Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1840,4,Mod(1,1840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1840.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1840 = 2^{4} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1840.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: | \(108.563514411\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 3x^{8} - 148x^{7} + 278x^{6} + 6502x^{5} - 4928x^{4} - 87343x^{3} + 42737x^{2} + 286800x + 53104 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | no (minimal twist has level 920) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.70964\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1840.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.70964 | −0.329020 | −0.164510 | − | 0.986375i | \(-0.552604\pi\) | ||||
−0.164510 | + | 0.986375i | \(0.552604\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −20.8693 | −1.12684 | −0.563418 | − | 0.826172i | \(-0.690514\pi\) | ||||
−0.563418 | + | 0.826172i | \(0.690514\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −24.0771 | −0.891746 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −23.6682 | −0.648749 | −0.324374 | − | 0.945929i | \(-0.605154\pi\) | ||||
−0.324374 | + | 0.945929i | \(0.605154\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 53.7383 | 1.14649 | 0.573243 | − | 0.819385i | \(-0.305685\pi\) | ||||
0.573243 | + | 0.819385i | \(0.305685\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 8.54819 | 0.147142 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 52.1336 | 0.743779 | 0.371890 | − | 0.928277i | \(-0.378710\pi\) | ||||
0.371890 | + | 0.928277i | \(0.378710\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.88364 | −0.0589676 | −0.0294838 | − | 0.999565i | \(-0.509386\pi\) | ||||
−0.0294838 | + | 0.999565i | \(0.509386\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 35.6789 | 0.370751 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 23.0000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 87.3234 | 0.622422 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −144.142 | −0.922980 | −0.461490 | − | 0.887145i | \(-0.652685\pi\) | ||||
−0.461490 | + | 0.887145i | \(0.652685\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 288.160 | 1.66952 | 0.834759 | − | 0.550616i | \(-0.185607\pi\) | ||||
0.834759 | + | 0.550616i | \(0.185607\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 40.4641 | 0.213451 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 104.346 | 0.503936 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 294.532 | 1.30867 | 0.654334 | − | 0.756206i | \(-0.272949\pi\) | ||||
0.654334 | + | 0.756206i | \(0.272949\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −91.8730 | −0.377217 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 333.215 | 1.26925 | 0.634627 | − | 0.772819i | \(-0.281154\pi\) | ||||
0.634627 | + | 0.772819i | \(0.281154\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.162395 | 0.000575930 0 | 0.000287965 | − | 1.00000i | \(-0.499908\pi\) | ||||
0.000287965 | 1.00000i | \(0.499908\pi\) | ||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 120.386 | 0.398801 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −529.988 | −1.64482 | −0.822412 | − | 0.568892i | \(-0.807372\pi\) | ||||
−0.822412 | + | 0.568892i | \(0.807372\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 92.5270 | 0.269758 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −89.1295 | −0.244718 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 116.147 | 0.301019 | 0.150510 | − | 0.988609i | \(-0.451909\pi\) | ||||
0.150510 | + | 0.988609i | \(0.451909\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 118.341 | 0.290129 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.34926 | 0.0194015 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 284.019 | 0.626714 | 0.313357 | − | 0.949635i | \(-0.398546\pi\) | ||||
0.313357 | + | 0.949635i | \(0.398546\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −120.262 | −0.252425 | −0.126213 | − | 0.992003i | \(-0.540282\pi\) | ||||
−0.126213 | + | 0.992003i | \(0.540282\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 502.473 | 1.00485 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −268.691 | −0.512724 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −194.900 | −0.355386 | −0.177693 | − | 0.984086i | \(-0.556863\pi\) | ||||
−0.177693 | + | 0.984086i | \(0.556863\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −39.3217 | −0.0686054 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −201.508 | −0.336826 | −0.168413 | − | 0.985717i | \(-0.553864\pi\) | ||||
−0.168413 | + | 0.985717i | \(0.553864\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 913.140 | 1.46404 | 0.732020 | − | 0.681283i | \(-0.238578\pi\) | ||||
0.732020 | + | 0.681283i | \(0.238578\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −42.7409 | −0.0658040 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 493.939 | 0.731033 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −901.712 | −1.28418 | −0.642092 | − | 0.766628i | \(-0.721933\pi\) | ||||
−0.642092 | + | 0.766628i | \(0.721933\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 500.791 | 0.686957 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −172.627 | −0.228292 | −0.114146 | − | 0.993464i | \(-0.536413\pi\) | ||||
−0.114146 | + | 0.993464i | \(0.536413\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −260.668 | −0.332628 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 246.430 | 0.303679 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1578.55 | −1.88006 | −0.940032 | − | 0.341085i | \(-0.889206\pi\) | ||||
−0.940032 | + | 0.341085i | \(0.889206\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1121.48 | −1.29190 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −492.649 | −0.549305 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 24.4182 | 0.0263711 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1720.14 | 1.80056 | 0.900279 | − | 0.435314i | \(-0.143363\pi\) | ||||
0.900279 | + | 0.435314i | \(0.143363\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 569.863 | 0.578519 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −548.016 | −0.539897 | −0.269949 | − | 0.962875i | \(-0.587007\pi\) | ||||
−0.269949 | + | 0.962875i | \(0.587007\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1654.89 | −1.58311 | −0.791557 | − | 0.611095i | \(-0.790729\pi\) | ||||
−0.791557 | + | 0.611095i | \(0.790729\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −178.395 | −0.165805 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1556.17 | −1.40599 | −0.702995 | − | 0.711194i | \(-0.748155\pi\) | ||||
−0.702995 | + | 0.711194i | \(0.748155\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −231.161 | −0.203131 | −0.101565 | − | 0.994829i | \(-0.532385\pi\) | ||||
−0.101565 | + | 0.994829i | \(0.532385\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −503.542 | −0.430578 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −403.835 | −0.336191 | −0.168096 | − | 0.985771i | \(-0.553762\pi\) | ||||
−0.168096 | + | 0.985771i | \(0.553762\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −115.000 | −0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1293.86 | −1.02237 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1087.99 | −0.838117 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −770.816 | −0.579125 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −569.676 | −0.417610 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1842.46 | 1.28734 | 0.643670 | − | 0.765303i | \(-0.277411\pi\) | ||||
0.643670 | + | 0.765303i | \(0.277411\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.277637 | −0.000189493 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1124.87 | −0.750231 | −0.375115 | − | 0.926978i | \(-0.622397\pi\) | ||||
−0.375115 | + | 0.926978i | \(0.622397\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 101.918 | 0.0664468 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −436.617 | −0.278356 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2675.29 | 1.66836 | 0.834181 | − | 0.551490i | \(-0.185941\pi\) | ||||
0.834181 | + | 0.551490i | \(0.185941\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1060.81 | −0.647316 | −0.323658 | − | 0.946174i | \(-0.604913\pi\) | ||||
−0.323658 | + | 0.946174i | \(0.604913\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 906.088 | 0.541180 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1271.89 | −0.743781 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 720.708 | 0.412769 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −158.188 | −0.0887558 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1582.20 | 0.869923 | 0.434961 | − | 0.900449i | \(-0.356762\pi\) | ||||
0.434961 | + | 0.900449i | \(0.356762\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1169.01 | 0.630020 | 0.315010 | − | 0.949088i | \(-0.397992\pi\) | ||||
0.315010 | + | 0.949088i | \(0.397992\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1255.23 | −0.663262 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1440.80 | −0.746631 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 361.463 | 0.183744 | 0.0918722 | − | 0.995771i | \(-0.470715\pi\) | ||||
0.0918722 | + | 0.995771i | \(0.470715\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −198.569 | −0.0990414 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −479.994 | −0.234961 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3143.56 | −1.51057 | −0.755283 | − | 0.655399i | \(-0.772501\pi\) | ||||
−0.755283 | + | 0.655399i | \(0.772501\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −202.320 | −0.0954583 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1624.03 | 0.752523 | 0.376262 | − | 0.926513i | \(-0.377209\pi\) | ||||
0.376262 | + | 0.926513i | \(0.377209\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 690.803 | 0.314430 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 117.584 | 0.0525841 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2491.15 | −1.09479 | −0.547395 | − | 0.836875i | \(-0.684380\pi\) | ||||
−0.547395 | + | 0.836875i | \(0.684380\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −521.732 | −0.225367 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −485.569 | −0.206201 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4074.96 | 1.70154 | 0.850772 | − | 0.525535i | \(-0.176135\pi\) | ||||
0.850772 | + | 0.525535i | \(0.176135\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3304.36 | 1.35697 | 0.678484 | − | 0.734615i | \(-0.262637\pi\) | ||||
0.678484 | + | 0.734615i | \(0.262637\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 205.604 | 0.0830529 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1472.66 | −0.585254 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1233.91 | −0.482526 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1822.38 | −0.701367 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 457.335 | 0.173254 | 0.0866272 | − | 0.996241i | \(-0.472391\pi\) | ||||
0.0866272 | + | 0.996241i | \(0.472391\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 230.793 | 0.0860770 | 0.0430385 | − | 0.999073i | \(-0.486296\pi\) | ||||
0.0430385 | + | 0.999073i | \(0.486296\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 459.365 | 0.168696 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1078.86 | −0.390180 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4525.53 | −1.61209 | −0.806046 | − | 0.591852i | \(-0.798397\pi\) | ||||
−0.806046 | + | 0.591852i | \(0.798397\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 333.209 | 0.116929 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3008.13 | 1.04005 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1666.07 | −0.567627 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −553.774 | −0.185942 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 115.587 | 0.0382551 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1359.68 | −0.443623 | −0.221812 | − | 0.975090i | \(-0.571197\pi\) | ||||
−0.221812 | + | 0.975090i | \(0.571197\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 344.506 | 0.110822 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.811975 | −0.000257564 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6013.69 | −1.88127 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1561.14 | −0.481698 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2801.57 | 0.852732 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3484.12 | 1.04625 | 0.523126 | − | 0.852256i | \(-0.324766\pi\) | ||||
0.523126 | + | 0.852256i | \(0.324766\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −601.928 | −0.178349 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5022.22 | −1.46844 | −0.734222 | − | 0.678910i | \(-0.762453\pi\) | ||||
−0.734222 | + | 0.678910i | \(0.762453\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3063.48 | 0.884020 | 0.442010 | − | 0.897010i | \(-0.354266\pi\) | ||||
0.442010 | + | 0.897010i | \(0.354266\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −844.456 | −0.240524 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 591.557 | 0.166327 | 0.0831635 | − | 0.996536i | \(-0.473498\pi\) | ||||
0.0831635 | + | 0.996536i | \(0.473498\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2649.94 | 0.735588 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1541.60 | 0.422522 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −864.562 | −0.233991 | −0.116996 | − | 0.993132i | \(-0.537326\pi\) | ||||
−0.116996 | + | 0.993132i | \(0.537326\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −690.020 | −0.184432 | −0.0922159 | − | 0.995739i | \(-0.529395\pi\) | ||||
−0.0922159 | + | 0.995739i | \(0.529395\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3213.90 | −0.848445 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −462.635 | −0.120639 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −262.439 | −0.0676055 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 295.130 | 0.0751127 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5057.07 | 1.27171 | 0.635855 | − | 0.771808i | \(-0.280647\pi\) | ||||
0.635855 | + | 0.771808i | \(0.280647\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −544.369 | −0.135273 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 445.648 | 0.109441 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3562.51 | −0.864682 | −0.432341 | − | 0.901710i | \(-0.642312\pi\) | ||||
−0.432341 | + | 0.901710i | \(0.642312\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6146.66 | −1.47465 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3470.52 | 0.823064 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1139.45 | −0.267154 | −0.133577 | − | 0.991038i | \(-0.542646\pi\) | ||||
−0.133577 | + | 0.991038i | \(0.542646\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −580.736 | −0.134620 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2698.75 | 0.618579 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6217.53 | −1.40925 | −0.704627 | − | 0.709578i | \(-0.748886\pi\) | ||||
−0.704627 | + | 0.709578i | \(0.748886\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2169.68 | −0.486343 | −0.243172 | − | 0.969983i | \(-0.578188\pi\) | ||||
−0.243172 | + | 0.969983i | \(0.578188\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1917.32 | 0.425061 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −591.705 | −0.129750 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6335.06 | 1.37414 | 0.687070 | − | 0.726591i | \(-0.258896\pi\) | ||||
0.687070 | + | 0.726591i | \(0.258896\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6938.07 | −1.48879 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4984.66 | −1.05822 | −0.529110 | − | 0.848553i | \(-0.677474\pi\) | ||||
−0.529110 | + | 0.848553i | \(0.677474\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3113.65 | −0.654018 | −0.327009 | − | 0.945021i | \(-0.606041\pi\) | ||||
−0.327009 | + | 0.945021i | \(0.606041\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −41.7463 | −0.00867662 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6953.95 | −1.43024 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2195.09 | −0.446792 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2940.82 | −0.592419 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1892.75 | −0.377390 | −0.188695 | − | 0.982036i | \(-0.560426\pi\) | ||||
−0.188695 | + | 0.982036i | \(0.560426\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1420.09 | −0.280275 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2066.79 | −0.403795 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1235.98 | 0.239059 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.38907 | −0.000648979 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 936.909 | 0.177637 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 601.309 | 0.112888 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9988.97 | −1.85701 | −0.928503 | − | 0.371326i | \(-0.878903\pi\) | ||||
−0.928503 | + | 0.371326i | \(0.878903\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2829.26 | 0.520876 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1724.91 | 0.314503 | 0.157252 | − | 0.987559i | \(-0.449737\pi\) | ||||
0.157252 | + | 0.987559i | \(0.449737\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9143.12 | −1.65112 | −0.825559 | − | 0.564316i | \(-0.809140\pi\) | ||||
−0.825559 | + | 0.564316i | \(0.809140\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2512.36 | −0.449383 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1203.47 | 0.213229 | 0.106615 | − | 0.994300i | \(-0.465999\pi\) | ||||
0.106615 | + | 0.994300i | \(0.465999\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3411.57 | 0.598782 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2660.49 | 0.462599 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −254.602 | −0.0438589 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1343.46 | 0.229297 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 395.202 | 0.0668340 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11060.5 | 1.85345 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6820.31 | 1.13256 | 0.566281 | − | 0.824212i | \(-0.308382\pi\) | ||||
0.566281 | + | 0.824212i | \(0.308382\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7091.48 | −1.16700 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 974.501 | 0.158933 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10495.4 | −1.69651 | −0.848254 | − | 0.529589i | \(-0.822346\pi\) | ||||
−0.848254 | + | 0.529589i | \(0.822346\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 690.411 | 0.110614 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6820.23 | −1.08310 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5227.19 | 0.822862 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 196.608 | 0.0306813 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1939.55 | 0.300059 | 0.150029 | − | 0.988682i | \(-0.452063\pi\) | ||||
0.150029 | + | 0.988682i | \(0.452063\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12226.5 | 1.87527 | 0.937636 | − | 0.347620i | \(-0.113010\pi\) | ||||
0.937636 | + | 0.347620i | \(0.113010\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4692.61 | 0.713598 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11190.9 | −1.68734 | −0.843672 | − | 0.536859i | \(-0.819611\pi\) | ||||
−0.843672 | + | 0.536859i | \(0.819611\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1007.54 | 0.150633 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1860.07 | 0.275757 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2874.12 | 0.422536 | 0.211268 | − | 0.977428i | \(-0.432241\pi\) | ||||
0.211268 | + | 0.977428i | \(0.432241\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6835.15 | −0.996523 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1317.82 | 0.190544 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4565.70 | −0.654738 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2930.03 | −0.416748 | −0.208374 | − | 0.978049i | \(-0.566817\pi\) | ||||
−0.208374 | + | 0.978049i | \(0.566817\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8022.86 | −1.13185 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2423.91 | −0.339199 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3597.70 | −0.499415 | −0.249707 | − | 0.968321i | \(-0.580334\pi\) | ||||
−0.249707 | + | 0.968321i | \(0.580334\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 213.705 | 0.0294284 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7745.92 | −1.05818 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7095.95 | 0.961727 | 0.480864 | − | 0.876795i | \(-0.340323\pi\) | ||||
0.480864 | + | 0.876795i | \(0.340323\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3149.94 | −0.423561 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2459.42 | 0.328121 | 0.164061 | − | 0.986450i | \(-0.447541\pi\) | ||||
0.164061 | + | 0.986450i | \(0.447541\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2469.69 | −0.326928 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.91001 | −0.000513584 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10638.6 | −1.38663 | −0.693315 | − | 0.720635i | \(-0.743850\pi\) | ||||
−0.693315 | + | 0.720635i | \(0.743850\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1199.07 | 0.155089 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1923.12 | 0.246841 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4508.56 | 0.574304 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1449.48 | 0.183242 | 0.0916212 | − | 0.995794i | \(-0.470795\pi\) | ||||
0.0916212 | + | 0.995794i | \(0.470795\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −174.243 | −0.0218623 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12093.8 | 1.50608 | 0.753040 | − | 0.657975i | \(-0.228587\pi\) | ||||
0.753040 | + | 0.657975i | \(0.228587\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15485.2 | 1.91408 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2503.96 | −0.307216 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6971.04 | −0.848996 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4947.12 | −0.598091 | −0.299046 | − | 0.954239i | \(-0.596668\pi\) | ||||
−0.299046 | + | 0.954239i | \(0.596668\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4573.78 | −0.548925 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5927.27 | −0.706203 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 863.135 | 0.102095 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1813.60 | 0.212980 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1894.55 | 0.220895 | 0.110447 | − | 0.993882i | \(-0.464772\pi\) | ||||
0.110447 | + | 0.993882i | \(0.464772\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3663.52 | 0.424107 | 0.212054 | − | 0.977258i | \(-0.431985\pi\) | ||||
0.212054 | + | 0.977258i | \(0.431985\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 12760.6 | 1.46677 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1303.34 | 0.148756 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2509.78 | 0.284442 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2174.47 | 0.244719 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6399.83 | −0.715241 | −0.357620 | − | 0.933867i | \(-0.616412\pi\) | ||||
−0.357620 | + | 0.933867i | \(0.616412\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12389.9 | −1.37511 | −0.687553 | − | 0.726134i | \(-0.741315\pi\) | ||||
−0.687553 | + | 0.726134i | \(0.741315\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1232.15 | −0.135809 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −112.324 | −0.0122956 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1186.74 | 0.129021 | 0.0645105 | − | 0.997917i | \(-0.479451\pi\) | ||||
0.0645105 | + | 0.997917i | \(0.479451\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2227.79 | −0.240556 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14040.8 | 1.50587 | 0.752934 | − | 0.658096i | \(-0.228638\pi\) | ||||
0.752934 | + | 0.658096i | \(0.228638\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7892.74 | 0.840791 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2704.98 | −0.286222 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3724.79 | −0.391500 | −0.195750 | − | 0.980654i | \(-0.562714\pi\) | ||||
−0.195750 | + | 0.980654i | \(0.562714\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7886.60 | −0.823426 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1998.59 | −0.207289 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5607.40 | 0.577756 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14267.4 | −1.46040 | −0.730199 | − | 0.683235i | \(-0.760573\pi\) | ||||
−0.730199 | + | 0.683235i | \(0.760573\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4552.48 | 0.462945 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15365.9 | 1.55242 | 0.776208 | − | 0.630477i | \(-0.217141\pi\) | ||||
0.776208 | + | 0.630477i | \(0.217141\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14467.7 | −1.45220 | −0.726101 | − | 0.687589i | \(-0.758669\pi\) | ||||
−0.726101 | + | 0.687589i | \(0.758669\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2463.25 | 0.245656 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3374.06 | −0.334332 | −0.167166 | − | 0.985929i | \(-0.553462\pi\) | ||||
−0.167166 | + | 0.985929i | \(0.553462\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4067.43 | 0.400462 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −617.970 | −0.0604556 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.84360 | −0.000373634 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −122.091 | −0.0117935 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2796.49 | −0.268433 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9289.09 | −0.886074 | −0.443037 | − | 0.896503i | \(-0.646099\pi\) | ||||
−0.443037 | + | 0.896503i | \(0.646099\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15827.6 | 1.50037 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 820.615 | 0.0773070 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8600.72 | −0.805234 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5685.30 | −0.529005 | −0.264503 | − | 0.964385i | \(-0.585208\pi\) | ||||
−0.264503 | + | 0.964385i | \(0.585208\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5374.34 | 0.497006 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5514.82 | 0.506885 | 0.253443 | − | 0.967350i | \(-0.418437\pi\) | ||||
0.253443 | + | 0.967350i | \(0.418437\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7514.62 | −0.686493 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2849.31 | −0.258721 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4205.33 | 0.379547 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17001.4 | 1.52523 | 0.762613 | − | 0.646855i | \(-0.223916\pi\) | ||||
0.762613 | + | 0.646855i | \(0.223916\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2776.51 | −0.247595 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13321.6 | −1.18088 | −0.590438 | − | 0.807083i | \(-0.701045\pi\) | ||||
−0.590438 | + | 0.807083i | \(0.701045\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2740.08 | 0.241449 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1181.02 | −0.103454 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17297.4 | −1.50628 | −0.753138 | − | 0.657863i | \(-0.771461\pi\) | ||||
−0.753138 | + | 0.657863i | \(0.771461\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −19056.6 | −1.64973 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −426.456 | −0.0367027 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8274.43 | 0.707990 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12543.9 | 1.06708 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4258.96 | 0.360207 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7265.77 | −0.610978 | −0.305489 | − | 0.952196i | \(-0.598820\pi\) | ||||
−0.305489 | + | 0.952196i | \(0.598820\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12383.0 | 1.03532 | 0.517658 | − | 0.855588i | \(-0.326804\pi\) | ||||
0.517658 | + | 0.855588i | \(0.326804\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 891.973 | 0.0741503 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 15022.8 | 1.24175 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6838.36 | −0.558869 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17906.4 | 1.45518 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7780.87 | 0.628778 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6966.70 | −0.559842 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2189.95 | −0.175005 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3946.64 | −0.313641 | −0.156820 | − | 0.987627i | \(-0.550124\pi\) | ||||
−0.156820 | + | 0.987627i | \(0.550124\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5649.26 | −0.446470 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1155.81 | 0.0908428 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20084.1 | −1.56990 | −0.784948 | − | 0.619562i | \(-0.787310\pi\) | ||||
−0.784948 | + | 0.619562i | \(0.787310\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2895.56 | 0.225099 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 703.936 | 0.0544259 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 18818.1 | 1.44706 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2517.71 | 0.192560 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5182.63 | −0.394246 | −0.197123 | − | 0.980379i | \(-0.563160\pi\) | ||||
−0.197123 | + | 0.980379i | \(0.563160\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.72683 | 0.000660296 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2109.54 | 0.158761 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2114.65 | 0.158298 | 0.0791492 | − | 0.996863i | \(-0.474780\pi\) | ||||
0.0791492 | + | 0.996863i | \(0.474780\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2019.17 | 0.150349 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −10451.2 | −0.774087 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15202.0 | −1.12003 | −0.560017 | − | 0.828481i | \(-0.689205\pi\) | ||||
−0.560017 | + | 0.828481i | \(0.689205\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18481.2 | 1.35449 | 0.677244 | − | 0.735759i | \(-0.263174\pi\) | ||||
0.677244 | + | 0.735759i | \(0.263174\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −781.877 | −0.0570042 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 575.000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14659.4 | −1.05768 | −0.528838 | − | 0.848723i | \(-0.677372\pi\) | ||||
−0.528838 | + | 0.848723i | \(0.677372\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −394.573 | −0.0283210 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3602.60 | 0.257248 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2748.99 | −0.195286 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6469.32 | 0.457220 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3361.40 | −0.236354 | −0.118177 | − | 0.992993i | \(-0.537705\pi\) | ||||
−0.118177 | + | 0.992993i | \(0.537705\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1407.27 | −0.0984474 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1844.46 | 0.128377 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9144.05 | 0.633223 | 0.316611 | − | 0.948555i | \(-0.397455\pi\) | ||||
0.316611 | + | 0.948555i | \(0.397455\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5439.95 | 0.374817 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7737.02 | 0.530411 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17440.0 | 1.18962 | 0.594808 | − | 0.803868i | \(-0.297228\pi\) | ||||
0.594808 | + | 0.803868i | \(0.297228\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2840.97 | 0.192821 | 0.0964105 | − | 0.995342i | \(-0.469264\pi\) | ||||
0.0964105 | + | 0.995342i | \(0.469264\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4692.64 | 0.316914 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3854.08 | 0.258993 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19233.4 | 1.28609 | 0.643047 | − | 0.765827i | \(-0.277670\pi\) | ||||
0.643047 | + | 0.765827i | \(0.277670\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5142.82 | −0.342196 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −28480.7 | −1.88577 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7979.89 | −0.525782 | −0.262891 | − | 0.964825i | \(-0.584676\pi\) | ||||
−0.262891 | + | 0.964825i | \(0.584676\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2848.38 | 0.186761 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12478.3 | 0.814194 | 0.407097 | − | 0.913385i | \(-0.366541\pi\) | ||||
0.407097 | + | 0.913385i | \(0.366541\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2461.50 | 0.159832 | 0.0799161 | − | 0.996802i | \(-0.474535\pi\) | ||||
0.0799161 | + | 0.996802i | \(0.474535\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2008.44 | 0.129784 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 32943.2 | 2.11852 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −197.612 | −0.0125867 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 15355.0 | 0.973360 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22359.4 | −1.41064 | −0.705320 | − | 0.708889i | \(-0.749197\pi\) | ||||
−0.705320 | + | 0.708889i | \(0.749197\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2324.57 | 0.145961 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9212.32 | −0.575716 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4972.24 | 0.309274 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4851.74 | 0.300363 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1666.84 | −0.102709 | −0.0513543 | − | 0.998680i | \(-0.516354\pi\) | ||||
−0.0513543 | + | 0.998680i | \(0.516354\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21155.7 | 1.29751 | 0.648756 | − | 0.760997i | \(-0.275290\pi\) | ||||
0.648756 | + | 0.760997i | \(0.275290\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.38818 | 8.47437e−5 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1277.13 | 0.0776031 | 0.0388015 | − | 0.999247i | \(-0.487646\pi\) | ||||
0.0388015 | + | 0.999247i | \(0.487646\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6722.22 | −0.406580 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10281.2 | 0.618976 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3834.25 | −0.229779 | −0.114890 | − | 0.993378i | \(-0.536651\pi\) | ||||
−0.114890 | + | 0.993378i | \(0.536651\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5624.34 | 0.335513 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −21985.8 | −1.30555 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4841.95 | −0.286215 | −0.143107 | − | 0.989707i | \(-0.545709\pi\) | ||||
−0.143107 | + | 0.989707i | \(0.545709\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22236.9 | 1.30850 | 0.654248 | − | 0.756280i | \(-0.272985\pi\) | ||||
0.654248 | + | 0.756280i | \(0.272985\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4789.67 | −0.280566 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −509.591 | −0.0297159 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3315.26 | −0.192455 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5956.59 | −0.344238 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2846.38 | 0.163760 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2519.67 | 0.144318 | 0.0721591 | − | 0.997393i | \(-0.477011\pi\) | ||||
0.0721591 | + | 0.997393i | \(0.477011\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2183.09 | 0.124484 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13978.4 | 0.793548 | 0.396774 | − | 0.917916i | \(-0.370130\pi\) | ||||
0.396774 | + | 0.917916i | \(0.370130\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −35898.2 | −2.02893 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8586.18 | 0.483147 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13974.4 | −0.782893 | −0.391447 | − | 0.920201i | \(-0.628025\pi\) | ||||
−0.391447 | + | 0.920201i | \(0.628025\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13376.5 | −0.746115 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5237.44 | −0.290860 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6241.55 | 0.345115 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6018.34 | 0.331329 | 0.165664 | − | 0.986182i | \(-0.447023\pi\) | ||||
0.165664 | + | 0.986182i | \(0.447023\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −11892.6 | −0.651896 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5304.06 | 0.289488 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 17371.7 | 0.944044 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1011.35 | −0.0547249 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17566.5 | 0.946475 | 0.473238 | − | 0.880935i | \(-0.343085\pi\) | ||||
0.473238 | + | 0.880935i | \(0.343085\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1438.39 | −0.0771690 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4530.44 | −0.242023 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11436.7 | 0.608375 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6581.64 | 0.348630 | 0.174315 | − | 0.984690i | \(-0.444229\pi\) | ||||
0.174315 | + | 0.984690i | \(0.444229\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 21710.6 | 1.14517 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6627.68 | 0.348118 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6359.44 | 0.332629 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1478.09 | 0.0769878 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17215.6 | −0.892955 | −0.446477 | − | 0.894795i | \(-0.647322\pi\) | ||||
−0.446477 | + | 0.894795i | \(0.647322\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 34536.3 | 1.78391 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1179.68 | 0.0606817 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3603.54 | −0.184596 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15420.8 | −0.786693 | −0.393347 | − | 0.919390i | \(-0.628683\pi\) | ||||
−0.393347 | + | 0.919390i | \(0.628683\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8026.76 | −0.407801 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.46623 | 0.000428365 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6057.78 | −0.305251 | −0.152626 | − | 0.988284i | \(-0.548773\pi\) | ||||
−0.152626 | + | 0.988284i | \(0.548773\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 790.938 | 0.0396928 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4612.94 | 0.230556 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4088.83 | −0.203532 | −0.101766 | − | 0.994808i | \(-0.532449\pi\) | ||||
−0.101766 | + | 0.994808i | \(0.532449\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 448.675 | 0.0222436 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21467.5 | 1.05998 | 0.529991 | − | 0.848003i | \(-0.322195\pi\) | ||||
0.529991 | + | 0.848003i | \(0.322195\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7910.98 | −0.389041 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4156.36 | 0.203579 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 32476.2 | 1.58432 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5285.55 | −0.256821 | −0.128410 | − | 0.991721i | \(-0.540987\pi\) | ||||
−0.128410 | + | 0.991721i | \(0.540987\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8645.76 | −0.418418 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5845.07 | −0.281753 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1748.30 | 0.0839405 | 0.0419702 | − | 0.999119i | \(-0.486637\pi\) | ||||
0.0419702 | + | 0.999119i | \(0.486637\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 930.674 | 0.0445077 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6405.11 | 0.305105 | 0.152553 | − | 0.988295i | \(-0.451251\pi\) | ||||
0.152553 | + | 0.988295i | \(0.451251\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4824.17 | 0.228895 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6276.14 | 0.296620 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 15262.7 | 0.718518 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32100.5 | 1.50530 | 0.752648 | − | 0.658423i | \(-0.228776\pi\) | ||||
0.752648 | + | 0.658423i | \(0.228776\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6090.60 | 0.284498 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −17226.1 | −0.801527 | −0.400764 | − | 0.916181i | \(-0.631255\pi\) | ||||
−0.400764 | + | 0.916181i | \(0.631255\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7204.00 | 0.333904 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 10508.6 | 0.485190 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1627.30 | −0.0748448 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4769.34 | 0.218515 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −12586.9 | −0.574483 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1807.31 | −0.0821730 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −35601.2 | −1.61251 | −0.806256 | − | 0.591566i | \(-0.798510\pi\) | ||||
−0.806256 | + | 0.591566i | \(0.798510\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1948.05 | 0.0878990 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8427.74 | 0.378832 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6462.66 | −0.289402 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 992.847 | 0.0442927 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −96.9760 | −0.00431000 | −0.00215500 | − | 0.999998i | \(-0.500686\pi\) | ||||
−0.00215500 | + | 0.999998i | \(0.500686\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −27630.2 | −1.22339 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 38006.9 | 1.67654 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −21612.4 | −0.949794 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2399.97 | 0.105078 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10629.7 | 0.463673 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −28065.0 | −1.21967 | −0.609836 | − | 0.792528i | \(-0.708765\pi\) | ||||
−0.609836 | + | 0.792528i | \(0.708765\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38011.9 | −1.64584 | −0.822921 | − | 0.568156i | \(-0.807657\pi\) | ||||
−0.822921 | + | 0.568156i | \(0.807657\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3709.38 | 0.160017 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 15717.8 | 0.675546 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.793079 | −3.39612e−5 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 27002.0 | 1.15205 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9423.34 | 0.400581 | 0.200290 | − | 0.979737i | \(-0.435811\pi\) | ||||
0.200290 | + | 0.979737i | \(0.435811\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23294.3 | 0.986621 | 0.493311 | − | 0.869853i | \(-0.335787\pi\) | ||||
0.493311 | + | 0.869853i | \(0.335787\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1011.60 | 0.0426902 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −21050.1 | −0.885106 | −0.442553 | − | 0.896742i | \(-0.645927\pi\) | ||||
−0.442553 | + | 0.896742i | \(0.645927\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30468.6 | 1.27650 | 0.638250 | − | 0.769830i | \(-0.279659\pi\) | ||||
0.638250 | + | 0.769830i | \(0.279659\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10830.7 | −0.452120 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4823.76 | 0.200640 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8120.16 | −0.336539 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 25163.1 | 1.03914 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −20156.4 | −0.829413 | −0.414706 | − | 0.909955i | \(-0.636116\pi\) | ||||
−0.414706 | + | 0.909955i | \(0.636116\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3612.20 | −0.148108 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8521.97 | 0.348176 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3454.01 | −0.140617 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16086.4 | 0.652579 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5323.21 | 0.215185 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6774.23 | 0.272876 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 48022.4 | 1.92761 | 0.963807 | − | 0.266602i | \(-0.0859008\pi\) | ||||
0.963807 | + | 0.266602i | \(0.0859008\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −587.921 | −0.0235163 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3811.01 | 0.151904 | 0.0759519 | − | 0.997111i | \(-0.475800\pi\) | ||||
0.0759519 | + | 0.997111i | \(0.475800\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2576.98 | −0.102358 | −0.0511789 | − | 0.998690i | \(-0.516298\pi\) | ||||
−0.0511789 | + | 0.998690i | \(0.516298\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11888.7 | 0.470577 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 10214.8 | 0.402915 | 0.201457 | − | 0.979497i | \(-0.435432\pi\) | ||||
0.201457 | + | 0.979497i | \(0.435432\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12455.7 | 0.489605 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3752.81 | 0.147004 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 21341.9 | 0.833112 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10473.6 | −0.407445 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −41416.1 | −1.60564 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2608.66 | 0.100787 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −41225.1 | −1.58731 | −0.793656 | − | 0.608367i | \(-0.791825\pi\) | ||||
−0.793656 | + | 0.608367i | \(0.791825\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3235.91 | 0.124169 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23955.4 | −0.916094 | −0.458047 | − | 0.888928i | \(-0.651451\pi\) | ||||
−0.458047 | + | 0.888928i | \(0.651451\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28679.2 | 1.09302 | 0.546508 | − | 0.837454i | \(-0.315957\pi\) | ||||
0.546508 | + | 0.837454i | \(0.315957\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2427.85 | 0.0922160 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −29456.1 | −1.11504 | −0.557520 | − | 0.830164i | \(-0.688247\pi\) | ||||
−0.557520 | + | 0.830164i | \(0.688247\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −38450.9 | −1.45062 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −11852.8 | −0.445662 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2588.27 | 0.0969913 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20374.8 | −0.760954 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2113.08 | −0.0786551 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −41535.8 | −1.54093 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6055.16 | 0.223892 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.79408 | 0.000213527 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −16521.8 | −0.606855 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −38637.7 | −1.41449 | −0.707246 | − | 0.706968i | \(-0.750063\pi\) | ||||
−0.707246 | + | 0.706968i | \(0.750063\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 13194.7 | 0.481451 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 43014.4 | 1.56436 | 0.782179 | − | 0.623053i | \(-0.214108\pi\) | ||||
0.782179 | + | 0.623053i | \(0.214108\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4085.77 | 0.148104 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1028.02 | −0.0371424 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 23475.2 | 0.845386 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25861.1 | 0.928267 | 0.464134 | − | 0.885765i | \(-0.346366\pi\) | ||||
0.464134 | + | 0.885765i | \(0.346366\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 17077.5 | 0.610992 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10828.7 | −0.386166 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7363.29 | 0.261734 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 39844.9 | 1.41174 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −50340.0 | −1.77783 | −0.888914 | − | 0.458073i | \(-0.848540\pi\) | ||||
−0.888914 | + | 0.458073i | \(0.848540\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −451.869 | −0.0159070 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2948.97 | −0.103478 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6169.54 | 0.215792 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −51360.8 | −1.79070 | −0.895349 | − | 0.445365i | \(-0.853074\pi\) | ||||
−0.895349 | + | 0.445365i | \(0.853074\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 15631.4 | 0.543251 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4590.77 | −0.159038 | −0.0795190 | − | 0.996833i | \(-0.525338\pi\) | ||||
−0.0795190 | + | 0.996833i | \(0.525338\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7663.94 | 0.264658 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 9111.88 | 0.313661 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8532.06 | 0.292772 | 0.146386 | − | 0.989228i | \(-0.453236\pi\) | ||||
0.146386 | + | 0.989228i | \(0.453236\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 49070.5 | 1.67850 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2057.50 | −0.0701567 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −38218.1 | −1.29906 | −0.649531 | − | 0.760335i | \(-0.725035\pi\) | ||||
−0.649531 | + | 0.760335i | \(0.725035\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2286.67 | −0.0774817 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5832.56 | −0.197011 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −55831.4 | −1.87997 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 53245.1 | 1.78729 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 37468.2 | 1.25379 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1153.97 | −0.0384948 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −581.187 | −0.0193275 | −0.00966376 | − | 0.999953i | \(-0.503076\pi\) | ||||
−0.00966376 | + | 0.999953i | \(0.503076\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 435.277 | 0.0144304 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 41718.0 | 1.37878 | 0.689389 | − | 0.724391i | \(-0.257879\pi\) | ||||
0.689389 | + | 0.724391i | \(0.257879\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 22138.4 | 0.729419 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2296.82 | −0.0754433 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 34468.0 | 1.12869 | 0.564344 | − | 0.825540i | \(-0.309129\pi\) | ||||
0.564344 | + | 0.825540i | \(0.309129\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 37361.4 | 1.21969 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5565.70 | 0.181141 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 43972.2 | 1.42675 | 0.713375 | − | 0.700783i | \(-0.247166\pi\) | ||||
0.713375 | + | 0.700783i | \(0.247166\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5394.29 | 0.174494 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −18909.4 | −0.609821 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.73509 | 0.000120090 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9819.21 | 0.314750 | 0.157375 | − | 0.987539i | \(-0.449697\pi\) | ||||
0.157375 | + | 0.987539i | \(0.449697\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −11660.3 | −0.372636 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 22627.7 | 0.720950 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2688.77 | 0.0854106 | 0.0427053 | − | 0.999088i | \(-0.486402\pi\) | ||||
0.0427053 | + | 0.999088i | \(0.486402\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 25719.5 | 0.814544 |
(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 | 1840.4.a.z.1.4 | 9 | ||
4.3 | odd | 2 | 920.4.a.e.1.6 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.4.a.e.1.6 | ✓ | 9 | 4.3 | odd | 2 | ||
1840.4.a.z.1.4 | 9 | 1.1 | even | 1 | trivial |