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: | \(60\) |
Twist minimal: | no (minimal twist has level 43) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.40707 | −1.55813 | −0.779067 | − | 0.626941i | \(-0.784307\pi\) | ||||
−0.779067 | + | 0.626941i | \(0.784307\pi\) | |||||||
\(3\) | −0.148254 | −0.0285314 | −0.0142657 | − | 0.999898i | \(-0.504541\pi\) | ||||
−0.0142657 | + | 0.999898i | \(0.504541\pi\) | |||||||
\(4\) | 11.4223 | 1.42778 | ||||||||
\(5\) | 15.4121 | 1.37850 | 0.689250 | − | 0.724523i | \(-0.257940\pi\) | ||||
0.689250 | + | 0.724523i | \(0.257940\pi\) | |||||||
\(6\) | 0.653363 | 0.0444558 | ||||||||
\(7\) | 27.6883 | 1.49503 | 0.747515 | − | 0.664245i | \(-0.231247\pi\) | ||||
0.747515 | + | 0.664245i | \(0.231247\pi\) | |||||||
\(8\) | −15.0821 | −0.666541 | ||||||||
\(9\) | −26.9780 | −0.999186 | ||||||||
\(10\) | −67.9222 | −2.14789 | ||||||||
\(11\) | −49.2082 | −1.34880 | −0.674401 | − | 0.738365i | \(-0.735598\pi\) | ||||
−0.674401 | + | 0.738365i | \(0.735598\pi\) | |||||||
\(12\) | −1.69339 | −0.0407366 | ||||||||
\(13\) | 14.7161 | 0.313962 | 0.156981 | − | 0.987602i | \(-0.449824\pi\) | ||||
0.156981 | + | 0.987602i | \(0.449824\pi\) | |||||||
\(14\) | −122.024 | −2.32946 | ||||||||
\(15\) | −2.28490 | −0.0393306 | ||||||||
\(16\) | −24.9102 | −0.389222 | ||||||||
\(17\) | −20.0795 | −0.286471 | −0.143235 | − | 0.989689i | \(-0.545751\pi\) | ||||
−0.143235 | + | 0.989689i | \(0.545751\pi\) | |||||||
\(18\) | 118.894 | 1.55687 | ||||||||
\(19\) | −125.091 | −1.51042 | −0.755208 | − | 0.655485i | \(-0.772464\pi\) | ||||
−0.755208 | + | 0.655485i | \(0.772464\pi\) | |||||||
\(20\) | 176.041 | 1.96820 | ||||||||
\(21\) | −4.10489 | −0.0426553 | ||||||||
\(22\) | 216.864 | 2.10162 | ||||||||
\(23\) | 148.291 | 1.34439 | 0.672193 | − | 0.740376i | \(-0.265353\pi\) | ||||
0.672193 | + | 0.740376i | \(0.265353\pi\) | |||||||
\(24\) | 2.23597 | 0.0190173 | ||||||||
\(25\) | 112.533 | 0.900264 | ||||||||
\(26\) | −64.8548 | −0.489195 | ||||||||
\(27\) | 8.00243 | 0.0570396 | ||||||||
\(28\) | 316.263 | 2.13458 | ||||||||
\(29\) | 152.891 | 0.979005 | 0.489503 | − | 0.872002i | \(-0.337178\pi\) | ||||
0.489503 | + | 0.872002i | \(0.337178\pi\) | |||||||
\(30\) | 10.0697 | 0.0612823 | ||||||||
\(31\) | −7.42094 | −0.0429948 | −0.0214974 | − | 0.999769i | \(-0.506843\pi\) | ||||
−0.0214974 | + | 0.999769i | \(0.506843\pi\) | |||||||
\(32\) | 230.438 | 1.27300 | ||||||||
\(33\) | 7.29529 | 0.0384832 | ||||||||
\(34\) | 88.4919 | 0.446360 | ||||||||
\(35\) | 426.736 | 2.06090 | ||||||||
\(36\) | −308.150 | −1.42662 | ||||||||
\(37\) | −209.184 | −0.929450 | −0.464725 | − | 0.885455i | \(-0.653847\pi\) | ||||
−0.464725 | + | 0.885455i | \(0.653847\pi\) | |||||||
\(38\) | 551.286 | 2.35343 | ||||||||
\(39\) | −2.18171 | −0.00895779 | ||||||||
\(40\) | −232.447 | −0.918827 | ||||||||
\(41\) | −136.945 | −0.521639 | −0.260819 | − | 0.965388i | \(-0.583993\pi\) | ||||
−0.260819 | + | 0.965388i | \(0.583993\pi\) | |||||||
\(42\) | 18.0905 | 0.0664627 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | −562.069 | −1.92580 | ||||||||
\(45\) | −415.788 | −1.37738 | ||||||||
\(46\) | −653.530 | −2.09473 | ||||||||
\(47\) | −18.4081 | −0.0571298 | −0.0285649 | − | 0.999592i | \(-0.509094\pi\) | ||||
−0.0285649 | + | 0.999592i | \(0.509094\pi\) | |||||||
\(48\) | 3.69302 | 0.0111050 | ||||||||
\(49\) | 423.644 | 1.23511 | ||||||||
\(50\) | −495.941 | −1.40273 | ||||||||
\(51\) | 2.97686 | 0.00817341 | ||||||||
\(52\) | 168.091 | 0.448270 | ||||||||
\(53\) | −67.1286 | −0.173978 | −0.0869889 | − | 0.996209i | \(-0.527724\pi\) | ||||
−0.0869889 | + | 0.996209i | \(0.527724\pi\) | |||||||
\(54\) | −35.2673 | −0.0888753 | ||||||||
\(55\) | −758.402 | −1.85933 | ||||||||
\(56\) | −417.598 | −0.996498 | ||||||||
\(57\) | 18.5452 | 0.0430943 | ||||||||
\(58\) | −673.801 | −1.52542 | ||||||||
\(59\) | 210.432 | 0.464338 | 0.232169 | − | 0.972675i | \(-0.425418\pi\) | ||||
0.232169 | + | 0.972675i | \(0.425418\pi\) | |||||||
\(60\) | −26.0987 | −0.0561554 | ||||||||
\(61\) | 842.655 | 1.76870 | 0.884352 | − | 0.466821i | \(-0.154601\pi\) | ||||
0.884352 | + | 0.466821i | \(0.154601\pi\) | |||||||
\(62\) | 32.7046 | 0.0669917 | ||||||||
\(63\) | −746.977 | −1.49381 | ||||||||
\(64\) | −816.273 | −1.59428 | ||||||||
\(65\) | 226.806 | 0.432797 | ||||||||
\(66\) | −32.1508 | −0.0599620 | ||||||||
\(67\) | −698.336 | −1.27336 | −0.636681 | − | 0.771127i | \(-0.719693\pi\) | ||||
−0.636681 | + | 0.771127i | \(0.719693\pi\) | |||||||
\(68\) | −229.353 | −0.409018 | ||||||||
\(69\) | −21.9847 | −0.0383572 | ||||||||
\(70\) | −1880.65 | −3.21116 | ||||||||
\(71\) | −1102.14 | −1.84225 | −0.921125 | − | 0.389266i | \(-0.872729\pi\) | ||||
−0.921125 | + | 0.389266i | \(0.872729\pi\) | |||||||
\(72\) | 406.885 | 0.665998 | ||||||||
\(73\) | −602.172 | −0.965465 | −0.482732 | − | 0.875768i | \(-0.660356\pi\) | ||||
−0.482732 | + | 0.875768i | \(0.660356\pi\) | |||||||
\(74\) | 921.888 | 1.44821 | ||||||||
\(75\) | −16.6834 | −0.0256858 | ||||||||
\(76\) | −1428.82 | −2.15654 | ||||||||
\(77\) | −1362.49 | −2.01650 | ||||||||
\(78\) | 9.61496 | 0.0139574 | ||||||||
\(79\) | 353.014 | 0.502748 | 0.251374 | − | 0.967890i | \(-0.419118\pi\) | ||||
0.251374 | + | 0.967890i | \(0.419118\pi\) | |||||||
\(80\) | −383.918 | −0.536542 | ||||||||
\(81\) | 727.220 | 0.997559 | ||||||||
\(82\) | 603.525 | 0.812783 | ||||||||
\(83\) | −907.095 | −1.19960 | −0.599799 | − | 0.800151i | \(-0.704753\pi\) | ||||
−0.599799 | + | 0.800151i | \(0.704753\pi\) | |||||||
\(84\) | −46.8871 | −0.0609024 | ||||||||
\(85\) | −309.468 | −0.394900 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −22.6666 | −0.0279324 | ||||||||
\(88\) | 742.163 | 0.899032 | ||||||||
\(89\) | 389.331 | 0.463697 | 0.231848 | − | 0.972752i | \(-0.425523\pi\) | ||||
0.231848 | + | 0.972752i | \(0.425523\pi\) | |||||||
\(90\) | 1832.41 | 2.14614 | ||||||||
\(91\) | 407.464 | 0.469383 | ||||||||
\(92\) | 1693.82 | 1.91949 | ||||||||
\(93\) | 1.10018 | 0.00122670 | ||||||||
\(94\) | 81.1258 | 0.0890158 | ||||||||
\(95\) | −1927.92 | −2.08211 | ||||||||
\(96\) | −34.1632 | −0.0363205 | ||||||||
\(97\) | 1796.17 | 1.88014 | 0.940069 | − | 0.340984i | \(-0.110760\pi\) | ||||
0.940069 | + | 0.340984i | \(0.110760\pi\) | |||||||
\(98\) | −1867.03 | −1.92447 | ||||||||
\(99\) | 1327.54 | 1.34770 | ||||||||
\(100\) | 1285.38 | 1.28538 | ||||||||
\(101\) | 95.9143 | 0.0944934 | 0.0472467 | − | 0.998883i | \(-0.484955\pi\) | ||||
0.0472467 | + | 0.998883i | \(0.484955\pi\) | |||||||
\(102\) | −13.1192 | −0.0127353 | ||||||||
\(103\) | −982.689 | −0.940070 | −0.470035 | − | 0.882648i | \(-0.655759\pi\) | ||||
−0.470035 | + | 0.882648i | \(0.655759\pi\) | |||||||
\(104\) | −221.950 | −0.209269 | ||||||||
\(105\) | −63.2651 | −0.0588004 | ||||||||
\(106\) | 295.840 | 0.271081 | ||||||||
\(107\) | −415.959 | −0.375816 | −0.187908 | − | 0.982187i | \(-0.560171\pi\) | ||||
−0.187908 | + | 0.982187i | \(0.560171\pi\) | |||||||
\(108\) | 91.4058 | 0.0814401 | ||||||||
\(109\) | −47.6757 | −0.0418946 | −0.0209473 | − | 0.999781i | \(-0.506668\pi\) | ||||
−0.0209473 | + | 0.999781i | \(0.506668\pi\) | |||||||
\(110\) | 3342.33 | 2.89708 | ||||||||
\(111\) | 31.0123 | 0.0265185 | ||||||||
\(112\) | −689.721 | −0.581898 | ||||||||
\(113\) | −1385.15 | −1.15313 | −0.576566 | − | 0.817051i | \(-0.695608\pi\) | ||||
−0.576566 | + | 0.817051i | \(0.695608\pi\) | |||||||
\(114\) | −81.7300 | −0.0671467 | ||||||||
\(115\) | 2285.48 | 1.85324 | ||||||||
\(116\) | 1746.36 | 1.39781 | ||||||||
\(117\) | −397.011 | −0.313707 | ||||||||
\(118\) | −927.389 | −0.723501 | ||||||||
\(119\) | −555.969 | −0.428282 | ||||||||
\(120\) | 34.4611 | 0.0262154 | ||||||||
\(121\) | 1090.45 | 0.819269 | ||||||||
\(122\) | −3713.64 | −2.75588 | ||||||||
\(123\) | 20.3026 | 0.0148831 | ||||||||
\(124\) | −84.7638 | −0.0613872 | ||||||||
\(125\) | −192.143 | −0.137486 | ||||||||
\(126\) | 3291.98 | 2.32756 | ||||||||
\(127\) | 57.3111 | 0.0400436 | 0.0200218 | − | 0.999800i | \(-0.493626\pi\) | ||||
0.0200218 | + | 0.999800i | \(0.493626\pi\) | |||||||
\(128\) | 1753.87 | 1.21111 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −999.550 | −0.674356 | ||||||||
\(131\) | 1651.64 | 1.10156 | 0.550782 | − | 0.834649i | \(-0.314330\pi\) | ||||
0.550782 | + | 0.834649i | \(0.314330\pi\) | |||||||
\(132\) | 83.3286 | 0.0549457 | ||||||||
\(133\) | −3463.57 | −2.25812 | ||||||||
\(134\) | 3077.61 | 1.98407 | ||||||||
\(135\) | 123.334 | 0.0786291 | ||||||||
\(136\) | 302.841 | 0.190944 | ||||||||
\(137\) | −1757.57 | −1.09605 | −0.548027 | − | 0.836461i | \(-0.684621\pi\) | ||||
−0.548027 | + | 0.836461i | \(0.684621\pi\) | |||||||
\(138\) | 96.8881 | 0.0597657 | ||||||||
\(139\) | −1440.14 | −0.878785 | −0.439393 | − | 0.898295i | \(-0.644806\pi\) | ||||
−0.439393 | + | 0.898295i | \(0.644806\pi\) | |||||||
\(140\) | 4874.28 | 2.94251 | ||||||||
\(141\) | 2.72907 | 0.00162999 | ||||||||
\(142\) | 4857.20 | 2.87047 | ||||||||
\(143\) | −724.153 | −0.423473 | ||||||||
\(144\) | 672.027 | 0.388905 | ||||||||
\(145\) | 2356.37 | 1.34956 | ||||||||
\(146\) | 2653.81 | 1.50432 | ||||||||
\(147\) | −62.8067 | −0.0352395 | ||||||||
\(148\) | −2389.35 | −1.32705 | ||||||||
\(149\) | −3154.30 | −1.73430 | −0.867148 | − | 0.498051i | \(-0.834049\pi\) | ||||
−0.867148 | + | 0.498051i | \(0.834049\pi\) | |||||||
\(150\) | 73.5249 | 0.0400219 | ||||||||
\(151\) | 494.931 | 0.266735 | 0.133367 | − | 0.991067i | \(-0.457421\pi\) | ||||
0.133367 | + | 0.991067i | \(0.457421\pi\) | |||||||
\(152\) | 1886.64 | 1.00675 | ||||||||
\(153\) | 541.706 | 0.286237 | ||||||||
\(154\) | 6004.60 | 3.14198 | ||||||||
\(155\) | −114.372 | −0.0592684 | ||||||||
\(156\) | −24.9201 | −0.0127898 | ||||||||
\(157\) | 483.013 | 0.245533 | 0.122766 | − | 0.992436i | \(-0.460823\pi\) | ||||
0.122766 | + | 0.992436i | \(0.460823\pi\) | |||||||
\(158\) | −1555.75 | −0.783349 | ||||||||
\(159\) | 9.95205 | 0.00496383 | ||||||||
\(160\) | 3551.53 | 1.75483 | ||||||||
\(161\) | 4105.94 | 2.00990 | ||||||||
\(162\) | −3204.91 | −1.55433 | ||||||||
\(163\) | 3585.81 | 1.72308 | 0.861540 | − | 0.507690i | \(-0.169500\pi\) | ||||
0.861540 | + | 0.507690i | \(0.169500\pi\) | |||||||
\(164\) | −1564.22 | −0.744786 | ||||||||
\(165\) | 112.436 | 0.0530492 | ||||||||
\(166\) | 3997.63 | 1.86913 | ||||||||
\(167\) | −286.311 | −0.132667 | −0.0663336 | − | 0.997797i | \(-0.521130\pi\) | ||||
−0.0663336 | + | 0.997797i | \(0.521130\pi\) | |||||||
\(168\) | 61.9104 | 0.0284315 | ||||||||
\(169\) | −1980.44 | −0.901428 | ||||||||
\(170\) | 1363.85 | 0.615307 | ||||||||
\(171\) | 3374.71 | 1.50919 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2073.21 | −0.911118 | −0.455559 | − | 0.890206i | \(-0.650561\pi\) | ||||
−0.455559 | + | 0.890206i | \(0.650561\pi\) | |||||||
\(174\) | 99.8934 | 0.0435224 | ||||||||
\(175\) | 3115.85 | 1.34592 | ||||||||
\(176\) | 1225.79 | 0.524983 | ||||||||
\(177\) | −31.1973 | −0.0132482 | ||||||||
\(178\) | −1715.81 | −0.722501 | ||||||||
\(179\) | −662.622 | −0.276685 | −0.138343 | − | 0.990384i | \(-0.544178\pi\) | ||||
−0.138343 | + | 0.990384i | \(0.544178\pi\) | |||||||
\(180\) | −4749.24 | −1.96660 | ||||||||
\(181\) | −3001.11 | −1.23243 | −0.616217 | − | 0.787576i | \(-0.711336\pi\) | ||||
−0.616217 | + | 0.787576i | \(0.711336\pi\) | |||||||
\(182\) | −1795.72 | −0.731362 | ||||||||
\(183\) | −124.927 | −0.0504636 | ||||||||
\(184\) | −2236.54 | −0.896088 | ||||||||
\(185\) | −3223.97 | −1.28125 | ||||||||
\(186\) | −4.84857 | −0.00191137 | ||||||||
\(187\) | 988.078 | 0.386392 | ||||||||
\(188\) | −210.262 | −0.0815688 | ||||||||
\(189\) | 221.574 | 0.0852759 | ||||||||
\(190\) | 8496.47 | 3.24420 | ||||||||
\(191\) | −3214.18 | −1.21764 | −0.608822 | − | 0.793307i | \(-0.708357\pi\) | ||||
−0.608822 | + | 0.793307i | \(0.708357\pi\) | |||||||
\(192\) | 121.015 | 0.0454871 | ||||||||
\(193\) | 2252.15 | 0.839966 | 0.419983 | − | 0.907532i | \(-0.362036\pi\) | ||||
0.419983 | + | 0.907532i | \(0.362036\pi\) | |||||||
\(194\) | −7915.84 | −2.92951 | ||||||||
\(195\) | −33.6248 | −0.0123483 | ||||||||
\(196\) | 4838.97 | 1.76347 | ||||||||
\(197\) | −1231.52 | −0.445393 | −0.222696 | − | 0.974888i | \(-0.571486\pi\) | ||||
−0.222696 | + | 0.974888i | \(0.571486\pi\) | |||||||
\(198\) | −5850.56 | −2.09990 | ||||||||
\(199\) | 1251.30 | 0.445740 | 0.222870 | − | 0.974848i | \(-0.428457\pi\) | ||||
0.222870 | + | 0.974848i | \(0.428457\pi\) | |||||||
\(200\) | −1697.23 | −0.600063 | ||||||||
\(201\) | 103.531 | 0.0363308 | ||||||||
\(202\) | −422.701 | −0.147233 | ||||||||
\(203\) | 4233.30 | 1.46364 | ||||||||
\(204\) | 34.0025 | 0.0116698 | ||||||||
\(205\) | −2110.61 | −0.719079 | ||||||||
\(206\) | 4330.78 | 1.46476 | ||||||||
\(207\) | −4000.61 | −1.34329 | ||||||||
\(208\) | −366.581 | −0.122201 | ||||||||
\(209\) | 6155.52 | 2.03725 | ||||||||
\(210\) | 278.813 | 0.0916188 | ||||||||
\(211\) | −2574.37 | −0.839938 | −0.419969 | − | 0.907538i | \(-0.637959\pi\) | ||||
−0.419969 | + | 0.907538i | \(0.637959\pi\) | |||||||
\(212\) | −766.759 | −0.248402 | ||||||||
\(213\) | 163.396 | 0.0525620 | ||||||||
\(214\) | 1833.16 | 0.585572 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −120.693 | −0.0380192 | ||||||||
\(217\) | −205.473 | −0.0642785 | ||||||||
\(218\) | 210.110 | 0.0652773 | ||||||||
\(219\) | 89.2742 | 0.0275461 | ||||||||
\(220\) | −8662.66 | −2.65471 | ||||||||
\(221\) | −295.492 | −0.0899410 | ||||||||
\(222\) | −136.673 | −0.0413194 | ||||||||
\(223\) | −324.499 | −0.0974443 | −0.0487221 | − | 0.998812i | \(-0.515515\pi\) | ||||
−0.0487221 | + | 0.998812i | \(0.515515\pi\) | |||||||
\(224\) | 6380.44 | 1.90317 | ||||||||
\(225\) | −3035.92 | −0.899531 | ||||||||
\(226\) | 6104.45 | 1.79673 | ||||||||
\(227\) | −2741.93 | −0.801710 | −0.400855 | − | 0.916142i | \(-0.631287\pi\) | ||||
−0.400855 | + | 0.916142i | \(0.631287\pi\) | |||||||
\(228\) | 211.828 | 0.0615292 | ||||||||
\(229\) | 995.241 | 0.287194 | 0.143597 | − | 0.989636i | \(-0.454133\pi\) | ||||
0.143597 | + | 0.989636i | \(0.454133\pi\) | |||||||
\(230\) | −10072.3 | −2.88759 | ||||||||
\(231\) | 201.994 | 0.0575336 | ||||||||
\(232\) | −2305.92 | −0.652547 | ||||||||
\(233\) | −2034.51 | −0.572041 | −0.286020 | − | 0.958224i | \(-0.592332\pi\) | ||||
−0.286020 | + | 0.958224i | \(0.592332\pi\) | |||||||
\(234\) | 1749.66 | 0.488797 | ||||||||
\(235\) | −283.708 | −0.0787534 | ||||||||
\(236\) | 2403.61 | 0.662973 | ||||||||
\(237\) | −52.3355 | −0.0143441 | ||||||||
\(238\) | 2450.19 | 0.667321 | ||||||||
\(239\) | 2343.82 | 0.634348 | 0.317174 | − | 0.948367i | \(-0.397266\pi\) | ||||
0.317174 | + | 0.948367i | \(0.397266\pi\) | |||||||
\(240\) | 56.9172 | 0.0153083 | ||||||||
\(241\) | 2300.34 | 0.614847 | 0.307423 | − | 0.951573i | \(-0.400533\pi\) | ||||
0.307423 | + | 0.951573i | \(0.400533\pi\) | |||||||
\(242\) | −4805.68 | −1.27653 | ||||||||
\(243\) | −323.879 | −0.0855013 | ||||||||
\(244\) | 9625.02 | 2.52532 | ||||||||
\(245\) | 6529.25 | 1.70261 | ||||||||
\(246\) | −89.4747 | −0.0231898 | ||||||||
\(247\) | −1840.85 | −0.474214 | ||||||||
\(248\) | 111.923 | 0.0286578 | ||||||||
\(249\) | 134.480 | 0.0342262 | ||||||||
\(250\) | 846.786 | 0.214222 | ||||||||
\(251\) | 2168.50 | 0.545316 | 0.272658 | − | 0.962111i | \(-0.412097\pi\) | ||||
0.272658 | + | 0.962111i | \(0.412097\pi\) | |||||||
\(252\) | −8532.15 | −2.13284 | ||||||||
\(253\) | −7297.15 | −1.81331 | ||||||||
\(254\) | −252.574 | −0.0623933 | ||||||||
\(255\) | 45.8797 | 0.0112671 | ||||||||
\(256\) | −1199.24 | −0.292783 | ||||||||
\(257\) | −7909.72 | −1.91982 | −0.959912 | − | 0.280302i | \(-0.909565\pi\) | ||||
−0.959912 | + | 0.280302i | \(0.909565\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5791.96 | −1.38956 | ||||||||
\(260\) | 2590.64 | 0.617940 | ||||||||
\(261\) | −4124.70 | −0.978208 | ||||||||
\(262\) | −7278.91 | −1.71638 | ||||||||
\(263\) | −96.5256 | −0.0226313 | −0.0113156 | − | 0.999936i | \(-0.503602\pi\) | ||||
−0.0113156 | + | 0.999936i | \(0.503602\pi\) | |||||||
\(264\) | −110.028 | −0.0256507 | ||||||||
\(265\) | −1034.59 | −0.239828 | ||||||||
\(266\) | 15264.2 | 3.51845 | ||||||||
\(267\) | −57.7197 | −0.0132299 | ||||||||
\(268\) | −7976.56 | −1.81808 | ||||||||
\(269\) | 4568.99 | 1.03560 | 0.517800 | − | 0.855502i | \(-0.326751\pi\) | ||||
0.517800 | + | 0.855502i | \(0.326751\pi\) | |||||||
\(270\) | −543.543 | −0.122515 | ||||||||
\(271\) | −4983.94 | −1.11717 | −0.558584 | − | 0.829448i | \(-0.688655\pi\) | ||||
−0.558584 | + | 0.829448i | \(0.688655\pi\) | |||||||
\(272\) | 500.185 | 0.111501 | ||||||||
\(273\) | −60.4080 | −0.0133922 | ||||||||
\(274\) | 7745.74 | 1.70780 | ||||||||
\(275\) | −5537.55 | −1.21428 | ||||||||
\(276\) | −251.115 | −0.0547657 | ||||||||
\(277\) | 4752.99 | 1.03097 | 0.515487 | − | 0.856898i | \(-0.327611\pi\) | ||||
0.515487 | + | 0.856898i | \(0.327611\pi\) | |||||||
\(278\) | 6346.80 | 1.36927 | ||||||||
\(279\) | 200.202 | 0.0429598 | ||||||||
\(280\) | −6436.07 | −1.37367 | ||||||||
\(281\) | 736.557 | 0.156368 | 0.0781838 | − | 0.996939i | \(-0.475088\pi\) | ||||
0.0781838 | + | 0.996939i | \(0.475088\pi\) | |||||||
\(282\) | −12.0272 | −0.00253975 | ||||||||
\(283\) | −2987.95 | −0.627616 | −0.313808 | − | 0.949486i | \(-0.601605\pi\) | ||||
−0.313808 | + | 0.949486i | \(0.601605\pi\) | |||||||
\(284\) | −12588.9 | −2.63033 | ||||||||
\(285\) | 285.821 | 0.0594055 | ||||||||
\(286\) | 3191.39 | 0.659828 | ||||||||
\(287\) | −3791.77 | −0.779865 | ||||||||
\(288\) | −6216.75 | −1.27196 | ||||||||
\(289\) | −4509.81 | −0.917935 | ||||||||
\(290\) | −10384.7 | −2.10279 | ||||||||
\(291\) | −266.289 | −0.0536430 | ||||||||
\(292\) | −6878.16 | −1.37847 | ||||||||
\(293\) | −4201.98 | −0.837823 | −0.418912 | − | 0.908027i | \(-0.637588\pi\) | ||||
−0.418912 | + | 0.908027i | \(0.637588\pi\) | |||||||
\(294\) | 276.794 | 0.0549079 | ||||||||
\(295\) | 3243.20 | 0.640090 | ||||||||
\(296\) | 3154.93 | 0.619516 | ||||||||
\(297\) | −393.785 | −0.0769352 | ||||||||
\(298\) | 13901.2 | 2.70226 | ||||||||
\(299\) | 2182.27 | 0.422087 | ||||||||
\(300\) | −190.562 | −0.0366737 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −2181.19 | −0.415608 | ||||||||
\(303\) | −14.2196 | −0.00269603 | ||||||||
\(304\) | 3116.04 | 0.587886 | ||||||||
\(305\) | 12987.1 | 2.43816 | ||||||||
\(306\) | −2387.34 | −0.445996 | ||||||||
\(307\) | 9337.54 | 1.73590 | 0.867950 | − | 0.496651i | \(-0.165437\pi\) | ||||
0.867950 | + | 0.496651i | \(0.165437\pi\) | |||||||
\(308\) | −15562.7 | −2.87912 | ||||||||
\(309\) | 145.687 | 0.0268215 | ||||||||
\(310\) | 504.046 | 0.0923481 | ||||||||
\(311\) | 592.021 | 0.107943 | 0.0539717 | − | 0.998542i | \(-0.482812\pi\) | ||||
0.0539717 | + | 0.998542i | \(0.482812\pi\) | |||||||
\(312\) | 32.9048 | 0.00597073 | ||||||||
\(313\) | −1752.01 | −0.316388 | −0.158194 | − | 0.987408i | \(-0.550567\pi\) | ||||
−0.158194 | + | 0.987408i | \(0.550567\pi\) | |||||||
\(314\) | −2128.67 | −0.382573 | ||||||||
\(315\) | −11512.5 | −2.05922 | ||||||||
\(316\) | 4032.21 | 0.717815 | ||||||||
\(317\) | −7339.63 | −1.30043 | −0.650213 | − | 0.759752i | \(-0.725320\pi\) | ||||
−0.650213 | + | 0.759752i | \(0.725320\pi\) | |||||||
\(318\) | −43.8594 | −0.00773431 | ||||||||
\(319\) | −7523.49 | −1.32049 | ||||||||
\(320\) | −12580.5 | −2.19772 | ||||||||
\(321\) | 61.6674 | 0.0107226 | ||||||||
\(322\) | −18095.2 | −3.13169 | ||||||||
\(323\) | 2511.77 | 0.432690 | ||||||||
\(324\) | 8306.49 | 1.42430 | ||||||||
\(325\) | 1656.05 | 0.282649 | ||||||||
\(326\) | −15802.9 | −2.68479 | ||||||||
\(327\) | 7.06809 | 0.00119531 | ||||||||
\(328\) | 2065.42 | 0.347694 | ||||||||
\(329\) | −509.690 | −0.0854107 | ||||||||
\(330\) | −495.512 | −0.0826577 | ||||||||
\(331\) | −5741.22 | −0.953372 | −0.476686 | − | 0.879074i | \(-0.658162\pi\) | ||||
−0.476686 | + | 0.879074i | \(0.658162\pi\) | |||||||
\(332\) | −10361.1 | −1.71276 | ||||||||
\(333\) | 5643.37 | 0.928693 | ||||||||
\(334\) | 1261.79 | 0.206713 | ||||||||
\(335\) | −10762.8 | −1.75533 | ||||||||
\(336\) | 102.254 | 0.0166024 | ||||||||
\(337\) | 4523.93 | 0.731259 | 0.365629 | − | 0.930761i | \(-0.380854\pi\) | ||||
0.365629 | + | 0.930761i | \(0.380854\pi\) | |||||||
\(338\) | 8727.92 | 1.40455 | ||||||||
\(339\) | 205.353 | 0.0329005 | ||||||||
\(340\) | −3534.82 | −0.563831 | ||||||||
\(341\) | 365.171 | 0.0579915 | ||||||||
\(342\) | −14872.6 | −2.35151 | ||||||||
\(343\) | 2232.90 | 0.351502 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −338.831 | −0.0528754 | ||||||||
\(346\) | 9136.78 | 1.41964 | ||||||||
\(347\) | 1795.05 | 0.277704 | 0.138852 | − | 0.990313i | \(-0.455659\pi\) | ||||
0.138852 | + | 0.990313i | \(0.455659\pi\) | |||||||
\(348\) | −258.904 | −0.0398814 | ||||||||
\(349\) | 5427.46 | 0.832451 | 0.416225 | − | 0.909261i | \(-0.363353\pi\) | ||||
0.416225 | + | 0.909261i | \(0.363353\pi\) | |||||||
\(350\) | −13731.8 | −2.09713 | ||||||||
\(351\) | 117.765 | 0.0179083 | ||||||||
\(352\) | −11339.4 | −1.71703 | ||||||||
\(353\) | 6592.90 | 0.994064 | 0.497032 | − | 0.867732i | \(-0.334423\pi\) | ||||
0.497032 | + | 0.867732i | \(0.334423\pi\) | |||||||
\(354\) | 137.489 | 0.0206425 | ||||||||
\(355\) | −16986.3 | −2.53954 | ||||||||
\(356\) | 4447.04 | 0.662057 | ||||||||
\(357\) | 82.4243 | 0.0122195 | ||||||||
\(358\) | 2920.22 | 0.431113 | ||||||||
\(359\) | −915.664 | −0.134615 | −0.0673077 | − | 0.997732i | \(-0.521441\pi\) | ||||
−0.0673077 | + | 0.997732i | \(0.521441\pi\) | |||||||
\(360\) | 6270.96 | 0.918079 | ||||||||
\(361\) | 8788.82 | 1.28136 | ||||||||
\(362\) | 13226.1 | 1.92030 | ||||||||
\(363\) | −161.663 | −0.0233749 | ||||||||
\(364\) | 4654.16 | 0.670176 | ||||||||
\(365\) | −9280.74 | −1.33089 | ||||||||
\(366\) | 550.560 | 0.0786291 | ||||||||
\(367\) | 5689.49 | 0.809235 | 0.404617 | − | 0.914486i | \(-0.367405\pi\) | ||||
0.404617 | + | 0.914486i | \(0.367405\pi\) | |||||||
\(368\) | −3693.96 | −0.523264 | ||||||||
\(369\) | 3694.50 | 0.521214 | ||||||||
\(370\) | 14208.2 | 1.99635 | ||||||||
\(371\) | −1858.68 | −0.260102 | ||||||||
\(372\) | 12.5665 | 0.00175146 | ||||||||
\(373\) | −5695.13 | −0.790570 | −0.395285 | − | 0.918558i | \(-0.629354\pi\) | ||||
−0.395285 | + | 0.918558i | \(0.629354\pi\) | |||||||
\(374\) | −4354.53 | −0.602051 | ||||||||
\(375\) | 28.4858 | 0.00392267 | ||||||||
\(376\) | 277.633 | 0.0380793 | ||||||||
\(377\) | 2249.96 | 0.307371 | ||||||||
\(378\) | −976.492 | −0.132871 | ||||||||
\(379\) | −9058.43 | −1.22771 | −0.613853 | − | 0.789420i | \(-0.710381\pi\) | ||||
−0.613853 | + | 0.789420i | \(0.710381\pi\) | |||||||
\(380\) | −22021.2 | −2.97280 | ||||||||
\(381\) | −8.49657 | −0.00114250 | ||||||||
\(382\) | 14165.1 | 1.89725 | ||||||||
\(383\) | −837.542 | −0.111740 | −0.0558700 | − | 0.998438i | \(-0.517793\pi\) | ||||
−0.0558700 | + | 0.998438i | \(0.517793\pi\) | |||||||
\(384\) | −260.017 | −0.0345546 | ||||||||
\(385\) | −20998.9 | −2.77975 | ||||||||
\(386\) | −9925.39 | −1.30878 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 20516.3 | 2.68443 | ||||||||
\(389\) | −5940.26 | −0.774250 | −0.387125 | − | 0.922027i | \(-0.626532\pi\) | ||||
−0.387125 | + | 0.922027i | \(0.626532\pi\) | |||||||
\(390\) | 148.187 | 0.0192403 | ||||||||
\(391\) | −2977.62 | −0.385127 | ||||||||
\(392\) | −6389.44 | −0.823254 | ||||||||
\(393\) | −244.862 | −0.0314292 | ||||||||
\(394\) | 5427.41 | 0.693982 | ||||||||
\(395\) | 5440.68 | 0.693039 | ||||||||
\(396\) | 15163.5 | 1.92423 | ||||||||
\(397\) | 13073.7 | 1.65277 | 0.826387 | − | 0.563103i | \(-0.190393\pi\) | ||||
0.826387 | + | 0.563103i | \(0.190393\pi\) | |||||||
\(398\) | −5514.56 | −0.694522 | ||||||||
\(399\) | 513.486 | 0.0644272 | ||||||||
\(400\) | −2803.22 | −0.350402 | ||||||||
\(401\) | −2500.54 | −0.311400 | −0.155700 | − | 0.987804i | \(-0.549763\pi\) | ||||
−0.155700 | + | 0.987804i | \(0.549763\pi\) | |||||||
\(402\) | −456.267 | −0.0566083 | ||||||||
\(403\) | −109.207 | −0.0134988 | ||||||||
\(404\) | 1095.56 | 0.134916 | ||||||||
\(405\) | 11208.0 | 1.37514 | ||||||||
\(406\) | −18656.4 | −2.28055 | ||||||||
\(407\) | 10293.6 | 1.25364 | ||||||||
\(408\) | −44.8973 | −0.00544791 | ||||||||
\(409\) | −3771.59 | −0.455974 | −0.227987 | − | 0.973664i | \(-0.573214\pi\) | ||||
−0.227987 | + | 0.973664i | \(0.573214\pi\) | |||||||
\(410\) | 9301.59 | 1.12042 | ||||||||
\(411\) | 260.566 | 0.0312720 | ||||||||
\(412\) | −11224.5 | −1.34221 | ||||||||
\(413\) | 5826.52 | 0.694199 | ||||||||
\(414\) | 17630.9 | 2.09303 | ||||||||
\(415\) | −13980.2 | −1.65365 | ||||||||
\(416\) | 3391.14 | 0.399674 | ||||||||
\(417\) | 213.506 | 0.0250730 | ||||||||
\(418\) | −27127.8 | −3.17431 | ||||||||
\(419\) | −8733.46 | −1.01828 | −0.509138 | − | 0.860685i | \(-0.670036\pi\) | ||||
−0.509138 | + | 0.860685i | \(0.670036\pi\) | |||||||
\(420\) | −722.629 | −0.0839541 | ||||||||
\(421\) | −1186.37 | −0.137340 | −0.0686698 | − | 0.997639i | \(-0.521875\pi\) | ||||
−0.0686698 | + | 0.997639i | \(0.521875\pi\) | |||||||
\(422\) | 11345.4 | 1.30874 | ||||||||
\(423\) | 496.614 | 0.0570833 | ||||||||
\(424\) | 1012.44 | 0.115963 | ||||||||
\(425\) | −2259.61 | −0.257899 | ||||||||
\(426\) | −720.097 | −0.0818986 | ||||||||
\(427\) | 23331.7 | 2.64426 | ||||||||
\(428\) | −4751.19 | −0.536583 | ||||||||
\(429\) | 107.358 | 0.0120823 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5136.09 | −0.574007 | −0.287003 | − | 0.957930i | \(-0.592659\pi\) | ||||
−0.287003 | + | 0.957930i | \(0.592659\pi\) | |||||||
\(432\) | −199.342 | −0.0222010 | ||||||||
\(433\) | 1680.47 | 0.186509 | 0.0932544 | − | 0.995642i | \(-0.470273\pi\) | ||||
0.0932544 | + | 0.995642i | \(0.470273\pi\) | |||||||
\(434\) | 905.535 | 0.100155 | ||||||||
\(435\) | −349.341 | −0.0385048 | ||||||||
\(436\) | −544.564 | −0.0598163 | ||||||||
\(437\) | −18549.9 | −2.03058 | ||||||||
\(438\) | −393.437 | −0.0429205 | ||||||||
\(439\) | −9868.00 | −1.07283 | −0.536417 | − | 0.843953i | \(-0.680222\pi\) | ||||
−0.536417 | + | 0.843953i | \(0.680222\pi\) | |||||||
\(440\) | 11438.3 | 1.23932 | ||||||||
\(441\) | −11429.1 | −1.23411 | ||||||||
\(442\) | 1302.25 | 0.140140 | ||||||||
\(443\) | −6533.37 | −0.700699 | −0.350350 | − | 0.936619i | \(-0.613937\pi\) | ||||
−0.350350 | + | 0.936619i | \(0.613937\pi\) | |||||||
\(444\) | 354.230 | 0.0378626 | ||||||||
\(445\) | 6000.41 | 0.639206 | ||||||||
\(446\) | 1430.09 | 0.151831 | ||||||||
\(447\) | 467.635 | 0.0494819 | ||||||||
\(448\) | −22601.2 | −2.38350 | ||||||||
\(449\) | 12041.4 | 1.26564 | 0.632818 | − | 0.774301i | \(-0.281898\pi\) | ||||
0.632818 | + | 0.774301i | \(0.281898\pi\) | |||||||
\(450\) | 13379.5 | 1.40159 | ||||||||
\(451\) | 6738.81 | 0.703588 | ||||||||
\(452\) | −15821.5 | −1.64642 | ||||||||
\(453\) | −73.3753 | −0.00761031 | ||||||||
\(454\) | 12083.9 | 1.24917 | ||||||||
\(455\) | 6279.88 | 0.647045 | ||||||||
\(456\) | −279.701 | −0.0287241 | ||||||||
\(457\) | −13506.5 | −1.38251 | −0.691257 | − | 0.722609i | \(-0.742943\pi\) | ||||
−0.691257 | + | 0.722609i | \(0.742943\pi\) | |||||||
\(458\) | −4386.10 | −0.447486 | ||||||||
\(459\) | −160.685 | −0.0163402 | ||||||||
\(460\) | 26105.3 | 2.64602 | ||||||||
\(461\) | 17597.0 | 1.77781 | 0.888907 | − | 0.458089i | \(-0.151466\pi\) | ||||
0.888907 | + | 0.458089i | \(0.151466\pi\) | |||||||
\(462\) | −890.203 | −0.0896450 | ||||||||
\(463\) | 10200.5 | 1.02388 | 0.511940 | − | 0.859021i | \(-0.328927\pi\) | ||||
0.511940 | + | 0.859021i | \(0.328927\pi\) | |||||||
\(464\) | −3808.54 | −0.381050 | ||||||||
\(465\) | 16.9561 | 0.00169101 | ||||||||
\(466\) | 8966.24 | 0.891316 | ||||||||
\(467\) | −9581.35 | −0.949405 | −0.474702 | − | 0.880146i | \(-0.657444\pi\) | ||||
−0.474702 | + | 0.880146i | \(0.657444\pi\) | |||||||
\(468\) | −4534.76 | −0.447905 | ||||||||
\(469\) | −19335.8 | −1.90371 | ||||||||
\(470\) | 1250.32 | 0.122708 | ||||||||
\(471\) | −71.6084 | −0.00700539 | ||||||||
\(472\) | −3173.76 | −0.309500 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 230.646 | 0.0223501 | ||||||||
\(475\) | −14076.9 | −1.35977 | ||||||||
\(476\) | −6350.42 | −0.611493 | ||||||||
\(477\) | 1811.00 | 0.173836 | ||||||||
\(478\) | −10329.4 | −0.988398 | ||||||||
\(479\) | 6024.59 | 0.574677 | 0.287339 | − | 0.957829i | \(-0.407230\pi\) | ||||
0.287339 | + | 0.957829i | \(0.407230\pi\) | |||||||
\(480\) | −526.527 | −0.0500678 | ||||||||
\(481\) | −3078.37 | −0.291812 | ||||||||
\(482\) | −10137.8 | −0.958014 | ||||||||
\(483\) | −608.720 | −0.0573452 | ||||||||
\(484\) | 12455.4 | 1.16974 | ||||||||
\(485\) | 27682.8 | 2.59177 | ||||||||
\(486\) | 1427.36 | 0.133223 | ||||||||
\(487\) | −10790.9 | −1.00407 | −0.502037 | − | 0.864846i | \(-0.667416\pi\) | ||||
−0.502037 | + | 0.864846i | \(0.667416\pi\) | |||||||
\(488\) | −12709.0 | −1.17891 | ||||||||
\(489\) | −531.608 | −0.0491619 | ||||||||
\(490\) | −28774.8 | −2.65289 | ||||||||
\(491\) | −2808.02 | −0.258094 | −0.129047 | − | 0.991638i | \(-0.541192\pi\) | ||||
−0.129047 | + | 0.991638i | \(0.541192\pi\) | |||||||
\(492\) | 231.901 | 0.0212498 | ||||||||
\(493\) | −3069.98 | −0.280456 | ||||||||
\(494\) | 8112.77 | 0.738888 | ||||||||
\(495\) | 20460.2 | 1.85781 | ||||||||
\(496\) | 184.857 | 0.0167345 | ||||||||
\(497\) | −30516.4 | −2.75422 | ||||||||
\(498\) | −592.663 | −0.0533290 | ||||||||
\(499\) | −11448.8 | −1.02709 | −0.513546 | − | 0.858062i | \(-0.671668\pi\) | ||||
−0.513546 | + | 0.858062i | \(0.671668\pi\) | |||||||
\(500\) | −2194.70 | −0.196300 | ||||||||
\(501\) | 42.4467 | 0.00378518 | ||||||||
\(502\) | −9556.72 | −0.849676 | ||||||||
\(503\) | −17619.7 | −1.56188 | −0.780940 | − | 0.624606i | \(-0.785260\pi\) | ||||
−0.780940 | + | 0.624606i | \(0.785260\pi\) | |||||||
\(504\) | 11266.0 | 0.995687 | ||||||||
\(505\) | 1478.24 | 0.130259 | ||||||||
\(506\) | 32159.0 | 2.82538 | ||||||||
\(507\) | 293.607 | 0.0257190 | ||||||||
\(508\) | 654.622 | 0.0571735 | ||||||||
\(509\) | 19675.8 | 1.71339 | 0.856696 | − | 0.515822i | \(-0.172513\pi\) | ||||
0.856696 | + | 0.515822i | \(0.172513\pi\) | |||||||
\(510\) | −202.195 | −0.0175556 | ||||||||
\(511\) | −16673.2 | −1.44340 | ||||||||
\(512\) | −8745.82 | −0.754911 | ||||||||
\(513\) | −1001.03 | −0.0861535 | ||||||||
\(514\) | 34858.7 | 2.99134 | ||||||||
\(515\) | −15145.3 | −1.29589 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 905.830 | 0.0770568 | ||||||||
\(518\) | 25525.6 | 2.16511 | ||||||||
\(519\) | 307.361 | 0.0259955 | ||||||||
\(520\) | −3420.71 | −0.288477 | ||||||||
\(521\) | −9437.66 | −0.793611 | −0.396805 | − | 0.917903i | \(-0.629881\pi\) | ||||
−0.396805 | + | 0.917903i | \(0.629881\pi\) | |||||||
\(522\) | 18177.8 | 1.52418 | ||||||||
\(523\) | 9442.26 | 0.789448 | 0.394724 | − | 0.918800i | \(-0.370840\pi\) | ||||
0.394724 | + | 0.918800i | \(0.370840\pi\) | |||||||
\(524\) | 18865.5 | 1.57279 | ||||||||
\(525\) | −461.936 | −0.0384010 | ||||||||
\(526\) | 425.395 | 0.0352626 | ||||||||
\(527\) | 149.009 | 0.0123168 | ||||||||
\(528\) | −181.727 | −0.0149785 | ||||||||
\(529\) | 9823.31 | 0.807373 | ||||||||
\(530\) | 4559.52 | 0.373685 | ||||||||
\(531\) | −5677.05 | −0.463960 | ||||||||
\(532\) | −39561.8 | −3.22410 | ||||||||
\(533\) | −2015.29 | −0.163775 | ||||||||
\(534\) | 254.375 | 0.0206140 | ||||||||
\(535\) | −6410.81 | −0.518062 | ||||||||
\(536\) | 10532.4 | 0.848748 | ||||||||
\(537\) | 98.2360 | 0.00789422 | ||||||||
\(538\) | −20135.9 | −1.61360 | ||||||||
\(539\) | −20846.8 | −1.66593 | ||||||||
\(540\) | 1408.76 | 0.112265 | ||||||||
\(541\) | −15227.6 | −1.21014 | −0.605069 | − | 0.796173i | \(-0.706854\pi\) | ||||
−0.605069 | + | 0.796173i | \(0.706854\pi\) | |||||||
\(542\) | 21964.6 | 1.74070 | ||||||||
\(543\) | 444.925 | 0.0351631 | ||||||||
\(544\) | −4627.08 | −0.364677 | ||||||||
\(545\) | −734.783 | −0.0577517 | ||||||||
\(546\) | 266.222 | 0.0208668 | ||||||||
\(547\) | 16610.6 | 1.29839 | 0.649196 | − | 0.760622i | \(-0.275106\pi\) | ||||
0.649196 | + | 0.760622i | \(0.275106\pi\) | |||||||
\(548\) | −20075.4 | −1.56493 | ||||||||
\(549\) | −22733.2 | −1.76726 | ||||||||
\(550\) | 24404.3 | 1.89201 | ||||||||
\(551\) | −19125.3 | −1.47870 | ||||||||
\(552\) | 331.576 | 0.0255667 | ||||||||
\(553\) | 9774.36 | 0.751624 | ||||||||
\(554\) | −20946.8 | −1.60639 | ||||||||
\(555\) | 477.964 | 0.0365558 | ||||||||
\(556\) | −16449.7 | −1.25471 | ||||||||
\(557\) | 299.887 | 0.0228126 | 0.0114063 | − | 0.999935i | \(-0.496369\pi\) | ||||
0.0114063 | + | 0.999935i | \(0.496369\pi\) | |||||||
\(558\) | −882.305 | −0.0669372 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −10630.1 | −0.802146 | ||||||||
\(561\) | −146.486 | −0.0110243 | ||||||||
\(562\) | −3246.06 | −0.243642 | ||||||||
\(563\) | 2044.50 | 0.153047 | 0.0765234 | − | 0.997068i | \(-0.475618\pi\) | ||||
0.0765234 | + | 0.997068i | \(0.475618\pi\) | |||||||
\(564\) | 31.1721 | 0.00232727 | ||||||||
\(565\) | −21348.1 | −1.58959 | ||||||||
\(566\) | 13168.1 | 0.977910 | ||||||||
\(567\) | 20135.5 | 1.49138 | ||||||||
\(568\) | 16622.6 | 1.22794 | ||||||||
\(569\) | −23154.9 | −1.70598 | −0.852990 | − | 0.521927i | \(-0.825213\pi\) | ||||
−0.852990 | + | 0.521927i | \(0.825213\pi\) | |||||||
\(570\) | −1259.63 | −0.0925617 | ||||||||
\(571\) | −9709.83 | −0.711635 | −0.355818 | − | 0.934555i | \(-0.615798\pi\) | ||||
−0.355818 | + | 0.934555i | \(0.615798\pi\) | |||||||
\(572\) | −8271.45 | −0.604627 | ||||||||
\(573\) | 476.513 | 0.0347411 | ||||||||
\(574\) | 16710.6 | 1.21513 | ||||||||
\(575\) | 16687.7 | 1.21030 | ||||||||
\(576\) | 22021.4 | 1.59299 | ||||||||
\(577\) | 11397.7 | 0.822342 | 0.411171 | − | 0.911558i | \(-0.365120\pi\) | ||||
0.411171 | + | 0.911558i | \(0.365120\pi\) | |||||||
\(578\) | 19875.1 | 1.43027 | ||||||||
\(579\) | −333.889 | −0.0239654 | ||||||||
\(580\) | 26915.1 | 1.92688 | ||||||||
\(581\) | −25116.0 | −1.79343 | ||||||||
\(582\) | 1173.55 | 0.0835830 | ||||||||
\(583\) | 3303.28 | 0.234662 | ||||||||
\(584\) | 9082.02 | 0.643522 | ||||||||
\(585\) | −6118.78 | −0.432445 | ||||||||
\(586\) | 18518.4 | 1.30544 | ||||||||
\(587\) | −14700.5 | −1.03366 | −0.516828 | − | 0.856089i | \(-0.672887\pi\) | ||||
−0.516828 | + | 0.856089i | \(0.672887\pi\) | |||||||
\(588\) | −717.394 | −0.0503144 | ||||||||
\(589\) | 928.294 | 0.0649401 | ||||||||
\(590\) | −14293.0 | −0.997347 | ||||||||
\(591\) | 182.578 | 0.0127077 | ||||||||
\(592\) | 5210.81 | 0.361762 | ||||||||
\(593\) | −7917.91 | −0.548313 | −0.274157 | − | 0.961685i | \(-0.588399\pi\) | ||||
−0.274157 | + | 0.961685i | \(0.588399\pi\) | |||||||
\(594\) | 1735.44 | 0.119875 | ||||||||
\(595\) | −8568.65 | −0.590387 | ||||||||
\(596\) | −36029.2 | −2.47619 | ||||||||
\(597\) | −185.509 | −0.0127176 | ||||||||
\(598\) | −9617.41 | −0.657667 | ||||||||
\(599\) | −8348.80 | −0.569487 | −0.284743 | − | 0.958604i | \(-0.591908\pi\) | ||||
−0.284743 | + | 0.958604i | \(0.591908\pi\) | |||||||
\(600\) | 251.621 | 0.0171206 | ||||||||
\(601\) | −9292.38 | −0.630689 | −0.315345 | − | 0.948977i | \(-0.602120\pi\) | ||||
−0.315345 | + | 0.948977i | \(0.602120\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 18839.7 | 1.27233 | ||||||||
\(604\) | 5653.23 | 0.380839 | ||||||||
\(605\) | 16806.1 | 1.12936 | ||||||||
\(606\) | 62.6669 | 0.00420078 | ||||||||
\(607\) | 7326.80 | 0.489927 | 0.244964 | − | 0.969532i | \(-0.421224\pi\) | ||||
0.244964 | + | 0.969532i | \(0.421224\pi\) | |||||||
\(608\) | −28825.7 | −1.92276 | ||||||||
\(609\) | −627.601 | −0.0417598 | ||||||||
\(610\) | −57235.0 | −3.79898 | ||||||||
\(611\) | −270.896 | −0.0179366 | ||||||||
\(612\) | 6187.50 | 0.408685 | ||||||||
\(613\) | 3020.41 | 0.199010 | 0.0995050 | − | 0.995037i | \(-0.468274\pi\) | ||||
0.0995050 | + | 0.995037i | \(0.468274\pi\) | |||||||
\(614\) | −41151.2 | −2.70477 | ||||||||
\(615\) | 312.905 | 0.0205163 | ||||||||
\(616\) | 20549.3 | 1.34408 | ||||||||
\(617\) | −10714.8 | −0.699130 | −0.349565 | − | 0.936912i | \(-0.613671\pi\) | ||||
−0.349565 | + | 0.936912i | \(0.613671\pi\) | |||||||
\(618\) | −642.053 | −0.0417915 | ||||||||
\(619\) | 233.807 | 0.0151818 | 0.00759088 | − | 0.999971i | \(-0.497584\pi\) | ||||
0.00759088 | + | 0.999971i | \(0.497584\pi\) | |||||||
\(620\) | −1306.39 | −0.0846223 | ||||||||
\(621\) | 1186.69 | 0.0766832 | ||||||||
\(622\) | −2609.08 | −0.168190 | ||||||||
\(623\) | 10779.9 | 0.693240 | ||||||||
\(624\) | 54.3469 | 0.00348656 | ||||||||
\(625\) | −17027.9 | −1.08979 | ||||||||
\(626\) | 7721.22 | 0.492975 | ||||||||
\(627\) | −912.577 | −0.0581257 | ||||||||
\(628\) | 5517.09 | 0.350567 | ||||||||
\(629\) | 4200.32 | 0.266260 | ||||||||
\(630\) | 50736.3 | 3.20854 | ||||||||
\(631\) | 223.889 | 0.0141250 | 0.00706250 | − | 0.999975i | \(-0.497752\pi\) | ||||
0.00706250 | + | 0.999975i | \(0.497752\pi\) | |||||||
\(632\) | −5324.18 | −0.335102 | ||||||||
\(633\) | 381.660 | 0.0239646 | ||||||||
\(634\) | 32346.3 | 2.02624 | ||||||||
\(635\) | 883.285 | 0.0552001 | ||||||||
\(636\) | 113.675 | 0.00708726 | ||||||||
\(637\) | 6234.39 | 0.387779 | ||||||||
\(638\) | 33156.5 | 2.05749 | ||||||||
\(639\) | 29733.5 | 1.84075 | ||||||||
\(640\) | 27030.8 | 1.66951 | ||||||||
\(641\) | 30800.3 | 1.89788 | 0.948938 | − | 0.315463i | \(-0.102160\pi\) | ||||
0.948938 | + | 0.315463i | \(0.102160\pi\) | |||||||
\(642\) | −271.773 | −0.0167072 | ||||||||
\(643\) | 16963.7 | 1.04041 | 0.520204 | − | 0.854042i | \(-0.325856\pi\) | ||||
0.520204 | + | 0.854042i | \(0.325856\pi\) | |||||||
\(644\) | 46899.1 | 2.86969 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −11069.6 | −0.674189 | ||||||||
\(647\) | −22076.7 | −1.34146 | −0.670730 | − | 0.741701i | \(-0.734019\pi\) | ||||
−0.670730 | + | 0.741701i | \(0.734019\pi\) | |||||||
\(648\) | −10968.0 | −0.664914 | ||||||||
\(649\) | −10355.0 | −0.626301 | ||||||||
\(650\) | −7298.31 | −0.440405 | ||||||||
\(651\) | 30.4622 | 0.00183396 | ||||||||
\(652\) | 40958.0 | 2.46018 | ||||||||
\(653\) | 629.038 | 0.0376970 | 0.0188485 | − | 0.999822i | \(-0.494000\pi\) | ||||
0.0188485 | + | 0.999822i | \(0.494000\pi\) | |||||||
\(654\) | −31.1496 | −0.00186245 | ||||||||
\(655\) | 25455.3 | 1.51851 | ||||||||
\(656\) | 3411.32 | 0.203033 | ||||||||
\(657\) | 16245.4 | 0.964679 | ||||||||
\(658\) | 2246.24 | 0.133081 | ||||||||
\(659\) | 22663.0 | 1.33964 | 0.669821 | − | 0.742523i | \(-0.266371\pi\) | ||||
0.669821 | + | 0.742523i | \(0.266371\pi\) | |||||||
\(660\) | 1284.27 | 0.0757426 | ||||||||
\(661\) | −8652.12 | −0.509120 | −0.254560 | − | 0.967057i | \(-0.581931\pi\) | ||||
−0.254560 | + | 0.967057i | \(0.581931\pi\) | |||||||
\(662\) | 25302.0 | 1.48548 | ||||||||
\(663\) | 43.8078 | 0.00256614 | ||||||||
\(664\) | 13680.9 | 0.799581 | ||||||||
\(665\) | −53380.9 | −3.11281 | ||||||||
\(666\) | −24870.7 | −1.44703 | ||||||||
\(667\) | 22672.4 | 1.31616 | ||||||||
\(668\) | −3270.32 | −0.189420 | ||||||||
\(669\) | 48.1081 | 0.00278022 | ||||||||
\(670\) | 47432.5 | 2.73504 | ||||||||
\(671\) | −41465.5 | −2.38563 | ||||||||
\(672\) | −945.922 | −0.0543002 | ||||||||
\(673\) | 27477.3 | 1.57381 | 0.786904 | − | 0.617076i | \(-0.211683\pi\) | ||||
0.786904 | + | 0.617076i | \(0.211683\pi\) | |||||||
\(674\) | −19937.3 | −1.13940 | ||||||||
\(675\) | 900.538 | 0.0513507 | ||||||||
\(676\) | −22621.0 | −1.28704 | ||||||||
\(677\) | 12923.5 | 0.733663 | 0.366831 | − | 0.930287i | \(-0.380443\pi\) | ||||
0.366831 | + | 0.930287i | \(0.380443\pi\) | |||||||
\(678\) | −905.006 | −0.0512633 | ||||||||
\(679\) | 49733.0 | 2.81086 | ||||||||
\(680\) | 4667.42 | 0.263217 | ||||||||
\(681\) | 406.501 | 0.0228739 | ||||||||
\(682\) | −1609.33 | −0.0903586 | ||||||||
\(683\) | −9451.83 | −0.529523 | −0.264762 | − | 0.964314i | \(-0.585293\pi\) | ||||
−0.264762 | + | 0.964314i | \(0.585293\pi\) | |||||||
\(684\) | 38546.8 | 2.15479 | ||||||||
\(685\) | −27087.9 | −1.51091 | ||||||||
\(686\) | −9840.55 | −0.547688 | ||||||||
\(687\) | −147.548 | −0.00819404 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −987.870 | −0.0546224 | ||||||||
\(690\) | 1493.25 | 0.0823870 | ||||||||
\(691\) | 30813.4 | 1.69638 | 0.848188 | − | 0.529696i | \(-0.177694\pi\) | ||||
0.848188 | + | 0.529696i | \(0.177694\pi\) | |||||||
\(692\) | −23680.7 | −1.30088 | ||||||||
\(693\) | 36757.4 | 2.01486 | ||||||||
\(694\) | −7910.91 | −0.432701 | ||||||||
\(695\) | −22195.6 | −1.21141 | ||||||||
\(696\) | 341.860 | 0.0186181 | ||||||||
\(697\) | 2749.79 | 0.149434 | ||||||||
\(698\) | −23919.2 | −1.29707 | ||||||||
\(699\) | 301.624 | 0.0163211 | ||||||||
\(700\) | 35590.0 | 1.92168 | ||||||||
\(701\) | 8156.30 | 0.439457 | 0.219728 | − | 0.975561i | \(-0.429483\pi\) | ||||
0.219728 | + | 0.975561i | \(0.429483\pi\) | |||||||
\(702\) | −518.996 | −0.0279035 | ||||||||
\(703\) | 26167.1 | 1.40386 | ||||||||
\(704\) | 40167.3 | 2.15037 | ||||||||
\(705\) | 42.0607 | 0.00224695 | ||||||||
\(706\) | −29055.4 | −1.54889 | ||||||||
\(707\) | 2655.71 | 0.141270 | ||||||||
\(708\) | −356.344 | −0.0189156 | ||||||||
\(709\) | 185.334 | 0.00981717 | 0.00490859 | − | 0.999988i | \(-0.498438\pi\) | ||||
0.00490859 | + | 0.999988i | \(0.498438\pi\) | |||||||
\(710\) | 74859.7 | 3.95695 | ||||||||
\(711\) | −9523.61 | −0.502339 | ||||||||
\(712\) | −5871.93 | −0.309073 | ||||||||
\(713\) | −1100.46 | −0.0578016 | ||||||||
\(714\) | −363.250 | −0.0190396 | ||||||||
\(715\) | −11160.7 | −0.583758 | ||||||||
\(716\) | −7568.64 | −0.395046 | ||||||||
\(717\) | −347.479 | −0.0180988 | ||||||||
\(718\) | 4035.40 | 0.209749 | ||||||||
\(719\) | 7215.59 | 0.374264 | 0.187132 | − | 0.982335i | \(-0.440081\pi\) | ||||
0.187132 | + | 0.982335i | \(0.440081\pi\) | |||||||
\(720\) | 10357.4 | 0.536105 | ||||||||
\(721\) | −27209.0 | −1.40543 | ||||||||
\(722\) | −38732.9 | −1.99652 | ||||||||
\(723\) | −341.034 | −0.0175424 | ||||||||
\(724\) | −34279.4 | −1.75965 | ||||||||
\(725\) | 17205.3 | 0.881363 | ||||||||
\(726\) | 712.458 | 0.0364212 | ||||||||
\(727\) | −32590.1 | −1.66259 | −0.831293 | − | 0.555835i | \(-0.812399\pi\) | ||||
−0.831293 | + | 0.555835i | \(0.812399\pi\) | |||||||
\(728\) | −6145.42 | −0.312863 | ||||||||
\(729\) | −19586.9 | −0.995119 | ||||||||
\(730\) | 40900.9 | 2.07371 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −1426.94 | −0.0720510 | ||||||||
\(733\) | −12464.9 | −0.628105 | −0.314052 | − | 0.949406i | \(-0.601687\pi\) | ||||
−0.314052 | + | 0.949406i | \(0.601687\pi\) | |||||||
\(734\) | −25074.0 | −1.26090 | ||||||||
\(735\) | −967.984 | −0.0485777 | ||||||||
\(736\) | 34171.9 | 1.71140 | ||||||||
\(737\) | 34363.8 | 1.71751 | ||||||||
\(738\) | −16281.9 | −0.812121 | ||||||||
\(739\) | 15442.3 | 0.768681 | 0.384340 | − | 0.923191i | \(-0.374429\pi\) | ||||
0.384340 | + | 0.923191i | \(0.374429\pi\) | |||||||
\(740\) | −36825.0 | −1.82934 | ||||||||
\(741\) | 272.913 | 0.0135300 | ||||||||
\(742\) | 8191.32 | 0.405274 | ||||||||
\(743\) | −3389.16 | −0.167343 | −0.0836717 | − | 0.996493i | \(-0.526665\pi\) | ||||
−0.0836717 | + | 0.996493i | \(0.526665\pi\) | |||||||
\(744\) | −16.5930 | −0.000817648 0 | ||||||||
\(745\) | −48614.3 | −2.39073 | ||||||||
\(746\) | 25098.8 | 1.23181 | ||||||||
\(747\) | 24471.6 | 1.19862 | ||||||||
\(748\) | 11286.1 | 0.551684 | ||||||||
\(749\) | −11517.2 | −0.561856 | ||||||||
\(750\) | −125.539 | −0.00611205 | ||||||||
\(751\) | −12106.9 | −0.588266 | −0.294133 | − | 0.955765i | \(-0.595031\pi\) | ||||
−0.294133 | + | 0.955765i | \(0.595031\pi\) | |||||||
\(752\) | 458.549 | 0.0222361 | ||||||||
\(753\) | −321.487 | −0.0155586 | ||||||||
\(754\) | −9915.72 | −0.478925 | ||||||||
\(755\) | 7627.93 | 0.367694 | ||||||||
\(756\) | 2530.87 | 0.121755 | ||||||||
\(757\) | 13089.0 | 0.628441 | 0.314220 | − | 0.949350i | \(-0.398257\pi\) | ||||
0.314220 | + | 0.949350i | \(0.398257\pi\) | |||||||
\(758\) | 39921.1 | 1.91293 | ||||||||
\(759\) | 1081.83 | 0.0517363 | ||||||||
\(760\) | 29077.1 | 1.38781 | ||||||||
\(761\) | −5492.31 | −0.261624 | −0.130812 | − | 0.991407i | \(-0.541758\pi\) | ||||
−0.130812 | + | 0.991407i | \(0.541758\pi\) | |||||||
\(762\) | 37.4450 | 0.00178017 | ||||||||
\(763\) | −1320.06 | −0.0626336 | ||||||||
\(764\) | −36713.2 | −1.73853 | ||||||||
\(765\) | 8348.83 | 0.394579 | ||||||||
\(766\) | 3691.10 | 0.174106 | ||||||||
\(767\) | 3096.74 | 0.145785 | ||||||||
\(768\) | 177.792 | 0.00835352 | ||||||||
\(769\) | −689.866 | −0.0323501 | −0.0161750 | − | 0.999869i | \(-0.505149\pi\) | ||||
−0.0161750 | + | 0.999869i | \(0.505149\pi\) | |||||||
\(770\) | 92543.6 | 4.33122 | ||||||||
\(771\) | 1172.64 | 0.0547753 | ||||||||
\(772\) | 25724.6 | 1.19929 | ||||||||
\(773\) | −24050.5 | −1.11906 | −0.559532 | − | 0.828809i | \(-0.689019\pi\) | ||||
−0.559532 | + | 0.828809i | \(0.689019\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −835.100 | −0.0387067 | ||||||||
\(776\) | −27090.0 | −1.25319 | ||||||||
\(777\) | 858.678 | 0.0396460 | ||||||||
\(778\) | 26179.2 | 1.20639 | ||||||||
\(779\) | 17130.6 | 0.787891 | ||||||||
\(780\) | −384.071 | −0.0176307 | ||||||||
\(781\) | 54234.3 | 2.48483 | ||||||||
\(782\) | 13122.6 | 0.600080 | ||||||||
\(783\) | 1223.50 | 0.0558420 | ||||||||
\(784\) | −10553.0 | −0.480733 | ||||||||
\(785\) | 7444.25 | 0.338467 | ||||||||
\(786\) | 1079.12 | 0.0489709 | ||||||||
\(787\) | 2373.63 | 0.107511 | 0.0537553 | − | 0.998554i | \(-0.482881\pi\) | ||||
0.0537553 | + | 0.998554i | \(0.482881\pi\) | |||||||
\(788\) | −14066.8 | −0.635924 | ||||||||
\(789\) | 14.3103 | 0.000645702 0 | ||||||||
\(790\) | −23977.5 | −1.07985 | ||||||||
\(791\) | −38352.5 | −1.72397 | ||||||||
\(792\) | −20022.1 | −0.898300 | ||||||||
\(793\) | 12400.6 | 0.555306 | ||||||||
\(794\) | −57616.8 | −2.57524 | ||||||||
\(795\) | 153.382 | 0.00684264 | ||||||||
\(796\) | 14292.6 | 0.636419 | ||||||||
\(797\) | 19870.8 | 0.883138 | 0.441569 | − | 0.897227i | \(-0.354422\pi\) | ||||
0.441569 | + | 0.897227i | \(0.354422\pi\) | |||||||
\(798\) | −2262.97 | −0.100386 | ||||||||
\(799\) | 369.626 | 0.0163660 | ||||||||
\(800\) | 25931.8 | 1.14604 | ||||||||
\(801\) | −10503.4 | −0.463319 | ||||||||
\(802\) | 11020.1 | 0.485202 | ||||||||
\(803\) | 29631.8 | 1.30222 | ||||||||
\(804\) | 1182.55 | 0.0518725 | ||||||||
\(805\) | 63281.2 | 2.77064 | ||||||||
\(806\) | 481.284 | 0.0210329 | ||||||||
\(807\) | −677.369 | −0.0295471 | ||||||||
\(808\) | −1446.59 | −0.0629837 | ||||||||
\(809\) | 43547.9 | 1.89254 | 0.946269 | − | 0.323380i | \(-0.104819\pi\) | ||||
0.946269 | + | 0.323380i | \(0.104819\pi\) | |||||||
\(810\) | −49394.4 | −2.14264 | ||||||||
\(811\) | 16180.7 | 0.700592 | 0.350296 | − | 0.936639i | \(-0.386081\pi\) | ||||
0.350296 | + | 0.936639i | \(0.386081\pi\) | |||||||
\(812\) | 48353.8 | 2.08976 | ||||||||
\(813\) | 738.887 | 0.0318744 | ||||||||
\(814\) | −45364.5 | −1.95335 | ||||||||
\(815\) | 55264.8 | 2.37527 | ||||||||
\(816\) | −74.1541 | −0.00318127 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 16621.7 | 0.710468 | ||||||||
\(819\) | −10992.6 | −0.469001 | ||||||||
\(820\) | −24107.9 | −1.02669 | ||||||||
\(821\) | 22531.5 | 0.957803 | 0.478901 | − | 0.877869i | \(-0.341035\pi\) | ||||
0.478901 | + | 0.877869i | \(0.341035\pi\) | |||||||
\(822\) | −1148.33 | −0.0487259 | ||||||||
\(823\) | 39498.4 | 1.67294 | 0.836468 | − | 0.548015i | \(-0.184616\pi\) | ||||
0.836468 | + | 0.548015i | \(0.184616\pi\) | |||||||
\(824\) | 14821.0 | 0.626595 | ||||||||
\(825\) | 820.961 | 0.0346451 | ||||||||
\(826\) | −25677.9 | −1.08166 | ||||||||
\(827\) | −13678.9 | −0.575165 | −0.287583 | − | 0.957756i | \(-0.592852\pi\) | ||||
−0.287583 | + | 0.957756i | \(0.592852\pi\) | |||||||
\(828\) | −45695.9 | −1.91793 | ||||||||
\(829\) | −20316.7 | −0.851178 | −0.425589 | − | 0.904917i | \(-0.639933\pi\) | ||||
−0.425589 | + | 0.904917i | \(0.639933\pi\) | |||||||
\(830\) | 61611.9 | 2.57660 | ||||||||
\(831\) | −704.648 | −0.0294151 | ||||||||
\(832\) | −12012.4 | −0.500545 | ||||||||
\(833\) | −8506.57 | −0.353824 | ||||||||
\(834\) | −940.935 | −0.0390671 | ||||||||
\(835\) | −4412.66 | −0.182882 | ||||||||
\(836\) | 70309.8 | 2.90875 | ||||||||
\(837\) | −59.3855 | −0.00245241 | ||||||||
\(838\) | 38489.0 | 1.58661 | ||||||||
\(839\) | 32447.8 | 1.33519 | 0.667593 | − | 0.744526i | \(-0.267325\pi\) | ||||
0.667593 | + | 0.744526i | \(0.267325\pi\) | |||||||
\(840\) | 954.170 | 0.0391928 | ||||||||
\(841\) | −1013.33 | −0.0415488 | ||||||||
\(842\) | 5228.40 | 0.213994 | ||||||||
\(843\) | −109.197 | −0.00446139 | ||||||||
\(844\) | −29405.1 | −1.19925 | ||||||||
\(845\) | −30522.7 | −1.24262 | ||||||||
\(846\) | −2188.61 | −0.0889434 | ||||||||
\(847\) | 30192.7 | 1.22483 | ||||||||
\(848\) | 1672.18 | 0.0677159 | ||||||||
\(849\) | 442.975 | 0.0179068 | ||||||||
\(850\) | 9958.26 | 0.401842 | ||||||||
\(851\) | −31020.2 | −1.24954 | ||||||||
\(852\) | 1866.35 | 0.0750471 | ||||||||
\(853\) | 11503.9 | 0.461765 | 0.230883 | − | 0.972982i | \(-0.425839\pi\) | ||||
0.230883 | + | 0.972982i | \(0.425839\pi\) | |||||||
\(854\) | −102824. | −4.12012 | ||||||||
\(855\) | 52011.4 | 2.08041 | ||||||||
\(856\) | 6273.54 | 0.250497 | ||||||||
\(857\) | −3256.25 | −0.129792 | −0.0648958 | − | 0.997892i | \(-0.520672\pi\) | ||||
−0.0648958 | + | 0.997892i | \(0.520672\pi\) | |||||||
\(858\) | −473.135 | −0.0188258 | ||||||||
\(859\) | 35756.2 | 1.42024 | 0.710119 | − | 0.704082i | \(-0.248641\pi\) | ||||
0.710119 | + | 0.704082i | \(0.248641\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 562.144 | 0.0222507 | ||||||||
\(862\) | 22635.1 | 0.894379 | ||||||||
\(863\) | −17388.1 | −0.685861 | −0.342930 | − | 0.939361i | \(-0.611420\pi\) | ||||
−0.342930 | + | 0.939361i | \(0.611420\pi\) | |||||||
\(864\) | 1844.06 | 0.0726114 | ||||||||
\(865\) | −31952.6 | −1.25598 | ||||||||
\(866\) | −7405.96 | −0.290606 | ||||||||
\(867\) | 668.596 | 0.0261900 | ||||||||
\(868\) | −2346.97 | −0.0917757 | ||||||||
\(869\) | −17371.2 | −0.678108 | ||||||||
\(870\) | 1539.57 | 0.0599957 | ||||||||
\(871\) | −10276.8 | −0.399788 | ||||||||
\(872\) | 719.050 | 0.0279244 | ||||||||
\(873\) | −48457.1 | −1.87861 | ||||||||
\(874\) | 81750.9 | 3.16392 | ||||||||
\(875\) | −5320.11 | −0.205546 | ||||||||
\(876\) | 1019.71 | 0.0393298 | ||||||||
\(877\) | 25399.9 | 0.977986 | 0.488993 | − | 0.872288i | \(-0.337364\pi\) | ||||
0.488993 | + | 0.872288i | \(0.337364\pi\) | |||||||
\(878\) | 43488.9 | 1.67162 | ||||||||
\(879\) | 622.958 | 0.0239043 | ||||||||
\(880\) | 18891.9 | 0.723690 | ||||||||
\(881\) | −35948.0 | −1.37471 | −0.687354 | − | 0.726323i | \(-0.741228\pi\) | ||||
−0.687354 | + | 0.726323i | \(0.741228\pi\) | |||||||
\(882\) | 50368.7 | 1.92291 | ||||||||
\(883\) | −19959.4 | −0.760689 | −0.380345 | − | 0.924845i | \(-0.624195\pi\) | ||||
−0.380345 | + | 0.924845i | \(0.624195\pi\) | |||||||
\(884\) | −3375.19 | −0.128416 | ||||||||
\(885\) | −480.816 | −0.0182627 | ||||||||
\(886\) | 28793.0 | 1.09178 | ||||||||
\(887\) | −46824.5 | −1.77251 | −0.886254 | − | 0.463200i | \(-0.846701\pi\) | ||||
−0.886254 | + | 0.463200i | \(0.846701\pi\) | |||||||
\(888\) | −467.730 | −0.0176757 | ||||||||
\(889\) | 1586.85 | 0.0598664 | ||||||||
\(890\) | −26444.2 | −0.995969 | ||||||||
\(891\) | −35785.2 | −1.34551 | ||||||||
\(892\) | −3706.51 | −0.139129 | ||||||||
\(893\) | 2302.69 | 0.0862897 | ||||||||
\(894\) | −2060.90 | −0.0770994 | ||||||||
\(895\) | −10212.4 | −0.381411 | ||||||||
\(896\) | 48561.7 | 1.81064 | ||||||||
\(897\) | −323.529 | −0.0120427 | ||||||||
\(898\) | −53067.4 | −1.97203 | ||||||||
\(899\) | −1134.59 | −0.0420922 | ||||||||
\(900\) | −34677.0 | −1.28433 | ||||||||
\(901\) | 1347.91 | 0.0498395 | ||||||||
\(902\) | −29698.4 | −1.09628 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 20891.0 | 0.768609 | ||||||||
\(905\) | −46253.4 | −1.69891 | ||||||||
\(906\) | 323.370 | 0.0118579 | ||||||||
\(907\) | −26158.1 | −0.957625 | −0.478813 | − | 0.877917i | \(-0.658933\pi\) | ||||
−0.478813 | + | 0.877917i | \(0.658933\pi\) | |||||||
\(908\) | −31319.0 | −1.14467 | ||||||||
\(909\) | −2587.58 | −0.0944165 | ||||||||
\(910\) | −27675.9 | −1.00818 | ||||||||
\(911\) | −4449.15 | −0.161808 | −0.0809038 | − | 0.996722i | \(-0.525781\pi\) | ||||
−0.0809038 | + | 0.996722i | \(0.525781\pi\) | |||||||
\(912\) | −461.965 | −0.0167732 | ||||||||
\(913\) | 44636.5 | 1.61802 | ||||||||
\(914\) | 59524.2 | 2.15414 | ||||||||
\(915\) | −1925.38 | −0.0695641 | ||||||||
\(916\) | 11367.9 | 0.410050 | ||||||||
\(917\) | 45731.3 | 1.64687 | ||||||||
\(918\) | 708.150 | 0.0254602 | ||||||||
\(919\) | −37998.1 | −1.36392 | −0.681959 | − | 0.731391i | \(-0.738872\pi\) | ||||
−0.681959 | + | 0.731391i | \(0.738872\pi\) | |||||||
\(920\) | −34469.9 | −1.23526 | ||||||||
\(921\) | −1384.32 | −0.0495277 | ||||||||
\(922\) | −77551.0 | −2.77007 | ||||||||
\(923\) | −16219.2 | −0.578397 | ||||||||
\(924\) | 2307.23 | 0.0821454 | ||||||||
\(925\) | −23540.1 | −0.836750 | ||||||||
\(926\) | −44954.2 | −1.59534 | ||||||||
\(927\) | 26511.0 | 0.939305 | ||||||||
\(928\) | 35231.8 | 1.24627 | ||||||||
\(929\) | −858.473 | −0.0303182 | −0.0151591 | − | 0.999885i | \(-0.504825\pi\) | ||||
−0.0151591 | + | 0.999885i | \(0.504825\pi\) | |||||||
\(930\) | −74.7267 | −0.00263482 | ||||||||
\(931\) | −52994.2 | −1.86554 | ||||||||
\(932\) | −23238.7 | −0.816749 | ||||||||
\(933\) | −87.7692 | −0.00307978 | ||||||||
\(934\) | 42225.7 | 1.47930 | ||||||||
\(935\) | 15228.4 | 0.532642 | ||||||||
\(936\) | 5987.76 | 0.209098 | ||||||||
\(937\) | −34170.2 | −1.19135 | −0.595674 | − | 0.803226i | \(-0.703115\pi\) | ||||
−0.595674 | + | 0.803226i | \(0.703115\pi\) | |||||||
\(938\) | 85214.0 | 2.96624 | ||||||||
\(939\) | 259.741 | 0.00902699 | ||||||||
\(940\) | −3240.58 | −0.112443 | ||||||||
\(941\) | 1570.56 | 0.0544088 | 0.0272044 | − | 0.999630i | \(-0.491340\pi\) | ||||
0.0272044 | + | 0.999630i | \(0.491340\pi\) | |||||||
\(942\) | 315.583 | 0.0109153 | ||||||||
\(943\) | −20307.7 | −0.701284 | ||||||||
\(944\) | −5241.90 | −0.180730 | ||||||||
\(945\) | 3414.92 | 0.117553 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −20920.3 | −0.717866 | −0.358933 | − | 0.933363i | \(-0.616859\pi\) | ||||
−0.358933 | + | 0.933363i | \(0.616859\pi\) | |||||||
\(948\) | −597.789 | −0.0204803 | ||||||||
\(949\) | −8861.62 | −0.303120 | ||||||||
\(950\) | 62037.8 | 2.11871 | ||||||||
\(951\) | 1088.13 | 0.0371030 | ||||||||
\(952\) | 8385.18 | 0.285468 | ||||||||
\(953\) | 10346.8 | 0.351696 | 0.175848 | − | 0.984417i | \(-0.443733\pi\) | ||||
0.175848 | + | 0.984417i | \(0.443733\pi\) | |||||||
\(954\) | −7981.18 | −0.270860 | ||||||||
\(955\) | −49537.3 | −1.67852 | ||||||||
\(956\) | 26771.7 | 0.905710 | ||||||||
\(957\) | 1115.38 | 0.0376753 | ||||||||
\(958\) | −26550.8 | −0.895424 | ||||||||
\(959\) | −48664.2 | −1.63863 | ||||||||
\(960\) | 1865.10 | 0.0627041 | ||||||||
\(961\) | −29735.9 | −0.998151 | ||||||||
\(962\) | 13566.6 | 0.454683 | ||||||||
\(963\) | 11221.8 | 0.375510 | ||||||||
\(964\) | 26275.1 | 0.877867 | ||||||||
\(965\) | 34710.4 | 1.15789 | ||||||||
\(966\) | 2682.67 | 0.0893515 | ||||||||
\(967\) | 17292.1 | 0.575052 | 0.287526 | − | 0.957773i | \(-0.407167\pi\) | ||||
0.287526 | + | 0.957773i | \(0.407167\pi\) | |||||||
\(968\) | −16446.2 | −0.546076 | ||||||||
\(969\) | −372.379 | −0.0123452 | ||||||||
\(970\) | −122000. | −4.03833 | ||||||||
\(971\) | 7077.25 | 0.233903 | 0.116951 | − | 0.993138i | \(-0.462688\pi\) | ||||
0.116951 | + | 0.993138i | \(0.462688\pi\) | |||||||
\(972\) | −3699.42 | −0.122077 | ||||||||
\(973\) | −39875.1 | −1.31381 | ||||||||
\(974\) | 47556.4 | 1.56448 | ||||||||
\(975\) | −245.515 | −0.00806437 | ||||||||
\(976\) | −20990.7 | −0.688418 | ||||||||
\(977\) | 369.048 | 0.0120849 | 0.00604243 | − | 0.999982i | \(-0.498077\pi\) | ||||
0.00604243 | + | 0.999982i | \(0.498077\pi\) | |||||||
\(978\) | 2342.83 | 0.0766008 | ||||||||
\(979\) | −19158.3 | −0.625435 | ||||||||
\(980\) | 74578.7 | 2.43095 | ||||||||
\(981\) | 1286.20 | 0.0418604 | ||||||||
\(982\) | 12375.1 | 0.402145 | ||||||||
\(983\) | −38678.1 | −1.25497 | −0.627487 | − | 0.778627i | \(-0.715916\pi\) | ||||
−0.627487 | + | 0.778627i | \(0.715916\pi\) | |||||||
\(984\) | −306.205 | −0.00992019 | ||||||||
\(985\) | −18980.4 | −0.613974 | ||||||||
\(986\) | 13529.6 | 0.436988 | ||||||||
\(987\) | 75.5633 | 0.00243689 | ||||||||
\(988\) | −21026.7 | −0.677073 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −90169.4 | −2.89472 | ||||||||
\(991\) | 33297.9 | 1.06735 | 0.533674 | − | 0.845690i | \(-0.320811\pi\) | ||||
0.533674 | + | 0.845690i | \(0.320811\pi\) | |||||||
\(992\) | −1710.06 | −0.0547324 | ||||||||
\(993\) | 851.156 | 0.0272010 | ||||||||
\(994\) | 134488. | 4.29144 | ||||||||
\(995\) | 19285.1 | 0.614453 | ||||||||
\(996\) | 1536.06 | 0.0488676 | ||||||||
\(997\) | −42935.5 | −1.36387 | −0.681936 | − | 0.731412i | \(-0.738862\pi\) | ||||
−0.681936 | + | 0.731412i | \(0.738862\pi\) | |||||||
\(998\) | 50455.6 | 1.60035 | ||||||||
\(999\) | −1673.98 | −0.0530154 |
(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.k.1.9 | 60 | ||
43.30 | odd | 42 | 43.4.g.a.40.2 | yes | 120 | ||
43.33 | odd | 42 | 43.4.g.a.14.2 | ✓ | 120 | ||
43.42 | odd | 2 | 1849.4.a.l.1.52 | 60 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.4.g.a.14.2 | ✓ | 120 | 43.33 | odd | 42 | ||
43.4.g.a.40.2 | yes | 120 | 43.30 | odd | 42 | ||
1849.4.a.k.1.9 | 60 | 1.1 | even | 1 | trivial | ||
1849.4.a.l.1.52 | 60 | 43.42 | odd | 2 |