Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2541,2,Mod(1,2541)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2541, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("2541.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2541 = 3 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2541.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: | \(20.2899871536\) |
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 231) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2541.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.618034 | −0.437016 | −0.218508 | − | 0.975835i | \(-0.570119\pi\) | ||||
−0.218508 | + | 0.975835i | \(0.570119\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.61803 | −0.809017 | ||||||||
\(5\) | −1.61803 | −0.723607 | −0.361803 | − | 0.932254i | \(-0.617839\pi\) | ||||
−0.361803 | + | 0.932254i | \(0.617839\pi\) | |||||||
\(6\) | 0.618034 | 0.252311 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 2.23607 | 0.790569 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 1.61803 | 0.467086 | ||||||||
\(13\) | −4.23607 | −1.17487 | −0.587437 | − | 0.809270i | \(-0.699863\pi\) | ||||
−0.587437 | + | 0.809270i | \(0.699863\pi\) | |||||||
\(14\) | −0.618034 | −0.165177 | ||||||||
\(15\) | 1.61803 | 0.417775 | ||||||||
\(16\) | 1.85410 | 0.463525 | ||||||||
\(17\) | 3.47214 | 0.842117 | 0.421058 | − | 0.907034i | \(-0.361659\pi\) | ||||
0.421058 | + | 0.907034i | \(0.361659\pi\) | |||||||
\(18\) | −0.618034 | −0.145672 | ||||||||
\(19\) | −6.47214 | −1.48481 | −0.742405 | − | 0.669951i | \(-0.766315\pi\) | ||||
−0.742405 | + | 0.669951i | \(0.766315\pi\) | |||||||
\(20\) | 2.61803 | 0.585410 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.70820 | 1.19024 | 0.595121 | − | 0.803636i | \(-0.297104\pi\) | ||||
0.595121 | + | 0.803636i | \(0.297104\pi\) | |||||||
\(24\) | −2.23607 | −0.456435 | ||||||||
\(25\) | −2.38197 | −0.476393 | ||||||||
\(26\) | 2.61803 | 0.513439 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.61803 | −0.305780 | ||||||||
\(29\) | 0.236068 | 0.0438367 | 0.0219184 | − | 0.999760i | \(-0.493023\pi\) | ||||
0.0219184 | + | 0.999760i | \(0.493023\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | 3.00000 | 0.538816 | 0.269408 | − | 0.963026i | \(-0.413172\pi\) | ||||
0.269408 | + | 0.963026i | \(0.413172\pi\) | |||||||
\(32\) | −5.61803 | −0.993137 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.14590 | −0.368018 | ||||||||
\(35\) | −1.61803 | −0.273498 | ||||||||
\(36\) | −1.61803 | −0.269672 | ||||||||
\(37\) | 6.00000 | 0.986394 | 0.493197 | − | 0.869918i | \(-0.335828\pi\) | ||||
0.493197 | + | 0.869918i | \(0.335828\pi\) | |||||||
\(38\) | 4.00000 | 0.648886 | ||||||||
\(39\) | 4.23607 | 0.678314 | ||||||||
\(40\) | −3.61803 | −0.572061 | ||||||||
\(41\) | 9.85410 | 1.53895 | 0.769476 | − | 0.638676i | \(-0.220517\pi\) | ||||
0.769476 | + | 0.638676i | \(0.220517\pi\) | |||||||
\(42\) | 0.618034 | 0.0953647 | ||||||||
\(43\) | 11.4721 | 1.74948 | 0.874742 | − | 0.484589i | \(-0.161031\pi\) | ||||
0.874742 | + | 0.484589i | \(0.161031\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.61803 | −0.241202 | ||||||||
\(46\) | −3.52786 | −0.520155 | ||||||||
\(47\) | −5.14590 | −0.750606 | −0.375303 | − | 0.926902i | \(-0.622461\pi\) | ||||
−0.375303 | + | 0.926902i | \(0.622461\pi\) | |||||||
\(48\) | −1.85410 | −0.267617 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.47214 | 0.208191 | ||||||||
\(51\) | −3.47214 | −0.486196 | ||||||||
\(52\) | 6.85410 | 0.950493 | ||||||||
\(53\) | −12.5623 | −1.72557 | −0.862783 | − | 0.505575i | \(-0.831280\pi\) | ||||
−0.862783 | + | 0.505575i | \(0.831280\pi\) | |||||||
\(54\) | 0.618034 | 0.0841038 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.23607 | 0.298807 | ||||||||
\(57\) | 6.47214 | 0.857255 | ||||||||
\(58\) | −0.145898 | −0.0191574 | ||||||||
\(59\) | −4.61803 | −0.601217 | −0.300608 | − | 0.953748i | \(-0.597190\pi\) | ||||
−0.300608 | + | 0.953748i | \(0.597190\pi\) | |||||||
\(60\) | −2.61803 | −0.337987 | ||||||||
\(61\) | 7.94427 | 1.01716 | 0.508580 | − | 0.861015i | \(-0.330171\pi\) | ||||
0.508580 | + | 0.861015i | \(0.330171\pi\) | |||||||
\(62\) | −1.85410 | −0.235471 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | −0.236068 | −0.0295085 | ||||||||
\(65\) | 6.85410 | 0.850147 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.2361 | 1.61704 | 0.808522 | − | 0.588467i | \(-0.200268\pi\) | ||||
0.808522 | + | 0.588467i | \(0.200268\pi\) | |||||||
\(68\) | −5.61803 | −0.681287 | ||||||||
\(69\) | −5.70820 | −0.687187 | ||||||||
\(70\) | 1.00000 | 0.119523 | ||||||||
\(71\) | −4.52786 | −0.537359 | −0.268679 | − | 0.963230i | \(-0.586587\pi\) | ||||
−0.268679 | + | 0.963230i | \(0.586587\pi\) | |||||||
\(72\) | 2.23607 | 0.263523 | ||||||||
\(73\) | −7.38197 | −0.863994 | −0.431997 | − | 0.901875i | \(-0.642191\pi\) | ||||
−0.431997 | + | 0.901875i | \(0.642191\pi\) | |||||||
\(74\) | −3.70820 | −0.431070 | ||||||||
\(75\) | 2.38197 | 0.275046 | ||||||||
\(76\) | 10.4721 | 1.20124 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.61803 | −0.296434 | ||||||||
\(79\) | 6.09017 | 0.685198 | 0.342599 | − | 0.939482i | \(-0.388693\pi\) | ||||
0.342599 | + | 0.939482i | \(0.388693\pi\) | |||||||
\(80\) | −3.00000 | −0.335410 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −6.09017 | −0.672547 | ||||||||
\(83\) | −8.47214 | −0.929938 | −0.464969 | − | 0.885327i | \(-0.653934\pi\) | ||||
−0.464969 | + | 0.885327i | \(0.653934\pi\) | |||||||
\(84\) | 1.61803 | 0.176542 | ||||||||
\(85\) | −5.61803 | −0.609361 | ||||||||
\(86\) | −7.09017 | −0.764553 | ||||||||
\(87\) | −0.236068 | −0.0253091 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.32624 | 0.140581 | 0.0702905 | − | 0.997527i | \(-0.477607\pi\) | ||||
0.0702905 | + | 0.997527i | \(0.477607\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | −4.23607 | −0.444061 | ||||||||
\(92\) | −9.23607 | −0.962927 | ||||||||
\(93\) | −3.00000 | −0.311086 | ||||||||
\(94\) | 3.18034 | 0.328027 | ||||||||
\(95\) | 10.4721 | 1.07442 | ||||||||
\(96\) | 5.61803 | 0.573388 | ||||||||
\(97\) | −5.29180 | −0.537300 | −0.268650 | − | 0.963238i | \(-0.586578\pi\) | ||||
−0.268650 | + | 0.963238i | \(0.586578\pi\) | |||||||
\(98\) | −0.618034 | −0.0624309 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.85410 | 0.385410 | ||||||||
\(101\) | −11.2361 | −1.11803 | −0.559015 | − | 0.829157i | \(-0.688821\pi\) | ||||
−0.559015 | + | 0.829157i | \(0.688821\pi\) | |||||||
\(102\) | 2.14590 | 0.212476 | ||||||||
\(103\) | −15.4721 | −1.52451 | −0.762257 | − | 0.647274i | \(-0.775909\pi\) | ||||
−0.762257 | + | 0.647274i | \(0.775909\pi\) | |||||||
\(104\) | −9.47214 | −0.928819 | ||||||||
\(105\) | 1.61803 | 0.157904 | ||||||||
\(106\) | 7.76393 | 0.754100 | ||||||||
\(107\) | −5.76393 | −0.557220 | −0.278610 | − | 0.960404i | \(-0.589874\pi\) | ||||
−0.278610 | + | 0.960404i | \(0.589874\pi\) | |||||||
\(108\) | 1.61803 | 0.155695 | ||||||||
\(109\) | 4.14590 | 0.397105 | 0.198553 | − | 0.980090i | \(-0.436376\pi\) | ||||
0.198553 | + | 0.980090i | \(0.436376\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.00000 | −0.569495 | ||||||||
\(112\) | 1.85410 | 0.175196 | ||||||||
\(113\) | −11.1803 | −1.05176 | −0.525879 | − | 0.850559i | \(-0.676264\pi\) | ||||
−0.525879 | + | 0.850559i | \(0.676264\pi\) | |||||||
\(114\) | −4.00000 | −0.374634 | ||||||||
\(115\) | −9.23607 | −0.861268 | ||||||||
\(116\) | −0.381966 | −0.0354647 | ||||||||
\(117\) | −4.23607 | −0.391625 | ||||||||
\(118\) | 2.85410 | 0.262741 | ||||||||
\(119\) | 3.47214 | 0.318290 | ||||||||
\(120\) | 3.61803 | 0.330280 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −4.90983 | −0.444515 | ||||||||
\(123\) | −9.85410 | −0.888514 | ||||||||
\(124\) | −4.85410 | −0.435911 | ||||||||
\(125\) | 11.9443 | 1.06833 | ||||||||
\(126\) | −0.618034 | −0.0550588 | ||||||||
\(127\) | 7.32624 | 0.650098 | 0.325049 | − | 0.945697i | \(-0.394619\pi\) | ||||
0.325049 | + | 0.945697i | \(0.394619\pi\) | |||||||
\(128\) | 11.3820 | 1.00603 | ||||||||
\(129\) | −11.4721 | −1.01007 | ||||||||
\(130\) | −4.23607 | −0.371528 | ||||||||
\(131\) | −6.85410 | −0.598846 | −0.299423 | − | 0.954121i | \(-0.596794\pi\) | ||||
−0.299423 | + | 0.954121i | \(0.596794\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.47214 | −0.561205 | ||||||||
\(134\) | −8.18034 | −0.706674 | ||||||||
\(135\) | 1.61803 | 0.139258 | ||||||||
\(136\) | 7.76393 | 0.665752 | ||||||||
\(137\) | −10.4721 | −0.894695 | −0.447347 | − | 0.894360i | \(-0.647631\pi\) | ||||
−0.447347 | + | 0.894360i | \(0.647631\pi\) | |||||||
\(138\) | 3.52786 | 0.300312 | ||||||||
\(139\) | −2.61803 | −0.222059 | −0.111029 | − | 0.993817i | \(-0.535415\pi\) | ||||
−0.111029 | + | 0.993817i | \(0.535415\pi\) | |||||||
\(140\) | 2.61803 | 0.221264 | ||||||||
\(141\) | 5.14590 | 0.433363 | ||||||||
\(142\) | 2.79837 | 0.234834 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.85410 | 0.154508 | ||||||||
\(145\) | −0.381966 | −0.0317206 | ||||||||
\(146\) | 4.56231 | 0.377579 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −9.70820 | −0.798009 | ||||||||
\(149\) | 1.38197 | 0.113215 | 0.0566075 | − | 0.998397i | \(-0.481972\pi\) | ||||
0.0566075 | + | 0.998397i | \(0.481972\pi\) | |||||||
\(150\) | −1.47214 | −0.120199 | ||||||||
\(151\) | −6.32624 | −0.514822 | −0.257411 | − | 0.966302i | \(-0.582869\pi\) | ||||
−0.257411 | + | 0.966302i | \(0.582869\pi\) | |||||||
\(152\) | −14.4721 | −1.17385 | ||||||||
\(153\) | 3.47214 | 0.280706 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.85410 | −0.389891 | ||||||||
\(156\) | −6.85410 | −0.548767 | ||||||||
\(157\) | −6.79837 | −0.542569 | −0.271285 | − | 0.962499i | \(-0.587448\pi\) | ||||
−0.271285 | + | 0.962499i | \(0.587448\pi\) | |||||||
\(158\) | −3.76393 | −0.299442 | ||||||||
\(159\) | 12.5623 | 0.996256 | ||||||||
\(160\) | 9.09017 | 0.718641 | ||||||||
\(161\) | 5.70820 | 0.449869 | ||||||||
\(162\) | −0.618034 | −0.0485573 | ||||||||
\(163\) | −18.3262 | −1.43542 | −0.717711 | − | 0.696341i | \(-0.754810\pi\) | ||||
−0.717711 | + | 0.696341i | \(0.754810\pi\) | |||||||
\(164\) | −15.9443 | −1.24504 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.23607 | 0.406398 | ||||||||
\(167\) | 2.14590 | 0.166055 | 0.0830273 | − | 0.996547i | \(-0.473541\pi\) | ||||
0.0830273 | + | 0.996547i | \(0.473541\pi\) | |||||||
\(168\) | −2.23607 | −0.172516 | ||||||||
\(169\) | 4.94427 | 0.380329 | ||||||||
\(170\) | 3.47214 | 0.266301 | ||||||||
\(171\) | −6.47214 | −0.494937 | ||||||||
\(172\) | −18.5623 | −1.41536 | ||||||||
\(173\) | −10.7984 | −0.820985 | −0.410493 | − | 0.911864i | \(-0.634643\pi\) | ||||
−0.410493 | + | 0.911864i | \(0.634643\pi\) | |||||||
\(174\) | 0.145898 | 0.0110605 | ||||||||
\(175\) | −2.38197 | −0.180060 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.61803 | 0.347113 | ||||||||
\(178\) | −0.819660 | −0.0614361 | ||||||||
\(179\) | −18.7082 | −1.39832 | −0.699158 | − | 0.714967i | \(-0.746442\pi\) | ||||
−0.699158 | + | 0.714967i | \(0.746442\pi\) | |||||||
\(180\) | 2.61803 | 0.195137 | ||||||||
\(181\) | −0.527864 | −0.0392358 | −0.0196179 | − | 0.999808i | \(-0.506245\pi\) | ||||
−0.0196179 | + | 0.999808i | \(0.506245\pi\) | |||||||
\(182\) | 2.61803 | 0.194062 | ||||||||
\(183\) | −7.94427 | −0.587257 | ||||||||
\(184\) | 12.7639 | 0.940970 | ||||||||
\(185\) | −9.70820 | −0.713761 | ||||||||
\(186\) | 1.85410 | 0.135949 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 8.32624 | 0.607253 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −6.47214 | −0.469538 | ||||||||
\(191\) | −16.2361 | −1.17480 | −0.587400 | − | 0.809297i | \(-0.699849\pi\) | ||||
−0.587400 | + | 0.809297i | \(0.699849\pi\) | |||||||
\(192\) | 0.236068 | 0.0170367 | ||||||||
\(193\) | −17.4164 | −1.25366 | −0.626830 | − | 0.779156i | \(-0.715648\pi\) | ||||
−0.626830 | + | 0.779156i | \(0.715648\pi\) | |||||||
\(194\) | 3.27051 | 0.234809 | ||||||||
\(195\) | −6.85410 | −0.490832 | ||||||||
\(196\) | −1.61803 | −0.115574 | ||||||||
\(197\) | −4.65248 | −0.331475 | −0.165738 | − | 0.986170i | \(-0.553000\pi\) | ||||
−0.165738 | + | 0.986170i | \(0.553000\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −26.2148 | −1.85832 | −0.929158 | − | 0.369682i | \(-0.879467\pi\) | ||||
−0.929158 | + | 0.369682i | \(0.879467\pi\) | |||||||
\(200\) | −5.32624 | −0.376622 | ||||||||
\(201\) | −13.2361 | −0.933600 | ||||||||
\(202\) | 6.94427 | 0.488597 | ||||||||
\(203\) | 0.236068 | 0.0165687 | ||||||||
\(204\) | 5.61803 | 0.393341 | ||||||||
\(205\) | −15.9443 | −1.11360 | ||||||||
\(206\) | 9.56231 | 0.666237 | ||||||||
\(207\) | 5.70820 | 0.396748 | ||||||||
\(208\) | −7.85410 | −0.544584 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −1.00000 | −0.0690066 | ||||||||
\(211\) | 18.7082 | 1.28793 | 0.643963 | − | 0.765057i | \(-0.277289\pi\) | ||||
0.643963 | + | 0.765057i | \(0.277289\pi\) | |||||||
\(212\) | 20.3262 | 1.39601 | ||||||||
\(213\) | 4.52786 | 0.310244 | ||||||||
\(214\) | 3.56231 | 0.243514 | ||||||||
\(215\) | −18.5623 | −1.26594 | ||||||||
\(216\) | −2.23607 | −0.152145 | ||||||||
\(217\) | 3.00000 | 0.203653 | ||||||||
\(218\) | −2.56231 | −0.173541 | ||||||||
\(219\) | 7.38197 | 0.498827 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.7082 | −0.989381 | ||||||||
\(222\) | 3.70820 | 0.248878 | ||||||||
\(223\) | 19.9443 | 1.33557 | 0.667784 | − | 0.744355i | \(-0.267243\pi\) | ||||
0.667784 | + | 0.744355i | \(0.267243\pi\) | |||||||
\(224\) | −5.61803 | −0.375371 | ||||||||
\(225\) | −2.38197 | −0.158798 | ||||||||
\(226\) | 6.90983 | 0.459635 | ||||||||
\(227\) | 0.909830 | 0.0603875 | 0.0301938 | − | 0.999544i | \(-0.490388\pi\) | ||||
0.0301938 | + | 0.999544i | \(0.490388\pi\) | |||||||
\(228\) | −10.4721 | −0.693534 | ||||||||
\(229\) | 15.1246 | 0.999462 | 0.499731 | − | 0.866181i | \(-0.333432\pi\) | ||||
0.499731 | + | 0.866181i | \(0.333432\pi\) | |||||||
\(230\) | 5.70820 | 0.376388 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.527864 | 0.0346560 | ||||||||
\(233\) | 15.7639 | 1.03273 | 0.516365 | − | 0.856369i | \(-0.327285\pi\) | ||||
0.516365 | + | 0.856369i | \(0.327285\pi\) | |||||||
\(234\) | 2.61803 | 0.171146 | ||||||||
\(235\) | 8.32624 | 0.543144 | ||||||||
\(236\) | 7.47214 | 0.486395 | ||||||||
\(237\) | −6.09017 | −0.395599 | ||||||||
\(238\) | −2.14590 | −0.139098 | ||||||||
\(239\) | 21.6180 | 1.39835 | 0.699177 | − | 0.714948i | \(-0.253550\pi\) | ||||
0.699177 | + | 0.714948i | \(0.253550\pi\) | |||||||
\(240\) | 3.00000 | 0.193649 | ||||||||
\(241\) | −10.4164 | −0.670980 | −0.335490 | − | 0.942044i | \(-0.608902\pi\) | ||||
−0.335490 | + | 0.942044i | \(0.608902\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −12.8541 | −0.822900 | ||||||||
\(245\) | −1.61803 | −0.103372 | ||||||||
\(246\) | 6.09017 | 0.388295 | ||||||||
\(247\) | 27.4164 | 1.74446 | ||||||||
\(248\) | 6.70820 | 0.425971 | ||||||||
\(249\) | 8.47214 | 0.536900 | ||||||||
\(250\) | −7.38197 | −0.466877 | ||||||||
\(251\) | −13.9443 | −0.880155 | −0.440077 | − | 0.897960i | \(-0.645049\pi\) | ||||
−0.440077 | + | 0.897960i | \(0.645049\pi\) | |||||||
\(252\) | −1.61803 | −0.101927 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −4.52786 | −0.284103 | ||||||||
\(255\) | 5.61803 | 0.351815 | ||||||||
\(256\) | −6.56231 | −0.410144 | ||||||||
\(257\) | 23.8885 | 1.49013 | 0.745063 | − | 0.666994i | \(-0.232419\pi\) | ||||
0.745063 | + | 0.666994i | \(0.232419\pi\) | |||||||
\(258\) | 7.09017 | 0.441415 | ||||||||
\(259\) | 6.00000 | 0.372822 | ||||||||
\(260\) | −11.0902 | −0.687783 | ||||||||
\(261\) | 0.236068 | 0.0146122 | ||||||||
\(262\) | 4.23607 | 0.261705 | ||||||||
\(263\) | 9.29180 | 0.572957 | 0.286478 | − | 0.958087i | \(-0.407515\pi\) | ||||
0.286478 | + | 0.958087i | \(0.407515\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 20.3262 | 1.24863 | ||||||||
\(266\) | 4.00000 | 0.245256 | ||||||||
\(267\) | −1.32624 | −0.0811644 | ||||||||
\(268\) | −21.4164 | −1.30822 | ||||||||
\(269\) | −29.1803 | −1.77916 | −0.889578 | − | 0.456783i | \(-0.849002\pi\) | ||||
−0.889578 | + | 0.456783i | \(0.849002\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | 22.1246 | 1.34397 | 0.671987 | − | 0.740563i | \(-0.265441\pi\) | ||||
0.671987 | + | 0.740563i | \(0.265441\pi\) | |||||||
\(272\) | 6.43769 | 0.390343 | ||||||||
\(273\) | 4.23607 | 0.256378 | ||||||||
\(274\) | 6.47214 | 0.390996 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 9.23607 | 0.555946 | ||||||||
\(277\) | −8.47214 | −0.509041 | −0.254521 | − | 0.967067i | \(-0.581918\pi\) | ||||
−0.254521 | + | 0.967067i | \(0.581918\pi\) | |||||||
\(278\) | 1.61803 | 0.0970432 | ||||||||
\(279\) | 3.00000 | 0.179605 | ||||||||
\(280\) | −3.61803 | −0.216219 | ||||||||
\(281\) | −10.8541 | −0.647501 | −0.323751 | − | 0.946142i | \(-0.604944\pi\) | ||||
−0.323751 | + | 0.946142i | \(0.604944\pi\) | |||||||
\(282\) | −3.18034 | −0.189386 | ||||||||
\(283\) | −12.8885 | −0.766144 | −0.383072 | − | 0.923718i | \(-0.625134\pi\) | ||||
−0.383072 | + | 0.923718i | \(0.625134\pi\) | |||||||
\(284\) | 7.32624 | 0.434732 | ||||||||
\(285\) | −10.4721 | −0.620316 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.85410 | 0.581669 | ||||||||
\(288\) | −5.61803 | −0.331046 | ||||||||
\(289\) | −4.94427 | −0.290840 | ||||||||
\(290\) | 0.236068 | 0.0138624 | ||||||||
\(291\) | 5.29180 | 0.310211 | ||||||||
\(292\) | 11.9443 | 0.698986 | ||||||||
\(293\) | 7.70820 | 0.450318 | 0.225159 | − | 0.974322i | \(-0.427710\pi\) | ||||
0.225159 | + | 0.974322i | \(0.427710\pi\) | |||||||
\(294\) | 0.618034 | 0.0360445 | ||||||||
\(295\) | 7.47214 | 0.435045 | ||||||||
\(296\) | 13.4164 | 0.779813 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.854102 | −0.0494768 | ||||||||
\(299\) | −24.1803 | −1.39839 | ||||||||
\(300\) | −3.85410 | −0.222517 | ||||||||
\(301\) | 11.4721 | 0.661243 | ||||||||
\(302\) | 3.90983 | 0.224985 | ||||||||
\(303\) | 11.2361 | 0.645495 | ||||||||
\(304\) | −12.0000 | −0.688247 | ||||||||
\(305\) | −12.8541 | −0.736024 | ||||||||
\(306\) | −2.14590 | −0.122673 | ||||||||
\(307\) | −8.05573 | −0.459765 | −0.229882 | − | 0.973218i | \(-0.573834\pi\) | ||||
−0.229882 | + | 0.973218i | \(0.573834\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15.4721 | 0.880179 | ||||||||
\(310\) | 3.00000 | 0.170389 | ||||||||
\(311\) | 6.79837 | 0.385500 | 0.192750 | − | 0.981248i | \(-0.438259\pi\) | ||||
0.192750 | + | 0.981248i | \(0.438259\pi\) | |||||||
\(312\) | 9.47214 | 0.536254 | ||||||||
\(313\) | 32.0902 | 1.81384 | 0.906922 | − | 0.421299i | \(-0.138426\pi\) | ||||
0.906922 | + | 0.421299i | \(0.138426\pi\) | |||||||
\(314\) | 4.20163 | 0.237111 | ||||||||
\(315\) | −1.61803 | −0.0911659 | ||||||||
\(316\) | −9.85410 | −0.554337 | ||||||||
\(317\) | −34.8885 | −1.95954 | −0.979768 | − | 0.200137i | \(-0.935861\pi\) | ||||
−0.979768 | + | 0.200137i | \(0.935861\pi\) | |||||||
\(318\) | −7.76393 | −0.435380 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0.381966 | 0.0213525 | ||||||||
\(321\) | 5.76393 | 0.321711 | ||||||||
\(322\) | −3.52786 | −0.196600 | ||||||||
\(323\) | −22.4721 | −1.25038 | ||||||||
\(324\) | −1.61803 | −0.0898908 | ||||||||
\(325\) | 10.0902 | 0.559702 | ||||||||
\(326\) | 11.3262 | 0.627302 | ||||||||
\(327\) | −4.14590 | −0.229269 | ||||||||
\(328\) | 22.0344 | 1.21665 | ||||||||
\(329\) | −5.14590 | −0.283703 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.2918 | −1.06037 | −0.530187 | − | 0.847881i | \(-0.677878\pi\) | ||||
−0.530187 | + | 0.847881i | \(0.677878\pi\) | |||||||
\(332\) | 13.7082 | 0.752335 | ||||||||
\(333\) | 6.00000 | 0.328798 | ||||||||
\(334\) | −1.32624 | −0.0725685 | ||||||||
\(335\) | −21.4164 | −1.17010 | ||||||||
\(336\) | −1.85410 | −0.101150 | ||||||||
\(337\) | 4.23607 | 0.230753 | 0.115377 | − | 0.993322i | \(-0.463192\pi\) | ||||
0.115377 | + | 0.993322i | \(0.463192\pi\) | |||||||
\(338\) | −3.05573 | −0.166210 | ||||||||
\(339\) | 11.1803 | 0.607233 | ||||||||
\(340\) | 9.09017 | 0.492984 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 4.00000 | 0.216295 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 25.6525 | 1.38309 | ||||||||
\(345\) | 9.23607 | 0.497253 | ||||||||
\(346\) | 6.67376 | 0.358784 | ||||||||
\(347\) | 0.472136 | 0.0253456 | 0.0126728 | − | 0.999920i | \(-0.495966\pi\) | ||||
0.0126728 | + | 0.999920i | \(0.495966\pi\) | |||||||
\(348\) | 0.381966 | 0.0204755 | ||||||||
\(349\) | 17.3262 | 0.927452 | 0.463726 | − | 0.885979i | \(-0.346512\pi\) | ||||
0.463726 | + | 0.885979i | \(0.346512\pi\) | |||||||
\(350\) | 1.47214 | 0.0786890 | ||||||||
\(351\) | 4.23607 | 0.226105 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.12461 | −0.219531 | −0.109765 | − | 0.993958i | \(-0.535010\pi\) | ||||
−0.109765 | + | 0.993958i | \(0.535010\pi\) | |||||||
\(354\) | −2.85410 | −0.151694 | ||||||||
\(355\) | 7.32624 | 0.388836 | ||||||||
\(356\) | −2.14590 | −0.113732 | ||||||||
\(357\) | −3.47214 | −0.183765 | ||||||||
\(358\) | 11.5623 | 0.611087 | ||||||||
\(359\) | −10.3820 | −0.547939 | −0.273970 | − | 0.961738i | \(-0.588337\pi\) | ||||
−0.273970 | + | 0.961738i | \(0.588337\pi\) | |||||||
\(360\) | −3.61803 | −0.190687 | ||||||||
\(361\) | 22.8885 | 1.20466 | ||||||||
\(362\) | 0.326238 | 0.0171467 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.85410 | 0.359253 | ||||||||
\(365\) | 11.9443 | 0.625192 | ||||||||
\(366\) | 4.90983 | 0.256641 | ||||||||
\(367\) | −5.00000 | −0.260998 | −0.130499 | − | 0.991448i | \(-0.541658\pi\) | ||||
−0.130499 | + | 0.991448i | \(0.541658\pi\) | |||||||
\(368\) | 10.5836 | 0.551708 | ||||||||
\(369\) | 9.85410 | 0.512984 | ||||||||
\(370\) | 6.00000 | 0.311925 | ||||||||
\(371\) | −12.5623 | −0.652202 | ||||||||
\(372\) | 4.85410 | 0.251673 | ||||||||
\(373\) | 20.2918 | 1.05067 | 0.525335 | − | 0.850896i | \(-0.323940\pi\) | ||||
0.525335 | + | 0.850896i | \(0.323940\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −11.9443 | −0.616800 | ||||||||
\(376\) | −11.5066 | −0.593406 | ||||||||
\(377\) | −1.00000 | −0.0515026 | ||||||||
\(378\) | 0.618034 | 0.0317882 | ||||||||
\(379\) | −1.90983 | −0.0981014 | −0.0490507 | − | 0.998796i | \(-0.515620\pi\) | ||||
−0.0490507 | + | 0.998796i | \(0.515620\pi\) | |||||||
\(380\) | −16.9443 | −0.869223 | ||||||||
\(381\) | −7.32624 | −0.375335 | ||||||||
\(382\) | 10.0344 | 0.513407 | ||||||||
\(383\) | −2.67376 | −0.136623 | −0.0683114 | − | 0.997664i | \(-0.521761\pi\) | ||||
−0.0683114 | + | 0.997664i | \(0.521761\pi\) | |||||||
\(384\) | −11.3820 | −0.580834 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 10.7639 | 0.547870 | ||||||||
\(387\) | 11.4721 | 0.583161 | ||||||||
\(388\) | 8.56231 | 0.434685 | ||||||||
\(389\) | −17.2361 | −0.873903 | −0.436952 | − | 0.899485i | \(-0.643942\pi\) | ||||
−0.436952 | + | 0.899485i | \(0.643942\pi\) | |||||||
\(390\) | 4.23607 | 0.214502 | ||||||||
\(391\) | 19.8197 | 1.00232 | ||||||||
\(392\) | 2.23607 | 0.112938 | ||||||||
\(393\) | 6.85410 | 0.345744 | ||||||||
\(394\) | 2.87539 | 0.144860 | ||||||||
\(395\) | −9.85410 | −0.495814 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.5623 | −0.530107 | −0.265053 | − | 0.964234i | \(-0.585390\pi\) | ||||
−0.265053 | + | 0.964234i | \(0.585390\pi\) | |||||||
\(398\) | 16.2016 | 0.812114 | ||||||||
\(399\) | 6.47214 | 0.324012 | ||||||||
\(400\) | −4.41641 | −0.220820 | ||||||||
\(401\) | 27.7426 | 1.38540 | 0.692701 | − | 0.721225i | \(-0.256421\pi\) | ||||
0.692701 | + | 0.721225i | \(0.256421\pi\) | |||||||
\(402\) | 8.18034 | 0.407998 | ||||||||
\(403\) | −12.7082 | −0.633041 | ||||||||
\(404\) | 18.1803 | 0.904506 | ||||||||
\(405\) | −1.61803 | −0.0804008 | ||||||||
\(406\) | −0.145898 | −0.00724080 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −7.76393 | −0.384372 | ||||||||
\(409\) | −8.20163 | −0.405544 | −0.202772 | − | 0.979226i | \(-0.564995\pi\) | ||||
−0.202772 | + | 0.979226i | \(0.564995\pi\) | |||||||
\(410\) | 9.85410 | 0.486659 | ||||||||
\(411\) | 10.4721 | 0.516552 | ||||||||
\(412\) | 25.0344 | 1.23336 | ||||||||
\(413\) | −4.61803 | −0.227239 | ||||||||
\(414\) | −3.52786 | −0.173385 | ||||||||
\(415\) | 13.7082 | 0.672909 | ||||||||
\(416\) | 23.7984 | 1.16681 | ||||||||
\(417\) | 2.61803 | 0.128206 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −35.6180 | −1.74005 | −0.870027 | − | 0.493003i | \(-0.835899\pi\) | ||||
−0.870027 | + | 0.493003i | \(0.835899\pi\) | |||||||
\(420\) | −2.61803 | −0.127747 | ||||||||
\(421\) | 18.1459 | 0.884377 | 0.442188 | − | 0.896922i | \(-0.354202\pi\) | ||||
0.442188 | + | 0.896922i | \(0.354202\pi\) | |||||||
\(422\) | −11.5623 | −0.562844 | ||||||||
\(423\) | −5.14590 | −0.250202 | ||||||||
\(424\) | −28.0902 | −1.36418 | ||||||||
\(425\) | −8.27051 | −0.401179 | ||||||||
\(426\) | −2.79837 | −0.135582 | ||||||||
\(427\) | 7.94427 | 0.384450 | ||||||||
\(428\) | 9.32624 | 0.450801 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 11.4721 | 0.553236 | ||||||||
\(431\) | 7.14590 | 0.344206 | 0.172103 | − | 0.985079i | \(-0.444944\pi\) | ||||
0.172103 | + | 0.985079i | \(0.444944\pi\) | |||||||
\(432\) | −1.85410 | −0.0892055 | ||||||||
\(433\) | −6.94427 | −0.333720 | −0.166860 | − | 0.985981i | \(-0.553363\pi\) | ||||
−0.166860 | + | 0.985981i | \(0.553363\pi\) | |||||||
\(434\) | −1.85410 | −0.0889997 | ||||||||
\(435\) | 0.381966 | 0.0183139 | ||||||||
\(436\) | −6.70820 | −0.321265 | ||||||||
\(437\) | −36.9443 | −1.76728 | ||||||||
\(438\) | −4.56231 | −0.217995 | ||||||||
\(439\) | −35.6525 | −1.70160 | −0.850800 | − | 0.525490i | \(-0.823882\pi\) | ||||
−0.850800 | + | 0.525490i | \(0.823882\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 9.09017 | 0.432375 | ||||||||
\(443\) | 24.6525 | 1.17127 | 0.585637 | − | 0.810573i | \(-0.300844\pi\) | ||||
0.585637 | + | 0.810573i | \(0.300844\pi\) | |||||||
\(444\) | 9.70820 | 0.460731 | ||||||||
\(445\) | −2.14590 | −0.101725 | ||||||||
\(446\) | −12.3262 | −0.583664 | ||||||||
\(447\) | −1.38197 | −0.0653647 | ||||||||
\(448\) | −0.236068 | −0.0111532 | ||||||||
\(449\) | −20.5967 | −0.972021 | −0.486010 | − | 0.873953i | \(-0.661548\pi\) | ||||
−0.486010 | + | 0.873953i | \(0.661548\pi\) | |||||||
\(450\) | 1.47214 | 0.0693972 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 18.0902 | 0.850890 | ||||||||
\(453\) | 6.32624 | 0.297233 | ||||||||
\(454\) | −0.562306 | −0.0263903 | ||||||||
\(455\) | 6.85410 | 0.321325 | ||||||||
\(456\) | 14.4721 | 0.677720 | ||||||||
\(457\) | −18.7426 | −0.876744 | −0.438372 | − | 0.898794i | \(-0.644445\pi\) | ||||
−0.438372 | + | 0.898794i | \(0.644445\pi\) | |||||||
\(458\) | −9.34752 | −0.436781 | ||||||||
\(459\) | −3.47214 | −0.162065 | ||||||||
\(460\) | 14.9443 | 0.696780 | ||||||||
\(461\) | −28.3050 | −1.31829 | −0.659147 | − | 0.752015i | \(-0.729082\pi\) | ||||
−0.659147 | + | 0.752015i | \(0.729082\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.9787 | −0.696120 | −0.348060 | − | 0.937472i | \(-0.613159\pi\) | ||||
−0.348060 | + | 0.937472i | \(0.613159\pi\) | |||||||
\(464\) | 0.437694 | 0.0203194 | ||||||||
\(465\) | 4.85410 | 0.225104 | ||||||||
\(466\) | −9.74265 | −0.451319 | ||||||||
\(467\) | −26.7082 | −1.23591 | −0.617954 | − | 0.786214i | \(-0.712038\pi\) | ||||
−0.617954 | + | 0.786214i | \(0.712038\pi\) | |||||||
\(468\) | 6.85410 | 0.316831 | ||||||||
\(469\) | 13.2361 | 0.611185 | ||||||||
\(470\) | −5.14590 | −0.237363 | ||||||||
\(471\) | 6.79837 | 0.313253 | ||||||||
\(472\) | −10.3262 | −0.475304 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 3.76393 | 0.172883 | ||||||||
\(475\) | 15.4164 | 0.707353 | ||||||||
\(476\) | −5.61803 | −0.257502 | ||||||||
\(477\) | −12.5623 | −0.575188 | ||||||||
\(478\) | −13.3607 | −0.611103 | ||||||||
\(479\) | −30.3820 | −1.38819 | −0.694094 | − | 0.719885i | \(-0.744195\pi\) | ||||
−0.694094 | + | 0.719885i | \(0.744195\pi\) | |||||||
\(480\) | −9.09017 | −0.414908 | ||||||||
\(481\) | −25.4164 | −1.15889 | ||||||||
\(482\) | 6.43769 | 0.293229 | ||||||||
\(483\) | −5.70820 | −0.259732 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.56231 | 0.388794 | ||||||||
\(486\) | 0.618034 | 0.0280346 | ||||||||
\(487\) | −15.3820 | −0.697023 | −0.348512 | − | 0.937304i | \(-0.613313\pi\) | ||||
−0.348512 | + | 0.937304i | \(0.613313\pi\) | |||||||
\(488\) | 17.7639 | 0.804135 | ||||||||
\(489\) | 18.3262 | 0.828741 | ||||||||
\(490\) | 1.00000 | 0.0451754 | ||||||||
\(491\) | 8.29180 | 0.374204 | 0.187102 | − | 0.982341i | \(-0.440091\pi\) | ||||
0.187102 | + | 0.982341i | \(0.440091\pi\) | |||||||
\(492\) | 15.9443 | 0.718823 | ||||||||
\(493\) | 0.819660 | 0.0369156 | ||||||||
\(494\) | −16.9443 | −0.762359 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.56231 | 0.249755 | ||||||||
\(497\) | −4.52786 | −0.203102 | ||||||||
\(498\) | −5.23607 | −0.234634 | ||||||||
\(499\) | 7.00000 | 0.313363 | 0.156682 | − | 0.987649i | \(-0.449920\pi\) | ||||
0.156682 | + | 0.987649i | \(0.449920\pi\) | |||||||
\(500\) | −19.3262 | −0.864296 | ||||||||
\(501\) | −2.14590 | −0.0958717 | ||||||||
\(502\) | 8.61803 | 0.384642 | ||||||||
\(503\) | 42.0132 | 1.87327 | 0.936637 | − | 0.350301i | \(-0.113921\pi\) | ||||
0.936637 | + | 0.350301i | \(0.113921\pi\) | |||||||
\(504\) | 2.23607 | 0.0996024 | ||||||||
\(505\) | 18.1803 | 0.809015 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.94427 | −0.219583 | ||||||||
\(508\) | −11.8541 | −0.525941 | ||||||||
\(509\) | 12.1246 | 0.537414 | 0.268707 | − | 0.963222i | \(-0.413404\pi\) | ||||
0.268707 | + | 0.963222i | \(0.413404\pi\) | |||||||
\(510\) | −3.47214 | −0.153749 | ||||||||
\(511\) | −7.38197 | −0.326559 | ||||||||
\(512\) | −18.7082 | −0.826794 | ||||||||
\(513\) | 6.47214 | 0.285752 | ||||||||
\(514\) | −14.7639 | −0.651209 | ||||||||
\(515\) | 25.0344 | 1.10315 | ||||||||
\(516\) | 18.5623 | 0.817160 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −3.70820 | −0.162929 | ||||||||
\(519\) | 10.7984 | 0.473996 | ||||||||
\(520\) | 15.3262 | 0.672100 | ||||||||
\(521\) | 8.41641 | 0.368730 | 0.184365 | − | 0.982858i | \(-0.440977\pi\) | ||||
0.184365 | + | 0.982858i | \(0.440977\pi\) | |||||||
\(522\) | −0.145898 | −0.00638578 | ||||||||
\(523\) | −29.5410 | −1.29174 | −0.645869 | − | 0.763448i | \(-0.723505\pi\) | ||||
−0.645869 | + | 0.763448i | \(0.723505\pi\) | |||||||
\(524\) | 11.0902 | 0.484476 | ||||||||
\(525\) | 2.38197 | 0.103958 | ||||||||
\(526\) | −5.74265 | −0.250391 | ||||||||
\(527\) | 10.4164 | 0.453746 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.58359 | 0.416678 | ||||||||
\(530\) | −12.5623 | −0.545672 | ||||||||
\(531\) | −4.61803 | −0.200406 | ||||||||
\(532\) | 10.4721 | 0.454025 | ||||||||
\(533\) | −41.7426 | −1.80807 | ||||||||
\(534\) | 0.819660 | 0.0354702 | ||||||||
\(535\) | 9.32624 | 0.403208 | ||||||||
\(536\) | 29.5967 | 1.27838 | ||||||||
\(537\) | 18.7082 | 0.807319 | ||||||||
\(538\) | 18.0344 | 0.777520 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.61803 | −0.112662 | ||||||||
\(541\) | 10.9656 | 0.471446 | 0.235723 | − | 0.971820i | \(-0.424254\pi\) | ||||
0.235723 | + | 0.971820i | \(0.424254\pi\) | |||||||
\(542\) | −13.6738 | −0.587338 | ||||||||
\(543\) | 0.527864 | 0.0226528 | ||||||||
\(544\) | −19.5066 | −0.836338 | ||||||||
\(545\) | −6.70820 | −0.287348 | ||||||||
\(546\) | −2.61803 | −0.112042 | ||||||||
\(547\) | 19.0689 | 0.815327 | 0.407663 | − | 0.913132i | \(-0.366344\pi\) | ||||
0.407663 | + | 0.913132i | \(0.366344\pi\) | |||||||
\(548\) | 16.9443 | 0.723823 | ||||||||
\(549\) | 7.94427 | 0.339053 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.52786 | −0.0650892 | ||||||||
\(552\) | −12.7639 | −0.543269 | ||||||||
\(553\) | 6.09017 | 0.258980 | ||||||||
\(554\) | 5.23607 | 0.222459 | ||||||||
\(555\) | 9.70820 | 0.412090 | ||||||||
\(556\) | 4.23607 | 0.179649 | ||||||||
\(557\) | 20.5410 | 0.870351 | 0.435175 | − | 0.900346i | \(-0.356686\pi\) | ||||
0.435175 | + | 0.900346i | \(0.356686\pi\) | |||||||
\(558\) | −1.85410 | −0.0784904 | ||||||||
\(559\) | −48.5967 | −2.05542 | ||||||||
\(560\) | −3.00000 | −0.126773 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.70820 | 0.282969 | ||||||||
\(563\) | 27.9443 | 1.17771 | 0.588855 | − | 0.808238i | \(-0.299579\pi\) | ||||
0.588855 | + | 0.808238i | \(0.299579\pi\) | |||||||
\(564\) | −8.32624 | −0.350598 | ||||||||
\(565\) | 18.0902 | 0.761059 | ||||||||
\(566\) | 7.96556 | 0.334817 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −10.1246 | −0.424819 | ||||||||
\(569\) | 38.7082 | 1.62273 | 0.811366 | − | 0.584538i | \(-0.198724\pi\) | ||||
0.811366 | + | 0.584538i | \(0.198724\pi\) | |||||||
\(570\) | 6.47214 | 0.271088 | ||||||||
\(571\) | −35.9443 | −1.50422 | −0.752110 | − | 0.659037i | \(-0.770964\pi\) | ||||
−0.752110 | + | 0.659037i | \(0.770964\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.2361 | 0.678271 | ||||||||
\(574\) | −6.09017 | −0.254199 | ||||||||
\(575\) | −13.5967 | −0.567024 | ||||||||
\(576\) | −0.236068 | −0.00983617 | ||||||||
\(577\) | 37.1459 | 1.54640 | 0.773202 | − | 0.634160i | \(-0.218654\pi\) | ||||
0.773202 | + | 0.634160i | \(0.218654\pi\) | |||||||
\(578\) | 3.05573 | 0.127102 | ||||||||
\(579\) | 17.4164 | 0.723801 | ||||||||
\(580\) | 0.618034 | 0.0256625 | ||||||||
\(581\) | −8.47214 | −0.351483 | ||||||||
\(582\) | −3.27051 | −0.135567 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −16.5066 | −0.683047 | ||||||||
\(585\) | 6.85410 | 0.283382 | ||||||||
\(586\) | −4.76393 | −0.196796 | ||||||||
\(587\) | −32.2492 | −1.33107 | −0.665534 | − | 0.746368i | \(-0.731796\pi\) | ||||
−0.665534 | + | 0.746368i | \(0.731796\pi\) | |||||||
\(588\) | 1.61803 | 0.0667266 | ||||||||
\(589\) | −19.4164 | −0.800039 | ||||||||
\(590\) | −4.61803 | −0.190121 | ||||||||
\(591\) | 4.65248 | 0.191377 | ||||||||
\(592\) | 11.1246 | 0.457219 | ||||||||
\(593\) | −10.0000 | −0.410651 | −0.205325 | − | 0.978694i | \(-0.565825\pi\) | ||||
−0.205325 | + | 0.978694i | \(0.565825\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.61803 | −0.230317 | ||||||||
\(596\) | −2.23607 | −0.0915929 | ||||||||
\(597\) | 26.2148 | 1.07290 | ||||||||
\(598\) | 14.9443 | 0.611117 | ||||||||
\(599\) | −14.5623 | −0.595000 | −0.297500 | − | 0.954722i | \(-0.596153\pi\) | ||||
−0.297500 | + | 0.954722i | \(0.596153\pi\) | |||||||
\(600\) | 5.32624 | 0.217443 | ||||||||
\(601\) | 4.58359 | 0.186969 | 0.0934843 | − | 0.995621i | \(-0.470200\pi\) | ||||
0.0934843 | + | 0.995621i | \(0.470200\pi\) | |||||||
\(602\) | −7.09017 | −0.288974 | ||||||||
\(603\) | 13.2361 | 0.539014 | ||||||||
\(604\) | 10.2361 | 0.416500 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −6.94427 | −0.282092 | ||||||||
\(607\) | 23.1591 | 0.939997 | 0.469998 | − | 0.882667i | \(-0.344254\pi\) | ||||
0.469998 | + | 0.882667i | \(0.344254\pi\) | |||||||
\(608\) | 36.3607 | 1.47462 | ||||||||
\(609\) | −0.236068 | −0.00956596 | ||||||||
\(610\) | 7.94427 | 0.321654 | ||||||||
\(611\) | 21.7984 | 0.881868 | ||||||||
\(612\) | −5.61803 | −0.227096 | ||||||||
\(613\) | −24.5623 | −0.992062 | −0.496031 | − | 0.868305i | \(-0.665210\pi\) | ||||
−0.496031 | + | 0.868305i | \(0.665210\pi\) | |||||||
\(614\) | 4.97871 | 0.200925 | ||||||||
\(615\) | 15.9443 | 0.642935 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.32624 | −0.0533923 | −0.0266962 | − | 0.999644i | \(-0.508499\pi\) | ||||
−0.0266962 | + | 0.999644i | \(0.508499\pi\) | |||||||
\(618\) | −9.56231 | −0.384652 | ||||||||
\(619\) | −22.1803 | −0.891503 | −0.445752 | − | 0.895157i | \(-0.647064\pi\) | ||||
−0.445752 | + | 0.895157i | \(0.647064\pi\) | |||||||
\(620\) | 7.85410 | 0.315428 | ||||||||
\(621\) | −5.70820 | −0.229062 | ||||||||
\(622\) | −4.20163 | −0.168470 | ||||||||
\(623\) | 1.32624 | 0.0531346 | ||||||||
\(624\) | 7.85410 | 0.314416 | ||||||||
\(625\) | −7.41641 | −0.296656 | ||||||||
\(626\) | −19.8328 | −0.792679 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 11.0000 | 0.438948 | ||||||||
\(629\) | 20.8328 | 0.830659 | ||||||||
\(630\) | 1.00000 | 0.0398410 | ||||||||
\(631\) | 0.708204 | 0.0281932 | 0.0140966 | − | 0.999901i | \(-0.495513\pi\) | ||||
0.0140966 | + | 0.999901i | \(0.495513\pi\) | |||||||
\(632\) | 13.6180 | 0.541696 | ||||||||
\(633\) | −18.7082 | −0.743584 | ||||||||
\(634\) | 21.5623 | 0.856349 | ||||||||
\(635\) | −11.8541 | −0.470416 | ||||||||
\(636\) | −20.3262 | −0.805988 | ||||||||
\(637\) | −4.23607 | −0.167839 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.52786 | −0.179120 | ||||||||
\(640\) | −18.4164 | −0.727972 | ||||||||
\(641\) | 9.32624 | 0.368364 | 0.184182 | − | 0.982892i | \(-0.441036\pi\) | ||||
0.184182 | + | 0.982892i | \(0.441036\pi\) | |||||||
\(642\) | −3.56231 | −0.140593 | ||||||||
\(643\) | 5.88854 | 0.232221 | 0.116111 | − | 0.993236i | \(-0.462957\pi\) | ||||
0.116111 | + | 0.993236i | \(0.462957\pi\) | |||||||
\(644\) | −9.23607 | −0.363952 | ||||||||
\(645\) | 18.5623 | 0.730890 | ||||||||
\(646\) | 13.8885 | 0.546437 | ||||||||
\(647\) | 14.8885 | 0.585329 | 0.292665 | − | 0.956215i | \(-0.405458\pi\) | ||||
0.292665 | + | 0.956215i | \(0.405458\pi\) | |||||||
\(648\) | 2.23607 | 0.0878410 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −6.23607 | −0.244599 | ||||||||
\(651\) | −3.00000 | −0.117579 | ||||||||
\(652\) | 29.6525 | 1.16128 | ||||||||
\(653\) | −31.1803 | −1.22018 | −0.610090 | − | 0.792332i | \(-0.708867\pi\) | ||||
−0.610090 | + | 0.792332i | \(0.708867\pi\) | |||||||
\(654\) | 2.56231 | 0.100194 | ||||||||
\(655\) | 11.0902 | 0.433329 | ||||||||
\(656\) | 18.2705 | 0.713344 | ||||||||
\(657\) | −7.38197 | −0.287998 | ||||||||
\(658\) | 3.18034 | 0.123983 | ||||||||
\(659\) | 20.8885 | 0.813702 | 0.406851 | − | 0.913495i | \(-0.366627\pi\) | ||||
0.406851 | + | 0.913495i | \(0.366627\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.5967 | 0.723330 | 0.361665 | − | 0.932308i | \(-0.382208\pi\) | ||||
0.361665 | + | 0.932308i | \(0.382208\pi\) | |||||||
\(662\) | 11.9230 | 0.463400 | ||||||||
\(663\) | 14.7082 | 0.571219 | ||||||||
\(664\) | −18.9443 | −0.735180 | ||||||||
\(665\) | 10.4721 | 0.406092 | ||||||||
\(666\) | −3.70820 | −0.143690 | ||||||||
\(667\) | 1.34752 | 0.0521763 | ||||||||
\(668\) | −3.47214 | −0.134341 | ||||||||
\(669\) | −19.9443 | −0.771090 | ||||||||
\(670\) | 13.2361 | 0.511354 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 5.61803 | 0.216720 | ||||||||
\(673\) | 18.0557 | 0.695997 | 0.347999 | − | 0.937495i | \(-0.386861\pi\) | ||||
0.347999 | + | 0.937495i | \(0.386861\pi\) | |||||||
\(674\) | −2.61803 | −0.100843 | ||||||||
\(675\) | 2.38197 | 0.0916819 | ||||||||
\(676\) | −8.00000 | −0.307692 | ||||||||
\(677\) | −13.6738 | −0.525525 | −0.262763 | − | 0.964860i | \(-0.584634\pi\) | ||||
−0.262763 | + | 0.964860i | \(0.584634\pi\) | |||||||
\(678\) | −6.90983 | −0.265370 | ||||||||
\(679\) | −5.29180 | −0.203080 | ||||||||
\(680\) | −12.5623 | −0.481742 | ||||||||
\(681\) | −0.909830 | −0.0348648 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.4721 | −0.592025 | −0.296012 | − | 0.955184i | \(-0.595657\pi\) | ||||
−0.296012 | + | 0.955184i | \(0.595657\pi\) | |||||||
\(684\) | 10.4721 | 0.400412 | ||||||||
\(685\) | 16.9443 | 0.647407 | ||||||||
\(686\) | −0.618034 | −0.0235966 | ||||||||
\(687\) | −15.1246 | −0.577040 | ||||||||
\(688\) | 21.2705 | 0.810931 | ||||||||
\(689\) | 53.2148 | 2.02732 | ||||||||
\(690\) | −5.70820 | −0.217308 | ||||||||
\(691\) | −0.965558 | −0.0367316 | −0.0183658 | − | 0.999831i | \(-0.505846\pi\) | ||||
−0.0183658 | + | 0.999831i | \(0.505846\pi\) | |||||||
\(692\) | 17.4721 | 0.664191 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.291796 | −0.0110764 | ||||||||
\(695\) | 4.23607 | 0.160683 | ||||||||
\(696\) | −0.527864 | −0.0200086 | ||||||||
\(697\) | 34.2148 | 1.29598 | ||||||||
\(698\) | −10.7082 | −0.405311 | ||||||||
\(699\) | −15.7639 | −0.596247 | ||||||||
\(700\) | 3.85410 | 0.145671 | ||||||||
\(701\) | −33.9443 | −1.28206 | −0.641029 | − | 0.767517i | \(-0.721492\pi\) | ||||
−0.641029 | + | 0.767517i | \(0.721492\pi\) | |||||||
\(702\) | −2.61803 | −0.0988113 | ||||||||
\(703\) | −38.8328 | −1.46461 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8.32624 | −0.313584 | ||||||||
\(706\) | 2.54915 | 0.0959385 | ||||||||
\(707\) | −11.2361 | −0.422576 | ||||||||
\(708\) | −7.47214 | −0.280820 | ||||||||
\(709\) | −5.70820 | −0.214376 | −0.107188 | − | 0.994239i | \(-0.534185\pi\) | ||||
−0.107188 | + | 0.994239i | \(0.534185\pi\) | |||||||
\(710\) | −4.52786 | −0.169928 | ||||||||
\(711\) | 6.09017 | 0.228399 | ||||||||
\(712\) | 2.96556 | 0.111139 | ||||||||
\(713\) | 17.1246 | 0.641322 | ||||||||
\(714\) | 2.14590 | 0.0803082 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 30.2705 | 1.13126 | ||||||||
\(717\) | −21.6180 | −0.807340 | ||||||||
\(718\) | 6.41641 | 0.239458 | ||||||||
\(719\) | −33.4508 | −1.24751 | −0.623753 | − | 0.781621i | \(-0.714393\pi\) | ||||
−0.623753 | + | 0.781621i | \(0.714393\pi\) | |||||||
\(720\) | −3.00000 | −0.111803 | ||||||||
\(721\) | −15.4721 | −0.576212 | ||||||||
\(722\) | −14.1459 | −0.526456 | ||||||||
\(723\) | 10.4164 | 0.387390 | ||||||||
\(724\) | 0.854102 | 0.0317424 | ||||||||
\(725\) | −0.562306 | −0.0208835 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.03444 | −0.0754533 | −0.0377266 | − | 0.999288i | \(-0.512012\pi\) | ||||
−0.0377266 | + | 0.999288i | \(0.512012\pi\) | |||||||
\(728\) | −9.47214 | −0.351061 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −7.38197 | −0.273219 | ||||||||
\(731\) | 39.8328 | 1.47327 | ||||||||
\(732\) | 12.8541 | 0.475101 | ||||||||
\(733\) | −17.5836 | −0.649465 | −0.324732 | − | 0.945806i | \(-0.605274\pi\) | ||||
−0.324732 | + | 0.945806i | \(0.605274\pi\) | |||||||
\(734\) | 3.09017 | 0.114060 | ||||||||
\(735\) | 1.61803 | 0.0596821 | ||||||||
\(736\) | −32.0689 | −1.18207 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −6.09017 | −0.224182 | ||||||||
\(739\) | 40.1459 | 1.47679 | 0.738395 | − | 0.674368i | \(-0.235584\pi\) | ||||
0.738395 | + | 0.674368i | \(0.235584\pi\) | |||||||
\(740\) | 15.7082 | 0.577445 | ||||||||
\(741\) | −27.4164 | −1.00717 | ||||||||
\(742\) | 7.76393 | 0.285023 | ||||||||
\(743\) | −38.0902 | −1.39739 | −0.698696 | − | 0.715418i | \(-0.746236\pi\) | ||||
−0.698696 | + | 0.715418i | \(0.746236\pi\) | |||||||
\(744\) | −6.70820 | −0.245935 | ||||||||
\(745\) | −2.23607 | −0.0819232 | ||||||||
\(746\) | −12.5410 | −0.459159 | ||||||||
\(747\) | −8.47214 | −0.309979 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.76393 | −0.210609 | ||||||||
\(750\) | 7.38197 | 0.269551 | ||||||||
\(751\) | 50.5623 | 1.84504 | 0.922522 | − | 0.385944i | \(-0.126124\pi\) | ||||
0.922522 | + | 0.385944i | \(0.126124\pi\) | |||||||
\(752\) | −9.54102 | −0.347925 | ||||||||
\(753\) | 13.9443 | 0.508158 | ||||||||
\(754\) | 0.618034 | 0.0225075 | ||||||||
\(755\) | 10.2361 | 0.372529 | ||||||||
\(756\) | 1.61803 | 0.0588473 | ||||||||
\(757\) | 51.1246 | 1.85816 | 0.929078 | − | 0.369884i | \(-0.120603\pi\) | ||||
0.929078 | + | 0.369884i | \(0.120603\pi\) | |||||||
\(758\) | 1.18034 | 0.0428719 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 23.4164 | 0.849402 | ||||||||
\(761\) | −30.8541 | −1.11846 | −0.559230 | − | 0.829012i | \(-0.688903\pi\) | ||||
−0.559230 | + | 0.829012i | \(0.688903\pi\) | |||||||
\(762\) | 4.52786 | 0.164027 | ||||||||
\(763\) | 4.14590 | 0.150092 | ||||||||
\(764\) | 26.2705 | 0.950434 | ||||||||
\(765\) | −5.61803 | −0.203120 | ||||||||
\(766\) | 1.65248 | 0.0597064 | ||||||||
\(767\) | 19.5623 | 0.706354 | ||||||||
\(768\) | 6.56231 | 0.236797 | ||||||||
\(769\) | 53.7771 | 1.93925 | 0.969626 | − | 0.244594i | \(-0.0786545\pi\) | ||||
0.969626 | + | 0.244594i | \(0.0786545\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −23.8885 | −0.860325 | ||||||||
\(772\) | 28.1803 | 1.01423 | ||||||||
\(773\) | −30.9443 | −1.11299 | −0.556494 | − | 0.830852i | \(-0.687854\pi\) | ||||
−0.556494 | + | 0.830852i | \(0.687854\pi\) | |||||||
\(774\) | −7.09017 | −0.254851 | ||||||||
\(775\) | −7.14590 | −0.256688 | ||||||||
\(776\) | −11.8328 | −0.424773 | ||||||||
\(777\) | −6.00000 | −0.215249 | ||||||||
\(778\) | 10.6525 | 0.381910 | ||||||||
\(779\) | −63.7771 | −2.28505 | ||||||||
\(780\) | 11.0902 | 0.397092 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −12.2492 | −0.438031 | ||||||||
\(783\) | −0.236068 | −0.00843638 | ||||||||
\(784\) | 1.85410 | 0.0662179 | ||||||||
\(785\) | 11.0000 | 0.392607 | ||||||||
\(786\) | −4.23607 | −0.151096 | ||||||||
\(787\) | −0.562306 | −0.0200440 | −0.0100220 | − | 0.999950i | \(-0.503190\pi\) | ||||
−0.0100220 | + | 0.999950i | \(0.503190\pi\) | |||||||
\(788\) | 7.52786 | 0.268169 | ||||||||
\(789\) | −9.29180 | −0.330797 | ||||||||
\(790\) | 6.09017 | 0.216679 | ||||||||
\(791\) | −11.1803 | −0.397527 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −33.6525 | −1.19503 | ||||||||
\(794\) | 6.52786 | 0.231665 | ||||||||
\(795\) | −20.3262 | −0.720897 | ||||||||
\(796\) | 42.4164 | 1.50341 | ||||||||
\(797\) | 37.1459 | 1.31578 | 0.657888 | − | 0.753116i | \(-0.271450\pi\) | ||||
0.657888 | + | 0.753116i | \(0.271450\pi\) | |||||||
\(798\) | −4.00000 | −0.141598 | ||||||||
\(799\) | −17.8673 | −0.632098 | ||||||||
\(800\) | 13.3820 | 0.473124 | ||||||||
\(801\) | 1.32624 | 0.0468603 | ||||||||
\(802\) | −17.1459 | −0.605443 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 21.4164 | 0.755298 | ||||||||
\(805\) | −9.23607 | −0.325529 | ||||||||
\(806\) | 7.85410 | 0.276649 | ||||||||
\(807\) | 29.1803 | 1.02720 | ||||||||
\(808\) | −25.1246 | −0.883881 | ||||||||
\(809\) | 54.3951 | 1.91243 | 0.956215 | − | 0.292664i | \(-0.0945418\pi\) | ||||
0.956215 | + | 0.292664i | \(0.0945418\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | −47.7082 | −1.67526 | −0.837631 | − | 0.546237i | \(-0.816060\pi\) | ||||
−0.837631 | + | 0.546237i | \(0.816060\pi\) | |||||||
\(812\) | −0.381966 | −0.0134044 | ||||||||
\(813\) | −22.1246 | −0.775944 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 29.6525 | 1.03868 | ||||||||
\(816\) | −6.43769 | −0.225364 | ||||||||
\(817\) | −74.2492 | −2.59765 | ||||||||
\(818\) | 5.06888 | 0.177229 | ||||||||
\(819\) | −4.23607 | −0.148020 | ||||||||
\(820\) | 25.7984 | 0.900918 | ||||||||
\(821\) | 13.8197 | 0.482309 | 0.241155 | − | 0.970487i | \(-0.422474\pi\) | ||||
0.241155 | + | 0.970487i | \(0.422474\pi\) | |||||||
\(822\) | −6.47214 | −0.225742 | ||||||||
\(823\) | 22.4721 | 0.783329 | 0.391665 | − | 0.920108i | \(-0.371899\pi\) | ||||
0.391665 | + | 0.920108i | \(0.371899\pi\) | |||||||
\(824\) | −34.5967 | −1.20523 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.85410 | 0.0993069 | ||||||||
\(827\) | −41.9443 | −1.45855 | −0.729273 | − | 0.684223i | \(-0.760141\pi\) | ||||
−0.729273 | + | 0.684223i | \(0.760141\pi\) | |||||||
\(828\) | −9.23607 | −0.320976 | ||||||||
\(829\) | −0.673762 | −0.0234007 | −0.0117004 | − | 0.999932i | \(-0.503724\pi\) | ||||
−0.0117004 | + | 0.999932i | \(0.503724\pi\) | |||||||
\(830\) | −8.47214 | −0.294072 | ||||||||
\(831\) | 8.47214 | 0.293895 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | 3.47214 | 0.120302 | ||||||||
\(834\) | −1.61803 | −0.0560279 | ||||||||
\(835\) | −3.47214 | −0.120158 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.00000 | −0.103695 | ||||||||
\(838\) | 22.0132 | 0.760432 | ||||||||
\(839\) | −14.5279 | −0.501558 | −0.250779 | − | 0.968044i | \(-0.580687\pi\) | ||||
−0.250779 | + | 0.968044i | \(0.580687\pi\) | |||||||
\(840\) | 3.61803 | 0.124834 | ||||||||
\(841\) | −28.9443 | −0.998078 | ||||||||
\(842\) | −11.2148 | −0.386487 | ||||||||
\(843\) | 10.8541 | 0.373835 | ||||||||
\(844\) | −30.2705 | −1.04195 | ||||||||
\(845\) | −8.00000 | −0.275208 | ||||||||
\(846\) | 3.18034 | 0.109342 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −23.2918 | −0.799844 | ||||||||
\(849\) | 12.8885 | 0.442334 | ||||||||
\(850\) | 5.11146 | 0.175322 | ||||||||
\(851\) | 34.2492 | 1.17405 | ||||||||
\(852\) | −7.32624 | −0.250993 | ||||||||
\(853\) | −24.7984 | −0.849080 | −0.424540 | − | 0.905409i | \(-0.639564\pi\) | ||||
−0.424540 | + | 0.905409i | \(0.639564\pi\) | |||||||
\(854\) | −4.90983 | −0.168011 | ||||||||
\(855\) | 10.4721 | 0.358139 | ||||||||
\(856\) | −12.8885 | −0.440521 | ||||||||
\(857\) | 31.9443 | 1.09120 | 0.545598 | − | 0.838047i | \(-0.316303\pi\) | ||||
0.545598 | + | 0.838047i | \(0.316303\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.65248 | 0.0563817 | 0.0281909 | − | 0.999603i | \(-0.491025\pi\) | ||||
0.0281909 | + | 0.999603i | \(0.491025\pi\) | |||||||
\(860\) | 30.0344 | 1.02417 | ||||||||
\(861\) | −9.85410 | −0.335827 | ||||||||
\(862\) | −4.41641 | −0.150423 | ||||||||
\(863\) | 31.2492 | 1.06374 | 0.531868 | − | 0.846827i | \(-0.321490\pi\) | ||||
0.531868 | + | 0.846827i | \(0.321490\pi\) | |||||||
\(864\) | 5.61803 | 0.191129 | ||||||||
\(865\) | 17.4721 | 0.594070 | ||||||||
\(866\) | 4.29180 | 0.145841 | ||||||||
\(867\) | 4.94427 | 0.167916 | ||||||||
\(868\) | −4.85410 | −0.164759 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −0.236068 | −0.00800345 | ||||||||
\(871\) | −56.0689 | −1.89982 | ||||||||
\(872\) | 9.27051 | 0.313939 | ||||||||
\(873\) | −5.29180 | −0.179100 | ||||||||
\(874\) | 22.8328 | 0.772332 | ||||||||
\(875\) | 11.9443 | 0.403790 | ||||||||
\(876\) | −11.9443 | −0.403560 | ||||||||
\(877\) | 12.1459 | 0.410138 | 0.205069 | − | 0.978748i | \(-0.434258\pi\) | ||||
0.205069 | + | 0.978748i | \(0.434258\pi\) | |||||||
\(878\) | 22.0344 | 0.743626 | ||||||||
\(879\) | −7.70820 | −0.259991 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.29180 | −0.178285 | −0.0891426 | − | 0.996019i | \(-0.528413\pi\) | ||||
−0.0891426 | + | 0.996019i | \(0.528413\pi\) | |||||||
\(882\) | −0.618034 | −0.0208103 | ||||||||
\(883\) | −44.0902 | −1.48375 | −0.741876 | − | 0.670537i | \(-0.766064\pi\) | ||||
−0.741876 | + | 0.670537i | \(0.766064\pi\) | |||||||
\(884\) | 23.7984 | 0.800426 | ||||||||
\(885\) | −7.47214 | −0.251173 | ||||||||
\(886\) | −15.2361 | −0.511866 | ||||||||
\(887\) | −38.7082 | −1.29969 | −0.649847 | − | 0.760065i | \(-0.725167\pi\) | ||||
−0.649847 | + | 0.760065i | \(0.725167\pi\) | |||||||
\(888\) | −13.4164 | −0.450225 | ||||||||
\(889\) | 7.32624 | 0.245714 | ||||||||
\(890\) | 1.32624 | 0.0444556 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −32.2705 | −1.08050 | ||||||||
\(893\) | 33.3050 | 1.11451 | ||||||||
\(894\) | 0.854102 | 0.0285654 | ||||||||
\(895\) | 30.2705 | 1.01183 | ||||||||
\(896\) | 11.3820 | 0.380245 | ||||||||
\(897\) | 24.1803 | 0.807358 | ||||||||
\(898\) | 12.7295 | 0.424789 | ||||||||
\(899\) | 0.708204 | 0.0236199 | ||||||||
\(900\) | 3.85410 | 0.128470 | ||||||||
\(901\) | −43.6180 | −1.45313 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −11.4721 | −0.381769 | ||||||||
\(904\) | −25.0000 | −0.831488 | ||||||||
\(905\) | 0.854102 | 0.0283913 | ||||||||
\(906\) | −3.90983 | −0.129895 | ||||||||
\(907\) | −11.4934 | −0.381633 | −0.190816 | − | 0.981626i | \(-0.561114\pi\) | ||||
−0.190816 | + | 0.981626i | \(0.561114\pi\) | |||||||
\(908\) | −1.47214 | −0.0488545 | ||||||||
\(909\) | −11.2361 | −0.372677 | ||||||||
\(910\) | −4.23607 | −0.140424 | ||||||||
\(911\) | −31.9098 | −1.05722 | −0.528610 | − | 0.848865i | \(-0.677287\pi\) | ||||
−0.528610 | + | 0.848865i | \(0.677287\pi\) | |||||||
\(912\) | 12.0000 | 0.397360 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 11.5836 | 0.383151 | ||||||||
\(915\) | 12.8541 | 0.424944 | ||||||||
\(916\) | −24.4721 | −0.808582 | ||||||||
\(917\) | −6.85410 | −0.226342 | ||||||||
\(918\) | 2.14590 | 0.0708252 | ||||||||
\(919\) | 4.00000 | 0.131948 | 0.0659739 | − | 0.997821i | \(-0.478985\pi\) | ||||
0.0659739 | + | 0.997821i | \(0.478985\pi\) | |||||||
\(920\) | −20.6525 | −0.680892 | ||||||||
\(921\) | 8.05573 | 0.265445 | ||||||||
\(922\) | 17.4934 | 0.576115 | ||||||||
\(923\) | 19.1803 | 0.631329 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14.2918 | −0.469911 | ||||||||
\(926\) | 9.25735 | 0.304216 | ||||||||
\(927\) | −15.4721 | −0.508172 | ||||||||
\(928\) | −1.32624 | −0.0435359 | ||||||||
\(929\) | −9.88854 | −0.324433 | −0.162216 | − | 0.986755i | \(-0.551864\pi\) | ||||
−0.162216 | + | 0.986755i | \(0.551864\pi\) | |||||||
\(930\) | −3.00000 | −0.0983739 | ||||||||
\(931\) | −6.47214 | −0.212116 | ||||||||
\(932\) | −25.5066 | −0.835496 | ||||||||
\(933\) | −6.79837 | −0.222569 | ||||||||
\(934\) | 16.5066 | 0.540112 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −9.47214 | −0.309606 | ||||||||
\(937\) | 22.1246 | 0.722780 | 0.361390 | − | 0.932415i | \(-0.382302\pi\) | ||||
0.361390 | + | 0.932415i | \(0.382302\pi\) | |||||||
\(938\) | −8.18034 | −0.267098 | ||||||||
\(939\) | −32.0902 | −1.04722 | ||||||||
\(940\) | −13.4721 | −0.439413 | ||||||||
\(941\) | 2.40325 | 0.0783438 | 0.0391719 | − | 0.999232i | \(-0.487528\pi\) | ||||
0.0391719 | + | 0.999232i | \(0.487528\pi\) | |||||||
\(942\) | −4.20163 | −0.136896 | ||||||||
\(943\) | 56.2492 | 1.83173 | ||||||||
\(944\) | −8.56231 | −0.278679 | ||||||||
\(945\) | 1.61803 | 0.0526346 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.97871 | 0.161786 | 0.0808932 | − | 0.996723i | \(-0.474223\pi\) | ||||
0.0808932 | + | 0.996723i | \(0.474223\pi\) | |||||||
\(948\) | 9.85410 | 0.320046 | ||||||||
\(949\) | 31.2705 | 1.01508 | ||||||||
\(950\) | −9.52786 | −0.309125 | ||||||||
\(951\) | 34.8885 | 1.13134 | ||||||||
\(952\) | 7.76393 | 0.251630 | ||||||||
\(953\) | 10.0344 | 0.325047 | 0.162524 | − | 0.986705i | \(-0.448037\pi\) | ||||
0.162524 | + | 0.986705i | \(0.448037\pi\) | |||||||
\(954\) | 7.76393 | 0.251367 | ||||||||
\(955\) | 26.2705 | 0.850094 | ||||||||
\(956\) | −34.9787 | −1.13129 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 18.7771 | 0.606660 | ||||||||
\(959\) | −10.4721 | −0.338163 | ||||||||
\(960\) | −0.381966 | −0.0123279 | ||||||||
\(961\) | −22.0000 | −0.709677 | ||||||||
\(962\) | 15.7082 | 0.506453 | ||||||||
\(963\) | −5.76393 | −0.185740 | ||||||||
\(964\) | 16.8541 | 0.542834 | ||||||||
\(965\) | 28.1803 | 0.907157 | ||||||||
\(966\) | 3.52786 | 0.113507 | ||||||||
\(967\) | 48.6525 | 1.56456 | 0.782279 | − | 0.622928i | \(-0.214057\pi\) | ||||
0.782279 | + | 0.622928i | \(0.214057\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 22.4721 | 0.721909 | ||||||||
\(970\) | −5.29180 | −0.169909 | ||||||||
\(971\) | −10.4164 | −0.334278 | −0.167139 | − | 0.985933i | \(-0.553453\pi\) | ||||
−0.167139 | + | 0.985933i | \(0.553453\pi\) | |||||||
\(972\) | 1.61803 | 0.0518985 | ||||||||
\(973\) | −2.61803 | −0.0839303 | ||||||||
\(974\) | 9.50658 | 0.304610 | ||||||||
\(975\) | −10.0902 | −0.323144 | ||||||||
\(976\) | 14.7295 | 0.471479 | ||||||||
\(977\) | 42.7771 | 1.36856 | 0.684280 | − | 0.729219i | \(-0.260117\pi\) | ||||
0.684280 | + | 0.729219i | \(0.260117\pi\) | |||||||
\(978\) | −11.3262 | −0.362173 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 2.61803 | 0.0836300 | ||||||||
\(981\) | 4.14590 | 0.132368 | ||||||||
\(982\) | −5.12461 | −0.163533 | ||||||||
\(983\) | 50.5967 | 1.61379 | 0.806893 | − | 0.590698i | \(-0.201147\pi\) | ||||
0.806893 | + | 0.590698i | \(0.201147\pi\) | |||||||
\(984\) | −22.0344 | −0.702432 | ||||||||
\(985\) | 7.52786 | 0.239858 | ||||||||
\(986\) | −0.506578 | −0.0161327 | ||||||||
\(987\) | 5.14590 | 0.163796 | ||||||||
\(988\) | −44.3607 | −1.41130 | ||||||||
\(989\) | 65.4853 | 2.08231 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28.6180 | −0.909082 | −0.454541 | − | 0.890726i | \(-0.650197\pi\) | ||||
−0.454541 | + | 0.890726i | \(0.650197\pi\) | |||||||
\(992\) | −16.8541 | −0.535118 | ||||||||
\(993\) | 19.2918 | 0.612207 | ||||||||
\(994\) | 2.79837 | 0.0887590 | ||||||||
\(995\) | 42.4164 | 1.34469 | ||||||||
\(996\) | −13.7082 | −0.434361 | ||||||||
\(997\) | 41.1935 | 1.30461 | 0.652306 | − | 0.757956i | \(-0.273802\pi\) | ||||
0.652306 | + | 0.757956i | \(0.273802\pi\) | |||||||
\(998\) | −4.32624 | −0.136945 | ||||||||
\(999\) | −6.00000 | −0.189832 |
(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 | 2541.2.a.x.1.1 | 2 | ||
3.2 | odd | 2 | 7623.2.a.z.1.2 | 2 | |||
11.2 | odd | 10 | 231.2.j.b.169.1 | ✓ | 4 | ||
11.6 | odd | 10 | 231.2.j.b.190.1 | yes | 4 | ||
11.10 | odd | 2 | 2541.2.a.p.1.2 | 2 | |||
33.2 | even | 10 | 693.2.m.d.631.1 | 4 | |||
33.17 | even | 10 | 693.2.m.d.190.1 | 4 | |||
33.32 | even | 2 | 7623.2.a.bo.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
231.2.j.b.169.1 | ✓ | 4 | 11.2 | odd | 10 | ||
231.2.j.b.190.1 | yes | 4 | 11.6 | odd | 10 | ||
693.2.m.d.190.1 | 4 | 33.17 | even | 10 | |||
693.2.m.d.631.1 | 4 | 33.2 | even | 10 | |||
2541.2.a.p.1.2 | 2 | 11.10 | odd | 2 | |||
2541.2.a.x.1.1 | 2 | 1.1 | even | 1 | trivial | ||
7623.2.a.z.1.2 | 2 | 3.2 | odd | 2 | |||
7623.2.a.bo.1.1 | 2 | 33.32 | even | 2 |