Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1183,2,Mod(1,1183)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1183, 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("1183.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1183 = 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1183.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: | \(9.44630255912\) |
Analytic rank: | \(1\) |
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 | \(\chi\) | \(=\) | 1183.1 |
$q$-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 | \(-0.772733\pi\) | ||||
−0.755761 | + | 0.654847i | \(0.772733\pi\) | |||||||
\(4\) | 4.85410 | 2.42705 | ||||||||
\(5\) | −2.61803 | −1.17082 | −0.585410 | − | 0.810737i | \(-0.699067\pi\) | ||||
−0.585410 | + | 0.810737i | \(0.699067\pi\) | |||||||
\(6\) | 6.85410 | 2.79818 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −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 | ||||||||
\(14\) | 2.61803 | 0.699699 | ||||||||
\(15\) | 6.85410 | 1.76972 | ||||||||
\(16\) | 9.85410 | 2.46353 | ||||||||
\(17\) | −1.47214 | −0.357045 | −0.178523 | − | 0.983936i | \(-0.557132\pi\) | ||||
−0.178523 | + | 0.983936i | \(0.557132\pi\) | |||||||
\(18\) | −10.0902 | −2.37828 | ||||||||
\(19\) | 1.85410 | 0.425360 | 0.212680 | − | 0.977122i | \(-0.431781\pi\) | ||||
0.212680 | + | 0.977122i | \(0.431781\pi\) | |||||||
\(20\) | −12.7082 | −2.84164 | ||||||||
\(21\) | 2.61803 | 0.571302 | ||||||||
\(22\) | 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 | ||||||||
\(28\) | −4.85410 | −0.917339 | ||||||||
\(29\) | 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 | \(-0.361044\pi\) | ||||
0.422809 | + | 0.906219i | \(0.361044\pi\) | |||||||
\(32\) | −10.8541 | −1.91875 | ||||||||
\(33\) | 4.85410 | 0.844991 | ||||||||
\(34\) | 3.85410 | 0.660973 | ||||||||
\(35\) | 2.61803 | 0.442529 | ||||||||
\(36\) | 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 | \(-0.518999\pi\) | ||||
−0.0596531 | + | 0.998219i | \(0.518999\pi\) | |||||||
\(42\) | −6.85410 | −1.05761 | ||||||||
\(43\) | 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 | \(-0.447856\pi\) | ||||
0.163082 | + | 0.986613i | \(0.447856\pi\) | |||||||
\(48\) | −25.7984 | −3.72367 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −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 | ||||||||
\(56\) | 7.47214 | 0.998506 | ||||||||
\(57\) | −4.85410 | −0.642942 | ||||||||
\(58\) | −18.5623 | −2.43735 | ||||||||
\(59\) | 2.23607 | 0.291111 | 0.145556 | − | 0.989350i | \(-0.453503\pi\) | ||||
0.145556 | + | 0.989350i | \(0.453503\pi\) | |||||||
\(60\) | 33.2705 | 4.29520 | ||||||||
\(61\) | −6.00000 | −0.768221 | −0.384111 | − | 0.923287i | \(-0.625492\pi\) | ||||
−0.384111 | + | 0.923287i | \(0.625492\pi\) | |||||||
\(62\) | −12.3262 | −1.56543 | ||||||||
\(63\) | −3.85410 | −0.485571 | ||||||||
\(64\) | 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 | ||||||||
\(70\) | −6.85410 | −0.819222 | ||||||||
\(71\) | 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 | \(-0.462659\pi\) | ||||
0.117041 | + | 0.993127i | \(0.462659\pi\) | |||||||
\(74\) | 10.4721 | 1.21736 | ||||||||
\(75\) | −4.85410 | −0.560503 | ||||||||
\(76\) | 9.00000 | 1.03237 | ||||||||
\(77\) | 1.85410 | 0.211295 | ||||||||
\(78\) | 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 | \(-0.620012\pi\) | ||||
−0.368161 | + | 0.929762i | \(0.620012\pi\) | |||||||
\(84\) | 12.7082 | 1.38658 | ||||||||
\(85\) | 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 | \(-0.583795\pi\) | ||||
−0.260220 | + | 0.965549i | \(0.583795\pi\) | |||||||
\(90\) | 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 | \(-0.906504\pi\) | ||||
−0.957172 | + | 0.289520i | \(0.906504\pi\) | |||||||
\(98\) | −2.61803 | −0.264461 | ||||||||
\(99\) | −7.14590 | −0.718190 | ||||||||
\(100\) | 9.00000 | 0.900000 | ||||||||
\(101\) | −11.5623 | −1.15049 | −0.575246 | − | 0.817980i | \(-0.695094\pi\) | ||||
−0.575246 | + | 0.817980i | \(0.695094\pi\) | |||||||
\(102\) | −10.0902 | −0.999076 | ||||||||
\(103\) | −8.70820 | −0.858045 | −0.429022 | − | 0.903294i | \(-0.641142\pi\) | ||||
−0.429022 | + | 0.903294i | \(0.641142\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.85410 | −0.668892 | ||||||||
\(106\) | −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 | ||||||||
\(112\) | −9.85410 | −0.931125 | ||||||||
\(113\) | 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 | ||||||||
\(119\) | 1.47214 | 0.134950 | ||||||||
\(120\) | −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 | ||||||||
\(126\) | 10.0902 | 0.898904 | ||||||||
\(127\) | −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 | \(-0.733504\pi\) | ||||
−0.669530 | + | 0.742785i | \(0.733504\pi\) | |||||||
\(132\) | 23.5623 | 2.05084 | ||||||||
\(133\) | −1.85410 | −0.160771 | ||||||||
\(134\) | −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 | \(-0.438021\pi\) | ||||
0.193485 | + | 0.981103i | \(0.438021\pi\) | |||||||
\(140\) | 12.7082 | 1.07404 | ||||||||
\(141\) | −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 | ||||||||
\(147\) | −2.61803 | −0.215932 | ||||||||
\(148\) | −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 | ||||||||
\(154\) | −4.85410 | −0.391155 | ||||||||
\(155\) | −12.3262 | −0.990067 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.8541 | 1.18549 | 0.592743 | − | 0.805392i | \(-0.298045\pi\) | ||||
0.592743 | + | 0.805392i | \(0.298045\pi\) | |||||||
\(158\) | −10.4721 | −0.833118 | ||||||||
\(159\) | −9.85410 | −0.781481 | ||||||||
\(160\) | 28.4164 | 2.24651 | ||||||||
\(161\) | 4.47214 | 0.352454 | ||||||||
\(162\) | 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 | \(-0.685681\pi\) | ||||
−0.550810 | + | 0.834631i | \(0.685681\pi\) | |||||||
\(168\) | −19.5623 | −1.50926 | ||||||||
\(169\) | 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 | \(-0.611148\pi\) | ||||
−0.342129 | + | 0.939653i | \(0.611148\pi\) | |||||||
\(174\) | 48.5967 | 3.68411 | ||||||||
\(175\) | −1.85410 | −0.140157 | ||||||||
\(176\) | −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 | \(-0.382503\pi\) | ||||
0.360803 | + | 0.932642i | \(0.382503\pi\) | |||||||
\(182\) | 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 | ||||||||
\(189\) | 2.23607 | 0.162650 | ||||||||
\(190\) | 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 | ||||||||
\(196\) | 4.85410 | 0.346722 | ||||||||
\(197\) | 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 | \(-0.832946\pi\) | ||||
−0.865417 | + | 0.501053i | \(0.832946\pi\) | |||||||
\(200\) | −13.8541 | −0.979633 | ||||||||
\(201\) | −33.2705 | −2.34672 | ||||||||
\(202\) | 30.2705 | 2.12983 | ||||||||
\(203\) | −7.09017 | −0.497632 | ||||||||
\(204\) | 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 | ||||||||
\(210\) | 17.9443 | 1.23827 | ||||||||
\(211\) | 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 | ||||||||
\(217\) | −4.70820 | −0.319614 | ||||||||
\(218\) | −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 | \(-0.737459\pi\) | ||||
−0.678707 | + | 0.734409i | \(0.737459\pi\) | |||||||
\(224\) | 10.8541 | 0.725220 | ||||||||
\(225\) | 7.14590 | 0.476393 | ||||||||
\(226\) | −3.85410 | −0.256371 | ||||||||
\(227\) | −1.47214 | −0.0977091 | −0.0488545 | − | 0.998806i | \(-0.515557\pi\) | ||||
−0.0488545 | + | 0.998806i | \(0.515557\pi\) | |||||||
\(228\) | −23.5623 | −1.56045 | ||||||||
\(229\) | 13.1246 | 0.867299 | 0.433649 | − | 0.901082i | \(-0.357226\pi\) | ||||
0.433649 | + | 0.901082i | \(0.357226\pi\) | |||||||
\(230\) | −30.6525 | −2.02116 | ||||||||
\(231\) | −4.85410 | −0.319376 | ||||||||
\(232\) | −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 | ||||||||
\(238\) | −3.85410 | −0.249824 | ||||||||
\(239\) | 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 | \(-0.790491\pi\) | ||||
−0.791099 | + | 0.611689i | \(0.790491\pi\) | |||||||
\(242\) | 19.7984 | 1.27269 | ||||||||
\(243\) | 21.6525 | 1.38901 | ||||||||
\(244\) | −29.1246 | −1.86451 | ||||||||
\(245\) | −2.61803 | −0.167260 | ||||||||
\(246\) | −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 | \(-0.492325\pi\) | ||||
0.0241095 | + | 0.999709i | \(0.492325\pi\) | |||||||
\(252\) | −18.7082 | −1.17851 | ||||||||
\(253\) | 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 | \(-0.325116\pi\) | ||||
0.522189 | + | 0.852830i | \(0.325116\pi\) | |||||||
\(258\) | 86.1033 | 5.36056 | ||||||||
\(259\) | 4.00000 | 0.248548 | ||||||||
\(260\) | 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 | ||||||||
\(266\) | 4.85410 | 0.297624 | ||||||||
\(267\) | 12.8541 | 0.786658 | ||||||||
\(268\) | 61.6869 | 3.76813 | ||||||||
\(269\) | −28.7426 | −1.75247 | −0.876235 | − | 0.481884i | \(-0.839953\pi\) | ||||
−0.876235 | + | 0.481884i | \(0.839953\pi\) | |||||||
\(270\) | −15.3262 | −0.932725 | ||||||||
\(271\) | 8.41641 | 0.511260 | 0.255630 | − | 0.966775i | \(-0.417717\pi\) | ||||
0.255630 | + | 0.966775i | \(0.417717\pi\) | |||||||
\(272\) | −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 | ||||||||
\(280\) | −19.5623 | −1.16907 | ||||||||
\(281\) | −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 | \(-0.369440\pi\) | ||||
0.398761 | + | 0.917055i | \(0.369440\pi\) | |||||||
\(284\) | 68.8328 | 4.08448 | ||||||||
\(285\) | 12.7082 | 0.752769 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.763932 | 0.0450935 | ||||||||
\(288\) | −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 | \(-0.436693\pi\) | ||||
0.197577 | + | 0.980287i | \(0.436693\pi\) | |||||||
\(294\) | 6.85410 | 0.399739 | ||||||||
\(295\) | −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 | ||||||||
\(301\) | −12.5623 | −0.724079 | ||||||||
\(302\) | −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 | \(-0.455766\pi\) | ||||
0.138519 | + | 0.990360i | \(0.455766\pi\) | |||||||
\(308\) | 9.00000 | 0.512823 | ||||||||
\(309\) | 22.7984 | 1.29695 | ||||||||
\(310\) | 32.2705 | 1.83284 | ||||||||
\(311\) | 3.32624 | 0.188614 | 0.0943068 | − | 0.995543i | \(-0.469937\pi\) | ||||
0.0943068 | + | 0.995543i | \(0.469937\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.1246 | 1.42013 | 0.710064 | − | 0.704138i | \(-0.248666\pi\) | ||||
0.710064 | + | 0.704138i | \(0.248666\pi\) | |||||||
\(314\) | −38.8885 | −2.19461 | ||||||||
\(315\) | 10.0902 | 0.568517 | ||||||||
\(316\) | 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 | ||||||||
\(322\) | −11.7082 | −0.652473 | ||||||||
\(323\) | −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 | ||||||||
\(329\) | −2.23607 | −0.123278 | ||||||||
\(330\) | 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 | ||||||||
\(336\) | 25.7984 | 1.40742 | ||||||||
\(337\) | −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 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −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 | \(-0.686992\pi\) | ||||
−0.554242 | + | 0.832355i | \(0.686992\pi\) | |||||||
\(350\) | 4.85410 | 0.259463 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 20.1246 | 1.07265 | ||||||||
\(353\) | −22.1459 | −1.17871 | −0.589354 | − | 0.807875i | \(-0.700618\pi\) | ||||
−0.589354 | + | 0.807875i | \(0.700618\pi\) | |||||||
\(354\) | 15.3262 | 0.814580 | ||||||||
\(355\) | −37.1246 | −1.97037 | ||||||||
\(356\) | −23.8328 | −1.26314 | ||||||||
\(357\) | −3.85410 | −0.203981 | ||||||||
\(358\) | 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 | \(-0.511770\pi\) | ||||
−0.0369679 | + | 0.999316i | \(0.511770\pi\) | |||||||
\(368\) | −44.0689 | −2.29725 | ||||||||
\(369\) | −2.94427 | −0.153273 | ||||||||
\(370\) | −27.4164 | −1.42531 | ||||||||
\(371\) | −3.76393 | −0.195414 | ||||||||
\(372\) | −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 | ||||||||
\(378\) | −5.85410 | −0.301103 | ||||||||
\(379\) | 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 | \(-0.310213\pi\) | ||||
0.561530 | + | 0.827456i | \(0.310213\pi\) | |||||||
\(384\) | 2.85410 | 0.145648 | ||||||||
\(385\) | −4.85410 | −0.247388 | ||||||||
\(386\) | −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 | ||||||||
\(392\) | −7.47214 | −0.377400 | ||||||||
\(393\) | 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 | \(-0.511316\pi\) | ||||
−0.0355437 | + | 0.999368i | \(0.511316\pi\) | |||||||
\(398\) | 63.9230 | 3.20417 | ||||||||
\(399\) | 4.85410 | 0.243009 | ||||||||
\(400\) | 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 | ||||||||
\(406\) | 18.5623 | 0.921232 | ||||||||
\(407\) | 7.41641 | 0.367618 | ||||||||
\(408\) | −28.7984 | −1.42573 | ||||||||
\(409\) | −14.4377 | −0.713898 | −0.356949 | − | 0.934124i | \(-0.616183\pi\) | ||||
−0.356949 | + | 0.934124i | \(0.616183\pi\) | |||||||
\(410\) | −5.23607 | −0.258591 | ||||||||
\(411\) | −6.85410 | −0.338088 | ||||||||
\(412\) | −42.2705 | −2.08252 | ||||||||
\(413\) | −2.23607 | −0.110030 | ||||||||
\(414\) | 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 | \(-0.594240\pi\) | ||||
−0.291758 | + | 0.956492i | \(0.594240\pi\) | |||||||
\(420\) | −33.2705 | −1.62343 | ||||||||
\(421\) | −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 | ||||||||
\(427\) | 6.00000 | 0.290360 | ||||||||
\(428\) | −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 | \(-0.492351\pi\) | ||||
0.0240285 | + | 0.999711i | \(0.492351\pi\) | |||||||
\(434\) | 12.3262 | 0.591678 | ||||||||
\(435\) | 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 | \(-0.384660\pi\) | ||||
0.354474 | + | 0.935066i | \(0.384660\pi\) | |||||||
\(440\) | −36.2705 | −1.72913 | ||||||||
\(441\) | 3.85410 | 0.183529 | ||||||||
\(442\) | 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 | ||||||||
\(448\) | −8.70820 | −0.411424 | ||||||||
\(449\) | −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 | \(-0.408189\pi\) | ||||
0.284450 | + | 0.958691i | \(0.408189\pi\) | |||||||
\(462\) | 12.7082 | 0.591239 | ||||||||
\(463\) | −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 | \(-0.482702\pi\) | ||||
0.0543152 | + | 0.998524i | \(0.482702\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.7082 | −0.586810 | ||||||||
\(470\) | 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 | ||||||||
\(476\) | 7.14590 | 0.327532 | ||||||||
\(477\) | 14.5066 | 0.664211 | ||||||||
\(478\) | −64.6869 | −2.95871 | ||||||||
\(479\) | −24.9787 | −1.14131 | −0.570653 | − | 0.821191i | \(-0.693310\pi\) | ||||
−0.570653 | + | 0.821191i | \(0.693310\pi\) | |||||||
\(480\) | −74.3951 | −3.39566 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 64.3050 | 2.92901 | ||||||||
\(483\) | −11.7082 | −0.532742 | ||||||||
\(484\) | −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 | ||||||||
\(490\) | 6.85410 | 0.309637 | ||||||||
\(491\) | 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 | ||||||||
\(497\) | −14.1803 | −0.636075 | ||||||||
\(498\) | −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 | \(-0.297777\pi\) | ||||
0.593420 | + | 0.804893i | \(0.297777\pi\) | |||||||
\(504\) | 28.7984 | 1.28278 | ||||||||
\(505\) | 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 | \(-0.364780\pi\) | ||||
0.412143 | + | 0.911119i | \(0.364780\pi\) | |||||||
\(510\) | 26.4164 | 1.16974 | ||||||||
\(511\) | −2.00000 | −0.0884748 | ||||||||
\(512\) | 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 | ||||||||
\(518\) | −10.4721 | −0.460119 | ||||||||
\(519\) | 23.5623 | 1.03427 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.6525 | 0.817180 | 0.408590 | − | 0.912718i | \(-0.366021\pi\) | ||||
0.408590 | + | 0.912718i | \(0.366021\pi\) | |||||||
\(522\) | −71.5410 | −3.13127 | ||||||||
\(523\) | 1.12461 | 0.0491758 | 0.0245879 | − | 0.999698i | \(-0.492173\pi\) | ||||
0.0245879 | + | 0.999698i | \(0.492173\pi\) | |||||||
\(524\) | −74.3951 | −3.24997 | ||||||||
\(525\) | 4.85410 | 0.211850 | ||||||||
\(526\) | −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 | ||||||||
\(532\) | −9.00000 | −0.390199 | ||||||||
\(533\) | 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 | ||||||||
\(539\) | −1.85410 | −0.0798618 | ||||||||
\(540\) | 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 | ||||||||
\(553\) | −4.00000 | −0.170097 | ||||||||
\(554\) | 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 | ||||||||
\(560\) | 25.7984 | 1.09018 | ||||||||
\(561\) | −7.14590 | −0.301700 | ||||||||
\(562\) | 52.8328 | 2.22862 | ||||||||
\(563\) | −21.0557 | −0.887393 | −0.443697 | − | 0.896177i | \(-0.646333\pi\) | ||||
−0.443697 | + | 0.896177i | \(0.646333\pi\) | |||||||
\(564\) | −28.4164 | −1.19655 | ||||||||
\(565\) | −3.85410 | −0.162143 | ||||||||
\(566\) | −35.1246 | −1.47640 | ||||||||
\(567\) | 5.70820 | 0.239722 | ||||||||
\(568\) | −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 | ||||||||
\(574\) | −2.00000 | −0.0834784 | ||||||||
\(575\) | −8.29180 | −0.345792 | ||||||||
\(576\) | 33.5623 | 1.39843 | ||||||||
\(577\) | 43.8328 | 1.82478 | 0.912392 | − | 0.409318i | \(-0.134233\pi\) | ||||
0.912392 | + | 0.409318i | \(0.134233\pi\) | |||||||
\(578\) | 38.8328 | 1.61523 | ||||||||
\(579\) | −15.7082 | −0.652811 | ||||||||
\(580\) | −90.1033 | −3.74134 | ||||||||
\(581\) | 6.70820 | 0.278303 | ||||||||
\(582\) | −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 | \(-0.365220\pi\) | ||||
0.410883 | + | 0.911688i | \(0.365220\pi\) | |||||||
\(588\) | −12.7082 | −0.524077 | ||||||||
\(589\) | 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 | \(-0.855917\pi\) | ||||
−0.899292 | + | 0.437349i | \(0.855917\pi\) | |||||||
\(594\) | −10.8541 | −0.445349 | ||||||||
\(595\) | −3.85410 | −0.158003 | ||||||||
\(596\) | −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 | \(-0.191807\pi\) | ||||
0.823876 | + | 0.566771i | \(0.191807\pi\) | |||||||
\(602\) | 32.8885 | 1.34044 | ||||||||
\(603\) | 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 | \(-0.654583\pi\) | ||||
−0.466771 | + | 0.884378i | \(0.654583\pi\) | |||||||
\(608\) | −20.1246 | −0.816161 | ||||||||
\(609\) | 18.5623 | 0.752183 | ||||||||
\(610\) | −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 | ||||||||
\(616\) | −13.8541 | −0.558198 | ||||||||
\(617\) | −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 | \(-0.560602\pi\) | ||||
−0.189239 | + | 0.981931i | \(0.560602\pi\) | |||||||
\(620\) | −59.8328 | −2.40294 | ||||||||
\(621\) | 10.0000 | 0.401286 | ||||||||
\(622\) | −8.70820 | −0.349167 | ||||||||
\(623\) | 4.90983 | 0.196708 | ||||||||
\(624\) | 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 | ||||||||
\(630\) | −26.4164 | −1.05245 | ||||||||
\(631\) | −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 | \(-0.455924\pi\) | ||||
0.138027 | + | 0.990429i | \(0.455924\pi\) | |||||||
\(644\) | 21.7082 | 0.855423 | ||||||||
\(645\) | 86.1033 | 3.39032 | ||||||||
\(646\) | 7.14590 | 0.281152 | ||||||||
\(647\) | 24.7639 | 0.973571 | 0.486785 | − | 0.873522i | \(-0.338169\pi\) | ||||
0.486785 | + | 0.873522i | \(0.338169\pi\) | |||||||
\(648\) | 42.6525 | 1.67555 | ||||||||
\(649\) | −4.14590 | −0.162741 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.3262 | 0.483103 | ||||||||
\(652\) | 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 | ||||||||
\(658\) | 5.85410 | 0.228217 | ||||||||
\(659\) | −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 | \(-0.107017\pi\) | ||||
0.944013 | + | 0.329907i | \(0.107017\pi\) | |||||||
\(662\) | −26.5623 | −1.03237 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 50.1246 | 1.94521 | ||||||||
\(665\) | 4.85410 | 0.188234 | ||||||||
\(666\) | 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 | ||||||||
\(672\) | −28.4164 | −1.09619 | ||||||||
\(673\) | −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 | \(-0.182212\pi\) | ||||
0.840583 | + | 0.541682i | \(0.182212\pi\) | |||||||
\(678\) | 10.0902 | 0.387511 | ||||||||
\(679\) | 18.8541 | 0.723554 | ||||||||
\(680\) | −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 | ||||||||
\(686\) | 2.61803 | 0.0999570 | ||||||||
\(687\) | −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 | \(-0.464482\pi\) | ||||
0.111350 | + | 0.993781i | \(0.464482\pi\) | |||||||
\(692\) | −43.6869 | −1.66073 | ||||||||
\(693\) | 7.14590 | 0.271450 | ||||||||
\(694\) | −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 | ||||||||
\(700\) | −9.00000 | −0.340168 | ||||||||
\(701\) | 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 | ||||||||
\(707\) | 11.5623 | 0.434845 | ||||||||
\(708\) | −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 | ||||||||
\(714\) | 10.0902 | 0.377615 | ||||||||
\(715\) | 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 | \(-0.451590\pi\) | ||||
0.151498 | + | 0.988457i | \(0.451590\pi\) | |||||||
\(720\) | −99.4296 | −3.70552 | ||||||||
\(721\) | 8.70820 | 0.324310 | ||||||||
\(722\) | 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 | \(-0.692845\pi\) | ||||
−0.569452 | + | 0.822025i | \(0.692845\pi\) | |||||||
\(728\) | 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 | \(-0.296768\pi\) | ||||
0.595969 | + | 0.803007i | \(0.296768\pi\) | |||||||
\(734\) | 3.70820 | 0.136872 | ||||||||
\(735\) | 6.85410 | 0.252817 | ||||||||
\(736\) | 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 | ||||||||
\(742\) | 9.85410 | 0.361755 | ||||||||
\(743\) | −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 | ||||||||
\(749\) | 3.38197 | 0.123574 | ||||||||
\(750\) | 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 | ||||||||
\(756\) | 10.8541 | 0.394760 | ||||||||
\(757\) | 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 | \(-0.324820\pi\) | ||||
0.522980 | + | 0.852345i | \(0.324820\pi\) | |||||||
\(762\) | −142.936 | −5.17803 | ||||||||
\(763\) | −2.70820 | −0.0980436 | ||||||||
\(764\) | 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 | \(-0.392258\pi\) | ||||
0.332056 | + | 0.943260i | \(0.392258\pi\) | |||||||
\(770\) | 12.7082 | 0.457972 | ||||||||
\(771\) | −43.8328 | −1.57860 | ||||||||
\(772\) | 29.1246 | 1.04822 | ||||||||
\(773\) | −25.3607 | −0.912160 | −0.456080 | − | 0.889939i | \(-0.650747\pi\) | ||||
−0.456080 | + | 0.889939i | \(0.650747\pi\) | |||||||
\(774\) | −126.756 | −4.55614 | ||||||||
\(775\) | 8.72949 | 0.313573 | ||||||||
\(776\) | 140.880 | 5.05731 | ||||||||
\(777\) | −10.4721 | −0.375686 | ||||||||
\(778\) | 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 | ||||||||
\(784\) | 9.85410 | 0.351932 | ||||||||
\(785\) | −38.8885 | −1.38799 | ||||||||
\(786\) | −105.048 | −3.74692 | ||||||||
\(787\) | −2.58359 | −0.0920951 | −0.0460476 | − | 0.998939i | \(-0.514663\pi\) | ||||
−0.0460476 | + | 0.998939i | \(0.514663\pi\) | |||||||
\(788\) | 81.5410 | 2.90478 | ||||||||
\(789\) | −23.5623 | −0.838840 | ||||||||
\(790\) | 27.4164 | 0.975432 | ||||||||
\(791\) | −1.47214 | −0.0523431 | ||||||||
\(792\) | 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 | \(-0.546280\pi\) | ||||
−0.144881 | + | 0.989449i | \(0.546280\pi\) | |||||||
\(798\) | −12.7082 | −0.449866 | ||||||||
\(799\) | −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 | ||||||||
\(805\) | −11.7082 | −0.412660 | ||||||||
\(806\) | 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 | \(-0.742164\pi\) | ||||
−0.689487 | + | 0.724298i | \(0.742164\pi\) | |||||||
\(812\) | −34.4164 | −1.20778 | ||||||||
\(813\) | −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 | ||||||||
\(826\) | 5.85410 | 0.203690 | ||||||||
\(827\) | −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 | \(-0.458077\pi\) | ||||
0.131325 | + | 0.991339i | \(0.458077\pi\) | |||||||
\(830\) | −45.9787 | −1.59594 | ||||||||
\(831\) | 13.0902 | 0.454093 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.47214 | −0.0510065 | ||||||||
\(834\) | 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 | \(-0.576238\pi\) | ||||
−0.237224 | + | 0.971455i | \(0.576238\pi\) | |||||||
\(840\) | 51.2148 | 1.76708 | ||||||||
\(841\) | 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 | ||||||||
\(847\) | 7.56231 | 0.259844 | ||||||||
\(848\) | 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 | \(-0.577741\pi\) | ||||
−0.241809 | + | 0.970324i | \(0.577741\pi\) | |||||||
\(854\) | −15.7082 | −0.537524 | ||||||||
\(855\) | −18.7082 | −0.639807 | ||||||||
\(856\) | 25.2705 | 0.863728 | ||||||||
\(857\) | −26.4508 | −0.903544 | −0.451772 | − | 0.892133i | \(-0.649208\pi\) | ||||
−0.451772 | + | 0.892133i | \(0.649208\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −44.2492 | −1.50976 | −0.754882 | − | 0.655861i | \(-0.772306\pi\) | ||||
−0.754882 | + | 0.655861i | \(0.772306\pi\) | |||||||
\(860\) | −159.644 | −5.44383 | ||||||||
\(861\) | −2.00000 | −0.0681598 | ||||||||
\(862\) | 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 | ||||||||
\(868\) | −22.8541 | −0.775719 | ||||||||
\(869\) | −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 | ||||||||
\(875\) | −8.23607 | −0.278430 | ||||||||
\(876\) | −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 | \(-0.711445\pi\) | ||||
−0.616488 | + | 0.787364i | \(0.711445\pi\) | |||||||
\(882\) | −10.0902 | −0.339754 | ||||||||
\(883\) | 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 | \(-0.130184\pi\) | ||||
0.917525 | + | 0.397677i | \(0.130184\pi\) | |||||||
\(888\) | −78.2492 | −2.62587 | ||||||||
\(889\) | 20.8541 | 0.699424 | ||||||||
\(890\) | −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 | ||||||||
\(896\) | 1.09017 | 0.0364200 | ||||||||
\(897\) | 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 | ||||||||
\(903\) | 32.8885 | 1.09446 | ||||||||
\(904\) | −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 | ||||||||
\(917\) | 15.3262 | 0.506117 | ||||||||
\(918\) | −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 | ||||||||
\(924\) | −23.5623 | −0.775143 | ||||||||
\(925\) | −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 | \(-0.558121\pi\) | ||||
−0.181579 | + | 0.983376i | \(0.558121\pi\) | |||||||
\(930\) | −84.4853 | −2.77038 | ||||||||
\(931\) | 1.85410 | 0.0607657 | ||||||||
\(932\) | 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 | \(-0.583496\pi\) | ||||
−0.259313 | + | 0.965793i | \(0.583496\pi\) | |||||||
\(938\) | 33.2705 | 1.08632 | ||||||||
\(939\) | −65.7771 | −2.14655 | ||||||||
\(940\) | −28.4164 | −0.926841 | ||||||||
\(941\) | −20.3475 | −0.663310 | −0.331655 | − | 0.943401i | \(-0.607607\pi\) | ||||
−0.331655 | + | 0.943401i | \(0.607607\pi\) | |||||||
\(942\) | 101.812 | 3.31720 | ||||||||
\(943\) | 3.41641 | 0.111254 | ||||||||
\(944\) | 22.0344 | 0.717160 | ||||||||
\(945\) | −5.85410 | −0.190434 | ||||||||
\(946\) | 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 | ||||||||
\(952\) | −11.0000 | −0.356512 | ||||||||
\(953\) | 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 | ||||||||
\(959\) | −2.61803 | −0.0845407 | ||||||||
\(960\) | 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 | ||||||||
\(966\) | 30.6525 | 0.986227 | ||||||||
\(967\) | 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 | \(-0.330835\pi\) | ||||
0.506783 | + | 0.862074i | \(0.330835\pi\) | |||||||
\(972\) | 105.103 | 3.37119 | ||||||||
\(973\) | −4.56231 | −0.146261 | ||||||||
\(974\) | 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 | ||||||||
\(980\) | −12.7082 | −0.405949 | ||||||||
\(981\) | 10.4377 | 0.333250 | ||||||||
\(982\) | −32.4164 | −1.03445 | ||||||||
\(983\) | −18.3820 | −0.586294 | −0.293147 | − | 0.956067i | \(-0.594702\pi\) | ||||
−0.293147 | + | 0.956067i | \(0.594702\pi\) | |||||||
\(984\) | −14.9443 | −0.476406 | ||||||||
\(985\) | −43.9787 | −1.40128 | ||||||||
\(986\) | 27.3262 | 0.870245 | ||||||||
\(987\) | 5.85410 | 0.186338 | ||||||||
\(988\) | 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 | ||||||||
\(994\) | 37.1246 | 1.17752 | ||||||||
\(995\) | 63.9230 | 2.02649 | ||||||||
\(996\) | 85.2492 | 2.70123 | ||||||||
\(997\) | 49.0000 | 1.55185 | 0.775923 | − | 0.630828i | \(-0.217285\pi\) | ||||
0.775923 | + | 0.630828i | \(0.217285\pi\) | |||||||
\(998\) | 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 | 1183.2.a.c.1.1 | 2 | ||
7.6 | odd | 2 | 8281.2.a.n.1.1 | 2 | |||
13.4 | even | 6 | 91.2.f.a.29.1 | yes | 4 | ||
13.5 | odd | 4 | 1183.2.c.c.337.4 | 4 | |||
13.8 | odd | 4 | 1183.2.c.c.337.1 | 4 | |||
13.10 | even | 6 | 91.2.f.a.22.1 | ✓ | 4 | ||
13.12 | even | 2 | 1183.2.a.g.1.2 | 2 | |||
39.17 | odd | 6 | 819.2.o.c.757.2 | 4 | |||
39.23 | odd | 6 | 819.2.o.c.568.2 | 4 | |||
52.23 | odd | 6 | 1456.2.s.h.113.1 | 4 | |||
52.43 | odd | 6 | 1456.2.s.h.1121.1 | 4 | |||
91.4 | even | 6 | 637.2.h.g.471.2 | 4 | |||
91.10 | odd | 6 | 637.2.g.c.373.1 | 4 | |||
91.17 | odd | 6 | 637.2.h.f.471.2 | 4 | |||
91.23 | even | 6 | 637.2.h.g.165.2 | 4 | |||
91.30 | even | 6 | 637.2.g.b.263.1 | 4 | |||
91.62 | odd | 6 | 637.2.f.c.295.1 | 4 | |||
91.69 | odd | 6 | 637.2.f.c.393.1 | 4 | |||
91.75 | odd | 6 | 637.2.h.f.165.2 | 4 | |||
91.82 | odd | 6 | 637.2.g.c.263.1 | 4 | |||
91.88 | even | 6 | 637.2.g.b.373.1 | 4 | |||
91.90 | odd | 2 | 8281.2.a.bb.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.f.a.22.1 | ✓ | 4 | 13.10 | even | 6 | ||
91.2.f.a.29.1 | yes | 4 | 13.4 | even | 6 | ||
637.2.f.c.295.1 | 4 | 91.62 | odd | 6 | |||
637.2.f.c.393.1 | 4 | 91.69 | odd | 6 | |||
637.2.g.b.263.1 | 4 | 91.30 | even | 6 | |||
637.2.g.b.373.1 | 4 | 91.88 | even | 6 | |||
637.2.g.c.263.1 | 4 | 91.82 | odd | 6 | |||
637.2.g.c.373.1 | 4 | 91.10 | odd | 6 | |||
637.2.h.f.165.2 | 4 | 91.75 | odd | 6 | |||
637.2.h.f.471.2 | 4 | 91.17 | odd | 6 | |||
637.2.h.g.165.2 | 4 | 91.23 | even | 6 | |||
637.2.h.g.471.2 | 4 | 91.4 | even | 6 | |||
819.2.o.c.568.2 | 4 | 39.23 | odd | 6 | |||
819.2.o.c.757.2 | 4 | 39.17 | odd | 6 | |||
1183.2.a.c.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1183.2.a.g.1.2 | 2 | 13.12 | even | 2 | |||
1183.2.c.c.337.1 | 4 | 13.8 | odd | 4 | |||
1183.2.c.c.337.4 | 4 | 13.5 | odd | 4 | |||
1456.2.s.h.113.1 | 4 | 52.23 | odd | 6 | |||
1456.2.s.h.1121.1 | 4 | 52.43 | odd | 6 | |||
8281.2.a.n.1.1 | 2 | 7.6 | odd | 2 | |||
8281.2.a.bb.1.2 | 2 | 91.90 | odd | 2 |