Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2523,2,Mod(1,2523)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2523, 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("2523.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2523 = 3 \cdot 29^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2523.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: | \(20.1462564300\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - x^{8} - 14x^{7} + 9x^{6} + 70x^{5} - 23x^{4} - 141x^{3} + 14x^{2} + 84x - 7 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 87) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(0.0831558\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2523.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.0831558 | −0.0588000 | −0.0294000 | − | 0.999568i | \(-0.509360\pi\) | ||||
−0.0294000 | + | 0.999568i | \(0.509360\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.99309 | −0.996543 | ||||||||
\(5\) | 1.93038 | 0.863291 | 0.431646 | − | 0.902043i | \(-0.357933\pi\) | ||||
0.431646 | + | 0.902043i | \(0.357933\pi\) | |||||||
\(6\) | 0.0831558 | 0.0339482 | ||||||||
\(7\) | 0.343925 | 0.129991 | 0.0649957 | − | 0.997886i | \(-0.479297\pi\) | ||||
0.0649957 | + | 0.997886i | \(0.479297\pi\) | |||||||
\(8\) | 0.332048 | 0.117397 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.160522 | −0.0507616 | ||||||||
\(11\) | −2.42414 | −0.730907 | −0.365454 | − | 0.930830i | \(-0.619086\pi\) | ||||
−0.365454 | + | 0.930830i | \(0.619086\pi\) | |||||||
\(12\) | 1.99309 | 0.575354 | ||||||||
\(13\) | 3.63120 | 1.00711 | 0.503557 | − | 0.863962i | \(-0.332024\pi\) | ||||
0.503557 | + | 0.863962i | \(0.332024\pi\) | |||||||
\(14\) | −0.0285993 | −0.00764350 | ||||||||
\(15\) | −1.93038 | −0.498422 | ||||||||
\(16\) | 3.95856 | 0.989640 | ||||||||
\(17\) | −6.15354 | −1.49245 | −0.746227 | − | 0.665692i | \(-0.768137\pi\) | ||||
−0.746227 | + | 0.665692i | \(0.768137\pi\) | |||||||
\(18\) | −0.0831558 | −0.0196000 | ||||||||
\(19\) | −1.35067 | −0.309866 | −0.154933 | − | 0.987925i | \(-0.549516\pi\) | ||||
−0.154933 | + | 0.987925i | \(0.549516\pi\) | |||||||
\(20\) | −3.84741 | −0.860307 | ||||||||
\(21\) | −0.343925 | −0.0750505 | ||||||||
\(22\) | 0.201582 | 0.0429774 | ||||||||
\(23\) | −3.46619 | −0.722751 | −0.361376 | − | 0.932420i | \(-0.617693\pi\) | ||||
−0.361376 | + | 0.932420i | \(0.617693\pi\) | |||||||
\(24\) | −0.332048 | −0.0677791 | ||||||||
\(25\) | −1.27364 | −0.254728 | ||||||||
\(26\) | −0.301955 | −0.0592183 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.685471 | −0.129542 | ||||||||
\(29\) | 0 | 0 | ||||||||
\(30\) | 0.160522 | 0.0293072 | ||||||||
\(31\) | 10.9901 | 1.97388 | 0.986941 | − | 0.161080i | \(-0.0514976\pi\) | ||||
0.986941 | + | 0.161080i | \(0.0514976\pi\) | |||||||
\(32\) | −0.993273 | −0.175588 | ||||||||
\(33\) | 2.42414 | 0.421989 | ||||||||
\(34\) | 0.511703 | 0.0877563 | ||||||||
\(35\) | 0.663905 | 0.112220 | ||||||||
\(36\) | −1.99309 | −0.332181 | ||||||||
\(37\) | −3.08722 | −0.507536 | −0.253768 | − | 0.967265i | \(-0.581670\pi\) | ||||
−0.253768 | + | 0.967265i | \(0.581670\pi\) | |||||||
\(38\) | 0.112316 | 0.0182201 | ||||||||
\(39\) | −3.63120 | −0.581457 | ||||||||
\(40\) | 0.640979 | 0.101348 | ||||||||
\(41\) | 5.28313 | 0.825086 | 0.412543 | − | 0.910938i | \(-0.364641\pi\) | ||||
0.412543 | + | 0.910938i | \(0.364641\pi\) | |||||||
\(42\) | 0.0285993 | 0.00441297 | ||||||||
\(43\) | −0.00844158 | −0.00128733 | −0.000643664 | − | 1.00000i | \(-0.500205\pi\) | ||||
−0.000643664 | 1.00000i | \(0.500205\pi\) | ||||||||
\(44\) | 4.83153 | 0.728380 | ||||||||
\(45\) | 1.93038 | 0.287764 | ||||||||
\(46\) | 0.288234 | 0.0424978 | ||||||||
\(47\) | −5.79676 | −0.845544 | −0.422772 | − | 0.906236i | \(-0.638943\pi\) | ||||
−0.422772 | + | 0.906236i | \(0.638943\pi\) | |||||||
\(48\) | −3.95856 | −0.571369 | ||||||||
\(49\) | −6.88172 | −0.983102 | ||||||||
\(50\) | 0.105911 | 0.0149780 | ||||||||
\(51\) | 6.15354 | 0.861668 | ||||||||
\(52\) | −7.23729 | −1.00363 | ||||||||
\(53\) | −4.14234 | −0.568994 | −0.284497 | − | 0.958677i | \(-0.591827\pi\) | ||||
−0.284497 | + | 0.958677i | \(0.591827\pi\) | |||||||
\(54\) | 0.0831558 | 0.0113161 | ||||||||
\(55\) | −4.67952 | −0.630986 | ||||||||
\(56\) | 0.114200 | 0.0152606 | ||||||||
\(57\) | 1.35067 | 0.178901 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.76819 | 0.750955 | 0.375477 | − | 0.926832i | \(-0.377479\pi\) | ||||
0.375477 | + | 0.926832i | \(0.377479\pi\) | |||||||
\(60\) | 3.84741 | 0.496698 | ||||||||
\(61\) | −6.23784 | −0.798673 | −0.399337 | − | 0.916804i | \(-0.630760\pi\) | ||||
−0.399337 | + | 0.916804i | \(0.630760\pi\) | |||||||
\(62\) | −0.913892 | −0.116064 | ||||||||
\(63\) | 0.343925 | 0.0433305 | ||||||||
\(64\) | −7.83452 | −0.979315 | ||||||||
\(65\) | 7.00959 | 0.869432 | ||||||||
\(66\) | −0.201582 | −0.0248130 | ||||||||
\(67\) | 11.0142 | 1.34560 | 0.672800 | − | 0.739824i | \(-0.265091\pi\) | ||||
0.672800 | + | 0.739824i | \(0.265091\pi\) | |||||||
\(68\) | 12.2645 | 1.48729 | ||||||||
\(69\) | 3.46619 | 0.417281 | ||||||||
\(70\) | −0.0552076 | −0.00659856 | ||||||||
\(71\) | 12.8548 | 1.52558 | 0.762791 | − | 0.646645i | \(-0.223829\pi\) | ||||
0.762791 | + | 0.646645i | \(0.223829\pi\) | |||||||
\(72\) | 0.332048 | 0.0391323 | ||||||||
\(73\) | 0.459207 | 0.0537461 | 0.0268731 | − | 0.999639i | \(-0.491445\pi\) | ||||
0.0268731 | + | 0.999639i | \(0.491445\pi\) | |||||||
\(74\) | 0.256721 | 0.0298432 | ||||||||
\(75\) | 1.27364 | 0.147067 | ||||||||
\(76\) | 2.69201 | 0.308794 | ||||||||
\(77\) | −0.833724 | −0.0950116 | ||||||||
\(78\) | 0.301955 | 0.0341897 | ||||||||
\(79\) | −12.4792 | −1.40402 | −0.702010 | − | 0.712167i | \(-0.747714\pi\) | ||||
−0.702010 | + | 0.712167i | \(0.747714\pi\) | |||||||
\(80\) | 7.64152 | 0.854347 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.439323 | −0.0485151 | ||||||||
\(83\) | 2.87846 | 0.315952 | 0.157976 | − | 0.987443i | \(-0.449503\pi\) | ||||
0.157976 | + | 0.987443i | \(0.449503\pi\) | |||||||
\(84\) | 0.685471 | 0.0747911 | ||||||||
\(85\) | −11.8787 | −1.28842 | ||||||||
\(86\) | 0.000701966 0 | 7.56950e−5 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.804933 | −0.0858061 | ||||||||
\(89\) | −12.2239 | −1.29574 | −0.647868 | − | 0.761753i | \(-0.724339\pi\) | ||||
−0.647868 | + | 0.761753i | \(0.724339\pi\) | |||||||
\(90\) | −0.160522 | −0.0169205 | ||||||||
\(91\) | 1.24886 | 0.130916 | ||||||||
\(92\) | 6.90842 | 0.720253 | ||||||||
\(93\) | −10.9901 | −1.13962 | ||||||||
\(94\) | 0.482034 | 0.0497180 | ||||||||
\(95\) | −2.60731 | −0.267504 | ||||||||
\(96\) | 0.993273 | 0.101376 | ||||||||
\(97\) | −2.72420 | −0.276601 | −0.138300 | − | 0.990390i | \(-0.544164\pi\) | ||||
−0.138300 | + | 0.990390i | \(0.544164\pi\) | |||||||
\(98\) | 0.572255 | 0.0578064 | ||||||||
\(99\) | −2.42414 | −0.243636 | ||||||||
\(100\) | 2.53847 | 0.253847 | ||||||||
\(101\) | −18.2696 | −1.81789 | −0.908947 | − | 0.416911i | \(-0.863113\pi\) | ||||
−0.908947 | + | 0.416911i | \(0.863113\pi\) | |||||||
\(102\) | −0.511703 | −0.0506661 | ||||||||
\(103\) | −16.0696 | −1.58339 | −0.791694 | − | 0.610918i | \(-0.790800\pi\) | ||||
−0.791694 | + | 0.610918i | \(0.790800\pi\) | |||||||
\(104\) | 1.20573 | 0.118232 | ||||||||
\(105\) | −0.663905 | −0.0647905 | ||||||||
\(106\) | 0.344459 | 0.0334569 | ||||||||
\(107\) | −16.1760 | −1.56379 | −0.781897 | − | 0.623408i | \(-0.785748\pi\) | ||||
−0.781897 | + | 0.623408i | \(0.785748\pi\) | |||||||
\(108\) | 1.99309 | 0.191785 | ||||||||
\(109\) | 9.19953 | 0.881155 | 0.440577 | − | 0.897715i | \(-0.354774\pi\) | ||||
0.440577 | + | 0.897715i | \(0.354774\pi\) | |||||||
\(110\) | 0.389129 | 0.0371020 | ||||||||
\(111\) | 3.08722 | 0.293026 | ||||||||
\(112\) | 1.36145 | 0.128645 | ||||||||
\(113\) | −20.2563 | −1.90555 | −0.952774 | − | 0.303679i | \(-0.901785\pi\) | ||||
−0.952774 | + | 0.303679i | \(0.901785\pi\) | |||||||
\(114\) | −0.112316 | −0.0105194 | ||||||||
\(115\) | −6.69107 | −0.623945 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.63120 | 0.335704 | ||||||||
\(118\) | −0.479659 | −0.0441562 | ||||||||
\(119\) | −2.11636 | −0.194006 | ||||||||
\(120\) | −0.640979 | −0.0585131 | ||||||||
\(121\) | −5.12352 | −0.465775 | ||||||||
\(122\) | 0.518713 | 0.0469620 | ||||||||
\(123\) | −5.28313 | −0.476364 | ||||||||
\(124\) | −21.9042 | −1.96706 | ||||||||
\(125\) | −12.1105 | −1.08320 | ||||||||
\(126\) | −0.0285993 | −0.00254783 | ||||||||
\(127\) | 9.56458 | 0.848719 | 0.424360 | − | 0.905494i | \(-0.360499\pi\) | ||||
0.424360 | + | 0.905494i | \(0.360499\pi\) | |||||||
\(128\) | 2.63803 | 0.233171 | ||||||||
\(129\) | 0.00844158 | 0.000743240 0 | ||||||||
\(130\) | −0.582888 | −0.0511227 | ||||||||
\(131\) | 16.8025 | 1.46804 | 0.734019 | − | 0.679129i | \(-0.237642\pi\) | ||||
0.734019 | + | 0.679129i | \(0.237642\pi\) | |||||||
\(132\) | −4.83153 | −0.420530 | ||||||||
\(133\) | −0.464530 | −0.0402799 | ||||||||
\(134\) | −0.915896 | −0.0791213 | ||||||||
\(135\) | −1.93038 | −0.166141 | ||||||||
\(136\) | −2.04327 | −0.175209 | ||||||||
\(137\) | −5.75126 | −0.491363 | −0.245682 | − | 0.969351i | \(-0.579012\pi\) | ||||
−0.245682 | + | 0.969351i | \(0.579012\pi\) | |||||||
\(138\) | −0.288234 | −0.0245361 | ||||||||
\(139\) | 1.56684 | 0.132898 | 0.0664488 | − | 0.997790i | \(-0.478833\pi\) | ||||
0.0664488 | + | 0.997790i | \(0.478833\pi\) | |||||||
\(140\) | −1.32322 | −0.111832 | ||||||||
\(141\) | 5.79676 | 0.488175 | ||||||||
\(142\) | −1.06895 | −0.0897043 | ||||||||
\(143\) | −8.80255 | −0.736106 | ||||||||
\(144\) | 3.95856 | 0.329880 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.0381857 | −0.00316027 | ||||||||
\(147\) | 6.88172 | 0.567594 | ||||||||
\(148\) | 6.15310 | 0.505782 | ||||||||
\(149\) | 12.6315 | 1.03481 | 0.517406 | − | 0.855740i | \(-0.326898\pi\) | ||||
0.517406 | + | 0.855740i | \(0.326898\pi\) | |||||||
\(150\) | −0.105911 | −0.00864756 | ||||||||
\(151\) | −10.2677 | −0.835572 | −0.417786 | − | 0.908545i | \(-0.637194\pi\) | ||||
−0.417786 | + | 0.908545i | \(0.637194\pi\) | |||||||
\(152\) | −0.448489 | −0.0363772 | ||||||||
\(153\) | −6.15354 | −0.497484 | ||||||||
\(154\) | 0.0693290 | 0.00558669 | ||||||||
\(155\) | 21.2151 | 1.70404 | ||||||||
\(156\) | 7.23729 | 0.579447 | ||||||||
\(157\) | −3.78665 | −0.302207 | −0.151104 | − | 0.988518i | \(-0.548283\pi\) | ||||
−0.151104 | + | 0.988518i | \(0.548283\pi\) | |||||||
\(158\) | 1.03772 | 0.0825564 | ||||||||
\(159\) | 4.14234 | 0.328509 | ||||||||
\(160\) | −1.91739 | −0.151583 | ||||||||
\(161\) | −1.19211 | −0.0939514 | ||||||||
\(162\) | −0.0831558 | −0.00653334 | ||||||||
\(163\) | −6.08181 | −0.476364 | −0.238182 | − | 0.971221i | \(-0.576552\pi\) | ||||
−0.238182 | + | 0.971221i | \(0.576552\pi\) | |||||||
\(164\) | −10.5297 | −0.822233 | ||||||||
\(165\) | 4.67952 | 0.364300 | ||||||||
\(166\) | −0.239361 | −0.0185780 | ||||||||
\(167\) | −7.67550 | −0.593948 | −0.296974 | − | 0.954886i | \(-0.595977\pi\) | ||||
−0.296974 | + | 0.954886i | \(0.595977\pi\) | |||||||
\(168\) | −0.114200 | −0.00881069 | ||||||||
\(169\) | 0.185607 | 0.0142774 | ||||||||
\(170\) | 0.987780 | 0.0757593 | ||||||||
\(171\) | −1.35067 | −0.103289 | ||||||||
\(172\) | 0.0168248 | 0.00128288 | ||||||||
\(173\) | −14.9932 | −1.13991 | −0.569956 | − | 0.821675i | \(-0.693040\pi\) | ||||
−0.569956 | + | 0.821675i | \(0.693040\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.438036 | −0.0331124 | ||||||||
\(176\) | −9.59612 | −0.723335 | ||||||||
\(177\) | −5.76819 | −0.433564 | ||||||||
\(178\) | 1.01649 | 0.0761893 | ||||||||
\(179\) | −16.0802 | −1.20189 | −0.600947 | − | 0.799289i | \(-0.705210\pi\) | ||||
−0.600947 | + | 0.799289i | \(0.705210\pi\) | |||||||
\(180\) | −3.84741 | −0.286769 | ||||||||
\(181\) | −5.67342 | −0.421702 | −0.210851 | − | 0.977518i | \(-0.567623\pi\) | ||||
−0.210851 | + | 0.977518i | \(0.567623\pi\) | |||||||
\(182\) | −0.103850 | −0.00769787 | ||||||||
\(183\) | 6.23784 | 0.461114 | ||||||||
\(184\) | −1.15094 | −0.0848487 | ||||||||
\(185\) | −5.95951 | −0.438152 | ||||||||
\(186\) | 0.913892 | 0.0670098 | ||||||||
\(187\) | 14.9171 | 1.09084 | ||||||||
\(188\) | 11.5534 | 0.842620 | ||||||||
\(189\) | −0.343925 | −0.0250168 | ||||||||
\(190\) | 0.216813 | 0.0157293 | ||||||||
\(191\) | 0.636893 | 0.0460839 | 0.0230420 | − | 0.999734i | \(-0.492665\pi\) | ||||
0.0230420 | + | 0.999734i | \(0.492665\pi\) | |||||||
\(192\) | 7.83452 | 0.565408 | ||||||||
\(193\) | −11.3433 | −0.816510 | −0.408255 | − | 0.912868i | \(-0.633863\pi\) | ||||
−0.408255 | + | 0.912868i | \(0.633863\pi\) | |||||||
\(194\) | 0.226533 | 0.0162641 | ||||||||
\(195\) | −7.00959 | −0.501967 | ||||||||
\(196\) | 13.7158 | 0.979703 | ||||||||
\(197\) | −16.9281 | −1.20608 | −0.603038 | − | 0.797712i | \(-0.706043\pi\) | ||||
−0.603038 | + | 0.797712i | \(0.706043\pi\) | |||||||
\(198\) | 0.201582 | 0.0143258 | ||||||||
\(199\) | 8.67794 | 0.615163 | 0.307581 | − | 0.951522i | \(-0.400480\pi\) | ||||
0.307581 | + | 0.951522i | \(0.400480\pi\) | |||||||
\(200\) | −0.422910 | −0.0299042 | ||||||||
\(201\) | −11.0142 | −0.776883 | ||||||||
\(202\) | 1.51922 | 0.106892 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −12.2645 | −0.858689 | ||||||||
\(205\) | 10.1984 | 0.712290 | ||||||||
\(206\) | 1.33628 | 0.0931032 | ||||||||
\(207\) | −3.46619 | −0.240917 | ||||||||
\(208\) | 14.3743 | 0.996679 | ||||||||
\(209\) | 3.27423 | 0.226483 | ||||||||
\(210\) | 0.0552076 | 0.00380968 | ||||||||
\(211\) | 12.7515 | 0.877850 | 0.438925 | − | 0.898524i | \(-0.355359\pi\) | ||||
0.438925 | + | 0.898524i | \(0.355359\pi\) | |||||||
\(212\) | 8.25603 | 0.567027 | ||||||||
\(213\) | −12.8548 | −0.880795 | ||||||||
\(214\) | 1.34513 | 0.0919511 | ||||||||
\(215\) | −0.0162954 | −0.00111134 | ||||||||
\(216\) | −0.332048 | −0.0225930 | ||||||||
\(217\) | 3.77977 | 0.256588 | ||||||||
\(218\) | −0.764994 | −0.0518119 | ||||||||
\(219\) | −0.459207 | −0.0310303 | ||||||||
\(220\) | 9.32667 | 0.628804 | ||||||||
\(221\) | −22.3447 | −1.50307 | ||||||||
\(222\) | −0.256721 | −0.0172300 | ||||||||
\(223\) | 19.1389 | 1.28164 | 0.640819 | − | 0.767692i | \(-0.278595\pi\) | ||||
0.640819 | + | 0.767692i | \(0.278595\pi\) | |||||||
\(224\) | −0.341611 | −0.0228249 | ||||||||
\(225\) | −1.27364 | −0.0849093 | ||||||||
\(226\) | 1.68443 | 0.112046 | ||||||||
\(227\) | −24.7509 | −1.64278 | −0.821389 | − | 0.570368i | \(-0.806800\pi\) | ||||
−0.821389 | + | 0.570368i | \(0.806800\pi\) | |||||||
\(228\) | −2.69201 | −0.178282 | ||||||||
\(229\) | −19.4336 | −1.28421 | −0.642106 | − | 0.766616i | \(-0.721939\pi\) | ||||
−0.642106 | + | 0.766616i | \(0.721939\pi\) | |||||||
\(230\) | 0.556401 | 0.0366880 | ||||||||
\(231\) | 0.833724 | 0.0548550 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.2842 | 1.19784 | 0.598918 | − | 0.800810i | \(-0.295598\pi\) | ||||
0.598918 | + | 0.800810i | \(0.295598\pi\) | |||||||
\(234\) | −0.301955 | −0.0197394 | ||||||||
\(235\) | −11.1899 | −0.729951 | ||||||||
\(236\) | −11.4965 | −0.748359 | ||||||||
\(237\) | 12.4792 | 0.810611 | ||||||||
\(238\) | 0.175987 | 0.0114076 | ||||||||
\(239\) | 8.19384 | 0.530015 | 0.265008 | − | 0.964246i | \(-0.414626\pi\) | ||||
0.265008 | + | 0.964246i | \(0.414626\pi\) | |||||||
\(240\) | −7.64152 | −0.493258 | ||||||||
\(241\) | −7.14233 | −0.460078 | −0.230039 | − | 0.973181i | \(-0.573885\pi\) | ||||
−0.230039 | + | 0.973181i | \(0.573885\pi\) | |||||||
\(242\) | 0.426051 | 0.0273876 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 12.4325 | 0.795912 | ||||||||
\(245\) | −13.2843 | −0.848704 | ||||||||
\(246\) | 0.439323 | 0.0280102 | ||||||||
\(247\) | −4.90456 | −0.312070 | ||||||||
\(248\) | 3.64925 | 0.231727 | ||||||||
\(249\) | −2.87846 | −0.182415 | ||||||||
\(250\) | 1.00706 | 0.0636919 | ||||||||
\(251\) | 2.32177 | 0.146549 | 0.0732744 | − | 0.997312i | \(-0.476655\pi\) | ||||
0.0732744 | + | 0.997312i | \(0.476655\pi\) | |||||||
\(252\) | −0.685471 | −0.0431806 | ||||||||
\(253\) | 8.40256 | 0.528264 | ||||||||
\(254\) | −0.795350 | −0.0499047 | ||||||||
\(255\) | 11.8787 | 0.743871 | ||||||||
\(256\) | 15.4497 | 0.965605 | ||||||||
\(257\) | −22.7822 | −1.42111 | −0.710557 | − | 0.703640i | \(-0.751557\pi\) | ||||
−0.710557 | + | 0.703640i | \(0.751557\pi\) | |||||||
\(258\) | −0.000701966 0 | −4.37025e−5 0 | ||||||||
\(259\) | −1.06177 | −0.0659754 | ||||||||
\(260\) | −13.9707 | −0.866426 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.39722 | −0.0863207 | ||||||||
\(263\) | −0.955452 | −0.0589157 | −0.0294578 | − | 0.999566i | \(-0.509378\pi\) | ||||
−0.0294578 | + | 0.999566i | \(0.509378\pi\) | |||||||
\(264\) | 0.804933 | 0.0495402 | ||||||||
\(265\) | −7.99628 | −0.491208 | ||||||||
\(266\) | 0.0386284 | 0.00236846 | ||||||||
\(267\) | 12.2239 | 0.748093 | ||||||||
\(268\) | −21.9523 | −1.34095 | ||||||||
\(269\) | 15.1464 | 0.923493 | 0.461746 | − | 0.887012i | \(-0.347223\pi\) | ||||
0.461746 | + | 0.887012i | \(0.347223\pi\) | |||||||
\(270\) | 0.160522 | 0.00976907 | ||||||||
\(271\) | −8.25078 | −0.501199 | −0.250600 | − | 0.968091i | \(-0.580628\pi\) | ||||
−0.250600 | + | 0.968091i | \(0.580628\pi\) | |||||||
\(272\) | −24.3592 | −1.47699 | ||||||||
\(273\) | −1.24886 | −0.0755844 | ||||||||
\(274\) | 0.478250 | 0.0288922 | ||||||||
\(275\) | 3.08749 | 0.186182 | ||||||||
\(276\) | −6.90842 | −0.415838 | ||||||||
\(277\) | 16.7332 | 1.00540 | 0.502700 | − | 0.864461i | \(-0.332340\pi\) | ||||
0.502700 | + | 0.864461i | \(0.332340\pi\) | |||||||
\(278\) | −0.130292 | −0.00781439 | ||||||||
\(279\) | 10.9901 | 0.657961 | ||||||||
\(280\) | 0.220448 | 0.0131743 | ||||||||
\(281\) | −22.1439 | −1.32099 | −0.660496 | − | 0.750830i | \(-0.729654\pi\) | ||||
−0.660496 | + | 0.750830i | \(0.729654\pi\) | |||||||
\(282\) | −0.482034 | −0.0287047 | ||||||||
\(283\) | −17.6596 | −1.04976 | −0.524878 | − | 0.851177i | \(-0.675889\pi\) | ||||
−0.524878 | + | 0.851177i | \(0.675889\pi\) | |||||||
\(284\) | −25.6207 | −1.52031 | ||||||||
\(285\) | 2.60731 | 0.154444 | ||||||||
\(286\) | 0.731983 | 0.0432831 | ||||||||
\(287\) | 1.81700 | 0.107254 | ||||||||
\(288\) | −0.993273 | −0.0585292 | ||||||||
\(289\) | 20.8661 | 1.22742 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.72420 | 0.159695 | ||||||||
\(292\) | −0.915239 | −0.0535603 | ||||||||
\(293\) | 23.1447 | 1.35213 | 0.676063 | − | 0.736844i | \(-0.263685\pi\) | ||||
0.676063 | + | 0.736844i | \(0.263685\pi\) | |||||||
\(294\) | −0.572255 | −0.0333746 | ||||||||
\(295\) | 11.1348 | 0.648293 | ||||||||
\(296\) | −1.02511 | −0.0595831 | ||||||||
\(297\) | 2.42414 | 0.140663 | ||||||||
\(298\) | −1.05038 | −0.0608470 | ||||||||
\(299\) | −12.5864 | −0.727893 | ||||||||
\(300\) | −2.53847 | −0.146559 | ||||||||
\(301\) | −0.00290327 | −0.000167342 0 | ||||||||
\(302\) | 0.853817 | 0.0491317 | ||||||||
\(303\) | 18.2696 | 1.04956 | ||||||||
\(304\) | −5.34672 | −0.306655 | ||||||||
\(305\) | −12.0414 | −0.689488 | ||||||||
\(306\) | 0.511703 | 0.0292521 | ||||||||
\(307\) | −22.9984 | −1.31259 | −0.656293 | − | 0.754506i | \(-0.727876\pi\) | ||||
−0.656293 | + | 0.754506i | \(0.727876\pi\) | |||||||
\(308\) | 1.66168 | 0.0946831 | ||||||||
\(309\) | 16.0696 | 0.914169 | ||||||||
\(310\) | −1.76416 | −0.100197 | ||||||||
\(311\) | 4.08071 | 0.231396 | 0.115698 | − | 0.993284i | \(-0.463090\pi\) | ||||
0.115698 | + | 0.993284i | \(0.463090\pi\) | |||||||
\(312\) | −1.20573 | −0.0682612 | ||||||||
\(313\) | 28.7526 | 1.62519 | 0.812597 | − | 0.582826i | \(-0.198053\pi\) | ||||
0.812597 | + | 0.582826i | \(0.198053\pi\) | |||||||
\(314\) | 0.314882 | 0.0177698 | ||||||||
\(315\) | 0.663905 | 0.0374068 | ||||||||
\(316\) | 24.8721 | 1.39917 | ||||||||
\(317\) | 11.5299 | 0.647583 | 0.323792 | − | 0.946128i | \(-0.395042\pi\) | ||||
0.323792 | + | 0.946128i | \(0.395042\pi\) | |||||||
\(318\) | −0.344459 | −0.0193163 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −15.1236 | −0.845434 | ||||||||
\(321\) | 16.1760 | 0.902857 | ||||||||
\(322\) | 0.0991309 | 0.00552435 | ||||||||
\(323\) | 8.31143 | 0.462460 | ||||||||
\(324\) | −1.99309 | −0.110727 | ||||||||
\(325\) | −4.62484 | −0.256540 | ||||||||
\(326\) | 0.505738 | 0.0280102 | ||||||||
\(327\) | −9.19953 | −0.508735 | ||||||||
\(328\) | 1.75425 | 0.0968624 | ||||||||
\(329\) | −1.99365 | −0.109913 | ||||||||
\(330\) | −0.389129 | −0.0214208 | ||||||||
\(331\) | 12.3038 | 0.676277 | 0.338139 | − | 0.941096i | \(-0.390203\pi\) | ||||
0.338139 | + | 0.941096i | \(0.390203\pi\) | |||||||
\(332\) | −5.73702 | −0.314860 | ||||||||
\(333\) | −3.08722 | −0.169179 | ||||||||
\(334\) | 0.638262 | 0.0349241 | ||||||||
\(335\) | 21.2616 | 1.16165 | ||||||||
\(336\) | −1.36145 | −0.0742730 | ||||||||
\(337\) | 30.5882 | 1.66624 | 0.833122 | − | 0.553089i | \(-0.186551\pi\) | ||||
0.833122 | + | 0.553089i | \(0.186551\pi\) | |||||||
\(338\) | −0.0154343 | −0.000839513 0 | ||||||||
\(339\) | 20.2563 | 1.10017 | ||||||||
\(340\) | 23.6752 | 1.28397 | ||||||||
\(341\) | −26.6416 | −1.44273 | ||||||||
\(342\) | 0.112316 | 0.00607337 | ||||||||
\(343\) | −4.77427 | −0.257786 | ||||||||
\(344\) | −0.00280301 | −0.000151128 0 | ||||||||
\(345\) | 6.69107 | 0.360235 | ||||||||
\(346\) | 1.24677 | 0.0670268 | ||||||||
\(347\) | −2.30431 | −0.123702 | −0.0618508 | − | 0.998085i | \(-0.519700\pi\) | ||||
−0.0618508 | + | 0.998085i | \(0.519700\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.12305 | 0.488345 | 0.244173 | − | 0.969732i | \(-0.421484\pi\) | ||||
0.244173 | + | 0.969732i | \(0.421484\pi\) | |||||||
\(350\) | 0.0364253 | 0.00194701 | ||||||||
\(351\) | −3.63120 | −0.193819 | ||||||||
\(352\) | 2.40784 | 0.128338 | ||||||||
\(353\) | −14.5658 | −0.775262 | −0.387631 | − | 0.921815i | \(-0.626706\pi\) | ||||
−0.387631 | + | 0.921815i | \(0.626706\pi\) | |||||||
\(354\) | 0.479659 | 0.0254936 | ||||||||
\(355\) | 24.8146 | 1.31702 | ||||||||
\(356\) | 24.3634 | 1.29126 | ||||||||
\(357\) | 2.11636 | 0.112009 | ||||||||
\(358\) | 1.33717 | 0.0706714 | ||||||||
\(359\) | 3.75107 | 0.197974 | 0.0989869 | − | 0.995089i | \(-0.468440\pi\) | ||||
0.0989869 | + | 0.995089i | \(0.468440\pi\) | |||||||
\(360\) | 0.640979 | 0.0337825 | ||||||||
\(361\) | −17.1757 | −0.903983 | ||||||||
\(362\) | 0.471778 | 0.0247961 | ||||||||
\(363\) | 5.12352 | 0.268915 | ||||||||
\(364\) | −2.48908 | −0.130463 | ||||||||
\(365\) | 0.886443 | 0.0463986 | ||||||||
\(366\) | −0.518713 | −0.0271135 | ||||||||
\(367\) | 13.9488 | 0.728119 | 0.364060 | − | 0.931376i | \(-0.381390\pi\) | ||||
0.364060 | + | 0.931376i | \(0.381390\pi\) | |||||||
\(368\) | −13.7211 | −0.715263 | ||||||||
\(369\) | 5.28313 | 0.275029 | ||||||||
\(370\) | 0.495568 | 0.0257633 | ||||||||
\(371\) | −1.42465 | −0.0739643 | ||||||||
\(372\) | 21.9042 | 1.13568 | ||||||||
\(373\) | −7.66007 | −0.396624 | −0.198312 | − | 0.980139i | \(-0.563546\pi\) | ||||
−0.198312 | + | 0.980139i | \(0.563546\pi\) | |||||||
\(374\) | −1.24044 | −0.0641417 | ||||||||
\(375\) | 12.1105 | 0.625383 | ||||||||
\(376\) | −1.92480 | −0.0992641 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0.0285993 | 0.00147099 | ||||||||
\(379\) | −12.5700 | −0.645676 | −0.322838 | − | 0.946454i | \(-0.604637\pi\) | ||||
−0.322838 | + | 0.946454i | \(0.604637\pi\) | |||||||
\(380\) | 5.19659 | 0.266580 | ||||||||
\(381\) | −9.56458 | −0.490008 | ||||||||
\(382\) | −0.0529613 | −0.00270974 | ||||||||
\(383\) | 23.5509 | 1.20340 | 0.601698 | − | 0.798724i | \(-0.294491\pi\) | ||||
0.601698 | + | 0.798724i | \(0.294491\pi\) | |||||||
\(384\) | −2.63803 | −0.134622 | ||||||||
\(385\) | −1.60940 | −0.0820227 | ||||||||
\(386\) | 0.943263 | 0.0480108 | ||||||||
\(387\) | −0.00844158 | −0.000429110 0 | ||||||||
\(388\) | 5.42956 | 0.275644 | ||||||||
\(389\) | −21.2485 | −1.07734 | −0.538671 | − | 0.842516i | \(-0.681073\pi\) | ||||
−0.538671 | + | 0.842516i | \(0.681073\pi\) | |||||||
\(390\) | 0.582888 | 0.0295157 | ||||||||
\(391\) | 21.3294 | 1.07867 | ||||||||
\(392\) | −2.28506 | −0.115413 | ||||||||
\(393\) | −16.8025 | −0.847572 | ||||||||
\(394\) | 1.40767 | 0.0709173 | ||||||||
\(395\) | −24.0896 | −1.21208 | ||||||||
\(396\) | 4.83153 | 0.242793 | ||||||||
\(397\) | 14.7291 | 0.739233 | 0.369617 | − | 0.929184i | \(-0.379489\pi\) | ||||
0.369617 | + | 0.929184i | \(0.379489\pi\) | |||||||
\(398\) | −0.721621 | −0.0361716 | ||||||||
\(399\) | 0.464530 | 0.0232556 | ||||||||
\(400\) | −5.04178 | −0.252089 | ||||||||
\(401\) | −12.6297 | −0.630696 | −0.315348 | − | 0.948976i | \(-0.602121\pi\) | ||||
−0.315348 | + | 0.948976i | \(0.602121\pi\) | |||||||
\(402\) | 0.915896 | 0.0456807 | ||||||||
\(403\) | 39.9073 | 1.98792 | ||||||||
\(404\) | 36.4129 | 1.81161 | ||||||||
\(405\) | 1.93038 | 0.0959213 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.48388 | 0.370962 | ||||||||
\(408\) | 2.04327 | 0.101157 | ||||||||
\(409\) | −33.7573 | −1.66919 | −0.834597 | − | 0.550862i | \(-0.814299\pi\) | ||||
−0.834597 | + | 0.550862i | \(0.814299\pi\) | |||||||
\(410\) | −0.848059 | −0.0418827 | ||||||||
\(411\) | 5.75126 | 0.283689 | ||||||||
\(412\) | 32.0281 | 1.57791 | ||||||||
\(413\) | 1.98383 | 0.0976177 | ||||||||
\(414\) | 0.288234 | 0.0141659 | ||||||||
\(415\) | 5.55652 | 0.272759 | ||||||||
\(416\) | −3.60677 | −0.176837 | ||||||||
\(417\) | −1.56684 | −0.0767285 | ||||||||
\(418\) | −0.272271 | −0.0133172 | ||||||||
\(419\) | −24.6416 | −1.20382 | −0.601911 | − | 0.798563i | \(-0.705594\pi\) | ||||
−0.601911 | + | 0.798563i | \(0.705594\pi\) | |||||||
\(420\) | 1.32322 | 0.0645665 | ||||||||
\(421\) | 12.2557 | 0.597309 | 0.298654 | − | 0.954361i | \(-0.403462\pi\) | ||||
0.298654 | + | 0.954361i | \(0.403462\pi\) | |||||||
\(422\) | −1.06036 | −0.0516176 | ||||||||
\(423\) | −5.79676 | −0.281848 | ||||||||
\(424\) | −1.37546 | −0.0667981 | ||||||||
\(425\) | 7.83740 | 0.380170 | ||||||||
\(426\) | 1.06895 | 0.0517908 | ||||||||
\(427\) | −2.14535 | −0.103821 | ||||||||
\(428\) | 32.2402 | 1.55839 | ||||||||
\(429\) | 8.80255 | 0.424991 | ||||||||
\(430\) | 0.00135506 | 6.53468e−5 0 | ||||||||
\(431\) | −8.39549 | −0.404397 | −0.202198 | − | 0.979345i | \(-0.564809\pi\) | ||||
−0.202198 | + | 0.979345i | \(0.564809\pi\) | |||||||
\(432\) | −3.95856 | −0.190456 | ||||||||
\(433\) | 9.24157 | 0.444122 | 0.222061 | − | 0.975033i | \(-0.428722\pi\) | ||||
0.222061 | + | 0.975033i | \(0.428722\pi\) | |||||||
\(434\) | −0.314310 | −0.0150874 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −18.3354 | −0.878108 | ||||||||
\(437\) | 4.68170 | 0.223956 | ||||||||
\(438\) | 0.0381857 | 0.00182458 | ||||||||
\(439\) | 17.4230 | 0.831552 | 0.415776 | − | 0.909467i | \(-0.363510\pi\) | ||||
0.415776 | + | 0.909467i | \(0.363510\pi\) | |||||||
\(440\) | −1.55382 | −0.0740757 | ||||||||
\(441\) | −6.88172 | −0.327701 | ||||||||
\(442\) | 1.85809 | 0.0883806 | ||||||||
\(443\) | 28.9972 | 1.37770 | 0.688850 | − | 0.724904i | \(-0.258116\pi\) | ||||
0.688850 | + | 0.724904i | \(0.258116\pi\) | |||||||
\(444\) | −6.15310 | −0.292013 | ||||||||
\(445\) | −23.5968 | −1.11860 | ||||||||
\(446\) | −1.59151 | −0.0753603 | ||||||||
\(447\) | −12.6315 | −0.597449 | ||||||||
\(448\) | −2.69449 | −0.127303 | ||||||||
\(449\) | −13.9198 | −0.656914 | −0.328457 | − | 0.944519i | \(-0.606529\pi\) | ||||
−0.328457 | + | 0.944519i | \(0.606529\pi\) | |||||||
\(450\) | 0.105911 | 0.00499267 | ||||||||
\(451\) | −12.8071 | −0.603061 | ||||||||
\(452\) | 40.3724 | 1.89896 | ||||||||
\(453\) | 10.2677 | 0.482418 | ||||||||
\(454\) | 2.05818 | 0.0965954 | ||||||||
\(455\) | 2.41077 | 0.113019 | ||||||||
\(456\) | 0.448489 | 0.0210024 | ||||||||
\(457\) | −0.999387 | −0.0467494 | −0.0233747 | − | 0.999727i | \(-0.507441\pi\) | ||||
−0.0233747 | + | 0.999727i | \(0.507441\pi\) | |||||||
\(458\) | 1.61602 | 0.0755117 | ||||||||
\(459\) | 6.15354 | 0.287223 | ||||||||
\(460\) | 13.3359 | 0.621788 | ||||||||
\(461\) | 15.5235 | 0.723003 | 0.361502 | − | 0.932371i | \(-0.382264\pi\) | ||||
0.361502 | + | 0.932371i | \(0.382264\pi\) | |||||||
\(462\) | −0.0693290 | −0.00322547 | ||||||||
\(463\) | 35.8295 | 1.66514 | 0.832568 | − | 0.553923i | \(-0.186870\pi\) | ||||
0.832568 | + | 0.553923i | \(0.186870\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −21.2151 | −0.983826 | ||||||||
\(466\) | −1.52043 | −0.0704328 | ||||||||
\(467\) | −4.17634 | −0.193258 | −0.0966290 | − | 0.995320i | \(-0.530806\pi\) | ||||
−0.0966290 | + | 0.995320i | \(0.530806\pi\) | |||||||
\(468\) | −7.23729 | −0.334544 | ||||||||
\(469\) | 3.78806 | 0.174916 | ||||||||
\(470\) | 0.930508 | 0.0429211 | ||||||||
\(471\) | 3.78665 | 0.174479 | ||||||||
\(472\) | 1.91532 | 0.0881597 | ||||||||
\(473\) | 0.0204636 | 0.000940918 0 | ||||||||
\(474\) | −1.03772 | −0.0476640 | ||||||||
\(475\) | 1.72027 | 0.0789314 | ||||||||
\(476\) | 4.21808 | 0.193335 | ||||||||
\(477\) | −4.14234 | −0.189665 | ||||||||
\(478\) | −0.681365 | −0.0311649 | ||||||||
\(479\) | −18.5452 | −0.847351 | −0.423675 | − | 0.905814i | \(-0.639260\pi\) | ||||
−0.423675 | + | 0.905814i | \(0.639260\pi\) | |||||||
\(480\) | 1.91739 | 0.0875166 | ||||||||
\(481\) | −11.2103 | −0.511147 | ||||||||
\(482\) | 0.593927 | 0.0270526 | ||||||||
\(483\) | 1.19211 | 0.0542429 | ||||||||
\(484\) | 10.2116 | 0.464164 | ||||||||
\(485\) | −5.25874 | −0.238787 | ||||||||
\(486\) | 0.0831558 | 0.00377202 | ||||||||
\(487\) | 19.5628 | 0.886474 | 0.443237 | − | 0.896404i | \(-0.353830\pi\) | ||||
0.443237 | + | 0.896404i | \(0.353830\pi\) | |||||||
\(488\) | −2.07126 | −0.0937617 | ||||||||
\(489\) | 6.08181 | 0.275029 | ||||||||
\(490\) | 1.10467 | 0.0499038 | ||||||||
\(491\) | 2.39192 | 0.107946 | 0.0539728 | − | 0.998542i | \(-0.482812\pi\) | ||||
0.0539728 | + | 0.998542i | \(0.482812\pi\) | |||||||
\(492\) | 10.5297 | 0.474717 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0.407843 | 0.0183497 | ||||||||
\(495\) | −4.67952 | −0.210329 | ||||||||
\(496\) | 43.5050 | 1.95343 | ||||||||
\(497\) | 4.42108 | 0.198312 | ||||||||
\(498\) | 0.239361 | 0.0107260 | ||||||||
\(499\) | −17.3897 | −0.778468 | −0.389234 | − | 0.921139i | \(-0.627260\pi\) | ||||
−0.389234 | + | 0.921139i | \(0.627260\pi\) | |||||||
\(500\) | 24.1373 | 1.07945 | ||||||||
\(501\) | 7.67550 | 0.342916 | ||||||||
\(502\) | −0.193069 | −0.00861707 | ||||||||
\(503\) | 20.1486 | 0.898381 | 0.449191 | − | 0.893436i | \(-0.351712\pi\) | ||||
0.449191 | + | 0.893436i | \(0.351712\pi\) | |||||||
\(504\) | 0.114200 | 0.00508686 | ||||||||
\(505\) | −35.2673 | −1.56937 | ||||||||
\(506\) | −0.698721 | −0.0310619 | ||||||||
\(507\) | −0.185607 | −0.00824307 | ||||||||
\(508\) | −19.0630 | −0.845785 | ||||||||
\(509\) | 28.9399 | 1.28274 | 0.641369 | − | 0.767232i | \(-0.278367\pi\) | ||||
0.641369 | + | 0.767232i | \(0.278367\pi\) | |||||||
\(510\) | −0.987780 | −0.0437396 | ||||||||
\(511\) | 0.157933 | 0.00698653 | ||||||||
\(512\) | −6.56080 | −0.289949 | ||||||||
\(513\) | 1.35067 | 0.0596337 | ||||||||
\(514\) | 1.89447 | 0.0835615 | ||||||||
\(515\) | −31.0205 | −1.36692 | ||||||||
\(516\) | −0.0168248 | −0.000740670 0 | ||||||||
\(517\) | 14.0522 | 0.618014 | ||||||||
\(518\) | 0.0882926 | 0.00387935 | ||||||||
\(519\) | 14.9932 | 0.658128 | ||||||||
\(520\) | 2.32752 | 0.102069 | ||||||||
\(521\) | −3.28970 | −0.144125 | −0.0720623 | − | 0.997400i | \(-0.522958\pi\) | ||||
−0.0720623 | + | 0.997400i | \(0.522958\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.291341 | −0.0127395 | −0.00636974 | − | 0.999980i | \(-0.502028\pi\) | ||||
−0.00636974 | + | 0.999980i | \(0.502028\pi\) | |||||||
\(524\) | −33.4887 | −1.46296 | ||||||||
\(525\) | 0.438036 | 0.0191175 | ||||||||
\(526\) | 0.0794513 | 0.00346424 | ||||||||
\(527\) | −67.6281 | −2.94593 | ||||||||
\(528\) | 9.59612 | 0.417617 | ||||||||
\(529\) | −10.9855 | −0.477630 | ||||||||
\(530\) | 0.664937 | 0.0288830 | ||||||||
\(531\) | 5.76819 | 0.250318 | ||||||||
\(532\) | 0.925848 | 0.0401406 | ||||||||
\(533\) | 19.1841 | 0.830955 | ||||||||
\(534\) | −1.01649 | −0.0439879 | ||||||||
\(535\) | −31.2258 | −1.35001 | ||||||||
\(536\) | 3.65725 | 0.157969 | ||||||||
\(537\) | 16.0802 | 0.693914 | ||||||||
\(538\) | −1.25951 | −0.0543014 | ||||||||
\(539\) | 16.6823 | 0.718556 | ||||||||
\(540\) | 3.84741 | 0.165566 | ||||||||
\(541\) | 27.6565 | 1.18905 | 0.594523 | − | 0.804078i | \(-0.297341\pi\) | ||||
0.594523 | + | 0.804078i | \(0.297341\pi\) | |||||||
\(542\) | 0.686101 | 0.0294705 | ||||||||
\(543\) | 5.67342 | 0.243470 | ||||||||
\(544\) | 6.11215 | 0.262056 | ||||||||
\(545\) | 17.7586 | 0.760693 | ||||||||
\(546\) | 0.103850 | 0.00444437 | ||||||||
\(547\) | 5.06702 | 0.216650 | 0.108325 | − | 0.994116i | \(-0.465451\pi\) | ||||
0.108325 | + | 0.994116i | \(0.465451\pi\) | |||||||
\(548\) | 11.4627 | 0.489664 | ||||||||
\(549\) | −6.23784 | −0.266224 | ||||||||
\(550\) | −0.256742 | −0.0109475 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 1.15094 | 0.0489874 | ||||||||
\(553\) | −4.29191 | −0.182510 | ||||||||
\(554\) | −1.39146 | −0.0591175 | ||||||||
\(555\) | 5.95951 | 0.252967 | ||||||||
\(556\) | −3.12285 | −0.132438 | ||||||||
\(557\) | 16.1639 | 0.684885 | 0.342443 | − | 0.939539i | \(-0.388746\pi\) | ||||
0.342443 | + | 0.939539i | \(0.388746\pi\) | |||||||
\(558\) | −0.913892 | −0.0386881 | ||||||||
\(559\) | −0.0306531 | −0.00129649 | ||||||||
\(560\) | 2.62811 | 0.111058 | ||||||||
\(561\) | −14.9171 | −0.629800 | ||||||||
\(562\) | 1.84139 | 0.0776744 | ||||||||
\(563\) | 7.45712 | 0.314280 | 0.157140 | − | 0.987576i | \(-0.449773\pi\) | ||||
0.157140 | + | 0.987576i | \(0.449773\pi\) | |||||||
\(564\) | −11.5534 | −0.486487 | ||||||||
\(565\) | −39.1022 | −1.64504 | ||||||||
\(566\) | 1.46850 | 0.0617257 | ||||||||
\(567\) | 0.343925 | 0.0144435 | ||||||||
\(568\) | 4.26841 | 0.179098 | ||||||||
\(569\) | 17.6440 | 0.739675 | 0.369837 | − | 0.929097i | \(-0.379413\pi\) | ||||
0.369837 | + | 0.929097i | \(0.379413\pi\) | |||||||
\(570\) | −0.216813 | −0.00908130 | ||||||||
\(571\) | 29.2430 | 1.22378 | 0.611890 | − | 0.790943i | \(-0.290410\pi\) | ||||
0.611890 | + | 0.790943i | \(0.290410\pi\) | |||||||
\(572\) | 17.5442 | 0.733561 | ||||||||
\(573\) | −0.636893 | −0.0266066 | ||||||||
\(574\) | −0.151094 | −0.00630654 | ||||||||
\(575\) | 4.41468 | 0.184105 | ||||||||
\(576\) | −7.83452 | −0.326438 | ||||||||
\(577\) | −17.0793 | −0.711023 | −0.355511 | − | 0.934672i | \(-0.615693\pi\) | ||||
−0.355511 | + | 0.934672i | \(0.615693\pi\) | |||||||
\(578\) | −1.73514 | −0.0721722 | ||||||||
\(579\) | 11.3433 | 0.471412 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.989975 | 0.0410711 | ||||||||
\(582\) | −0.226533 | −0.00939009 | ||||||||
\(583\) | 10.0416 | 0.415882 | ||||||||
\(584\) | 0.152479 | 0.00630962 | ||||||||
\(585\) | 7.00959 | 0.289811 | ||||||||
\(586\) | −1.92461 | −0.0795051 | ||||||||
\(587\) | −34.0645 | −1.40599 | −0.702996 | − | 0.711193i | \(-0.748155\pi\) | ||||
−0.702996 | + | 0.711193i | \(0.748155\pi\) | |||||||
\(588\) | −13.7158 | −0.565632 | ||||||||
\(589\) | −14.8441 | −0.611639 | ||||||||
\(590\) | −0.925923 | −0.0381196 | ||||||||
\(591\) | 16.9281 | 0.696329 | ||||||||
\(592\) | −12.2210 | −0.502278 | ||||||||
\(593\) | −42.8511 | −1.75969 | −0.879843 | − | 0.475265i | \(-0.842352\pi\) | ||||
−0.879843 | + | 0.475265i | \(0.842352\pi\) | |||||||
\(594\) | −0.201582 | −0.00827100 | ||||||||
\(595\) | −4.08537 | −0.167484 | ||||||||
\(596\) | −25.1756 | −1.03123 | ||||||||
\(597\) | −8.67794 | −0.355164 | ||||||||
\(598\) | 1.04664 | 0.0428001 | ||||||||
\(599\) | 5.69345 | 0.232628 | 0.116314 | − | 0.993212i | \(-0.462892\pi\) | ||||
0.116314 | + | 0.993212i | \(0.462892\pi\) | |||||||
\(600\) | 0.422910 | 0.0172652 | ||||||||
\(601\) | −8.96083 | −0.365520 | −0.182760 | − | 0.983158i | \(-0.558503\pi\) | ||||
−0.182760 | + | 0.983158i | \(0.558503\pi\) | |||||||
\(602\) | 0.000241424 0 | 9.83969e−6 0 | ||||||||
\(603\) | 11.0142 | 0.448533 | ||||||||
\(604\) | 20.4644 | 0.832683 | ||||||||
\(605\) | −9.89034 | −0.402099 | ||||||||
\(606\) | −1.51922 | −0.0617143 | ||||||||
\(607\) | 28.3175 | 1.14937 | 0.574685 | − | 0.818374i | \(-0.305124\pi\) | ||||
0.574685 | + | 0.818374i | \(0.305124\pi\) | |||||||
\(608\) | 1.34159 | 0.0544086 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.00131 | 0.0405419 | ||||||||
\(611\) | −21.0492 | −0.851558 | ||||||||
\(612\) | 12.2645 | 0.495764 | ||||||||
\(613\) | −32.0123 | −1.29296 | −0.646482 | − | 0.762929i | \(-0.723760\pi\) | ||||
−0.646482 | + | 0.762929i | \(0.723760\pi\) | |||||||
\(614\) | 1.91245 | 0.0771801 | ||||||||
\(615\) | −10.1984 | −0.411241 | ||||||||
\(616\) | −0.276836 | −0.0111541 | ||||||||
\(617\) | −6.10052 | −0.245598 | −0.122799 | − | 0.992432i | \(-0.539187\pi\) | ||||
−0.122799 | + | 0.992432i | \(0.539187\pi\) | |||||||
\(618\) | −1.33628 | −0.0537532 | ||||||||
\(619\) | 0.710979 | 0.0285766 | 0.0142883 | − | 0.999898i | \(-0.495452\pi\) | ||||
0.0142883 | + | 0.999898i | \(0.495452\pi\) | |||||||
\(620\) | −42.2835 | −1.69814 | ||||||||
\(621\) | 3.46619 | 0.139094 | ||||||||
\(622\) | −0.339335 | −0.0136061 | ||||||||
\(623\) | −4.20412 | −0.168434 | ||||||||
\(624\) | −14.3743 | −0.575433 | ||||||||
\(625\) | −17.0096 | −0.680386 | ||||||||
\(626\) | −2.39095 | −0.0955615 | ||||||||
\(627\) | −3.27423 | −0.130760 | ||||||||
\(628\) | 7.54711 | 0.301162 | ||||||||
\(629\) | 18.9974 | 0.757475 | ||||||||
\(630\) | −0.0552076 | −0.00219952 | ||||||||
\(631\) | −27.0861 | −1.07828 | −0.539140 | − | 0.842216i | \(-0.681251\pi\) | ||||
−0.539140 | + | 0.842216i | \(0.681251\pi\) | |||||||
\(632\) | −4.14370 | −0.164827 | ||||||||
\(633\) | −12.7515 | −0.506827 | ||||||||
\(634\) | −0.958777 | −0.0380779 | ||||||||
\(635\) | 18.4633 | 0.732692 | ||||||||
\(636\) | −8.25603 | −0.327373 | ||||||||
\(637\) | −24.9889 | −0.990095 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.8548 | 0.508527 | ||||||||
\(640\) | 5.09240 | 0.201295 | ||||||||
\(641\) | 27.4704 | 1.08501 | 0.542507 | − | 0.840051i | \(-0.317475\pi\) | ||||
0.542507 | + | 0.840051i | \(0.317475\pi\) | |||||||
\(642\) | −1.34513 | −0.0530880 | ||||||||
\(643\) | −26.5921 | −1.04869 | −0.524345 | − | 0.851506i | \(-0.675690\pi\) | ||||
−0.524345 | + | 0.851506i | \(0.675690\pi\) | |||||||
\(644\) | 2.37598 | 0.0936266 | ||||||||
\(645\) | 0.0162954 | 0.000641632 0 | ||||||||
\(646\) | −0.691143 | −0.0271927 | ||||||||
\(647\) | −24.3504 | −0.957314 | −0.478657 | − | 0.878002i | \(-0.658876\pi\) | ||||
−0.478657 | + | 0.878002i | \(0.658876\pi\) | |||||||
\(648\) | 0.332048 | 0.0130441 | ||||||||
\(649\) | −13.9829 | −0.548878 | ||||||||
\(650\) | 0.384582 | 0.0150846 | ||||||||
\(651\) | −3.77977 | −0.148141 | ||||||||
\(652\) | 12.1216 | 0.474717 | ||||||||
\(653\) | 20.7490 | 0.811973 | 0.405986 | − | 0.913879i | \(-0.366928\pi\) | ||||
0.405986 | + | 0.913879i | \(0.366928\pi\) | |||||||
\(654\) | 0.764994 | 0.0299136 | ||||||||
\(655\) | 32.4351 | 1.26734 | ||||||||
\(656\) | 20.9136 | 0.816538 | ||||||||
\(657\) | 0.459207 | 0.0179154 | ||||||||
\(658\) | 0.165783 | 0.00646291 | ||||||||
\(659\) | −13.3618 | −0.520504 | −0.260252 | − | 0.965541i | \(-0.583806\pi\) | ||||
−0.260252 | + | 0.965541i | \(0.583806\pi\) | |||||||
\(660\) | −9.32667 | −0.363040 | ||||||||
\(661\) | 34.6065 | 1.34604 | 0.673018 | − | 0.739626i | \(-0.264998\pi\) | ||||
0.673018 | + | 0.739626i | \(0.264998\pi\) | |||||||
\(662\) | −1.02313 | −0.0397651 | ||||||||
\(663\) | 22.3447 | 0.867798 | ||||||||
\(664\) | 0.955788 | 0.0370918 | ||||||||
\(665\) | −0.896719 | −0.0347733 | ||||||||
\(666\) | 0.256721 | 0.00994772 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 15.2979 | 0.591894 | ||||||||
\(669\) | −19.1389 | −0.739954 | ||||||||
\(670\) | −1.76803 | −0.0683048 | ||||||||
\(671\) | 15.1214 | 0.583756 | ||||||||
\(672\) | 0.341611 | 0.0131779 | ||||||||
\(673\) | 36.9298 | 1.42354 | 0.711770 | − | 0.702413i | \(-0.247894\pi\) | ||||
0.711770 | + | 0.702413i | \(0.247894\pi\) | |||||||
\(674\) | −2.54358 | −0.0979752 | ||||||||
\(675\) | 1.27364 | 0.0490224 | ||||||||
\(676\) | −0.369930 | −0.0142281 | ||||||||
\(677\) | −3.93509 | −0.151238 | −0.0756189 | − | 0.997137i | \(-0.524093\pi\) | ||||
−0.0756189 | + | 0.997137i | \(0.524093\pi\) | |||||||
\(678\) | −1.68443 | −0.0646900 | ||||||||
\(679\) | −0.936920 | −0.0359557 | ||||||||
\(680\) | −3.94429 | −0.151257 | ||||||||
\(681\) | 24.7509 | 0.948458 | ||||||||
\(682\) | 2.21541 | 0.0848323 | ||||||||
\(683\) | 3.88519 | 0.148663 | 0.0743314 | − | 0.997234i | \(-0.476318\pi\) | ||||
0.0743314 | + | 0.997234i | \(0.476318\pi\) | |||||||
\(684\) | 2.69201 | 0.102931 | ||||||||
\(685\) | −11.1021 | −0.424190 | ||||||||
\(686\) | 0.397008 | 0.0151578 | ||||||||
\(687\) | 19.4336 | 0.741440 | ||||||||
\(688\) | −0.0334165 | −0.00127399 | ||||||||
\(689\) | −15.0417 | −0.573041 | ||||||||
\(690\) | −0.556401 | −0.0211818 | ||||||||
\(691\) | 7.66976 | 0.291771 | 0.145886 | − | 0.989301i | \(-0.453397\pi\) | ||||
0.145886 | + | 0.989301i | \(0.453397\pi\) | |||||||
\(692\) | 29.8827 | 1.13597 | ||||||||
\(693\) | −0.833724 | −0.0316705 | ||||||||
\(694\) | 0.191616 | 0.00727366 | ||||||||
\(695\) | 3.02459 | 0.114729 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −32.5100 | −1.23140 | ||||||||
\(698\) | −0.758634 | −0.0287147 | ||||||||
\(699\) | −18.2842 | −0.691571 | ||||||||
\(700\) | 0.873043 | 0.0329979 | ||||||||
\(701\) | 39.3445 | 1.48602 | 0.743011 | − | 0.669279i | \(-0.233397\pi\) | ||||
0.743011 | + | 0.669279i | \(0.233397\pi\) | |||||||
\(702\) | 0.301955 | 0.0113966 | ||||||||
\(703\) | 4.16983 | 0.157268 | ||||||||
\(704\) | 18.9920 | 0.715788 | ||||||||
\(705\) | 11.1899 | 0.421437 | ||||||||
\(706\) | 1.21123 | 0.0455854 | ||||||||
\(707\) | −6.28337 | −0.236311 | ||||||||
\(708\) | 11.4965 | 0.432065 | ||||||||
\(709\) | 37.5849 | 1.41153 | 0.705765 | − | 0.708446i | \(-0.250603\pi\) | ||||
0.705765 | + | 0.708446i | \(0.250603\pi\) | |||||||
\(710\) | −2.06348 | −0.0774409 | ||||||||
\(711\) | −12.4792 | −0.468007 | ||||||||
\(712\) | −4.05894 | −0.152115 | ||||||||
\(713\) | −38.0939 | −1.42663 | ||||||||
\(714\) | −0.175987 | −0.00658616 | ||||||||
\(715\) | −16.9923 | −0.635474 | ||||||||
\(716\) | 32.0493 | 1.19774 | ||||||||
\(717\) | −8.19384 | −0.306004 | ||||||||
\(718\) | −0.311923 | −0.0116409 | ||||||||
\(719\) | 4.63300 | 0.172782 | 0.0863910 | − | 0.996261i | \(-0.472467\pi\) | ||||
0.0863910 | + | 0.996261i | \(0.472467\pi\) | |||||||
\(720\) | 7.64152 | 0.284782 | ||||||||
\(721\) | −5.52674 | −0.205827 | ||||||||
\(722\) | 1.42826 | 0.0531542 | ||||||||
\(723\) | 7.14233 | 0.265626 | ||||||||
\(724\) | 11.3076 | 0.420244 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.426051 | −0.0158122 | ||||||||
\(727\) | 5.51391 | 0.204500 | 0.102250 | − | 0.994759i | \(-0.467396\pi\) | ||||
0.102250 | + | 0.994759i | \(0.467396\pi\) | |||||||
\(728\) | 0.414682 | 0.0153691 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −0.0737129 | −0.00272824 | ||||||||
\(731\) | 0.0519456 | 0.00192128 | ||||||||
\(732\) | −12.4325 | −0.459520 | ||||||||
\(733\) | 43.4421 | 1.60457 | 0.802285 | − | 0.596941i | \(-0.203617\pi\) | ||||
0.802285 | + | 0.596941i | \(0.203617\pi\) | |||||||
\(734\) | −1.15992 | −0.0428134 | ||||||||
\(735\) | 13.2843 | 0.489999 | ||||||||
\(736\) | 3.44288 | 0.126906 | ||||||||
\(737\) | −26.7000 | −0.983509 | ||||||||
\(738\) | −0.439323 | −0.0161717 | ||||||||
\(739\) | 44.2848 | 1.62904 | 0.814522 | − | 0.580133i | \(-0.196999\pi\) | ||||
0.814522 | + | 0.580133i | \(0.196999\pi\) | |||||||
\(740\) | 11.8778 | 0.436637 | ||||||||
\(741\) | 4.90456 | 0.180174 | ||||||||
\(742\) | 0.118468 | 0.00434910 | ||||||||
\(743\) | −35.4033 | −1.29882 | −0.649411 | − | 0.760438i | \(-0.724984\pi\) | ||||
−0.649411 | + | 0.760438i | \(0.724984\pi\) | |||||||
\(744\) | −3.64925 | −0.133788 | ||||||||
\(745\) | 24.3836 | 0.893345 | ||||||||
\(746\) | 0.636980 | 0.0233215 | ||||||||
\(747\) | 2.87846 | 0.105317 | ||||||||
\(748\) | −29.7310 | −1.08707 | ||||||||
\(749\) | −5.56333 | −0.203280 | ||||||||
\(750\) | −1.00706 | −0.0367726 | ||||||||
\(751\) | −3.55544 | −0.129740 | −0.0648698 | − | 0.997894i | \(-0.520663\pi\) | ||||
−0.0648698 | + | 0.997894i | \(0.520663\pi\) | |||||||
\(752\) | −22.9468 | −0.836784 | ||||||||
\(753\) | −2.32177 | −0.0846100 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −19.8205 | −0.721342 | ||||||||
\(756\) | 0.685471 | 0.0249304 | ||||||||
\(757\) | 21.6056 | 0.785268 | 0.392634 | − | 0.919695i | \(-0.371564\pi\) | ||||
0.392634 | + | 0.919695i | \(0.371564\pi\) | |||||||
\(758\) | 1.04527 | 0.0379658 | ||||||||
\(759\) | −8.40256 | −0.304993 | ||||||||
\(760\) | −0.865753 | −0.0314041 | ||||||||
\(761\) | 16.5313 | 0.599260 | 0.299630 | − | 0.954055i | \(-0.403137\pi\) | ||||
0.299630 | + | 0.954055i | \(0.403137\pi\) | |||||||
\(762\) | 0.795350 | 0.0288125 | ||||||||
\(763\) | 3.16395 | 0.114543 | ||||||||
\(764\) | −1.26938 | −0.0459246 | ||||||||
\(765\) | −11.8787 | −0.429474 | ||||||||
\(766\) | −1.95839 | −0.0707597 | ||||||||
\(767\) | 20.9455 | 0.756297 | ||||||||
\(768\) | −15.4497 | −0.557492 | ||||||||
\(769\) | −0.202502 | −0.00730241 | −0.00365120 | − | 0.999993i | \(-0.501162\pi\) | ||||
−0.00365120 | + | 0.999993i | \(0.501162\pi\) | |||||||
\(770\) | 0.133831 | 0.00482294 | ||||||||
\(771\) | 22.7822 | 0.820480 | ||||||||
\(772\) | 22.6082 | 0.813687 | ||||||||
\(773\) | −14.5159 | −0.522100 | −0.261050 | − | 0.965325i | \(-0.584069\pi\) | ||||
−0.261050 | + | 0.965325i | \(0.584069\pi\) | |||||||
\(774\) | 0.000701966 0 | 2.52317e−5 0 | ||||||||
\(775\) | −13.9974 | −0.502803 | ||||||||
\(776\) | −0.904565 | −0.0324720 | ||||||||
\(777\) | 1.06177 | 0.0380909 | ||||||||
\(778\) | 1.76694 | 0.0633477 | ||||||||
\(779\) | −7.13578 | −0.255666 | ||||||||
\(780\) | 13.9707 | 0.500232 | ||||||||
\(781\) | −31.1618 | −1.11506 | ||||||||
\(782\) | −1.77366 | −0.0634260 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −27.2417 | −0.972917 | ||||||||
\(785\) | −7.30966 | −0.260893 | ||||||||
\(786\) | 1.39722 | 0.0498373 | ||||||||
\(787\) | −34.0857 | −1.21503 | −0.607513 | − | 0.794310i | \(-0.707833\pi\) | ||||
−0.607513 | + | 0.794310i | \(0.707833\pi\) | |||||||
\(788\) | 33.7391 | 1.20191 | ||||||||
\(789\) | 0.955452 | 0.0340150 | ||||||||
\(790\) | 2.00319 | 0.0712702 | ||||||||
\(791\) | −6.96663 | −0.247705 | ||||||||
\(792\) | −0.804933 | −0.0286020 | ||||||||
\(793\) | −22.6508 | −0.804355 | ||||||||
\(794\) | −1.22481 | −0.0434669 | ||||||||
\(795\) | 7.99628 | 0.283599 | ||||||||
\(796\) | −17.2959 | −0.613036 | ||||||||
\(797\) | 14.3592 | 0.508628 | 0.254314 | − | 0.967122i | \(-0.418150\pi\) | ||||
0.254314 | + | 0.967122i | \(0.418150\pi\) | |||||||
\(798\) | −0.0386284 | −0.00136743 | ||||||||
\(799\) | 35.6706 | 1.26193 | ||||||||
\(800\) | 1.26507 | 0.0447271 | ||||||||
\(801\) | −12.2239 | −0.431912 | ||||||||
\(802\) | 1.05023 | 0.0370849 | ||||||||
\(803\) | −1.11318 | −0.0392834 | ||||||||
\(804\) | 21.9523 | 0.774197 | ||||||||
\(805\) | −2.30122 | −0.0811075 | ||||||||
\(806\) | −3.31852 | −0.116890 | ||||||||
\(807\) | −15.1464 | −0.533179 | ||||||||
\(808\) | −6.06639 | −0.213415 | ||||||||
\(809\) | −28.3982 | −0.998429 | −0.499214 | − | 0.866479i | \(-0.666378\pi\) | ||||
−0.499214 | + | 0.866479i | \(0.666378\pi\) | |||||||
\(810\) | −0.160522 | −0.00564017 | ||||||||
\(811\) | −41.4768 | −1.45645 | −0.728224 | − | 0.685339i | \(-0.759654\pi\) | ||||
−0.728224 | + | 0.685339i | \(0.759654\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.25078 | 0.289368 | ||||||||
\(814\) | −0.622328 | −0.0218126 | ||||||||
\(815\) | −11.7402 | −0.411241 | ||||||||
\(816\) | 24.3592 | 0.852741 | ||||||||
\(817\) | 0.0114018 | 0.000398899 0 | ||||||||
\(818\) | 2.80712 | 0.0981486 | ||||||||
\(819\) | 1.24886 | 0.0436387 | ||||||||
\(820\) | −20.3264 | −0.709827 | ||||||||
\(821\) | −45.2453 | −1.57907 | −0.789535 | − | 0.613705i | \(-0.789678\pi\) | ||||
−0.789535 | + | 0.613705i | \(0.789678\pi\) | |||||||
\(822\) | −0.478250 | −0.0166809 | ||||||||
\(823\) | −1.80834 | −0.0630349 | −0.0315174 | − | 0.999503i | \(-0.510034\pi\) | ||||
−0.0315174 | + | 0.999503i | \(0.510034\pi\) | |||||||
\(824\) | −5.33589 | −0.185885 | ||||||||
\(825\) | −3.08749 | −0.107492 | ||||||||
\(826\) | −0.164967 | −0.00573992 | ||||||||
\(827\) | −22.9341 | −0.797497 | −0.398748 | − | 0.917060i | \(-0.630555\pi\) | ||||
−0.398748 | + | 0.917060i | \(0.630555\pi\) | |||||||
\(828\) | 6.90842 | 0.240084 | ||||||||
\(829\) | −9.99341 | −0.347085 | −0.173543 | − | 0.984826i | \(-0.555521\pi\) | ||||
−0.173543 | + | 0.984826i | \(0.555521\pi\) | |||||||
\(830\) | −0.462057 | −0.0160382 | ||||||||
\(831\) | −16.7332 | −0.580468 | ||||||||
\(832\) | −28.4487 | −0.986281 | ||||||||
\(833\) | 42.3469 | 1.46723 | ||||||||
\(834\) | 0.130292 | 0.00451164 | ||||||||
\(835\) | −14.8166 | −0.512750 | ||||||||
\(836\) | −6.52581 | −0.225700 | ||||||||
\(837\) | −10.9901 | −0.379874 | ||||||||
\(838\) | 2.04909 | 0.0707848 | ||||||||
\(839\) | 24.1584 | 0.834042 | 0.417021 | − | 0.908897i | \(-0.363074\pi\) | ||||
0.417021 | + | 0.908897i | \(0.363074\pi\) | |||||||
\(840\) | −0.220448 | −0.00760619 | ||||||||
\(841\) | 0 | 0 | ||||||||
\(842\) | −1.01914 | −0.0351218 | ||||||||
\(843\) | 22.1439 | 0.762675 | ||||||||
\(844\) | −25.4149 | −0.874815 | ||||||||
\(845\) | 0.358291 | 0.0123256 | ||||||||
\(846\) | 0.482034 | 0.0165727 | ||||||||
\(847\) | −1.76211 | −0.0605467 | ||||||||
\(848\) | −16.3977 | −0.563099 | ||||||||
\(849\) | 17.6596 | 0.606077 | ||||||||
\(850\) | −0.651725 | −0.0223540 | ||||||||
\(851\) | 10.7009 | 0.366823 | ||||||||
\(852\) | 25.6207 | 0.877750 | ||||||||
\(853\) | 12.9629 | 0.443842 | 0.221921 | − | 0.975065i | \(-0.428767\pi\) | ||||
0.221921 | + | 0.975065i | \(0.428767\pi\) | |||||||
\(854\) | 0.178398 | 0.00610466 | ||||||||
\(855\) | −2.60731 | −0.0891681 | ||||||||
\(856\) | −5.37121 | −0.183584 | ||||||||
\(857\) | −21.5162 | −0.734980 | −0.367490 | − | 0.930027i | \(-0.619783\pi\) | ||||
−0.367490 | + | 0.930027i | \(0.619783\pi\) | |||||||
\(858\) | −0.731983 | −0.0249895 | ||||||||
\(859\) | −4.60632 | −0.157165 | −0.0785827 | − | 0.996908i | \(-0.525039\pi\) | ||||
−0.0785827 | + | 0.996908i | \(0.525039\pi\) | |||||||
\(860\) | 0.0324782 | 0.00110750 | ||||||||
\(861\) | −1.81700 | −0.0619232 | ||||||||
\(862\) | 0.698134 | 0.0237785 | ||||||||
\(863\) | −19.2332 | −0.654707 | −0.327354 | − | 0.944902i | \(-0.606157\pi\) | ||||
−0.327354 | + | 0.944902i | \(0.606157\pi\) | |||||||
\(864\) | 0.993273 | 0.0337918 | ||||||||
\(865\) | −28.9425 | −0.984076 | ||||||||
\(866\) | −0.768490 | −0.0261144 | ||||||||
\(867\) | −20.8661 | −0.708650 | ||||||||
\(868\) | −7.53341 | −0.255701 | ||||||||
\(869\) | 30.2514 | 1.02621 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 39.9948 | 1.35517 | ||||||||
\(872\) | 3.05469 | 0.103445 | ||||||||
\(873\) | −2.72420 | −0.0922002 | ||||||||
\(874\) | −0.389310 | −0.0131686 | ||||||||
\(875\) | −4.16510 | −0.140806 | ||||||||
\(876\) | 0.915239 | 0.0309230 | ||||||||
\(877\) | −27.8752 | −0.941279 | −0.470640 | − | 0.882326i | \(-0.655977\pi\) | ||||
−0.470640 | + | 0.882326i | \(0.655977\pi\) | |||||||
\(878\) | −1.44882 | −0.0488953 | ||||||||
\(879\) | −23.1447 | −0.780651 | ||||||||
\(880\) | −18.5241 | −0.624449 | ||||||||
\(881\) | 27.7676 | 0.935514 | 0.467757 | − | 0.883857i | \(-0.345062\pi\) | ||||
0.467757 | + | 0.883857i | \(0.345062\pi\) | |||||||
\(882\) | 0.572255 | 0.0192688 | ||||||||
\(883\) | −0.320213 | −0.0107760 | −0.00538802 | − | 0.999985i | \(-0.501715\pi\) | ||||
−0.00538802 | + | 0.999985i | \(0.501715\pi\) | |||||||
\(884\) | 44.5350 | 1.49787 | ||||||||
\(885\) | −11.1348 | −0.374292 | ||||||||
\(886\) | −2.41129 | −0.0810088 | ||||||||
\(887\) | −24.7909 | −0.832397 | −0.416198 | − | 0.909274i | \(-0.636638\pi\) | ||||
−0.416198 | + | 0.909274i | \(0.636638\pi\) | |||||||
\(888\) | 1.02511 | 0.0344003 | ||||||||
\(889\) | 3.28950 | 0.110326 | ||||||||
\(890\) | 1.96221 | 0.0657735 | ||||||||
\(891\) | −2.42414 | −0.0812119 | ||||||||
\(892\) | −38.1455 | −1.27721 | ||||||||
\(893\) | 7.82952 | 0.262005 | ||||||||
\(894\) | 1.05038 | 0.0351300 | ||||||||
\(895\) | −31.0410 | −1.03758 | ||||||||
\(896\) | 0.907285 | 0.0303103 | ||||||||
\(897\) | 12.5864 | 0.420249 | ||||||||
\(898\) | 1.15751 | 0.0386266 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 2.53847 | 0.0846157 | ||||||||
\(901\) | 25.4901 | 0.849197 | ||||||||
\(902\) | 1.06498 | 0.0354600 | ||||||||
\(903\) | 0.00290327 | 9.66147e−5 0 | ||||||||
\(904\) | −6.72605 | −0.223705 | ||||||||
\(905\) | −10.9518 | −0.364052 | ||||||||
\(906\) | −0.853817 | −0.0283662 | ||||||||
\(907\) | −44.0205 | −1.46168 | −0.730839 | − | 0.682550i | \(-0.760871\pi\) | ||||
−0.730839 | + | 0.682550i | \(0.760871\pi\) | |||||||
\(908\) | 49.3307 | 1.63710 | ||||||||
\(909\) | −18.2696 | −0.605965 | ||||||||
\(910\) | −0.200470 | −0.00664550 | ||||||||
\(911\) | 58.6374 | 1.94275 | 0.971373 | − | 0.237561i | \(-0.0763480\pi\) | ||||
0.971373 | + | 0.237561i | \(0.0763480\pi\) | |||||||
\(912\) | 5.34672 | 0.177048 | ||||||||
\(913\) | −6.97781 | −0.230932 | ||||||||
\(914\) | 0.0831048 | 0.00274886 | ||||||||
\(915\) | 12.0414 | 0.398076 | ||||||||
\(916\) | 38.7329 | 1.27977 | ||||||||
\(917\) | 5.77879 | 0.190832 | ||||||||
\(918\) | −0.511703 | −0.0168887 | ||||||||
\(919\) | −36.3681 | −1.19967 | −0.599837 | − | 0.800122i | \(-0.704768\pi\) | ||||
−0.599837 | + | 0.800122i | \(0.704768\pi\) | |||||||
\(920\) | −2.22176 | −0.0732491 | ||||||||
\(921\) | 22.9984 | 0.757822 | ||||||||
\(922\) | −1.29087 | −0.0425126 | ||||||||
\(923\) | 46.6783 | 1.53643 | ||||||||
\(924\) | −1.66168 | −0.0546653 | ||||||||
\(925\) | 3.93201 | 0.129284 | ||||||||
\(926\) | −2.97943 | −0.0979101 | ||||||||
\(927\) | −16.0696 | −0.527796 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.895129 | 0.0293682 | 0.0146841 | − | 0.999892i | \(-0.495326\pi\) | ||||
0.0146841 | + | 0.999892i | \(0.495326\pi\) | |||||||
\(930\) | 1.76416 | 0.0578490 | ||||||||
\(931\) | 9.29495 | 0.304630 | ||||||||
\(932\) | −36.4419 | −1.19369 | ||||||||
\(933\) | −4.08071 | −0.133596 | ||||||||
\(934\) | 0.347287 | 0.0113636 | ||||||||
\(935\) | 28.7956 | 0.941717 | ||||||||
\(936\) | 1.20573 | 0.0394106 | ||||||||
\(937\) | 23.2168 | 0.758460 | 0.379230 | − | 0.925302i | \(-0.376189\pi\) | ||||
0.379230 | + | 0.925302i | \(0.376189\pi\) | |||||||
\(938\) | −0.314999 | −0.0102851 | ||||||||
\(939\) | −28.7526 | −0.938306 | ||||||||
\(940\) | 22.3025 | 0.727427 | ||||||||
\(941\) | 26.3658 | 0.859501 | 0.429750 | − | 0.902948i | \(-0.358602\pi\) | ||||
0.429750 | + | 0.902948i | \(0.358602\pi\) | |||||||
\(942\) | −0.314882 | −0.0102594 | ||||||||
\(943\) | −18.3123 | −0.596332 | ||||||||
\(944\) | 22.8337 | 0.743175 | ||||||||
\(945\) | −0.663905 | −0.0215968 | ||||||||
\(946\) | −0.00170167 | −5.53260e−5 0 | ||||||||
\(947\) | 50.9638 | 1.65610 | 0.828051 | − | 0.560653i | \(-0.189450\pi\) | ||||
0.828051 | + | 0.560653i | \(0.189450\pi\) | |||||||
\(948\) | −24.8721 | −0.807809 | ||||||||
\(949\) | 1.66747 | 0.0541284 | ||||||||
\(950\) | −0.143050 | −0.00464117 | ||||||||
\(951\) | −11.5299 | −0.373882 | ||||||||
\(952\) | −0.702732 | −0.0227757 | ||||||||
\(953\) | −25.1414 | −0.814410 | −0.407205 | − | 0.913337i | \(-0.633497\pi\) | ||||
−0.407205 | + | 0.913337i | \(0.633497\pi\) | |||||||
\(954\) | 0.344459 | 0.0111523 | ||||||||
\(955\) | 1.22944 | 0.0397839 | ||||||||
\(956\) | −16.3310 | −0.528183 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.54214 | 0.0498243 | ||||||||
\(959\) | −1.97800 | −0.0638730 | ||||||||
\(960\) | 15.1236 | 0.488112 | ||||||||
\(961\) | 89.7826 | 2.89621 | ||||||||
\(962\) | 0.932203 | 0.0300554 | ||||||||
\(963\) | −16.1760 | −0.521264 | ||||||||
\(964\) | 14.2353 | 0.458488 | ||||||||
\(965\) | −21.8969 | −0.704886 | ||||||||
\(966\) | −0.0991309 | −0.00318948 | ||||||||
\(967\) | 50.2105 | 1.61466 | 0.807330 | − | 0.590100i | \(-0.200912\pi\) | ||||
0.807330 | + | 0.590100i | \(0.200912\pi\) | |||||||
\(968\) | −1.70126 | −0.0546804 | ||||||||
\(969\) | −8.31143 | −0.267001 | ||||||||
\(970\) | 0.437294 | 0.0140407 | ||||||||
\(971\) | −32.5354 | −1.04411 | −0.522055 | − | 0.852912i | \(-0.674834\pi\) | ||||
−0.522055 | + | 0.852912i | \(0.674834\pi\) | |||||||
\(972\) | 1.99309 | 0.0639282 | ||||||||
\(973\) | 0.538875 | 0.0172755 | ||||||||
\(974\) | −1.62676 | −0.0521247 | ||||||||
\(975\) | 4.62484 | 0.148113 | ||||||||
\(976\) | −24.6929 | −0.790399 | ||||||||
\(977\) | −32.6634 | −1.04500 | −0.522498 | − | 0.852641i | \(-0.675000\pi\) | ||||
−0.522498 | + | 0.852641i | \(0.675000\pi\) | |||||||
\(978\) | −0.505738 | −0.0161717 | ||||||||
\(979\) | 29.6326 | 0.947062 | ||||||||
\(980\) | 26.4768 | 0.845769 | ||||||||
\(981\) | 9.19953 | 0.293718 | ||||||||
\(982\) | −0.198902 | −0.00634721 | ||||||||
\(983\) | 1.79101 | 0.0571245 | 0.0285622 | − | 0.999592i | \(-0.490907\pi\) | ||||
0.0285622 | + | 0.999592i | \(0.490907\pi\) | |||||||
\(984\) | −1.75425 | −0.0559236 | ||||||||
\(985\) | −32.6776 | −1.04120 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.99365 | 0.0634585 | ||||||||
\(988\) | 9.77521 | 0.310991 | ||||||||
\(989\) | 0.0292602 | 0.000930419 0 | ||||||||
\(990\) | 0.389129 | 0.0123673 | ||||||||
\(991\) | 28.6772 | 0.910960 | 0.455480 | − | 0.890246i | \(-0.349468\pi\) | ||||
0.455480 | + | 0.890246i | \(0.349468\pi\) | |||||||
\(992\) | −10.9162 | −0.346589 | ||||||||
\(993\) | −12.3038 | −0.390449 | ||||||||
\(994\) | −0.367638 | −0.0116608 | ||||||||
\(995\) | 16.7517 | 0.531065 | ||||||||
\(996\) | 5.73702 | 0.181784 | ||||||||
\(997\) | −34.6674 | −1.09793 | −0.548964 | − | 0.835846i | \(-0.684977\pi\) | ||||
−0.548964 | + | 0.835846i | \(0.684977\pi\) | |||||||
\(998\) | 1.44605 | 0.0457739 | ||||||||
\(999\) | 3.08722 | 0.0976754 |
(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 | 2523.2.a.p.1.5 | 9 | ||
3.2 | odd | 2 | 7569.2.a.bl.1.5 | 9 | |||
29.16 | even | 7 | 87.2.g.b.82.2 | yes | 18 | ||
29.20 | even | 7 | 87.2.g.b.52.2 | ✓ | 18 | ||
29.28 | even | 2 | 2523.2.a.q.1.5 | 9 | |||
87.20 | odd | 14 | 261.2.k.b.226.2 | 18 | |||
87.74 | odd | 14 | 261.2.k.b.82.2 | 18 | |||
87.86 | odd | 2 | 7569.2.a.bk.1.5 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
87.2.g.b.52.2 | ✓ | 18 | 29.20 | even | 7 | ||
87.2.g.b.82.2 | yes | 18 | 29.16 | even | 7 | ||
261.2.k.b.82.2 | 18 | 87.74 | odd | 14 | |||
261.2.k.b.226.2 | 18 | 87.20 | odd | 14 | |||
2523.2.a.p.1.5 | 9 | 1.1 | even | 1 | trivial | ||
2523.2.a.q.1.5 | 9 | 29.28 | even | 2 | |||
7569.2.a.bk.1.5 | 9 | 87.86 | odd | 2 | |||
7569.2.a.bl.1.5 | 9 | 3.2 | odd | 2 |