Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [39,4,Mod(1,39)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(39, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("39.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 39 = 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 39.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(2.30107449022\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{14}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - 14 \)
|
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.74166\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 39.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.74166 | 1.67643 | 0.838215 | − | 0.545341i | \(-0.183600\pi\) | ||||
0.838215 | + | 0.545341i | \(0.183600\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 14.4833 | 1.81041 | ||||||||
\(5\) | 4.51669 | 0.403985 | 0.201992 | − | 0.979387i | \(-0.435258\pi\) | ||||
0.201992 | + | 0.979387i | \(0.435258\pi\) | |||||||
\(6\) | −14.2250 | −0.967887 | ||||||||
\(7\) | −7.48331 | −0.404061 | −0.202031 | − | 0.979379i | \(-0.564754\pi\) | ||||
−0.202031 | + | 0.979379i | \(0.564754\pi\) | |||||||
\(8\) | 30.7417 | 1.35860 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 21.4166 | 0.677252 | ||||||||
\(11\) | −66.8999 | −1.83373 | −0.916867 | − | 0.399193i | \(-0.869290\pi\) | ||||
−0.916867 | + | 0.399193i | \(0.869290\pi\) | |||||||
\(12\) | −43.4499 | −1.04524 | ||||||||
\(13\) | −13.0000 | −0.277350 | ||||||||
\(14\) | −35.4833 | −0.677380 | ||||||||
\(15\) | −13.5501 | −0.233241 | ||||||||
\(16\) | 29.8999 | 0.467186 | ||||||||
\(17\) | 96.9666 | 1.38340 | 0.691702 | − | 0.722183i | \(-0.256861\pi\) | ||||
0.691702 | + | 0.722183i | \(0.256861\pi\) | |||||||
\(18\) | 42.6749 | 0.558810 | ||||||||
\(19\) | 31.4833 | 0.380146 | 0.190073 | − | 0.981770i | \(-0.439128\pi\) | ||||
0.190073 | + | 0.981770i | \(0.439128\pi\) | |||||||
\(20\) | 65.4166 | 0.731380 | ||||||||
\(21\) | 22.4499 | 0.233285 | ||||||||
\(22\) | −317.216 | −3.07413 | ||||||||
\(23\) | 183.600 | 1.66448 | 0.832242 | − | 0.554412i | \(-0.187057\pi\) | ||||
0.832242 | + | 0.554412i | \(0.187057\pi\) | |||||||
\(24\) | −92.2250 | −0.784389 | ||||||||
\(25\) | −104.600 | −0.836796 | ||||||||
\(26\) | −61.6415 | −0.464958 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | −108.383 | −0.731518 | ||||||||
\(29\) | 112.200 | 0.718450 | 0.359225 | − | 0.933251i | \(-0.383041\pi\) | ||||
0.359225 | + | 0.933251i | \(0.383041\pi\) | |||||||
\(30\) | −64.2497 | −0.391011 | ||||||||
\(31\) | −77.2831 | −0.447757 | −0.223878 | − | 0.974617i | \(-0.571872\pi\) | ||||
−0.223878 | + | 0.974617i | \(0.571872\pi\) | |||||||
\(32\) | −104.158 | −0.575398 | ||||||||
\(33\) | 200.700 | 1.05871 | ||||||||
\(34\) | 459.783 | 2.31918 | ||||||||
\(35\) | −33.7998 | −0.163234 | ||||||||
\(36\) | 130.350 | 0.603471 | ||||||||
\(37\) | 54.7664 | 0.243339 | 0.121669 | − | 0.992571i | \(-0.461175\pi\) | ||||
0.121669 | + | 0.992571i | \(0.461175\pi\) | |||||||
\(38\) | 149.283 | 0.637287 | ||||||||
\(39\) | 39.0000 | 0.160128 | ||||||||
\(40\) | 138.850 | 0.548854 | ||||||||
\(41\) | 451.716 | 1.72064 | 0.860319 | − | 0.509756i | \(-0.170264\pi\) | ||||
0.860319 | + | 0.509756i | \(0.170264\pi\) | |||||||
\(42\) | 106.450 | 0.391085 | ||||||||
\(43\) | −113.434 | −0.402291 | −0.201145 | − | 0.979561i | \(-0.564466\pi\) | ||||
−0.201145 | + | 0.979561i | \(0.564466\pi\) | |||||||
\(44\) | −968.932 | −3.31982 | ||||||||
\(45\) | 40.6502 | 0.134662 | ||||||||
\(46\) | 870.566 | 2.79039 | ||||||||
\(47\) | −42.2670 | −0.131176 | −0.0655880 | − | 0.997847i | \(-0.520892\pi\) | ||||
−0.0655880 | + | 0.997847i | \(0.520892\pi\) | |||||||
\(48\) | −89.6997 | −0.269730 | ||||||||
\(49\) | −287.000 | −0.836735 | ||||||||
\(50\) | −495.975 | −1.40283 | ||||||||
\(51\) | −290.900 | −0.798708 | ||||||||
\(52\) | −188.283 | −0.502119 | ||||||||
\(53\) | −530.999 | −1.37619 | −0.688097 | − | 0.725618i | \(-0.741554\pi\) | ||||
−0.688097 | + | 0.725618i | \(0.741554\pi\) | |||||||
\(54\) | −128.025 | −0.322629 | ||||||||
\(55\) | −302.166 | −0.740800 | ||||||||
\(56\) | −230.049 | −0.548958 | ||||||||
\(57\) | −94.4499 | −0.219477 | ||||||||
\(58\) | 532.015 | 1.20443 | ||||||||
\(59\) | 219.666 | 0.484714 | 0.242357 | − | 0.970187i | \(-0.422080\pi\) | ||||
0.242357 | + | 0.970187i | \(0.422080\pi\) | |||||||
\(60\) | −196.250 | −0.422262 | ||||||||
\(61\) | 822.865 | 1.72717 | 0.863583 | − | 0.504207i | \(-0.168215\pi\) | ||||
0.863583 | + | 0.504207i | \(0.168215\pi\) | |||||||
\(62\) | −366.450 | −0.750632 | ||||||||
\(63\) | −67.3498 | −0.134687 | ||||||||
\(64\) | −733.082 | −1.43180 | ||||||||
\(65\) | −58.7169 | −0.112045 | ||||||||
\(66\) | 951.649 | 1.77485 | ||||||||
\(67\) | −872.082 | −1.59018 | −0.795088 | − | 0.606495i | \(-0.792575\pi\) | ||||
−0.795088 | + | 0.606495i | \(0.792575\pi\) | |||||||
\(68\) | 1404.40 | 2.50453 | ||||||||
\(69\) | −550.799 | −0.960991 | ||||||||
\(70\) | −160.267 | −0.273651 | ||||||||
\(71\) | −100.299 | −0.167653 | −0.0838263 | − | 0.996480i | \(-0.526714\pi\) | ||||
−0.0838263 | + | 0.996480i | \(0.526714\pi\) | |||||||
\(72\) | 276.675 | 0.452867 | ||||||||
\(73\) | −165.634 | −0.265562 | −0.132781 | − | 0.991145i | \(-0.542391\pi\) | ||||
−0.132781 | + | 0.991145i | \(0.542391\pi\) | |||||||
\(74\) | 259.684 | 0.407941 | ||||||||
\(75\) | 313.799 | 0.483125 | ||||||||
\(76\) | 455.983 | 0.688221 | ||||||||
\(77\) | 500.633 | 0.740940 | ||||||||
\(78\) | 184.925 | 0.268443 | ||||||||
\(79\) | −545.266 | −0.776547 | −0.388273 | − | 0.921544i | \(-0.626928\pi\) | ||||
−0.388273 | + | 0.921544i | \(0.626928\pi\) | |||||||
\(80\) | 135.048 | 0.188736 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 2141.88 | 2.88453 | ||||||||
\(83\) | −454.534 | −0.601103 | −0.300552 | − | 0.953766i | \(-0.597171\pi\) | ||||
−0.300552 | + | 0.953766i | \(0.597171\pi\) | |||||||
\(84\) | 325.150 | 0.422342 | ||||||||
\(85\) | 437.968 | 0.558874 | ||||||||
\(86\) | −537.864 | −0.674412 | ||||||||
\(87\) | −336.601 | −0.414797 | ||||||||
\(88\) | −2056.61 | −2.49132 | ||||||||
\(89\) | −230.915 | −0.275022 | −0.137511 | − | 0.990500i | \(-0.543910\pi\) | ||||
−0.137511 | + | 0.990500i | \(0.543910\pi\) | |||||||
\(90\) | 192.749 | 0.225751 | ||||||||
\(91\) | 97.2831 | 0.112066 | ||||||||
\(92\) | 2659.13 | 3.01341 | ||||||||
\(93\) | 231.849 | 0.258512 | ||||||||
\(94\) | −200.415 | −0.219907 | ||||||||
\(95\) | 142.200 | 0.153573 | ||||||||
\(96\) | 312.475 | 0.332206 | ||||||||
\(97\) | −1089.16 | −1.14008 | −0.570041 | − | 0.821616i | \(-0.693073\pi\) | ||||
−0.570041 | + | 0.821616i | \(0.693073\pi\) | |||||||
\(98\) | −1360.86 | −1.40273 | ||||||||
\(99\) | −602.099 | −0.611245 | ||||||||
\(100\) | −1514.95 | −1.51495 | ||||||||
\(101\) | −77.2336 | −0.0760894 | −0.0380447 | − | 0.999276i | \(-0.512113\pi\) | ||||
−0.0380447 | + | 0.999276i | \(0.512113\pi\) | |||||||
\(102\) | −1379.35 | −1.33898 | ||||||||
\(103\) | 1351.36 | 1.29275 | 0.646377 | − | 0.763018i | \(-0.276283\pi\) | ||||
0.646377 | + | 0.763018i | \(0.276283\pi\) | |||||||
\(104\) | −399.642 | −0.376808 | ||||||||
\(105\) | 101.399 | 0.0942434 | ||||||||
\(106\) | −2517.81 | −2.30709 | ||||||||
\(107\) | 1133.67 | 1.02426 | 0.512129 | − | 0.858908i | \(-0.328857\pi\) | ||||
0.512129 | + | 0.858908i | \(0.328857\pi\) | |||||||
\(108\) | −391.049 | −0.348414 | ||||||||
\(109\) | 1017.66 | 0.894262 | 0.447131 | − | 0.894469i | \(-0.352446\pi\) | ||||
0.447131 | + | 0.894469i | \(0.352446\pi\) | |||||||
\(110\) | −1432.77 | −1.24190 | ||||||||
\(111\) | −164.299 | −0.140492 | ||||||||
\(112\) | −223.750 | −0.188772 | ||||||||
\(113\) | 1570.06 | 1.30707 | 0.653536 | − | 0.756895i | \(-0.273285\pi\) | ||||
0.653536 | + | 0.756895i | \(0.273285\pi\) | |||||||
\(114\) | −447.849 | −0.367938 | ||||||||
\(115\) | 829.261 | 0.672426 | ||||||||
\(116\) | 1625.03 | 1.30069 | ||||||||
\(117\) | −117.000 | −0.0924500 | ||||||||
\(118\) | 1041.58 | 0.812588 | ||||||||
\(119\) | −725.632 | −0.558979 | ||||||||
\(120\) | −416.551 | −0.316881 | ||||||||
\(121\) | 3144.60 | 2.36258 | ||||||||
\(122\) | 3901.75 | 2.89547 | ||||||||
\(123\) | −1355.15 | −0.993411 | ||||||||
\(124\) | −1119.32 | −0.810625 | ||||||||
\(125\) | −1037.03 | −0.742037 | ||||||||
\(126\) | −319.350 | −0.225793 | ||||||||
\(127\) | −1248.16 | −0.872099 | −0.436050 | − | 0.899923i | \(-0.643623\pi\) | ||||
−0.436050 | + | 0.899923i | \(0.643623\pi\) | |||||||
\(128\) | −2642.76 | −1.82491 | ||||||||
\(129\) | 340.301 | 0.232263 | ||||||||
\(130\) | −278.415 | −0.187836 | ||||||||
\(131\) | −1274.80 | −0.850227 | −0.425113 | − | 0.905140i | \(-0.639766\pi\) | ||||
−0.425113 | + | 0.905140i | \(0.639766\pi\) | |||||||
\(132\) | 2906.80 | 1.91670 | ||||||||
\(133\) | −235.600 | −0.153602 | ||||||||
\(134\) | −4135.11 | −2.66582 | ||||||||
\(135\) | −121.951 | −0.0777469 | ||||||||
\(136\) | 2980.91 | 1.87950 | ||||||||
\(137\) | 874.915 | 0.545613 | 0.272807 | − | 0.962069i | \(-0.412048\pi\) | ||||
0.272807 | + | 0.962069i | \(0.412048\pi\) | |||||||
\(138\) | −2611.70 | −1.61103 | ||||||||
\(139\) | 310.334 | 0.189368 | 0.0946840 | − | 0.995507i | \(-0.469816\pi\) | ||||
0.0946840 | + | 0.995507i | \(0.469816\pi\) | |||||||
\(140\) | −489.533 | −0.295522 | ||||||||
\(141\) | 126.801 | 0.0757345 | ||||||||
\(142\) | −475.585 | −0.281058 | ||||||||
\(143\) | 869.699 | 0.508586 | ||||||||
\(144\) | 269.099 | 0.155729 | ||||||||
\(145\) | 506.773 | 0.290243 | ||||||||
\(146\) | −785.380 | −0.445195 | ||||||||
\(147\) | 861.000 | 0.483089 | ||||||||
\(148\) | 793.199 | 0.440544 | ||||||||
\(149\) | 5.08064 | 0.00279344 | 0.00139672 | − | 0.999999i | \(-0.499555\pi\) | ||||
0.00139672 | + | 0.999999i | \(0.499555\pi\) | |||||||
\(150\) | 1487.93 | 0.809924 | ||||||||
\(151\) | 6.54894 | 0.00352944 | 0.00176472 | − | 0.999998i | \(-0.499438\pi\) | ||||
0.00176472 | + | 0.999998i | \(0.499438\pi\) | |||||||
\(152\) | 967.849 | 0.516467 | ||||||||
\(153\) | 872.700 | 0.461135 | ||||||||
\(154\) | 2373.83 | 1.24213 | ||||||||
\(155\) | −349.063 | −0.180887 | ||||||||
\(156\) | 564.849 | 0.289898 | ||||||||
\(157\) | −2297.60 | −1.16795 | −0.583975 | − | 0.811772i | \(-0.698503\pi\) | ||||
−0.583975 | + | 0.811772i | \(0.698503\pi\) | |||||||
\(158\) | −2585.46 | −1.30183 | ||||||||
\(159\) | 1593.00 | 0.794546 | ||||||||
\(160\) | −470.450 | −0.232452 | ||||||||
\(161\) | −1373.93 | −0.672553 | ||||||||
\(162\) | 384.074 | 0.186270 | ||||||||
\(163\) | −1085.49 | −0.521606 | −0.260803 | − | 0.965392i | \(-0.583987\pi\) | ||||
−0.260803 | + | 0.965392i | \(0.583987\pi\) | |||||||
\(164\) | 6542.34 | 3.11507 | ||||||||
\(165\) | 906.497 | 0.427701 | ||||||||
\(166\) | −2155.24 | −1.00771 | ||||||||
\(167\) | −109.066 | −0.0505374 | −0.0252687 | − | 0.999681i | \(-0.508044\pi\) | ||||
−0.0252687 | + | 0.999681i | \(0.508044\pi\) | |||||||
\(168\) | 690.148 | 0.316941 | ||||||||
\(169\) | 169.000 | 0.0769231 | ||||||||
\(170\) | 2076.69 | 0.936912 | ||||||||
\(171\) | 283.350 | 0.126715 | ||||||||
\(172\) | −1642.90 | −0.728313 | ||||||||
\(173\) | −1889.17 | −0.830236 | −0.415118 | − | 0.909768i | \(-0.636260\pi\) | ||||
−0.415118 | + | 0.909768i | \(0.636260\pi\) | |||||||
\(174\) | −1596.05 | −0.695379 | ||||||||
\(175\) | 782.751 | 0.338117 | ||||||||
\(176\) | −2000.30 | −0.856694 | ||||||||
\(177\) | −658.999 | −0.279850 | ||||||||
\(178\) | −1094.92 | −0.461054 | ||||||||
\(179\) | 3427.86 | 1.43134 | 0.715672 | − | 0.698437i | \(-0.246121\pi\) | ||||
0.715672 | + | 0.698437i | \(0.246121\pi\) | |||||||
\(180\) | 588.749 | 0.243793 | ||||||||
\(181\) | 208.403 | 0.0855826 | 0.0427913 | − | 0.999084i | \(-0.486375\pi\) | ||||
0.0427913 | + | 0.999084i | \(0.486375\pi\) | |||||||
\(182\) | 461.283 | 0.187871 | ||||||||
\(183\) | −2468.60 | −0.997180 | ||||||||
\(184\) | 5644.15 | 2.26137 | ||||||||
\(185\) | 247.363 | 0.0983052 | ||||||||
\(186\) | 1099.35 | 0.433378 | ||||||||
\(187\) | −6487.06 | −2.53679 | ||||||||
\(188\) | −612.166 | −0.237483 | ||||||||
\(189\) | 202.049 | 0.0777616 | ||||||||
\(190\) | 674.265 | 0.257454 | ||||||||
\(191\) | 957.735 | 0.362824 | 0.181412 | − | 0.983407i | \(-0.441933\pi\) | ||||
0.181412 | + | 0.983407i | \(0.441933\pi\) | |||||||
\(192\) | 2199.25 | 0.826650 | ||||||||
\(193\) | −512.730 | −0.191228 | −0.0956142 | − | 0.995418i | \(-0.530482\pi\) | ||||
−0.0956142 | + | 0.995418i | \(0.530482\pi\) | |||||||
\(194\) | −5164.45 | −1.91127 | ||||||||
\(195\) | 176.151 | 0.0646893 | ||||||||
\(196\) | −4156.71 | −1.51484 | ||||||||
\(197\) | −3870.35 | −1.39975 | −0.699876 | − | 0.714265i | \(-0.746761\pi\) | ||||
−0.699876 | + | 0.714265i | \(0.746761\pi\) | |||||||
\(198\) | −2854.95 | −1.02471 | ||||||||
\(199\) | 2305.83 | 0.821388 | 0.410694 | − | 0.911773i | \(-0.365286\pi\) | ||||
0.410694 | + | 0.911773i | \(0.365286\pi\) | |||||||
\(200\) | −3215.56 | −1.13687 | ||||||||
\(201\) | 2616.25 | 0.918088 | ||||||||
\(202\) | −366.215 | −0.127558 | ||||||||
\(203\) | −839.630 | −0.290298 | ||||||||
\(204\) | −4213.19 | −1.44599 | ||||||||
\(205\) | 2040.26 | 0.695111 | ||||||||
\(206\) | 6407.70 | 2.16721 | ||||||||
\(207\) | 1652.40 | 0.554828 | ||||||||
\(208\) | −388.699 | −0.129574 | ||||||||
\(209\) | −2106.23 | −0.697086 | ||||||||
\(210\) | 480.801 | 0.157992 | ||||||||
\(211\) | −3672.40 | −1.19819 | −0.599096 | − | 0.800677i | \(-0.704473\pi\) | ||||
−0.599096 | + | 0.800677i | \(0.704473\pi\) | |||||||
\(212\) | −7690.62 | −2.49148 | ||||||||
\(213\) | 300.898 | 0.0967942 | ||||||||
\(214\) | 5375.46 | 1.71710 | ||||||||
\(215\) | −512.345 | −0.162519 | ||||||||
\(216\) | −830.025 | −0.261463 | ||||||||
\(217\) | 578.334 | 0.180921 | ||||||||
\(218\) | 4825.41 | 1.49917 | ||||||||
\(219\) | 496.902 | 0.153322 | ||||||||
\(220\) | −4376.36 | −1.34116 | ||||||||
\(221\) | −1260.57 | −0.383687 | ||||||||
\(222\) | −779.051 | −0.235525 | ||||||||
\(223\) | 5087.05 | 1.52760 | 0.763798 | − | 0.645455i | \(-0.223332\pi\) | ||||
0.763798 | + | 0.645455i | \(0.223332\pi\) | |||||||
\(224\) | 779.449 | 0.232496 | ||||||||
\(225\) | −941.396 | −0.278932 | ||||||||
\(226\) | 7444.71 | 2.19122 | ||||||||
\(227\) | −2625.83 | −0.767763 | −0.383882 | − | 0.923382i | \(-0.625413\pi\) | ||||
−0.383882 | + | 0.923382i | \(0.625413\pi\) | |||||||
\(228\) | −1367.95 | −0.397345 | ||||||||
\(229\) | 1678.73 | 0.484425 | 0.242213 | − | 0.970223i | \(-0.422127\pi\) | ||||
0.242213 | + | 0.970223i | \(0.422127\pi\) | |||||||
\(230\) | 3932.07 | 1.12727 | ||||||||
\(231\) | −1501.90 | −0.427782 | ||||||||
\(232\) | 3449.22 | 0.976088 | ||||||||
\(233\) | 648.506 | 0.182339 | 0.0911696 | − | 0.995835i | \(-0.470939\pi\) | ||||
0.0911696 | + | 0.995835i | \(0.470939\pi\) | |||||||
\(234\) | −554.774 | −0.154986 | ||||||||
\(235\) | −190.907 | −0.0529931 | ||||||||
\(236\) | 3181.50 | 0.877533 | ||||||||
\(237\) | 1635.80 | 0.448340 | ||||||||
\(238\) | −3440.70 | −0.937089 | ||||||||
\(239\) | 5219.69 | 1.41269 | 0.706347 | − | 0.707866i | \(-0.250342\pi\) | ||||
0.706347 | + | 0.707866i | \(0.250342\pi\) | |||||||
\(240\) | −405.145 | −0.108967 | ||||||||
\(241\) | 6103.56 | 1.63139 | 0.815695 | − | 0.578483i | \(-0.196355\pi\) | ||||
0.815695 | + | 0.578483i | \(0.196355\pi\) | |||||||
\(242\) | 14910.6 | 3.96070 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 11917.8 | 3.12689 | ||||||||
\(245\) | −1296.29 | −0.338028 | ||||||||
\(246\) | −6425.64 | −1.66538 | ||||||||
\(247\) | −409.283 | −0.105433 | ||||||||
\(248\) | −2375.81 | −0.608323 | ||||||||
\(249\) | 1363.60 | 0.347047 | ||||||||
\(250\) | −4917.24 | −1.24397 | ||||||||
\(251\) | 6423.40 | 1.61530 | 0.807652 | − | 0.589660i | \(-0.200738\pi\) | ||||
0.807652 | + | 0.589660i | \(0.200738\pi\) | |||||||
\(252\) | −975.449 | −0.243839 | ||||||||
\(253\) | −12282.8 | −3.05222 | ||||||||
\(254\) | −5918.36 | −1.46201 | ||||||||
\(255\) | −1313.90 | −0.322666 | ||||||||
\(256\) | −6666.39 | −1.62754 | ||||||||
\(257\) | −1230.23 | −0.298597 | −0.149299 | − | 0.988792i | \(-0.547702\pi\) | ||||
−0.149299 | + | 0.988792i | \(0.547702\pi\) | |||||||
\(258\) | 1613.59 | 0.389372 | ||||||||
\(259\) | −409.834 | −0.0983238 | ||||||||
\(260\) | −850.415 | −0.202848 | ||||||||
\(261\) | 1009.80 | 0.239483 | ||||||||
\(262\) | −6044.66 | −1.42534 | ||||||||
\(263\) | −514.992 | −0.120744 | −0.0603722 | − | 0.998176i | \(-0.519229\pi\) | ||||
−0.0603722 | + | 0.998176i | \(0.519229\pi\) | |||||||
\(264\) | 6169.84 | 1.43836 | ||||||||
\(265\) | −2398.35 | −0.555961 | ||||||||
\(266\) | −1117.13 | −0.257503 | ||||||||
\(267\) | 692.745 | 0.158784 | ||||||||
\(268\) | −12630.6 | −2.87888 | ||||||||
\(269\) | −5132.60 | −1.16335 | −0.581673 | − | 0.813423i | \(-0.697602\pi\) | ||||
−0.581673 | + | 0.813423i | \(0.697602\pi\) | |||||||
\(270\) | −578.247 | −0.130337 | ||||||||
\(271\) | −4300.00 | −0.963862 | −0.481931 | − | 0.876209i | \(-0.660064\pi\) | ||||
−0.481931 | + | 0.876209i | \(0.660064\pi\) | |||||||
\(272\) | 2899.29 | 0.646306 | ||||||||
\(273\) | −291.849 | −0.0647015 | ||||||||
\(274\) | 4148.55 | 0.914682 | ||||||||
\(275\) | 6997.70 | 1.53446 | ||||||||
\(276\) | −7977.39 | −1.73979 | ||||||||
\(277\) | −1812.80 | −0.393215 | −0.196607 | − | 0.980482i | \(-0.562992\pi\) | ||||
−0.196607 | + | 0.980482i | \(0.562992\pi\) | |||||||
\(278\) | 1471.50 | 0.317462 | ||||||||
\(279\) | −695.548 | −0.149252 | ||||||||
\(280\) | −1039.06 | −0.221771 | ||||||||
\(281\) | −4073.08 | −0.864696 | −0.432348 | − | 0.901707i | \(-0.642315\pi\) | ||||
−0.432348 | + | 0.901707i | \(0.642315\pi\) | |||||||
\(282\) | 601.246 | 0.126963 | ||||||||
\(283\) | 6346.29 | 1.33303 | 0.666516 | − | 0.745491i | \(-0.267785\pi\) | ||||
0.666516 | + | 0.745491i | \(0.267785\pi\) | |||||||
\(284\) | −1452.67 | −0.303520 | ||||||||
\(285\) | −426.601 | −0.0886654 | ||||||||
\(286\) | 4123.81 | 0.852609 | ||||||||
\(287\) | −3380.33 | −0.695243 | ||||||||
\(288\) | −937.424 | −0.191799 | ||||||||
\(289\) | 4489.53 | 0.913806 | ||||||||
\(290\) | 2402.94 | 0.486572 | ||||||||
\(291\) | 3267.49 | 0.658226 | ||||||||
\(292\) | −2398.93 | −0.480777 | ||||||||
\(293\) | −8390.97 | −1.67306 | −0.836529 | − | 0.547923i | \(-0.815419\pi\) | ||||
−0.836529 | + | 0.547923i | \(0.815419\pi\) | |||||||
\(294\) | 4082.57 | 0.809864 | ||||||||
\(295\) | 992.164 | 0.195817 | ||||||||
\(296\) | 1683.61 | 0.330601 | ||||||||
\(297\) | 1806.30 | 0.352902 | ||||||||
\(298\) | 24.0907 | 0.00468300 | ||||||||
\(299\) | −2386.79 | −0.461645 | ||||||||
\(300\) | 4544.84 | 0.874656 | ||||||||
\(301\) | 848.861 | 0.162550 | ||||||||
\(302\) | 31.0528 | 0.00591685 | ||||||||
\(303\) | 231.701 | 0.0439302 | ||||||||
\(304\) | 941.348 | 0.177599 | ||||||||
\(305\) | 3716.62 | 0.697748 | ||||||||
\(306\) | 4138.04 | 0.773059 | ||||||||
\(307\) | 4005.27 | 0.744603 | 0.372301 | − | 0.928112i | \(-0.378569\pi\) | ||||
0.372301 | + | 0.928112i | \(0.378569\pi\) | |||||||
\(308\) | 7250.82 | 1.34141 | ||||||||
\(309\) | −4054.09 | −0.746372 | ||||||||
\(310\) | −1655.14 | −0.303244 | ||||||||
\(311\) | 5836.53 | 1.06418 | 0.532088 | − | 0.846689i | \(-0.321407\pi\) | ||||
0.532088 | + | 0.846689i | \(0.321407\pi\) | |||||||
\(312\) | 1198.92 | 0.217550 | ||||||||
\(313\) | 1763.19 | 0.318407 | 0.159204 | − | 0.987246i | \(-0.449107\pi\) | ||||
0.159204 | + | 0.987246i | \(0.449107\pi\) | |||||||
\(314\) | −10894.4 | −1.95798 | ||||||||
\(315\) | −304.198 | −0.0544115 | ||||||||
\(316\) | −7897.26 | −1.40587 | ||||||||
\(317\) | −6106.35 | −1.08191 | −0.540957 | − | 0.841050i | \(-0.681938\pi\) | ||||
−0.540957 | + | 0.841050i | \(0.681938\pi\) | |||||||
\(318\) | 7553.44 | 1.33200 | ||||||||
\(319\) | −7506.18 | −1.31745 | ||||||||
\(320\) | −3311.10 | −0.578425 | ||||||||
\(321\) | −3401.00 | −0.591356 | ||||||||
\(322\) | −6514.72 | −1.12749 | ||||||||
\(323\) | 3052.83 | 0.525895 | ||||||||
\(324\) | 1173.15 | 0.201157 | ||||||||
\(325\) | 1359.79 | 0.232086 | ||||||||
\(326\) | −5147.00 | −0.874436 | ||||||||
\(327\) | −3052.99 | −0.516302 | ||||||||
\(328\) | 13886.5 | 2.33766 | ||||||||
\(329\) | 316.297 | 0.0530031 | ||||||||
\(330\) | 4298.30 | 0.717011 | ||||||||
\(331\) | 7490.38 | 1.24383 | 0.621916 | − | 0.783084i | \(-0.286354\pi\) | ||||
0.621916 | + | 0.783084i | \(0.286354\pi\) | |||||||
\(332\) | −6583.16 | −1.08825 | ||||||||
\(333\) | 492.898 | 0.0811130 | ||||||||
\(334\) | −517.152 | −0.0847224 | ||||||||
\(335\) | −3938.92 | −0.642406 | ||||||||
\(336\) | 671.251 | 0.108987 | ||||||||
\(337\) | 9462.46 | 1.52953 | 0.764767 | − | 0.644307i | \(-0.222854\pi\) | ||||
0.764767 | + | 0.644307i | \(0.222854\pi\) | |||||||
\(338\) | 801.340 | 0.128956 | ||||||||
\(339\) | −4710.19 | −0.754639 | ||||||||
\(340\) | 6343.22 | 1.01179 | ||||||||
\(341\) | 5170.23 | 0.821066 | ||||||||
\(342\) | 1343.55 | 0.212429 | ||||||||
\(343\) | 4714.49 | 0.742153 | ||||||||
\(344\) | −3487.14 | −0.546553 | ||||||||
\(345\) | −2487.78 | −0.388226 | ||||||||
\(346\) | −8957.79 | −1.39183 | ||||||||
\(347\) | 11460.3 | 1.77297 | 0.886487 | − | 0.462753i | \(-0.153138\pi\) | ||||
0.886487 | + | 0.462753i | \(0.153138\pi\) | |||||||
\(348\) | −4875.09 | −0.750955 | ||||||||
\(349\) | −3673.96 | −0.563503 | −0.281751 | − | 0.959487i | \(-0.590915\pi\) | ||||
−0.281751 | + | 0.959487i | \(0.590915\pi\) | |||||||
\(350\) | 3711.54 | 0.566829 | ||||||||
\(351\) | 351.000 | 0.0533761 | ||||||||
\(352\) | 6968.17 | 1.05513 | ||||||||
\(353\) | 3388.65 | 0.510935 | 0.255467 | − | 0.966818i | \(-0.417771\pi\) | ||||
0.255467 | + | 0.966818i | \(0.417771\pi\) | |||||||
\(354\) | −3124.75 | −0.469148 | ||||||||
\(355\) | −453.020 | −0.0677290 | ||||||||
\(356\) | −3344.41 | −0.497903 | ||||||||
\(357\) | 2176.90 | 0.322727 | ||||||||
\(358\) | 16253.7 | 2.39955 | ||||||||
\(359\) | −9673.98 | −1.42221 | −0.711105 | − | 0.703086i | \(-0.751805\pi\) | ||||
−0.711105 | + | 0.703086i | \(0.751805\pi\) | |||||||
\(360\) | 1249.65 | 0.182951 | ||||||||
\(361\) | −5867.80 | −0.855489 | ||||||||
\(362\) | 988.174 | 0.143473 | ||||||||
\(363\) | −9433.79 | −1.36404 | ||||||||
\(364\) | 1408.98 | 0.202887 | ||||||||
\(365\) | −748.117 | −0.107283 | ||||||||
\(366\) | −11705.2 | −1.67170 | ||||||||
\(367\) | −8715.98 | −1.23970 | −0.619851 | − | 0.784720i | \(-0.712807\pi\) | ||||
−0.619851 | + | 0.784720i | \(0.712807\pi\) | |||||||
\(368\) | 5489.61 | 0.777624 | ||||||||
\(369\) | 4065.44 | 0.573546 | ||||||||
\(370\) | 1172.91 | 0.164802 | ||||||||
\(371\) | 3973.63 | 0.556067 | ||||||||
\(372\) | 3357.95 | 0.468014 | ||||||||
\(373\) | 4667.99 | 0.647987 | 0.323994 | − | 0.946059i | \(-0.394974\pi\) | ||||
0.323994 | + | 0.946059i | \(0.394974\pi\) | |||||||
\(374\) | −30759.4 | −4.25276 | ||||||||
\(375\) | 3111.09 | 0.428416 | ||||||||
\(376\) | −1299.36 | −0.178216 | ||||||||
\(377\) | −1458.60 | −0.199262 | ||||||||
\(378\) | 958.049 | 0.130362 | ||||||||
\(379\) | 10862.7 | 1.47225 | 0.736123 | − | 0.676848i | \(-0.236655\pi\) | ||||
0.736123 | + | 0.676848i | \(0.236655\pi\) | |||||||
\(380\) | 2059.53 | 0.278031 | ||||||||
\(381\) | 3744.49 | 0.503507 | ||||||||
\(382\) | 4541.25 | 0.608248 | ||||||||
\(383\) | 10054.2 | 1.34137 | 0.670686 | − | 0.741742i | \(-0.266000\pi\) | ||||
0.670686 | + | 0.741742i | \(0.266000\pi\) | |||||||
\(384\) | 7928.27 | 1.05361 | ||||||||
\(385\) | 2261.20 | 0.299329 | ||||||||
\(386\) | −2431.19 | −0.320581 | ||||||||
\(387\) | −1020.90 | −0.134097 | ||||||||
\(388\) | −15774.7 | −2.06402 | ||||||||
\(389\) | 6418.50 | 0.836584 | 0.418292 | − | 0.908313i | \(-0.362629\pi\) | ||||
0.418292 | + | 0.908313i | \(0.362629\pi\) | |||||||
\(390\) | 835.246 | 0.108447 | ||||||||
\(391\) | 17803.0 | 2.30265 | ||||||||
\(392\) | −8822.86 | −1.13679 | ||||||||
\(393\) | 3824.40 | 0.490879 | ||||||||
\(394\) | −18351.9 | −2.34658 | ||||||||
\(395\) | −2462.79 | −0.313713 | ||||||||
\(396\) | −8720.39 | −1.10661 | ||||||||
\(397\) | −12019.9 | −1.51955 | −0.759775 | − | 0.650186i | \(-0.774691\pi\) | ||||
−0.759775 | + | 0.650186i | \(0.774691\pi\) | |||||||
\(398\) | 10933.5 | 1.37700 | ||||||||
\(399\) | 706.799 | 0.0886822 | ||||||||
\(400\) | −3127.52 | −0.390939 | ||||||||
\(401\) | 3599.80 | 0.448293 | 0.224147 | − | 0.974555i | \(-0.428041\pi\) | ||||
0.224147 | + | 0.974555i | \(0.428041\pi\) | |||||||
\(402\) | 12405.3 | 1.53911 | ||||||||
\(403\) | 1004.68 | 0.124185 | ||||||||
\(404\) | −1118.60 | −0.137753 | ||||||||
\(405\) | 365.852 | 0.0448872 | ||||||||
\(406\) | −3981.24 | −0.486664 | ||||||||
\(407\) | −3663.87 | −0.446219 | ||||||||
\(408\) | −8942.74 | −1.08513 | ||||||||
\(409\) | −48.0968 | −0.00581475 | −0.00290737 | − | 0.999996i | \(-0.500925\pi\) | ||||
−0.00290737 | + | 0.999996i | \(0.500925\pi\) | |||||||
\(410\) | 9674.20 | 1.16530 | ||||||||
\(411\) | −2624.74 | −0.315010 | ||||||||
\(412\) | 19572.2 | 2.34042 | ||||||||
\(413\) | −1643.83 | −0.195854 | ||||||||
\(414\) | 7835.10 | 0.930130 | ||||||||
\(415\) | −2052.99 | −0.242837 | ||||||||
\(416\) | 1354.06 | 0.159587 | ||||||||
\(417\) | −931.001 | −0.109332 | ||||||||
\(418\) | −9987.02 | −1.16862 | ||||||||
\(419\) | 723.462 | 0.0843518 | 0.0421759 | − | 0.999110i | \(-0.486571\pi\) | ||||
0.0421759 | + | 0.999110i | \(0.486571\pi\) | |||||||
\(420\) | 1468.60 | 0.170620 | ||||||||
\(421\) | −14845.5 | −1.71859 | −0.859295 | − | 0.511481i | \(-0.829097\pi\) | ||||
−0.859295 | + | 0.511481i | \(0.829097\pi\) | |||||||
\(422\) | −17413.3 | −2.00868 | ||||||||
\(423\) | −380.403 | −0.0437253 | ||||||||
\(424\) | −16323.8 | −1.86970 | ||||||||
\(425\) | −10142.7 | −1.15763 | ||||||||
\(426\) | 1426.75 | 0.162269 | ||||||||
\(427\) | −6157.76 | −0.697880 | ||||||||
\(428\) | 16419.2 | 1.85433 | ||||||||
\(429\) | −2609.10 | −0.293632 | ||||||||
\(430\) | −2429.36 | −0.272452 | ||||||||
\(431\) | 1103.11 | 0.123283 | 0.0616417 | − | 0.998098i | \(-0.480366\pi\) | ||||
0.0616417 | + | 0.998098i | \(0.480366\pi\) | |||||||
\(432\) | −807.297 | −0.0899099 | ||||||||
\(433\) | 8893.53 | 0.987057 | 0.493528 | − | 0.869730i | \(-0.335707\pi\) | ||||
0.493528 | + | 0.869730i | \(0.335707\pi\) | |||||||
\(434\) | 2742.26 | 0.303301 | ||||||||
\(435\) | −1520.32 | −0.167572 | ||||||||
\(436\) | 14739.1 | 1.61898 | ||||||||
\(437\) | 5780.32 | 0.632747 | ||||||||
\(438\) | 2356.14 | 0.257034 | ||||||||
\(439\) | −10901.7 | −1.18521 | −0.592607 | − | 0.805492i | \(-0.701901\pi\) | ||||
−0.592607 | + | 0.805492i | \(0.701901\pi\) | |||||||
\(440\) | −9289.08 | −1.00645 | ||||||||
\(441\) | −2583.00 | −0.278912 | ||||||||
\(442\) | −5977.17 | −0.643224 | ||||||||
\(443\) | −3781.37 | −0.405550 | −0.202775 | − | 0.979225i | \(-0.564996\pi\) | ||||
−0.202775 | + | 0.979225i | \(0.564996\pi\) | |||||||
\(444\) | −2379.60 | −0.254348 | ||||||||
\(445\) | −1042.97 | −0.111105 | ||||||||
\(446\) | 24121.0 | 2.56091 | ||||||||
\(447\) | −15.2419 | −0.00161279 | ||||||||
\(448\) | 5485.88 | 0.578535 | ||||||||
\(449\) | 106.834 | 0.0112289 | 0.00561447 | − | 0.999984i | \(-0.498213\pi\) | ||||
0.00561447 | + | 0.999984i | \(0.498213\pi\) | |||||||
\(450\) | −4463.78 | −0.467610 | ||||||||
\(451\) | −30219.7 | −3.15519 | ||||||||
\(452\) | 22739.7 | 2.36634 | ||||||||
\(453\) | −19.6468 | −0.00203772 | ||||||||
\(454\) | −12450.8 | −1.28710 | ||||||||
\(455\) | 439.397 | 0.0452731 | ||||||||
\(456\) | −2903.55 | −0.298182 | ||||||||
\(457\) | −1237.64 | −0.126684 | −0.0633419 | − | 0.997992i | \(-0.520176\pi\) | ||||
−0.0633419 | + | 0.997992i | \(0.520176\pi\) | |||||||
\(458\) | 7959.95 | 0.812105 | ||||||||
\(459\) | −2618.10 | −0.266236 | ||||||||
\(460\) | 12010.5 | 1.21737 | ||||||||
\(461\) | 8790.90 | 0.888141 | 0.444071 | − | 0.895992i | \(-0.353534\pi\) | ||||
0.444071 | + | 0.895992i | \(0.353534\pi\) | |||||||
\(462\) | −7121.49 | −0.717146 | ||||||||
\(463\) | −3861.55 | −0.387606 | −0.193803 | − | 0.981040i | \(-0.562082\pi\) | ||||
−0.193803 | + | 0.981040i | \(0.562082\pi\) | |||||||
\(464\) | 3354.77 | 0.335650 | ||||||||
\(465\) | 1047.19 | 0.104435 | ||||||||
\(466\) | 3074.99 | 0.305679 | ||||||||
\(467\) | −8991.38 | −0.890945 | −0.445473 | − | 0.895296i | \(-0.646964\pi\) | ||||
−0.445473 | + | 0.895296i | \(0.646964\pi\) | |||||||
\(468\) | −1694.55 | −0.167373 | ||||||||
\(469\) | 6526.06 | 0.642528 | ||||||||
\(470\) | −905.214 | −0.0888391 | ||||||||
\(471\) | 6892.79 | 0.674316 | ||||||||
\(472\) | 6752.91 | 0.658533 | ||||||||
\(473\) | 7588.71 | 0.737694 | ||||||||
\(474\) | 7756.39 | 0.751609 | ||||||||
\(475\) | −3293.14 | −0.318105 | ||||||||
\(476\) | −10509.6 | −1.01198 | ||||||||
\(477\) | −4778.99 | −0.458731 | ||||||||
\(478\) | 24750.0 | 2.36828 | ||||||||
\(479\) | 4179.82 | 0.398707 | 0.199354 | − | 0.979928i | \(-0.436116\pi\) | ||||
0.199354 | + | 0.979928i | \(0.436116\pi\) | |||||||
\(480\) | 1411.35 | 0.134206 | ||||||||
\(481\) | −711.963 | −0.0674901 | ||||||||
\(482\) | 28941.0 | 2.73491 | ||||||||
\(483\) | 4121.80 | 0.388299 | ||||||||
\(484\) | 45544.2 | 4.27725 | ||||||||
\(485\) | −4919.41 | −0.460575 | ||||||||
\(486\) | −1152.22 | −0.107543 | ||||||||
\(487\) | −18443.8 | −1.71616 | −0.858078 | − | 0.513519i | \(-0.828342\pi\) | ||||
−0.858078 | + | 0.513519i | \(0.828342\pi\) | |||||||
\(488\) | 25296.2 | 2.34653 | ||||||||
\(489\) | 3256.46 | 0.301149 | ||||||||
\(490\) | −6146.56 | −0.566680 | ||||||||
\(491\) | 8093.26 | 0.743877 | 0.371939 | − | 0.928257i | \(-0.378693\pi\) | ||||
0.371939 | + | 0.928257i | \(0.378693\pi\) | |||||||
\(492\) | −19627.0 | −1.79849 | ||||||||
\(493\) | 10879.7 | 0.993907 | ||||||||
\(494\) | −1940.68 | −0.176752 | ||||||||
\(495\) | −2719.49 | −0.246933 | ||||||||
\(496\) | −2310.76 | −0.209185 | ||||||||
\(497\) | 750.571 | 0.0677418 | ||||||||
\(498\) | 6465.73 | 0.581800 | ||||||||
\(499\) | −10941.6 | −0.981591 | −0.490796 | − | 0.871275i | \(-0.663294\pi\) | ||||
−0.490796 | + | 0.871275i | \(0.663294\pi\) | |||||||
\(500\) | −15019.6 | −1.34340 | ||||||||
\(501\) | 327.197 | 0.0291778 | ||||||||
\(502\) | 30457.5 | 2.70794 | ||||||||
\(503\) | −9260.11 | −0.820851 | −0.410425 | − | 0.911894i | \(-0.634620\pi\) | ||||
−0.410425 | + | 0.911894i | \(0.634620\pi\) | |||||||
\(504\) | −2070.45 | −0.182986 | ||||||||
\(505\) | −348.840 | −0.0307389 | ||||||||
\(506\) | −58240.8 | −5.11684 | ||||||||
\(507\) | −507.000 | −0.0444116 | ||||||||
\(508\) | −18077.5 | −1.57886 | ||||||||
\(509\) | −9996.40 | −0.870497 | −0.435248 | − | 0.900310i | \(-0.643339\pi\) | ||||
−0.435248 | + | 0.900310i | \(0.643339\pi\) | |||||||
\(510\) | −6230.08 | −0.540927 | ||||||||
\(511\) | 1239.49 | 0.107303 | ||||||||
\(512\) | −10467.7 | −0.903538 | ||||||||
\(513\) | −850.049 | −0.0731591 | ||||||||
\(514\) | −5833.32 | −0.500577 | ||||||||
\(515\) | 6103.68 | 0.522253 | ||||||||
\(516\) | 4928.69 | 0.420491 | ||||||||
\(517\) | 2827.66 | 0.240542 | ||||||||
\(518\) | −1943.29 | −0.164833 | ||||||||
\(519\) | 5667.51 | 0.479337 | ||||||||
\(520\) | −1805.06 | −0.152225 | ||||||||
\(521\) | 11427.9 | 0.960973 | 0.480486 | − | 0.877002i | \(-0.340460\pi\) | ||||
0.480486 | + | 0.877002i | \(0.340460\pi\) | |||||||
\(522\) | 4788.14 | 0.401477 | ||||||||
\(523\) | −4810.47 | −0.402193 | −0.201097 | − | 0.979571i | \(-0.564451\pi\) | ||||
−0.201097 | + | 0.979571i | \(0.564451\pi\) | |||||||
\(524\) | −18463.3 | −1.53926 | ||||||||
\(525\) | −2348.25 | −0.195212 | ||||||||
\(526\) | −2441.92 | −0.202419 | ||||||||
\(527\) | −7493.88 | −0.619428 | ||||||||
\(528\) | 6000.90 | 0.494613 | ||||||||
\(529\) | 21541.8 | 1.77051 | ||||||||
\(530\) | −11372.2 | −0.932030 | ||||||||
\(531\) | 1977.00 | 0.161571 | ||||||||
\(532\) | −3412.26 | −0.278083 | ||||||||
\(533\) | −5872.31 | −0.477219 | ||||||||
\(534\) | 3284.76 | 0.266190 | ||||||||
\(535\) | 5120.41 | 0.413785 | ||||||||
\(536\) | −26809.2 | −2.16042 | ||||||||
\(537\) | −10283.6 | −0.826386 | ||||||||
\(538\) | −24337.0 | −1.95027 | ||||||||
\(539\) | 19200.3 | 1.53435 | ||||||||
\(540\) | −1766.25 | −0.140754 | ||||||||
\(541\) | 2411.99 | 0.191681 | 0.0958406 | − | 0.995397i | \(-0.469446\pi\) | ||||
0.0958406 | + | 0.995397i | \(0.469446\pi\) | |||||||
\(542\) | −20389.1 | −1.61585 | ||||||||
\(543\) | −625.208 | −0.0494111 | ||||||||
\(544\) | −10099.9 | −0.796008 | ||||||||
\(545\) | 4596.47 | 0.361268 | ||||||||
\(546\) | −1383.85 | −0.108468 | ||||||||
\(547\) | −4396.34 | −0.343646 | −0.171823 | − | 0.985128i | \(-0.554966\pi\) | ||||
−0.171823 | + | 0.985128i | \(0.554966\pi\) | |||||||
\(548\) | 12671.7 | 0.987786 | ||||||||
\(549\) | 7405.79 | 0.575722 | ||||||||
\(550\) | 33180.7 | 2.57242 | ||||||||
\(551\) | 3532.43 | 0.273116 | ||||||||
\(552\) | −16932.5 | −1.30560 | ||||||||
\(553\) | 4080.40 | 0.313772 | ||||||||
\(554\) | −8595.67 | −0.659197 | ||||||||
\(555\) | −742.088 | −0.0567565 | ||||||||
\(556\) | 4494.66 | 0.342835 | ||||||||
\(557\) | −17488.0 | −1.33032 | −0.665160 | − | 0.746701i | \(-0.731637\pi\) | ||||
−0.665160 | + | 0.746701i | \(0.731637\pi\) | |||||||
\(558\) | −3298.05 | −0.250211 | ||||||||
\(559\) | 1474.64 | 0.111575 | ||||||||
\(560\) | −1010.61 | −0.0762608 | ||||||||
\(561\) | 19461.2 | 1.46462 | ||||||||
\(562\) | −19313.2 | −1.44960 | ||||||||
\(563\) | −6881.77 | −0.515154 | −0.257577 | − | 0.966258i | \(-0.582924\pi\) | ||||
−0.257577 | + | 0.966258i | \(0.582924\pi\) | |||||||
\(564\) | 1836.50 | 0.137111 | ||||||||
\(565\) | 7091.49 | 0.528037 | ||||||||
\(566\) | 30092.0 | 2.23473 | ||||||||
\(567\) | −606.148 | −0.0448957 | ||||||||
\(568\) | −3083.36 | −0.227773 | ||||||||
\(569\) | 14733.5 | 1.08552 | 0.542758 | − | 0.839889i | \(-0.317380\pi\) | ||||
0.542758 | + | 0.839889i | \(0.317380\pi\) | |||||||
\(570\) | −2022.79 | −0.148641 | ||||||||
\(571\) | 4488.51 | 0.328964 | 0.164482 | − | 0.986380i | \(-0.447405\pi\) | ||||
0.164482 | + | 0.986380i | \(0.447405\pi\) | |||||||
\(572\) | 12596.1 | 0.920752 | ||||||||
\(573\) | −2873.21 | −0.209476 | ||||||||
\(574\) | −16028.4 | −1.16553 | ||||||||
\(575\) | −19204.4 | −1.39284 | ||||||||
\(576\) | −6597.74 | −0.477267 | ||||||||
\(577\) | −10552.2 | −0.761338 | −0.380669 | − | 0.924711i | \(-0.624306\pi\) | ||||
−0.380669 | + | 0.924711i | \(0.624306\pi\) | |||||||
\(578\) | 21287.8 | 1.53193 | ||||||||
\(579\) | 1538.19 | 0.110406 | ||||||||
\(580\) | 7339.75 | 0.525460 | ||||||||
\(581\) | 3401.42 | 0.242882 | ||||||||
\(582\) | 15493.3 | 1.10347 | ||||||||
\(583\) | 35523.8 | 2.52357 | ||||||||
\(584\) | −5091.86 | −0.360793 | ||||||||
\(585\) | −528.452 | −0.0373484 | ||||||||
\(586\) | −39787.1 | −2.80476 | ||||||||
\(587\) | −1637.20 | −0.115118 | −0.0575591 | − | 0.998342i | \(-0.518332\pi\) | ||||
−0.0575591 | + | 0.998342i | \(0.518332\pi\) | |||||||
\(588\) | 12470.1 | 0.874591 | ||||||||
\(589\) | −2433.13 | −0.170213 | ||||||||
\(590\) | 4704.50 | 0.328273 | ||||||||
\(591\) | 11611.1 | 0.808147 | ||||||||
\(592\) | 1637.51 | 0.113685 | ||||||||
\(593\) | 14024.0 | 0.971155 | 0.485577 | − | 0.874194i | \(-0.338609\pi\) | ||||
0.485577 | + | 0.874194i | \(0.338609\pi\) | |||||||
\(594\) | 8564.84 | 0.591616 | ||||||||
\(595\) | −3277.45 | −0.225819 | ||||||||
\(596\) | 73.5845 | 0.00505728 | ||||||||
\(597\) | −6917.50 | −0.474229 | ||||||||
\(598\) | −11317.4 | −0.773915 | ||||||||
\(599\) | 365.860 | 0.0249560 | 0.0124780 | − | 0.999922i | \(-0.496028\pi\) | ||||
0.0124780 | + | 0.999922i | \(0.496028\pi\) | |||||||
\(600\) | 9646.69 | 0.656374 | ||||||||
\(601\) | −10128.9 | −0.687465 | −0.343733 | − | 0.939068i | \(-0.611691\pi\) | ||||
−0.343733 | + | 0.939068i | \(0.611691\pi\) | |||||||
\(602\) | 4025.01 | 0.272503 | ||||||||
\(603\) | −7848.74 | −0.530058 | ||||||||
\(604\) | 94.8504 | 0.00638975 | ||||||||
\(605\) | 14203.1 | 0.954446 | ||||||||
\(606\) | 1098.65 | 0.0736459 | ||||||||
\(607\) | 2324.97 | 0.155465 | 0.0777327 | − | 0.996974i | \(-0.475232\pi\) | ||||
0.0777327 | + | 0.996974i | \(0.475232\pi\) | |||||||
\(608\) | −3279.25 | −0.218735 | ||||||||
\(609\) | 2518.89 | 0.167603 | ||||||||
\(610\) | 17623.0 | 1.16973 | ||||||||
\(611\) | 549.471 | 0.0363817 | ||||||||
\(612\) | 12639.6 | 0.834845 | ||||||||
\(613\) | 633.133 | 0.0417162 | 0.0208581 | − | 0.999782i | \(-0.493360\pi\) | ||||
0.0208581 | + | 0.999782i | \(0.493360\pi\) | |||||||
\(614\) | 18991.6 | 1.24827 | ||||||||
\(615\) | −6120.77 | −0.401323 | ||||||||
\(616\) | 15390.3 | 1.00664 | ||||||||
\(617\) | −2981.85 | −0.194562 | −0.0972810 | − | 0.995257i | \(-0.531015\pi\) | ||||
−0.0972810 | + | 0.995257i | \(0.531015\pi\) | |||||||
\(618\) | −19223.1 | −1.25124 | ||||||||
\(619\) | 15158.6 | 0.984292 | 0.492146 | − | 0.870513i | \(-0.336213\pi\) | ||||
0.492146 | + | 0.870513i | \(0.336213\pi\) | |||||||
\(620\) | −5055.60 | −0.327480 | ||||||||
\(621\) | −4957.19 | −0.320330 | ||||||||
\(622\) | 27674.8 | 1.78402 | ||||||||
\(623\) | 1728.01 | 0.111126 | ||||||||
\(624\) | 1166.10 | 0.0748096 | ||||||||
\(625\) | 8391.01 | 0.537025 | ||||||||
\(626\) | 8360.45 | 0.533787 | ||||||||
\(627\) | 6318.69 | 0.402463 | ||||||||
\(628\) | −33276.8 | −2.11447 | ||||||||
\(629\) | 5310.51 | 0.336636 | ||||||||
\(630\) | −1442.40 | −0.0912170 | ||||||||
\(631\) | 5562.30 | 0.350922 | 0.175461 | − | 0.984486i | \(-0.443858\pi\) | ||||
0.175461 | + | 0.984486i | \(0.443858\pi\) | |||||||
\(632\) | −16762.4 | −1.05502 | ||||||||
\(633\) | 11017.2 | 0.691776 | ||||||||
\(634\) | −28954.2 | −1.81375 | ||||||||
\(635\) | −5637.56 | −0.352315 | ||||||||
\(636\) | 23071.9 | 1.43846 | ||||||||
\(637\) | 3731.00 | 0.232068 | ||||||||
\(638\) | −35591.7 | −2.20861 | ||||||||
\(639\) | −902.693 | −0.0558842 | ||||||||
\(640\) | −11936.5 | −0.737237 | ||||||||
\(641\) | −24140.7 | −1.48752 | −0.743761 | − | 0.668446i | \(-0.766960\pi\) | ||||
−0.743761 | + | 0.668446i | \(0.766960\pi\) | |||||||
\(642\) | −16126.4 | −0.991366 | ||||||||
\(643\) | −1749.69 | −0.107311 | −0.0536555 | − | 0.998560i | \(-0.517087\pi\) | ||||
−0.0536555 | + | 0.998560i | \(0.517087\pi\) | |||||||
\(644\) | −19899.1 | −1.21760 | ||||||||
\(645\) | 1537.03 | 0.0938305 | ||||||||
\(646\) | 14475.5 | 0.881626 | ||||||||
\(647\) | 1489.51 | 0.0905083 | 0.0452542 | − | 0.998976i | \(-0.485590\pi\) | ||||
0.0452542 | + | 0.998976i | \(0.485590\pi\) | |||||||
\(648\) | 2490.07 | 0.150956 | ||||||||
\(649\) | −14695.7 | −0.888836 | ||||||||
\(650\) | 6447.68 | 0.389075 | ||||||||
\(651\) | −1735.00 | −0.104455 | ||||||||
\(652\) | −15721.4 | −0.944323 | ||||||||
\(653\) | 10668.2 | 0.639327 | 0.319663 | − | 0.947531i | \(-0.396430\pi\) | ||||
0.319663 | + | 0.947531i | \(0.396430\pi\) | |||||||
\(654\) | −14476.2 | −0.865544 | ||||||||
\(655\) | −5757.86 | −0.343478 | ||||||||
\(656\) | 13506.3 | 0.803858 | ||||||||
\(657\) | −1490.71 | −0.0885205 | ||||||||
\(658\) | 1499.77 | 0.0888559 | ||||||||
\(659\) | −13933.1 | −0.823608 | −0.411804 | − | 0.911272i | \(-0.635101\pi\) | ||||
−0.411804 | + | 0.911272i | \(0.635101\pi\) | |||||||
\(660\) | 13129.1 | 0.774317 | ||||||||
\(661\) | −2349.69 | −0.138264 | −0.0691320 | − | 0.997608i | \(-0.522023\pi\) | ||||
−0.0691320 | + | 0.997608i | \(0.522023\pi\) | |||||||
\(662\) | 35516.8 | 2.08520 | ||||||||
\(663\) | 3781.70 | 0.221522 | ||||||||
\(664\) | −13973.1 | −0.816660 | ||||||||
\(665\) | −1064.13 | −0.0620529 | ||||||||
\(666\) | 2337.15 | 0.135980 | ||||||||
\(667\) | 20599.9 | 1.19585 | ||||||||
\(668\) | −1579.63 | −0.0914937 | ||||||||
\(669\) | −15261.1 | −0.881958 | ||||||||
\(670\) | −18677.0 | −1.07695 | ||||||||
\(671\) | −55049.6 | −3.16716 | ||||||||
\(672\) | −2338.35 | −0.134232 | ||||||||
\(673\) | −32421.0 | −1.85697 | −0.928483 | − | 0.371374i | \(-0.878887\pi\) | ||||
−0.928483 | + | 0.371374i | \(0.878887\pi\) | |||||||
\(674\) | 44867.7 | 2.56415 | ||||||||
\(675\) | 2824.19 | 0.161042 | ||||||||
\(676\) | 2447.68 | 0.139263 | ||||||||
\(677\) | −1071.74 | −0.0608421 | −0.0304211 | − | 0.999537i | \(-0.509685\pi\) | ||||
−0.0304211 | + | 0.999537i | \(0.509685\pi\) | |||||||
\(678\) | −22334.1 | −1.26510 | ||||||||
\(679\) | 8150.56 | 0.460663 | ||||||||
\(680\) | 13463.9 | 0.759287 | ||||||||
\(681\) | 7877.48 | 0.443268 | ||||||||
\(682\) | 24515.5 | 1.37646 | ||||||||
\(683\) | −305.487 | −0.0171144 | −0.00855721 | − | 0.999963i | \(-0.502724\pi\) | ||||
−0.00855721 | + | 0.999963i | \(0.502724\pi\) | |||||||
\(684\) | 4103.84 | 0.229407 | ||||||||
\(685\) | 3951.72 | 0.220419 | ||||||||
\(686\) | 22354.5 | 1.24417 | ||||||||
\(687\) | −5036.18 | −0.279683 | ||||||||
\(688\) | −3391.66 | −0.187944 | ||||||||
\(689\) | 6902.99 | 0.381688 | ||||||||
\(690\) | −11796.2 | −0.650833 | ||||||||
\(691\) | 2180.81 | 0.120061 | 0.0600303 | − | 0.998197i | \(-0.480880\pi\) | ||||
0.0600303 | + | 0.998197i | \(0.480880\pi\) | |||||||
\(692\) | −27361.4 | −1.50307 | ||||||||
\(693\) | 4505.70 | 0.246980 | ||||||||
\(694\) | 54340.9 | 2.97227 | ||||||||
\(695\) | 1401.68 | 0.0765018 | ||||||||
\(696\) | −10347.7 | −0.563545 | ||||||||
\(697\) | 43801.4 | 2.38034 | ||||||||
\(698\) | −17420.6 | −0.944672 | ||||||||
\(699\) | −1945.52 | −0.105274 | ||||||||
\(700\) | 11336.8 | 0.612132 | ||||||||
\(701\) | −15168.3 | −0.817259 | −0.408629 | − | 0.912700i | \(-0.633993\pi\) | ||||
−0.408629 | + | 0.912700i | \(0.633993\pi\) | |||||||
\(702\) | 1664.32 | 0.0894812 | ||||||||
\(703\) | 1724.23 | 0.0925043 | ||||||||
\(704\) | 49043.1 | 2.62554 | ||||||||
\(705\) | 572.720 | 0.0305956 | ||||||||
\(706\) | 16067.8 | 0.856545 | ||||||||
\(707\) | 577.963 | 0.0307448 | ||||||||
\(708\) | −9544.49 | −0.506644 | ||||||||
\(709\) | −8988.17 | −0.476104 | −0.238052 | − | 0.971252i | \(-0.576509\pi\) | ||||
−0.238052 | + | 0.971252i | \(0.576509\pi\) | |||||||
\(710\) | −2148.07 | −0.113543 | ||||||||
\(711\) | −4907.39 | −0.258849 | ||||||||
\(712\) | −7098.71 | −0.373645 | ||||||||
\(713\) | −14189.1 | −0.745284 | ||||||||
\(714\) | 10322.1 | 0.541029 | ||||||||
\(715\) | 3928.15 | 0.205461 | ||||||||
\(716\) | 49646.8 | 2.59132 | ||||||||
\(717\) | −15659.1 | −0.815619 | ||||||||
\(718\) | −45870.7 | −2.38423 | ||||||||
\(719\) | 8448.18 | 0.438198 | 0.219099 | − | 0.975703i | \(-0.429688\pi\) | ||||
0.219099 | + | 0.975703i | \(0.429688\pi\) | |||||||
\(720\) | 1215.44 | 0.0629120 | ||||||||
\(721\) | −10112.7 | −0.522352 | ||||||||
\(722\) | −27823.1 | −1.43417 | ||||||||
\(723\) | −18310.7 | −0.941883 | ||||||||
\(724\) | 3018.36 | 0.154940 | ||||||||
\(725\) | −11736.1 | −0.601197 | ||||||||
\(726\) | −44731.8 | −2.28671 | ||||||||
\(727\) | −8624.18 | −0.439963 | −0.219982 | − | 0.975504i | \(-0.570600\pi\) | ||||
−0.219982 | + | 0.975504i | \(0.570600\pi\) | |||||||
\(728\) | 2990.64 | 0.152254 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −3547.31 | −0.179852 | ||||||||
\(731\) | −10999.3 | −0.556530 | ||||||||
\(732\) | −35753.5 | −1.80531 | ||||||||
\(733\) | 31124.2 | 1.56835 | 0.784174 | − | 0.620541i | \(-0.213087\pi\) | ||||
0.784174 | + | 0.620541i | \(0.213087\pi\) | |||||||
\(734\) | −41328.2 | −2.07827 | ||||||||
\(735\) | 3888.87 | 0.195161 | ||||||||
\(736\) | −19123.4 | −0.957742 | ||||||||
\(737\) | 58342.2 | 2.91596 | ||||||||
\(738\) | 19276.9 | 0.961509 | ||||||||
\(739\) | −17671.1 | −0.879626 | −0.439813 | − | 0.898089i | \(-0.644955\pi\) | ||||
−0.439813 | + | 0.898089i | \(0.644955\pi\) | |||||||
\(740\) | 3582.63 | 0.177973 | ||||||||
\(741\) | 1227.85 | 0.0608720 | ||||||||
\(742\) | 18841.6 | 0.932206 | ||||||||
\(743\) | −21331.1 | −1.05325 | −0.526623 | − | 0.850099i | \(-0.676542\pi\) | ||||
−0.526623 | + | 0.850099i | \(0.676542\pi\) | |||||||
\(744\) | 7127.43 | 0.351215 | ||||||||
\(745\) | 22.9477 | 0.00112851 | ||||||||
\(746\) | 22134.0 | 1.08630 | ||||||||
\(747\) | −4090.81 | −0.200368 | ||||||||
\(748\) | −93954.1 | −4.59265 | ||||||||
\(749\) | −8483.58 | −0.413863 | ||||||||
\(750\) | 14751.7 | 0.718208 | ||||||||
\(751\) | 11712.9 | 0.569122 | 0.284561 | − | 0.958658i | \(-0.408152\pi\) | ||||
0.284561 | + | 0.958658i | \(0.408152\pi\) | |||||||
\(752\) | −1263.78 | −0.0612835 | ||||||||
\(753\) | −19270.2 | −0.932596 | ||||||||
\(754\) | −6916.20 | −0.334049 | ||||||||
\(755\) | 29.5795 | 0.00142584 | ||||||||
\(756\) | 2926.35 | 0.140781 | ||||||||
\(757\) | −16610.9 | −0.797537 | −0.398768 | − | 0.917052i | \(-0.630562\pi\) | ||||
−0.398768 | + | 0.917052i | \(0.630562\pi\) | |||||||
\(758\) | 51507.4 | 2.46812 | ||||||||
\(759\) | 36848.4 | 1.76220 | ||||||||
\(760\) | 4371.47 | 0.208645 | ||||||||
\(761\) | −29365.5 | −1.39882 | −0.699408 | − | 0.714723i | \(-0.746553\pi\) | ||||
−0.699408 | + | 0.714723i | \(0.746553\pi\) | |||||||
\(762\) | 17755.1 | 0.844093 | ||||||||
\(763\) | −7615.50 | −0.361336 | ||||||||
\(764\) | 13871.2 | 0.656861 | ||||||||
\(765\) | 3941.71 | 0.186291 | ||||||||
\(766\) | 47673.5 | 2.24871 | ||||||||
\(767\) | −2855.66 | −0.134435 | ||||||||
\(768\) | 19999.2 | 0.939659 | ||||||||
\(769\) | −28599.9 | −1.34114 | −0.670572 | − | 0.741844i | \(-0.733951\pi\) | ||||
−0.670572 | + | 0.741844i | \(0.733951\pi\) | |||||||
\(770\) | 10721.8 | 0.501803 | ||||||||
\(771\) | 3690.68 | 0.172395 | ||||||||
\(772\) | −7426.03 | −0.346203 | ||||||||
\(773\) | 13491.8 | 0.627772 | 0.313886 | − | 0.949461i | \(-0.398369\pi\) | ||||
0.313886 | + | 0.949461i | \(0.398369\pi\) | |||||||
\(774\) | −4840.78 | −0.224804 | ||||||||
\(775\) | 8083.78 | 0.374681 | ||||||||
\(776\) | −33482.7 | −1.54892 | ||||||||
\(777\) | 1229.50 | 0.0567673 | ||||||||
\(778\) | 30434.3 | 1.40247 | ||||||||
\(779\) | 14221.5 | 0.654093 | ||||||||
\(780\) | 2551.25 | 0.117114 | ||||||||
\(781\) | 6710.01 | 0.307430 | ||||||||
\(782\) | 84415.9 | 3.86024 | ||||||||
\(783\) | −3029.41 | −0.138266 | ||||||||
\(784\) | −8581.27 | −0.390911 | ||||||||
\(785\) | −10377.5 | −0.471834 | ||||||||
\(786\) | 18134.0 | 0.822923 | ||||||||
\(787\) | 25876.7 | 1.17205 | 0.586025 | − | 0.810293i | \(-0.300692\pi\) | ||||
0.586025 | + | 0.810293i | \(0.300692\pi\) | |||||||
\(788\) | −56055.5 | −2.53413 | ||||||||
\(789\) | 1544.98 | 0.0697118 | ||||||||
\(790\) | −11677.7 | −0.525918 | ||||||||
\(791\) | −11749.3 | −0.528137 | ||||||||
\(792\) | −18509.5 | −0.830438 | ||||||||
\(793\) | −10697.3 | −0.479030 | ||||||||
\(794\) | −56994.2 | −2.54742 | ||||||||
\(795\) | 7195.06 | 0.320984 | ||||||||
\(796\) | 33396.1 | 1.48705 | ||||||||
\(797\) | 21936.4 | 0.974938 | 0.487469 | − | 0.873140i | \(-0.337920\pi\) | ||||
0.487469 | + | 0.873140i | \(0.337920\pi\) | |||||||
\(798\) | 3351.40 | 0.148669 | ||||||||
\(799\) | −4098.49 | −0.181469 | ||||||||
\(800\) | 10894.9 | 0.481491 | ||||||||
\(801\) | −2078.23 | −0.0916739 | ||||||||
\(802\) | 17069.0 | 0.751531 | ||||||||
\(803\) | 11080.9 | 0.486969 | ||||||||
\(804\) | 37891.9 | 1.66212 | ||||||||
\(805\) | −6205.62 | −0.271701 | ||||||||
\(806\) | 4763.85 | 0.208188 | ||||||||
\(807\) | 15397.8 | 0.671658 | ||||||||
\(808\) | −2374.29 | −0.103375 | ||||||||
\(809\) | 5583.23 | 0.242640 | 0.121320 | − | 0.992613i | \(-0.461287\pi\) | ||||
0.121320 | + | 0.992613i | \(0.461287\pi\) | |||||||
\(810\) | 1734.74 | 0.0752502 | ||||||||
\(811\) | 12925.4 | 0.559647 | 0.279823 | − | 0.960052i | \(-0.409724\pi\) | ||||
0.279823 | + | 0.960052i | \(0.409724\pi\) | |||||||
\(812\) | −12160.6 | −0.525559 | ||||||||
\(813\) | 12900.0 | 0.556486 | ||||||||
\(814\) | −17372.8 | −0.748054 | ||||||||
\(815\) | −4902.80 | −0.210721 | ||||||||
\(816\) | −8697.87 | −0.373145 | ||||||||
\(817\) | −3571.27 | −0.152929 | ||||||||
\(818\) | −228.058 | −0.00974801 | ||||||||
\(819\) | 875.548 | 0.0373555 | ||||||||
\(820\) | 29549.7 | 1.25844 | ||||||||
\(821\) | −10153.2 | −0.431608 | −0.215804 | − | 0.976437i | \(-0.569237\pi\) | ||||
−0.215804 | + | 0.976437i | \(0.569237\pi\) | |||||||
\(822\) | −12445.6 | −0.528092 | ||||||||
\(823\) | 3282.93 | 0.139047 | 0.0695235 | − | 0.997580i | \(-0.477852\pi\) | ||||
0.0695235 | + | 0.997580i | \(0.477852\pi\) | |||||||
\(824\) | 41543.1 | 1.75634 | ||||||||
\(825\) | −20993.1 | −0.885922 | ||||||||
\(826\) | −7794.49 | −0.328335 | ||||||||
\(827\) | −17689.3 | −0.743795 | −0.371897 | − | 0.928274i | \(-0.621293\pi\) | ||||
−0.371897 | + | 0.928274i | \(0.621293\pi\) | |||||||
\(828\) | 23932.2 | 1.00447 | ||||||||
\(829\) | 38181.5 | 1.59964 | 0.799818 | − | 0.600243i | \(-0.204930\pi\) | ||||
0.799818 | + | 0.600243i | \(0.204930\pi\) | |||||||
\(830\) | −9734.56 | −0.407098 | ||||||||
\(831\) | 5438.40 | 0.227023 | ||||||||
\(832\) | 9530.06 | 0.397110 | ||||||||
\(833\) | −27829.4 | −1.15754 | ||||||||
\(834\) | −4414.49 | −0.183287 | ||||||||
\(835\) | −492.615 | −0.0204163 | ||||||||
\(836\) | −30505.2 | −1.26201 | ||||||||
\(837\) | 2086.64 | 0.0861708 | ||||||||
\(838\) | 3430.41 | 0.141410 | ||||||||
\(839\) | 43895.2 | 1.80623 | 0.903117 | − | 0.429395i | \(-0.141273\pi\) | ||||
0.903117 | + | 0.429395i | \(0.141273\pi\) | |||||||
\(840\) | 3117.18 | 0.128039 | ||||||||
\(841\) | −11800.1 | −0.483829 | ||||||||
\(842\) | −70392.4 | −2.88109 | ||||||||
\(843\) | 12219.2 | 0.499233 | ||||||||
\(844\) | −53188.5 | −2.16922 | ||||||||
\(845\) | 763.320 | 0.0310757 | ||||||||
\(846\) | −1803.74 | −0.0733024 | ||||||||
\(847\) | −23532.0 | −0.954627 | ||||||||
\(848\) | −15876.8 | −0.642938 | ||||||||
\(849\) | −19038.9 | −0.769626 | ||||||||
\(850\) | −48093.0 | −1.94068 | ||||||||
\(851\) | 10055.1 | 0.405034 | ||||||||
\(852\) | 4358.00 | 0.175238 | ||||||||
\(853\) | −19955.2 | −0.800998 | −0.400499 | − | 0.916297i | \(-0.631163\pi\) | ||||
−0.400499 | + | 0.916297i | \(0.631163\pi\) | |||||||
\(854\) | −29198.0 | −1.16995 | ||||||||
\(855\) | 1279.80 | 0.0511910 | ||||||||
\(856\) | 34850.8 | 1.39156 | ||||||||
\(857\) | 26030.4 | 1.03755 | 0.518776 | − | 0.854910i | \(-0.326388\pi\) | ||||
0.518776 | + | 0.854910i | \(0.326388\pi\) | |||||||
\(858\) | −12371.4 | −0.492254 | ||||||||
\(859\) | −45617.4 | −1.81193 | −0.905964 | − | 0.423354i | \(-0.860853\pi\) | ||||
−0.905964 | + | 0.423354i | \(0.860853\pi\) | |||||||
\(860\) | −7420.45 | −0.294227 | ||||||||
\(861\) | 10141.0 | 0.401399 | ||||||||
\(862\) | 5230.59 | 0.206676 | ||||||||
\(863\) | −2010.93 | −0.0793195 | −0.0396597 | − | 0.999213i | \(-0.512627\pi\) | ||||
−0.0396597 | + | 0.999213i | \(0.512627\pi\) | |||||||
\(864\) | 2812.27 | 0.110735 | ||||||||
\(865\) | −8532.78 | −0.335403 | ||||||||
\(866\) | 42170.1 | 1.65473 | ||||||||
\(867\) | −13468.6 | −0.527586 | ||||||||
\(868\) | 8376.19 | 0.327542 | ||||||||
\(869\) | 36478.2 | 1.42398 | ||||||||
\(870\) | −7208.83 | −0.280922 | ||||||||
\(871\) | 11337.1 | 0.441035 | ||||||||
\(872\) | 31284.7 | 1.21495 | ||||||||
\(873\) | −9802.48 | −0.380027 | ||||||||
\(874\) | 27408.3 | 1.06076 | ||||||||
\(875\) | 7760.41 | 0.299828 | ||||||||
\(876\) | 7196.79 | 0.277576 | ||||||||
\(877\) | −36767.3 | −1.41567 | −0.707836 | − | 0.706376i | \(-0.750329\pi\) | ||||
−0.707836 | + | 0.706376i | \(0.750329\pi\) | |||||||
\(878\) | −51692.0 | −1.98693 | ||||||||
\(879\) | 25172.9 | 0.965940 | ||||||||
\(880\) | −9034.72 | −0.346091 | ||||||||
\(881\) | 35401.2 | 1.35380 | 0.676899 | − | 0.736076i | \(-0.263323\pi\) | ||||
0.676899 | + | 0.736076i | \(0.263323\pi\) | |||||||
\(882\) | −12247.7 | −0.467575 | ||||||||
\(883\) | −11928.0 | −0.454596 | −0.227298 | − | 0.973825i | \(-0.572989\pi\) | ||||
−0.227298 | + | 0.973825i | \(0.572989\pi\) | |||||||
\(884\) | −18257.2 | −0.694633 | ||||||||
\(885\) | −2976.49 | −0.113055 | ||||||||
\(886\) | −17930.0 | −0.679875 | ||||||||
\(887\) | −32939.3 | −1.24689 | −0.623447 | − | 0.781866i | \(-0.714268\pi\) | ||||
−0.623447 | + | 0.781866i | \(0.714268\pi\) | |||||||
\(888\) | −5050.83 | −0.190872 | ||||||||
\(889\) | 9340.40 | 0.352381 | ||||||||
\(890\) | −4945.41 | −0.186259 | ||||||||
\(891\) | −5418.89 | −0.203748 | ||||||||
\(892\) | 73677.3 | 2.76558 | ||||||||
\(893\) | −1330.70 | −0.0498660 | ||||||||
\(894\) | −72.2720 | −0.00270373 | ||||||||
\(895\) | 15482.6 | 0.578241 | ||||||||
\(896\) | 19776.6 | 0.737376 | ||||||||
\(897\) | 7160.38 | 0.266531 | ||||||||
\(898\) | 506.569 | 0.0188245 | ||||||||
\(899\) | −8671.18 | −0.321691 | ||||||||
\(900\) | −13634.5 | −0.504983 | ||||||||
\(901\) | −51489.2 | −1.90383 | ||||||||
\(902\) | −143292. | −5.28946 | ||||||||
\(903\) | −2546.58 | −0.0938483 | ||||||||
\(904\) | 48266.4 | 1.77579 | ||||||||
\(905\) | 941.289 | 0.0345740 | ||||||||
\(906\) | −93.1585 | −0.00341610 | ||||||||
\(907\) | 1500.89 | 0.0549461 | 0.0274731 | − | 0.999623i | \(-0.491254\pi\) | ||||
0.0274731 | + | 0.999623i | \(0.491254\pi\) | |||||||
\(908\) | −38030.7 | −1.38997 | ||||||||
\(909\) | −695.102 | −0.0253631 | ||||||||
\(910\) | 2083.47 | 0.0758971 | ||||||||
\(911\) | 19728.2 | 0.717481 | 0.358740 | − | 0.933437i | \(-0.383206\pi\) | ||||
0.358740 | + | 0.933437i | \(0.383206\pi\) | |||||||
\(912\) | −2824.04 | −0.102537 | ||||||||
\(913\) | 30408.3 | 1.10226 | ||||||||
\(914\) | −5868.48 | −0.212376 | ||||||||
\(915\) | −11149.9 | −0.402845 | ||||||||
\(916\) | 24313.5 | 0.877011 | ||||||||
\(917\) | 9539.72 | 0.343543 | ||||||||
\(918\) | −12414.1 | −0.446326 | ||||||||
\(919\) | 19992.0 | 0.717602 | 0.358801 | − | 0.933414i | \(-0.383186\pi\) | ||||
0.358801 | + | 0.933414i | \(0.383186\pi\) | |||||||
\(920\) | 25492.9 | 0.913560 | ||||||||
\(921\) | −12015.8 | −0.429897 | ||||||||
\(922\) | 41683.4 | 1.48891 | ||||||||
\(923\) | 1303.89 | 0.0464984 | ||||||||
\(924\) | −21752.5 | −0.774463 | ||||||||
\(925\) | −5728.54 | −0.203625 | ||||||||
\(926\) | −18310.2 | −0.649794 | ||||||||
\(927\) | 12162.3 | 0.430918 | ||||||||
\(928\) | −11686.6 | −0.413395 | ||||||||
\(929\) | −1923.62 | −0.0679354 | −0.0339677 | − | 0.999423i | \(-0.510814\pi\) | ||||
−0.0339677 | + | 0.999423i | \(0.510814\pi\) | |||||||
\(930\) | 4965.42 | 0.175078 | ||||||||
\(931\) | −9035.71 | −0.318081 | ||||||||
\(932\) | 9392.52 | 0.330110 | ||||||||
\(933\) | −17509.6 | −0.614403 | ||||||||
\(934\) | −42634.0 | −1.49361 | ||||||||
\(935\) | −29300.0 | −1.02483 | ||||||||
\(936\) | −3596.77 | −0.125603 | ||||||||
\(937\) | −10252.9 | −0.357468 | −0.178734 | − | 0.983897i | \(-0.557200\pi\) | ||||
−0.178734 | + | 0.983897i | \(0.557200\pi\) | |||||||
\(938\) | 30944.4 | 1.07715 | ||||||||
\(939\) | −5289.58 | −0.183833 | ||||||||
\(940\) | −2764.96 | −0.0959394 | ||||||||
\(941\) | 11043.0 | 0.382563 | 0.191282 | − | 0.981535i | \(-0.438736\pi\) | ||||
0.191282 | + | 0.981535i | \(0.438736\pi\) | |||||||
\(942\) | 32683.2 | 1.13044 | ||||||||
\(943\) | 82934.8 | 2.86398 | ||||||||
\(944\) | 6568.00 | 0.226451 | ||||||||
\(945\) | 912.594 | 0.0314145 | ||||||||
\(946\) | 35983.1 | 1.23669 | ||||||||
\(947\) | 32105.2 | 1.10167 | 0.550833 | − | 0.834615i | \(-0.314310\pi\) | ||||
0.550833 | + | 0.834615i | \(0.314310\pi\) | |||||||
\(948\) | 23691.8 | 0.811680 | ||||||||
\(949\) | 2153.24 | 0.0736535 | ||||||||
\(950\) | −15614.9 | −0.533280 | ||||||||
\(951\) | 18319.0 | 0.624643 | ||||||||
\(952\) | −22307.1 | −0.759431 | ||||||||
\(953\) | −9473.37 | −0.322007 | −0.161003 | − | 0.986954i | \(-0.551473\pi\) | ||||
−0.161003 | + | 0.986954i | \(0.551473\pi\) | |||||||
\(954\) | −22660.3 | −0.769031 | ||||||||
\(955\) | 4325.79 | 0.146575 | ||||||||
\(956\) | 75598.4 | 2.55756 | ||||||||
\(957\) | 22518.5 | 0.760628 | ||||||||
\(958\) | 19819.3 | 0.668404 | ||||||||
\(959\) | −6547.26 | −0.220461 | ||||||||
\(960\) | 9933.30 | 0.333954 | ||||||||
\(961\) | −23818.3 | −0.799514 | ||||||||
\(962\) | −3375.89 | −0.113142 | ||||||||
\(963\) | 10203.0 | 0.341419 | ||||||||
\(964\) | 88399.8 | 2.95349 | ||||||||
\(965\) | −2315.84 | −0.0772534 | ||||||||
\(966\) | 19544.2 | 0.650956 | ||||||||
\(967\) | −5310.75 | −0.176610 | −0.0883052 | − | 0.996093i | \(-0.528145\pi\) | ||||
−0.0883052 | + | 0.996093i | \(0.528145\pi\) | |||||||
\(968\) | 96670.1 | 3.20981 | ||||||||
\(969\) | −9158.49 | −0.303626 | ||||||||
\(970\) | −23326.2 | −0.772122 | ||||||||
\(971\) | 24271.2 | 0.802164 | 0.401082 | − | 0.916042i | \(-0.368634\pi\) | ||||
0.401082 | + | 0.916042i | \(0.368634\pi\) | |||||||
\(972\) | −3519.45 | −0.116138 | ||||||||
\(973\) | −2322.32 | −0.0765163 | ||||||||
\(974\) | −87454.2 | −2.87702 | ||||||||
\(975\) | −4079.38 | −0.133995 | ||||||||
\(976\) | 24603.6 | 0.806907 | ||||||||
\(977\) | −49602.5 | −1.62428 | −0.812142 | − | 0.583460i | \(-0.801699\pi\) | ||||
−0.812142 | + | 0.583460i | \(0.801699\pi\) | |||||||
\(978\) | 15441.0 | 0.504856 | ||||||||
\(979\) | 15448.2 | 0.504317 | ||||||||
\(980\) | −18774.6 | −0.611971 | ||||||||
\(981\) | 9158.98 | 0.298087 | ||||||||
\(982\) | 38375.5 | 1.24706 | ||||||||
\(983\) | 47385.7 | 1.53751 | 0.768753 | − | 0.639545i | \(-0.220877\pi\) | ||||
0.768753 | + | 0.639545i | \(0.220877\pi\) | |||||||
\(984\) | −41659.5 | −1.34965 | ||||||||
\(985\) | −17481.2 | −0.565478 | ||||||||
\(986\) | 51587.7 | 1.66621 | ||||||||
\(987\) | −948.891 | −0.0306014 | ||||||||
\(988\) | −5927.78 | −0.190878 | ||||||||
\(989\) | −20826.4 | −0.669607 | ||||||||
\(990\) | −12894.9 | −0.413966 | ||||||||
\(991\) | −8947.33 | −0.286802 | −0.143401 | − | 0.989665i | \(-0.545804\pi\) | ||||
−0.143401 | + | 0.989665i | \(0.545804\pi\) | |||||||
\(992\) | 8049.67 | 0.257638 | ||||||||
\(993\) | −22471.1 | −0.718127 | ||||||||
\(994\) | 3558.95 | 0.113564 | ||||||||
\(995\) | 10414.7 | 0.331828 | ||||||||
\(996\) | 19749.5 | 0.628299 | ||||||||
\(997\) | −14908.6 | −0.473582 | −0.236791 | − | 0.971561i | \(-0.576096\pi\) | ||||
−0.236791 | + | 0.971561i | \(0.576096\pi\) | |||||||
\(998\) | −51881.4 | −1.64557 | ||||||||
\(999\) | −1478.69 | −0.0468306 |
(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 | 39.4.a.b.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 117.4.a.c.1.1 | 2 | |||
4.3 | odd | 2 | 624.4.a.r.1.1 | 2 | |||
5.4 | even | 2 | 975.4.a.j.1.1 | 2 | |||
7.6 | odd | 2 | 1911.4.a.h.1.2 | 2 | |||
8.3 | odd | 2 | 2496.4.a.s.1.2 | 2 | |||
8.5 | even | 2 | 2496.4.a.bc.1.2 | 2 | |||
12.11 | even | 2 | 1872.4.a.t.1.2 | 2 | |||
13.5 | odd | 4 | 507.4.b.f.337.1 | 4 | |||
13.8 | odd | 4 | 507.4.b.f.337.4 | 4 | |||
13.12 | even | 2 | 507.4.a.f.1.1 | 2 | |||
39.38 | odd | 2 | 1521.4.a.s.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.a.b.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
117.4.a.c.1.1 | 2 | 3.2 | odd | 2 | |||
507.4.a.f.1.1 | 2 | 13.12 | even | 2 | |||
507.4.b.f.337.1 | 4 | 13.5 | odd | 4 | |||
507.4.b.f.337.4 | 4 | 13.8 | odd | 4 | |||
624.4.a.r.1.1 | 2 | 4.3 | odd | 2 | |||
975.4.a.j.1.1 | 2 | 5.4 | even | 2 | |||
1521.4.a.s.1.2 | 2 | 39.38 | odd | 2 | |||
1872.4.a.t.1.2 | 2 | 12.11 | even | 2 | |||
1911.4.a.h.1.2 | 2 | 7.6 | odd | 2 | |||
2496.4.a.s.1.2 | 2 | 8.3 | odd | 2 | |||
2496.4.a.bc.1.2 | 2 | 8.5 | even | 2 |