Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1521,4,Mod(1,1521)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1521, 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("1521.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1521 = 3^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1521.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: | \(89.7419051187\) |
Analytic rank: | \(1\) |
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 | 1.2 | ||
Root | \(3.74166\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1521.1 |
$q$-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 | \(0.183600\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 14.4833 | 1.81041 | ||||||||
\(5\) | 4.51669 | 0.403985 | 0.201992 | − | 0.979387i | \(-0.435258\pi\) | ||||
0.201992 | + | 0.979387i | \(0.435258\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.48331 | 0.404061 | 0.202031 | − | 0.979379i | \(-0.435246\pi\) | ||||
0.202031 | + | 0.979379i | \(0.435246\pi\) | |||||||
\(8\) | 30.7417 | 1.35860 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 21.4166 | 0.677252 | ||||||||
\(11\) | −66.8999 | −1.83373 | −0.916867 | − | 0.399193i | \(-0.869290\pi\) | ||||
−0.916867 | + | 0.399193i | \(0.869290\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 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 | \(0.743139\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −31.4833 | −0.380146 | −0.190073 | − | 0.981770i | \(-0.560872\pi\) | ||||
−0.190073 | + | 0.981770i | \(0.560872\pi\) | |||||||
\(20\) | 65.4166 | 0.731380 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −317.216 | −3.07413 | ||||||||
\(23\) | −183.600 | −1.66448 | −0.832242 | − | 0.554412i | \(-0.812943\pi\) | ||||
−0.832242 | + | 0.554412i | \(0.812943\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −104.600 | −0.836796 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 108.383 | 0.731518 | ||||||||
\(29\) | −112.200 | −0.718450 | −0.359225 | − | 0.933251i | \(-0.616959\pi\) | ||||
−0.359225 | + | 0.933251i | \(0.616959\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 77.2831 | 0.447757 | 0.223878 | − | 0.974617i | \(-0.428128\pi\) | ||||
0.223878 | + | 0.974617i | \(0.428128\pi\) | |||||||
\(32\) | −104.158 | −0.575398 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −459.783 | −2.31918 | ||||||||
\(35\) | 33.7998 | 0.163234 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −54.7664 | −0.243339 | −0.121669 | − | 0.992571i | \(-0.538825\pi\) | ||||
−0.121669 | + | 0.992571i | \(0.538825\pi\) | |||||||
\(38\) | −149.283 | −0.637287 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 138.850 | 0.548854 | ||||||||
\(41\) | 451.716 | 1.72064 | 0.860319 | − | 0.509756i | \(-0.170264\pi\) | ||||
0.860319 | + | 0.509756i | \(0.170264\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −113.434 | −0.402291 | −0.201145 | − | 0.979561i | \(-0.564466\pi\) | ||||
−0.201145 | + | 0.979561i | \(0.564466\pi\) | |||||||
\(44\) | −968.932 | −3.31982 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −870.566 | −2.79039 | ||||||||
\(47\) | −42.2670 | −0.131176 | −0.0655880 | − | 0.997847i | \(-0.520892\pi\) | ||||
−0.0655880 | + | 0.997847i | \(0.520892\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −287.000 | −0.836735 | ||||||||
\(50\) | −495.975 | −1.40283 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 530.999 | 1.37619 | 0.688097 | − | 0.725618i | \(-0.258446\pi\) | ||||
0.688097 | + | 0.725618i | \(0.258446\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −302.166 | −0.740800 | ||||||||
\(56\) | 230.049 | 0.548958 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −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 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −733.082 | −1.43180 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 872.082 | 1.59018 | 0.795088 | − | 0.606495i | \(-0.207425\pi\) | ||||
0.795088 | + | 0.606495i | \(0.207425\pi\) | |||||||
\(68\) | −1404.40 | −2.50453 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 160.267 | 0.273651 | ||||||||
\(71\) | −100.299 | −0.167653 | −0.0838263 | − | 0.996480i | \(-0.526714\pi\) | ||||
−0.0838263 | + | 0.996480i | \(0.526714\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 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 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −545.266 | −0.776547 | −0.388273 | − | 0.921544i | \(-0.626928\pi\) | ||||
−0.388273 | + | 0.921544i | \(0.626928\pi\) | |||||||
\(80\) | 135.048 | 0.188736 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2141.88 | 2.88453 | ||||||||
\(83\) | −454.534 | −0.601103 | −0.300552 | − | 0.953766i | \(-0.597171\pi\) | ||||
−0.300552 | + | 0.953766i | \(0.597171\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −437.968 | −0.558874 | ||||||||
\(86\) | −537.864 | −0.674412 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −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 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2659.13 | −3.01341 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −200.415 | −0.219907 | ||||||||
\(95\) | −142.200 | −0.153573 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1089.16 | 1.14008 | 0.570041 | − | 0.821616i | \(-0.306927\pi\) | ||||
0.570041 | + | 0.821616i | \(0.306927\pi\) | |||||||
\(98\) | −1360.86 | −1.40273 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1514.95 | −1.51495 | ||||||||
\(101\) | 77.2336 | 0.0760894 | 0.0380447 | − | 0.999276i | \(-0.487887\pi\) | ||||
0.0380447 | + | 0.999276i | \(0.487887\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1351.36 | 1.29275 | 0.646377 | − | 0.763018i | \(-0.276283\pi\) | ||||
0.646377 | + | 0.763018i | \(0.276283\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2517.81 | 2.30709 | ||||||||
\(107\) | −1133.67 | −1.02426 | −0.512129 | − | 0.858908i | \(-0.671143\pi\) | ||||
−0.512129 | + | 0.858908i | \(0.671143\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1017.66 | −0.894262 | −0.447131 | − | 0.894469i | \(-0.647554\pi\) | ||||
−0.447131 | + | 0.894469i | \(0.647554\pi\) | |||||||
\(110\) | −1432.77 | −1.24190 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 223.750 | 0.188772 | ||||||||
\(113\) | −1570.06 | −1.30707 | −0.653536 | − | 0.756895i | \(-0.726715\pi\) | ||||
−0.653536 | + | 0.756895i | \(0.726715\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −829.261 | −0.672426 | ||||||||
\(116\) | −1625.03 | −1.30069 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1041.58 | 0.812588 | ||||||||
\(119\) | −725.632 | −0.558979 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3144.60 | 2.36258 | ||||||||
\(122\) | 3901.75 | 2.89547 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1119.32 | 0.810625 | ||||||||
\(125\) | −1037.03 | −0.742037 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1248.16 | −0.872099 | −0.436050 | − | 0.899923i | \(-0.643623\pi\) | ||||
−0.436050 | + | 0.899923i | \(0.643623\pi\) | |||||||
\(128\) | −2642.76 | −1.82491 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1274.80 | 0.850227 | 0.425113 | − | 0.905140i | \(-0.360234\pi\) | ||||
0.425113 | + | 0.905140i | \(0.360234\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −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 | \(-0.412048\pi\) | ||||
0.272807 | + | 0.962069i | \(0.412048\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 310.334 | 0.189368 | 0.0946840 | − | 0.995507i | \(-0.469816\pi\) | ||||
0.0946840 | + | 0.995507i | \(0.469816\pi\) | |||||||
\(140\) | 489.533 | 0.295522 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −475.585 | −0.281058 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −506.773 | −0.290243 | ||||||||
\(146\) | 785.380 | 0.445195 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −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 | \(-0.500562\pi\) | ||||
−0.00176472 | + | 0.999998i | \(0.500562\pi\) | |||||||
\(152\) | −967.849 | −0.516467 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2373.83 | −1.24213 | ||||||||
\(155\) | 349.063 | 0.180887 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2297.60 | −1.16795 | −0.583975 | − | 0.811772i | \(-0.698503\pi\) | ||||
−0.583975 | + | 0.811772i | \(0.698503\pi\) | |||||||
\(158\) | −2585.46 | −1.30183 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −470.450 | −0.232452 | ||||||||
\(161\) | −1373.93 | −0.672553 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 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 | \(-0.508044\pi\) | ||||
−0.0252687 | + | 0.999681i | \(0.508044\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −2076.69 | −0.936912 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1642.90 | −0.728313 | ||||||||
\(173\) | 1889.17 | 0.830236 | 0.415118 | − | 0.909768i | \(-0.363740\pi\) | ||||
0.415118 | + | 0.909768i | \(0.363740\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −782.751 | −0.338117 | ||||||||
\(176\) | −2000.30 | −0.856694 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1094.92 | −0.461054 | ||||||||
\(179\) | −3427.86 | −1.43134 | −0.715672 | − | 0.698437i | \(-0.753879\pi\) | ||||
−0.715672 | + | 0.698437i | \(0.753879\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 208.403 | 0.0855826 | 0.0427913 | − | 0.999084i | \(-0.486375\pi\) | ||||
0.0427913 | + | 0.999084i | \(0.486375\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5644.15 | −2.26137 | ||||||||
\(185\) | −247.363 | −0.0983052 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6487.06 | 2.53679 | ||||||||
\(188\) | −612.166 | −0.237483 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −674.265 | −0.257454 | ||||||||
\(191\) | −957.735 | −0.362824 | −0.181412 | − | 0.983407i | \(-0.558067\pi\) | ||||
−0.181412 | + | 0.983407i | \(0.558067\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 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 | \(-0.746761\pi\) | ||||
−0.699876 | + | 0.714265i | \(0.746761\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2305.83 | 0.821388 | 0.410694 | − | 0.911773i | \(-0.365286\pi\) | ||||
0.410694 | + | 0.911773i | \(0.365286\pi\) | |||||||
\(200\) | −3215.56 | −1.13687 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 366.215 | 0.127558 | ||||||||
\(203\) | −839.630 | −0.290298 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2040.26 | 0.695111 | ||||||||
\(206\) | 6407.70 | 2.16721 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 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 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5375.46 | −1.71710 | ||||||||
\(215\) | −512.345 | −0.162519 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 578.334 | 0.180921 | ||||||||
\(218\) | −4825.41 | −1.49917 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4376.36 | −1.34116 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −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 | \(-0.625413\pi\) | ||||
−0.383882 | + | 0.923382i | \(0.625413\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1678.73 | −0.484425 | −0.242213 | − | 0.970223i | \(-0.577873\pi\) | ||||
−0.242213 | + | 0.970223i | \(0.577873\pi\) | |||||||
\(230\) | −3932.07 | −1.12727 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3449.22 | −0.976088 | ||||||||
\(233\) | −648.506 | −0.182339 | −0.0911696 | − | 0.995835i | \(-0.529061\pi\) | ||||
−0.0911696 | + | 0.995835i | \(0.529061\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −190.907 | −0.0529931 | ||||||||
\(236\) | 3181.50 | 0.877533 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −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 | \(-0.803645\pi\) | ||||
−0.815695 | + | 0.578483i | \(0.803645\pi\) | |||||||
\(242\) | 14910.6 | 3.96070 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 11917.8 | 3.12689 | ||||||||
\(245\) | −1296.29 | −0.338028 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 2375.81 | 0.608323 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −4917.24 | −1.24397 | ||||||||
\(251\) | −6423.40 | −1.61530 | −0.807652 | − | 0.589660i | \(-0.799262\pi\) | ||||
−0.807652 | + | 0.589660i | \(0.799262\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 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 | \(0.452298\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −409.834 | −0.0983238 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6044.66 | 1.42534 | ||||||||
\(263\) | 514.992 | 0.120744 | 0.0603722 | − | 0.998176i | \(-0.480771\pi\) | ||||
0.0603722 | + | 0.998176i | \(0.480771\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2398.35 | 0.555961 | ||||||||
\(266\) | −1117.13 | −0.257503 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 12630.6 | 2.87888 | ||||||||
\(269\) | 5132.60 | 1.16335 | 0.581673 | − | 0.813423i | \(-0.302398\pi\) | ||||
0.581673 | + | 0.813423i | \(0.302398\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4300.00 | 0.963862 | 0.481931 | − | 0.876209i | \(-0.339936\pi\) | ||||
0.481931 | + | 0.876209i | \(0.339936\pi\) | |||||||
\(272\) | −2899.29 | −0.646306 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4148.55 | 0.914682 | ||||||||
\(275\) | 6997.70 | 1.53446 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1812.80 | −0.393215 | −0.196607 | − | 0.980482i | \(-0.562992\pi\) | ||||
−0.196607 | + | 0.980482i | \(0.562992\pi\) | |||||||
\(278\) | 1471.50 | 0.317462 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1039.06 | 0.221771 | ||||||||
\(281\) | −4073.08 | −0.864696 | −0.432348 | − | 0.901707i | \(-0.642315\pi\) | ||||
−0.432348 | + | 0.901707i | \(0.642315\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6346.29 | 1.33303 | 0.666516 | − | 0.745491i | \(-0.267785\pi\) | ||||
0.666516 | + | 0.745491i | \(0.267785\pi\) | |||||||
\(284\) | −1452.67 | −0.303520 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3380.33 | 0.695243 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4489.53 | 0.913806 | ||||||||
\(290\) | −2402.94 | −0.486572 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2398.93 | 0.480777 | ||||||||
\(293\) | −8390.97 | −1.67306 | −0.836529 | − | 0.547923i | \(-0.815419\pi\) | ||||
−0.836529 | + | 0.547923i | \(0.815419\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 992.164 | 0.195817 | ||||||||
\(296\) | −1683.61 | −0.330601 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 24.0907 | 0.00468300 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −848.861 | −0.162550 | ||||||||
\(302\) | −31.0528 | −0.00591685 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −941.348 | −0.177599 | ||||||||
\(305\) | 3716.62 | 0.697748 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4005.27 | −0.744603 | −0.372301 | − | 0.928112i | \(-0.621431\pi\) | ||||
−0.372301 | + | 0.928112i | \(0.621431\pi\) | |||||||
\(308\) | −7250.82 | −1.34141 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1655.14 | 0.303244 | ||||||||
\(311\) | −5836.53 | −1.06418 | −0.532088 | − | 0.846689i | \(-0.678593\pi\) | ||||
−0.532088 | + | 0.846689i | \(0.678593\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1763.19 | 0.318407 | 0.159204 | − | 0.987246i | \(-0.449107\pi\) | ||||
0.159204 | + | 0.987246i | \(0.449107\pi\) | |||||||
\(314\) | −10894.4 | −1.95798 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7897.26 | −1.40587 | ||||||||
\(317\) | −6106.35 | −1.08191 | −0.540957 | − | 0.841050i | \(-0.681938\pi\) | ||||
−0.540957 | + | 0.841050i | \(0.681938\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7506.18 | 1.31745 | ||||||||
\(320\) | −3311.10 | −0.578425 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6514.72 | −1.12749 | ||||||||
\(323\) | 3052.83 | 0.525895 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5147.00 | 0.874436 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 13886.5 | 2.33766 | ||||||||
\(329\) | −316.297 | −0.0530031 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7490.38 | −1.24383 | −0.621916 | − | 0.783084i | \(-0.713646\pi\) | ||||
−0.621916 | + | 0.783084i | \(0.713646\pi\) | |||||||
\(332\) | −6583.16 | −1.08825 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −517.152 | −0.0847224 | ||||||||
\(335\) | 3938.92 | 0.642406 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9462.46 | 1.52953 | 0.764767 | − | 0.644307i | \(-0.222854\pi\) | ||||
0.764767 | + | 0.644307i | \(0.222854\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −6343.22 | −1.01179 | ||||||||
\(341\) | −5170.23 | −0.821066 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −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 | \(0.846862\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3673.96 | 0.563503 | 0.281751 | − | 0.959487i | \(-0.409085\pi\) | ||||
0.281751 | + | 0.959487i | \(0.409085\pi\) | |||||||
\(350\) | −3711.54 | −0.566829 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6968.17 | 1.05513 | ||||||||
\(353\) | 3388.65 | 0.510935 | 0.255467 | − | 0.966818i | \(-0.417771\pi\) | ||||
0.255467 | + | 0.966818i | \(0.417771\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −453.020 | −0.0677290 | ||||||||
\(356\) | −3344.41 | −0.497903 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −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 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 748.117 | 0.107283 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8715.98 | −1.23970 | −0.619851 | − | 0.784720i | \(-0.712807\pi\) | ||||
−0.619851 | + | 0.784720i | \(0.712807\pi\) | |||||||
\(368\) | −5489.61 | −0.777624 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1172.91 | −0.164802 | ||||||||
\(371\) | 3973.63 | 0.556067 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4667.99 | 0.647987 | 0.323994 | − | 0.946059i | \(-0.394974\pi\) | ||||
0.323994 | + | 0.946059i | \(0.394974\pi\) | |||||||
\(374\) | 30759.4 | 4.25276 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1299.36 | −0.178216 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10862.7 | −1.47225 | −0.736123 | − | 0.676848i | \(-0.763345\pi\) | ||||
−0.736123 | + | 0.676848i | \(0.763345\pi\) | |||||||
\(380\) | −2059.53 | −0.278031 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4541.25 | −0.608248 | ||||||||
\(383\) | 10054.2 | 1.34137 | 0.670686 | − | 0.741742i | \(-0.266000\pi\) | ||||
0.670686 | + | 0.741742i | \(0.266000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2261.20 | −0.299329 | ||||||||
\(386\) | 2431.19 | 0.320581 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 15774.7 | 2.06402 | ||||||||
\(389\) | −6418.50 | −0.836584 | −0.418292 | − | 0.908313i | \(-0.637371\pi\) | ||||
−0.418292 | + | 0.908313i | \(0.637371\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17803.0 | 2.30265 | ||||||||
\(392\) | −8822.86 | −1.13679 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −18351.9 | −2.34658 | ||||||||
\(395\) | −2462.79 | −0.313713 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12019.9 | 1.51955 | 0.759775 | − | 0.650186i | \(-0.225309\pi\) | ||||
0.759775 | + | 0.650186i | \(0.225309\pi\) | |||||||
\(398\) | 10933.5 | 1.37700 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3127.52 | −0.390939 | ||||||||
\(401\) | 3599.80 | 0.448293 | 0.224147 | − | 0.974555i | \(-0.428041\pi\) | ||||
0.224147 | + | 0.974555i | \(0.428041\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 1118.60 | 0.137753 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3981.24 | −0.486664 | ||||||||
\(407\) | 3663.87 | 0.446219 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 48.0968 | 0.00581475 | 0.00290737 | − | 0.999996i | \(-0.499075\pi\) | ||||
0.00290737 | + | 0.999996i | \(0.499075\pi\) | |||||||
\(410\) | 9674.20 | 1.16530 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 19572.2 | 2.34042 | ||||||||
\(413\) | 1643.83 | 0.195854 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2052.99 | −0.242837 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 9987.02 | 1.16862 | ||||||||
\(419\) | −723.462 | −0.0843518 | −0.0421759 | − | 0.999110i | \(-0.513429\pi\) | ||||
−0.0421759 | + | 0.999110i | \(0.513429\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14845.5 | 1.71859 | 0.859295 | − | 0.511481i | \(-0.170903\pi\) | ||||
0.859295 | + | 0.511481i | \(0.170903\pi\) | |||||||
\(422\) | −17413.3 | −2.00868 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 16323.8 | 1.86970 | ||||||||
\(425\) | 10142.7 | 1.15763 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6157.76 | 0.697880 | ||||||||
\(428\) | −16419.2 | −1.85433 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2429.36 | −0.272452 | ||||||||
\(431\) | 1103.11 | 0.123283 | 0.0616417 | − | 0.998098i | \(-0.480366\pi\) | ||||
0.0616417 | + | 0.998098i | \(0.480366\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8893.53 | 0.987057 | 0.493528 | − | 0.869730i | \(-0.335707\pi\) | ||||
0.493528 | + | 0.869730i | \(0.335707\pi\) | |||||||
\(434\) | 2742.26 | 0.303301 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −14739.1 | −1.61898 | ||||||||
\(437\) | 5780.32 | 0.632747 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10901.7 | −1.18521 | −0.592607 | − | 0.805492i | \(-0.701901\pi\) | ||||
−0.592607 | + | 0.805492i | \(0.701901\pi\) | |||||||
\(440\) | −9289.08 | −1.00645 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3781.37 | 0.405550 | 0.202775 | − | 0.979225i | \(-0.435004\pi\) | ||||
0.202775 | + | 0.979225i | \(0.435004\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1042.97 | −0.111105 | ||||||||
\(446\) | −24121.0 | −2.56091 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −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 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −12450.8 | −1.28710 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1237.64 | 0.126684 | 0.0633419 | − | 0.997992i | \(-0.479824\pi\) | ||||
0.0633419 | + | 0.997992i | \(0.479824\pi\) | |||||||
\(458\) | −7959.95 | −0.812105 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −12010.5 | −1.21737 | ||||||||
\(461\) | 8790.90 | 0.888141 | 0.444071 | − | 0.895992i | \(-0.353534\pi\) | ||||
0.444071 | + | 0.895992i | \(0.353534\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 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 | \(0.353036\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6526.06 | 0.642528 | ||||||||
\(470\) | −905.214 | −0.0888391 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6752.91 | 0.658533 | ||||||||
\(473\) | 7588.71 | 0.737694 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3293.14 | 0.318105 | ||||||||
\(476\) | −10509.6 | −1.01198 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 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 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −28941.0 | −2.73491 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 45544.2 | 4.27725 | ||||||||
\(485\) | 4919.41 | 0.460575 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18443.8 | 1.71616 | 0.858078 | − | 0.513519i | \(-0.171658\pi\) | ||||
0.858078 | + | 0.513519i | \(0.171658\pi\) | |||||||
\(488\) | 25296.2 | 2.34653 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −6146.56 | −0.566680 | ||||||||
\(491\) | −8093.26 | −0.743877 | −0.371939 | − | 0.928257i | \(-0.621307\pi\) | ||||
−0.371939 | + | 0.928257i | \(0.621307\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10879.7 | 0.993907 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2310.76 | 0.209185 | ||||||||
\(497\) | −750.571 | −0.0677418 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10941.6 | 0.981591 | 0.490796 | − | 0.871275i | \(-0.336706\pi\) | ||||
0.490796 | + | 0.871275i | \(0.336706\pi\) | |||||||
\(500\) | −15019.6 | −1.34340 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −30457.5 | −2.70794 | ||||||||
\(503\) | 9260.11 | 0.820851 | 0.410425 | − | 0.911894i | \(-0.365380\pi\) | ||||
0.410425 | + | 0.911894i | \(0.365380\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 348.840 | 0.0307389 | ||||||||
\(506\) | 58240.8 | 5.11684 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −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 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5833.32 | 0.500577 | ||||||||
\(515\) | 6103.68 | 0.522253 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2827.66 | 0.240542 | ||||||||
\(518\) | −1943.29 | −0.164833 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11427.9 | −0.960973 | −0.480486 | − | 0.877002i | \(-0.659540\pi\) | ||||
−0.480486 | + | 0.877002i | \(0.659540\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4810.47 | −0.402193 | −0.201097 | − | 0.979571i | \(-0.564451\pi\) | ||||
−0.201097 | + | 0.979571i | \(0.564451\pi\) | |||||||
\(524\) | 18463.3 | 1.53926 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2441.92 | 0.202419 | ||||||||
\(527\) | −7493.88 | −0.619428 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21541.8 | 1.77051 | ||||||||
\(530\) | 11372.2 | 0.932030 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3412.26 | −0.278083 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5120.41 | −0.413785 | ||||||||
\(536\) | 26809.2 | 2.16042 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 24337.0 | 1.95027 | ||||||||
\(539\) | 19200.3 | 1.53435 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2411.99 | −0.191681 | −0.0958406 | − | 0.995397i | \(-0.530554\pi\) | ||||
−0.0958406 | + | 0.995397i | \(0.530554\pi\) | |||||||
\(542\) | 20389.1 | 1.61585 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 10099.9 | 0.796008 | ||||||||
\(545\) | −4596.47 | −0.361268 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4396.34 | −0.343646 | −0.171823 | − | 0.985128i | \(-0.554966\pi\) | ||||
−0.171823 | + | 0.985128i | \(0.554966\pi\) | |||||||
\(548\) | 12671.7 | 0.987786 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 33180.7 | 2.57242 | ||||||||
\(551\) | 3532.43 | 0.273116 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −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 | \(-0.731637\pi\) | ||||
−0.665160 | + | 0.746701i | \(0.731637\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 1010.61 | 0.0762608 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −19313.2 | −1.44960 | ||||||||
\(563\) | 6881.77 | 0.515154 | 0.257577 | − | 0.966258i | \(-0.417076\pi\) | ||||
0.257577 | + | 0.966258i | \(0.417076\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7091.49 | −0.528037 | ||||||||
\(566\) | 30092.0 | 2.23473 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3083.36 | −0.227773 | ||||||||
\(569\) | −14733.5 | −1.08552 | −0.542758 | − | 0.839889i | \(-0.682620\pi\) | ||||
−0.542758 | + | 0.839889i | \(0.682620\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4488.51 | 0.328964 | 0.164482 | − | 0.986380i | \(-0.447405\pi\) | ||||
0.164482 | + | 0.986380i | \(0.447405\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 16028.4 | 1.16553 | ||||||||
\(575\) | 19204.4 | 1.39284 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10552.2 | 0.761338 | 0.380669 | − | 0.924711i | \(-0.375694\pi\) | ||||
0.380669 | + | 0.924711i | \(0.375694\pi\) | |||||||
\(578\) | 21287.8 | 1.53193 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −7339.75 | −0.525460 | ||||||||
\(581\) | −3401.42 | −0.242882 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −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 | \(-0.518332\pi\) | ||||
−0.0575591 | + | 0.998342i | \(0.518332\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2433.13 | −0.170213 | ||||||||
\(590\) | 4704.50 | 0.328273 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1637.51 | −0.113685 | ||||||||
\(593\) | 14024.0 | 0.971155 | 0.485577 | − | 0.874194i | \(-0.338609\pi\) | ||||
0.485577 | + | 0.874194i | \(0.338609\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3277.45 | −0.225819 | ||||||||
\(596\) | 73.5845 | 0.00505728 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −365.860 | −0.0249560 | −0.0124780 | − | 0.999922i | \(-0.503972\pi\) | ||||
−0.0124780 | + | 0.999922i | \(0.503972\pi\) | |||||||
\(600\) | 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 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −94.8504 | −0.00638975 | ||||||||
\(605\) | 14203.1 | 0.954446 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2324.97 | 0.155465 | 0.0777327 | − | 0.996974i | \(-0.475232\pi\) | ||||
0.0777327 | + | 0.996974i | \(0.475232\pi\) | |||||||
\(608\) | 3279.25 | 0.218735 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 17623.0 | 1.16973 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −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 | \(-0.531015\pi\) | ||||
−0.0972810 | + | 0.995257i | \(0.531015\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15158.6 | −0.984292 | −0.492146 | − | 0.870513i | \(-0.663787\pi\) | ||||
−0.492146 | + | 0.870513i | \(0.663787\pi\) | |||||||
\(620\) | 5055.60 | 0.327480 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −27674.8 | −1.78402 | ||||||||
\(623\) | −1728.01 | −0.111126 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8391.01 | 0.537025 | ||||||||
\(626\) | 8360.45 | 0.533787 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −33276.8 | −2.11447 | ||||||||
\(629\) | 5310.51 | 0.336636 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5562.30 | −0.350922 | −0.175461 | − | 0.984486i | \(-0.556142\pi\) | ||||
−0.175461 | + | 0.984486i | \(0.556142\pi\) | |||||||
\(632\) | −16762.4 | −1.05502 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −28954.2 | −1.81375 | ||||||||
\(635\) | −5637.56 | −0.352315 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 35591.7 | 2.20861 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −11936.5 | −0.737237 | ||||||||
\(641\) | 24140.7 | 1.48752 | 0.743761 | − | 0.668446i | \(-0.233040\pi\) | ||||
0.743761 | + | 0.668446i | \(0.233040\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 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 | \(0.514410\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14695.7 | −0.888836 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 15721.4 | 0.944323 | ||||||||
\(653\) | −10668.2 | −0.639327 | −0.319663 | − | 0.947531i | \(-0.603570\pi\) | ||||
−0.319663 | + | 0.947531i | \(0.603570\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5757.86 | 0.343478 | ||||||||
\(656\) | 13506.3 | 0.803858 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1499.77 | −0.0888559 | ||||||||
\(659\) | 13933.1 | 0.823608 | 0.411804 | − | 0.911272i | \(-0.364899\pi\) | ||||
0.411804 | + | 0.911272i | \(0.364899\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2349.69 | 0.138264 | 0.0691320 | − | 0.997608i | \(-0.477977\pi\) | ||||
0.0691320 | + | 0.997608i | \(0.477977\pi\) | |||||||
\(662\) | −35516.8 | −2.08520 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −13973.1 | −0.816660 | ||||||||
\(665\) | −1064.13 | −0.0620529 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20599.9 | 1.19585 | ||||||||
\(668\) | −1579.63 | −0.0914937 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 18677.0 | 1.07695 | ||||||||
\(671\) | −55049.6 | −3.16716 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −32421.0 | −1.85697 | −0.928483 | − | 0.371374i | \(-0.878887\pi\) | ||||
−0.928483 | + | 0.371374i | \(0.878887\pi\) | |||||||
\(674\) | 44867.7 | 2.56415 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1071.74 | 0.0608421 | 0.0304211 | − | 0.999537i | \(-0.490315\pi\) | ||||
0.0304211 | + | 0.999537i | \(0.490315\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8150.56 | 0.460663 | ||||||||
\(680\) | −13463.9 | −0.759287 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −24515.5 | −1.37646 | ||||||||
\(683\) | −305.487 | −0.0171144 | −0.00855721 | − | 0.999963i | \(-0.502724\pi\) | ||||
−0.00855721 | + | 0.999963i | \(0.502724\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3951.72 | 0.220419 | ||||||||
\(686\) | −22354.5 | −1.24417 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3391.66 | −0.187944 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2180.81 | −0.120061 | −0.0600303 | − | 0.998197i | \(-0.519120\pi\) | ||||
−0.0600303 | + | 0.998197i | \(0.519120\pi\) | |||||||
\(692\) | 27361.4 | 1.50307 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −54340.9 | −2.97227 | ||||||||
\(695\) | 1401.68 | 0.0765018 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −43801.4 | −2.38034 | ||||||||
\(698\) | 17420.6 | 0.944672 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −11336.8 | −0.612132 | ||||||||
\(701\) | 15168.3 | 0.817259 | 0.408629 | − | 0.912700i | \(-0.366007\pi\) | ||||
0.408629 | + | 0.912700i | \(0.366007\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1724.23 | 0.0925043 | ||||||||
\(704\) | 49043.1 | 2.62554 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 16067.8 | 0.856545 | ||||||||
\(707\) | 577.963 | 0.0307448 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8988.17 | 0.476104 | 0.238052 | − | 0.971252i | \(-0.423491\pi\) | ||||
0.238052 | + | 0.971252i | \(0.423491\pi\) | |||||||
\(710\) | −2148.07 | −0.113543 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −7098.71 | −0.373645 | ||||||||
\(713\) | −14189.1 | −0.745284 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −49646.8 | −2.59132 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −45870.7 | −2.38423 | ||||||||
\(719\) | −8448.18 | −0.438198 | −0.219099 | − | 0.975703i | \(-0.570312\pi\) | ||||
−0.219099 | + | 0.975703i | \(0.570312\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10112.7 | 0.522352 | ||||||||
\(722\) | −27823.1 | −1.43417 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3018.36 | 0.154940 | ||||||||
\(725\) | 11736.1 | 0.601197 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8624.18 | −0.439963 | −0.219982 | − | 0.975504i | \(-0.570600\pi\) | ||||
−0.219982 | + | 0.975504i | \(0.570600\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3547.31 | 0.179852 | ||||||||
\(731\) | 10999.3 | 0.556530 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −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 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17671.1 | 0.879626 | 0.439813 | − | 0.898089i | \(-0.355045\pi\) | ||||
0.439813 | + | 0.898089i | \(0.355045\pi\) | |||||||
\(740\) | −3582.63 | −0.177973 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 18841.6 | 0.932206 | ||||||||
\(743\) | −21331.1 | −1.05325 | −0.526623 | − | 0.850099i | \(-0.676542\pi\) | ||||
−0.526623 | + | 0.850099i | \(0.676542\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 22.9477 | 0.00112851 | ||||||||
\(746\) | 22134.0 | 1.08630 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 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 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −29.5795 | −0.00142584 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16610.9 | −0.797537 | −0.398768 | − | 0.917052i | \(-0.630562\pi\) | ||||
−0.398768 | + | 0.917052i | \(0.630562\pi\) | |||||||
\(758\) | −51507.4 | −2.46812 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4371.47 | −0.208645 | ||||||||
\(761\) | −29365.5 | −1.39882 | −0.699408 | − | 0.714723i | \(-0.746553\pi\) | ||||
−0.699408 | + | 0.714723i | \(0.746553\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7615.50 | −0.361336 | ||||||||
\(764\) | −13871.2 | −0.656861 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 47673.5 | 2.24871 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28599.9 | 1.34114 | 0.670572 | − | 0.741844i | \(-0.266049\pi\) | ||||
0.670572 | + | 0.741844i | \(0.266049\pi\) | |||||||
\(770\) | −10721.8 | −0.501803 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 7426.03 | 0.346203 | ||||||||
\(773\) | 13491.8 | 0.627772 | 0.313886 | − | 0.949461i | \(-0.398369\pi\) | ||||
0.313886 | + | 0.949461i | \(0.398369\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8083.78 | −0.374681 | ||||||||
\(776\) | 33482.7 | 1.54892 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −30434.3 | −1.40247 | ||||||||
\(779\) | −14221.5 | −0.654093 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6710.01 | 0.307430 | ||||||||
\(782\) | 84415.9 | 3.86024 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −8581.27 | −0.390911 | ||||||||
\(785\) | −10377.5 | −0.471834 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25876.7 | −1.17205 | −0.586025 | − | 0.810293i | \(-0.699308\pi\) | ||||
−0.586025 | + | 0.810293i | \(0.699308\pi\) | |||||||
\(788\) | −56055.5 | −2.53413 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −11677.7 | −0.525918 | ||||||||
\(791\) | −11749.3 | −0.528137 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 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 | \(0.662080\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4098.49 | 0.181469 | ||||||||
\(800\) | 10894.9 | 0.481491 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 17069.0 | 0.751531 | ||||||||
\(803\) | −11080.9 | −0.486969 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6205.62 | −0.271701 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2374.29 | 0.103375 | ||||||||
\(809\) | −5583.23 | −0.242640 | −0.121320 | − | 0.992613i | \(-0.538713\pi\) | ||||
−0.121320 | + | 0.992613i | \(0.538713\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12925.4 | −0.559647 | −0.279823 | − | 0.960052i | \(-0.590276\pi\) | ||||
−0.279823 | + | 0.960052i | \(0.590276\pi\) | |||||||
\(812\) | −12160.6 | −0.525559 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 17372.8 | 0.748054 | ||||||||
\(815\) | 4902.80 | 0.210721 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3571.27 | 0.152929 | ||||||||
\(818\) | 228.058 | 0.00974801 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 29549.7 | 1.25844 | ||||||||
\(821\) | −10153.2 | −0.431608 | −0.215804 | − | 0.976437i | \(-0.569237\pi\) | ||||
−0.215804 | + | 0.976437i | \(0.569237\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3282.93 | 0.139047 | 0.0695235 | − | 0.997580i | \(-0.477852\pi\) | ||||
0.0695235 | + | 0.997580i | \(0.477852\pi\) | |||||||
\(824\) | 41543.1 | 1.75634 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7794.49 | 0.328335 | ||||||||
\(827\) | −17689.3 | −0.743795 | −0.371897 | − | 0.928274i | \(-0.621293\pi\) | ||||
−0.371897 | + | 0.928274i | \(0.621293\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 38181.5 | 1.59964 | 0.799818 | − | 0.600243i | \(-0.204930\pi\) | ||||
0.799818 | + | 0.600243i | \(0.204930\pi\) | |||||||
\(830\) | −9734.56 | −0.407098 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 27829.4 | 1.15754 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −492.615 | −0.0204163 | ||||||||
\(836\) | 30505.2 | 1.26201 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −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 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −53188.5 | −2.16922 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 23532.0 | 0.954627 | ||||||||
\(848\) | 15876.8 | 0.642938 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 48093.0 | 1.94068 | ||||||||
\(851\) | 10055.1 | 0.405034 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 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 | \(0.673612\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −45617.4 | −1.81193 | −0.905964 | − | 0.423354i | \(-0.860853\pi\) | ||||
−0.905964 | + | 0.423354i | \(0.860853\pi\) | |||||||
\(860\) | −7420.45 | −0.294227 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5230.59 | 0.206676 | ||||||||
\(863\) | −2010.93 | −0.0793195 | −0.0396597 | − | 0.999213i | \(-0.512627\pi\) | ||||
−0.0396597 | + | 0.999213i | \(0.512627\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8532.78 | 0.335403 | ||||||||
\(866\) | 42170.1 | 1.65473 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 8376.19 | 0.327542 | ||||||||
\(869\) | 36478.2 | 1.42398 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −31284.7 | −1.21495 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 27408.3 | 1.06076 | ||||||||
\(875\) | −7760.41 | −0.299828 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 36767.3 | 1.41567 | 0.707836 | − | 0.706376i | \(-0.249671\pi\) | ||||
0.707836 | + | 0.706376i | \(0.249671\pi\) | |||||||
\(878\) | −51692.0 | −1.98693 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −9034.72 | −0.346091 | ||||||||
\(881\) | −35401.2 | −1.35380 | −0.676899 | − | 0.736076i | \(-0.736677\pi\) | ||||
−0.676899 | + | 0.736076i | \(0.736677\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11928.0 | −0.454596 | −0.227298 | − | 0.973825i | \(-0.572989\pi\) | ||||
−0.227298 | + | 0.973825i | \(0.572989\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 17930.0 | 0.679875 | ||||||||
\(887\) | 32939.3 | 1.24689 | 0.623447 | − | 0.781866i | \(-0.285732\pi\) | ||||
0.623447 | + | 0.781866i | \(0.285732\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9340.40 | −0.352381 | ||||||||
\(890\) | −4945.41 | −0.186259 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −73677.3 | −2.76558 | ||||||||
\(893\) | 1330.70 | 0.0498660 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15482.6 | −0.578241 | ||||||||
\(896\) | −19776.6 | −0.737376 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 506.569 | 0.0188245 | ||||||||
\(899\) | −8671.18 | −0.321691 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −51489.2 | −1.90383 | ||||||||
\(902\) | −143292. | −5.28946 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −48266.4 | −1.77579 | ||||||||
\(905\) | 941.289 | 0.0345740 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1500.89 | 0.0549461 | 0.0274731 | − | 0.999623i | \(-0.491254\pi\) | ||||
0.0274731 | + | 0.999623i | \(0.491254\pi\) | |||||||
\(908\) | −38030.7 | −1.38997 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19728.2 | −0.717481 | −0.358740 | − | 0.933437i | \(-0.616794\pi\) | ||||
−0.358740 | + | 0.933437i | \(0.616794\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 30408.3 | 1.10226 | ||||||||
\(914\) | 5868.48 | 0.212376 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −24313.5 | −0.877011 | ||||||||
\(917\) | 9539.72 | 0.343543 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19992.0 | 0.717602 | 0.358801 | − | 0.933414i | \(-0.383186\pi\) | ||||
0.358801 | + | 0.933414i | \(0.383186\pi\) | |||||||
\(920\) | −25492.9 | −0.913560 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 41683.4 | 1.48891 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5728.54 | 0.203625 | ||||||||
\(926\) | 18310.2 | 0.649794 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 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 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 42634.0 | 1.49361 | ||||||||
\(935\) | 29300.0 | 1.02483 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10252.9 | −0.357468 | −0.178734 | − | 0.983897i | \(-0.557200\pi\) | ||||
−0.178734 | + | 0.983897i | \(0.557200\pi\) | |||||||
\(938\) | 30944.4 | 1.07715 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2764.96 | −0.0959394 | ||||||||
\(941\) | 11043.0 | 0.382563 | 0.191282 | − | 0.981535i | \(-0.438736\pi\) | ||||
0.191282 | + | 0.981535i | \(0.438736\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −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 | \(-0.314310\pi\) | ||||
0.550833 | + | 0.834615i | \(0.314310\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 15614.9 | 0.533280 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −22307.1 | −0.759431 | ||||||||
\(953\) | 9473.37 | 0.322007 | 0.161003 | − | 0.986954i | \(-0.448527\pi\) | ||||
0.161003 | + | 0.986954i | \(0.448527\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4325.79 | −0.146575 | ||||||||
\(956\) | 75598.4 | 2.55756 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 19819.3 | 0.668404 | ||||||||
\(959\) | 6547.26 | 0.220461 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23818.3 | −0.799514 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −88399.8 | −2.95349 | ||||||||
\(965\) | 2315.84 | 0.0772534 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5310.75 | 0.176610 | 0.0883052 | − | 0.996093i | \(-0.471855\pi\) | ||||
0.0883052 | + | 0.996093i | \(0.471855\pi\) | |||||||
\(968\) | 96670.1 | 3.20981 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 23326.2 | 0.772122 | ||||||||
\(971\) | −24271.2 | −0.802164 | −0.401082 | − | 0.916042i | \(-0.631366\pi\) | ||||
−0.401082 | + | 0.916042i | \(0.631366\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 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 | \(-0.801699\pi\) | ||||
−0.812142 | + | 0.583460i | \(0.801699\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15448.2 | 0.504317 | ||||||||
\(980\) | −18774.6 | −0.611971 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −38375.5 | −1.24706 | ||||||||
\(983\) | 47385.7 | 1.53751 | 0.768753 | − | 0.639545i | \(-0.220877\pi\) | ||||
0.768753 | + | 0.639545i | \(0.220877\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17481.2 | −0.565478 | ||||||||
\(986\) | 51587.7 | 1.66621 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 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 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3558.95 | −0.113564 | ||||||||
\(995\) | 10414.7 | 0.331828 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14908.6 | −0.473582 | −0.236791 | − | 0.971561i | \(-0.576096\pi\) | ||||
−0.236791 | + | 0.971561i | \(0.576096\pi\) | |||||||
\(998\) | 51881.4 | 1.64557 | ||||||||
\(999\) | 0 | 0 |
(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 | 1521.4.a.s.1.2 | 2 | ||
3.2 | odd | 2 | 507.4.a.f.1.1 | 2 | |||
13.12 | even | 2 | 117.4.a.c.1.1 | 2 | |||
39.5 | even | 4 | 507.4.b.f.337.4 | 4 | |||
39.8 | even | 4 | 507.4.b.f.337.1 | 4 | |||
39.38 | odd | 2 | 39.4.a.b.1.2 | ✓ | 2 | ||
52.51 | odd | 2 | 1872.4.a.t.1.2 | 2 | |||
156.155 | even | 2 | 624.4.a.r.1.1 | 2 | |||
195.194 | odd | 2 | 975.4.a.j.1.1 | 2 | |||
273.272 | even | 2 | 1911.4.a.h.1.2 | 2 | |||
312.77 | odd | 2 | 2496.4.a.bc.1.2 | 2 | |||
312.155 | even | 2 | 2496.4.a.s.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.a.b.1.2 | ✓ | 2 | 39.38 | odd | 2 | ||
117.4.a.c.1.1 | 2 | 13.12 | even | 2 | |||
507.4.a.f.1.1 | 2 | 3.2 | odd | 2 | |||
507.4.b.f.337.1 | 4 | 39.8 | even | 4 | |||
507.4.b.f.337.4 | 4 | 39.5 | even | 4 | |||
624.4.a.r.1.1 | 2 | 156.155 | even | 2 | |||
975.4.a.j.1.1 | 2 | 195.194 | odd | 2 | |||
1521.4.a.s.1.2 | 2 | 1.1 | even | 1 | trivial | ||
1872.4.a.t.1.2 | 2 | 52.51 | odd | 2 | |||
1911.4.a.h.1.2 | 2 | 273.272 | even | 2 | |||
2496.4.a.s.1.2 | 2 | 312.155 | even | 2 | |||
2496.4.a.bc.1.2 | 2 | 312.77 | odd | 2 |