi\) | ||||
0.149271 | + | 0.988796i | \(0.452307\pi\) | |||||||
\(18\) | 151.572 | 1.98477 | ||||||||
\(19\) | −25.4332 | −0.307093 | −0.153547 | − | 0.988141i | \(-0.549070\pi\) | ||||
−0.153547 | + | 0.988141i | \(0.549070\pi\) | |||||||
\(20\) | 68.4497 | 0.765291 | ||||||||
\(21\) | −235.749 | −2.44974 | ||||||||
\(22\) | −205.733 | −1.99375 | ||||||||
\(23\) | 103.780 | 0.940856 | 0.470428 | − | 0.882438i | \(-0.344099\pi\) | ||||
0.470428 | + | 0.882438i | \(0.344099\pi\) | |||||||
\(24\) | −73.9407 | −0.628878 | ||||||||
\(25\) | 26.1057 | 0.208846 | ||||||||
\(26\) | −261.337 | −1.97125 | ||||||||
\(27\) | 116.799 | 0.832520 | ||||||||
\(28\) | −159.020 | −1.07328 | ||||||||
\(29\) | −94.0840 | −0.602447 | −0.301224 | − | 0.953554i | \(-0.597395\pi\) | ||||
−0.301224 | + | 0.953554i | \(0.597395\pi\) | |||||||
\(30\) | 373.795 | 2.27484 | ||||||||
\(31\) | 16.0997 | 0.0932771 | 0.0466386 | − | 0.998912i | \(-0.485149\pi\) | ||||
0.0466386 | + | 0.998912i | \(0.485149\pi\) | |||||||
\(32\) | −213.967 | −1.18201 | ||||||||
\(33\) | −461.072 | −2.43219 | ||||||||
\(34\) | 77.0801 | 0.388798 | ||||||||
\(35\) | −351.044 | −1.69535 | ||||||||
\(36\) | 229.132 | 1.06080 | ||||||||
\(37\) | 23.8504 | 0.105972 | 0.0529862 | − | 0.998595i | \(-0.483126\pi\) | ||||
0.0529862 | + | 0.998595i | \(0.483126\pi\) | |||||||
\(38\) | −93.6840 | −0.399935 | ||||||||
\(39\) | −585.686 | −2.40474 | ||||||||
\(40\) | −110.102 | −0.435217 | ||||||||
\(41\) | −75.5892 | −0.287928 | −0.143964 | − | 0.989583i | \(-0.545985\pi\) | ||||
−0.143964 | + | 0.989583i | \(0.545985\pi\) | |||||||
\(42\) | −868.388 | −3.19036 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | −311.008 | −1.06560 | ||||||||
\(45\) | 505.819 | 1.67562 | ||||||||
\(46\) | 382.278 | 1.22530 | ||||||||
\(47\) | −5.56130 | −0.0172596 | −0.00862978 | − | 0.999963i | \(-0.502747\pi\) | ||||
−0.00862978 | + | 0.999963i | \(0.502747\pi\) | |||||||
\(48\) | −640.110 | −1.92483 | ||||||||
\(49\) | 472.534 | 1.37765 | ||||||||
\(50\) | 96.1613 | 0.271985 | ||||||||
\(51\) | 172.745 | 0.474297 | ||||||||
\(52\) | −395.064 | −1.05357 | ||||||||
\(53\) | 622.211 | 1.61259 | 0.806294 | − | 0.591515i | \(-0.201470\pi\) | ||||
0.806294 | + | 0.591515i | \(0.201470\pi\) | |||||||
\(54\) | 430.234 | 1.08421 | ||||||||
\(55\) | −686.564 | −1.68320 | ||||||||
\(56\) | 255.786 | 0.610371 | ||||||||
\(57\) | −209.956 | −0.487884 | ||||||||
\(58\) | −346.562 | −0.784582 | ||||||||
\(59\) | 189.542 | 0.418242 | 0.209121 | − | 0.977890i | \(-0.432940\pi\) | ||||
0.209121 | + | 0.977890i | \(0.432940\pi\) | |||||||
\(60\) | 565.067 | 1.21583 | ||||||||
\(61\) | 371.320 | 0.779388 | 0.389694 | − | 0.920944i | \(-0.372581\pi\) | ||||
0.389694 | + | 0.920944i | \(0.372581\pi\) | |||||||
\(62\) | 59.3037 | 0.121477 | ||||||||
\(63\) | −1175.10 | −2.34998 | ||||||||
\(64\) | −167.832 | −0.327798 | ||||||||
\(65\) | −872.121 | −1.66420 | ||||||||
\(66\) | −1698.37 | −3.16751 | ||||||||
\(67\) | −620.843 | −1.13206 | −0.566030 | − | 0.824384i | \(-0.691521\pi\) | ||||
−0.566030 | + | 0.824384i | \(0.691521\pi\) | |||||||
\(68\) | 116.522 | 0.207800 | ||||||||
\(69\) | 856.729 | 1.49475 | ||||||||
\(70\) | −1293.08 | −2.20790 | ||||||||
\(71\) | −644.449 | −1.07721 | −0.538606 | − | 0.842558i | \(-0.681049\pi\) | ||||
−0.538606 | + | 0.842558i | \(0.681049\pi\) | |||||||
\(72\) | −368.561 | −0.603269 | ||||||||
\(73\) | −488.895 | −0.783847 | −0.391924 | − | 0.919998i | \(-0.628190\pi\) | ||||
−0.391924 | + | 0.919998i | \(0.628190\pi\) | |||||||
\(74\) | 87.8536 | 0.138010 | ||||||||
\(75\) | 215.508 | 0.331797 | ||||||||
\(76\) | −141.622 | −0.213753 | ||||||||
\(77\) | 1595.00 | 2.36062 | ||||||||
\(78\) | −2157.39 | −3.13175 | ||||||||
\(79\) | −1110.49 | −1.58151 | −0.790755 | − | 0.612132i | \(-0.790312\pi\) | ||||
−0.790755 | + | 0.612132i | \(0.790312\pi\) | |||||||
\(80\) | −953.162 | −1.33208 | ||||||||
\(81\) | −146.808 | −0.201382 | ||||||||
\(82\) | −278.435 | −0.374976 | ||||||||
\(83\) | −351.896 | −0.465368 | −0.232684 | − | 0.972552i | \(-0.574751\pi\) | ||||
−0.232684 | + | 0.972552i | \(0.574751\pi\) | |||||||
\(84\) | −1312.74 | −1.70515 | ||||||||
\(85\) | 257.228 | 0.328239 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −776.684 | −0.957118 | ||||||||
\(88\) | 500.260 | 0.605999 | ||||||||
\(89\) | 429.648 | 0.511715 | 0.255857 | − | 0.966715i | \(-0.417642\pi\) | ||||
0.255857 | + | 0.966715i | \(0.417642\pi\) | |||||||
\(90\) | 1863.20 | 2.18221 | ||||||||
\(91\) | 2026.08 | 2.33397 | ||||||||
\(92\) | 577.891 | 0.654884 | ||||||||
\(93\) | 132.906 | 0.148191 | ||||||||
\(94\) | −20.4852 | −0.0224776 | ||||||||
\(95\) | −312.638 | −0.337642 | ||||||||
\(96\) | −1766.34 | −1.87788 | ||||||||
\(97\) | 1183.38 | 1.23870 | 0.619352 | − | 0.785114i | \(-0.287396\pi\) | ||||
0.619352 | + | 0.785114i | \(0.287396\pi\) | |||||||
\(98\) | 1740.59 | 1.79415 | ||||||||
\(99\) | −2298.24 | −2.33315 | ||||||||
\(100\) | 145.367 | 0.145367 | ||||||||
\(101\) | −1990.58 | −1.96109 | −0.980547 | − | 0.196283i | \(-0.937113\pi\) | ||||
−0.980547 | + | 0.196283i | \(0.937113\pi\) | |||||||
\(102\) | 636.313 | 0.617690 | ||||||||
\(103\) | −412.891 | −0.394984 | −0.197492 | − | 0.980305i | \(-0.563280\pi\) | ||||
−0.197492 | + | 0.980305i | \(0.563280\pi\) | |||||||
\(104\) | 635.465 | 0.599158 | ||||||||
\(105\) | −2897.94 | −2.69343 | ||||||||
\(106\) | 2291.93 | 2.10011 | ||||||||
\(107\) | 47.8596 | 0.0432408 | 0.0216204 | − | 0.999766i | \(-0.493117\pi\) | ||||
0.0216204 | + | 0.999766i | \(0.493117\pi\) | |||||||
\(108\) | 650.386 | 0.579476 | ||||||||
\(109\) | 684.904 | 0.601852 | 0.300926 | − | 0.953647i | \(-0.402704\pi\) | ||||
0.300926 | + | 0.953647i | \(0.402704\pi\) | |||||||
\(110\) | −2528.98 | −2.19208 | ||||||||
\(111\) | 196.890 | 0.168360 | ||||||||
\(112\) | 2214.36 | 1.86819 | ||||||||
\(113\) | 503.311 | 0.419005 | 0.209502 | − | 0.977808i | \(-0.432816\pi\) | ||||
0.209502 | + | 0.977808i | \(0.432816\pi\) | |||||||
\(114\) | −773.381 | −0.635384 | ||||||||
\(115\) | 1275.72 | 1.03445 | ||||||||
\(116\) | −523.898 | −0.419334 | ||||||||
\(117\) | −2919.38 | −2.30681 | ||||||||
\(118\) | 698.185 | 0.544688 | ||||||||
\(119\) | −597.584 | −0.460340 | ||||||||
\(120\) | −908.916 | −0.691436 | ||||||||
\(121\) | 1788.47 | 1.34371 | ||||||||
\(122\) | 1367.77 | 1.01502 | ||||||||
\(123\) | −624.005 | −0.457436 | ||||||||
\(124\) | 89.6497 | 0.0649256 | ||||||||
\(125\) | −1215.66 | −0.869854 | ||||||||
\(126\) | −4328.53 | −3.06044 | ||||||||
\(127\) | −1896.38 | −1.32501 | −0.662507 | − | 0.749056i | \(-0.730507\pi\) | ||||
−0.662507 | + | 0.749056i | \(0.730507\pi\) | |||||||
\(128\) | 1093.52 | 0.755111 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3212.49 | −2.16734 | ||||||||
\(131\) | 57.7668 | 0.0385275 | 0.0192638 | − | 0.999814i | \(-0.493868\pi\) | ||||
0.0192638 | + | 0.999814i | \(0.493868\pi\) | |||||||
\(132\) | −2567.44 | −1.69293 | ||||||||
\(133\) | 726.310 | 0.473527 | ||||||||
\(134\) | −2286.90 | −1.47431 | ||||||||
\(135\) | 1435.76 | 0.915335 | ||||||||
\(136\) | −187.427 | −0.118175 | ||||||||
\(137\) | 2080.41 | 1.29738 | 0.648692 | − | 0.761051i | \(-0.275316\pi\) | ||||
0.648692 | + | 0.761051i | \(0.275316\pi\) | |||||||
\(138\) | 3155.79 | 1.94666 | ||||||||
\(139\) | −1936.42 | −1.18162 | −0.590809 | − | 0.806811i | \(-0.701191\pi\) | ||||
−0.590809 | + | 0.806811i | \(0.701191\pi\) | |||||||
\(140\) | −1954.76 | −1.18005 | ||||||||
\(141\) | −45.9097 | −0.0274206 | ||||||||
\(142\) | −2373.85 | −1.40288 | ||||||||
\(143\) | 3962.57 | 2.31725 | ||||||||
\(144\) | −3190.66 | −1.84645 | ||||||||
\(145\) | −1156.53 | −0.662376 | ||||||||
\(146\) | −1800.86 | −1.02082 | ||||||||
\(147\) | 3900.87 | 2.18869 | ||||||||
\(148\) | 132.809 | 0.0737622 | ||||||||
\(149\) | −488.602 | −0.268643 | −0.134322 | − | 0.990938i | \(-0.542885\pi\) | ||||
−0.134322 | + | 0.990938i | \(0.542885\pi\) | |||||||
\(150\) | 793.832 | 0.432107 | ||||||||
\(151\) | 3294.70 | 1.77562 | 0.887810 | − | 0.460211i | \(-0.152226\pi\) | ||||
0.887810 | + | 0.460211i | \(0.152226\pi\) | |||||||
\(152\) | 227.801 | 0.121560 | ||||||||
\(153\) | 861.058 | 0.454983 | ||||||||
\(154\) | 5875.24 | 3.07429 | ||||||||
\(155\) | 197.906 | 0.102556 | ||||||||
\(156\) | −3261.34 | −1.67382 | ||||||||
\(157\) | 561.132 | 0.285243 | 0.142622 | − | 0.989777i | \(-0.454447\pi\) | ||||
0.142622 | + | 0.989777i | \(0.454447\pi\) | |||||||
\(158\) | −4090.51 | −2.05964 | ||||||||
\(159\) | 5136.48 | 2.56195 | ||||||||
\(160\) | −2630.19 | −1.29959 | ||||||||
\(161\) | −2963.71 | −1.45077 | ||||||||
\(162\) | −540.771 | −0.262265 | ||||||||
\(163\) | −647.402 | −0.311095 | −0.155547 | − | 0.987828i | \(-0.549714\pi\) | ||||
−0.155547 | + | 0.987828i | \(0.549714\pi\) | |||||||
\(164\) | −420.912 | −0.200413 | ||||||||
\(165\) | −5667.73 | −2.67414 | ||||||||
\(166\) | −1296.22 | −0.606061 | ||||||||
\(167\) | 2604.15 | 1.20668 | 0.603339 | − | 0.797485i | \(-0.293837\pi\) | ||||
0.603339 | + | 0.797485i | \(0.293837\pi\) | |||||||
\(168\) | 2111.56 | 0.969707 | ||||||||
\(169\) | 2836.53 | 1.29109 | ||||||||
\(170\) | 947.508 | 0.427474 | ||||||||
\(171\) | −1046.54 | −0.468017 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1969.05 | 0.865344 | 0.432672 | − | 0.901552i | \(-0.357571\pi\) | ||||
0.432672 | + | 0.901552i | \(0.357571\pi\) | |||||||
\(174\) | −2860.94 | −1.24648 | ||||||||
\(175\) | −745.516 | −0.322033 | ||||||||
\(176\) | 4330.79 | 1.85480 | ||||||||
\(177\) | 1564.71 | 0.664469 | ||||||||
\(178\) | 1582.62 | 0.666419 | ||||||||
\(179\) | 1327.24 | 0.554203 | 0.277102 | − | 0.960841i | \(-0.410626\pi\) | ||||
0.277102 | + | 0.960841i | \(0.410626\pi\) | |||||||
\(180\) | 2816.61 | 1.16632 | ||||||||
\(181\) | −2504.61 | −1.02854 | −0.514272 | − | 0.857627i | \(-0.671938\pi\) | ||||
−0.514272 | + | 0.857627i | \(0.671938\pi\) | |||||||
\(182\) | 7463.14 | 3.03959 | ||||||||
\(183\) | 3065.33 | 1.23823 | ||||||||
\(184\) | −929.544 | −0.372429 | ||||||||
\(185\) | 293.181 | 0.116514 | ||||||||
\(186\) | 489.565 | 0.192993 | ||||||||
\(187\) | −1168.74 | −0.457042 | ||||||||
\(188\) | −30.9676 | −0.0120135 | ||||||||
\(189\) | −3335.50 | −1.28371 | ||||||||
\(190\) | −1151.61 | −0.439719 | ||||||||
\(191\) | −1610.67 | −0.610179 | −0.305090 | − | 0.952324i | \(-0.598686\pi\) | ||||
−0.305090 | + | 0.952324i | \(0.598686\pi\) | |||||||
\(192\) | −1385.49 | −0.520777 | ||||||||
\(193\) | −3546.59 | −1.32274 | −0.661371 | − | 0.750059i | \(-0.730025\pi\) | ||||
−0.661371 | + | 0.750059i | \(0.730025\pi\) | |||||||
\(194\) | 4359.02 | 1.61319 | ||||||||
\(195\) | −7199.54 | −2.64395 | ||||||||
\(196\) | 2631.26 | 0.958914 | ||||||||
\(197\) | 2862.77 | 1.03535 | 0.517674 | − | 0.855578i | \(-0.326798\pi\) | ||||
0.517674 | + | 0.855578i | \(0.326798\pi\) | |||||||
\(198\) | −8465.63 | −3.03852 | ||||||||
\(199\) | −1776.37 | −0.632781 | −0.316390 | − | 0.948629i | \(-0.602471\pi\) | ||||
−0.316390 | + | 0.948629i | \(0.602471\pi\) | |||||||
\(200\) | −233.825 | −0.0826696 | ||||||||
\(201\) | −5125.19 | −1.79852 | ||||||||
\(202\) | −7332.38 | −2.55398 | ||||||||
\(203\) | 2686.81 | 0.928951 | ||||||||
\(204\) | 961.916 | 0.330135 | ||||||||
\(205\) | −929.181 | −0.316570 | ||||||||
\(206\) | −1520.90 | −0.514398 | ||||||||
\(207\) | 4270.41 | 1.43388 | ||||||||
\(208\) | 5501.27 | 1.83387 | ||||||||
\(209\) | 1420.50 | 0.470134 | ||||||||
\(210\) | −10674.7 | −3.50772 | ||||||||
\(211\) | 5127.05 | 1.67280 | 0.836400 | − | 0.548120i | \(-0.184656\pi\) | ||||
0.836400 | + | 0.548120i | \(0.184656\pi\) | |||||||
\(212\) | 3464.72 | 1.12244 | ||||||||
\(213\) | −5320.06 | −1.71138 | ||||||||
\(214\) | 176.292 | 0.0563136 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1046.15 | −0.329545 | ||||||||
\(217\) | −459.768 | −0.143830 | ||||||||
\(218\) | 2522.87 | 0.783807 | ||||||||
\(219\) | −4035.93 | −1.24531 | ||||||||
\(220\) | −3823.07 | −1.17160 | ||||||||
\(221\) | −1484.62 | −0.451883 | ||||||||
\(222\) | 725.250 | 0.219260 | ||||||||
\(223\) | 557.733 | 0.167482 | 0.0837412 | − | 0.996488i | \(-0.473313\pi\) | ||||
0.0837412 | + | 0.996488i | \(0.473313\pi\) | |||||||
\(224\) | 6110.36 | 1.82262 | ||||||||
\(225\) | 1074.21 | 0.318285 | ||||||||
\(226\) | 1853.96 | 0.545680 | ||||||||
\(227\) | −2998.43 | −0.876709 | −0.438355 | − | 0.898802i | \(-0.644439\pi\) | ||||
−0.438355 | + | 0.898802i | \(0.644439\pi\) | |||||||
\(228\) | −1169.12 | −0.339592 | ||||||||
\(229\) | 946.354 | 0.273087 | 0.136543 | − | 0.990634i | \(-0.456401\pi\) | ||||
0.136543 | + | 0.990634i | \(0.456401\pi\) | |||||||
\(230\) | 4699.16 | 1.34719 | ||||||||
\(231\) | 13167.1 | 3.75035 | ||||||||
\(232\) | 842.696 | 0.238473 | ||||||||
\(233\) | 993.000 | 0.279200 | 0.139600 | − | 0.990208i | \(-0.455418\pi\) | ||||
0.139600 | + | 0.990208i | \(0.455418\pi\) | |||||||
\(234\) | −10753.6 | −3.00422 | ||||||||
\(235\) | −68.3624 | −0.0189765 | ||||||||
\(236\) | 1055.45 | 0.291118 | ||||||||
\(237\) | −9167.29 | −2.51257 | ||||||||
\(238\) | −2201.22 | −0.599512 | ||||||||
\(239\) | −2419.96 | −0.654954 | −0.327477 | − | 0.944859i | \(-0.606198\pi\) | ||||
−0.327477 | + | 0.944859i | \(0.606198\pi\) | |||||||
\(240\) | −7868.56 | −2.11630 | ||||||||
\(241\) | −58.0078 | −0.0155046 | −0.00775231 | − | 0.999970i | \(-0.502468\pi\) | ||||
−0.00775231 | + | 0.999970i | \(0.502468\pi\) | |||||||
\(242\) | 6587.89 | 1.74994 | ||||||||
\(243\) | −4365.51 | −1.15246 | ||||||||
\(244\) | 2067.66 | 0.542494 | ||||||||
\(245\) | 5808.62 | 1.51469 | ||||||||
\(246\) | −2298.54 | −0.595731 | ||||||||
\(247\) | 1804.42 | 0.464827 | ||||||||
\(248\) | −144.202 | −0.0369229 | ||||||||
\(249\) | −2904.97 | −0.739338 | ||||||||
\(250\) | −4477.92 | −1.13283 | ||||||||
\(251\) | −1283.94 | −0.322876 | −0.161438 | − | 0.986883i | \(-0.551613\pi\) | ||||
−0.161438 | + | 0.986883i | \(0.551613\pi\) | |||||||
\(252\) | −6543.45 | −1.63571 | ||||||||
\(253\) | −5796.36 | −1.44037 | ||||||||
\(254\) | −6985.38 | −1.72560 | ||||||||
\(255\) | 2123.47 | 0.521478 | ||||||||
\(256\) | 5370.67 | 1.31120 | ||||||||
\(257\) | 2588.04 | 0.628162 | 0.314081 | − | 0.949396i | \(-0.398304\pi\) | ||||
0.314081 | + | 0.949396i | \(0.398304\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −681.108 | −0.163405 | ||||||||
\(260\) | −4856.33 | −1.15837 | ||||||||
\(261\) | −3871.42 | −0.918142 | ||||||||
\(262\) | 212.786 | 0.0501754 | ||||||||
\(263\) | 3698.37 | 0.867116 | 0.433558 | − | 0.901126i | \(-0.357258\pi\) | ||||
0.433558 | + | 0.901126i | \(0.357258\pi\) | |||||||
\(264\) | 4129.75 | 0.962760 | ||||||||
\(265\) | 7648.53 | 1.77300 | ||||||||
\(266\) | 2675.38 | 0.616686 | ||||||||
\(267\) | 3546.84 | 0.812970 | ||||||||
\(268\) | −3457.11 | −0.787972 | ||||||||
\(269\) | −2299.84 | −0.521278 | −0.260639 | − | 0.965436i | \(-0.583933\pi\) | ||||
−0.260639 | + | 0.965436i | \(0.583933\pi\) | |||||||
\(270\) | 5288.65 | 1.19206 | ||||||||
\(271\) | 7070.12 | 1.58479 | 0.792397 | − | 0.610006i | \(-0.208833\pi\) | ||||
0.792397 | + | 0.610006i | \(0.208833\pi\) | |||||||
\(272\) | −1622.57 | −0.361702 | ||||||||
\(273\) | 16725.7 | 3.70802 | ||||||||
\(274\) | 7663.26 | 1.68962 | ||||||||
\(275\) | −1458.06 | −0.319726 | ||||||||
\(276\) | 4770.62 | 1.04043 | ||||||||
\(277\) | 708.917 | 0.153771 | 0.0768857 | − | 0.997040i | \(-0.475502\pi\) | ||||
0.0768857 | + | 0.997040i | \(0.475502\pi\) | |||||||
\(278\) | −7132.87 | −1.53885 | ||||||||
\(279\) | 662.479 | 0.142156 | ||||||||
\(280\) | 3144.25 | 0.671088 | ||||||||
\(281\) | 8502.44 | 1.80503 | 0.902514 | − | 0.430660i | \(-0.141719\pi\) | ||||
0.902514 | + | 0.430660i | \(0.141719\pi\) | |||||||
\(282\) | −169.110 | −0.0357105 | ||||||||
\(283\) | −813.075 | −0.170786 | −0.0853928 | − | 0.996347i | \(-0.527215\pi\) | ||||
−0.0853928 | + | 0.996347i | \(0.527215\pi\) | |||||||
\(284\) | −3588.56 | −0.749794 | ||||||||
\(285\) | −2580.89 | −0.536417 | ||||||||
\(286\) | 14596.2 | 3.01781 | ||||||||
\(287\) | 2158.64 | 0.443974 | ||||||||
\(288\) | −8804.42 | −1.80141 | ||||||||
\(289\) | −4475.12 | −0.910873 | ||||||||
\(290\) | −4260.11 | −0.862628 | ||||||||
\(291\) | 9769.07 | 1.96795 | ||||||||
\(292\) | −2722.37 | −0.545598 | ||||||||
\(293\) | −4761.50 | −0.949385 | −0.474693 | − | 0.880152i | \(-0.657441\pi\) | ||||
−0.474693 | + | 0.880152i | \(0.657441\pi\) | |||||||
\(294\) | 14369.0 | 2.85039 | ||||||||
\(295\) | 2329.95 | 0.459847 | ||||||||
\(296\) | −213.624 | −0.0419481 | ||||||||
\(297\) | −6523.50 | −1.27452 | ||||||||
\(298\) | −1799.78 | −0.349861 | ||||||||
\(299\) | −7362.94 | −1.42411 | ||||||||
\(300\) | 1200.04 | 0.230948 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 12136.1 | 2.31243 | ||||||||
\(303\) | −16432.7 | −3.11562 | ||||||||
\(304\) | 1972.09 | 0.372063 | ||||||||
\(305\) | 4564.46 | 0.856918 | ||||||||
\(306\) | 3171.73 | 0.592536 | ||||||||
\(307\) | −8092.16 | −1.50438 | −0.752189 | − | 0.658948i | \(-0.771002\pi\) | ||||
−0.752189 | + | 0.658948i | \(0.771002\pi\) | |||||||
\(308\) | 8881.63 | 1.64311 | ||||||||
\(309\) | −3408.50 | −0.627517 | ||||||||
\(310\) | 728.992 | 0.133561 | ||||||||
\(311\) | 2093.98 | 0.381797 | 0.190899 | − | 0.981610i | \(-0.438860\pi\) | ||||
0.190899 | + | 0.981610i | \(0.438860\pi\) | |||||||
\(312\) | 5245.90 | 0.951892 | ||||||||
\(313\) | −5734.10 | −1.03550 | −0.517748 | − | 0.855533i | \(-0.673230\pi\) | ||||
−0.517748 | + | 0.855533i | \(0.673230\pi\) | |||||||
\(314\) | 2066.95 | 0.371480 | ||||||||
\(315\) | −14444.9 | −2.58375 | ||||||||
\(316\) | −6183.64 | −1.10081 | ||||||||
\(317\) | −9549.73 | −1.69201 | −0.846003 | − | 0.533178i | \(-0.820998\pi\) | ||||
−0.846003 | + | 0.533178i | \(0.820998\pi\) | |||||||
\(318\) | 18920.4 | 3.33649 | ||||||||
\(319\) | 5254.80 | 0.922296 | ||||||||
\(320\) | −2063.08 | −0.360405 | ||||||||
\(321\) | 395.091 | 0.0686973 | ||||||||
\(322\) | −10916.9 | −1.88937 | ||||||||
\(323\) | −532.205 | −0.0916801 | ||||||||
\(324\) | −817.485 | −0.140172 | ||||||||
\(325\) | −1852.13 | −0.316116 | ||||||||
\(326\) | −2384.73 | −0.405147 | ||||||||
\(327\) | 5654.03 | 0.956173 | ||||||||
\(328\) | 677.041 | 0.113974 | ||||||||
\(329\) | 158.817 | 0.0266136 | ||||||||
\(330\) | −20877.3 | −3.48259 | ||||||||
\(331\) | 1228.97 | 0.204079 | 0.102040 | − | 0.994780i | \(-0.467463\pi\) | ||||
0.102040 | + | 0.994780i | \(0.467463\pi\) | |||||||
\(332\) | −1959.50 | −0.323920 | ||||||||
\(333\) | 981.408 | 0.161504 | ||||||||
\(334\) | 9592.47 | 1.57149 | ||||||||
\(335\) | −7631.72 | −1.24467 | ||||||||
\(336\) | 18280.0 | 2.96802 | ||||||||
\(337\) | −2889.26 | −0.467027 | −0.233514 | − | 0.972354i | \(-0.575022\pi\) | ||||
−0.233514 | + | 0.972354i | \(0.575022\pi\) | |||||||
\(338\) | 10448.4 | 1.68142 | ||||||||
\(339\) | 4154.94 | 0.665679 | ||||||||
\(340\) | 1432.35 | 0.228471 | ||||||||
\(341\) | −899.204 | −0.142799 | ||||||||
\(342\) | −3854.96 | −0.609510 | ||||||||
\(343\) | −3699.17 | −0.582321 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 10531.3 | 1.64345 | ||||||||
\(346\) | 7253.07 | 1.12696 | ||||||||
\(347\) | 1936.22 | 0.299544 | 0.149772 | − | 0.988721i | \(-0.452146\pi\) | ||||
0.149772 | + | 0.988721i | \(0.452146\pi\) | |||||||
\(348\) | −4324.89 | −0.666203 | ||||||||
\(349\) | −1821.71 | −0.279410 | −0.139705 | − | 0.990193i | \(-0.544615\pi\) | ||||
−0.139705 | + | 0.990193i | \(0.544615\pi\) | |||||||
\(350\) | −2746.13 | −0.419391 | ||||||||
\(351\) | −8286.60 | −1.26013 | ||||||||
\(352\) | 11950.5 | 1.80956 | ||||||||
\(353\) | −845.304 | −0.127453 | −0.0637267 | − | 0.997967i | \(-0.520299\pi\) | ||||
−0.0637267 | + | 0.997967i | \(0.520299\pi\) | |||||||
\(354\) | 5763.67 | 0.865354 | ||||||||
\(355\) | −7921.89 | −1.18437 | ||||||||
\(356\) | 2392.46 | 0.356180 | ||||||||
\(357\) | −4933.18 | −0.731349 | ||||||||
\(358\) | 4888.92 | 0.721753 | ||||||||
\(359\) | −8399.94 | −1.23491 | −0.617454 | − | 0.786607i | \(-0.711836\pi\) | ||||
−0.617454 | + | 0.786607i | \(0.711836\pi\) | |||||||
\(360\) | −4530.54 | −0.663279 | ||||||||
\(361\) | −6212.15 | −0.905694 | ||||||||
\(362\) | −9225.83 | −1.33950 | ||||||||
\(363\) | 14764.2 | 2.13477 | ||||||||
\(364\) | 11282.1 | 1.62456 | ||||||||
\(365\) | −6009.75 | −0.861821 | ||||||||
\(366\) | 11291.2 | 1.61257 | ||||||||
\(367\) | −6905.35 | −0.982170 | −0.491085 | − | 0.871112i | \(-0.663399\pi\) | ||||
−0.491085 | + | 0.871112i | \(0.663399\pi\) | |||||||
\(368\) | −8047.14 | −1.13991 | ||||||||
\(369\) | −3110.39 | −0.438808 | ||||||||
\(370\) | 1079.94 | 0.151739 | ||||||||
\(371\) | −17768.8 | −2.48655 | ||||||||
\(372\) | 740.077 | 0.103148 | ||||||||
\(373\) | 8411.92 | 1.16770 | 0.583850 | − | 0.811861i | \(-0.301545\pi\) | ||||
0.583850 | + | 0.811861i | \(0.301545\pi\) | |||||||
\(374\) | −4305.10 | −0.595217 | ||||||||
\(375\) | −10035.5 | −1.38195 | ||||||||
\(376\) | 49.8117 | 0.00683203 | ||||||||
\(377\) | 6675.01 | 0.911885 | ||||||||
\(378\) | −12286.4 | −1.67181 | ||||||||
\(379\) | 6112.46 | 0.828433 | 0.414216 | − | 0.910178i | \(-0.364056\pi\) | ||||
0.414216 | + | 0.910178i | \(0.364056\pi\) | |||||||
\(380\) | −1740.89 | −0.235016 | ||||||||
\(381\) | −15655.0 | −2.10507 | ||||||||
\(382\) | −5932.97 | −0.794652 | ||||||||
\(383\) | −10015.6 | −1.33622 | −0.668110 | − | 0.744062i | \(-0.732897\pi\) | ||||
−0.668110 | + | 0.744062i | \(0.732897\pi\) | |||||||
\(384\) | 9027.22 | 1.19966 | ||||||||
\(385\) | 19606.6 | 2.59544 | ||||||||
\(386\) | −13064.0 | −1.72264 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6589.55 | 0.862201 | ||||||||
\(389\) | −1981.11 | −0.258216 | −0.129108 | − | 0.991631i | \(-0.541211\pi\) | ||||
−0.129108 | + | 0.991631i | \(0.541211\pi\) | |||||||
\(390\) | −26519.8 | −3.44328 | ||||||||
\(391\) | 2171.67 | 0.280884 | ||||||||
\(392\) | −4232.41 | −0.545329 | ||||||||
\(393\) | 476.877 | 0.0612094 | ||||||||
\(394\) | 10545.1 | 1.34836 | ||||||||
\(395\) | −13650.6 | −1.73883 | ||||||||
\(396\) | −12797.5 | −1.62399 | ||||||||
\(397\) | 3781.76 | 0.478088 | 0.239044 | − | 0.971009i | \(-0.423166\pi\) | ||||
0.239044 | + | 0.971009i | \(0.423166\pi\) | |||||||
\(398\) | −6543.31 | −0.824086 | ||||||||
\(399\) | 5995.84 | 0.752300 | ||||||||
\(400\) | −2024.24 | −0.253030 | ||||||||
\(401\) | 13602.5 | 1.69395 | 0.846976 | − | 0.531632i | \(-0.178421\pi\) | ||||
0.846976 | + | 0.531632i | \(0.178421\pi\) | |||||||
\(402\) | −18878.8 | −2.34226 | ||||||||
\(403\) | −1142.23 | −0.141188 | ||||||||
\(404\) | −11084.4 | −1.36502 | ||||||||
\(405\) | −1804.64 | −0.221415 | ||||||||
\(406\) | 9896.95 | 1.20980 | ||||||||
\(407\) | −1332.10 | −0.162235 | ||||||||
\(408\) | −1547.25 | −0.187746 | ||||||||
\(409\) | −9450.00 | −1.14248 | −0.571238 | − | 0.820785i | \(-0.693537\pi\) | ||||
−0.571238 | + | 0.820785i | \(0.693537\pi\) | |||||||
\(410\) | −3422.67 | −0.412277 | ||||||||
\(411\) | 17174.2 | 2.06118 | ||||||||
\(412\) | −2299.14 | −0.274929 | ||||||||
\(413\) | −5412.86 | −0.644914 | ||||||||
\(414\) | 15730.2 | 1.86738 | ||||||||
\(415\) | −4325.68 | −0.511661 | ||||||||
\(416\) | 15180.4 | 1.78913 | ||||||||
\(417\) | −15985.6 | −1.87726 | ||||||||
\(418\) | 5232.46 | 0.612268 | ||||||||
\(419\) | −5265.77 | −0.613961 | −0.306980 | − | 0.951716i | \(-0.599319\pi\) | ||||
−0.306980 | + | 0.951716i | \(0.599319\pi\) | |||||||
\(420\) | −16136.9 | −1.87477 | ||||||||
\(421\) | −708.957 | −0.0820723 | −0.0410361 | − | 0.999158i | \(-0.513066\pi\) | ||||
−0.0410361 | + | 0.999158i | \(0.513066\pi\) | |||||||
\(422\) | 18885.7 | 2.17853 | ||||||||
\(423\) | −228.840 | −0.0263039 | ||||||||
\(424\) | −5573.04 | −0.638328 | ||||||||
\(425\) | 546.278 | 0.0623491 | ||||||||
\(426\) | −19596.6 | −2.22878 | ||||||||
\(427\) | −10604.0 | −1.20179 | ||||||||
\(428\) | 266.502 | 0.0300978 | ||||||||
\(429\) | 32711.8 | 3.68145 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12530.7 | 1.40042 | 0.700210 | − | 0.713937i | \(-0.253090\pi\) | ||||
0.700210 | + | 0.713937i | \(0.253090\pi\) | |||||||
\(432\) | −9056.63 | −1.00865 | ||||||||
\(433\) | −13633.0 | −1.51307 | −0.756534 | − | 0.653954i | \(-0.773109\pi\) | ||||
−0.756534 | + | 0.653954i | \(0.773109\pi\) | |||||||
\(434\) | −1693.57 | −0.187313 | ||||||||
\(435\) | −9547.39 | −1.05233 | ||||||||
\(436\) | 3813.82 | 0.418920 | ||||||||
\(437\) | −2639.47 | −0.288931 | ||||||||
\(438\) | −14866.5 | −1.62180 | ||||||||
\(439\) | −16838.6 | −1.83067 | −0.915336 | − | 0.402691i | \(-0.868075\pi\) | ||||
−0.915336 | + | 0.402691i | \(0.868075\pi\) | |||||||
\(440\) | 6149.45 | 0.666280 | ||||||||
\(441\) | 19444.1 | 2.09957 | ||||||||
\(442\) | −5468.63 | −0.588498 | ||||||||
\(443\) | −7973.21 | −0.855121 | −0.427561 | − | 0.903987i | \(-0.640627\pi\) | ||||
−0.427561 | + | 0.903987i | \(0.640627\pi\) | |||||||
\(444\) | 1096.36 | 0.117187 | ||||||||
\(445\) | 5281.45 | 0.562618 | ||||||||
\(446\) | 2054.43 | 0.218117 | ||||||||
\(447\) | −4033.51 | −0.426798 | ||||||||
\(448\) | 4792.88 | 0.505452 | ||||||||
\(449\) | 248.826 | 0.0261533 | 0.0130766 | − | 0.999914i | \(-0.495837\pi\) | ||||
0.0130766 | + | 0.999914i | \(0.495837\pi\) | |||||||
\(450\) | 3956.90 | 0.414511 | ||||||||
\(451\) | 4221.83 | 0.440794 | ||||||||
\(452\) | 2802.64 | 0.291649 | ||||||||
\(453\) | 27198.4 | 2.82096 | ||||||||
\(454\) | −11044.8 | −1.14176 | ||||||||
\(455\) | 24905.6 | 2.56614 | ||||||||
\(456\) | 1880.55 | 0.193124 | ||||||||
\(457\) | −18522.3 | −1.89593 | −0.947964 | − | 0.318379i | \(-0.896862\pi\) | ||||
−0.947964 | + | 0.318379i | \(0.896862\pi\) | |||||||
\(458\) | 3485.93 | 0.355648 | ||||||||
\(459\) | 2444.09 | 0.248542 | ||||||||
\(460\) | 7103.73 | 0.720029 | ||||||||
\(461\) | 3120.99 | 0.315313 | 0.157656 | − | 0.987494i | \(-0.449606\pi\) | ||||
0.157656 | + | 0.987494i | \(0.449606\pi\) | |||||||
\(462\) | 48501.4 | 4.88418 | ||||||||
\(463\) | 2643.00 | 0.265293 | 0.132647 | − | 0.991163i | \(-0.457652\pi\) | ||||
0.132647 | + | 0.991163i | \(0.457652\pi\) | |||||||
\(464\) | 7295.28 | 0.729903 | ||||||||
\(465\) | 1633.75 | 0.162932 | ||||||||
\(466\) | 3657.75 | 0.363609 | ||||||||
\(467\) | 14644.0 | 1.45106 | 0.725528 | − | 0.688192i | \(-0.241595\pi\) | ||||
0.725528 | + | 0.688192i | \(0.241595\pi\) | |||||||
\(468\) | −16256.3 | −1.60566 | ||||||||
\(469\) | 17729.8 | 1.74560 | ||||||||
\(470\) | −251.815 | −0.0247135 | ||||||||
\(471\) | 4632.26 | 0.453171 | ||||||||
\(472\) | −1697.70 | −0.165557 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −33768.0 | −3.27219 | ||||||||
\(475\) | −663.952 | −0.0641352 | ||||||||
\(476\) | −3327.59 | −0.320420 | ||||||||
\(477\) | 25603.1 | 2.45762 | ||||||||
\(478\) | −8913.99 | −0.852964 | ||||||||
\(479\) | 16033.1 | 1.52938 | 0.764689 | − | 0.644399i | \(-0.222892\pi\) | ||||
0.764689 | + | 0.644399i | \(0.222892\pi\) | |||||||
\(480\) | −21712.8 | −2.06468 | ||||||||
\(481\) | −1692.12 | −0.160404 | ||||||||
\(482\) | −213.674 | −0.0201921 | ||||||||
\(483\) | −24466.1 | −2.30486 | ||||||||
\(484\) | 9958.94 | 0.935287 | ||||||||
\(485\) | 14546.7 | 1.36192 | ||||||||
\(486\) | −16080.5 | −1.50088 | ||||||||
\(487\) | −15972.8 | −1.48624 | −0.743119 | − | 0.669159i | \(-0.766654\pi\) | ||||
−0.743119 | + | 0.669159i | \(0.766654\pi\) | |||||||
\(488\) | −3325.86 | −0.308513 | ||||||||
\(489\) | −5344.44 | −0.494242 | ||||||||
\(490\) | 21396.3 | 1.97262 | ||||||||
\(491\) | −13730.1 | −1.26197 | −0.630987 | − | 0.775793i | \(-0.717350\pi\) | ||||
−0.630987 | + | 0.775793i | \(0.717350\pi\) | |||||||
\(492\) | −3474.71 | −0.318399 | ||||||||
\(493\) | −1968.76 | −0.179855 | ||||||||
\(494\) | 6646.63 | 0.605356 | ||||||||
\(495\) | −28251.1 | −2.56524 | ||||||||
\(496\) | −1248.37 | −0.113011 | ||||||||
\(497\) | 18403.9 | 1.66102 | ||||||||
\(498\) | −10700.6 | −0.962859 | ||||||||
\(499\) | 15534.6 | 1.39364 | 0.696820 | − | 0.717246i | \(-0.254598\pi\) | ||||
0.696820 | + | 0.717246i | \(0.254598\pi\) | |||||||
\(500\) | −6769.28 | −0.605463 | ||||||||
\(501\) | 21497.8 | 1.91707 | ||||||||
\(502\) | −4729.45 | −0.420489 | ||||||||
\(503\) | −8754.61 | −0.776041 | −0.388021 | − | 0.921651i | \(-0.626841\pi\) | ||||
−0.388021 | + | 0.921651i | \(0.626841\pi\) | |||||||
\(504\) | 10525.2 | 0.930218 | ||||||||
\(505\) | −24469.3 | −2.15617 | ||||||||
\(506\) | −21351.1 | −1.87583 | ||||||||
\(507\) | 23416.1 | 2.05118 | ||||||||
\(508\) | −10559.8 | −0.922277 | ||||||||
\(509\) | 14111.2 | 1.22882 | 0.614408 | − | 0.788989i | \(-0.289395\pi\) | ||||
0.614408 | + | 0.788989i | \(0.289395\pi\) | |||||||
\(510\) | 7821.88 | 0.679134 | ||||||||
\(511\) | 13961.6 | 1.20866 | ||||||||
\(512\) | 11034.9 | 0.952495 | ||||||||
\(513\) | −2970.58 | −0.255661 | ||||||||
\(514\) | 9533.13 | 0.818071 | ||||||||
\(515\) | −5075.46 | −0.434275 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 310.611 | 0.0264230 | ||||||||
\(518\) | −2508.88 | −0.212807 | ||||||||
\(519\) | 16255.0 | 1.37479 | ||||||||
\(520\) | 7811.45 | 0.658759 | ||||||||
\(521\) | 5869.85 | 0.493595 | 0.246797 | − | 0.969067i | \(-0.420622\pi\) | ||||
0.246797 | + | 0.969067i | \(0.420622\pi\) | |||||||
\(522\) | −14260.5 | −1.19572 | ||||||||
\(523\) | −16310.7 | −1.36370 | −0.681851 | − | 0.731491i | \(-0.738825\pi\) | ||||
−0.681851 | + | 0.731491i | \(0.738825\pi\) | |||||||
\(524\) | 321.669 | 0.0268171 | ||||||||
\(525\) | −6154.39 | −0.511618 | ||||||||
\(526\) | 13623.1 | 1.12927 | ||||||||
\(527\) | 336.896 | 0.0278471 | ||||||||
\(528\) | 35751.6 | 2.94676 | ||||||||
\(529\) | −1396.64 | −0.114789 | ||||||||
\(530\) | 28173.6 | 2.30902 | ||||||||
\(531\) | 7799.39 | 0.637410 | ||||||||
\(532\) | 4044.39 | 0.329599 | ||||||||
\(533\) | 5362.85 | 0.435818 | ||||||||
\(534\) | 13064.9 | 1.05875 | ||||||||
\(535\) | 588.315 | 0.0475422 | ||||||||
\(536\) | 5560.80 | 0.448115 | ||||||||
\(537\) | 10956.6 | 0.880472 | ||||||||
\(538\) | −8471.54 | −0.678874 | ||||||||
\(539\) | −26392.1 | −2.10907 | ||||||||
\(540\) | 7994.88 | 0.637120 | ||||||||
\(541\) | −6431.70 | −0.511129 | −0.255564 | − | 0.966792i | \(-0.582261\pi\) | ||||
−0.255564 | + | 0.966792i | \(0.582261\pi\) | |||||||
\(542\) | 26043.0 | 2.06392 | ||||||||
\(543\) | −20676.1 | −1.63407 | ||||||||
\(544\) | −4477.38 | −0.352879 | ||||||||
\(545\) | 8419.18 | 0.661722 | ||||||||
\(546\) | 61609.8 | 4.82904 | ||||||||
\(547\) | 7509.24 | 0.586969 | 0.293484 | − | 0.955964i | \(-0.405185\pi\) | ||||
0.293484 | + | 0.955964i | \(0.405185\pi\) | |||||||
\(548\) | 11584.6 | 0.903045 | ||||||||
\(549\) | 15279.3 | 1.18780 | ||||||||
\(550\) | −5370.82 | −0.416387 | ||||||||
\(551\) | 2392.86 | 0.185008 | ||||||||
\(552\) | −7673.59 | −0.591684 | ||||||||
\(553\) | 31712.7 | 2.43863 | ||||||||
\(554\) | 2611.32 | 0.200260 | ||||||||
\(555\) | 2420.27 | 0.185108 | ||||||||
\(556\) | −10782.8 | −0.822467 | ||||||||
\(557\) | −16812.6 | −1.27895 | −0.639474 | − | 0.768813i | \(-0.720848\pi\) | ||||
−0.639474 | + | 0.768813i | \(0.720848\pi\) | |||||||
\(558\) | 2440.26 | 0.185134 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 27220.0 | 2.05402 | ||||||||
\(561\) | −9648.21 | −0.726110 | ||||||||
\(562\) | 31319.0 | 2.35073 | ||||||||
\(563\) | −10965.3 | −0.820840 | −0.410420 | − | 0.911897i | \(-0.634618\pi\) | ||||
−0.410420 | + | 0.911897i | \(0.634618\pi\) | |||||||
\(564\) | −255.644 | −0.0190861 | ||||||||
\(565\) | 6186.95 | 0.460685 | ||||||||
\(566\) | −2994.99 | −0.222418 | ||||||||
\(567\) | 4192.47 | 0.310524 | ||||||||
\(568\) | 5772.23 | 0.426404 | ||||||||
\(569\) | −12831.2 | −0.945364 | −0.472682 | − | 0.881233i | \(-0.656714\pi\) | ||||
−0.472682 | + | 0.881233i | \(0.656714\pi\) | |||||||
\(570\) | −9506.79 | −0.698589 | ||||||||
\(571\) | −9947.46 | −0.729051 | −0.364526 | − | 0.931193i | \(-0.618769\pi\) | ||||
−0.364526 | + | 0.931193i | \(0.618769\pi\) | |||||||
\(572\) | 22065.2 | 1.61292 | ||||||||
\(573\) | −13296.5 | −0.969402 | ||||||||
\(574\) | 7951.43 | 0.578199 | ||||||||
\(575\) | 2709.26 | 0.196494 | ||||||||
\(576\) | −6906.06 | −0.499570 | ||||||||
\(577\) | 1301.43 | 0.0938978 | 0.0469489 | − | 0.998897i | \(-0.485050\pi\) | ||||
0.0469489 | + | 0.998897i | \(0.485050\pi\) | |||||||
\(578\) | −16484.2 | −1.18625 | ||||||||
\(579\) | −29277.8 | −2.10146 | ||||||||
\(580\) | −6440.02 | −0.461047 | ||||||||
\(581\) | 10049.3 | 0.717581 | ||||||||
\(582\) | 35984.7 | 2.56291 | ||||||||
\(583\) | −34751.8 | −2.46874 | ||||||||
\(584\) | 4378.96 | 0.310278 | ||||||||
\(585\) | −35886.5 | −2.53628 | ||||||||
\(586\) | −17539.1 | −1.23641 | ||||||||
\(587\) | −9125.56 | −0.641656 | −0.320828 | − | 0.947137i | \(-0.603961\pi\) | ||||
−0.320828 | + | 0.947137i | \(0.603961\pi\) | |||||||
\(588\) | 21721.6 | 1.52344 | ||||||||
\(589\) | −409.467 | −0.0286448 | ||||||||
\(590\) | 8582.44 | 0.598871 | ||||||||
\(591\) | 23632.7 | 1.64487 | ||||||||
\(592\) | −1849.36 | −0.128392 | ||||||||
\(593\) | 20848.4 | 1.44375 | 0.721873 | − | 0.692025i | \(-0.243281\pi\) | ||||
0.721873 | + | 0.692025i | \(0.243281\pi\) | |||||||
\(594\) | −24029.5 | −1.65984 | ||||||||
\(595\) | −7345.80 | −0.506132 | ||||||||
\(596\) | −2720.73 | −0.186989 | ||||||||
\(597\) | −14664.3 | −1.00531 | ||||||||
\(598\) | −27121.6 | −1.85466 | ||||||||
\(599\) | −794.230 | −0.0541759 | −0.0270879 | − | 0.999633i | \(-0.508623\pi\) | ||||
−0.0270879 | + | 0.999633i | \(0.508623\pi\) | |||||||
\(600\) | −1930.28 | −0.131339 | ||||||||
\(601\) | −1489.20 | −0.101075 | −0.0505373 | − | 0.998722i | \(-0.516093\pi\) | ||||
−0.0505373 | + | 0.998722i | \(0.516093\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −25546.8 | −1.72528 | ||||||||
\(604\) | 18346.2 | 1.23592 | ||||||||
\(605\) | 21984.8 | 1.47737 | ||||||||
\(606\) | −60530.4 | −4.05755 | ||||||||
\(607\) | −20951.2 | −1.40096 | −0.700480 | − | 0.713672i | \(-0.747031\pi\) | ||||
−0.700480 | + | 0.713672i | \(0.747031\pi\) | |||||||
\(608\) | 5441.86 | 0.362987 | ||||||||
\(609\) | 22180.2 | 1.47584 | ||||||||
\(610\) | 16813.3 | 1.11599 | ||||||||
\(611\) | 394.560 | 0.0261247 | ||||||||
\(612\) | 4794.72 | 0.316691 | ||||||||
\(613\) | −17473.3 | −1.15129 | −0.575646 | − | 0.817699i | \(-0.695249\pi\) | ||||
−0.575646 | + | 0.817699i | \(0.695249\pi\) | |||||||
\(614\) | −29807.7 | −1.95919 | ||||||||
\(615\) | −7670.59 | −0.502940 | ||||||||
\(616\) | −14286.2 | −0.934427 | ||||||||
\(617\) | −5000.48 | −0.326275 | −0.163138 | − | 0.986603i | \(-0.552161\pi\) | ||||
−0.163138 | + | 0.986603i | \(0.552161\pi\) | |||||||
\(618\) | −12555.3 | −0.817232 | ||||||||
\(619\) | 8385.16 | 0.544472 | 0.272236 | − | 0.962231i | \(-0.412237\pi\) | ||||
0.272236 | + | 0.962231i | \(0.412237\pi\) | |||||||
\(620\) | 1102.02 | 0.0713841 | ||||||||
\(621\) | 12121.5 | 0.783281 | ||||||||
\(622\) | 7713.26 | 0.497224 | ||||||||
\(623\) | −12269.7 | −0.789045 | ||||||||
\(624\) | 45414.1 | 2.91349 | ||||||||
\(625\) | −18206.7 | −1.16523 | ||||||||
\(626\) | −21121.7 | −1.34855 | ||||||||
\(627\) | 11726.5 | 0.746910 | ||||||||
\(628\) | 3124.61 | 0.198544 | ||||||||
\(629\) | 499.083 | 0.0316371 | ||||||||
\(630\) | −53208.4 | −3.36488 | ||||||||
\(631\) | −18872.3 | −1.19064 | −0.595320 | − | 0.803489i | \(-0.702975\pi\) | ||||
−0.595320 | + | 0.803489i | \(0.702975\pi\) | |||||||
\(632\) | 9946.45 | 0.626026 | ||||||||
\(633\) | 42324.9 | 2.65761 | ||||||||
\(634\) | −35176.7 | −2.20354 | ||||||||
\(635\) | −23311.3 | −1.45682 | ||||||||
\(636\) | 28602.0 | 1.78325 | ||||||||
\(637\) | −33525.0 | −2.08526 | ||||||||
\(638\) | 19356.2 | 1.20113 | ||||||||
\(639\) | −26518.1 | −1.64169 | ||||||||
\(640\) | 13442.1 | 0.830226 | ||||||||
\(641\) | 1488.27 | 0.0917054 | 0.0458527 | − | 0.998948i | \(-0.485400\pi\) | ||||
0.0458527 | + | 0.998948i | \(0.485400\pi\) | |||||||
\(642\) | 1455.33 | 0.0894663 | ||||||||
\(643\) | 4204.04 | 0.257840 | 0.128920 | − | 0.991655i | \(-0.458849\pi\) | ||||
0.128920 | + | 0.991655i | \(0.458849\pi\) | |||||||
\(644\) | −16503.2 | −1.00981 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1960.39 | −0.119397 | ||||||||
\(647\) | 19185.2 | 1.16576 | 0.582882 | − | 0.812557i | \(-0.301925\pi\) | ||||
0.582882 | + | 0.812557i | \(0.301925\pi\) | |||||||
\(648\) | 1314.93 | 0.0797153 | ||||||||
\(649\) | −10586.4 | −0.640294 | ||||||||
\(650\) | −6822.39 | −0.411686 | ||||||||
\(651\) | −3795.48 | −0.228505 | ||||||||
\(652\) | −3605.00 | −0.216538 | ||||||||
\(653\) | −18907.5 | −1.13309 | −0.566544 | − | 0.824031i | \(-0.691720\pi\) | ||||
−0.566544 | + | 0.824031i | \(0.691720\pi\) | |||||||
\(654\) | 20826.8 | 1.24525 | ||||||||
\(655\) | 710.099 | 0.0423601 | ||||||||
\(656\) | 5861.19 | 0.348843 | ||||||||
\(657\) | −20117.3 | −1.19460 | ||||||||
\(658\) | 585.008 | 0.0346596 | ||||||||
\(659\) | 24740.8 | 1.46247 | 0.731234 | − | 0.682127i | \(-0.238945\pi\) | ||||
0.731234 | + | 0.682127i | \(0.238945\pi\) | |||||||
\(660\) | −31560.2 | −1.86133 | ||||||||
\(661\) | 11817.8 | 0.695400 | 0.347700 | − | 0.937606i | \(-0.386963\pi\) | ||||
0.347700 | + | 0.937606i | \(0.386963\pi\) | |||||||
\(662\) | 4526.95 | 0.265778 | ||||||||
\(663\) | −12255.8 | −0.717913 | ||||||||
\(664\) | 3151.88 | 0.184212 | ||||||||
\(665\) | 8928.17 | 0.520631 | ||||||||
\(666\) | 3615.05 | 0.210331 | ||||||||
\(667\) | −9764.07 | −0.566816 | ||||||||
\(668\) | 14501.0 | 0.839910 | ||||||||
\(669\) | 4604.21 | 0.266082 | ||||||||
\(670\) | −28111.7 | −1.62097 | ||||||||
\(671\) | −20739.1 | −1.19318 | ||||||||
\(672\) | 50442.4 | 2.89562 | ||||||||
\(673\) | 9905.49 | 0.567353 | 0.283676 | − | 0.958920i | \(-0.408446\pi\) | ||||
0.283676 | + | 0.958920i | \(0.408446\pi\) | |||||||
\(674\) | −10642.7 | −0.608221 | ||||||||
\(675\) | 3049.13 | 0.173868 | ||||||||
\(676\) | 15794.9 | 0.898666 | ||||||||
\(677\) | 1165.33 | 0.0661555 | 0.0330778 | − | 0.999453i | \(-0.489469\pi\) | ||||
0.0330778 | + | 0.999453i | \(0.489469\pi\) | |||||||
\(678\) | 15304.9 | 0.866931 | ||||||||
\(679\) | −33794.5 | −1.91003 | ||||||||
\(680\) | −2303.95 | −0.129930 | ||||||||
\(681\) | −24752.7 | −1.39284 | ||||||||
\(682\) | −3312.25 | −0.185971 | ||||||||
\(683\) | 6889.70 | 0.385984 | 0.192992 | − | 0.981200i | \(-0.438181\pi\) | ||||
0.192992 | + | 0.981200i | \(0.438181\pi\) | |||||||
\(684\) | −5827.56 | −0.325763 | ||||||||
\(685\) | 25573.5 | 1.42644 | ||||||||
\(686\) | −13626.0 | −0.758371 | ||||||||
\(687\) | 7812.35 | 0.433857 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −44144.2 | −2.44087 | ||||||||
\(690\) | 38792.5 | 2.14030 | ||||||||
\(691\) | 6806.51 | 0.374720 | 0.187360 | − | 0.982291i | \(-0.440007\pi\) | ||||
0.187360 | + | 0.982291i | \(0.440007\pi\) | |||||||
\(692\) | 10964.5 | 0.602323 | ||||||||
\(693\) | 65632.1 | 3.59763 | ||||||||
\(694\) | 7132.13 | 0.390104 | ||||||||
\(695\) | −23803.5 | −1.29916 | ||||||||
\(696\) | 6956.64 | 0.378866 | ||||||||
\(697\) | −1581.75 | −0.0859584 | ||||||||
\(698\) | −6710.33 | −0.363882 | ||||||||
\(699\) | 8197.43 | 0.443570 | ||||||||
\(700\) | −4151.34 | −0.224151 | ||||||||
\(701\) | 32393.6 | 1.74535 | 0.872674 | − | 0.488304i | \(-0.162384\pi\) | ||||
0.872674 | + | 0.488304i | \(0.162384\pi\) | |||||||
\(702\) | −30524.0 | −1.64110 | ||||||||
\(703\) | −606.591 | −0.0325434 | ||||||||
\(704\) | 9373.81 | 0.501831 | ||||||||
\(705\) | −564.346 | −0.0301482 | ||||||||
\(706\) | −3113.71 | −0.165986 | ||||||||
\(707\) | 56846.2 | 3.02393 | ||||||||
\(708\) | 8712.95 | 0.462504 | ||||||||
\(709\) | 6305.19 | 0.333987 | 0.166993 | − | 0.985958i | \(-0.446594\pi\) | ||||
0.166993 | + | 0.985958i | \(0.446594\pi\) | |||||||
\(710\) | −29180.5 | −1.54243 | ||||||||
\(711\) | −45694.9 | −2.41025 | ||||||||
\(712\) | −3848.29 | −0.202557 | ||||||||
\(713\) | 1670.83 | 0.0877604 | ||||||||
\(714\) | −18171.5 | −0.952454 | ||||||||
\(715\) | 48709.9 | 2.54776 | ||||||||
\(716\) | 7390.60 | 0.385754 | ||||||||
\(717\) | −19977.3 | −1.04054 | ||||||||
\(718\) | −30941.5 | −1.60825 | ||||||||
\(719\) | −8766.36 | −0.454701 | −0.227351 | − | 0.973813i | \(-0.573006\pi\) | ||||
−0.227351 | + | 0.973813i | \(0.573006\pi\) | |||||||
\(720\) | −39221.2 | −2.03012 | ||||||||
\(721\) | 11791.2 | 0.609050 | ||||||||
\(722\) | −22882.7 | −1.17951 | ||||||||
\(723\) | −478.867 | −0.0246324 | ||||||||
\(724\) | −13946.7 | −0.715919 | ||||||||
\(725\) | −2456.13 | −0.125819 | ||||||||
\(726\) | 54384.5 | 2.78016 | ||||||||
\(727\) | −2282.96 | −0.116465 | −0.0582327 | − | 0.998303i | \(-0.518547\pi\) | ||||
−0.0582327 | + | 0.998303i | \(0.518547\pi\) | |||||||
\(728\) | −18147.3 | −0.923879 | ||||||||
\(729\) | −32074.4 | −1.62955 | ||||||||
\(730\) | −22137.1 | −1.12237 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 17069.0 | 0.861869 | ||||||||
\(733\) | −11976.6 | −0.603500 | −0.301750 | − | 0.953387i | \(-0.597571\pi\) | ||||
−0.301750 | + | 0.953387i | \(0.597571\pi\) | |||||||
\(734\) | −25436.1 | −1.27910 | ||||||||
\(735\) | 47951.4 | 2.40642 | ||||||||
\(736\) | −22205.5 | −1.11210 | ||||||||
\(737\) | 34675.5 | 1.73309 | ||||||||
\(738\) | −11457.2 | −0.571471 | ||||||||
\(739\) | −18648.1 | −0.928255 | −0.464127 | − | 0.885769i | \(-0.653632\pi\) | ||||
−0.464127 | + | 0.885769i | \(0.653632\pi\) | |||||||
\(740\) | 1632.55 | 0.0810997 | ||||||||
\(741\) | 14895.9 | 0.738479 | ||||||||
\(742\) | −65452.0 | −3.23830 | ||||||||
\(743\) | −841.949 | −0.0415722 | −0.0207861 | − | 0.999784i | \(-0.506617\pi\) | ||||
−0.0207861 | + | 0.999784i | \(0.506617\pi\) | |||||||
\(744\) | −1190.42 | −0.0586599 | ||||||||
\(745\) | −6006.14 | −0.295366 | ||||||||
\(746\) | 30985.6 | 1.52073 | ||||||||
\(747\) | −14480.0 | −0.709231 | ||||||||
\(748\) | −6508.03 | −0.318124 | ||||||||
\(749\) | −1366.75 | −0.0666757 | ||||||||
\(750\) | −36966.2 | −1.79975 | ||||||||
\(751\) | −24798.5 | −1.20494 | −0.602469 | − | 0.798142i | \(-0.705816\pi\) | ||||
−0.602469 | + | 0.798142i | \(0.705816\pi\) | |||||||
\(752\) | 431.224 | 0.0209111 | ||||||||
\(753\) | −10599.2 | −0.512958 | ||||||||
\(754\) | 24587.6 | 1.18757 | ||||||||
\(755\) | 40500.1 | 1.95225 | ||||||||
\(756\) | −18573.4 | −0.893531 | ||||||||
\(757\) | 16188.4 | 0.777248 | 0.388624 | − | 0.921396i | \(-0.372950\pi\) | ||||
0.388624 | + | 0.921396i | \(0.372950\pi\) | |||||||
\(758\) | 22515.4 | 1.07889 | ||||||||
\(759\) | −47850.2 | −2.28834 | ||||||||
\(760\) | 2800.25 | 0.133652 | ||||||||
\(761\) | −3997.42 | −0.190416 | −0.0952078 | − | 0.995457i | \(-0.530352\pi\) | ||||
−0.0952078 | + | 0.995457i | \(0.530352\pi\) | |||||||
\(762\) | −57665.8 | −2.74149 | ||||||||
\(763\) | −19559.2 | −0.928034 | ||||||||
\(764\) | −8968.89 | −0.424716 | ||||||||
\(765\) | 10584.6 | 0.500243 | ||||||||
\(766\) | −36892.7 | −1.74019 | ||||||||
\(767\) | −13447.5 | −0.633066 | ||||||||
\(768\) | 44336.0 | 2.08312 | ||||||||
\(769\) | 11416.7 | 0.535367 | 0.267683 | − | 0.963507i | \(-0.413742\pi\) | ||||
0.267683 | + | 0.963507i | \(0.413742\pi\) | |||||||
\(770\) | 72221.5 | 3.38011 | ||||||||
\(771\) | 21364.8 | 0.997971 | ||||||||
\(772\) | −19748.9 | −0.920695 | ||||||||
\(773\) | 25632.5 | 1.19267 | 0.596337 | − | 0.802734i | \(-0.296622\pi\) | ||||
0.596337 | + | 0.802734i | \(0.296622\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 420.294 | 0.0194805 | ||||||||
\(776\) | −10599.4 | −0.490329 | ||||||||
\(777\) | −5622.69 | −0.259605 | ||||||||
\(778\) | −7297.47 | −0.336282 | ||||||||
\(779\) | 1922.47 | 0.0884208 | ||||||||
\(780\) | −40090.0 | −1.84032 | ||||||||
\(781\) | 35993.9 | 1.64912 | ||||||||
\(782\) | 7999.40 | 0.365803 | ||||||||
\(783\) | −10988.9 | −0.501549 | ||||||||
\(784\) | −36640.3 | −1.66911 | ||||||||
\(785\) | 6897.72 | 0.313618 | ||||||||
\(786\) | 1756.59 | 0.0797145 | ||||||||
\(787\) | −1740.19 | −0.0788198 | −0.0394099 | − | 0.999223i | \(-0.512548\pi\) | ||||
−0.0394099 | + | 0.999223i | \(0.512548\pi\) | |||||||
\(788\) | 15941.0 | 0.720655 | ||||||||
\(789\) | 30530.9 | 1.37760 | ||||||||
\(790\) | −50282.6 | −2.26453 | ||||||||
\(791\) | −14373.3 | −0.646089 | ||||||||
\(792\) | 20585.0 | 0.923554 | ||||||||
\(793\) | −26344.2 | −1.17971 | ||||||||
\(794\) | 13930.2 | 0.622626 | ||||||||
\(795\) | 63140.2 | 2.81680 | ||||||||
\(796\) | −9891.54 | −0.440448 | ||||||||
\(797\) | −22762.5 | −1.01165 | −0.505827 | − | 0.862635i | \(-0.668813\pi\) | ||||
−0.505827 | + | 0.862635i | \(0.668813\pi\) | |||||||
\(798\) | 22085.9 | 0.979739 | ||||||||
\(799\) | −116.374 | −0.00515269 | ||||||||
\(800\) | −5585.76 | −0.246858 | ||||||||
\(801\) | 17679.4 | 0.779864 | ||||||||
\(802\) | 50105.1 | 2.20608 | ||||||||
\(803\) | 27305.9 | 1.20000 | ||||||||
\(804\) | −28539.2 | −1.25186 | ||||||||
\(805\) | −36431.5 | −1.59508 | ||||||||
\(806\) | −4207.44 | −0.183872 | ||||||||
\(807\) | −18985.7 | −0.828163 | ||||||||
\(808\) | 17829.4 | 0.776280 | ||||||||
\(809\) | 9835.50 | 0.427439 | 0.213719 | − | 0.976895i | \(-0.431442\pi\) | ||||
0.213719 | + | 0.976895i | \(0.431442\pi\) | |||||||
\(810\) | −6647.43 | −0.288354 | ||||||||
\(811\) | −28928.9 | −1.25257 | −0.626283 | − | 0.779595i | \(-0.715425\pi\) | ||||
−0.626283 | + | 0.779595i | \(0.715425\pi\) | |||||||
\(812\) | 14961.3 | 0.646597 | ||||||||
\(813\) | 58365.3 | 2.51779 | ||||||||
\(814\) | −4906.82 | −0.211283 | ||||||||
\(815\) | −7958.20 | −0.342041 | ||||||||
\(816\) | −13394.7 | −0.574642 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −34809.4 | −1.48787 | ||||||||
\(819\) | 83370.4 | 3.55702 | ||||||||
\(820\) | −5174.06 | −0.220349 | ||||||||
\(821\) | −7886.08 | −0.335233 | −0.167616 | − | 0.985852i | \(-0.553607\pi\) | ||||
−0.167616 | + | 0.985852i | \(0.553607\pi\) | |||||||
\(822\) | 63261.9 | 2.68432 | ||||||||
\(823\) | 8877.58 | 0.376006 | 0.188003 | − | 0.982168i | \(-0.439799\pi\) | ||||
0.188003 | + | 0.982168i | \(0.439799\pi\) | |||||||
\(824\) | 3698.20 | 0.156351 | ||||||||
\(825\) | −12036.6 | −0.507953 | ||||||||
\(826\) | −19938.5 | −0.839888 | ||||||||
\(827\) | 14776.4 | 0.621312 | 0.310656 | − | 0.950522i | \(-0.399451\pi\) | ||||
0.310656 | + | 0.950522i | \(0.399451\pi\) | |||||||
\(828\) | 23779.4 | 0.998057 | ||||||||
\(829\) | −40753.4 | −1.70739 | −0.853695 | − | 0.520774i | \(-0.825643\pi\) | ||||
−0.853695 | + | 0.520774i | \(0.825643\pi\) | |||||||
\(830\) | −15933.8 | −0.666349 | ||||||||
\(831\) | 5852.26 | 0.244299 | ||||||||
\(832\) | 11907.3 | 0.496166 | ||||||||
\(833\) | 9888.05 | 0.411285 | ||||||||
\(834\) | −58883.3 | −2.44480 | ||||||||
\(835\) | 32011.5 | 1.32671 | ||||||||
\(836\) | 7909.93 | 0.327238 | ||||||||
\(837\) | 1880.43 | 0.0776551 | ||||||||
\(838\) | −19396.6 | −0.799577 | ||||||||
\(839\) | 32492.3 | 1.33702 | 0.668509 | − | 0.743704i | \(-0.266933\pi\) | ||||
0.668509 | + | 0.743704i | \(0.266933\pi\) | |||||||
\(840\) | 25956.4 | 1.06617 | ||||||||
\(841\) | −15537.2 | −0.637058 | ||||||||
\(842\) | −2611.46 | −0.106885 | ||||||||
\(843\) | 70189.4 | 2.86768 | ||||||||
\(844\) | 28549.5 | 1.16435 | ||||||||
\(845\) | 34868.0 | 1.41952 | ||||||||
\(846\) | −842.938 | −0.0342563 | ||||||||
\(847\) | −51074.4 | −2.07194 | ||||||||
\(848\) | −48246.3 | −1.95375 | ||||||||
\(849\) | −6712.11 | −0.271330 | ||||||||
\(850\) | 2012.23 | 0.0811988 | ||||||||
\(851\) | 2475.20 | 0.0997048 | ||||||||
\(852\) | −29624.3 | −1.19121 | ||||||||
\(853\) | 9047.76 | 0.363176 | 0.181588 | − | 0.983375i | \(-0.441876\pi\) | ||||
0.181588 | + | 0.983375i | \(0.441876\pi\) | |||||||
\(854\) | −39060.2 | −1.56512 | ||||||||
\(855\) | −12864.6 | −0.514573 | ||||||||
\(856\) | −428.671 | −0.0171164 | ||||||||
\(857\) | 5782.99 | 0.230505 | 0.115253 | − | 0.993336i | \(-0.463232\pi\) | ||||
0.115253 | + | 0.993336i | \(0.463232\pi\) | |||||||
\(858\) | 120495. | 4.79445 | ||||||||
\(859\) | −46957.7 | −1.86516 | −0.932582 | − | 0.360959i | \(-0.882450\pi\) | ||||
−0.932582 | + | 0.360959i | \(0.882450\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 17820.1 | 0.705349 | ||||||||
\(862\) | 46157.1 | 1.82380 | ||||||||
\(863\) | −35843.8 | −1.41383 | −0.706915 | − | 0.707298i | \(-0.749914\pi\) | ||||
−0.706915 | + | 0.707298i | \(0.749914\pi\) | |||||||
\(864\) | −24991.2 | −0.984047 | ||||||||
\(865\) | 24204.6 | 0.951424 | ||||||||
\(866\) | −50217.5 | −1.97051 | ||||||||
\(867\) | −36943.1 | −1.44712 | ||||||||
\(868\) | −2560.18 | −0.100113 | ||||||||
\(869\) | 62023.1 | 2.42116 | ||||||||
\(870\) | −35168.1 | −1.37047 | ||||||||
\(871\) | 44047.2 | 1.71353 | ||||||||
\(872\) | −6134.58 | −0.238237 | ||||||||
\(873\) | 48694.4 | 1.88781 | ||||||||
\(874\) | −9722.55 | −0.376282 | ||||||||
\(875\) | 34716.2 | 1.34128 | ||||||||
\(876\) | −22473.7 | −0.866800 | ||||||||
\(877\) | −10540.2 | −0.405837 | −0.202918 | − | 0.979196i | \(-0.565043\pi\) | ||||
−0.202918 | + | 0.979196i | \(0.565043\pi\) | |||||||
\(878\) | −62025.7 | −2.38413 | ||||||||
\(879\) | −39307.2 | −1.50830 | ||||||||
\(880\) | 53236.2 | 2.03931 | ||||||||
\(881\) | 9958.34 | 0.380823 | 0.190411 | − | 0.981704i | \(-0.439018\pi\) | ||||
0.190411 | + | 0.981704i | \(0.439018\pi\) | |||||||
\(882\) | 71622.9 | 2.73432 | ||||||||
\(883\) | −4226.86 | −0.161093 | −0.0805465 | − | 0.996751i | \(-0.525667\pi\) | ||||
−0.0805465 | + | 0.996751i | \(0.525667\pi\) | |||||||
\(884\) | −8266.95 | −0.314533 | ||||||||
\(885\) | 19234.2 | 0.730567 | ||||||||
\(886\) | −29369.6 | −1.11365 | ||||||||
\(887\) | −28768.5 | −1.08901 | −0.544504 | − | 0.838758i | \(-0.683282\pi\) | ||||
−0.544504 | + | 0.838758i | \(0.683282\pi\) | |||||||
\(888\) | −1763.51 | −0.0666437 | ||||||||
\(889\) | 54156.0 | 2.04312 | ||||||||
\(890\) | 19454.4 | 0.732711 | ||||||||
\(891\) | 8199.54 | 0.308300 | ||||||||
\(892\) | 3105.69 | 0.116576 | ||||||||
\(893\) | 141.442 | 0.00530030 | ||||||||
\(894\) | −14857.6 | −0.555829 | ||||||||
\(895\) | 16315.1 | 0.609333 | ||||||||
\(896\) | −31228.2 | −1.16435 | ||||||||
\(897\) | −60782.6 | −2.26251 | ||||||||
\(898\) | 916.559 | 0.0340601 | ||||||||
\(899\) | −1514.72 | −0.0561945 | ||||||||
\(900\) | 5981.66 | 0.221543 | ||||||||
\(901\) | 13020.1 | 0.481424 | ||||||||
\(902\) | 15551.2 | 0.574057 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4508.08 | −0.165859 | ||||||||
\(905\) | −30788.0 | −1.13086 | ||||||||
\(906\) | 100186. | 3.67380 | ||||||||
\(907\) | −17393.0 | −0.636742 | −0.318371 | − | 0.947966i | \(-0.603136\pi\) | ||||
−0.318371 | + | 0.947966i | \(0.603136\pi\) | |||||||
\(908\) | −16696.5 | −0.610234 | ||||||||
\(909\) | −81909.7 | −2.98875 | ||||||||
\(910\) | 91740.7 | 3.34195 | ||||||||
\(911\) | 24542.3 | 0.892560 | 0.446280 | − | 0.894893i | \(-0.352749\pi\) | ||||
0.446280 | + | 0.894893i | \(0.352749\pi\) | |||||||
\(912\) | 16280.0 | 0.591103 | ||||||||
\(913\) | 19654.2 | 0.712440 | ||||||||
\(914\) | −68227.7 | −2.46911 | ||||||||
\(915\) | 37680.6 | 1.36140 | ||||||||
\(916\) | 5269.69 | 0.190082 | ||||||||
\(917\) | −1649.68 | −0.0594080 | ||||||||
\(918\) | 9002.90 | 0.323682 | ||||||||
\(919\) | 47170.9 | 1.69317 | 0.846586 | − | 0.532252i | \(-0.178654\pi\) | ||||
0.846586 | + | 0.532252i | \(0.178654\pi\) | |||||||
\(920\) | −11426.4 | −0.409476 | ||||||||
\(921\) | −66802.5 | −2.39003 | ||||||||
\(922\) | 11496.3 | 0.410640 | ||||||||
\(923\) | 45722.0 | 1.63051 | ||||||||
\(924\) | 73319.7 | 2.61044 | ||||||||
\(925\) | 622.632 | 0.0221319 | ||||||||
\(926\) | 9735.58 | 0.345498 | ||||||||
\(927\) | −16989.9 | −0.601964 | ||||||||
\(928\) | 20130.8 | 0.712098 | ||||||||
\(929\) | 42375.1 | 1.49654 | 0.748268 | − | 0.663397i | \(-0.230886\pi\) | ||||
0.748268 | + | 0.663397i | \(0.230886\pi\) | |||||||
\(930\) | 6017.98 | 0.212191 | ||||||||
\(931\) | −12018.0 | −0.423067 | ||||||||
\(932\) | 5529.43 | 0.194338 | ||||||||
\(933\) | 17286.3 | 0.606568 | ||||||||
\(934\) | 53941.6 | 1.88975 | ||||||||
\(935\) | −14366.8 | −0.502506 | ||||||||
\(936\) | 26148.4 | 0.913129 | ||||||||
\(937\) | 2978.79 | 0.103856 | 0.0519278 | − | 0.998651i | \(-0.483463\pi\) | ||||
0.0519278 | + | 0.998651i | \(0.483463\pi\) | |||||||
\(938\) | 65308.1 | 2.27333 | ||||||||
\(939\) | −47336.2 | −1.64511 | ||||||||
\(940\) | −380.670 | −0.0132086 | ||||||||
\(941\) | 18777.6 | 0.650511 | 0.325255 | − | 0.945626i | \(-0.394550\pi\) | ||||
0.325255 | + | 0.945626i | \(0.394550\pi\) | |||||||
\(942\) | 17063.1 | 0.590176 | ||||||||
\(943\) | −7844.67 | −0.270899 | ||||||||
\(944\) | −14697.1 | −0.506727 | ||||||||
\(945\) | −41001.7 | −1.41141 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 53490.4 | 1.83548 | 0.917742 | − | 0.397177i | \(-0.130010\pi\) | ||||
0.917742 | + | 0.397177i | \(0.130010\pi\) | |||||||
\(948\) | −51047.2 | −1.74888 | ||||||||
\(949\) | 34685.8 | 1.18646 | ||||||||
\(950\) | −2445.69 | −0.0835249 | ||||||||
\(951\) | −78835.0 | −2.68812 | ||||||||
\(952\) | 5352.46 | 0.182221 | ||||||||
\(953\) | 2203.86 | 0.0749108 | 0.0374554 | − | 0.999298i | \(-0.488075\pi\) | ||||
0.0374554 | + | 0.999298i | \(0.488075\pi\) | |||||||
\(954\) | 94309.7 | 3.20062 | ||||||||
\(955\) | −19799.2 | −0.670877 | ||||||||
\(956\) | −13475.3 | −0.455882 | ||||||||
\(957\) | 43379.5 | 1.46527 | ||||||||
\(958\) | 59058.5 | 1.99175 | ||||||||
\(959\) | −59411.5 | −2.00052 | ||||||||
\(960\) | −17031.2 | −0.572582 | ||||||||
\(961\) | −29531.8 | −0.991299 | ||||||||
\(962\) | −6232.98 | −0.208898 | ||||||||
\(963\) | 1969.35 | 0.0658998 | ||||||||
\(964\) | −323.011 | −0.0107920 | ||||||||
\(965\) | −43596.5 | −1.45432 | ||||||||
\(966\) | −90121.6 | −3.00167 | ||||||||
\(967\) | −13488.8 | −0.448572 | −0.224286 | − | 0.974523i | \(-0.572005\pi\) | ||||
−0.224286 | + | 0.974523i | \(0.572005\pi\) | |||||||
\(968\) | −16019.1 | −0.531893 | ||||||||
\(969\) | −4393.46 | −0.145654 | ||||||||
\(970\) | 53583.3 | 1.77367 | ||||||||
\(971\) | 11027.9 | 0.364473 | 0.182237 | − | 0.983255i | \(-0.441666\pi\) | ||||
0.182237 | + | 0.983255i | \(0.441666\pi\) | |||||||
\(972\) | −24308.9 | −0.802171 | ||||||||
\(973\) | 55299.4 | 1.82201 | ||||||||
\(974\) | −58836.4 | −1.93556 | ||||||||
\(975\) | −15289.8 | −0.502219 | ||||||||
\(976\) | −28792.2 | −0.944279 | ||||||||
\(977\) | 4624.99 | 0.151450 | 0.0757250 | − | 0.997129i | \(-0.475873\pi\) | ||||
0.0757250 | + | 0.997129i | \(0.475873\pi\) | |||||||
\(978\) | −19686.4 | −0.643663 | ||||||||
\(979\) | −23996.8 | −0.783392 | ||||||||
\(980\) | 32344.8 | 1.05430 | ||||||||
\(981\) | 28182.8 | 0.917235 | ||||||||
\(982\) | −50575.2 | −1.64350 | ||||||||
\(983\) | 34064.0 | 1.10526 | 0.552631 | − | 0.833426i | \(-0.313624\pi\) | ||||
0.552631 | + | 0.833426i | \(0.313624\pi\) | |||||||
\(984\) | 5589.12 | 0.181072 | ||||||||
\(985\) | 35190.6 | 1.13834 | ||||||||
\(986\) | −7252.01 | −0.234230 | ||||||||
\(987\) | 1311.07 | 0.0422815 | ||||||||
\(988\) | 10047.7 | 0.323544 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −104064. | −3.34077 | ||||||||
\(991\) | 16168.7 | 0.518280 | 0.259140 | − | 0.965840i | \(-0.416561\pi\) | ||||
0.259140 | + | 0.965840i | \(0.416561\pi\) | |||||||
\(992\) | −3444.80 | −0.110254 | ||||||||
\(993\) | 10145.4 | 0.324224 | ||||||||
\(994\) | 67791.3 | 2.16319 | ||||||||
\(995\) | −21836.0 | −0.695727 | ||||||||
\(996\) | −16176.1 | −0.514617 | ||||||||
\(997\) | −25391.2 | −0.806568 | −0.403284 | − | 0.915075i | \(-0.632131\pi\) | ||||
−0.403284 | + | 0.915075i | \(0.632131\pi\) | |||||||
\(998\) | 57222.4 | 1.81497 | ||||||||
\(999\) | 2785.71 | 0.0882241 |
(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 | 1849.4.a.g.1.24 | 30 | ||
43.2 | odd | 14 | 43.4.e.a.4.3 | ✓ | 60 | ||
43.22 | odd | 14 | 43.4.e.a.11.3 | yes | 60 | ||
43.42 | odd | 2 | 1849.4.a.h.1.7 | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.4.e.a.4.3 | ✓ | 60 | 43.2 | odd | 14 | ||
43.4.e.a.11.3 | yes | 60 | 43.22 | odd | 14 | ||
1849.4.a.g.1.24 | 30 | 1.1 | even | 1 | trivial | ||
1849.4.a.h.1.7 | 30 | 43.42 | odd | 2 |