Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [538,2,Mod(1,538)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(538, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("538.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 538 = 2 \cdot 269 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 538.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: | \(4.29595162874\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 538.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0.618034 | 0.356822 | 0.178411 | − | 0.983956i | \(-0.442904\pi\) | ||||
0.178411 | + | 0.983956i | \(0.442904\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.61803 | −1.61803 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(6\) | 0.618034 | 0.252311 | ||||||||
\(7\) | −4.23607 | −1.60108 | −0.800542 | − | 0.599277i | \(-0.795455\pi\) | ||||
−0.800542 | + | 0.599277i | \(0.795455\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.61803 | −0.872678 | ||||||||
\(10\) | −3.61803 | −1.14412 | ||||||||
\(11\) | 0.236068 | 0.0711772 | 0.0355886 | − | 0.999367i | \(-0.488669\pi\) | ||||
0.0355886 | + | 0.999367i | \(0.488669\pi\) | |||||||
\(12\) | 0.618034 | 0.178411 | ||||||||
\(13\) | −1.00000 | −0.277350 | −0.138675 | − | 0.990338i | \(-0.544284\pi\) | ||||
−0.138675 | + | 0.990338i | \(0.544284\pi\) | |||||||
\(14\) | −4.23607 | −1.13214 | ||||||||
\(15\) | −2.23607 | −0.577350 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.236068 | 0.0572549 | 0.0286274 | − | 0.999590i | \(-0.490886\pi\) | ||||
0.0286274 | + | 0.999590i | \(0.490886\pi\) | |||||||
\(18\) | −2.61803 | −0.617077 | ||||||||
\(19\) | 2.00000 | 0.458831 | 0.229416 | − | 0.973329i | \(-0.426318\pi\) | ||||
0.229416 | + | 0.973329i | \(0.426318\pi\) | |||||||
\(20\) | −3.61803 | −0.809017 | ||||||||
\(21\) | −2.61803 | −0.571302 | ||||||||
\(22\) | 0.236068 | 0.0503299 | ||||||||
\(23\) | −8.23607 | −1.71734 | −0.858669 | − | 0.512530i | \(-0.828708\pi\) | ||||
−0.858669 | + | 0.512530i | \(0.828708\pi\) | |||||||
\(24\) | 0.618034 | 0.126156 | ||||||||
\(25\) | 8.09017 | 1.61803 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | −3.47214 | −0.668213 | ||||||||
\(28\) | −4.23607 | −0.800542 | ||||||||
\(29\) | 0.854102 | 0.158603 | 0.0793014 | − | 0.996851i | \(-0.474731\pi\) | ||||
0.0793014 | + | 0.996851i | \(0.474731\pi\) | |||||||
\(30\) | −2.23607 | −0.408248 | ||||||||
\(31\) | 7.47214 | 1.34204 | 0.671018 | − | 0.741441i | \(-0.265857\pi\) | ||||
0.671018 | + | 0.741441i | \(0.265857\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0.145898 | 0.0253976 | ||||||||
\(34\) | 0.236068 | 0.0404853 | ||||||||
\(35\) | 15.3262 | 2.59061 | ||||||||
\(36\) | −2.61803 | −0.436339 | ||||||||
\(37\) | −8.70820 | −1.43162 | −0.715810 | − | 0.698295i | \(-0.753942\pi\) | ||||
−0.715810 | + | 0.698295i | \(0.753942\pi\) | |||||||
\(38\) | 2.00000 | 0.324443 | ||||||||
\(39\) | −0.618034 | −0.0989646 | ||||||||
\(40\) | −3.61803 | −0.572061 | ||||||||
\(41\) | 7.70820 | 1.20382 | 0.601910 | − | 0.798564i | \(-0.294407\pi\) | ||||
0.601910 | + | 0.798564i | \(0.294407\pi\) | |||||||
\(42\) | −2.61803 | −0.403971 | ||||||||
\(43\) | 2.23607 | 0.340997 | 0.170499 | − | 0.985358i | \(-0.445462\pi\) | ||||
0.170499 | + | 0.985358i | \(0.445462\pi\) | |||||||
\(44\) | 0.236068 | 0.0355886 | ||||||||
\(45\) | 9.47214 | 1.41202 | ||||||||
\(46\) | −8.23607 | −1.21434 | ||||||||
\(47\) | −6.85410 | −0.999774 | −0.499887 | − | 0.866091i | \(-0.666625\pi\) | ||||
−0.499887 | + | 0.866091i | \(0.666625\pi\) | |||||||
\(48\) | 0.618034 | 0.0892055 | ||||||||
\(49\) | 10.9443 | 1.56347 | ||||||||
\(50\) | 8.09017 | 1.14412 | ||||||||
\(51\) | 0.145898 | 0.0204298 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | −3.47214 | −0.472498 | ||||||||
\(55\) | −0.854102 | −0.115167 | ||||||||
\(56\) | −4.23607 | −0.566068 | ||||||||
\(57\) | 1.23607 | 0.163721 | ||||||||
\(58\) | 0.854102 | 0.112149 | ||||||||
\(59\) | −6.56231 | −0.854339 | −0.427170 | − | 0.904171i | \(-0.640489\pi\) | ||||
−0.427170 | + | 0.904171i | \(0.640489\pi\) | |||||||
\(60\) | −2.23607 | −0.288675 | ||||||||
\(61\) | −5.47214 | −0.700635 | −0.350318 | − | 0.936631i | \(-0.613926\pi\) | ||||
−0.350318 | + | 0.936631i | \(0.613926\pi\) | |||||||
\(62\) | 7.47214 | 0.948962 | ||||||||
\(63\) | 11.0902 | 1.39723 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.61803 | 0.448762 | ||||||||
\(66\) | 0.145898 | 0.0179588 | ||||||||
\(67\) | 1.76393 | 0.215499 | 0.107749 | − | 0.994178i | \(-0.465636\pi\) | ||||
0.107749 | + | 0.994178i | \(0.465636\pi\) | |||||||
\(68\) | 0.236068 | 0.0286274 | ||||||||
\(69\) | −5.09017 | −0.612784 | ||||||||
\(70\) | 15.3262 | 1.83184 | ||||||||
\(71\) | 9.70820 | 1.15215 | 0.576076 | − | 0.817396i | \(-0.304583\pi\) | ||||
0.576076 | + | 0.817396i | \(0.304583\pi\) | |||||||
\(72\) | −2.61803 | −0.308538 | ||||||||
\(73\) | −10.7082 | −1.25330 | −0.626650 | − | 0.779301i | \(-0.715575\pi\) | ||||
−0.626650 | + | 0.779301i | \(0.715575\pi\) | |||||||
\(74\) | −8.70820 | −1.01231 | ||||||||
\(75\) | 5.00000 | 0.577350 | ||||||||
\(76\) | 2.00000 | 0.229416 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | −0.618034 | −0.0699786 | ||||||||
\(79\) | −13.7984 | −1.55244 | −0.776219 | − | 0.630463i | \(-0.782865\pi\) | ||||
−0.776219 | + | 0.630463i | \(0.782865\pi\) | |||||||
\(80\) | −3.61803 | −0.404508 | ||||||||
\(81\) | 5.70820 | 0.634245 | ||||||||
\(82\) | 7.70820 | 0.851229 | ||||||||
\(83\) | −5.23607 | −0.574733 | −0.287367 | − | 0.957821i | \(-0.592780\pi\) | ||||
−0.287367 | + | 0.957821i | \(0.592780\pi\) | |||||||
\(84\) | −2.61803 | −0.285651 | ||||||||
\(85\) | −0.854102 | −0.0926404 | ||||||||
\(86\) | 2.23607 | 0.241121 | ||||||||
\(87\) | 0.527864 | 0.0565930 | ||||||||
\(88\) | 0.236068 | 0.0251649 | ||||||||
\(89\) | −9.79837 | −1.03863 | −0.519313 | − | 0.854584i | \(-0.673812\pi\) | ||||
−0.519313 | + | 0.854584i | \(0.673812\pi\) | |||||||
\(90\) | 9.47214 | 0.998451 | ||||||||
\(91\) | 4.23607 | 0.444061 | ||||||||
\(92\) | −8.23607 | −0.858669 | ||||||||
\(93\) | 4.61803 | 0.478868 | ||||||||
\(94\) | −6.85410 | −0.706947 | ||||||||
\(95\) | −7.23607 | −0.742405 | ||||||||
\(96\) | 0.618034 | 0.0630778 | ||||||||
\(97\) | 12.6525 | 1.28466 | 0.642332 | − | 0.766426i | \(-0.277967\pi\) | ||||
0.642332 | + | 0.766426i | \(0.277967\pi\) | |||||||
\(98\) | 10.9443 | 1.10554 | ||||||||
\(99\) | −0.618034 | −0.0621148 | ||||||||
\(100\) | 8.09017 | 0.809017 | ||||||||
\(101\) | −5.09017 | −0.506491 | −0.253245 | − | 0.967402i | \(-0.581498\pi\) | ||||
−0.253245 | + | 0.967402i | \(0.581498\pi\) | |||||||
\(102\) | 0.145898 | 0.0144461 | ||||||||
\(103\) | 10.8541 | 1.06949 | 0.534743 | − | 0.845015i | \(-0.320408\pi\) | ||||
0.534743 | + | 0.845015i | \(0.320408\pi\) | |||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 9.47214 | 0.924386 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.2361 | −1.18291 | −0.591453 | − | 0.806340i | \(-0.701445\pi\) | ||||
−0.591453 | + | 0.806340i | \(0.701445\pi\) | |||||||
\(108\) | −3.47214 | −0.334106 | ||||||||
\(109\) | −4.70820 | −0.450964 | −0.225482 | − | 0.974247i | \(-0.572396\pi\) | ||||
−0.225482 | + | 0.974247i | \(0.572396\pi\) | |||||||
\(110\) | −0.854102 | −0.0814354 | ||||||||
\(111\) | −5.38197 | −0.510834 | ||||||||
\(112\) | −4.23607 | −0.400271 | ||||||||
\(113\) | −15.3820 | −1.44701 | −0.723507 | − | 0.690317i | \(-0.757471\pi\) | ||||
−0.723507 | + | 0.690317i | \(0.757471\pi\) | |||||||
\(114\) | 1.23607 | 0.115768 | ||||||||
\(115\) | 29.7984 | 2.77871 | ||||||||
\(116\) | 0.854102 | 0.0793014 | ||||||||
\(117\) | 2.61803 | 0.242037 | ||||||||
\(118\) | −6.56231 | −0.604109 | ||||||||
\(119\) | −1.00000 | −0.0916698 | ||||||||
\(120\) | −2.23607 | −0.204124 | ||||||||
\(121\) | −10.9443 | −0.994934 | ||||||||
\(122\) | −5.47214 | −0.495424 | ||||||||
\(123\) | 4.76393 | 0.429549 | ||||||||
\(124\) | 7.47214 | 0.671018 | ||||||||
\(125\) | −11.1803 | −1.00000 | ||||||||
\(126\) | 11.0902 | 0.987991 | ||||||||
\(127\) | 20.7984 | 1.84556 | 0.922779 | − | 0.385331i | \(-0.125913\pi\) | ||||
0.922779 | + | 0.385331i | \(0.125913\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 1.38197 | 0.121675 | ||||||||
\(130\) | 3.61803 | 0.317323 | ||||||||
\(131\) | 2.76393 | 0.241486 | 0.120743 | − | 0.992684i | \(-0.461472\pi\) | ||||
0.120743 | + | 0.992684i | \(0.461472\pi\) | |||||||
\(132\) | 0.145898 | 0.0126988 | ||||||||
\(133\) | −8.47214 | −0.734627 | ||||||||
\(134\) | 1.76393 | 0.152381 | ||||||||
\(135\) | 12.5623 | 1.08119 | ||||||||
\(136\) | 0.236068 | 0.0202427 | ||||||||
\(137\) | −15.6180 | −1.33434 | −0.667169 | − | 0.744906i | \(-0.732494\pi\) | ||||
−0.667169 | + | 0.744906i | \(0.732494\pi\) | |||||||
\(138\) | −5.09017 | −0.433304 | ||||||||
\(139\) | 10.5623 | 0.895883 | 0.447942 | − | 0.894063i | \(-0.352157\pi\) | ||||
0.447942 | + | 0.894063i | \(0.352157\pi\) | |||||||
\(140\) | 15.3262 | 1.29530 | ||||||||
\(141\) | −4.23607 | −0.356741 | ||||||||
\(142\) | 9.70820 | 0.814694 | ||||||||
\(143\) | −0.236068 | −0.0197410 | ||||||||
\(144\) | −2.61803 | −0.218169 | ||||||||
\(145\) | −3.09017 | −0.256625 | ||||||||
\(146\) | −10.7082 | −0.886217 | ||||||||
\(147\) | 6.76393 | 0.557880 | ||||||||
\(148\) | −8.70820 | −0.715810 | ||||||||
\(149\) | 0.326238 | 0.0267265 | 0.0133632 | − | 0.999911i | \(-0.495746\pi\) | ||||
0.0133632 | + | 0.999911i | \(0.495746\pi\) | |||||||
\(150\) | 5.00000 | 0.408248 | ||||||||
\(151\) | −9.94427 | −0.809253 | −0.404627 | − | 0.914482i | \(-0.632599\pi\) | ||||
−0.404627 | + | 0.914482i | \(0.632599\pi\) | |||||||
\(152\) | 2.00000 | 0.162221 | ||||||||
\(153\) | −0.618034 | −0.0499651 | ||||||||
\(154\) | −1.00000 | −0.0805823 | ||||||||
\(155\) | −27.0344 | −2.17146 | ||||||||
\(156\) | −0.618034 | −0.0494823 | ||||||||
\(157\) | 22.6525 | 1.80786 | 0.903932 | − | 0.427676i | \(-0.140668\pi\) | ||||
0.903932 | + | 0.427676i | \(0.140668\pi\) | |||||||
\(158\) | −13.7984 | −1.09774 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.61803 | −0.286031 | ||||||||
\(161\) | 34.8885 | 2.74960 | ||||||||
\(162\) | 5.70820 | 0.448479 | ||||||||
\(163\) | 17.3262 | 1.35710 | 0.678548 | − | 0.734556i | \(-0.262610\pi\) | ||||
0.678548 | + | 0.734556i | \(0.262610\pi\) | |||||||
\(164\) | 7.70820 | 0.601910 | ||||||||
\(165\) | −0.527864 | −0.0410942 | ||||||||
\(166\) | −5.23607 | −0.406398 | ||||||||
\(167\) | 3.61803 | 0.279972 | 0.139986 | − | 0.990153i | \(-0.455294\pi\) | ||||
0.139986 | + | 0.990153i | \(0.455294\pi\) | |||||||
\(168\) | −2.61803 | −0.201986 | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | −0.854102 | −0.0655066 | ||||||||
\(171\) | −5.23607 | −0.400412 | ||||||||
\(172\) | 2.23607 | 0.170499 | ||||||||
\(173\) | −7.47214 | −0.568096 | −0.284048 | − | 0.958810i | \(-0.591678\pi\) | ||||
−0.284048 | + | 0.958810i | \(0.591678\pi\) | |||||||
\(174\) | 0.527864 | 0.0400173 | ||||||||
\(175\) | −34.2705 | −2.59061 | ||||||||
\(176\) | 0.236068 | 0.0177943 | ||||||||
\(177\) | −4.05573 | −0.304847 | ||||||||
\(178\) | −9.79837 | −0.734419 | ||||||||
\(179\) | 18.7082 | 1.39832 | 0.699158 | − | 0.714967i | \(-0.253558\pi\) | ||||
0.699158 | + | 0.714967i | \(0.253558\pi\) | |||||||
\(180\) | 9.47214 | 0.706011 | ||||||||
\(181\) | 19.4164 | 1.44321 | 0.721605 | − | 0.692305i | \(-0.243405\pi\) | ||||
0.721605 | + | 0.692305i | \(0.243405\pi\) | |||||||
\(182\) | 4.23607 | 0.313998 | ||||||||
\(183\) | −3.38197 | −0.250002 | ||||||||
\(184\) | −8.23607 | −0.607171 | ||||||||
\(185\) | 31.5066 | 2.31641 | ||||||||
\(186\) | 4.61803 | 0.338611 | ||||||||
\(187\) | 0.0557281 | 0.00407524 | ||||||||
\(188\) | −6.85410 | −0.499887 | ||||||||
\(189\) | 14.7082 | 1.06986 | ||||||||
\(190\) | −7.23607 | −0.524960 | ||||||||
\(191\) | −5.05573 | −0.365820 | −0.182910 | − | 0.983130i | \(-0.558552\pi\) | ||||
−0.182910 | + | 0.983130i | \(0.558552\pi\) | |||||||
\(192\) | 0.618034 | 0.0446028 | ||||||||
\(193\) | −8.23607 | −0.592845 | −0.296423 | − | 0.955057i | \(-0.595794\pi\) | ||||
−0.296423 | + | 0.955057i | \(0.595794\pi\) | |||||||
\(194\) | 12.6525 | 0.908395 | ||||||||
\(195\) | 2.23607 | 0.160128 | ||||||||
\(196\) | 10.9443 | 0.781734 | ||||||||
\(197\) | −22.3820 | −1.59465 | −0.797325 | − | 0.603551i | \(-0.793752\pi\) | ||||
−0.797325 | + | 0.603551i | \(0.793752\pi\) | |||||||
\(198\) | −0.618034 | −0.0439218 | ||||||||
\(199\) | −5.38197 | −0.381517 | −0.190759 | − | 0.981637i | \(-0.561095\pi\) | ||||
−0.190759 | + | 0.981637i | \(0.561095\pi\) | |||||||
\(200\) | 8.09017 | 0.572061 | ||||||||
\(201\) | 1.09017 | 0.0768947 | ||||||||
\(202\) | −5.09017 | −0.358143 | ||||||||
\(203\) | −3.61803 | −0.253936 | ||||||||
\(204\) | 0.145898 | 0.0102149 | ||||||||
\(205\) | −27.8885 | −1.94782 | ||||||||
\(206\) | 10.8541 | 0.756241 | ||||||||
\(207\) | 21.5623 | 1.49868 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | 0.472136 | 0.0326583 | ||||||||
\(210\) | 9.47214 | 0.653639 | ||||||||
\(211\) | 0.854102 | 0.0587988 | 0.0293994 | − | 0.999568i | \(-0.490641\pi\) | ||||
0.0293994 | + | 0.999568i | \(0.490641\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.00000 | 0.411113 | ||||||||
\(214\) | −12.2361 | −0.836440 | ||||||||
\(215\) | −8.09017 | −0.551745 | ||||||||
\(216\) | −3.47214 | −0.236249 | ||||||||
\(217\) | −31.6525 | −2.14871 | ||||||||
\(218\) | −4.70820 | −0.318880 | ||||||||
\(219\) | −6.61803 | −0.447205 | ||||||||
\(220\) | −0.854102 | −0.0575835 | ||||||||
\(221\) | −0.236068 | −0.0158797 | ||||||||
\(222\) | −5.38197 | −0.361214 | ||||||||
\(223\) | −5.32624 | −0.356671 | −0.178336 | − | 0.983970i | \(-0.557071\pi\) | ||||
−0.178336 | + | 0.983970i | \(0.557071\pi\) | |||||||
\(224\) | −4.23607 | −0.283034 | ||||||||
\(225\) | −21.1803 | −1.41202 | ||||||||
\(226\) | −15.3820 | −1.02319 | ||||||||
\(227\) | −24.0344 | −1.59522 | −0.797611 | − | 0.603172i | \(-0.793903\pi\) | ||||
−0.797611 | + | 0.603172i | \(0.793903\pi\) | |||||||
\(228\) | 1.23607 | 0.0818606 | ||||||||
\(229\) | −10.7082 | −0.707618 | −0.353809 | − | 0.935318i | \(-0.615114\pi\) | ||||
−0.353809 | + | 0.935318i | \(0.615114\pi\) | |||||||
\(230\) | 29.7984 | 1.96485 | ||||||||
\(231\) | −0.618034 | −0.0406637 | ||||||||
\(232\) | 0.854102 | 0.0560745 | ||||||||
\(233\) | 4.23607 | 0.277514 | 0.138757 | − | 0.990326i | \(-0.455689\pi\) | ||||
0.138757 | + | 0.990326i | \(0.455689\pi\) | |||||||
\(234\) | 2.61803 | 0.171146 | ||||||||
\(235\) | 24.7984 | 1.61767 | ||||||||
\(236\) | −6.56231 | −0.427170 | ||||||||
\(237\) | −8.52786 | −0.553944 | ||||||||
\(238\) | −1.00000 | −0.0648204 | ||||||||
\(239\) | −19.2705 | −1.24651 | −0.623253 | − | 0.782020i | \(-0.714189\pi\) | ||||
−0.623253 | + | 0.782020i | \(0.714189\pi\) | |||||||
\(240\) | −2.23607 | −0.144338 | ||||||||
\(241\) | −4.70820 | −0.303282 | −0.151641 | − | 0.988436i | \(-0.548456\pi\) | ||||
−0.151641 | + | 0.988436i | \(0.548456\pi\) | |||||||
\(242\) | −10.9443 | −0.703524 | ||||||||
\(243\) | 13.9443 | 0.894525 | ||||||||
\(244\) | −5.47214 | −0.350318 | ||||||||
\(245\) | −39.5967 | −2.52974 | ||||||||
\(246\) | 4.76393 | 0.303737 | ||||||||
\(247\) | −2.00000 | −0.127257 | ||||||||
\(248\) | 7.47214 | 0.474481 | ||||||||
\(249\) | −3.23607 | −0.205077 | ||||||||
\(250\) | −11.1803 | −0.707107 | ||||||||
\(251\) | 24.0902 | 1.52056 | 0.760279 | − | 0.649597i | \(-0.225062\pi\) | ||||
0.760279 | + | 0.649597i | \(0.225062\pi\) | |||||||
\(252\) | 11.0902 | 0.698615 | ||||||||
\(253\) | −1.94427 | −0.122235 | ||||||||
\(254\) | 20.7984 | 1.30501 | ||||||||
\(255\) | −0.527864 | −0.0330561 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −5.47214 | −0.341342 | −0.170671 | − | 0.985328i | \(-0.554594\pi\) | ||||
−0.170671 | + | 0.985328i | \(0.554594\pi\) | |||||||
\(258\) | 1.38197 | 0.0860374 | ||||||||
\(259\) | 36.8885 | 2.29214 | ||||||||
\(260\) | 3.61803 | 0.224381 | ||||||||
\(261\) | −2.23607 | −0.138409 | ||||||||
\(262\) | 2.76393 | 0.170756 | ||||||||
\(263\) | 23.2705 | 1.43492 | 0.717461 | − | 0.696599i | \(-0.245304\pi\) | ||||
0.717461 | + | 0.696599i | \(0.245304\pi\) | |||||||
\(264\) | 0.145898 | 0.00897940 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −8.47214 | −0.519460 | ||||||||
\(267\) | −6.05573 | −0.370605 | ||||||||
\(268\) | 1.76393 | 0.107749 | ||||||||
\(269\) | 1.00000 | 0.0609711 | ||||||||
\(270\) | 12.5623 | 0.764518 | ||||||||
\(271\) | 24.1246 | 1.46547 | 0.732733 | − | 0.680516i | \(-0.238244\pi\) | ||||
0.732733 | + | 0.680516i | \(0.238244\pi\) | |||||||
\(272\) | 0.236068 | 0.0143137 | ||||||||
\(273\) | 2.61803 | 0.158451 | ||||||||
\(274\) | −15.6180 | −0.943520 | ||||||||
\(275\) | 1.90983 | 0.115167 | ||||||||
\(276\) | −5.09017 | −0.306392 | ||||||||
\(277\) | −21.3820 | −1.28472 | −0.642359 | − | 0.766404i | \(-0.722044\pi\) | ||||
−0.642359 | + | 0.766404i | \(0.722044\pi\) | |||||||
\(278\) | 10.5623 | 0.633485 | ||||||||
\(279\) | −19.5623 | −1.17116 | ||||||||
\(280\) | 15.3262 | 0.915918 | ||||||||
\(281\) | −29.1803 | −1.74075 | −0.870377 | − | 0.492387i | \(-0.836125\pi\) | ||||
−0.870377 | + | 0.492387i | \(0.836125\pi\) | |||||||
\(282\) | −4.23607 | −0.252254 | ||||||||
\(283\) | 5.76393 | 0.342630 | 0.171315 | − | 0.985216i | \(-0.445198\pi\) | ||||
0.171315 | + | 0.985216i | \(0.445198\pi\) | |||||||
\(284\) | 9.70820 | 0.576076 | ||||||||
\(285\) | −4.47214 | −0.264906 | ||||||||
\(286\) | −0.236068 | −0.0139590 | ||||||||
\(287\) | −32.6525 | −1.92741 | ||||||||
\(288\) | −2.61803 | −0.154269 | ||||||||
\(289\) | −16.9443 | −0.996722 | ||||||||
\(290\) | −3.09017 | −0.181461 | ||||||||
\(291\) | 7.81966 | 0.458397 | ||||||||
\(292\) | −10.7082 | −0.626650 | ||||||||
\(293\) | 7.52786 | 0.439783 | 0.219891 | − | 0.975524i | \(-0.429430\pi\) | ||||
0.219891 | + | 0.975524i | \(0.429430\pi\) | |||||||
\(294\) | 6.76393 | 0.394481 | ||||||||
\(295\) | 23.7426 | 1.38235 | ||||||||
\(296\) | −8.70820 | −0.506154 | ||||||||
\(297\) | −0.819660 | −0.0475615 | ||||||||
\(298\) | 0.326238 | 0.0188985 | ||||||||
\(299\) | 8.23607 | 0.476304 | ||||||||
\(300\) | 5.00000 | 0.288675 | ||||||||
\(301\) | −9.47214 | −0.545965 | ||||||||
\(302\) | −9.94427 | −0.572229 | ||||||||
\(303\) | −3.14590 | −0.180727 | ||||||||
\(304\) | 2.00000 | 0.114708 | ||||||||
\(305\) | 19.7984 | 1.13365 | ||||||||
\(306\) | −0.618034 | −0.0353307 | ||||||||
\(307\) | 32.1246 | 1.83345 | 0.916724 | − | 0.399521i | \(-0.130823\pi\) | ||||
0.916724 | + | 0.399521i | \(0.130823\pi\) | |||||||
\(308\) | −1.00000 | −0.0569803 | ||||||||
\(309\) | 6.70820 | 0.381616 | ||||||||
\(310\) | −27.0344 | −1.53545 | ||||||||
\(311\) | −17.2361 | −0.977368 | −0.488684 | − | 0.872461i | \(-0.662523\pi\) | ||||
−0.488684 | + | 0.872461i | \(0.662523\pi\) | |||||||
\(312\) | −0.618034 | −0.0349893 | ||||||||
\(313\) | 13.1459 | 0.743050 | 0.371525 | − | 0.928423i | \(-0.378835\pi\) | ||||
0.371525 | + | 0.928423i | \(0.378835\pi\) | |||||||
\(314\) | 22.6525 | 1.27835 | ||||||||
\(315\) | −40.1246 | −2.26077 | ||||||||
\(316\) | −13.7984 | −0.776219 | ||||||||
\(317\) | −30.2361 | −1.69823 | −0.849113 | − | 0.528211i | \(-0.822863\pi\) | ||||
−0.849113 | + | 0.528211i | \(0.822863\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.201626 | 0.0112889 | ||||||||
\(320\) | −3.61803 | −0.202254 | ||||||||
\(321\) | −7.56231 | −0.422087 | ||||||||
\(322\) | 34.8885 | 1.94426 | ||||||||
\(323\) | 0.472136 | 0.0262703 | ||||||||
\(324\) | 5.70820 | 0.317122 | ||||||||
\(325\) | −8.09017 | −0.448762 | ||||||||
\(326\) | 17.3262 | 0.959612 | ||||||||
\(327\) | −2.90983 | −0.160914 | ||||||||
\(328\) | 7.70820 | 0.425614 | ||||||||
\(329\) | 29.0344 | 1.60072 | ||||||||
\(330\) | −0.527864 | −0.0290580 | ||||||||
\(331\) | 0.819660 | 0.0450526 | 0.0225263 | − | 0.999746i | \(-0.492829\pi\) | ||||
0.0225263 | + | 0.999746i | \(0.492829\pi\) | |||||||
\(332\) | −5.23607 | −0.287367 | ||||||||
\(333\) | 22.7984 | 1.24934 | ||||||||
\(334\) | 3.61803 | 0.197970 | ||||||||
\(335\) | −6.38197 | −0.348684 | ||||||||
\(336\) | −2.61803 | −0.142825 | ||||||||
\(337\) | −27.9787 | −1.52410 | −0.762049 | − | 0.647520i | \(-0.775806\pi\) | ||||
−0.762049 | + | 0.647520i | \(0.775806\pi\) | |||||||
\(338\) | −12.0000 | −0.652714 | ||||||||
\(339\) | −9.50658 | −0.516326 | ||||||||
\(340\) | −0.854102 | −0.0463202 | ||||||||
\(341\) | 1.76393 | 0.0955223 | ||||||||
\(342\) | −5.23607 | −0.283134 | ||||||||
\(343\) | −16.7082 | −0.902158 | ||||||||
\(344\) | 2.23607 | 0.120561 | ||||||||
\(345\) | 18.4164 | 0.991506 | ||||||||
\(346\) | −7.47214 | −0.401705 | ||||||||
\(347\) | 13.3607 | 0.717239 | 0.358619 | − | 0.933484i | \(-0.383248\pi\) | ||||
0.358619 | + | 0.933484i | \(0.383248\pi\) | |||||||
\(348\) | 0.527864 | 0.0282965 | ||||||||
\(349\) | 21.2705 | 1.13858 | 0.569292 | − | 0.822135i | \(-0.307217\pi\) | ||||
0.569292 | + | 0.822135i | \(0.307217\pi\) | |||||||
\(350\) | −34.2705 | −1.83184 | ||||||||
\(351\) | 3.47214 | 0.185329 | ||||||||
\(352\) | 0.236068 | 0.0125825 | ||||||||
\(353\) | −9.85410 | −0.524481 | −0.262240 | − | 0.965003i | \(-0.584461\pi\) | ||||
−0.262240 | + | 0.965003i | \(0.584461\pi\) | |||||||
\(354\) | −4.05573 | −0.215560 | ||||||||
\(355\) | −35.1246 | −1.86422 | ||||||||
\(356\) | −9.79837 | −0.519313 | ||||||||
\(357\) | −0.618034 | −0.0327098 | ||||||||
\(358\) | 18.7082 | 0.988759 | ||||||||
\(359\) | −16.9443 | −0.894284 | −0.447142 | − | 0.894463i | \(-0.647558\pi\) | ||||
−0.447142 | + | 0.894463i | \(0.647558\pi\) | |||||||
\(360\) | 9.47214 | 0.499225 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 19.4164 | 1.02050 | ||||||||
\(363\) | −6.76393 | −0.355014 | ||||||||
\(364\) | 4.23607 | 0.222030 | ||||||||
\(365\) | 38.7426 | 2.02788 | ||||||||
\(366\) | −3.38197 | −0.176778 | ||||||||
\(367\) | −9.20163 | −0.480321 | −0.240160 | − | 0.970733i | \(-0.577200\pi\) | ||||
−0.240160 | + | 0.970733i | \(0.577200\pi\) | |||||||
\(368\) | −8.23607 | −0.429335 | ||||||||
\(369\) | −20.1803 | −1.05055 | ||||||||
\(370\) | 31.5066 | 1.63795 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 4.61803 | 0.239434 | ||||||||
\(373\) | 6.94427 | 0.359561 | 0.179780 | − | 0.983707i | \(-0.442461\pi\) | ||||
0.179780 | + | 0.983707i | \(0.442461\pi\) | |||||||
\(374\) | 0.0557281 | 0.00288163 | ||||||||
\(375\) | −6.90983 | −0.356822 | ||||||||
\(376\) | −6.85410 | −0.353473 | ||||||||
\(377\) | −0.854102 | −0.0439885 | ||||||||
\(378\) | 14.7082 | 0.756508 | ||||||||
\(379\) | 6.14590 | 0.315694 | 0.157847 | − | 0.987464i | \(-0.449545\pi\) | ||||
0.157847 | + | 0.987464i | \(0.449545\pi\) | |||||||
\(380\) | −7.23607 | −0.371202 | ||||||||
\(381\) | 12.8541 | 0.658536 | ||||||||
\(382\) | −5.05573 | −0.258674 | ||||||||
\(383\) | −17.3820 | −0.888177 | −0.444088 | − | 0.895983i | \(-0.646472\pi\) | ||||
−0.444088 | + | 0.895983i | \(0.646472\pi\) | |||||||
\(384\) | 0.618034 | 0.0315389 | ||||||||
\(385\) | 3.61803 | 0.184392 | ||||||||
\(386\) | −8.23607 | −0.419205 | ||||||||
\(387\) | −5.85410 | −0.297581 | ||||||||
\(388\) | 12.6525 | 0.642332 | ||||||||
\(389\) | 28.9443 | 1.46753 | 0.733766 | − | 0.679402i | \(-0.237761\pi\) | ||||
0.733766 | + | 0.679402i | \(0.237761\pi\) | |||||||
\(390\) | 2.23607 | 0.113228 | ||||||||
\(391\) | −1.94427 | −0.0983261 | ||||||||
\(392\) | 10.9443 | 0.552769 | ||||||||
\(393\) | 1.70820 | 0.0861675 | ||||||||
\(394\) | −22.3820 | −1.12759 | ||||||||
\(395\) | 49.9230 | 2.51190 | ||||||||
\(396\) | −0.618034 | −0.0310574 | ||||||||
\(397\) | −34.2705 | −1.71999 | −0.859994 | − | 0.510304i | \(-0.829533\pi\) | ||||
−0.859994 | + | 0.510304i | \(0.829533\pi\) | |||||||
\(398\) | −5.38197 | −0.269774 | ||||||||
\(399\) | −5.23607 | −0.262131 | ||||||||
\(400\) | 8.09017 | 0.404508 | ||||||||
\(401\) | −4.27051 | −0.213259 | −0.106630 | − | 0.994299i | \(-0.534006\pi\) | ||||
−0.106630 | + | 0.994299i | \(0.534006\pi\) | |||||||
\(402\) | 1.09017 | 0.0543727 | ||||||||
\(403\) | −7.47214 | −0.372214 | ||||||||
\(404\) | −5.09017 | −0.253245 | ||||||||
\(405\) | −20.6525 | −1.02623 | ||||||||
\(406\) | −3.61803 | −0.179560 | ||||||||
\(407\) | −2.05573 | −0.101899 | ||||||||
\(408\) | 0.145898 | 0.00722303 | ||||||||
\(409\) | −11.6525 | −0.576178 | −0.288089 | − | 0.957604i | \(-0.593020\pi\) | ||||
−0.288089 | + | 0.957604i | \(0.593020\pi\) | |||||||
\(410\) | −27.8885 | −1.37732 | ||||||||
\(411\) | −9.65248 | −0.476122 | ||||||||
\(412\) | 10.8541 | 0.534743 | ||||||||
\(413\) | 27.7984 | 1.36787 | ||||||||
\(414\) | 21.5623 | 1.05973 | ||||||||
\(415\) | 18.9443 | 0.929938 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | 6.52786 | 0.319671 | ||||||||
\(418\) | 0.472136 | 0.0230929 | ||||||||
\(419\) | −17.4377 | −0.851887 | −0.425944 | − | 0.904750i | \(-0.640058\pi\) | ||||
−0.425944 | + | 0.904750i | \(0.640058\pi\) | |||||||
\(420\) | 9.47214 | 0.462193 | ||||||||
\(421\) | 11.4721 | 0.559118 | 0.279559 | − | 0.960129i | \(-0.409812\pi\) | ||||
0.279559 | + | 0.960129i | \(0.409812\pi\) | |||||||
\(422\) | 0.854102 | 0.0415770 | ||||||||
\(423\) | 17.9443 | 0.872480 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.90983 | 0.0926404 | ||||||||
\(426\) | 6.00000 | 0.290701 | ||||||||
\(427\) | 23.1803 | 1.12178 | ||||||||
\(428\) | −12.2361 | −0.591453 | ||||||||
\(429\) | −0.145898 | −0.00704402 | ||||||||
\(430\) | −8.09017 | −0.390143 | ||||||||
\(431\) | −15.4721 | −0.745267 | −0.372633 | − | 0.927979i | \(-0.621545\pi\) | ||||
−0.372633 | + | 0.927979i | \(0.621545\pi\) | |||||||
\(432\) | −3.47214 | −0.167053 | ||||||||
\(433\) | 12.2016 | 0.586373 | 0.293186 | − | 0.956055i | \(-0.405284\pi\) | ||||
0.293186 | + | 0.956055i | \(0.405284\pi\) | |||||||
\(434\) | −31.6525 | −1.51937 | ||||||||
\(435\) | −1.90983 | −0.0915693 | ||||||||
\(436\) | −4.70820 | −0.225482 | ||||||||
\(437\) | −16.4721 | −0.787969 | ||||||||
\(438\) | −6.61803 | −0.316222 | ||||||||
\(439\) | 19.1459 | 0.913784 | 0.456892 | − | 0.889522i | \(-0.348963\pi\) | ||||
0.456892 | + | 0.889522i | \(0.348963\pi\) | |||||||
\(440\) | −0.854102 | −0.0407177 | ||||||||
\(441\) | −28.6525 | −1.36440 | ||||||||
\(442\) | −0.236068 | −0.0112286 | ||||||||
\(443\) | 33.4164 | 1.58766 | 0.793831 | − | 0.608139i | \(-0.208084\pi\) | ||||
0.793831 | + | 0.608139i | \(0.208084\pi\) | |||||||
\(444\) | −5.38197 | −0.255417 | ||||||||
\(445\) | 35.4508 | 1.68053 | ||||||||
\(446\) | −5.32624 | −0.252205 | ||||||||
\(447\) | 0.201626 | 0.00953659 | ||||||||
\(448\) | −4.23607 | −0.200135 | ||||||||
\(449\) | 2.90983 | 0.137323 | 0.0686617 | − | 0.997640i | \(-0.478127\pi\) | ||||
0.0686617 | + | 0.997640i | \(0.478127\pi\) | |||||||
\(450\) | −21.1803 | −0.998451 | ||||||||
\(451\) | 1.81966 | 0.0856844 | ||||||||
\(452\) | −15.3820 | −0.723507 | ||||||||
\(453\) | −6.14590 | −0.288759 | ||||||||
\(454\) | −24.0344 | −1.12799 | ||||||||
\(455\) | −15.3262 | −0.718505 | ||||||||
\(456\) | 1.23607 | 0.0578842 | ||||||||
\(457\) | 26.7984 | 1.25358 | 0.626788 | − | 0.779190i | \(-0.284369\pi\) | ||||
0.626788 | + | 0.779190i | \(0.284369\pi\) | |||||||
\(458\) | −10.7082 | −0.500362 | ||||||||
\(459\) | −0.819660 | −0.0382585 | ||||||||
\(460\) | 29.7984 | 1.38936 | ||||||||
\(461\) | 21.1246 | 0.983871 | 0.491936 | − | 0.870632i | \(-0.336290\pi\) | ||||
0.491936 | + | 0.870632i | \(0.336290\pi\) | |||||||
\(462\) | −0.618034 | −0.0287535 | ||||||||
\(463\) | −20.0902 | −0.933669 | −0.466835 | − | 0.884345i | \(-0.654606\pi\) | ||||
−0.466835 | + | 0.884345i | \(0.654606\pi\) | |||||||
\(464\) | 0.854102 | 0.0396507 | ||||||||
\(465\) | −16.7082 | −0.774824 | ||||||||
\(466\) | 4.23607 | 0.196232 | ||||||||
\(467\) | −6.58359 | −0.304652 | −0.152326 | − | 0.988330i | \(-0.548676\pi\) | ||||
−0.152326 | + | 0.988330i | \(0.548676\pi\) | |||||||
\(468\) | 2.61803 | 0.121019 | ||||||||
\(469\) | −7.47214 | −0.345031 | ||||||||
\(470\) | 24.7984 | 1.14386 | ||||||||
\(471\) | 14.0000 | 0.645086 | ||||||||
\(472\) | −6.56231 | −0.302055 | ||||||||
\(473\) | 0.527864 | 0.0242712 | ||||||||
\(474\) | −8.52786 | −0.391698 | ||||||||
\(475\) | 16.1803 | 0.742405 | ||||||||
\(476\) | −1.00000 | −0.0458349 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −19.2705 | −0.881413 | ||||||||
\(479\) | −36.5967 | −1.67215 | −0.836074 | − | 0.548617i | \(-0.815155\pi\) | ||||
−0.836074 | + | 0.548617i | \(0.815155\pi\) | |||||||
\(480\) | −2.23607 | −0.102062 | ||||||||
\(481\) | 8.70820 | 0.397060 | ||||||||
\(482\) | −4.70820 | −0.214453 | ||||||||
\(483\) | 21.5623 | 0.981119 | ||||||||
\(484\) | −10.9443 | −0.497467 | ||||||||
\(485\) | −45.7771 | −2.07863 | ||||||||
\(486\) | 13.9443 | 0.632525 | ||||||||
\(487\) | −14.8328 | −0.672139 | −0.336070 | − | 0.941837i | \(-0.609098\pi\) | ||||
−0.336070 | + | 0.941837i | \(0.609098\pi\) | |||||||
\(488\) | −5.47214 | −0.247712 | ||||||||
\(489\) | 10.7082 | 0.484242 | ||||||||
\(490\) | −39.5967 | −1.78880 | ||||||||
\(491\) | 6.76393 | 0.305252 | 0.152626 | − | 0.988284i | \(-0.451227\pi\) | ||||
0.152626 | + | 0.988284i | \(0.451227\pi\) | |||||||
\(492\) | 4.76393 | 0.214775 | ||||||||
\(493\) | 0.201626 | 0.00908078 | ||||||||
\(494\) | −2.00000 | −0.0899843 | ||||||||
\(495\) | 2.23607 | 0.100504 | ||||||||
\(496\) | 7.47214 | 0.335509 | ||||||||
\(497\) | −41.1246 | −1.84469 | ||||||||
\(498\) | −3.23607 | −0.145012 | ||||||||
\(499\) | 11.9443 | 0.534699 | 0.267350 | − | 0.963600i | \(-0.413852\pi\) | ||||
0.267350 | + | 0.963600i | \(0.413852\pi\) | |||||||
\(500\) | −11.1803 | −0.500000 | ||||||||
\(501\) | 2.23607 | 0.0999001 | ||||||||
\(502\) | 24.0902 | 1.07520 | ||||||||
\(503\) | 34.3607 | 1.53207 | 0.766033 | − | 0.642801i | \(-0.222228\pi\) | ||||
0.766033 | + | 0.642801i | \(0.222228\pi\) | |||||||
\(504\) | 11.0902 | 0.493995 | ||||||||
\(505\) | 18.4164 | 0.819519 | ||||||||
\(506\) | −1.94427 | −0.0864334 | ||||||||
\(507\) | −7.41641 | −0.329374 | ||||||||
\(508\) | 20.7984 | 0.922779 | ||||||||
\(509\) | 26.6738 | 1.18229 | 0.591147 | − | 0.806564i | \(-0.298675\pi\) | ||||
0.591147 | + | 0.806564i | \(0.298675\pi\) | |||||||
\(510\) | −0.527864 | −0.0233742 | ||||||||
\(511\) | 45.3607 | 2.00664 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −6.94427 | −0.306597 | ||||||||
\(514\) | −5.47214 | −0.241366 | ||||||||
\(515\) | −39.2705 | −1.73047 | ||||||||
\(516\) | 1.38197 | 0.0608377 | ||||||||
\(517\) | −1.61803 | −0.0711611 | ||||||||
\(518\) | 36.8885 | 1.62079 | ||||||||
\(519\) | −4.61803 | −0.202709 | ||||||||
\(520\) | 3.61803 | 0.158661 | ||||||||
\(521\) | 30.4164 | 1.33257 | 0.666284 | − | 0.745699i | \(-0.267884\pi\) | ||||
0.666284 | + | 0.745699i | \(0.267884\pi\) | |||||||
\(522\) | −2.23607 | −0.0978700 | ||||||||
\(523\) | 27.6180 | 1.20765 | 0.603826 | − | 0.797116i | \(-0.293642\pi\) | ||||
0.603826 | + | 0.797116i | \(0.293642\pi\) | |||||||
\(524\) | 2.76393 | 0.120743 | ||||||||
\(525\) | −21.1803 | −0.924386 | ||||||||
\(526\) | 23.2705 | 1.01464 | ||||||||
\(527\) | 1.76393 | 0.0768381 | ||||||||
\(528\) | 0.145898 | 0.00634940 | ||||||||
\(529\) | 44.8328 | 1.94925 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 17.1803 | 0.745563 | ||||||||
\(532\) | −8.47214 | −0.367314 | ||||||||
\(533\) | −7.70820 | −0.333879 | ||||||||
\(534\) | −6.05573 | −0.262057 | ||||||||
\(535\) | 44.2705 | 1.91398 | ||||||||
\(536\) | 1.76393 | 0.0761903 | ||||||||
\(537\) | 11.5623 | 0.498950 | ||||||||
\(538\) | 1.00000 | 0.0431131 | ||||||||
\(539\) | 2.58359 | 0.111283 | ||||||||
\(540\) | 12.5623 | 0.540596 | ||||||||
\(541\) | 20.4721 | 0.880166 | 0.440083 | − | 0.897957i | \(-0.354949\pi\) | ||||
0.440083 | + | 0.897957i | \(0.354949\pi\) | |||||||
\(542\) | 24.1246 | 1.03624 | ||||||||
\(543\) | 12.0000 | 0.514969 | ||||||||
\(544\) | 0.236068 | 0.0101213 | ||||||||
\(545\) | 17.0344 | 0.729675 | ||||||||
\(546\) | 2.61803 | 0.112042 | ||||||||
\(547\) | 3.20163 | 0.136892 | 0.0684458 | − | 0.997655i | \(-0.478196\pi\) | ||||
0.0684458 | + | 0.997655i | \(0.478196\pi\) | |||||||
\(548\) | −15.6180 | −0.667169 | ||||||||
\(549\) | 14.3262 | 0.611429 | ||||||||
\(550\) | 1.90983 | 0.0814354 | ||||||||
\(551\) | 1.70820 | 0.0727719 | ||||||||
\(552\) | −5.09017 | −0.216652 | ||||||||
\(553\) | 58.4508 | 2.48558 | ||||||||
\(554\) | −21.3820 | −0.908433 | ||||||||
\(555\) | 19.4721 | 0.826546 | ||||||||
\(556\) | 10.5623 | 0.447942 | ||||||||
\(557\) | 28.2918 | 1.19876 | 0.599381 | − | 0.800464i | \(-0.295413\pi\) | ||||
0.599381 | + | 0.800464i | \(0.295413\pi\) | |||||||
\(558\) | −19.5623 | −0.828138 | ||||||||
\(559\) | −2.23607 | −0.0945756 | ||||||||
\(560\) | 15.3262 | 0.647652 | ||||||||
\(561\) | 0.0344419 | 0.00145414 | ||||||||
\(562\) | −29.1803 | −1.23090 | ||||||||
\(563\) | 7.29180 | 0.307313 | 0.153656 | − | 0.988124i | \(-0.450895\pi\) | ||||
0.153656 | + | 0.988124i | \(0.450895\pi\) | |||||||
\(564\) | −4.23607 | −0.178371 | ||||||||
\(565\) | 55.6525 | 2.34132 | ||||||||
\(566\) | 5.76393 | 0.242276 | ||||||||
\(567\) | −24.1803 | −1.01548 | ||||||||
\(568\) | 9.70820 | 0.407347 | ||||||||
\(569\) | −5.90983 | −0.247753 | −0.123876 | − | 0.992298i | \(-0.539533\pi\) | ||||
−0.123876 | + | 0.992298i | \(0.539533\pi\) | |||||||
\(570\) | −4.47214 | −0.187317 | ||||||||
\(571\) | 10.0000 | 0.418487 | 0.209243 | − | 0.977864i | \(-0.432900\pi\) | ||||
0.209243 | + | 0.977864i | \(0.432900\pi\) | |||||||
\(572\) | −0.236068 | −0.00987050 | ||||||||
\(573\) | −3.12461 | −0.130533 | ||||||||
\(574\) | −32.6525 | −1.36289 | ||||||||
\(575\) | −66.6312 | −2.77871 | ||||||||
\(576\) | −2.61803 | −0.109085 | ||||||||
\(577\) | 3.00000 | 0.124892 | 0.0624458 | − | 0.998048i | \(-0.480110\pi\) | ||||
0.0624458 | + | 0.998048i | \(0.480110\pi\) | |||||||
\(578\) | −16.9443 | −0.704789 | ||||||||
\(579\) | −5.09017 | −0.211540 | ||||||||
\(580\) | −3.09017 | −0.128312 | ||||||||
\(581\) | 22.1803 | 0.920196 | ||||||||
\(582\) | 7.81966 | 0.324135 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −10.7082 | −0.443109 | ||||||||
\(585\) | −9.47214 | −0.391625 | ||||||||
\(586\) | 7.52786 | 0.310973 | ||||||||
\(587\) | −10.6738 | −0.440553 | −0.220277 | − | 0.975437i | \(-0.570696\pi\) | ||||
−0.220277 | + | 0.975437i | \(0.570696\pi\) | |||||||
\(588\) | 6.76393 | 0.278940 | ||||||||
\(589\) | 14.9443 | 0.615768 | ||||||||
\(590\) | 23.7426 | 0.977469 | ||||||||
\(591\) | −13.8328 | −0.569006 | ||||||||
\(592\) | −8.70820 | −0.357905 | ||||||||
\(593\) | −0.583592 | −0.0239653 | −0.0119826 | − | 0.999928i | \(-0.503814\pi\) | ||||
−0.0119826 | + | 0.999928i | \(0.503814\pi\) | |||||||
\(594\) | −0.819660 | −0.0336311 | ||||||||
\(595\) | 3.61803 | 0.148325 | ||||||||
\(596\) | 0.326238 | 0.0133632 | ||||||||
\(597\) | −3.32624 | −0.136134 | ||||||||
\(598\) | 8.23607 | 0.336798 | ||||||||
\(599\) | −15.5967 | −0.637266 | −0.318633 | − | 0.947878i | \(-0.603224\pi\) | ||||
−0.318633 | + | 0.947878i | \(0.603224\pi\) | |||||||
\(600\) | 5.00000 | 0.204124 | ||||||||
\(601\) | −25.6869 | −1.04779 | −0.523896 | − | 0.851782i | \(-0.675522\pi\) | ||||
−0.523896 | + | 0.851782i | \(0.675522\pi\) | |||||||
\(602\) | −9.47214 | −0.386055 | ||||||||
\(603\) | −4.61803 | −0.188061 | ||||||||
\(604\) | −9.94427 | −0.404627 | ||||||||
\(605\) | 39.5967 | 1.60984 | ||||||||
\(606\) | −3.14590 | −0.127793 | ||||||||
\(607\) | 47.5755 | 1.93103 | 0.965514 | − | 0.260350i | \(-0.0838381\pi\) | ||||
0.965514 | + | 0.260350i | \(0.0838381\pi\) | |||||||
\(608\) | 2.00000 | 0.0811107 | ||||||||
\(609\) | −2.23607 | −0.0906100 | ||||||||
\(610\) | 19.7984 | 0.801613 | ||||||||
\(611\) | 6.85410 | 0.277287 | ||||||||
\(612\) | −0.618034 | −0.0249825 | ||||||||
\(613\) | −26.5279 | −1.07145 | −0.535725 | − | 0.844392i | \(-0.679962\pi\) | ||||
−0.535725 | + | 0.844392i | \(0.679962\pi\) | |||||||
\(614\) | 32.1246 | 1.29644 | ||||||||
\(615\) | −17.2361 | −0.695025 | ||||||||
\(616\) | −1.00000 | −0.0402911 | ||||||||
\(617\) | 36.1591 | 1.45571 | 0.727854 | − | 0.685732i | \(-0.240518\pi\) | ||||
0.727854 | + | 0.685732i | \(0.240518\pi\) | |||||||
\(618\) | 6.70820 | 0.269844 | ||||||||
\(619\) | −40.8328 | −1.64121 | −0.820605 | − | 0.571496i | \(-0.806363\pi\) | ||||
−0.820605 | + | 0.571496i | \(0.806363\pi\) | |||||||
\(620\) | −27.0344 | −1.08573 | ||||||||
\(621\) | 28.5967 | 1.14755 | ||||||||
\(622\) | −17.2361 | −0.691103 | ||||||||
\(623\) | 41.5066 | 1.66293 | ||||||||
\(624\) | −0.618034 | −0.0247412 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 13.1459 | 0.525416 | ||||||||
\(627\) | 0.291796 | 0.0116532 | ||||||||
\(628\) | 22.6525 | 0.903932 | ||||||||
\(629\) | −2.05573 | −0.0819672 | ||||||||
\(630\) | −40.1246 | −1.59860 | ||||||||
\(631\) | 5.20163 | 0.207073 | 0.103537 | − | 0.994626i | \(-0.466984\pi\) | ||||
0.103537 | + | 0.994626i | \(0.466984\pi\) | |||||||
\(632\) | −13.7984 | −0.548870 | ||||||||
\(633\) | 0.527864 | 0.0209807 | ||||||||
\(634\) | −30.2361 | −1.20083 | ||||||||
\(635\) | −75.2492 | −2.98617 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.9443 | −0.433628 | ||||||||
\(638\) | 0.201626 | 0.00798245 | ||||||||
\(639\) | −25.4164 | −1.00546 | ||||||||
\(640\) | −3.61803 | −0.143015 | ||||||||
\(641\) | 3.18034 | 0.125616 | 0.0628079 | − | 0.998026i | \(-0.479994\pi\) | ||||
0.0628079 | + | 0.998026i | \(0.479994\pi\) | |||||||
\(642\) | −7.56231 | −0.298460 | ||||||||
\(643\) | −4.14590 | −0.163498 | −0.0817491 | − | 0.996653i | \(-0.526051\pi\) | ||||
−0.0817491 | + | 0.996653i | \(0.526051\pi\) | |||||||
\(644\) | 34.8885 | 1.37480 | ||||||||
\(645\) | −5.00000 | −0.196875 | ||||||||
\(646\) | 0.472136 | 0.0185759 | ||||||||
\(647\) | −2.81966 | −0.110852 | −0.0554261 | − | 0.998463i | \(-0.517652\pi\) | ||||
−0.0554261 | + | 0.998463i | \(0.517652\pi\) | |||||||
\(648\) | 5.70820 | 0.224239 | ||||||||
\(649\) | −1.54915 | −0.0608095 | ||||||||
\(650\) | −8.09017 | −0.317323 | ||||||||
\(651\) | −19.5623 | −0.766707 | ||||||||
\(652\) | 17.3262 | 0.678548 | ||||||||
\(653\) | −27.5410 | −1.07776 | −0.538882 | − | 0.842381i | \(-0.681153\pi\) | ||||
−0.538882 | + | 0.842381i | \(0.681153\pi\) | |||||||
\(654\) | −2.90983 | −0.113783 | ||||||||
\(655\) | −10.0000 | −0.390732 | ||||||||
\(656\) | 7.70820 | 0.300955 | ||||||||
\(657\) | 28.0344 | 1.09373 | ||||||||
\(658\) | 29.0344 | 1.13188 | ||||||||
\(659\) | −31.3262 | −1.22030 | −0.610148 | − | 0.792287i | \(-0.708890\pi\) | ||||
−0.610148 | + | 0.792287i | \(0.708890\pi\) | |||||||
\(660\) | −0.527864 | −0.0205471 | ||||||||
\(661\) | −20.8541 | −0.811131 | −0.405565 | − | 0.914066i | \(-0.632925\pi\) | ||||
−0.405565 | + | 0.914066i | \(0.632925\pi\) | |||||||
\(662\) | 0.819660 | 0.0318570 | ||||||||
\(663\) | −0.145898 | −0.00566621 | ||||||||
\(664\) | −5.23607 | −0.203199 | ||||||||
\(665\) | 30.6525 | 1.18865 | ||||||||
\(666\) | 22.7984 | 0.883419 | ||||||||
\(667\) | −7.03444 | −0.272375 | ||||||||
\(668\) | 3.61803 | 0.139986 | ||||||||
\(669\) | −3.29180 | −0.127268 | ||||||||
\(670\) | −6.38197 | −0.246557 | ||||||||
\(671\) | −1.29180 | −0.0498692 | ||||||||
\(672\) | −2.61803 | −0.100993 | ||||||||
\(673\) | 10.7082 | 0.412771 | 0.206385 | − | 0.978471i | \(-0.433830\pi\) | ||||
0.206385 | + | 0.978471i | \(0.433830\pi\) | |||||||
\(674\) | −27.9787 | −1.07770 | ||||||||
\(675\) | −28.0902 | −1.08119 | ||||||||
\(676\) | −12.0000 | −0.461538 | ||||||||
\(677\) | −17.4377 | −0.670185 | −0.335093 | − | 0.942185i | \(-0.608768\pi\) | ||||
−0.335093 | + | 0.942185i | \(0.608768\pi\) | |||||||
\(678\) | −9.50658 | −0.365098 | ||||||||
\(679\) | −53.5967 | −2.05685 | ||||||||
\(680\) | −0.854102 | −0.0327533 | ||||||||
\(681\) | −14.8541 | −0.569210 | ||||||||
\(682\) | 1.76393 | 0.0675444 | ||||||||
\(683\) | −21.2361 | −0.812576 | −0.406288 | − | 0.913745i | \(-0.633177\pi\) | ||||
−0.406288 | + | 0.913745i | \(0.633177\pi\) | |||||||
\(684\) | −5.23607 | −0.200206 | ||||||||
\(685\) | 56.5066 | 2.15901 | ||||||||
\(686\) | −16.7082 | −0.637922 | ||||||||
\(687\) | −6.61803 | −0.252494 | ||||||||
\(688\) | 2.23607 | 0.0852493 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 18.4164 | 0.701101 | ||||||||
\(691\) | −15.1246 | −0.575367 | −0.287684 | − | 0.957725i | \(-0.592885\pi\) | ||||
−0.287684 | + | 0.957725i | \(0.592885\pi\) | |||||||
\(692\) | −7.47214 | −0.284048 | ||||||||
\(693\) | 2.61803 | 0.0994509 | ||||||||
\(694\) | 13.3607 | 0.507164 | ||||||||
\(695\) | −38.2148 | −1.44957 | ||||||||
\(696\) | 0.527864 | 0.0200086 | ||||||||
\(697\) | 1.81966 | 0.0689245 | ||||||||
\(698\) | 21.2705 | 0.805101 | ||||||||
\(699\) | 2.61803 | 0.0990231 | ||||||||
\(700\) | −34.2705 | −1.29530 | ||||||||
\(701\) | −10.9787 | −0.414660 | −0.207330 | − | 0.978271i | \(-0.566477\pi\) | ||||
−0.207330 | + | 0.978271i | \(0.566477\pi\) | |||||||
\(702\) | 3.47214 | 0.131047 | ||||||||
\(703\) | −17.4164 | −0.656872 | ||||||||
\(704\) | 0.236068 | 0.00889715 | ||||||||
\(705\) | 15.3262 | 0.577220 | ||||||||
\(706\) | −9.85410 | −0.370864 | ||||||||
\(707\) | 21.5623 | 0.810934 | ||||||||
\(708\) | −4.05573 | −0.152424 | ||||||||
\(709\) | −37.9443 | −1.42503 | −0.712514 | − | 0.701658i | \(-0.752443\pi\) | ||||
−0.712514 | + | 0.701658i | \(0.752443\pi\) | |||||||
\(710\) | −35.1246 | −1.31820 | ||||||||
\(711\) | 36.1246 | 1.35478 | ||||||||
\(712\) | −9.79837 | −0.367210 | ||||||||
\(713\) | −61.5410 | −2.30473 | ||||||||
\(714\) | −0.618034 | −0.0231293 | ||||||||
\(715\) | 0.854102 | 0.0319416 | ||||||||
\(716\) | 18.7082 | 0.699158 | ||||||||
\(717\) | −11.9098 | −0.444781 | ||||||||
\(718\) | −16.9443 | −0.632355 | ||||||||
\(719\) | 42.1803 | 1.57306 | 0.786531 | − | 0.617551i | \(-0.211875\pi\) | ||||
0.786531 | + | 0.617551i | \(0.211875\pi\) | |||||||
\(720\) | 9.47214 | 0.353006 | ||||||||
\(721\) | −45.9787 | −1.71234 | ||||||||
\(722\) | −15.0000 | −0.558242 | ||||||||
\(723\) | −2.90983 | −0.108218 | ||||||||
\(724\) | 19.4164 | 0.721605 | ||||||||
\(725\) | 6.90983 | 0.256625 | ||||||||
\(726\) | −6.76393 | −0.251033 | ||||||||
\(727\) | −44.7082 | −1.65814 | −0.829068 | − | 0.559148i | \(-0.811128\pi\) | ||||
−0.829068 | + | 0.559148i | \(0.811128\pi\) | |||||||
\(728\) | 4.23607 | 0.156999 | ||||||||
\(729\) | −8.50658 | −0.315058 | ||||||||
\(730\) | 38.7426 | 1.43393 | ||||||||
\(731\) | 0.527864 | 0.0195238 | ||||||||
\(732\) | −3.38197 | −0.125001 | ||||||||
\(733\) | −33.3607 | −1.23220 | −0.616102 | − | 0.787666i | \(-0.711289\pi\) | ||||
−0.616102 | + | 0.787666i | \(0.711289\pi\) | |||||||
\(734\) | −9.20163 | −0.339638 | ||||||||
\(735\) | −24.4721 | −0.902668 | ||||||||
\(736\) | −8.23607 | −0.303585 | ||||||||
\(737\) | 0.416408 | 0.0153386 | ||||||||
\(738\) | −20.1803 | −0.742849 | ||||||||
\(739\) | 35.0344 | 1.28876 | 0.644381 | − | 0.764704i | \(-0.277115\pi\) | ||||
0.644381 | + | 0.764704i | \(0.277115\pi\) | |||||||
\(740\) | 31.5066 | 1.15820 | ||||||||
\(741\) | −1.23607 | −0.0454081 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9.20163 | −0.337575 | −0.168787 | − | 0.985652i | \(-0.553985\pi\) | ||||
−0.168787 | + | 0.985652i | \(0.553985\pi\) | |||||||
\(744\) | 4.61803 | 0.169305 | ||||||||
\(745\) | −1.18034 | −0.0432443 | ||||||||
\(746\) | 6.94427 | 0.254248 | ||||||||
\(747\) | 13.7082 | 0.501557 | ||||||||
\(748\) | 0.0557281 | 0.00203762 | ||||||||
\(749\) | 51.8328 | 1.89393 | ||||||||
\(750\) | −6.90983 | −0.252311 | ||||||||
\(751\) | 39.8673 | 1.45478 | 0.727388 | − | 0.686226i | \(-0.240734\pi\) | ||||
0.727388 | + | 0.686226i | \(0.240734\pi\) | |||||||
\(752\) | −6.85410 | −0.249943 | ||||||||
\(753\) | 14.8885 | 0.542569 | ||||||||
\(754\) | −0.854102 | −0.0311046 | ||||||||
\(755\) | 35.9787 | 1.30940 | ||||||||
\(756\) | 14.7082 | 0.534932 | ||||||||
\(757\) | −38.9443 | −1.41545 | −0.707727 | − | 0.706486i | \(-0.750279\pi\) | ||||
−0.707727 | + | 0.706486i | \(0.750279\pi\) | |||||||
\(758\) | 6.14590 | 0.223229 | ||||||||
\(759\) | −1.20163 | −0.0436163 | ||||||||
\(760\) | −7.23607 | −0.262480 | ||||||||
\(761\) | −1.41641 | −0.0513447 | −0.0256724 | − | 0.999670i | \(-0.508173\pi\) | ||||
−0.0256724 | + | 0.999670i | \(0.508173\pi\) | |||||||
\(762\) | 12.8541 | 0.465655 | ||||||||
\(763\) | 19.9443 | 0.722031 | ||||||||
\(764\) | −5.05573 | −0.182910 | ||||||||
\(765\) | 2.23607 | 0.0808452 | ||||||||
\(766\) | −17.3820 | −0.628036 | ||||||||
\(767\) | 6.56231 | 0.236951 | ||||||||
\(768\) | 0.618034 | 0.0223014 | ||||||||
\(769\) | −33.3262 | −1.20177 | −0.600887 | − | 0.799334i | \(-0.705186\pi\) | ||||
−0.600887 | + | 0.799334i | \(0.705186\pi\) | |||||||
\(770\) | 3.61803 | 0.130385 | ||||||||
\(771\) | −3.38197 | −0.121799 | ||||||||
\(772\) | −8.23607 | −0.296423 | ||||||||
\(773\) | 47.5967 | 1.71194 | 0.855968 | − | 0.517029i | \(-0.172962\pi\) | ||||
0.855968 | + | 0.517029i | \(0.172962\pi\) | |||||||
\(774\) | −5.85410 | −0.210421 | ||||||||
\(775\) | 60.4508 | 2.17146 | ||||||||
\(776\) | 12.6525 | 0.454197 | ||||||||
\(777\) | 22.7984 | 0.817887 | ||||||||
\(778\) | 28.9443 | 1.03770 | ||||||||
\(779\) | 15.4164 | 0.552350 | ||||||||
\(780\) | 2.23607 | 0.0800641 | ||||||||
\(781\) | 2.29180 | 0.0820069 | ||||||||
\(782\) | −1.94427 | −0.0695270 | ||||||||
\(783\) | −2.96556 | −0.105980 | ||||||||
\(784\) | 10.9443 | 0.390867 | ||||||||
\(785\) | −81.9574 | −2.92519 | ||||||||
\(786\) | 1.70820 | 0.0609296 | ||||||||
\(787\) | −2.34752 | −0.0836802 | −0.0418401 | − | 0.999124i | \(-0.513322\pi\) | ||||
−0.0418401 | + | 0.999124i | \(0.513322\pi\) | |||||||
\(788\) | −22.3820 | −0.797325 | ||||||||
\(789\) | 14.3820 | 0.512012 | ||||||||
\(790\) | 49.9230 | 1.77618 | ||||||||
\(791\) | 65.1591 | 2.31679 | ||||||||
\(792\) | −0.618034 | −0.0219609 | ||||||||
\(793\) | 5.47214 | 0.194321 | ||||||||
\(794\) | −34.2705 | −1.21621 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.38197 | −0.190759 | ||||||||
\(797\) | 13.2016 | 0.467626 | 0.233813 | − | 0.972282i | \(-0.424880\pi\) | ||||
0.233813 | + | 0.972282i | \(0.424880\pi\) | |||||||
\(798\) | −5.23607 | −0.185355 | ||||||||
\(799\) | −1.61803 | −0.0572419 | ||||||||
\(800\) | 8.09017 | 0.286031 | ||||||||
\(801\) | 25.6525 | 0.906386 | ||||||||
\(802\) | −4.27051 | −0.150797 | ||||||||
\(803\) | −2.52786 | −0.0892064 | ||||||||
\(804\) | 1.09017 | 0.0384473 | ||||||||
\(805\) | −126.228 | −4.44895 | ||||||||
\(806\) | −7.47214 | −0.263195 | ||||||||
\(807\) | 0.618034 | 0.0217558 | ||||||||
\(808\) | −5.09017 | −0.179072 | ||||||||
\(809\) | 15.5279 | 0.545931 | 0.272965 | − | 0.962024i | \(-0.411996\pi\) | ||||
0.272965 | + | 0.962024i | \(0.411996\pi\) | |||||||
\(810\) | −20.6525 | −0.725654 | ||||||||
\(811\) | −47.5967 | −1.67135 | −0.835674 | − | 0.549226i | \(-0.814923\pi\) | ||||
−0.835674 | + | 0.549226i | \(0.814923\pi\) | |||||||
\(812\) | −3.61803 | −0.126968 | ||||||||
\(813\) | 14.9098 | 0.522911 | ||||||||
\(814\) | −2.05573 | −0.0720532 | ||||||||
\(815\) | −62.6869 | −2.19583 | ||||||||
\(816\) | 0.145898 | 0.00510745 | ||||||||
\(817\) | 4.47214 | 0.156460 | ||||||||
\(818\) | −11.6525 | −0.407419 | ||||||||
\(819\) | −11.0902 | −0.387522 | ||||||||
\(820\) | −27.8885 | −0.973910 | ||||||||
\(821\) | 38.3607 | 1.33880 | 0.669398 | − | 0.742904i | \(-0.266552\pi\) | ||||
0.669398 | + | 0.742904i | \(0.266552\pi\) | |||||||
\(822\) | −9.65248 | −0.336669 | ||||||||
\(823\) | −50.8885 | −1.77386 | −0.886932 | − | 0.461901i | \(-0.847168\pi\) | ||||
−0.886932 | + | 0.461901i | \(0.847168\pi\) | |||||||
\(824\) | 10.8541 | 0.378121 | ||||||||
\(825\) | 1.18034 | 0.0410942 | ||||||||
\(826\) | 27.7984 | 0.967229 | ||||||||
\(827\) | −37.7426 | −1.31244 | −0.656220 | − | 0.754569i | \(-0.727846\pi\) | ||||
−0.656220 | + | 0.754569i | \(0.727846\pi\) | |||||||
\(828\) | 21.5623 | 0.749342 | ||||||||
\(829\) | 43.7984 | 1.52118 | 0.760590 | − | 0.649232i | \(-0.224910\pi\) | ||||
0.760590 | + | 0.649232i | \(0.224910\pi\) | |||||||
\(830\) | 18.9443 | 0.657565 | ||||||||
\(831\) | −13.2148 | −0.458416 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | 2.58359 | 0.0895162 | ||||||||
\(834\) | 6.52786 | 0.226041 | ||||||||
\(835\) | −13.0902 | −0.453004 | ||||||||
\(836\) | 0.472136 | 0.0163292 | ||||||||
\(837\) | −25.9443 | −0.896765 | ||||||||
\(838\) | −17.4377 | −0.602375 | ||||||||
\(839\) | 14.4508 | 0.498899 | 0.249449 | − | 0.968388i | \(-0.419750\pi\) | ||||
0.249449 | + | 0.968388i | \(0.419750\pi\) | |||||||
\(840\) | 9.47214 | 0.326820 | ||||||||
\(841\) | −28.2705 | −0.974845 | ||||||||
\(842\) | 11.4721 | 0.395356 | ||||||||
\(843\) | −18.0344 | −0.621139 | ||||||||
\(844\) | 0.854102 | 0.0293994 | ||||||||
\(845\) | 43.4164 | 1.49357 | ||||||||
\(846\) | 17.9443 | 0.616937 | ||||||||
\(847\) | 46.3607 | 1.59297 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.56231 | 0.122258 | ||||||||
\(850\) | 1.90983 | 0.0655066 | ||||||||
\(851\) | 71.7214 | 2.45858 | ||||||||
\(852\) | 6.00000 | 0.205557 | ||||||||
\(853\) | 51.8115 | 1.77399 | 0.886996 | − | 0.461776i | \(-0.152788\pi\) | ||||
0.886996 | + | 0.461776i | \(0.152788\pi\) | |||||||
\(854\) | 23.1803 | 0.793215 | ||||||||
\(855\) | 18.9443 | 0.647880 | ||||||||
\(856\) | −12.2361 | −0.418220 | ||||||||
\(857\) | −42.0689 | −1.43705 | −0.718523 | − | 0.695503i | \(-0.755181\pi\) | ||||
−0.718523 | + | 0.695503i | \(0.755181\pi\) | |||||||
\(858\) | −0.145898 | −0.00498088 | ||||||||
\(859\) | −12.7426 | −0.434773 | −0.217387 | − | 0.976086i | \(-0.569753\pi\) | ||||
−0.217387 | + | 0.976086i | \(0.569753\pi\) | |||||||
\(860\) | −8.09017 | −0.275873 | ||||||||
\(861\) | −20.1803 | −0.687744 | ||||||||
\(862\) | −15.4721 | −0.526983 | ||||||||
\(863\) | 17.3262 | 0.589792 | 0.294896 | − | 0.955529i | \(-0.404715\pi\) | ||||
0.294896 | + | 0.955529i | \(0.404715\pi\) | |||||||
\(864\) | −3.47214 | −0.118124 | ||||||||
\(865\) | 27.0344 | 0.919199 | ||||||||
\(866\) | 12.2016 | 0.414628 | ||||||||
\(867\) | −10.4721 | −0.355652 | ||||||||
\(868\) | −31.6525 | −1.07436 | ||||||||
\(869\) | −3.25735 | −0.110498 | ||||||||
\(870\) | −1.90983 | −0.0647493 | ||||||||
\(871\) | −1.76393 | −0.0597686 | ||||||||
\(872\) | −4.70820 | −0.159440 | ||||||||
\(873\) | −33.1246 | −1.12110 | ||||||||
\(874\) | −16.4721 | −0.557178 | ||||||||
\(875\) | 47.3607 | 1.60108 | ||||||||
\(876\) | −6.61803 | −0.223603 | ||||||||
\(877\) | 42.5755 | 1.43767 | 0.718836 | − | 0.695180i | \(-0.244675\pi\) | ||||
0.718836 | + | 0.695180i | \(0.244675\pi\) | |||||||
\(878\) | 19.1459 | 0.646143 | ||||||||
\(879\) | 4.65248 | 0.156924 | ||||||||
\(880\) | −0.854102 | −0.0287918 | ||||||||
\(881\) | −44.5066 | −1.49946 | −0.749732 | − | 0.661741i | \(-0.769818\pi\) | ||||
−0.749732 | + | 0.661741i | \(0.769818\pi\) | |||||||
\(882\) | −28.6525 | −0.964779 | ||||||||
\(883\) | −50.1935 | −1.68915 | −0.844573 | − | 0.535441i | \(-0.820146\pi\) | ||||
−0.844573 | + | 0.535441i | \(0.820146\pi\) | |||||||
\(884\) | −0.236068 | −0.00793983 | ||||||||
\(885\) | 14.6738 | 0.493253 | ||||||||
\(886\) | 33.4164 | 1.12265 | ||||||||
\(887\) | −13.8328 | −0.464460 | −0.232230 | − | 0.972661i | \(-0.574602\pi\) | ||||
−0.232230 | + | 0.972661i | \(0.574602\pi\) | |||||||
\(888\) | −5.38197 | −0.180607 | ||||||||
\(889\) | −88.1033 | −2.95489 | ||||||||
\(890\) | 35.4508 | 1.18832 | ||||||||
\(891\) | 1.34752 | 0.0451438 | ||||||||
\(892\) | −5.32624 | −0.178336 | ||||||||
\(893\) | −13.7082 | −0.458728 | ||||||||
\(894\) | 0.201626 | 0.00674339 | ||||||||
\(895\) | −67.6869 | −2.26252 | ||||||||
\(896\) | −4.23607 | −0.141517 | ||||||||
\(897\) | 5.09017 | 0.169956 | ||||||||
\(898\) | 2.90983 | 0.0971023 | ||||||||
\(899\) | 6.38197 | 0.212850 | ||||||||
\(900\) | −21.1803 | −0.706011 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 1.81966 | 0.0605881 | ||||||||
\(903\) | −5.85410 | −0.194812 | ||||||||
\(904\) | −15.3820 | −0.511597 | ||||||||
\(905\) | −70.2492 | −2.33516 | ||||||||
\(906\) | −6.14590 | −0.204184 | ||||||||
\(907\) | −14.1246 | −0.469000 | −0.234500 | − | 0.972116i | \(-0.575345\pi\) | ||||
−0.234500 | + | 0.972116i | \(0.575345\pi\) | |||||||
\(908\) | −24.0344 | −0.797611 | ||||||||
\(909\) | 13.3262 | 0.442003 | ||||||||
\(910\) | −15.3262 | −0.508060 | ||||||||
\(911\) | 47.3394 | 1.56842 | 0.784212 | − | 0.620493i | \(-0.213067\pi\) | ||||
0.784212 | + | 0.620493i | \(0.213067\pi\) | |||||||
\(912\) | 1.23607 | 0.0409303 | ||||||||
\(913\) | −1.23607 | −0.0409079 | ||||||||
\(914\) | 26.7984 | 0.886411 | ||||||||
\(915\) | 12.2361 | 0.404512 | ||||||||
\(916\) | −10.7082 | −0.353809 | ||||||||
\(917\) | −11.7082 | −0.386639 | ||||||||
\(918\) | −0.819660 | −0.0270528 | ||||||||
\(919\) | −5.34752 | −0.176399 | −0.0881993 | − | 0.996103i | \(-0.528111\pi\) | ||||
−0.0881993 | + | 0.996103i | \(0.528111\pi\) | |||||||
\(920\) | 29.7984 | 0.982423 | ||||||||
\(921\) | 19.8541 | 0.654215 | ||||||||
\(922\) | 21.1246 | 0.695702 | ||||||||
\(923\) | −9.70820 | −0.319549 | ||||||||
\(924\) | −0.618034 | −0.0203318 | ||||||||
\(925\) | −70.4508 | −2.31641 | ||||||||
\(926\) | −20.0902 | −0.660204 | ||||||||
\(927\) | −28.4164 | −0.933317 | ||||||||
\(928\) | 0.854102 | 0.0280373 | ||||||||
\(929\) | 17.8197 | 0.584644 | 0.292322 | − | 0.956320i | \(-0.405572\pi\) | ||||
0.292322 | + | 0.956320i | \(0.405572\pi\) | |||||||
\(930\) | −16.7082 | −0.547884 | ||||||||
\(931\) | 21.8885 | 0.717368 | ||||||||
\(932\) | 4.23607 | 0.138757 | ||||||||
\(933\) | −10.6525 | −0.348746 | ||||||||
\(934\) | −6.58359 | −0.215422 | ||||||||
\(935\) | −0.201626 | −0.00659388 | ||||||||
\(936\) | 2.61803 | 0.0855731 | ||||||||
\(937\) | −33.0902 | −1.08101 | −0.540504 | − | 0.841341i | \(-0.681767\pi\) | ||||
−0.540504 | + | 0.841341i | \(0.681767\pi\) | |||||||
\(938\) | −7.47214 | −0.243974 | ||||||||
\(939\) | 8.12461 | 0.265137 | ||||||||
\(940\) | 24.7984 | 0.808834 | ||||||||
\(941\) | −46.9787 | −1.53146 | −0.765731 | − | 0.643161i | \(-0.777623\pi\) | ||||
−0.765731 | + | 0.643161i | \(0.777623\pi\) | |||||||
\(942\) | 14.0000 | 0.456145 | ||||||||
\(943\) | −63.4853 | −2.06737 | ||||||||
\(944\) | −6.56231 | −0.213585 | ||||||||
\(945\) | −53.2148 | −1.73108 | ||||||||
\(946\) | 0.527864 | 0.0171623 | ||||||||
\(947\) | −50.2148 | −1.63176 | −0.815881 | − | 0.578220i | \(-0.803747\pi\) | ||||
−0.815881 | + | 0.578220i | \(0.803747\pi\) | |||||||
\(948\) | −8.52786 | −0.276972 | ||||||||
\(949\) | 10.7082 | 0.347603 | ||||||||
\(950\) | 16.1803 | 0.524960 | ||||||||
\(951\) | −18.6869 | −0.605965 | ||||||||
\(952\) | −1.00000 | −0.0324102 | ||||||||
\(953\) | 25.3050 | 0.819708 | 0.409854 | − | 0.912151i | \(-0.365580\pi\) | ||||
0.409854 | + | 0.912151i | \(0.365580\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18.2918 | 0.591909 | ||||||||
\(956\) | −19.2705 | −0.623253 | ||||||||
\(957\) | 0.124612 | 0.00402813 | ||||||||
\(958\) | −36.5967 | −1.18239 | ||||||||
\(959\) | 66.1591 | 2.13639 | ||||||||
\(960\) | −2.23607 | −0.0721688 | ||||||||
\(961\) | 24.8328 | 0.801059 | ||||||||
\(962\) | 8.70820 | 0.280764 | ||||||||
\(963\) | 32.0344 | 1.03230 | ||||||||
\(964\) | −4.70820 | −0.151641 | ||||||||
\(965\) | 29.7984 | 0.959244 | ||||||||
\(966\) | 21.5623 | 0.693756 | ||||||||
\(967\) | 1.85410 | 0.0596239 | 0.0298119 | − | 0.999556i | \(-0.490509\pi\) | ||||
0.0298119 | + | 0.999556i | \(0.490509\pi\) | |||||||
\(968\) | −10.9443 | −0.351762 | ||||||||
\(969\) | 0.291796 | 0.00937384 | ||||||||
\(970\) | −45.7771 | −1.46981 | ||||||||
\(971\) | −0.652476 | −0.0209389 | −0.0104695 | − | 0.999945i | \(-0.503333\pi\) | ||||
−0.0104695 | + | 0.999945i | \(0.503333\pi\) | |||||||
\(972\) | 13.9443 | 0.447263 | ||||||||
\(973\) | −44.7426 | −1.43438 | ||||||||
\(974\) | −14.8328 | −0.475274 | ||||||||
\(975\) | −5.00000 | −0.160128 | ||||||||
\(976\) | −5.47214 | −0.175159 | ||||||||
\(977\) | 31.1459 | 0.996446 | 0.498223 | − | 0.867049i | \(-0.333986\pi\) | ||||
0.498223 | + | 0.867049i | \(0.333986\pi\) | |||||||
\(978\) | 10.7082 | 0.342411 | ||||||||
\(979\) | −2.31308 | −0.0739264 | ||||||||
\(980\) | −39.5967 | −1.26487 | ||||||||
\(981\) | 12.3262 | 0.393546 | ||||||||
\(982\) | 6.76393 | 0.215846 | ||||||||
\(983\) | −31.4377 | −1.00271 | −0.501353 | − | 0.865243i | \(-0.667164\pi\) | ||||
−0.501353 | + | 0.865243i | \(0.667164\pi\) | |||||||
\(984\) | 4.76393 | 0.151869 | ||||||||
\(985\) | 80.9787 | 2.58020 | ||||||||
\(986\) | 0.201626 | 0.00642108 | ||||||||
\(987\) | 17.9443 | 0.571172 | ||||||||
\(988\) | −2.00000 | −0.0636285 | ||||||||
\(989\) | −18.4164 | −0.585608 | ||||||||
\(990\) | 2.23607 | 0.0710669 | ||||||||
\(991\) | −16.3820 | −0.520390 | −0.260195 | − | 0.965556i | \(-0.583787\pi\) | ||||
−0.260195 | + | 0.965556i | \(0.583787\pi\) | |||||||
\(992\) | 7.47214 | 0.237241 | ||||||||
\(993\) | 0.506578 | 0.0160758 | ||||||||
\(994\) | −41.1246 | −1.30439 | ||||||||
\(995\) | 19.4721 | 0.617308 | ||||||||
\(996\) | −3.23607 | −0.102539 | ||||||||
\(997\) | −17.5836 | −0.556878 | −0.278439 | − | 0.960454i | \(-0.589817\pi\) | ||||
−0.278439 | + | 0.960454i | \(0.589817\pi\) | |||||||
\(998\) | 11.9443 | 0.378089 | ||||||||
\(999\) | 30.2361 | 0.956627 |
(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 | 538.2.a.a.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 4842.2.a.f.1.2 | 2 | |||
4.3 | odd | 2 | 4304.2.a.d.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
538.2.a.a.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
4304.2.a.d.1.1 | 2 | 4.3 | odd | 2 | |||
4842.2.a.f.1.2 | 2 | 3.2 | odd | 2 |