Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8281,2,Mod(1,8281)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8281, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8281.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8281 = 7^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8281.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: | \(66.1241179138\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8281.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.61803 | −1.85123 | −0.925615 | − | 0.378467i | \(-0.876451\pi\) | ||||
−0.925615 | + | 0.378467i | \(0.876451\pi\) | |||||||
\(3\) | 2.61803 | 1.51152 | 0.755761 | − | 0.654847i | \(-0.227267\pi\) | ||||
0.755761 | + | 0.654847i | \(0.227267\pi\) | |||||||
\(4\) | 4.85410 | 2.42705 | ||||||||
\(5\) | 2.61803 | 1.17082 | 0.585410 | − | 0.810737i | \(-0.300933\pi\) | ||||
0.585410 | + | 0.810737i | \(0.300933\pi\) | |||||||
\(6\) | −6.85410 | −2.79818 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −7.47214 | −2.64180 | ||||||||
\(9\) | 3.85410 | 1.28470 | ||||||||
\(10\) | −6.85410 | −2.16746 | ||||||||
\(11\) | −1.85410 | −0.559033 | −0.279516 | − | 0.960141i | \(-0.590174\pi\) | ||||
−0.279516 | + | 0.960141i | \(0.590174\pi\) | |||||||
\(12\) | 12.7082 | 3.66854 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.85410 | 1.76972 | ||||||||
\(16\) | 9.85410 | 2.46353 | ||||||||
\(17\) | 1.47214 | 0.357045 | 0.178523 | − | 0.983936i | \(-0.442868\pi\) | ||||
0.178523 | + | 0.983936i | \(0.442868\pi\) | |||||||
\(18\) | −10.0902 | −2.37828 | ||||||||
\(19\) | −1.85410 | −0.425360 | −0.212680 | − | 0.977122i | \(-0.568219\pi\) | ||||
−0.212680 | + | 0.977122i | \(0.568219\pi\) | |||||||
\(20\) | 12.7082 | 2.84164 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.85410 | 1.03490 | ||||||||
\(23\) | −4.47214 | −0.932505 | −0.466252 | − | 0.884652i | \(-0.654396\pi\) | ||||
−0.466252 | + | 0.884652i | \(0.654396\pi\) | |||||||
\(24\) | −19.5623 | −3.99314 | ||||||||
\(25\) | 1.85410 | 0.370820 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.23607 | 0.430331 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.09017 | 1.31661 | 0.658306 | − | 0.752751i | \(-0.271273\pi\) | ||||
0.658306 | + | 0.752751i | \(0.271273\pi\) | |||||||
\(30\) | −17.9443 | −3.27616 | ||||||||
\(31\) | −4.70820 | −0.845618 | −0.422809 | − | 0.906219i | \(-0.638956\pi\) | ||||
−0.422809 | + | 0.906219i | \(0.638956\pi\) | |||||||
\(32\) | −10.8541 | −1.91875 | ||||||||
\(33\) | −4.85410 | −0.844991 | ||||||||
\(34\) | −3.85410 | −0.660973 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 18.7082 | 3.11803 | ||||||||
\(37\) | −4.00000 | −0.657596 | −0.328798 | − | 0.944400i | \(-0.606644\pi\) | ||||
−0.328798 | + | 0.944400i | \(0.606644\pi\) | |||||||
\(38\) | 4.85410 | 0.787439 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −19.5623 | −3.09307 | ||||||||
\(41\) | 0.763932 | 0.119306 | 0.0596531 | − | 0.998219i | \(-0.481001\pi\) | ||||
0.0596531 | + | 0.998219i | \(0.481001\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.5623 | 1.91573 | 0.957867 | − | 0.287213i | \(-0.0927286\pi\) | ||||
0.957867 | + | 0.287213i | \(0.0927286\pi\) | |||||||
\(44\) | −9.00000 | −1.35680 | ||||||||
\(45\) | 10.0902 | 1.50415 | ||||||||
\(46\) | 11.7082 | 1.72628 | ||||||||
\(47\) | −2.23607 | −0.326164 | −0.163082 | − | 0.986613i | \(-0.552144\pi\) | ||||
−0.163082 | + | 0.986613i | \(0.552144\pi\) | |||||||
\(48\) | 25.7984 | 3.72367 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4.85410 | −0.686474 | ||||||||
\(51\) | 3.85410 | 0.539682 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.76393 | 0.517016 | 0.258508 | − | 0.966009i | \(-0.416769\pi\) | ||||
0.258508 | + | 0.966009i | \(0.416769\pi\) | |||||||
\(54\) | −5.85410 | −0.796642 | ||||||||
\(55\) | −4.85410 | −0.654527 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.85410 | −0.642942 | ||||||||
\(58\) | −18.5623 | −2.43735 | ||||||||
\(59\) | −2.23607 | −0.291111 | −0.145556 | − | 0.989350i | \(-0.546497\pi\) | ||||
−0.145556 | + | 0.989350i | \(0.546497\pi\) | |||||||
\(60\) | 33.2705 | 4.29520 | ||||||||
\(61\) | 6.00000 | 0.768221 | 0.384111 | − | 0.923287i | \(-0.374508\pi\) | ||||
0.384111 | + | 0.923287i | \(0.374508\pi\) | |||||||
\(62\) | 12.3262 | 1.56543 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.70820 | 1.08853 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 12.7082 | 1.56427 | ||||||||
\(67\) | 12.7082 | 1.55255 | 0.776277 | − | 0.630392i | \(-0.217106\pi\) | ||||
0.776277 | + | 0.630392i | \(0.217106\pi\) | |||||||
\(68\) | 7.14590 | 0.866567 | ||||||||
\(69\) | −11.7082 | −1.40950 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.1803 | 1.68290 | 0.841448 | − | 0.540338i | \(-0.181703\pi\) | ||||
0.841448 | + | 0.540338i | \(0.181703\pi\) | |||||||
\(72\) | −28.7984 | −3.39392 | ||||||||
\(73\) | −2.00000 | −0.234082 | −0.117041 | − | 0.993127i | \(-0.537341\pi\) | ||||
−0.117041 | + | 0.993127i | \(0.537341\pi\) | |||||||
\(74\) | 10.4721 | 1.21736 | ||||||||
\(75\) | 4.85410 | 0.560503 | ||||||||
\(76\) | −9.00000 | −1.03237 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.00000 | 0.450035 | 0.225018 | − | 0.974355i | \(-0.427756\pi\) | ||||
0.225018 | + | 0.974355i | \(0.427756\pi\) | |||||||
\(80\) | 25.7984 | 2.88435 | ||||||||
\(81\) | −5.70820 | −0.634245 | ||||||||
\(82\) | −2.00000 | −0.220863 | ||||||||
\(83\) | 6.70820 | 0.736321 | 0.368161 | − | 0.929762i | \(-0.379988\pi\) | ||||
0.368161 | + | 0.929762i | \(0.379988\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.85410 | 0.418036 | ||||||||
\(86\) | −32.8885 | −3.54646 | ||||||||
\(87\) | 18.5623 | 1.99009 | ||||||||
\(88\) | 13.8541 | 1.47685 | ||||||||
\(89\) | 4.90983 | 0.520441 | 0.260220 | − | 0.965549i | \(-0.416205\pi\) | ||||
0.260220 | + | 0.965549i | \(0.416205\pi\) | |||||||
\(90\) | −26.4164 | −2.78453 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −21.7082 | −2.26324 | ||||||||
\(93\) | −12.3262 | −1.27817 | ||||||||
\(94\) | 5.85410 | 0.603805 | ||||||||
\(95\) | −4.85410 | −0.498020 | ||||||||
\(96\) | −28.4164 | −2.90024 | ||||||||
\(97\) | 18.8541 | 1.91434 | 0.957172 | − | 0.289520i | \(-0.0934956\pi\) | ||||
0.957172 | + | 0.289520i | \(0.0934956\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.14590 | −0.718190 | ||||||||
\(100\) | 9.00000 | 0.900000 | ||||||||
\(101\) | 11.5623 | 1.15049 | 0.575246 | − | 0.817980i | \(-0.304906\pi\) | ||||
0.575246 | + | 0.817980i | \(0.304906\pi\) | |||||||
\(102\) | −10.0902 | −0.999076 | ||||||||
\(103\) | 8.70820 | 0.858045 | 0.429022 | − | 0.903294i | \(-0.358858\pi\) | ||||
0.429022 | + | 0.903294i | \(0.358858\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.85410 | −0.957115 | ||||||||
\(107\) | −3.38197 | −0.326947 | −0.163473 | − | 0.986548i | \(-0.552270\pi\) | ||||
−0.163473 | + | 0.986548i | \(0.552270\pi\) | |||||||
\(108\) | 10.8541 | 1.04444 | ||||||||
\(109\) | 2.70820 | 0.259399 | 0.129699 | − | 0.991553i | \(-0.458599\pi\) | ||||
0.129699 | + | 0.991553i | \(0.458599\pi\) | |||||||
\(110\) | 12.7082 | 1.21168 | ||||||||
\(111\) | −10.4721 | −0.993971 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.47214 | 0.138487 | 0.0692435 | − | 0.997600i | \(-0.477941\pi\) | ||||
0.0692435 | + | 0.997600i | \(0.477941\pi\) | |||||||
\(114\) | 12.7082 | 1.19023 | ||||||||
\(115\) | −11.7082 | −1.09180 | ||||||||
\(116\) | 34.4164 | 3.19548 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.85410 | 0.538914 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −51.2148 | −4.67525 | ||||||||
\(121\) | −7.56231 | −0.687482 | ||||||||
\(122\) | −15.7082 | −1.42215 | ||||||||
\(123\) | 2.00000 | 0.180334 | ||||||||
\(124\) | −22.8541 | −2.05236 | ||||||||
\(125\) | −8.23607 | −0.736656 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −20.8541 | −1.85050 | −0.925251 | − | 0.379355i | \(-0.876146\pi\) | ||||
−0.925251 | + | 0.379355i | \(0.876146\pi\) | |||||||
\(128\) | −1.09017 | −0.0963583 | ||||||||
\(129\) | 32.8885 | 2.89567 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.3262 | 1.33906 | 0.669530 | − | 0.742785i | \(-0.266496\pi\) | ||||
0.669530 | + | 0.742785i | \(0.266496\pi\) | |||||||
\(132\) | −23.5623 | −2.05084 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −33.2705 | −2.87413 | ||||||||
\(135\) | 5.85410 | 0.503841 | ||||||||
\(136\) | −11.0000 | −0.943242 | ||||||||
\(137\) | 2.61803 | 0.223674 | 0.111837 | − | 0.993727i | \(-0.464327\pi\) | ||||
0.111837 | + | 0.993727i | \(0.464327\pi\) | |||||||
\(138\) | 30.6525 | 2.60931 | ||||||||
\(139\) | −4.56231 | −0.386970 | −0.193485 | − | 0.981103i | \(-0.561979\pi\) | ||||
−0.193485 | + | 0.981103i | \(0.561979\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.85410 | −0.493004 | ||||||||
\(142\) | −37.1246 | −3.11543 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 37.9787 | 3.16489 | ||||||||
\(145\) | 18.5623 | 1.54152 | ||||||||
\(146\) | 5.23607 | 0.433340 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −19.4164 | −1.59602 | ||||||||
\(149\) | −1.85410 | −0.151894 | −0.0759470 | − | 0.997112i | \(-0.524198\pi\) | ||||
−0.0759470 | + | 0.997112i | \(0.524198\pi\) | |||||||
\(150\) | −12.7082 | −1.03762 | ||||||||
\(151\) | 1.29180 | 0.105125 | 0.0525624 | − | 0.998618i | \(-0.483261\pi\) | ||||
0.0525624 | + | 0.998618i | \(0.483261\pi\) | |||||||
\(152\) | 13.8541 | 1.12372 | ||||||||
\(153\) | 5.67376 | 0.458696 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.3262 | −0.990067 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.8541 | −1.18549 | −0.592743 | − | 0.805392i | \(-0.701955\pi\) | ||||
−0.592743 | + | 0.805392i | \(0.701955\pi\) | |||||||
\(158\) | −10.4721 | −0.833118 | ||||||||
\(159\) | 9.85410 | 0.781481 | ||||||||
\(160\) | −28.4164 | −2.24651 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 14.9443 | 1.17413 | ||||||||
\(163\) | 3.70820 | 0.290449 | 0.145224 | − | 0.989399i | \(-0.453610\pi\) | ||||
0.145224 | + | 0.989399i | \(0.453610\pi\) | |||||||
\(164\) | 3.70820 | 0.289562 | ||||||||
\(165\) | −12.7082 | −0.989332 | ||||||||
\(166\) | −17.5623 | −1.36310 | ||||||||
\(167\) | 14.2361 | 1.10162 | 0.550810 | − | 0.834631i | \(-0.314319\pi\) | ||||
0.550810 | + | 0.834631i | \(0.314319\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −10.0902 | −0.773881 | ||||||||
\(171\) | −7.14590 | −0.546460 | ||||||||
\(172\) | 60.9787 | 4.64958 | ||||||||
\(173\) | 9.00000 | 0.684257 | 0.342129 | − | 0.939653i | \(-0.388852\pi\) | ||||
0.342129 | + | 0.939653i | \(0.388852\pi\) | |||||||
\(174\) | −48.5967 | −3.68411 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −18.2705 | −1.37719 | ||||||||
\(177\) | −5.85410 | −0.440021 | ||||||||
\(178\) | −12.8541 | −0.963456 | ||||||||
\(179\) | −9.00000 | −0.672692 | −0.336346 | − | 0.941739i | \(-0.609191\pi\) | ||||
−0.336346 | + | 0.941739i | \(0.609191\pi\) | |||||||
\(180\) | 48.9787 | 3.65066 | ||||||||
\(181\) | −9.70820 | −0.721605 | −0.360803 | − | 0.932642i | \(-0.617497\pi\) | ||||
−0.360803 | + | 0.932642i | \(0.617497\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 15.7082 | 1.16118 | ||||||||
\(184\) | 33.4164 | 2.46349 | ||||||||
\(185\) | −10.4721 | −0.769927 | ||||||||
\(186\) | 32.2705 | 2.36619 | ||||||||
\(187\) | −2.72949 | −0.199600 | ||||||||
\(188\) | −10.8541 | −0.791617 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 12.7082 | 0.921950 | ||||||||
\(191\) | 21.3820 | 1.54714 | 0.773572 | − | 0.633708i | \(-0.218468\pi\) | ||||
0.773572 | + | 0.633708i | \(0.218468\pi\) | |||||||
\(192\) | 22.7984 | 1.64533 | ||||||||
\(193\) | 6.00000 | 0.431889 | 0.215945 | − | 0.976406i | \(-0.430717\pi\) | ||||
0.215945 | + | 0.976406i | \(0.430717\pi\) | |||||||
\(194\) | −49.3607 | −3.54389 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.7984 | 1.19683 | 0.598417 | − | 0.801185i | \(-0.295797\pi\) | ||||
0.598417 | + | 0.801185i | \(0.295797\pi\) | |||||||
\(198\) | 18.7082 | 1.32953 | ||||||||
\(199\) | 24.4164 | 1.73083 | 0.865417 | − | 0.501053i | \(-0.167054\pi\) | ||||
0.865417 | + | 0.501053i | \(0.167054\pi\) | |||||||
\(200\) | −13.8541 | −0.979633 | ||||||||
\(201\) | 33.2705 | 2.34672 | ||||||||
\(202\) | −30.2705 | −2.12983 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 18.7082 | 1.30984 | ||||||||
\(205\) | 2.00000 | 0.139686 | ||||||||
\(206\) | −22.7984 | −1.58844 | ||||||||
\(207\) | −17.2361 | −1.19799 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.43769 | 0.237790 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.70820 | 0.324126 | 0.162063 | − | 0.986780i | \(-0.448185\pi\) | ||||
0.162063 | + | 0.986780i | \(0.448185\pi\) | |||||||
\(212\) | 18.2705 | 1.25482 | ||||||||
\(213\) | 37.1246 | 2.54374 | ||||||||
\(214\) | 8.85410 | 0.605254 | ||||||||
\(215\) | 32.8885 | 2.24298 | ||||||||
\(216\) | −16.7082 | −1.13685 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −7.09017 | −0.480207 | ||||||||
\(219\) | −5.23607 | −0.353821 | ||||||||
\(220\) | −23.5623 | −1.58857 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 27.4164 | 1.84007 | ||||||||
\(223\) | 20.2705 | 1.35741 | 0.678707 | − | 0.734409i | \(-0.262541\pi\) | ||||
0.678707 | + | 0.734409i | \(0.262541\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.14590 | 0.476393 | ||||||||
\(226\) | −3.85410 | −0.256371 | ||||||||
\(227\) | 1.47214 | 0.0977091 | 0.0488545 | − | 0.998806i | \(-0.484443\pi\) | ||||
0.0488545 | + | 0.998806i | \(0.484443\pi\) | |||||||
\(228\) | −23.5623 | −1.56045 | ||||||||
\(229\) | −13.1246 | −0.867299 | −0.433649 | − | 0.901082i | \(-0.642774\pi\) | ||||
−0.433649 | + | 0.901082i | \(0.642774\pi\) | |||||||
\(230\) | 30.6525 | 2.02116 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −52.9787 | −3.47822 | ||||||||
\(233\) | 2.61803 | 0.171513 | 0.0857566 | − | 0.996316i | \(-0.472669\pi\) | ||||
0.0857566 | + | 0.996316i | \(0.472669\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.85410 | −0.381880 | ||||||||
\(236\) | −10.8541 | −0.706542 | ||||||||
\(237\) | 10.4721 | 0.680238 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24.7082 | 1.59824 | 0.799120 | − | 0.601171i | \(-0.205299\pi\) | ||||
0.799120 | + | 0.601171i | \(0.205299\pi\) | |||||||
\(240\) | 67.5410 | 4.35975 | ||||||||
\(241\) | 24.5623 | 1.58220 | 0.791099 | − | 0.611689i | \(-0.209509\pi\) | ||||
0.791099 | + | 0.611689i | \(0.209509\pi\) | |||||||
\(242\) | 19.7984 | 1.27269 | ||||||||
\(243\) | −21.6525 | −1.38901 | ||||||||
\(244\) | 29.1246 | 1.86451 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −5.23607 | −0.333840 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 35.1803 | 2.23395 | ||||||||
\(249\) | 17.5623 | 1.11297 | ||||||||
\(250\) | 21.5623 | 1.36372 | ||||||||
\(251\) | −0.763932 | −0.0482190 | −0.0241095 | − | 0.999709i | \(-0.507675\pi\) | ||||
−0.0241095 | + | 0.999709i | \(0.507675\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.29180 | 0.521301 | ||||||||
\(254\) | 54.5967 | 3.42570 | ||||||||
\(255\) | 10.0902 | 0.631871 | ||||||||
\(256\) | −14.5623 | −0.910144 | ||||||||
\(257\) | −16.7426 | −1.04438 | −0.522189 | − | 0.852830i | \(-0.674884\pi\) | ||||
−0.522189 | + | 0.852830i | \(0.674884\pi\) | |||||||
\(258\) | −86.1033 | −5.36056 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 27.3262 | 1.69145 | ||||||||
\(262\) | −40.1246 | −2.47891 | ||||||||
\(263\) | 9.00000 | 0.554964 | 0.277482 | − | 0.960731i | \(-0.410500\pi\) | ||||
0.277482 | + | 0.960731i | \(0.410500\pi\) | |||||||
\(264\) | 36.2705 | 2.23230 | ||||||||
\(265\) | 9.85410 | 0.605333 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.8541 | 0.786658 | ||||||||
\(268\) | 61.6869 | 3.76813 | ||||||||
\(269\) | 28.7426 | 1.75247 | 0.876235 | − | 0.481884i | \(-0.160047\pi\) | ||||
0.876235 | + | 0.481884i | \(0.160047\pi\) | |||||||
\(270\) | −15.3262 | −0.932725 | ||||||||
\(271\) | −8.41641 | −0.511260 | −0.255630 | − | 0.966775i | \(-0.582283\pi\) | ||||
−0.255630 | + | 0.966775i | \(0.582283\pi\) | |||||||
\(272\) | 14.5066 | 0.879590 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.85410 | −0.414071 | ||||||||
\(275\) | −3.43769 | −0.207301 | ||||||||
\(276\) | −56.8328 | −3.42093 | ||||||||
\(277\) | −5.00000 | −0.300421 | −0.150210 | − | 0.988654i | \(-0.547995\pi\) | ||||
−0.150210 | + | 0.988654i | \(0.547995\pi\) | |||||||
\(278\) | 11.9443 | 0.716370 | ||||||||
\(279\) | −18.1459 | −1.08637 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.1803 | −1.20386 | −0.601929 | − | 0.798550i | \(-0.705601\pi\) | ||||
−0.601929 | + | 0.798550i | \(0.705601\pi\) | |||||||
\(282\) | 15.3262 | 0.912664 | ||||||||
\(283\) | −13.4164 | −0.797523 | −0.398761 | − | 0.917055i | \(-0.630560\pi\) | ||||
−0.398761 | + | 0.917055i | \(0.630560\pi\) | |||||||
\(284\) | 68.8328 | 4.08448 | ||||||||
\(285\) | −12.7082 | −0.752769 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −41.8328 | −2.46502 | ||||||||
\(289\) | −14.8328 | −0.872519 | ||||||||
\(290\) | −48.5967 | −2.85370 | ||||||||
\(291\) | 49.3607 | 2.89357 | ||||||||
\(292\) | −9.70820 | −0.568130 | ||||||||
\(293\) | −6.76393 | −0.395153 | −0.197577 | − | 0.980287i | \(-0.563307\pi\) | ||||
−0.197577 | + | 0.980287i | \(0.563307\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.85410 | −0.340839 | ||||||||
\(296\) | 29.8885 | 1.73724 | ||||||||
\(297\) | −4.14590 | −0.240569 | ||||||||
\(298\) | 4.85410 | 0.281191 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 23.5623 | 1.36037 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3.38197 | −0.194610 | ||||||||
\(303\) | 30.2705 | 1.73900 | ||||||||
\(304\) | −18.2705 | −1.04789 | ||||||||
\(305\) | 15.7082 | 0.899449 | ||||||||
\(306\) | −14.8541 | −0.849152 | ||||||||
\(307\) | −4.85410 | −0.277038 | −0.138519 | − | 0.990360i | \(-0.544234\pi\) | ||||
−0.138519 | + | 0.990360i | \(0.544234\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 22.7984 | 1.29695 | ||||||||
\(310\) | 32.2705 | 1.83284 | ||||||||
\(311\) | −3.32624 | −0.188614 | −0.0943068 | − | 0.995543i | \(-0.530063\pi\) | ||||
−0.0943068 | + | 0.995543i | \(0.530063\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −25.1246 | −1.42013 | −0.710064 | − | 0.704138i | \(-0.751334\pi\) | ||||
−0.710064 | + | 0.704138i | \(0.751334\pi\) | |||||||
\(314\) | 38.8885 | 2.19461 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 19.4164 | 1.09226 | ||||||||
\(317\) | −26.2361 | −1.47356 | −0.736782 | − | 0.676130i | \(-0.763656\pi\) | ||||
−0.736782 | + | 0.676130i | \(0.763656\pi\) | |||||||
\(318\) | −25.7984 | −1.44670 | ||||||||
\(319\) | −13.1459 | −0.736029 | ||||||||
\(320\) | 22.7984 | 1.27447 | ||||||||
\(321\) | −8.85410 | −0.494188 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.72949 | −0.151873 | ||||||||
\(324\) | −27.7082 | −1.53934 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −9.70820 | −0.537688 | ||||||||
\(327\) | 7.09017 | 0.392087 | ||||||||
\(328\) | −5.70820 | −0.315183 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 33.2705 | 1.83148 | ||||||||
\(331\) | 10.1459 | 0.557669 | 0.278834 | − | 0.960339i | \(-0.410052\pi\) | ||||
0.278834 | + | 0.960339i | \(0.410052\pi\) | |||||||
\(332\) | 32.5623 | 1.78709 | ||||||||
\(333\) | −15.4164 | −0.844814 | ||||||||
\(334\) | −37.2705 | −2.03935 | ||||||||
\(335\) | 33.2705 | 1.81776 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.5623 | −0.629839 | −0.314919 | − | 0.949118i | \(-0.601978\pi\) | ||||
−0.314919 | + | 0.949118i | \(0.601978\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.85410 | 0.209326 | ||||||||
\(340\) | 18.7082 | 1.01459 | ||||||||
\(341\) | 8.72949 | 0.472728 | ||||||||
\(342\) | 18.7082 | 1.01162 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −93.8673 | −5.06098 | ||||||||
\(345\) | −30.6525 | −1.65027 | ||||||||
\(346\) | −23.5623 | −1.26672 | ||||||||
\(347\) | 30.7639 | 1.65149 | 0.825747 | − | 0.564040i | \(-0.190754\pi\) | ||||
0.825747 | + | 0.564040i | \(0.190754\pi\) | |||||||
\(348\) | 90.1033 | 4.83005 | ||||||||
\(349\) | 20.7082 | 1.10848 | 0.554242 | − | 0.832355i | \(-0.313008\pi\) | ||||
0.554242 | + | 0.832355i | \(0.313008\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 20.1246 | 1.07265 | ||||||||
\(353\) | 22.1459 | 1.17871 | 0.589354 | − | 0.807875i | \(-0.299382\pi\) | ||||
0.589354 | + | 0.807875i | \(0.299382\pi\) | |||||||
\(354\) | 15.3262 | 0.814580 | ||||||||
\(355\) | 37.1246 | 1.97037 | ||||||||
\(356\) | 23.8328 | 1.26314 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 23.5623 | 1.24531 | ||||||||
\(359\) | 22.0902 | 1.16587 | 0.582937 | − | 0.812517i | \(-0.301903\pi\) | ||||
0.582937 | + | 0.812517i | \(0.301903\pi\) | |||||||
\(360\) | −75.3951 | −3.97367 | ||||||||
\(361\) | −15.5623 | −0.819069 | ||||||||
\(362\) | 25.4164 | 1.33586 | ||||||||
\(363\) | −19.7984 | −1.03915 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.23607 | −0.274068 | ||||||||
\(366\) | −41.1246 | −2.14962 | ||||||||
\(367\) | 1.41641 | 0.0739359 | 0.0369679 | − | 0.999316i | \(-0.488230\pi\) | ||||
0.0369679 | + | 0.999316i | \(0.488230\pi\) | |||||||
\(368\) | −44.0689 | −2.29725 | ||||||||
\(369\) | 2.94427 | 0.153273 | ||||||||
\(370\) | 27.4164 | 1.42531 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −59.8328 | −3.10219 | ||||||||
\(373\) | −20.5623 | −1.06468 | −0.532338 | − | 0.846532i | \(-0.678686\pi\) | ||||
−0.532338 | + | 0.846532i | \(0.678686\pi\) | |||||||
\(374\) | 7.14590 | 0.369506 | ||||||||
\(375\) | −21.5623 | −1.11347 | ||||||||
\(376\) | 16.7082 | 0.861660 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.14590 | 0.315694 | 0.157847 | − | 0.987464i | \(-0.449545\pi\) | ||||
0.157847 | + | 0.987464i | \(0.449545\pi\) | |||||||
\(380\) | −23.5623 | −1.20872 | ||||||||
\(381\) | −54.5967 | −2.79708 | ||||||||
\(382\) | −55.9787 | −2.86412 | ||||||||
\(383\) | −21.9787 | −1.12306 | −0.561530 | − | 0.827456i | \(-0.689787\pi\) | ||||
−0.561530 | + | 0.827456i | \(0.689787\pi\) | |||||||
\(384\) | −2.85410 | −0.145648 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −15.7082 | −0.799527 | ||||||||
\(387\) | 48.4164 | 2.46114 | ||||||||
\(388\) | 91.5197 | 4.64621 | ||||||||
\(389\) | −11.8885 | −0.602773 | −0.301387 | − | 0.953502i | \(-0.597449\pi\) | ||||
−0.301387 | + | 0.953502i | \(0.597449\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.58359 | −0.332947 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 40.1246 | 2.02402 | ||||||||
\(394\) | −43.9787 | −2.21562 | ||||||||
\(395\) | 10.4721 | 0.526910 | ||||||||
\(396\) | −34.6869 | −1.74308 | ||||||||
\(397\) | 1.41641 | 0.0710875 | 0.0355437 | − | 0.999368i | \(-0.488684\pi\) | ||||
0.0355437 | + | 0.999368i | \(0.488684\pi\) | |||||||
\(398\) | −63.9230 | −3.20417 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 18.2705 | 0.913525 | ||||||||
\(401\) | −35.4508 | −1.77033 | −0.885165 | − | 0.465276i | \(-0.845955\pi\) | ||||
−0.885165 | + | 0.465276i | \(0.845955\pi\) | |||||||
\(402\) | −87.1033 | −4.34432 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 56.1246 | 2.79230 | ||||||||
\(405\) | −14.9443 | −0.742587 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.41641 | 0.367618 | ||||||||
\(408\) | −28.7984 | −1.42573 | ||||||||
\(409\) | 14.4377 | 0.713898 | 0.356949 | − | 0.934124i | \(-0.383817\pi\) | ||||
0.356949 | + | 0.934124i | \(0.383817\pi\) | |||||||
\(410\) | −5.23607 | −0.258591 | ||||||||
\(411\) | 6.85410 | 0.338088 | ||||||||
\(412\) | 42.2705 | 2.08252 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 45.1246 | 2.21775 | ||||||||
\(415\) | 17.5623 | 0.862100 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11.9443 | −0.584914 | ||||||||
\(418\) | −9.00000 | −0.440204 | ||||||||
\(419\) | 11.9443 | 0.583516 | 0.291758 | − | 0.956492i | \(-0.405760\pi\) | ||||
0.291758 | + | 0.956492i | \(0.405760\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.41641 | −0.0690315 | −0.0345157 | − | 0.999404i | \(-0.510989\pi\) | ||||
−0.0345157 | + | 0.999404i | \(0.510989\pi\) | |||||||
\(422\) | −12.3262 | −0.600032 | ||||||||
\(423\) | −8.61803 | −0.419023 | ||||||||
\(424\) | −28.1246 | −1.36585 | ||||||||
\(425\) | 2.72949 | 0.132400 | ||||||||
\(426\) | −97.1935 | −4.70904 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −16.4164 | −0.793517 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −86.1033 | −4.15227 | ||||||||
\(431\) | −7.79837 | −0.375634 | −0.187817 | − | 0.982204i | \(-0.560141\pi\) | ||||
−0.187817 | + | 0.982204i | \(0.560141\pi\) | |||||||
\(432\) | 22.0344 | 1.06013 | ||||||||
\(433\) | −1.00000 | −0.0480569 | −0.0240285 | − | 0.999711i | \(-0.507649\pi\) | ||||
−0.0240285 | + | 0.999711i | \(0.507649\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 48.5967 | 2.33004 | ||||||||
\(436\) | 13.1459 | 0.629574 | ||||||||
\(437\) | 8.29180 | 0.396650 | ||||||||
\(438\) | 13.7082 | 0.655003 | ||||||||
\(439\) | −14.8541 | −0.708948 | −0.354474 | − | 0.935066i | \(-0.615340\pi\) | ||||
−0.354474 | + | 0.935066i | \(0.615340\pi\) | |||||||
\(440\) | 36.2705 | 1.72913 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.23607 | −0.248773 | −0.124387 | − | 0.992234i | \(-0.539696\pi\) | ||||
−0.124387 | + | 0.992234i | \(0.539696\pi\) | |||||||
\(444\) | −50.8328 | −2.41242 | ||||||||
\(445\) | 12.8541 | 0.609343 | ||||||||
\(446\) | −53.0689 | −2.51288 | ||||||||
\(447\) | −4.85410 | −0.229591 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.5279 | −0.921577 | −0.460788 | − | 0.887510i | \(-0.652433\pi\) | ||||
−0.460788 | + | 0.887510i | \(0.652433\pi\) | |||||||
\(450\) | −18.7082 | −0.881913 | ||||||||
\(451\) | −1.41641 | −0.0666960 | ||||||||
\(452\) | 7.14590 | 0.336115 | ||||||||
\(453\) | 3.38197 | 0.158899 | ||||||||
\(454\) | −3.85410 | −0.180882 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 36.2705 | 1.69852 | ||||||||
\(457\) | −15.4164 | −0.721149 | −0.360575 | − | 0.932730i | \(-0.617419\pi\) | ||||
−0.360575 | + | 0.932730i | \(0.617419\pi\) | |||||||
\(458\) | 34.3607 | 1.60557 | ||||||||
\(459\) | 3.29180 | 0.153648 | ||||||||
\(460\) | −56.8328 | −2.64984 | ||||||||
\(461\) | −12.2148 | −0.568899 | −0.284450 | − | 0.958691i | \(-0.591811\pi\) | ||||
−0.284450 | + | 0.958691i | \(0.591811\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.70820 | −0.311757 | −0.155878 | − | 0.987776i | \(-0.549821\pi\) | ||||
−0.155878 | + | 0.987776i | \(0.549821\pi\) | |||||||
\(464\) | 69.8673 | 3.24351 | ||||||||
\(465\) | −32.2705 | −1.49651 | ||||||||
\(466\) | −6.85410 | −0.317510 | ||||||||
\(467\) | −2.34752 | −0.108630 | −0.0543152 | − | 0.998524i | \(-0.517298\pi\) | ||||
−0.0543152 | + | 0.998524i | \(0.517298\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 15.3262 | 0.706947 | ||||||||
\(471\) | −38.8885 | −1.79189 | ||||||||
\(472\) | 16.7082 | 0.769057 | ||||||||
\(473\) | −23.2918 | −1.07096 | ||||||||
\(474\) | −27.4164 | −1.25928 | ||||||||
\(475\) | −3.43769 | −0.157732 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 14.5066 | 0.664211 | ||||||||
\(478\) | −64.6869 | −2.95871 | ||||||||
\(479\) | 24.9787 | 1.14131 | 0.570653 | − | 0.821191i | \(-0.306690\pi\) | ||||
0.570653 | + | 0.821191i | \(0.306690\pi\) | |||||||
\(480\) | −74.3951 | −3.39566 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −64.3050 | −2.92901 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −36.7082 | −1.66855 | ||||||||
\(485\) | 49.3607 | 2.24135 | ||||||||
\(486\) | 56.6869 | 2.57137 | ||||||||
\(487\) | −29.9787 | −1.35847 | −0.679233 | − | 0.733923i | \(-0.737687\pi\) | ||||
−0.679233 | + | 0.733923i | \(0.737687\pi\) | |||||||
\(488\) | −44.8328 | −2.02949 | ||||||||
\(489\) | 9.70820 | 0.439020 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.3820 | 0.558790 | 0.279395 | − | 0.960176i | \(-0.409866\pi\) | ||||
0.279395 | + | 0.960176i | \(0.409866\pi\) | |||||||
\(492\) | 9.70820 | 0.437680 | ||||||||
\(493\) | 10.4377 | 0.470090 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −18.7082 | −0.840871 | ||||||||
\(496\) | −46.3951 | −2.08320 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −45.9787 | −2.06036 | ||||||||
\(499\) | −14.8541 | −0.664961 | −0.332480 | − | 0.943110i | \(-0.607886\pi\) | ||||
−0.332480 | + | 0.943110i | \(0.607886\pi\) | |||||||
\(500\) | −39.9787 | −1.78790 | ||||||||
\(501\) | 37.2705 | 1.66512 | ||||||||
\(502\) | 2.00000 | 0.0892644 | ||||||||
\(503\) | −26.6180 | −1.18684 | −0.593420 | − | 0.804893i | \(-0.702223\pi\) | ||||
−0.593420 | + | 0.804893i | \(0.702223\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 30.2705 | 1.34702 | ||||||||
\(506\) | −21.7082 | −0.965047 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −101.228 | −4.49126 | ||||||||
\(509\) | −18.5967 | −0.824286 | −0.412143 | − | 0.911119i | \(-0.635220\pi\) | ||||
−0.412143 | + | 0.911119i | \(0.635220\pi\) | |||||||
\(510\) | −26.4164 | −1.16974 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 40.3050 | 1.78124 | ||||||||
\(513\) | −4.14590 | −0.183046 | ||||||||
\(514\) | 43.8328 | 1.93338 | ||||||||
\(515\) | 22.7984 | 1.00462 | ||||||||
\(516\) | 159.644 | 7.02795 | ||||||||
\(517\) | 4.14590 | 0.182336 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 23.5623 | 1.03427 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.6525 | −0.817180 | −0.408590 | − | 0.912718i | \(-0.633979\pi\) | ||||
−0.408590 | + | 0.912718i | \(0.633979\pi\) | |||||||
\(522\) | −71.5410 | −3.13127 | ||||||||
\(523\) | −1.12461 | −0.0491758 | −0.0245879 | − | 0.999698i | \(-0.507827\pi\) | ||||
−0.0245879 | + | 0.999698i | \(0.507827\pi\) | |||||||
\(524\) | 74.3951 | 3.24997 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −23.5623 | −1.02737 | ||||||||
\(527\) | −6.93112 | −0.301924 | ||||||||
\(528\) | −47.8328 | −2.08166 | ||||||||
\(529\) | −3.00000 | −0.130435 | ||||||||
\(530\) | −25.7984 | −1.12061 | ||||||||
\(531\) | −8.61803 | −0.373991 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −33.6525 | −1.45629 | ||||||||
\(535\) | −8.85410 | −0.382796 | ||||||||
\(536\) | −94.9574 | −4.10154 | ||||||||
\(537\) | −23.5623 | −1.01679 | ||||||||
\(538\) | −75.2492 | −3.24422 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 28.4164 | 1.22285 | ||||||||
\(541\) | −35.2705 | −1.51640 | −0.758199 | − | 0.652023i | \(-0.773920\pi\) | ||||
−0.758199 | + | 0.652023i | \(0.773920\pi\) | |||||||
\(542\) | 22.0344 | 0.946460 | ||||||||
\(543\) | −25.4164 | −1.09072 | ||||||||
\(544\) | −15.9787 | −0.685082 | ||||||||
\(545\) | 7.09017 | 0.303710 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.00000 | −0.128271 | −0.0641354 | − | 0.997941i | \(-0.520429\pi\) | ||||
−0.0641354 | + | 0.997941i | \(0.520429\pi\) | |||||||
\(548\) | 12.7082 | 0.542868 | ||||||||
\(549\) | 23.1246 | 0.986934 | ||||||||
\(550\) | 9.00000 | 0.383761 | ||||||||
\(551\) | −13.1459 | −0.560034 | ||||||||
\(552\) | 87.4853 | 3.72362 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 13.0902 | 0.556148 | ||||||||
\(555\) | −27.4164 | −1.16376 | ||||||||
\(556\) | −22.1459 | −0.939195 | ||||||||
\(557\) | 27.9787 | 1.18550 | 0.592748 | − | 0.805388i | \(-0.298043\pi\) | ||||
0.592748 | + | 0.805388i | \(0.298043\pi\) | |||||||
\(558\) | 47.5066 | 2.01111 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.14590 | −0.301700 | ||||||||
\(562\) | 52.8328 | 2.22862 | ||||||||
\(563\) | 21.0557 | 0.887393 | 0.443697 | − | 0.896177i | \(-0.353667\pi\) | ||||
0.443697 | + | 0.896177i | \(0.353667\pi\) | |||||||
\(564\) | −28.4164 | −1.19655 | ||||||||
\(565\) | 3.85410 | 0.162143 | ||||||||
\(566\) | 35.1246 | 1.47640 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −105.957 | −4.44587 | ||||||||
\(569\) | 14.9443 | 0.626496 | 0.313248 | − | 0.949671i | \(-0.398583\pi\) | ||||
0.313248 | + | 0.949671i | \(0.398583\pi\) | |||||||
\(570\) | 33.2705 | 1.39355 | ||||||||
\(571\) | 24.6869 | 1.03312 | 0.516558 | − | 0.856252i | \(-0.327213\pi\) | ||||
0.516558 | + | 0.856252i | \(0.327213\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 55.9787 | 2.33854 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.29180 | −0.345792 | ||||||||
\(576\) | 33.5623 | 1.39843 | ||||||||
\(577\) | −43.8328 | −1.82478 | −0.912392 | − | 0.409318i | \(-0.865767\pi\) | ||||
−0.912392 | + | 0.409318i | \(0.865767\pi\) | |||||||
\(578\) | 38.8328 | 1.61523 | ||||||||
\(579\) | 15.7082 | 0.652811 | ||||||||
\(580\) | 90.1033 | 3.74134 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −129.228 | −5.35667 | ||||||||
\(583\) | −6.97871 | −0.289029 | ||||||||
\(584\) | 14.9443 | 0.618398 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 17.7082 | 0.731519 | ||||||||
\(587\) | −19.9098 | −0.821767 | −0.410883 | − | 0.911688i | \(-0.634780\pi\) | ||||
−0.410883 | + | 0.911688i | \(0.634780\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.72949 | 0.359692 | ||||||||
\(590\) | 15.3262 | 0.630971 | ||||||||
\(591\) | 43.9787 | 1.80904 | ||||||||
\(592\) | −39.4164 | −1.62000 | ||||||||
\(593\) | 43.7984 | 1.79858 | 0.899292 | − | 0.437349i | \(-0.144083\pi\) | ||||
0.899292 | + | 0.437349i | \(0.144083\pi\) | |||||||
\(594\) | 10.8541 | 0.445349 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −9.00000 | −0.368654 | ||||||||
\(597\) | 63.9230 | 2.61619 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 29.5066 | 1.20561 | 0.602803 | − | 0.797890i | \(-0.294050\pi\) | ||||
0.602803 | + | 0.797890i | \(0.294050\pi\) | |||||||
\(600\) | −36.2705 | −1.48074 | ||||||||
\(601\) | −40.3951 | −1.64775 | −0.823876 | − | 0.566771i | \(-0.808193\pi\) | ||||
−0.823876 | + | 0.566771i | \(0.808193\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 48.9787 | 1.99457 | ||||||||
\(604\) | 6.27051 | 0.255143 | ||||||||
\(605\) | −19.7984 | −0.804918 | ||||||||
\(606\) | −79.2492 | −3.21928 | ||||||||
\(607\) | 23.0000 | 0.933541 | 0.466771 | − | 0.884378i | \(-0.345417\pi\) | ||||
0.466771 | + | 0.884378i | \(0.345417\pi\) | |||||||
\(608\) | 20.1246 | 0.816161 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −41.1246 | −1.66509 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 27.5410 | 1.11328 | ||||||||
\(613\) | −34.5623 | −1.39596 | −0.697979 | − | 0.716118i | \(-0.745917\pi\) | ||||
−0.697979 | + | 0.716118i | \(0.745917\pi\) | |||||||
\(614\) | 12.7082 | 0.512861 | ||||||||
\(615\) | 5.23607 | 0.211139 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.0557281 | −0.00224353 | −0.00112176 | − | 0.999999i | \(-0.500357\pi\) | ||||
−0.00112176 | + | 0.999999i | \(0.500357\pi\) | |||||||
\(618\) | −59.6869 | −2.40096 | ||||||||
\(619\) | 9.41641 | 0.378477 | 0.189239 | − | 0.981931i | \(-0.439398\pi\) | ||||
0.189239 | + | 0.981931i | \(0.439398\pi\) | |||||||
\(620\) | −59.8328 | −2.40294 | ||||||||
\(621\) | −10.0000 | −0.401286 | ||||||||
\(622\) | 8.70820 | 0.349167 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.8328 | −1.23331 | ||||||||
\(626\) | 65.7771 | 2.62898 | ||||||||
\(627\) | 9.00000 | 0.359425 | ||||||||
\(628\) | −72.1033 | −2.87724 | ||||||||
\(629\) | −5.88854 | −0.234792 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.3951 | −1.36925 | −0.684624 | − | 0.728896i | \(-0.740034\pi\) | ||||
−0.684624 | + | 0.728896i | \(0.740034\pi\) | |||||||
\(632\) | −29.8885 | −1.18890 | ||||||||
\(633\) | 12.3262 | 0.489924 | ||||||||
\(634\) | 68.6869 | 2.72791 | ||||||||
\(635\) | −54.5967 | −2.16661 | ||||||||
\(636\) | 47.8328 | 1.89669 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 34.4164 | 1.36256 | ||||||||
\(639\) | 54.6525 | 2.16202 | ||||||||
\(640\) | −2.85410 | −0.112818 | ||||||||
\(641\) | −47.5066 | −1.87640 | −0.938199 | − | 0.346098i | \(-0.887507\pi\) | ||||
−0.938199 | + | 0.346098i | \(0.887507\pi\) | |||||||
\(642\) | 23.1803 | 0.914855 | ||||||||
\(643\) | −7.00000 | −0.276053 | −0.138027 | − | 0.990429i | \(-0.544076\pi\) | ||||
−0.138027 | + | 0.990429i | \(0.544076\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 86.1033 | 3.39032 | ||||||||
\(646\) | 7.14590 | 0.281152 | ||||||||
\(647\) | −24.7639 | −0.973571 | −0.486785 | − | 0.873522i | \(-0.661831\pi\) | ||||
−0.486785 | + | 0.873522i | \(0.661831\pi\) | |||||||
\(648\) | 42.6525 | 1.67555 | ||||||||
\(649\) | 4.14590 | 0.162741 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 18.0000 | 0.704934 | ||||||||
\(653\) | −0.381966 | −0.0149475 | −0.00747374 | − | 0.999972i | \(-0.502379\pi\) | ||||
−0.00747374 | + | 0.999972i | \(0.502379\pi\) | |||||||
\(654\) | −18.5623 | −0.725844 | ||||||||
\(655\) | 40.1246 | 1.56780 | ||||||||
\(656\) | 7.52786 | 0.293914 | ||||||||
\(657\) | −7.70820 | −0.300726 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −23.8885 | −0.930566 | −0.465283 | − | 0.885162i | \(-0.654047\pi\) | ||||
−0.465283 | + | 0.885162i | \(0.654047\pi\) | |||||||
\(660\) | −61.6869 | −2.40116 | ||||||||
\(661\) | −48.5410 | −1.88803 | −0.944013 | − | 0.329907i | \(-0.892983\pi\) | ||||
−0.944013 | + | 0.329907i | \(0.892983\pi\) | |||||||
\(662\) | −26.5623 | −1.03237 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −50.1246 | −1.94521 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 40.3607 | 1.56394 | ||||||||
\(667\) | −31.7082 | −1.22775 | ||||||||
\(668\) | 69.1033 | 2.67369 | ||||||||
\(669\) | 53.0689 | 2.05176 | ||||||||
\(670\) | −87.1033 | −3.36510 | ||||||||
\(671\) | −11.1246 | −0.429461 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −39.2492 | −1.51295 | −0.756473 | − | 0.654025i | \(-0.773079\pi\) | ||||
−0.756473 | + | 0.654025i | \(0.773079\pi\) | |||||||
\(674\) | 30.2705 | 1.16598 | ||||||||
\(675\) | 4.14590 | 0.159576 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −43.7426 | −1.68117 | −0.840583 | − | 0.541682i | \(-0.817788\pi\) | ||||
−0.840583 | + | 0.541682i | \(0.817788\pi\) | |||||||
\(678\) | −10.0902 | −0.387511 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −28.7984 | −1.10437 | ||||||||
\(681\) | 3.85410 | 0.147690 | ||||||||
\(682\) | −22.8541 | −0.875129 | ||||||||
\(683\) | −1.47214 | −0.0563297 | −0.0281649 | − | 0.999603i | \(-0.508966\pi\) | ||||
−0.0281649 | + | 0.999603i | \(0.508966\pi\) | |||||||
\(684\) | −34.6869 | −1.32629 | ||||||||
\(685\) | 6.85410 | 0.261882 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −34.3607 | −1.31094 | ||||||||
\(688\) | 123.790 | 4.71946 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 80.2492 | 3.05504 | ||||||||
\(691\) | −5.85410 | −0.222701 | −0.111350 | − | 0.993781i | \(-0.535518\pi\) | ||||
−0.111350 | + | 0.993781i | \(0.535518\pi\) | |||||||
\(692\) | 43.6869 | 1.66073 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −80.5410 | −3.05730 | ||||||||
\(695\) | −11.9443 | −0.453072 | ||||||||
\(696\) | −138.700 | −5.25741 | ||||||||
\(697\) | 1.12461 | 0.0425977 | ||||||||
\(698\) | −54.2148 | −2.05206 | ||||||||
\(699\) | 6.85410 | 0.259246 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.2361 | 0.424380 | 0.212190 | − | 0.977228i | \(-0.431940\pi\) | ||||
0.212190 | + | 0.977228i | \(0.431940\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.41641 | 0.279715 | ||||||||
\(704\) | −16.1459 | −0.608521 | ||||||||
\(705\) | −15.3262 | −0.577220 | ||||||||
\(706\) | −57.9787 | −2.18206 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −28.4164 | −1.06795 | ||||||||
\(709\) | −23.5623 | −0.884901 | −0.442450 | − | 0.896793i | \(-0.645891\pi\) | ||||
−0.442450 | + | 0.896793i | \(0.645891\pi\) | |||||||
\(710\) | −97.1935 | −3.64761 | ||||||||
\(711\) | 15.4164 | 0.578160 | ||||||||
\(712\) | −36.6869 | −1.37490 | ||||||||
\(713\) | 21.0557 | 0.788543 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −43.6869 | −1.63266 | ||||||||
\(717\) | 64.6869 | 2.41578 | ||||||||
\(718\) | −57.8328 | −2.15830 | ||||||||
\(719\) | −8.12461 | −0.302997 | −0.151498 | − | 0.988457i | \(-0.548410\pi\) | ||||
−0.151498 | + | 0.988457i | \(0.548410\pi\) | |||||||
\(720\) | 99.4296 | 3.70552 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 40.7426 | 1.51628 | ||||||||
\(723\) | 64.3050 | 2.39153 | ||||||||
\(724\) | −47.1246 | −1.75137 | ||||||||
\(725\) | 13.1459 | 0.488226 | ||||||||
\(726\) | 51.8328 | 1.92370 | ||||||||
\(727\) | 30.7082 | 1.13890 | 0.569452 | − | 0.822025i | \(-0.307155\pi\) | ||||
0.569452 | + | 0.822025i | \(0.307155\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −39.5623 | −1.46527 | ||||||||
\(730\) | 13.7082 | 0.507363 | ||||||||
\(731\) | 18.4934 | 0.684004 | ||||||||
\(732\) | 76.2492 | 2.81825 | ||||||||
\(733\) | −32.2705 | −1.19194 | −0.595969 | − | 0.803007i | \(-0.703232\pi\) | ||||
−0.595969 | + | 0.803007i | \(0.703232\pi\) | |||||||
\(734\) | −3.70820 | −0.136872 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 48.5410 | 1.78925 | ||||||||
\(737\) | −23.5623 | −0.867929 | ||||||||
\(738\) | −7.70820 | −0.283743 | ||||||||
\(739\) | 6.87539 | 0.252915 | 0.126458 | − | 0.991972i | \(-0.459639\pi\) | ||||
0.126458 | + | 0.991972i | \(0.459639\pi\) | |||||||
\(740\) | −50.8328 | −1.86865 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −39.3262 | −1.44274 | −0.721370 | − | 0.692550i | \(-0.756487\pi\) | ||||
−0.721370 | + | 0.692550i | \(0.756487\pi\) | |||||||
\(744\) | 92.1033 | 3.37667 | ||||||||
\(745\) | −4.85410 | −0.177841 | ||||||||
\(746\) | 53.8328 | 1.97096 | ||||||||
\(747\) | 25.8541 | 0.945952 | ||||||||
\(748\) | −13.2492 | −0.484440 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 56.4508 | 2.06129 | ||||||||
\(751\) | 22.7082 | 0.828634 | 0.414317 | − | 0.910133i | \(-0.364020\pi\) | ||||
0.414317 | + | 0.910133i | \(0.364020\pi\) | |||||||
\(752\) | −22.0344 | −0.803513 | ||||||||
\(753\) | −2.00000 | −0.0728841 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.38197 | 0.123082 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.0000 | 1.01768 | 0.508839 | − | 0.860862i | \(-0.330075\pi\) | ||||
0.508839 | + | 0.860862i | \(0.330075\pi\) | |||||||
\(758\) | −16.0902 | −0.584421 | ||||||||
\(759\) | 21.7082 | 0.787958 | ||||||||
\(760\) | 36.2705 | 1.31567 | ||||||||
\(761\) | −28.8541 | −1.04596 | −0.522980 | − | 0.852345i | \(-0.675180\pi\) | ||||
−0.522980 | + | 0.852345i | \(0.675180\pi\) | |||||||
\(762\) | 142.936 | 5.17803 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 103.790 | 3.75500 | ||||||||
\(765\) | 14.8541 | 0.537051 | ||||||||
\(766\) | 57.5410 | 2.07904 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −38.1246 | −1.37570 | ||||||||
\(769\) | −18.4164 | −0.664113 | −0.332056 | − | 0.943260i | \(-0.607742\pi\) | ||||
−0.332056 | + | 0.943260i | \(0.607742\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −43.8328 | −1.57860 | ||||||||
\(772\) | 29.1246 | 1.04822 | ||||||||
\(773\) | 25.3607 | 0.912160 | 0.456080 | − | 0.889939i | \(-0.349253\pi\) | ||||
0.456080 | + | 0.889939i | \(0.349253\pi\) | |||||||
\(774\) | −126.756 | −4.55614 | ||||||||
\(775\) | −8.72949 | −0.313573 | ||||||||
\(776\) | −140.880 | −5.05731 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 31.1246 | 1.11587 | ||||||||
\(779\) | −1.41641 | −0.0507481 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −26.2918 | −0.940794 | ||||||||
\(782\) | 17.2361 | 0.616361 | ||||||||
\(783\) | 15.8541 | 0.566579 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −38.8885 | −1.38799 | ||||||||
\(786\) | −105.048 | −3.74692 | ||||||||
\(787\) | 2.58359 | 0.0920951 | 0.0460476 | − | 0.998939i | \(-0.485337\pi\) | ||||
0.0460476 | + | 0.998939i | \(0.485337\pi\) | |||||||
\(788\) | 81.5410 | 2.90478 | ||||||||
\(789\) | 23.5623 | 0.838840 | ||||||||
\(790\) | −27.4164 | −0.975432 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 53.3951 | 1.89731 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −3.70820 | −0.131599 | ||||||||
\(795\) | 25.7984 | 0.914974 | ||||||||
\(796\) | 118.520 | 4.20082 | ||||||||
\(797\) | 8.18034 | 0.289763 | 0.144881 | − | 0.989449i | \(-0.453720\pi\) | ||||
0.144881 | + | 0.989449i | \(0.453720\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.29180 | −0.116455 | ||||||||
\(800\) | −20.1246 | −0.711512 | ||||||||
\(801\) | 18.9230 | 0.668611 | ||||||||
\(802\) | 92.8115 | 3.27729 | ||||||||
\(803\) | 3.70820 | 0.130860 | ||||||||
\(804\) | 161.498 | 5.69561 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 75.2492 | 2.64890 | ||||||||
\(808\) | −86.3951 | −3.03937 | ||||||||
\(809\) | −4.41641 | −0.155273 | −0.0776363 | − | 0.996982i | \(-0.524737\pi\) | ||||
−0.0776363 | + | 0.996982i | \(0.524737\pi\) | |||||||
\(810\) | 39.1246 | 1.37470 | ||||||||
\(811\) | 39.2705 | 1.37897 | 0.689487 | − | 0.724298i | \(-0.257836\pi\) | ||||
0.689487 | + | 0.724298i | \(0.257836\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −22.0344 | −0.772782 | ||||||||
\(814\) | −19.4164 | −0.680545 | ||||||||
\(815\) | 9.70820 | 0.340064 | ||||||||
\(816\) | 37.9787 | 1.32952 | ||||||||
\(817\) | −23.2918 | −0.814877 | ||||||||
\(818\) | −37.7984 | −1.32159 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9.70820 | 0.339025 | ||||||||
\(821\) | 7.36068 | 0.256889 | 0.128445 | − | 0.991717i | \(-0.459002\pi\) | ||||
0.128445 | + | 0.991717i | \(0.459002\pi\) | |||||||
\(822\) | −17.9443 | −0.625878 | ||||||||
\(823\) | −38.4164 | −1.33911 | −0.669556 | − | 0.742762i | \(-0.733516\pi\) | ||||
−0.669556 | + | 0.742762i | \(0.733516\pi\) | |||||||
\(824\) | −65.0689 | −2.26678 | ||||||||
\(825\) | −9.00000 | −0.313340 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −15.9787 | −0.555634 | −0.277817 | − | 0.960634i | \(-0.589611\pi\) | ||||
−0.277817 | + | 0.960634i | \(0.589611\pi\) | |||||||
\(828\) | −83.6656 | −2.90758 | ||||||||
\(829\) | −7.56231 | −0.262650 | −0.131325 | − | 0.991339i | \(-0.541923\pi\) | ||||
−0.131325 | + | 0.991339i | \(0.541923\pi\) | |||||||
\(830\) | −45.9787 | −1.59594 | ||||||||
\(831\) | −13.0902 | −0.454093 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 31.2705 | 1.08281 | ||||||||
\(835\) | 37.2705 | 1.28980 | ||||||||
\(836\) | 16.6869 | 0.577129 | ||||||||
\(837\) | −10.5279 | −0.363896 | ||||||||
\(838\) | −31.2705 | −1.08022 | ||||||||
\(839\) | 13.7426 | 0.474449 | 0.237224 | − | 0.971455i | \(-0.423762\pi\) | ||||
0.237224 | + | 0.971455i | \(0.423762\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.2705 | 0.733466 | ||||||||
\(842\) | 3.70820 | 0.127793 | ||||||||
\(843\) | −52.8328 | −1.81966 | ||||||||
\(844\) | 22.8541 | 0.786671 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 22.5623 | 0.775708 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 37.0902 | 1.27368 | ||||||||
\(849\) | −35.1246 | −1.20547 | ||||||||
\(850\) | −7.14590 | −0.245102 | ||||||||
\(851\) | 17.8885 | 0.613211 | ||||||||
\(852\) | 180.207 | 6.17378 | ||||||||
\(853\) | 14.1246 | 0.483617 | 0.241809 | − | 0.970324i | \(-0.422259\pi\) | ||||
0.241809 | + | 0.970324i | \(0.422259\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −18.7082 | −0.639807 | ||||||||
\(856\) | 25.2705 | 0.863728 | ||||||||
\(857\) | 26.4508 | 0.903544 | 0.451772 | − | 0.892133i | \(-0.350792\pi\) | ||||
0.451772 | + | 0.892133i | \(0.350792\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44.2492 | 1.50976 | 0.754882 | − | 0.655861i | \(-0.227694\pi\) | ||||
0.754882 | + | 0.655861i | \(0.227694\pi\) | |||||||
\(860\) | 159.644 | 5.44383 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 20.4164 | 0.695386 | ||||||||
\(863\) | −11.8885 | −0.404691 | −0.202345 | − | 0.979314i | \(-0.564856\pi\) | ||||
−0.202345 | + | 0.979314i | \(0.564856\pi\) | |||||||
\(864\) | −24.2705 | −0.825700 | ||||||||
\(865\) | 23.5623 | 0.801142 | ||||||||
\(866\) | 2.61803 | 0.0889644 | ||||||||
\(867\) | −38.8328 | −1.31883 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.41641 | −0.251584 | ||||||||
\(870\) | −127.228 | −4.31343 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −20.2361 | −0.685280 | ||||||||
\(873\) | 72.6656 | 2.45936 | ||||||||
\(874\) | −21.7082 | −0.734291 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −25.4164 | −0.858741 | ||||||||
\(877\) | −0.708204 | −0.0239143 | −0.0119572 | − | 0.999929i | \(-0.503806\pi\) | ||||
−0.0119572 | + | 0.999929i | \(0.503806\pi\) | |||||||
\(878\) | 38.8885 | 1.31242 | ||||||||
\(879\) | −17.7082 | −0.597283 | ||||||||
\(880\) | −47.8328 | −1.61244 | ||||||||
\(881\) | 36.5967 | 1.23298 | 0.616488 | − | 0.787364i | \(-0.288555\pi\) | ||||
0.616488 | + | 0.787364i | \(0.288555\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.0000 | 0.975928 | 0.487964 | − | 0.872864i | \(-0.337740\pi\) | ||||
0.487964 | + | 0.872864i | \(0.337740\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −15.3262 | −0.515186 | ||||||||
\(886\) | 13.7082 | 0.460536 | ||||||||
\(887\) | −54.6525 | −1.83505 | −0.917525 | − | 0.397677i | \(-0.869816\pi\) | ||||
−0.917525 | + | 0.397677i | \(0.869816\pi\) | |||||||
\(888\) | 78.2492 | 2.62587 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −33.6525 | −1.12803 | ||||||||
\(891\) | 10.5836 | 0.354564 | ||||||||
\(892\) | 98.3951 | 3.29451 | ||||||||
\(893\) | 4.14590 | 0.138737 | ||||||||
\(894\) | 12.7082 | 0.425026 | ||||||||
\(895\) | −23.5623 | −0.787601 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 51.1246 | 1.70605 | ||||||||
\(899\) | −33.3820 | −1.11335 | ||||||||
\(900\) | 34.6869 | 1.15623 | ||||||||
\(901\) | 5.54102 | 0.184598 | ||||||||
\(902\) | 3.70820 | 0.123470 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −11.0000 | −0.365855 | ||||||||
\(905\) | −25.4164 | −0.844870 | ||||||||
\(906\) | −8.85410 | −0.294158 | ||||||||
\(907\) | −24.0000 | −0.796907 | −0.398453 | − | 0.917189i | \(-0.630453\pi\) | ||||
−0.398453 | + | 0.917189i | \(0.630453\pi\) | |||||||
\(908\) | 7.14590 | 0.237145 | ||||||||
\(909\) | 44.5623 | 1.47804 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.6869 | −0.751651 | −0.375826 | − | 0.926690i | \(-0.622641\pi\) | ||||
−0.375826 | + | 0.926690i | \(0.622641\pi\) | |||||||
\(912\) | −47.8328 | −1.58390 | ||||||||
\(913\) | −12.4377 | −0.411628 | ||||||||
\(914\) | 40.3607 | 1.33501 | ||||||||
\(915\) | 41.1246 | 1.35954 | ||||||||
\(916\) | −63.7082 | −2.10498 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −8.61803 | −0.284438 | ||||||||
\(919\) | −30.0000 | −0.989609 | −0.494804 | − | 0.869004i | \(-0.664760\pi\) | ||||
−0.494804 | + | 0.869004i | \(0.664760\pi\) | |||||||
\(920\) | 87.4853 | 2.88430 | ||||||||
\(921\) | −12.7082 | −0.418750 | ||||||||
\(922\) | 31.9787 | 1.05316 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.41641 | −0.243850 | ||||||||
\(926\) | 17.5623 | 0.577133 | ||||||||
\(927\) | 33.5623 | 1.10233 | ||||||||
\(928\) | −76.9574 | −2.52625 | ||||||||
\(929\) | 11.0689 | 0.363158 | 0.181579 | − | 0.983376i | \(-0.441879\pi\) | ||||
0.181579 | + | 0.983376i | \(0.441879\pi\) | |||||||
\(930\) | 84.4853 | 2.77038 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 12.7082 | 0.416271 | ||||||||
\(933\) | −8.70820 | −0.285094 | ||||||||
\(934\) | 6.14590 | 0.201100 | ||||||||
\(935\) | −7.14590 | −0.233696 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15.8754 | 0.518626 | 0.259313 | − | 0.965793i | \(-0.416504\pi\) | ||||
0.259313 | + | 0.965793i | \(0.416504\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −65.7771 | −2.14655 | ||||||||
\(940\) | −28.4164 | −0.926841 | ||||||||
\(941\) | 20.3475 | 0.663310 | 0.331655 | − | 0.943401i | \(-0.392393\pi\) | ||||
0.331655 | + | 0.943401i | \(0.392393\pi\) | |||||||
\(942\) | 101.812 | 3.31720 | ||||||||
\(943\) | −3.41641 | −0.111254 | ||||||||
\(944\) | −22.0344 | −0.717160 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 60.9787 | 1.98259 | ||||||||
\(947\) | 36.8673 | 1.19802 | 0.599012 | − | 0.800740i | \(-0.295560\pi\) | ||||
0.599012 | + | 0.800740i | \(0.295560\pi\) | |||||||
\(948\) | 50.8328 | 1.65097 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 9.00000 | 0.291999 | ||||||||
\(951\) | −68.6869 | −2.22733 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26.7771 | 0.867395 | 0.433697 | − | 0.901059i | \(-0.357209\pi\) | ||||
0.433697 | + | 0.901059i | \(0.357209\pi\) | |||||||
\(954\) | −37.9787 | −1.22961 | ||||||||
\(955\) | 55.9787 | 1.81143 | ||||||||
\(956\) | 119.936 | 3.87901 | ||||||||
\(957\) | −34.4164 | −1.11252 | ||||||||
\(958\) | −65.3951 | −2.11282 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 59.6869 | 1.92639 | ||||||||
\(961\) | −8.83282 | −0.284930 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13.0344 | −0.420029 | ||||||||
\(964\) | 119.228 | 3.84007 | ||||||||
\(965\) | 15.7082 | 0.505665 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 39.0000 | 1.25416 | 0.627078 | − | 0.778957i | \(-0.284251\pi\) | ||||
0.627078 | + | 0.778957i | \(0.284251\pi\) | |||||||
\(968\) | 56.5066 | 1.81619 | ||||||||
\(969\) | −7.14590 | −0.229559 | ||||||||
\(970\) | −129.228 | −4.14926 | ||||||||
\(971\) | −31.5836 | −1.01357 | −0.506783 | − | 0.862074i | \(-0.669165\pi\) | ||||
−0.506783 | + | 0.862074i | \(0.669165\pi\) | |||||||
\(972\) | −105.103 | −3.37119 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 78.4853 | 2.51483 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 59.1246 | 1.89253 | ||||||||
\(977\) | 22.5279 | 0.720730 | 0.360365 | − | 0.932811i | \(-0.382652\pi\) | ||||
0.360365 | + | 0.932811i | \(0.382652\pi\) | |||||||
\(978\) | −25.4164 | −0.812727 | ||||||||
\(979\) | −9.10333 | −0.290944 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.4377 | 0.333250 | ||||||||
\(982\) | −32.4164 | −1.03445 | ||||||||
\(983\) | 18.3820 | 0.586294 | 0.293147 | − | 0.956067i | \(-0.405298\pi\) | ||||
0.293147 | + | 0.956067i | \(0.405298\pi\) | |||||||
\(984\) | −14.9443 | −0.476406 | ||||||||
\(985\) | 43.9787 | 1.40128 | ||||||||
\(986\) | −27.3262 | −0.870245 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −56.1803 | −1.78643 | ||||||||
\(990\) | 48.9787 | 1.55665 | ||||||||
\(991\) | −16.1459 | −0.512891 | −0.256446 | − | 0.966559i | \(-0.582551\pi\) | ||||
−0.256446 | + | 0.966559i | \(0.582551\pi\) | |||||||
\(992\) | 51.1033 | 1.62253 | ||||||||
\(993\) | 26.5623 | 0.842929 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 63.9230 | 2.02649 | ||||||||
\(996\) | 85.2492 | 2.70123 | ||||||||
\(997\) | −49.0000 | −1.55185 | −0.775923 | − | 0.630828i | \(-0.782715\pi\) | ||||
−0.775923 | + | 0.630828i | \(0.782715\pi\) | |||||||
\(998\) | 38.8885 | 1.23100 | ||||||||
\(999\) | −8.94427 | −0.282984 |
(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 | 8281.2.a.n.1.1 | 2 | ||
7.6 | odd | 2 | 1183.2.a.c.1.1 | 2 | |||
13.4 | even | 6 | 637.2.f.c.393.1 | 4 | |||
13.10 | even | 6 | 637.2.f.c.295.1 | 4 | |||
13.12 | even | 2 | 8281.2.a.bb.1.2 | 2 | |||
91.4 | even | 6 | 637.2.h.f.471.2 | 4 | |||
91.10 | odd | 6 | 637.2.g.b.373.1 | 4 | |||
91.17 | odd | 6 | 637.2.h.g.471.2 | 4 | |||
91.23 | even | 6 | 637.2.h.f.165.2 | 4 | |||
91.30 | even | 6 | 637.2.g.c.263.1 | 4 | |||
91.34 | even | 4 | 1183.2.c.c.337.1 | 4 | |||
91.62 | odd | 6 | 91.2.f.a.22.1 | ✓ | 4 | ||
91.69 | odd | 6 | 91.2.f.a.29.1 | yes | 4 | ||
91.75 | odd | 6 | 637.2.h.g.165.2 | 4 | |||
91.82 | odd | 6 | 637.2.g.b.263.1 | 4 | |||
91.83 | even | 4 | 1183.2.c.c.337.4 | 4 | |||
91.88 | even | 6 | 637.2.g.c.373.1 | 4 | |||
91.90 | odd | 2 | 1183.2.a.g.1.2 | 2 | |||
273.62 | even | 6 | 819.2.o.c.568.2 | 4 | |||
273.251 | even | 6 | 819.2.o.c.757.2 | 4 | |||
364.251 | even | 6 | 1456.2.s.h.1121.1 | 4 | |||
364.335 | even | 6 | 1456.2.s.h.113.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.f.a.22.1 | ✓ | 4 | 91.62 | odd | 6 | ||
91.2.f.a.29.1 | yes | 4 | 91.69 | odd | 6 | ||
637.2.f.c.295.1 | 4 | 13.10 | even | 6 | |||
637.2.f.c.393.1 | 4 | 13.4 | even | 6 | |||
637.2.g.b.263.1 | 4 | 91.82 | odd | 6 | |||
637.2.g.b.373.1 | 4 | 91.10 | odd | 6 | |||
637.2.g.c.263.1 | 4 | 91.30 | even | 6 | |||
637.2.g.c.373.1 | 4 | 91.88 | even | 6 | |||
637.2.h.f.165.2 | 4 | 91.23 | even | 6 | |||
637.2.h.f.471.2 | 4 | 91.4 | even | 6 | |||
637.2.h.g.165.2 | 4 | 91.75 | odd | 6 | |||
637.2.h.g.471.2 | 4 | 91.17 | odd | 6 | |||
819.2.o.c.568.2 | 4 | 273.62 | even | 6 | |||
819.2.o.c.757.2 | 4 | 273.251 | even | 6 | |||
1183.2.a.c.1.1 | 2 | 7.6 | odd | 2 | |||
1183.2.a.g.1.2 | 2 | 91.90 | odd | 2 | |||
1183.2.c.c.337.1 | 4 | 91.34 | even | 4 | |||
1183.2.c.c.337.4 | 4 | 91.83 | even | 4 | |||
1456.2.s.h.113.1 | 4 | 364.335 | even | 6 | |||
1456.2.s.h.1121.1 | 4 | 364.251 | even | 6 | |||
8281.2.a.n.1.1 | 2 | 1.1 | even | 1 | trivial | ||
8281.2.a.bb.1.2 | 2 | 13.12 | even | 2 |