Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [975,4,Mod(1,975)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(975, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("975.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 975 = 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 975.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: | \(57.5268622556\) |
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: | no (minimal twist has level 39) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.74166\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 975.1 |
$q$-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 | \(-0.816400\pi\) | ||||
−0.838215 | + | 0.545341i | \(0.816400\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 14.4833 | 1.81041 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −14.2250 | −0.967887 | ||||||||
\(7\) | 7.48331 | 0.404061 | 0.202031 | − | 0.979379i | \(-0.435246\pi\) | ||||
0.202031 | + | 0.979379i | \(0.435246\pi\) | |||||||
\(8\) | −30.7417 | −1.35860 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −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 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 29.8999 | 0.467186 | ||||||||
\(17\) | −96.9666 | −1.38340 | −0.691702 | − | 0.722183i | \(-0.743139\pi\) | ||||
−0.691702 | + | 0.722183i | \(0.743139\pi\) | |||||||
\(18\) | −42.6749 | −0.558810 | ||||||||
\(19\) | 31.4833 | 0.380146 | 0.190073 | − | 0.981770i | \(-0.439128\pi\) | ||||
0.190073 | + | 0.981770i | \(0.439128\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 22.4499 | 0.233285 | ||||||||
\(22\) | 317.216 | 3.07413 | ||||||||
\(23\) | −183.600 | −1.66448 | −0.832242 | − | 0.554412i | \(-0.812943\pi\) | ||||
−0.832242 | + | 0.554412i | \(0.812943\pi\) | |||||||
\(24\) | −92.2250 | −0.784389 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −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 | \(0.383041\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −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 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 130.350 | 0.603471 | ||||||||
\(37\) | −54.7664 | −0.243339 | −0.121669 | − | 0.992571i | \(-0.538825\pi\) | ||||
−0.121669 | + | 0.992571i | \(0.538825\pi\) | |||||||
\(38\) | −149.283 | −0.637287 | ||||||||
\(39\) | 39.0000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 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 | \(-0.435534\pi\) | ||||
0.201145 | + | 0.979561i | \(0.435534\pi\) | |||||||
\(44\) | −968.932 | −3.31982 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 870.566 | 2.79039 | ||||||||
\(47\) | 42.2670 | 0.131176 | 0.0655880 | − | 0.997847i | \(-0.479108\pi\) | ||||
0.0655880 | + | 0.997847i | \(0.479108\pi\) | |||||||
\(48\) | 89.6997 | 0.269730 | ||||||||
\(49\) | −287.000 | −0.836735 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −290.900 | −0.798708 | ||||||||
\(52\) | 188.283 | 0.502119 | ||||||||
\(53\) | 530.999 | 1.37619 | 0.688097 | − | 0.725618i | \(-0.258446\pi\) | ||||
0.688097 | + | 0.725618i | \(0.258446\pi\) | |||||||
\(54\) | −128.025 | −0.322629 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −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 | \(0.422080\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 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 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 951.649 | 1.77485 | ||||||||
\(67\) | 872.082 | 1.59018 | 0.795088 | − | 0.606495i | \(-0.207425\pi\) | ||||
0.795088 | + | 0.606495i | \(0.207425\pi\) | |||||||
\(68\) | −1404.40 | −2.50453 | ||||||||
\(69\) | −550.799 | −0.960991 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −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 | \(-0.457609\pi\) | ||||
0.132781 | + | 0.991145i | \(0.457609\pi\) | |||||||
\(74\) | 259.684 | 0.407941 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 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 | \(0.626928\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −2141.88 | −2.88453 | ||||||||
\(83\) | 454.534 | 0.601103 | 0.300552 | − | 0.953766i | \(-0.402829\pi\) | ||||
0.300552 | + | 0.953766i | \(0.402829\pi\) | |||||||
\(84\) | 325.150 | 0.422342 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −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 | \(0.543910\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 97.2831 | 0.112066 | ||||||||
\(92\) | −2659.13 | −3.01341 | ||||||||
\(93\) | −231.849 | −0.258512 | ||||||||
\(94\) | −200.415 | −0.219907 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 312.475 | 0.332206 | ||||||||
\(97\) | 1089.16 | 1.14008 | 0.570041 | − | 0.821616i | \(-0.306927\pi\) | ||||
0.570041 | + | 0.821616i | \(0.306927\pi\) | |||||||
\(98\) | 1360.86 | 1.40273 | ||||||||
\(99\) | −602.099 | −0.611245 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −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 | \(-0.723717\pi\) | ||||
−0.646377 | + | 0.763018i | \(0.723717\pi\) | |||||||
\(104\) | −399.642 | −0.376808 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2517.81 | −2.30709 | ||||||||
\(107\) | −1133.67 | −1.02426 | −0.512129 | − | 0.858908i | \(-0.671143\pi\) | ||||
−0.512129 | + | 0.858908i | \(0.671143\pi\) | |||||||
\(108\) | 391.049 | 0.348414 | ||||||||
\(109\) | 1017.66 | 0.894262 | 0.447131 | − | 0.894469i | \(-0.352446\pi\) | ||||
0.447131 | + | 0.894469i | \(0.352446\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −164.299 | −0.140492 | ||||||||
\(112\) | 223.750 | 0.188772 | ||||||||
\(113\) | −1570.06 | −1.30707 | −0.653536 | − | 0.756895i | \(-0.726715\pi\) | ||||
−0.653536 | + | 0.756895i | \(0.726715\pi\) | |||||||
\(114\) | −447.849 | −0.367938 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1625.03 | 1.30069 | ||||||||
\(117\) | 117.000 | 0.0924500 | ||||||||
\(118\) | −1041.58 | −0.812588 | ||||||||
\(119\) | −725.632 | −0.558979 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3144.60 | 2.36258 | ||||||||
\(122\) | −3901.75 | −2.89547 | ||||||||
\(123\) | 1355.15 | 0.993411 | ||||||||
\(124\) | −1119.32 | −0.810625 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −319.350 | −0.225793 | ||||||||
\(127\) | 1248.16 | 0.872099 | 0.436050 | − | 0.899923i | \(-0.356377\pi\) | ||||
0.436050 | + | 0.899923i | \(0.356377\pi\) | |||||||
\(128\) | 2642.76 | 1.82491 | ||||||||
\(129\) | 340.301 | 0.232263 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −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 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2980.91 | 1.87950 | ||||||||
\(137\) | −874.915 | −0.545613 | −0.272807 | − | 0.962069i | \(-0.587952\pi\) | ||||
−0.272807 | + | 0.962069i | \(0.587952\pi\) | |||||||
\(138\) | 2611.70 | 1.61103 | ||||||||
\(139\) | 310.334 | 0.189368 | 0.0946840 | − | 0.995507i | \(-0.469816\pi\) | ||||
0.0946840 | + | 0.995507i | \(0.469816\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 126.801 | 0.0757345 | ||||||||
\(142\) | 475.585 | 0.281058 | ||||||||
\(143\) | −869.699 | −0.508586 | ||||||||
\(144\) | 269.099 | 0.155729 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −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 | \(0.499555\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 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 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 564.849 | 0.289898 | ||||||||
\(157\) | 2297.60 | 1.16795 | 0.583975 | − | 0.811772i | \(-0.301497\pi\) | ||||
0.583975 | + | 0.811772i | \(0.301497\pi\) | |||||||
\(158\) | 2585.46 | 1.30183 | ||||||||
\(159\) | 1593.00 | 0.794546 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1373.93 | −0.672553 | ||||||||
\(162\) | −384.074 | −0.186270 | ||||||||
\(163\) | 1085.49 | 0.521606 | 0.260803 | − | 0.965392i | \(-0.416013\pi\) | ||||
0.260803 | + | 0.965392i | \(0.416013\pi\) | |||||||
\(164\) | 6542.34 | 3.11507 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2155.24 | −1.00771 | ||||||||
\(167\) | 109.066 | 0.0505374 | 0.0252687 | − | 0.999681i | \(-0.491956\pi\) | ||||
0.0252687 | + | 0.999681i | \(0.491956\pi\) | |||||||
\(168\) | −690.148 | −0.316941 | ||||||||
\(169\) | 169.000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 283.350 | 0.126715 | ||||||||
\(172\) | 1642.90 | 0.728313 | ||||||||
\(173\) | 1889.17 | 0.830236 | 0.415118 | − | 0.909768i | \(-0.363740\pi\) | ||||
0.415118 | + | 0.909768i | \(0.363740\pi\) | |||||||
\(174\) | −1596.05 | −0.695379 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −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 | \(0.246121\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 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 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1099.35 | 0.433378 | ||||||||
\(187\) | 6487.06 | 2.53679 | ||||||||
\(188\) | 612.166 | 0.237483 | ||||||||
\(189\) | 202.049 | 0.0777616 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 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 | \(-0.469518\pi\) | ||||
0.0956142 | + | 0.995418i | \(0.469518\pi\) | |||||||
\(194\) | −5164.45 | −1.91127 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4156.71 | −1.51484 | ||||||||
\(197\) | 3870.35 | 1.39975 | 0.699876 | − | 0.714265i | \(-0.253239\pi\) | ||||
0.699876 | + | 0.714265i | \(0.253239\pi\) | |||||||
\(198\) | 2854.95 | 1.02471 | ||||||||
\(199\) | 2305.83 | 0.821388 | 0.410694 | − | 0.911773i | \(-0.365286\pi\) | ||||
0.410694 | + | 0.911773i | \(0.365286\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2616.25 | 0.918088 | ||||||||
\(202\) | 366.215 | 0.127558 | ||||||||
\(203\) | 839.630 | 0.290298 | ||||||||
\(204\) | −4213.19 | −1.44599 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 6407.70 | 2.16721 | ||||||||
\(207\) | −1652.40 | −0.554828 | ||||||||
\(208\) | 388.699 | 0.129574 | ||||||||
\(209\) | −2106.23 | −0.697086 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −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 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −830.025 | −0.261463 | ||||||||
\(217\) | −578.334 | −0.180921 | ||||||||
\(218\) | −4825.41 | −1.49917 | ||||||||
\(219\) | 496.902 | 0.153322 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1260.57 | −0.383687 | ||||||||
\(222\) | 779.051 | 0.235525 | ||||||||
\(223\) | −5087.05 | −1.52760 | −0.763798 | − | 0.645455i | \(-0.776668\pi\) | ||||
−0.763798 | + | 0.645455i | \(0.776668\pi\) | |||||||
\(224\) | 779.449 | 0.232496 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7444.71 | 2.19122 | ||||||||
\(227\) | 2625.83 | 0.767763 | 0.383882 | − | 0.923382i | \(-0.374587\pi\) | ||||
0.383882 | + | 0.923382i | \(0.374587\pi\) | |||||||
\(228\) | 1367.95 | 0.397345 | ||||||||
\(229\) | 1678.73 | 0.484425 | 0.242213 | − | 0.970223i | \(-0.422127\pi\) | ||||
0.242213 | + | 0.970223i | \(0.422127\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1501.90 | −0.427782 | ||||||||
\(232\) | −3449.22 | −0.976088 | ||||||||
\(233\) | −648.506 | −0.182339 | −0.0911696 | − | 0.995835i | \(-0.529061\pi\) | ||||
−0.0911696 | + | 0.995835i | \(0.529061\pi\) | |||||||
\(234\) | −554.774 | −0.154986 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 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 | \(0.250342\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 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 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6425.64 | −1.66538 | ||||||||
\(247\) | 409.283 | 0.105433 | ||||||||
\(248\) | 2375.81 | 0.608323 | ||||||||
\(249\) | 1363.60 | 0.347047 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 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 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6666.39 | −1.62754 | ||||||||
\(257\) | 1230.23 | 0.298597 | 0.149299 | − | 0.988792i | \(-0.452298\pi\) | ||||
0.149299 | + | 0.988792i | \(0.452298\pi\) | |||||||
\(258\) | −1613.59 | −0.389372 | ||||||||
\(259\) | −409.834 | −0.0983238 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1009.80 | 0.239483 | ||||||||
\(262\) | 6044.66 | 1.42534 | ||||||||
\(263\) | 514.992 | 0.120744 | 0.0603722 | − | 0.998176i | \(-0.480771\pi\) | ||||
0.0603722 | + | 0.998176i | \(0.480771\pi\) | |||||||
\(264\) | 6169.84 | 1.43836 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −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 | \(0.697602\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −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 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −7977.39 | −1.73979 | ||||||||
\(277\) | 1812.80 | 0.393215 | 0.196607 | − | 0.980482i | \(-0.437008\pi\) | ||||
0.196607 | + | 0.980482i | \(0.437008\pi\) | |||||||
\(278\) | −1471.50 | −0.317462 | ||||||||
\(279\) | −695.548 | −0.149252 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −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 | \(-0.732215\pi\) | ||||
−0.666516 | + | 0.745491i | \(0.732215\pi\) | |||||||
\(284\) | −1452.67 | −0.303520 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4123.81 | 0.852609 | ||||||||
\(287\) | 3380.33 | 0.695243 | ||||||||
\(288\) | 937.424 | 0.191799 | ||||||||
\(289\) | 4489.53 | 0.913806 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3267.49 | 0.658226 | ||||||||
\(292\) | 2398.93 | 0.480777 | ||||||||
\(293\) | 8390.97 | 1.67306 | 0.836529 | − | 0.547923i | \(-0.184581\pi\) | ||||
0.836529 | + | 0.547923i | \(0.184581\pi\) | |||||||
\(294\) | 4082.57 | 0.809864 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1683.61 | 0.330601 | ||||||||
\(297\) | −1806.30 | −0.352902 | ||||||||
\(298\) | −24.0907 | −0.00468300 | ||||||||
\(299\) | −2386.79 | −0.461645 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 848.861 | 0.162550 | ||||||||
\(302\) | −31.0528 | −0.00591685 | ||||||||
\(303\) | −231.701 | −0.0439302 | ||||||||
\(304\) | 941.348 | 0.177599 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 4138.04 | 0.773059 | ||||||||
\(307\) | −4005.27 | −0.744603 | −0.372301 | − | 0.928112i | \(-0.621431\pi\) | ||||
−0.372301 | + | 0.928112i | \(0.621431\pi\) | |||||||
\(308\) | −7250.82 | −1.34141 | ||||||||
\(309\) | −4054.09 | −0.746372 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 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 | \(-0.550893\pi\) | ||||
−0.159204 | + | 0.987246i | \(0.550893\pi\) | |||||||
\(314\) | −10894.4 | −1.95798 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7897.26 | −1.40587 | ||||||||
\(317\) | 6106.35 | 1.08191 | 0.540957 | − | 0.841050i | \(-0.318062\pi\) | ||||
0.540957 | + | 0.841050i | \(0.318062\pi\) | |||||||
\(318\) | −7553.44 | −1.33200 | ||||||||
\(319\) | −7506.18 | −1.31745 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3401.00 | −0.591356 | ||||||||
\(322\) | 6514.72 | 1.12749 | ||||||||
\(323\) | −3052.83 | −0.525895 | ||||||||
\(324\) | 1173.15 | 0.201157 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −5147.00 | −0.874436 | ||||||||
\(327\) | 3052.99 | 0.516302 | ||||||||
\(328\) | −13886.5 | −2.33766 | ||||||||
\(329\) | 316.297 | 0.0530031 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 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 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 671.251 | 0.108987 | ||||||||
\(337\) | −9462.46 | −1.52953 | −0.764767 | − | 0.644307i | \(-0.777146\pi\) | ||||
−0.764767 | + | 0.644307i | \(0.777146\pi\) | |||||||
\(338\) | −801.340 | −0.128956 | ||||||||
\(339\) | −4710.19 | −0.754639 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5170.23 | 0.821066 | ||||||||
\(342\) | −1343.55 | −0.212429 | ||||||||
\(343\) | −4714.49 | −0.742153 | ||||||||
\(344\) | −3487.14 | −0.546553 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8957.79 | −1.39183 | ||||||||
\(347\) | −11460.3 | −1.77297 | −0.886487 | − | 0.462753i | \(-0.846862\pi\) | ||||
−0.886487 | + | 0.462753i | \(0.846862\pi\) | |||||||
\(348\) | 4875.09 | 0.750955 | ||||||||
\(349\) | −3673.96 | −0.563503 | −0.281751 | − | 0.959487i | \(-0.590915\pi\) | ||||
−0.281751 | + | 0.959487i | \(0.590915\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 351.000 | 0.0533761 | ||||||||
\(352\) | −6968.17 | −1.05513 | ||||||||
\(353\) | −3388.65 | −0.510935 | −0.255467 | − | 0.966818i | \(-0.582229\pi\) | ||||
−0.255467 | + | 0.966818i | \(0.582229\pi\) | |||||||
\(354\) | −3124.75 | −0.469148 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −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 | \(0.751805\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5867.80 | −0.855489 | ||||||||
\(362\) | −988.174 | −0.143473 | ||||||||
\(363\) | 9433.79 | 1.36404 | ||||||||
\(364\) | 1408.98 | 0.202887 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −11705.2 | −1.67170 | ||||||||
\(367\) | 8715.98 | 1.23970 | 0.619851 | − | 0.784720i | \(-0.287193\pi\) | ||||
0.619851 | + | 0.784720i | \(0.287193\pi\) | |||||||
\(368\) | −5489.61 | −0.777624 | ||||||||
\(369\) | 4065.44 | 0.573546 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3973.63 | 0.556067 | ||||||||
\(372\) | −3357.95 | −0.468014 | ||||||||
\(373\) | −4667.99 | −0.647987 | −0.323994 | − | 0.946059i | \(-0.605026\pi\) | ||||
−0.323994 | + | 0.946059i | \(0.605026\pi\) | |||||||
\(374\) | −30759.4 | −4.25276 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −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 | \(0.236655\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3744.49 | 0.503507 | ||||||||
\(382\) | −4541.25 | −0.608248 | ||||||||
\(383\) | −10054.2 | −1.34137 | −0.670686 | − | 0.741742i | \(-0.734000\pi\) | ||||
−0.670686 | + | 0.741742i | \(0.734000\pi\) | |||||||
\(384\) | 7928.27 | 1.05361 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −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 | \(0.362629\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17803.0 | 2.30265 | ||||||||
\(392\) | 8822.86 | 1.13679 | ||||||||
\(393\) | −3824.40 | −0.490879 | ||||||||
\(394\) | −18351.9 | −2.34658 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −8720.39 | −1.10661 | ||||||||
\(397\) | 12019.9 | 1.51955 | 0.759775 | − | 0.650186i | \(-0.225309\pi\) | ||||
0.759775 | + | 0.650186i | \(0.225309\pi\) | |||||||
\(398\) | −10933.5 | −1.37700 | ||||||||
\(399\) | 706.799 | 0.0886822 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 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 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −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 | \(0.500925\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2624.74 | −0.315010 | ||||||||
\(412\) | −19572.2 | −2.34042 | ||||||||
\(413\) | 1643.83 | 0.195854 | ||||||||
\(414\) | 7835.10 | 0.930130 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 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 | \(0.486571\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −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 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1426.75 | 0.162269 | ||||||||
\(427\) | 6157.76 | 0.697880 | ||||||||
\(428\) | −16419.2 | −1.85433 | ||||||||
\(429\) | −2609.10 | −0.293632 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 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 | \(-0.664293\pi\) | ||||
−0.493528 | + | 0.869730i | \(0.664293\pi\) | |||||||
\(434\) | 2742.26 | 0.303301 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 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 | \(0.701901\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2583.00 | −0.278912 | ||||||||
\(442\) | 5977.17 | 0.643224 | ||||||||
\(443\) | 3781.37 | 0.405550 | 0.202775 | − | 0.979225i | \(-0.435004\pi\) | ||||
0.202775 | + | 0.979225i | \(0.435004\pi\) | |||||||
\(444\) | −2379.60 | −0.254348 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 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 | \(0.498213\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −30219.7 | −3.15519 | ||||||||
\(452\) | −22739.7 | −2.36634 | ||||||||
\(453\) | 19.6468 | 0.00203772 | ||||||||
\(454\) | −12450.8 | −1.28710 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2903.55 | −0.298182 | ||||||||
\(457\) | 1237.64 | 0.126684 | 0.0633419 | − | 0.997992i | \(-0.479824\pi\) | ||||
0.0633419 | + | 0.997992i | \(0.479824\pi\) | |||||||
\(458\) | −7959.95 | −0.812105 | ||||||||
\(459\) | −2618.10 | −0.266236 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 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 | \(-0.437918\pi\) | ||||
0.193803 | + | 0.981040i | \(0.437918\pi\) | |||||||
\(464\) | 3354.77 | 0.335650 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3074.99 | 0.305679 | ||||||||
\(467\) | 8991.38 | 0.890945 | 0.445473 | − | 0.895296i | \(-0.353036\pi\) | ||||
0.445473 | + | 0.895296i | \(0.353036\pi\) | |||||||
\(468\) | 1694.55 | 0.167373 | ||||||||
\(469\) | 6526.06 | 0.642528 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6892.79 | 0.674316 | ||||||||
\(472\) | −6752.91 | −0.658533 | ||||||||
\(473\) | −7588.71 | −0.737694 | ||||||||
\(474\) | 7756.39 | 0.751609 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −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 | \(0.436116\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −711.963 | −0.0674901 | ||||||||
\(482\) | −28941.0 | −2.73491 | ||||||||
\(483\) | −4121.80 | −0.388299 | ||||||||
\(484\) | 45544.2 | 4.27725 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1152.22 | −0.107543 | ||||||||
\(487\) | 18443.8 | 1.71616 | 0.858078 | − | 0.513519i | \(-0.171658\pi\) | ||||
0.858078 | + | 0.513519i | \(0.171658\pi\) | |||||||
\(488\) | −25296.2 | −2.34653 | ||||||||
\(489\) | 3256.46 | 0.301149 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 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 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −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 | \(0.663294\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 327.197 | 0.0291778 | ||||||||
\(502\) | −30457.5 | −2.70794 | ||||||||
\(503\) | 9260.11 | 0.820851 | 0.410425 | − | 0.911894i | \(-0.365380\pi\) | ||||
0.410425 | + | 0.911894i | \(0.365380\pi\) | |||||||
\(504\) | −2070.45 | −0.182986 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −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 | \(0.643339\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1239.49 | 0.107303 | ||||||||
\(512\) | 10467.7 | 0.903538 | ||||||||
\(513\) | 850.049 | 0.0731591 | ||||||||
\(514\) | −5833.32 | −0.500577 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 4928.69 | 0.420491 | ||||||||
\(517\) | −2827.66 | −0.240542 | ||||||||
\(518\) | 1943.29 | 0.164833 | ||||||||
\(519\) | 5667.51 | 0.479337 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 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 | \(-0.435549\pi\) | ||||
0.201097 | + | 0.979571i | \(0.435549\pi\) | |||||||
\(524\) | −18463.3 | −1.53926 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2441.92 | −0.202419 | ||||||||
\(527\) | 7493.88 | 0.619428 | ||||||||
\(528\) | −6000.90 | −0.494613 | ||||||||
\(529\) | 21541.8 | 1.77051 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1977.00 | 0.161571 | ||||||||
\(532\) | 3412.26 | 0.278083 | ||||||||
\(533\) | 5872.31 | 0.477219 | ||||||||
\(534\) | 3284.76 | 0.266190 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −26809.2 | −2.16042 | ||||||||
\(537\) | 10283.6 | 0.826386 | ||||||||
\(538\) | 24337.0 | 1.95027 | ||||||||
\(539\) | 19200.3 | 1.53435 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 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 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1383.85 | −0.108468 | ||||||||
\(547\) | 4396.34 | 0.343646 | 0.171823 | − | 0.985128i | \(-0.445034\pi\) | ||||
0.171823 | + | 0.985128i | \(0.445034\pi\) | |||||||
\(548\) | −12671.7 | −0.987786 | ||||||||
\(549\) | 7405.79 | 0.575722 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3532.43 | 0.273116 | ||||||||
\(552\) | 16932.5 | 1.30560 | ||||||||
\(553\) | −4080.40 | −0.313772 | ||||||||
\(554\) | −8595.67 | −0.659197 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4494.66 | 0.342835 | ||||||||
\(557\) | 17488.0 | 1.33032 | 0.665160 | − | 0.746701i | \(-0.268363\pi\) | ||||
0.665160 | + | 0.746701i | \(0.268363\pi\) | |||||||
\(558\) | 3298.05 | 0.250211 | ||||||||
\(559\) | 1474.64 | 0.111575 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 19461.2 | 1.46462 | ||||||||
\(562\) | 19313.2 | 1.44960 | ||||||||
\(563\) | 6881.77 | 0.515154 | 0.257577 | − | 0.966258i | \(-0.417076\pi\) | ||||
0.257577 | + | 0.966258i | \(0.417076\pi\) | |||||||
\(564\) | 1836.50 | 0.137111 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 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 | \(0.317380\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 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 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −6597.74 | −0.477267 | ||||||||
\(577\) | 10552.2 | 0.761338 | 0.380669 | − | 0.924711i | \(-0.375694\pi\) | ||||
0.380669 | + | 0.924711i | \(0.375694\pi\) | |||||||
\(578\) | −21287.8 | −1.53193 | ||||||||
\(579\) | 1538.19 | 0.110406 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3401.42 | 0.242882 | ||||||||
\(582\) | −15493.3 | −1.10347 | ||||||||
\(583\) | −35523.8 | −2.52357 | ||||||||
\(584\) | −5091.86 | −0.360793 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −39787.1 | −2.80476 | ||||||||
\(587\) | 1637.20 | 0.115118 | 0.0575591 | − | 0.998342i | \(-0.481668\pi\) | ||||
0.0575591 | + | 0.998342i | \(0.481668\pi\) | |||||||
\(588\) | −12470.1 | −0.874591 | ||||||||
\(589\) | −2433.13 | −0.170213 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11611.1 | 0.808147 | ||||||||
\(592\) | −1637.51 | −0.113685 | ||||||||
\(593\) | −14024.0 | −0.971155 | −0.485577 | − | 0.874194i | \(-0.661391\pi\) | ||||
−0.485577 | + | 0.874194i | \(0.661391\pi\) | |||||||
\(594\) | 8564.84 | 0.591616 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 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 | \(0.496028\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −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 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1098.65 | 0.0736459 | ||||||||
\(607\) | −2324.97 | −0.155465 | −0.0777327 | − | 0.996974i | \(-0.524768\pi\) | ||||
−0.0777327 | + | 0.996974i | \(0.524768\pi\) | |||||||
\(608\) | 3279.25 | 0.218735 | ||||||||
\(609\) | 2518.89 | 0.167603 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 549.471 | 0.0363817 | ||||||||
\(612\) | −12639.6 | −0.834845 | ||||||||
\(613\) | −633.133 | −0.0417162 | −0.0208581 | − | 0.999782i | \(-0.506640\pi\) | ||||
−0.0208581 | + | 0.999782i | \(0.506640\pi\) | |||||||
\(614\) | 18991.6 | 1.24827 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 15390.3 | 1.00664 | ||||||||
\(617\) | 2981.85 | 0.194562 | 0.0972810 | − | 0.995257i | \(-0.468985\pi\) | ||||
0.0972810 | + | 0.995257i | \(0.468985\pi\) | |||||||
\(618\) | 19223.1 | 1.25124 | ||||||||
\(619\) | 15158.6 | 0.984292 | 0.492146 | − | 0.870513i | \(-0.336213\pi\) | ||||
0.492146 | + | 0.870513i | \(0.336213\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4957.19 | −0.320330 | ||||||||
\(622\) | −27674.8 | −1.78402 | ||||||||
\(623\) | −1728.01 | −0.111126 | ||||||||
\(624\) | 1166.10 | 0.0748096 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 8360.45 | 0.533787 | ||||||||
\(627\) | −6318.69 | −0.402463 | ||||||||
\(628\) | 33276.8 | 2.11447 | ||||||||
\(629\) | 5310.51 | 0.336636 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 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 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 23071.9 | 1.43846 | ||||||||
\(637\) | −3731.00 | −0.232068 | ||||||||
\(638\) | 35591.7 | 2.20861 | ||||||||
\(639\) | −902.693 | −0.0558842 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −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 | \(-0.482913\pi\) | ||||
0.0536555 | + | 0.998560i | \(0.482913\pi\) | |||||||
\(644\) | −19899.1 | −1.21760 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 14475.5 | 0.881626 | ||||||||
\(647\) | −1489.51 | −0.0905083 | −0.0452542 | − | 0.998976i | \(-0.514410\pi\) | ||||
−0.0452542 | + | 0.998976i | \(0.514410\pi\) | |||||||
\(648\) | −2490.07 | −0.150956 | ||||||||
\(649\) | −14695.7 | −0.888836 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1735.00 | −0.104455 | ||||||||
\(652\) | 15721.4 | 0.944323 | ||||||||
\(653\) | −10668.2 | −0.639327 | −0.319663 | − | 0.947531i | \(-0.603570\pi\) | ||||
−0.319663 | + | 0.947531i | \(0.603570\pi\) | |||||||
\(654\) | −14476.2 | −0.865544 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 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 | \(0.635101\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −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 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2337.15 | 0.135980 | ||||||||
\(667\) | −20599.9 | −1.19585 | ||||||||
\(668\) | 1579.63 | 0.0914937 | ||||||||
\(669\) | −15261.1 | −0.881958 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −55049.6 | −3.16716 | ||||||||
\(672\) | 2338.35 | 0.134232 | ||||||||
\(673\) | 32421.0 | 1.85697 | 0.928483 | − | 0.371374i | \(-0.121113\pi\) | ||||
0.928483 | + | 0.371374i | \(0.121113\pi\) | |||||||
\(674\) | 44867.7 | 2.56415 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2447.68 | 0.139263 | ||||||||
\(677\) | 1071.74 | 0.0608421 | 0.0304211 | − | 0.999537i | \(-0.490315\pi\) | ||||
0.0304211 | + | 0.999537i | \(0.490315\pi\) | |||||||
\(678\) | 22334.1 | 1.26510 | ||||||||
\(679\) | 8150.56 | 0.460663 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7877.48 | 0.443268 | ||||||||
\(682\) | −24515.5 | −1.37646 | ||||||||
\(683\) | 305.487 | 0.0171144 | 0.00855721 | − | 0.999963i | \(-0.497276\pi\) | ||||
0.00855721 | + | 0.999963i | \(0.497276\pi\) | |||||||
\(684\) | 4103.84 | 0.229407 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 22354.5 | 1.24417 | ||||||||
\(687\) | 5036.18 | 0.279683 | ||||||||
\(688\) | 3391.66 | 0.187944 | ||||||||
\(689\) | 6902.99 | 0.381688 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 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 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −10347.7 | −0.563545 | ||||||||
\(697\) | −43801.4 | −2.38034 | ||||||||
\(698\) | 17420.6 | 0.944672 | ||||||||
\(699\) | −1945.52 | −0.105274 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −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 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 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 | \(0.576509\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4907.39 | −0.258849 | ||||||||
\(712\) | 7098.71 | 0.373645 | ||||||||
\(713\) | 14189.1 | 0.745284 | ||||||||
\(714\) | 10322.1 | 0.541029 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 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 | \(0.429688\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10112.7 | −0.522352 | ||||||||
\(722\) | 27823.1 | 1.43417 | ||||||||
\(723\) | 18310.7 | 0.941883 | ||||||||
\(724\) | 3018.36 | 0.154940 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −44731.8 | −2.28671 | ||||||||
\(727\) | 8624.18 | 0.439963 | 0.219982 | − | 0.975504i | \(-0.429400\pi\) | ||||
0.219982 | + | 0.975504i | \(0.429400\pi\) | |||||||
\(728\) | −2990.64 | −0.152254 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10999.3 | −0.556530 | ||||||||
\(732\) | 35753.5 | 1.80531 | ||||||||
\(733\) | −31124.2 | −1.56835 | −0.784174 | − | 0.620541i | \(-0.786913\pi\) | ||||
−0.784174 | + | 0.620541i | \(0.786913\pi\) | |||||||
\(734\) | −41328.2 | −2.07827 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −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 | \(0.644955\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1227.85 | 0.0608720 | ||||||||
\(742\) | −18841.6 | −0.932206 | ||||||||
\(743\) | 21331.1 | 1.05325 | 0.526623 | − | 0.850099i | \(-0.323458\pi\) | ||||
0.526623 | + | 0.850099i | \(0.323458\pi\) | |||||||
\(744\) | 7127.43 | 0.351215 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 22134.0 | 1.08630 | ||||||||
\(747\) | 4090.81 | 0.200368 | ||||||||
\(748\) | 93954.1 | 4.59265 | ||||||||
\(749\) | −8483.58 | −0.413863 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 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 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2926.35 | 0.140781 | ||||||||
\(757\) | 16610.9 | 0.797537 | 0.398768 | − | 0.917052i | \(-0.369438\pi\) | ||||
0.398768 | + | 0.917052i | \(0.369438\pi\) | |||||||
\(758\) | −51507.4 | −2.46812 | ||||||||
\(759\) | 36848.4 | 1.76220 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −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 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 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 | \(0.733951\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3690.68 | 0.172395 | ||||||||
\(772\) | 7426.03 | 0.346203 | ||||||||
\(773\) | −13491.8 | −0.627772 | −0.313886 | − | 0.949461i | \(-0.601631\pi\) | ||||
−0.313886 | + | 0.949461i | \(0.601631\pi\) | |||||||
\(774\) | −4840.78 | −0.224804 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −33482.7 | −1.54892 | ||||||||
\(777\) | −1229.50 | −0.0567673 | ||||||||
\(778\) | −30434.3 | −1.40247 | ||||||||
\(779\) | 14221.5 | 0.654093 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6710.01 | 0.307430 | ||||||||
\(782\) | −84415.9 | −3.86024 | ||||||||
\(783\) | 3029.41 | 0.138266 | ||||||||
\(784\) | −8581.27 | −0.390911 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 18134.0 | 0.822923 | ||||||||
\(787\) | −25876.7 | −1.17205 | −0.586025 | − | 0.810293i | \(-0.699308\pi\) | ||||
−0.586025 | + | 0.810293i | \(0.699308\pi\) | |||||||
\(788\) | 56055.5 | 2.53413 | ||||||||
\(789\) | 1544.98 | 0.0697118 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11749.3 | −0.528137 | ||||||||
\(792\) | 18509.5 | 0.830438 | ||||||||
\(793\) | 10697.3 | 0.479030 | ||||||||
\(794\) | −56994.2 | −2.54742 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 33396.1 | 1.48705 | ||||||||
\(797\) | −21936.4 | −0.974938 | −0.487469 | − | 0.873140i | \(-0.662080\pi\) | ||||
−0.487469 | + | 0.873140i | \(0.662080\pi\) | |||||||
\(798\) | −3351.40 | −0.148669 | ||||||||
\(799\) | −4098.49 | −0.181469 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2078.23 | −0.0916739 | ||||||||
\(802\) | −17069.0 | −0.751531 | ||||||||
\(803\) | −11080.9 | −0.486969 | ||||||||
\(804\) | 37891.9 | 1.66212 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 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 | \(0.461287\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 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 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −8697.87 | −0.373145 | ||||||||
\(817\) | 3571.27 | 0.152929 | ||||||||
\(818\) | 228.058 | 0.00974801 | ||||||||
\(819\) | 875.548 | 0.0373555 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −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 | \(-0.522148\pi\) | ||||
−0.0695235 | + | 0.997580i | \(0.522148\pi\) | |||||||
\(824\) | 41543.1 | 1.75634 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7794.49 | −0.328335 | ||||||||
\(827\) | 17689.3 | 0.743795 | 0.371897 | − | 0.928274i | \(-0.378707\pi\) | ||||
0.371897 | + | 0.928274i | \(0.378707\pi\) | |||||||
\(828\) | −23932.2 | −1.00447 | ||||||||
\(829\) | 38181.5 | 1.59964 | 0.799818 | − | 0.600243i | \(-0.204930\pi\) | ||||
0.799818 | + | 0.600243i | \(0.204930\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5438.40 | 0.227023 | ||||||||
\(832\) | −9530.06 | −0.397110 | ||||||||
\(833\) | 27829.4 | 1.15754 | ||||||||
\(834\) | −4414.49 | −0.183287 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −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 | \(0.141273\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11800.1 | −0.483829 | ||||||||
\(842\) | 70392.4 | 2.88109 | ||||||||
\(843\) | −12219.2 | −0.499233 | ||||||||
\(844\) | −53188.5 | −2.16922 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1803.74 | −0.0733024 | ||||||||
\(847\) | 23532.0 | 0.954627 | ||||||||
\(848\) | 15876.8 | 0.642938 | ||||||||
\(849\) | −19038.9 | −0.769626 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10055.1 | 0.405034 | ||||||||
\(852\) | −4358.00 | −0.175238 | ||||||||
\(853\) | 19955.2 | 0.800998 | 0.400499 | − | 0.916297i | \(-0.368837\pi\) | ||||
0.400499 | + | 0.916297i | \(0.368837\pi\) | |||||||
\(854\) | −29198.0 | −1.16995 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 34850.8 | 1.39156 | ||||||||
\(857\) | −26030.4 | −1.03755 | −0.518776 | − | 0.854910i | \(-0.673612\pi\) | ||||
−0.518776 | + | 0.854910i | \(0.673612\pi\) | |||||||
\(858\) | 12371.4 | 0.492254 | ||||||||
\(859\) | −45617.4 | −1.81193 | −0.905964 | − | 0.423354i | \(-0.860853\pi\) | ||||
−0.905964 | + | 0.423354i | \(0.860853\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10141.0 | 0.401399 | ||||||||
\(862\) | −5230.59 | −0.206676 | ||||||||
\(863\) | 2010.93 | 0.0793195 | 0.0396597 | − | 0.999213i | \(-0.487373\pi\) | ||||
0.0396597 | + | 0.999213i | \(0.487373\pi\) | |||||||
\(864\) | 2812.27 | 0.110735 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 42170.1 | 1.65473 | ||||||||
\(867\) | 13468.6 | 0.527586 | ||||||||
\(868\) | −8376.19 | −0.327542 | ||||||||
\(869\) | 36478.2 | 1.42398 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11337.1 | 0.441035 | ||||||||
\(872\) | −31284.7 | −1.21495 | ||||||||
\(873\) | 9802.48 | 0.380027 | ||||||||
\(874\) | 27408.3 | 1.06076 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 7196.79 | 0.277576 | ||||||||
\(877\) | 36767.3 | 1.41567 | 0.707836 | − | 0.706376i | \(-0.249671\pi\) | ||||
0.707836 | + | 0.706376i | \(0.249671\pi\) | |||||||
\(878\) | 51692.0 | 1.98693 | ||||||||
\(879\) | 25172.9 | 0.965940 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 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 | \(-0.427011\pi\) | ||||
0.227298 | + | 0.973825i | \(0.427011\pi\) | |||||||
\(884\) | −18257.2 | −0.694633 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −17930.0 | −0.679875 | ||||||||
\(887\) | 32939.3 | 1.24689 | 0.623447 | − | 0.781866i | \(-0.285732\pi\) | ||||
0.623447 | + | 0.781866i | \(0.285732\pi\) | |||||||
\(888\) | 5050.83 | 0.190872 | ||||||||
\(889\) | 9340.40 | 0.352381 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5418.89 | −0.203748 | ||||||||
\(892\) | −73677.3 | −2.76558 | ||||||||
\(893\) | 1330.70 | 0.0498660 | ||||||||
\(894\) | −72.2720 | −0.00270373 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 19776.6 | 0.737376 | ||||||||
\(897\) | −7160.38 | −0.266531 | ||||||||
\(898\) | −506.569 | −0.0188245 | ||||||||
\(899\) | −8671.18 | −0.321691 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −51489.2 | −1.90383 | ||||||||
\(902\) | 143292. | 5.28946 | ||||||||
\(903\) | 2546.58 | 0.0938483 | ||||||||
\(904\) | 48266.4 | 1.77579 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −93.1585 | −0.00341610 | ||||||||
\(907\) | −1500.89 | −0.0549461 | −0.0274731 | − | 0.999623i | \(-0.508746\pi\) | ||||
−0.0274731 | + | 0.999623i | \(0.508746\pi\) | |||||||
\(908\) | 38030.7 | 1.38997 | ||||||||
\(909\) | −695.102 | −0.0253631 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 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 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 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 | \(0.383186\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12015.8 | −0.429897 | ||||||||
\(922\) | −41683.4 | −1.48891 | ||||||||
\(923\) | −1303.89 | −0.0464984 | ||||||||
\(924\) | −21752.5 | −0.774463 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −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 | \(0.510814\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9035.71 | −0.318081 | ||||||||
\(932\) | −9392.52 | −0.330110 | ||||||||
\(933\) | 17509.6 | 0.614403 | ||||||||
\(934\) | −42634.0 | −1.49361 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3596.77 | −0.125603 | ||||||||
\(937\) | 10252.9 | 0.357468 | 0.178734 | − | 0.983897i | \(-0.442800\pi\) | ||||
0.178734 | + | 0.983897i | \(0.442800\pi\) | |||||||
\(938\) | −30944.4 | −1.07715 | ||||||||
\(939\) | −5289.58 | −0.183833 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 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 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 35983.1 | 1.23669 | ||||||||
\(947\) | −32105.2 | −1.10167 | −0.550833 | − | 0.834615i | \(-0.685690\pi\) | ||||
−0.550833 | + | 0.834615i | \(0.685690\pi\) | |||||||
\(948\) | −23691.8 | −0.811680 | ||||||||
\(949\) | 2153.24 | 0.0736535 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 18319.0 | 0.624643 | ||||||||
\(952\) | 22307.1 | 0.759431 | ||||||||
\(953\) | 9473.37 | 0.322007 | 0.161003 | − | 0.986954i | \(-0.448527\pi\) | ||||
0.161003 | + | 0.986954i | \(0.448527\pi\) | |||||||
\(954\) | −22660.3 | −0.769031 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 75598.4 | 2.55756 | ||||||||
\(957\) | −22518.5 | −0.760628 | ||||||||
\(958\) | −19819.3 | −0.668404 | ||||||||
\(959\) | −6547.26 | −0.220461 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23818.3 | −0.799514 | ||||||||
\(962\) | 3375.89 | 0.113142 | ||||||||
\(963\) | −10203.0 | −0.341419 | ||||||||
\(964\) | 88399.8 | 2.95349 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 19544.2 | 0.650956 | ||||||||
\(967\) | 5310.75 | 0.176610 | 0.0883052 | − | 0.996093i | \(-0.471855\pi\) | ||||
0.0883052 | + | 0.996093i | \(0.471855\pi\) | |||||||
\(968\) | −96670.1 | −3.20981 | ||||||||
\(969\) | −9158.49 | −0.303626 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 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 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 24603.6 | 0.806907 | ||||||||
\(977\) | 49602.5 | 1.62428 | 0.812142 | − | 0.583460i | \(-0.198301\pi\) | ||||
0.812142 | + | 0.583460i | \(0.198301\pi\) | |||||||
\(978\) | −15441.0 | −0.504856 | ||||||||
\(979\) | 15448.2 | 0.504317 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9158.98 | 0.298087 | ||||||||
\(982\) | −38375.5 | −1.24706 | ||||||||
\(983\) | −47385.7 | −1.53751 | −0.768753 | − | 0.639545i | \(-0.779123\pi\) | ||||
−0.768753 | + | 0.639545i | \(0.779123\pi\) | |||||||
\(984\) | −41659.5 | −1.34965 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 51587.7 | 1.66621 | ||||||||
\(987\) | 948.891 | 0.0306014 | ||||||||
\(988\) | 5927.78 | 0.190878 | ||||||||
\(989\) | −20826.4 | −0.669607 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −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 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 19749.5 | 0.628299 | ||||||||
\(997\) | 14908.6 | 0.473582 | 0.236791 | − | 0.971561i | \(-0.423904\pi\) | ||||
0.236791 | + | 0.971561i | \(0.423904\pi\) | |||||||
\(998\) | 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 | 975.4.a.j.1.1 | 2 | ||
5.4 | even | 2 | 39.4.a.b.1.2 | ✓ | 2 | ||
15.14 | odd | 2 | 117.4.a.c.1.1 | 2 | |||
20.19 | odd | 2 | 624.4.a.r.1.1 | 2 | |||
35.34 | odd | 2 | 1911.4.a.h.1.2 | 2 | |||
40.19 | odd | 2 | 2496.4.a.s.1.2 | 2 | |||
40.29 | even | 2 | 2496.4.a.bc.1.2 | 2 | |||
60.59 | even | 2 | 1872.4.a.t.1.2 | 2 | |||
65.34 | odd | 4 | 507.4.b.f.337.4 | 4 | |||
65.44 | odd | 4 | 507.4.b.f.337.1 | 4 | |||
65.64 | even | 2 | 507.4.a.f.1.1 | 2 | |||
195.194 | 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 | 5.4 | even | 2 | ||
117.4.a.c.1.1 | 2 | 15.14 | odd | 2 | |||
507.4.a.f.1.1 | 2 | 65.64 | even | 2 | |||
507.4.b.f.337.1 | 4 | 65.44 | odd | 4 | |||
507.4.b.f.337.4 | 4 | 65.34 | odd | 4 | |||
624.4.a.r.1.1 | 2 | 20.19 | odd | 2 | |||
975.4.a.j.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1521.4.a.s.1.2 | 2 | 195.194 | odd | 2 | |||
1872.4.a.t.1.2 | 2 | 60.59 | even | 2 | |||
1911.4.a.h.1.2 | 2 | 35.34 | odd | 2 | |||
2496.4.a.s.1.2 | 2 | 40.19 | odd | 2 | |||
2496.4.a.bc.1.2 | 2 | 40.29 | even | 2 |