Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3822,2,Mod(1,3822)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3822, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3822.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3822.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: | \(30.5188236525\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.10304.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 7x^{2} + 8x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.16053\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3822.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −4.16053 | −1.86065 | −0.930323 | − | 0.366741i | \(-0.880474\pi\) | ||||
−0.930323 | + | 0.366741i | \(0.880474\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 4.16053 | 1.31568 | ||||||||
\(11\) | 3.72335 | 1.12263 | 0.561316 | − | 0.827602i | \(-0.310295\pi\) | ||||
0.561316 | + | 0.827602i | \(0.310295\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.16053 | 1.07424 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.59771 | −0.630038 | −0.315019 | − | 0.949085i | \(-0.602011\pi\) | ||||
−0.315019 | + | 0.949085i | \(0.602011\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −2.37069 | −0.543873 | −0.271937 | − | 0.962315i | \(-0.587664\pi\) | ||||
−0.271937 | + | 0.962315i | \(0.587664\pi\) | |||||||
\(20\) | −4.16053 | −0.930323 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.72335 | −0.793821 | ||||||||
\(23\) | −3.95037 | −0.823710 | −0.411855 | − | 0.911249i | \(-0.635119\pi\) | ||||
−0.411855 | + | 0.911249i | \(0.635119\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 12.3100 | 2.46200 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.84035 | −0.898831 | −0.449416 | − | 0.893323i | \(-0.648368\pi\) | ||||
−0.449416 | + | 0.893323i | \(0.648368\pi\) | |||||||
\(30\) | −4.16053 | −0.759606 | ||||||||
\(31\) | −0.227026 | −0.0407750 | −0.0203875 | − | 0.999792i | \(-0.506490\pi\) | ||||
−0.0203875 | + | 0.999792i | \(0.506490\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −3.72335 | −0.648152 | ||||||||
\(34\) | 2.59771 | 0.445504 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 1.04352 | 0.171554 | 0.0857772 | − | 0.996314i | \(-0.472663\pi\) | ||||
0.0857772 | + | 0.996314i | \(0.472663\pi\) | |||||||
\(38\) | 2.37069 | 0.384576 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 4.16053 | 0.657838 | ||||||||
\(41\) | −2.35876 | −0.368377 | −0.184188 | − | 0.982891i | \(-0.558966\pi\) | ||||
−0.184188 | + | 0.982891i | \(0.558966\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.95037 | 1.21242 | 0.606210 | − | 0.795304i | \(-0.292689\pi\) | ||||
0.606210 | + | 0.795304i | \(0.292689\pi\) | |||||||
\(44\) | 3.72335 | 0.561316 | ||||||||
\(45\) | −4.16053 | −0.620215 | ||||||||
\(46\) | 3.95037 | 0.582451 | ||||||||
\(47\) | 2.17246 | 0.316886 | 0.158443 | − | 0.987368i | \(-0.449353\pi\) | ||||
0.158443 | + | 0.987368i | \(0.449353\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −12.3100 | −1.74090 | ||||||||
\(51\) | 2.59771 | 0.363753 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | −4.17246 | −0.573131 | −0.286566 | − | 0.958061i | \(-0.592514\pi\) | ||||
−0.286566 | + | 0.958061i | \(0.592514\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −15.4911 | −2.08882 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.37069 | 0.314005 | ||||||||
\(58\) | 4.84035 | 0.635570 | ||||||||
\(59\) | 7.54073 | 0.981720 | 0.490860 | − | 0.871238i | \(-0.336683\pi\) | ||||
0.490860 | + | 0.871238i | \(0.336683\pi\) | |||||||
\(60\) | 4.16053 | 0.537122 | ||||||||
\(61\) | −12.4525 | −1.59438 | −0.797191 | − | 0.603727i | \(-0.793682\pi\) | ||||
−0.797191 | + | 0.603727i | \(0.793682\pi\) | |||||||
\(62\) | 0.227026 | 0.0288323 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.16053 | −0.516050 | ||||||||
\(66\) | 3.72335 | 0.458313 | ||||||||
\(67\) | −6.56370 | −0.801884 | −0.400942 | − | 0.916103i | \(-0.631317\pi\) | ||||
−0.400942 | + | 0.916103i | \(0.631317\pi\) | |||||||
\(68\) | −2.59771 | −0.315019 | ||||||||
\(69\) | 3.95037 | 0.475569 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.88388 | −0.935644 | −0.467822 | − | 0.883823i | \(-0.654961\pi\) | ||||
−0.467822 | + | 0.883823i | \(0.654961\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 13.2641 | 1.55244 | 0.776222 | − | 0.630460i | \(-0.217134\pi\) | ||||
0.776222 | + | 0.630460i | \(0.217134\pi\) | |||||||
\(74\) | −1.04352 | −0.121307 | ||||||||
\(75\) | −12.3100 | −1.42144 | ||||||||
\(76\) | −2.37069 | −0.271937 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | −12.3379 | −1.38813 | −0.694063 | − | 0.719914i | \(-0.744181\pi\) | ||||
−0.694063 | + | 0.719914i | \(0.744181\pi\) | |||||||
\(80\) | −4.16053 | −0.465162 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.35876 | 0.260482 | ||||||||
\(83\) | −17.9779 | −1.97333 | −0.986666 | − | 0.162756i | \(-0.947962\pi\) | ||||
−0.986666 | + | 0.162756i | \(0.947962\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.8079 | 1.17228 | ||||||||
\(86\) | −7.95037 | −0.857311 | ||||||||
\(87\) | 4.84035 | 0.518941 | ||||||||
\(88\) | −3.72335 | −0.396910 | ||||||||
\(89\) | −4.79594 | −0.508369 | −0.254185 | − | 0.967156i | \(-0.581807\pi\) | ||||
−0.254185 | + | 0.967156i | \(0.581807\pi\) | |||||||
\(90\) | 4.16053 | 0.438559 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.95037 | −0.411855 | ||||||||
\(93\) | 0.227026 | 0.0235415 | ||||||||
\(94\) | −2.17246 | −0.224072 | ||||||||
\(95\) | 9.86332 | 1.01196 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −11.6807 | −1.18600 | −0.592998 | − | 0.805204i | \(-0.702056\pi\) | ||||
−0.592998 | + | 0.805204i | \(0.702056\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.72335 | 0.374211 | ||||||||
\(100\) | 12.3100 | 1.23100 | ||||||||
\(101\) | −14.9562 | −1.48820 | −0.744099 | − | 0.668070i | \(-0.767121\pi\) | ||||
−0.744099 | + | 0.668070i | \(0.767121\pi\) | |||||||
\(102\) | −2.59771 | −0.257212 | ||||||||
\(103\) | 6.32600 | 0.623320 | 0.311660 | − | 0.950194i | \(-0.399115\pi\) | ||||
0.311660 | + | 0.950194i | \(0.399115\pi\) | |||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.17246 | 0.405265 | ||||||||
\(107\) | 18.7617 | 1.81376 | 0.906879 | − | 0.421391i | \(-0.138458\pi\) | ||||
0.906879 | + | 0.421391i | \(0.138458\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −14.1709 | −1.35733 | −0.678665 | − | 0.734448i | \(-0.737441\pi\) | ||||
−0.678665 | + | 0.734448i | \(0.737441\pi\) | |||||||
\(110\) | 15.4911 | 1.47702 | ||||||||
\(111\) | −1.04352 | −0.0990470 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.50950 | 0.518291 | 0.259145 | − | 0.965838i | \(-0.416559\pi\) | ||||
0.259145 | + | 0.965838i | \(0.416559\pi\) | |||||||
\(114\) | −2.37069 | −0.222035 | ||||||||
\(115\) | 16.4357 | 1.53263 | ||||||||
\(116\) | −4.84035 | −0.449416 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | −7.54073 | −0.694181 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −4.16053 | −0.379803 | ||||||||
\(121\) | 2.86332 | 0.260302 | ||||||||
\(122\) | 12.4525 | 1.12740 | ||||||||
\(123\) | 2.35876 | 0.212682 | ||||||||
\(124\) | −0.227026 | −0.0203875 | ||||||||
\(125\) | −30.4136 | −2.72027 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.0481 | 1.24657 | 0.623284 | − | 0.781996i | \(-0.285798\pi\) | ||||
0.623284 | + | 0.781996i | \(0.285798\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −7.95037 | −0.699991 | ||||||||
\(130\) | 4.16053 | 0.364903 | ||||||||
\(131\) | 14.9837 | 1.30914 | 0.654568 | − | 0.756003i | \(-0.272851\pi\) | ||||
0.654568 | + | 0.756003i | \(0.272851\pi\) | |||||||
\(132\) | −3.72335 | −0.324076 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 6.56370 | 0.567018 | ||||||||
\(135\) | 4.16053 | 0.358082 | ||||||||
\(136\) | 2.59771 | 0.222752 | ||||||||
\(137\) | 14.4647 | 1.23580 | 0.617902 | − | 0.786255i | \(-0.287983\pi\) | ||||
0.617902 | + | 0.786255i | \(0.287983\pi\) | |||||||
\(138\) | −3.95037 | −0.336278 | ||||||||
\(139\) | 9.39338 | 0.796736 | 0.398368 | − | 0.917226i | \(-0.369577\pi\) | ||||
0.398368 | + | 0.917226i | \(0.369577\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.17246 | −0.182954 | ||||||||
\(142\) | 7.88388 | 0.661601 | ||||||||
\(143\) | 3.72335 | 0.311362 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 20.1384 | 1.67241 | ||||||||
\(146\) | −13.2641 | −1.09774 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.04352 | 0.0857772 | ||||||||
\(149\) | −13.1495 | −1.07725 | −0.538624 | − | 0.842546i | \(-0.681056\pi\) | ||||
−0.538624 | + | 0.842546i | \(0.681056\pi\) | |||||||
\(150\) | 12.3100 | 1.00511 | ||||||||
\(151\) | −17.4041 | −1.41632 | −0.708161 | − | 0.706051i | \(-0.750475\pi\) | ||||
−0.708161 | + | 0.706051i | \(0.750475\pi\) | |||||||
\(152\) | 2.37069 | 0.192288 | ||||||||
\(153\) | −2.59771 | −0.210013 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.944547 | 0.0758679 | ||||||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | 23.7013 | 1.89157 | 0.945783 | − | 0.324798i | \(-0.105296\pi\) | ||||
0.945783 | + | 0.324798i | \(0.105296\pi\) | |||||||
\(158\) | 12.3379 | 0.981553 | ||||||||
\(159\) | 4.17246 | 0.330898 | ||||||||
\(160\) | 4.16053 | 0.328919 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 3.06408 | 0.239997 | 0.119999 | − | 0.992774i | \(-0.461711\pi\) | ||||
0.119999 | + | 0.992774i | \(0.461711\pi\) | |||||||
\(164\) | −2.35876 | −0.184188 | ||||||||
\(165\) | 15.4911 | 1.20598 | ||||||||
\(166\) | 17.9779 | 1.39536 | ||||||||
\(167\) | 9.92488 | 0.768010 | 0.384005 | − | 0.923331i | \(-0.374545\pi\) | ||||
0.384005 | + | 0.923331i | \(0.374545\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −10.8079 | −0.828926 | ||||||||
\(171\) | −2.37069 | −0.181291 | ||||||||
\(172\) | 7.95037 | 0.606210 | ||||||||
\(173\) | 14.1590 | 1.07649 | 0.538245 | − | 0.842789i | \(-0.319088\pi\) | ||||
0.538245 | + | 0.842789i | \(0.319088\pi\) | |||||||
\(174\) | −4.84035 | −0.366946 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.72335 | 0.280658 | ||||||||
\(177\) | −7.54073 | −0.566796 | ||||||||
\(178\) | 4.79594 | 0.359471 | ||||||||
\(179\) | −10.8609 | −0.811783 | −0.405891 | − | 0.913921i | \(-0.633039\pi\) | ||||
−0.405891 | + | 0.913921i | \(0.633039\pi\) | |||||||
\(180\) | −4.16053 | −0.310108 | ||||||||
\(181\) | 16.8523 | 1.25262 | 0.626310 | − | 0.779574i | \(-0.284564\pi\) | ||||
0.626310 | + | 0.779574i | \(0.284564\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.4525 | 0.920517 | ||||||||
\(184\) | 3.95037 | 0.291225 | ||||||||
\(185\) | −4.34162 | −0.319202 | ||||||||
\(186\) | −0.227026 | −0.0166463 | ||||||||
\(187\) | −9.67220 | −0.707301 | ||||||||
\(188\) | 2.17246 | 0.158443 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −9.86332 | −0.715561 | ||||||||
\(191\) | 11.9405 | 0.863984 | 0.431992 | − | 0.901877i | \(-0.357811\pi\) | ||||
0.431992 | + | 0.901877i | \(0.357811\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 21.9610 | 1.58079 | 0.790395 | − | 0.612597i | \(-0.209875\pi\) | ||||
0.790395 | + | 0.612597i | \(0.209875\pi\) | |||||||
\(194\) | 11.6807 | 0.838626 | ||||||||
\(195\) | 4.16053 | 0.297942 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.823213 | −0.0586515 | −0.0293257 | − | 0.999570i | \(-0.509336\pi\) | ||||
−0.0293257 | + | 0.999570i | \(0.509336\pi\) | |||||||
\(198\) | −3.72335 | −0.264607 | ||||||||
\(199\) | 13.9951 | 0.992083 | 0.496042 | − | 0.868299i | \(-0.334786\pi\) | ||||
0.496042 | + | 0.868299i | \(0.334786\pi\) | |||||||
\(200\) | −12.3100 | −0.870450 | ||||||||
\(201\) | 6.56370 | 0.462968 | ||||||||
\(202\) | 14.9562 | 1.05231 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 2.59771 | 0.181876 | ||||||||
\(205\) | 9.81370 | 0.685418 | ||||||||
\(206\) | −6.32600 | −0.440754 | ||||||||
\(207\) | −3.95037 | −0.274570 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | −8.82690 | −0.610569 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 25.2420 | 1.73773 | 0.868865 | − | 0.495048i | \(-0.164850\pi\) | ||||
0.868865 | + | 0.495048i | \(0.164850\pi\) | |||||||
\(212\) | −4.17246 | −0.286566 | ||||||||
\(213\) | 7.88388 | 0.540195 | ||||||||
\(214\) | −18.7617 | −1.28252 | ||||||||
\(215\) | −33.0778 | −2.25589 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 14.1709 | 0.959777 | ||||||||
\(219\) | −13.2641 | −0.896304 | ||||||||
\(220\) | −15.4911 | −1.04441 | ||||||||
\(221\) | −2.59771 | −0.174741 | ||||||||
\(222\) | 1.04352 | 0.0700368 | ||||||||
\(223\) | 26.4969 | 1.77437 | 0.887183 | − | 0.461418i | \(-0.152659\pi\) | ||||
0.887183 | + | 0.461418i | \(0.152659\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 12.3100 | 0.820668 | ||||||||
\(226\) | −5.50950 | −0.366487 | ||||||||
\(227\) | 6.78210 | 0.450144 | 0.225072 | − | 0.974342i | \(-0.427738\pi\) | ||||
0.225072 | + | 0.974342i | \(0.427738\pi\) | |||||||
\(228\) | 2.37069 | 0.157003 | ||||||||
\(229\) | −9.90774 | −0.654722 | −0.327361 | − | 0.944899i | \(-0.606159\pi\) | ||||
−0.327361 | + | 0.944899i | \(0.606159\pi\) | |||||||
\(230\) | −16.4357 | −1.08374 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.84035 | 0.317785 | ||||||||
\(233\) | −2.38603 | −0.156314 | −0.0781570 | − | 0.996941i | \(-0.524904\pi\) | ||||
−0.0781570 | + | 0.996941i | \(0.524904\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | −9.03858 | −0.589612 | ||||||||
\(236\) | 7.54073 | 0.490860 | ||||||||
\(237\) | 12.3379 | 0.801435 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.68108 | 0.173424 | 0.0867122 | − | 0.996233i | \(-0.472364\pi\) | ||||
0.0867122 | + | 0.996233i | \(0.472364\pi\) | |||||||
\(240\) | 4.16053 | 0.268561 | ||||||||
\(241\) | 17.8327 | 1.14871 | 0.574353 | − | 0.818607i | \(-0.305254\pi\) | ||||
0.574353 | + | 0.818607i | \(0.305254\pi\) | |||||||
\(242\) | −2.86332 | −0.184061 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −12.4525 | −0.797191 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.35876 | −0.150389 | ||||||||
\(247\) | −2.37069 | −0.150843 | ||||||||
\(248\) | 0.227026 | 0.0144161 | ||||||||
\(249\) | 17.9779 | 1.13930 | ||||||||
\(250\) | 30.4136 | 1.92352 | ||||||||
\(251\) | 0.317763 | 0.0200570 | 0.0100285 | − | 0.999950i | \(-0.496808\pi\) | ||||
0.0100285 | + | 0.999950i | \(0.496808\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.7086 | −0.924723 | ||||||||
\(254\) | −14.0481 | −0.881456 | ||||||||
\(255\) | −10.8079 | −0.676815 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 2.13299 | 0.133052 | 0.0665261 | − | 0.997785i | \(-0.478808\pi\) | ||||
0.0665261 | + | 0.997785i | \(0.478808\pi\) | |||||||
\(258\) | 7.95037 | 0.494969 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −4.16053 | −0.258025 | ||||||||
\(261\) | −4.84035 | −0.299610 | ||||||||
\(262\) | −14.9837 | −0.925699 | ||||||||
\(263\) | −6.29898 | −0.388412 | −0.194206 | − | 0.980961i | \(-0.562213\pi\) | ||||
−0.194206 | + | 0.980961i | \(0.562213\pi\) | |||||||
\(264\) | 3.72335 | 0.229156 | ||||||||
\(265\) | 17.3596 | 1.06639 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.79594 | 0.293507 | ||||||||
\(268\) | −6.56370 | −0.400942 | ||||||||
\(269\) | 5.76077 | 0.351241 | 0.175620 | − | 0.984458i | \(-0.443807\pi\) | ||||
0.175620 | + | 0.984458i | \(0.443807\pi\) | |||||||
\(270\) | −4.16053 | −0.253202 | ||||||||
\(271\) | 19.0793 | 1.15899 | 0.579493 | − | 0.814977i | \(-0.303251\pi\) | ||||
0.579493 | + | 0.814977i | \(0.303251\pi\) | |||||||
\(272\) | −2.59771 | −0.157510 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −14.4647 | −0.873846 | ||||||||
\(275\) | 45.8345 | 2.76392 | ||||||||
\(276\) | 3.95037 | 0.237785 | ||||||||
\(277\) | 15.6204 | 0.938539 | 0.469270 | − | 0.883055i | \(-0.344517\pi\) | ||||
0.469270 | + | 0.883055i | \(0.344517\pi\) | |||||||
\(278\) | −9.39338 | −0.563378 | ||||||||
\(279\) | −0.227026 | −0.0135917 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.9926 | 0.655766 | 0.327883 | − | 0.944718i | \(-0.393665\pi\) | ||||
0.327883 | + | 0.944718i | \(0.393665\pi\) | |||||||
\(282\) | 2.17246 | 0.129368 | ||||||||
\(283\) | −1.20280 | −0.0714992 | −0.0357496 | − | 0.999361i | \(-0.511382\pi\) | ||||
−0.0357496 | + | 0.999361i | \(0.511382\pi\) | |||||||
\(284\) | −7.88388 | −0.467822 | ||||||||
\(285\) | −9.86332 | −0.584253 | ||||||||
\(286\) | −3.72335 | −0.220166 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −10.2519 | −0.603052 | ||||||||
\(290\) | −20.1384 | −1.18257 | ||||||||
\(291\) | 11.6807 | 0.684735 | ||||||||
\(292\) | 13.2641 | 0.776222 | ||||||||
\(293\) | −6.25610 | −0.365485 | −0.182743 | − | 0.983161i | \(-0.558497\pi\) | ||||
−0.182743 | + | 0.983161i | \(0.558497\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −31.3735 | −1.82663 | ||||||||
\(296\) | −1.04352 | −0.0606537 | ||||||||
\(297\) | −3.72335 | −0.216051 | ||||||||
\(298\) | 13.1495 | 0.761729 | ||||||||
\(299\) | −3.95037 | −0.228456 | ||||||||
\(300\) | −12.3100 | −0.710719 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 17.4041 | 1.00149 | ||||||||
\(303\) | 14.9562 | 0.859211 | ||||||||
\(304\) | −2.37069 | −0.135968 | ||||||||
\(305\) | 51.8091 | 2.96658 | ||||||||
\(306\) | 2.59771 | 0.148501 | ||||||||
\(307\) | −23.2145 | −1.32492 | −0.662460 | − | 0.749098i | \(-0.730487\pi\) | ||||
−0.662460 | + | 0.749098i | \(0.730487\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.32600 | −0.359874 | ||||||||
\(310\) | −0.944547 | −0.0536467 | ||||||||
\(311\) | −3.79162 | −0.215003 | −0.107501 | − | 0.994205i | \(-0.534285\pi\) | ||||
−0.107501 | + | 0.994205i | \(0.534285\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | 1.62260 | 0.0917147 | 0.0458573 | − | 0.998948i | \(-0.485398\pi\) | ||||
0.0458573 | + | 0.998948i | \(0.485398\pi\) | |||||||
\(314\) | −23.7013 | −1.33754 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.3379 | −0.694063 | ||||||||
\(317\) | −18.5719 | −1.04310 | −0.521552 | − | 0.853219i | \(-0.674647\pi\) | ||||
−0.521552 | + | 0.853219i | \(0.674647\pi\) | |||||||
\(318\) | −4.17246 | −0.233980 | ||||||||
\(319\) | −18.0223 | −1.00906 | ||||||||
\(320\) | −4.16053 | −0.232581 | ||||||||
\(321\) | −18.7617 | −1.04717 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.15837 | 0.342661 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 12.3100 | 0.682837 | ||||||||
\(326\) | −3.06408 | −0.169704 | ||||||||
\(327\) | 14.1709 | 0.783654 | ||||||||
\(328\) | 2.35876 | 0.130241 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −15.4911 | −0.852757 | ||||||||
\(331\) | −31.3289 | −1.72199 | −0.860997 | − | 0.508610i | \(-0.830160\pi\) | ||||
−0.860997 | + | 0.508610i | \(0.830160\pi\) | |||||||
\(332\) | −17.9779 | −0.986666 | ||||||||
\(333\) | 1.04352 | 0.0571848 | ||||||||
\(334\) | −9.92488 | −0.543065 | ||||||||
\(335\) | 27.3085 | 1.49202 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.4577 | 1.00546 | 0.502729 | − | 0.864444i | \(-0.332330\pi\) | ||||
0.502729 | + | 0.864444i | \(0.332330\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | −5.50950 | −0.299235 | ||||||||
\(340\) | 10.8079 | 0.586139 | ||||||||
\(341\) | −0.845296 | −0.0457753 | ||||||||
\(342\) | 2.37069 | 0.128192 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −7.95037 | −0.428655 | ||||||||
\(345\) | −16.4357 | −0.884866 | ||||||||
\(346\) | −14.1590 | −0.761193 | ||||||||
\(347\) | 4.75001 | 0.254994 | 0.127497 | − | 0.991839i | \(-0.459306\pi\) | ||||
0.127497 | + | 0.991839i | \(0.459306\pi\) | |||||||
\(348\) | 4.84035 | 0.259470 | ||||||||
\(349\) | −25.4433 | −1.36195 | −0.680973 | − | 0.732308i | \(-0.738443\pi\) | ||||
−0.680973 | + | 0.732308i | \(0.738443\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | −3.72335 | −0.198455 | ||||||||
\(353\) | −24.1382 | −1.28475 | −0.642373 | − | 0.766392i | \(-0.722050\pi\) | ||||
−0.642373 | + | 0.766392i | \(0.722050\pi\) | |||||||
\(354\) | 7.54073 | 0.400785 | ||||||||
\(355\) | 32.8011 | 1.74090 | ||||||||
\(356\) | −4.79594 | −0.254185 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 10.8609 | 0.574017 | ||||||||
\(359\) | 31.0282 | 1.63760 | 0.818802 | − | 0.574076i | \(-0.194639\pi\) | ||||
0.818802 | + | 0.574076i | \(0.194639\pi\) | |||||||
\(360\) | 4.16053 | 0.219279 | ||||||||
\(361\) | −13.3798 | −0.704202 | ||||||||
\(362\) | −16.8523 | −0.885736 | ||||||||
\(363\) | −2.86332 | −0.150286 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −55.1856 | −2.88855 | ||||||||
\(366\) | −12.4525 | −0.650904 | ||||||||
\(367\) | −7.08794 | −0.369987 | −0.184994 | − | 0.982740i | \(-0.559226\pi\) | ||||
−0.184994 | + | 0.982740i | \(0.559226\pi\) | |||||||
\(368\) | −3.95037 | −0.205927 | ||||||||
\(369\) | −2.35876 | −0.122792 | ||||||||
\(370\) | 4.34162 | 0.225710 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.227026 | 0.0117707 | ||||||||
\(373\) | 20.7994 | 1.07695 | 0.538475 | − | 0.842642i | \(-0.319001\pi\) | ||||
0.538475 | + | 0.842642i | \(0.319001\pi\) | |||||||
\(374\) | 9.67220 | 0.500137 | ||||||||
\(375\) | 30.4136 | 1.57055 | ||||||||
\(376\) | −2.17246 | −0.112036 | ||||||||
\(377\) | −4.84035 | −0.249291 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.16294 | −0.265203 | −0.132601 | − | 0.991169i | \(-0.542333\pi\) | ||||
−0.132601 | + | 0.991169i | \(0.542333\pi\) | |||||||
\(380\) | 9.86332 | 0.505978 | ||||||||
\(381\) | −14.0481 | −0.719706 | ||||||||
\(382\) | −11.9405 | −0.610929 | ||||||||
\(383\) | −11.4685 | −0.586013 | −0.293007 | − | 0.956110i | \(-0.594656\pi\) | ||||
−0.293007 | + | 0.956110i | \(0.594656\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −21.9610 | −1.11779 | ||||||||
\(387\) | 7.95037 | 0.404140 | ||||||||
\(388\) | −11.6807 | −0.592998 | ||||||||
\(389\) | 34.3796 | 1.74311 | 0.871556 | − | 0.490295i | \(-0.163111\pi\) | ||||
0.871556 | + | 0.490295i | \(0.163111\pi\) | |||||||
\(390\) | −4.16053 | −0.210677 | ||||||||
\(391\) | 10.2619 | 0.518969 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −14.9837 | −0.755830 | ||||||||
\(394\) | 0.823213 | 0.0414728 | ||||||||
\(395\) | 51.3323 | 2.58281 | ||||||||
\(396\) | 3.72335 | 0.187105 | ||||||||
\(397\) | −17.2916 | −0.867842 | −0.433921 | − | 0.900951i | \(-0.642870\pi\) | ||||
−0.433921 | + | 0.900951i | \(0.642870\pi\) | |||||||
\(398\) | −13.9951 | −0.701509 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 12.3100 | 0.615501 | ||||||||
\(401\) | 12.4541 | 0.621926 | 0.310963 | − | 0.950422i | \(-0.399349\pi\) | ||||
0.310963 | + | 0.950422i | \(0.399349\pi\) | |||||||
\(402\) | −6.56370 | −0.327368 | ||||||||
\(403\) | −0.227026 | −0.0113090 | ||||||||
\(404\) | −14.9562 | −0.744099 | ||||||||
\(405\) | −4.16053 | −0.206738 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.88541 | 0.192592 | ||||||||
\(408\) | −2.59771 | −0.128606 | ||||||||
\(409\) | −29.8651 | −1.47673 | −0.738367 | − | 0.674399i | \(-0.764403\pi\) | ||||
−0.738367 | + | 0.674399i | \(0.764403\pi\) | |||||||
\(410\) | −9.81370 | −0.484664 | ||||||||
\(411\) | −14.4647 | −0.713492 | ||||||||
\(412\) | 6.32600 | 0.311660 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 3.95037 | 0.194150 | ||||||||
\(415\) | 74.7977 | 3.67167 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | −9.39338 | −0.459996 | ||||||||
\(418\) | 8.82690 | 0.431738 | ||||||||
\(419\) | 32.4084 | 1.58325 | 0.791626 | − | 0.611006i | \(-0.209235\pi\) | ||||
0.791626 | + | 0.611006i | \(0.209235\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.5732 | 1.44131 | 0.720655 | − | 0.693294i | \(-0.243841\pi\) | ||||
0.720655 | + | 0.693294i | \(0.243841\pi\) | |||||||
\(422\) | −25.2420 | −1.22876 | ||||||||
\(423\) | 2.17246 | 0.105629 | ||||||||
\(424\) | 4.17246 | 0.202633 | ||||||||
\(425\) | −31.9779 | −1.55116 | ||||||||
\(426\) | −7.88388 | −0.381975 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 18.7617 | 0.906879 | ||||||||
\(429\) | −3.72335 | −0.179765 | ||||||||
\(430\) | 33.0778 | 1.59515 | ||||||||
\(431\) | 19.9147 | 0.959258 | 0.479629 | − | 0.877471i | \(-0.340771\pi\) | ||||
0.479629 | + | 0.877471i | \(0.340771\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 4.56154 | 0.219214 | 0.109607 | − | 0.993975i | \(-0.465041\pi\) | ||||
0.109607 | + | 0.993975i | \(0.465041\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −20.1384 | −0.965565 | ||||||||
\(436\) | −14.1709 | −0.678665 | ||||||||
\(437\) | 9.36511 | 0.447994 | ||||||||
\(438\) | 13.2641 | 0.633782 | ||||||||
\(439\) | −2.09376 | −0.0999299 | −0.0499649 | − | 0.998751i | \(-0.515911\pi\) | ||||
−0.0499649 | + | 0.998751i | \(0.515911\pi\) | |||||||
\(440\) | 15.4911 | 0.738510 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.59771 | 0.123561 | ||||||||
\(443\) | −15.2686 | −0.725435 | −0.362717 | − | 0.931899i | \(-0.618151\pi\) | ||||
−0.362717 | + | 0.931899i | \(0.618151\pi\) | |||||||
\(444\) | −1.04352 | −0.0495235 | ||||||||
\(445\) | 19.9537 | 0.945895 | ||||||||
\(446\) | −26.4969 | −1.25467 | ||||||||
\(447\) | 13.1495 | 0.621950 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 26.3992 | 1.24586 | 0.622928 | − | 0.782279i | \(-0.285943\pi\) | ||||
0.622928 | + | 0.782279i | \(0.285943\pi\) | |||||||
\(450\) | −12.3100 | −0.580300 | ||||||||
\(451\) | −8.78249 | −0.413551 | ||||||||
\(452\) | 5.50950 | 0.259145 | ||||||||
\(453\) | 17.4041 | 0.817714 | ||||||||
\(454\) | −6.78210 | −0.318300 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.37069 | −0.111018 | ||||||||
\(457\) | 6.42553 | 0.300574 | 0.150287 | − | 0.988642i | \(-0.451980\pi\) | ||||
0.150287 | + | 0.988642i | \(0.451980\pi\) | |||||||
\(458\) | 9.90774 | 0.462958 | ||||||||
\(459\) | 2.59771 | 0.121251 | ||||||||
\(460\) | 16.4357 | 0.766316 | ||||||||
\(461\) | 25.7009 | 1.19701 | 0.598505 | − | 0.801119i | \(-0.295762\pi\) | ||||
0.598505 | + | 0.801119i | \(0.295762\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.83910 | 0.317840 | 0.158920 | − | 0.987291i | \(-0.449199\pi\) | ||||
0.158920 | + | 0.987291i | \(0.449199\pi\) | |||||||
\(464\) | −4.84035 | −0.224708 | ||||||||
\(465\) | −0.944547 | −0.0438023 | ||||||||
\(466\) | 2.38603 | 0.110531 | ||||||||
\(467\) | −12.7472 | −0.589871 | −0.294936 | − | 0.955517i | \(-0.595298\pi\) | ||||
−0.294936 | + | 0.955517i | \(0.595298\pi\) | |||||||
\(468\) | 1.00000 | 0.0462250 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 9.03858 | 0.416919 | ||||||||
\(471\) | −23.7013 | −1.09210 | ||||||||
\(472\) | −7.54073 | −0.347090 | ||||||||
\(473\) | 29.6020 | 1.36110 | ||||||||
\(474\) | −12.3379 | −0.566700 | ||||||||
\(475\) | −29.1832 | −1.33902 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.17246 | −0.191044 | ||||||||
\(478\) | −2.68108 | −0.122630 | ||||||||
\(479\) | 6.61800 | 0.302384 | 0.151192 | − | 0.988504i | \(-0.451689\pi\) | ||||
0.151192 | + | 0.988504i | \(0.451689\pi\) | |||||||
\(480\) | −4.16053 | −0.189901 | ||||||||
\(481\) | 1.04352 | 0.0475806 | ||||||||
\(482\) | −17.8327 | −0.812258 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.86332 | 0.130151 | ||||||||
\(485\) | 48.5980 | 2.20672 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −32.2292 | −1.46044 | −0.730222 | − | 0.683210i | \(-0.760583\pi\) | ||||
−0.730222 | + | 0.683210i | \(0.760583\pi\) | |||||||
\(488\) | 12.4525 | 0.563699 | ||||||||
\(489\) | −3.06408 | −0.138563 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.5511 | 0.792072 | 0.396036 | − | 0.918235i | \(-0.370386\pi\) | ||||
0.396036 | + | 0.918235i | \(0.370386\pi\) | |||||||
\(492\) | 2.35876 | 0.106341 | ||||||||
\(493\) | 12.5739 | 0.566298 | ||||||||
\(494\) | 2.37069 | 0.106662 | ||||||||
\(495\) | −15.4911 | −0.696274 | ||||||||
\(496\) | −0.227026 | −0.0101938 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −17.9779 | −0.805610 | ||||||||
\(499\) | −14.7304 | −0.659425 | −0.329712 | − | 0.944081i | \(-0.606952\pi\) | ||||
−0.329712 | + | 0.944081i | \(0.606952\pi\) | |||||||
\(500\) | −30.4136 | −1.36014 | ||||||||
\(501\) | −9.92488 | −0.443411 | ||||||||
\(502\) | −0.317763 | −0.0141825 | ||||||||
\(503\) | 36.6344 | 1.63345 | 0.816724 | − | 0.577029i | \(-0.195788\pi\) | ||||
0.816724 | + | 0.577029i | \(0.195788\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 62.2257 | 2.76901 | ||||||||
\(506\) | 14.7086 | 0.653878 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 14.0481 | 0.623284 | ||||||||
\(509\) | −23.8296 | −1.05623 | −0.528114 | − | 0.849174i | \(-0.677101\pi\) | ||||
−0.528114 | + | 0.849174i | \(0.677101\pi\) | |||||||
\(510\) | 10.8079 | 0.478581 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 2.37069 | 0.104668 | ||||||||
\(514\) | −2.13299 | −0.0940821 | ||||||||
\(515\) | −26.3195 | −1.15978 | ||||||||
\(516\) | −7.95037 | −0.349996 | ||||||||
\(517\) | 8.08882 | 0.355746 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −14.1590 | −0.621511 | ||||||||
\(520\) | 4.16053 | 0.182451 | ||||||||
\(521\) | 31.4378 | 1.37731 | 0.688657 | − | 0.725087i | \(-0.258200\pi\) | ||||
0.688657 | + | 0.725087i | \(0.258200\pi\) | |||||||
\(522\) | 4.84035 | 0.211857 | ||||||||
\(523\) | 9.56282 | 0.418153 | 0.209076 | − | 0.977899i | \(-0.432954\pi\) | ||||
0.209076 | + | 0.977899i | \(0.432954\pi\) | |||||||
\(524\) | 14.9837 | 0.654568 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.29898 | 0.274649 | ||||||||
\(527\) | 0.589748 | 0.0256898 | ||||||||
\(528\) | −3.72335 | −0.162038 | ||||||||
\(529\) | −7.39454 | −0.321502 | ||||||||
\(530\) | −17.3596 | −0.754055 | ||||||||
\(531\) | 7.54073 | 0.327240 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.35876 | −0.102169 | ||||||||
\(534\) | −4.79594 | −0.207541 | ||||||||
\(535\) | −78.0585 | −3.37476 | ||||||||
\(536\) | 6.56370 | 0.283509 | ||||||||
\(537\) | 10.8609 | 0.468683 | ||||||||
\(538\) | −5.76077 | −0.248365 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 4.16053 | 0.179041 | ||||||||
\(541\) | −35.6636 | −1.53330 | −0.766648 | − | 0.642067i | \(-0.778077\pi\) | ||||
−0.766648 | + | 0.642067i | \(0.778077\pi\) | |||||||
\(542\) | −19.0793 | −0.819526 | ||||||||
\(543\) | −16.8523 | −0.723201 | ||||||||
\(544\) | 2.59771 | 0.111376 | ||||||||
\(545\) | 58.9586 | 2.52551 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.1348 | −0.604359 | −0.302179 | − | 0.953251i | \(-0.597714\pi\) | ||||
−0.302179 | + | 0.953251i | \(0.597714\pi\) | |||||||
\(548\) | 14.4647 | 0.617902 | ||||||||
\(549\) | −12.4525 | −0.531461 | ||||||||
\(550\) | −45.8345 | −1.95439 | ||||||||
\(551\) | 11.4750 | 0.488850 | ||||||||
\(552\) | −3.95037 | −0.168139 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −15.6204 | −0.663648 | ||||||||
\(555\) | 4.34162 | 0.184291 | ||||||||
\(556\) | 9.39338 | 0.398368 | ||||||||
\(557\) | 23.6470 | 1.00195 | 0.500977 | − | 0.865460i | \(-0.332974\pi\) | ||||
0.500977 | + | 0.865460i | \(0.332974\pi\) | |||||||
\(558\) | 0.227026 | 0.00961076 | ||||||||
\(559\) | 7.95037 | 0.336265 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.67220 | 0.408360 | ||||||||
\(562\) | −10.9926 | −0.463697 | ||||||||
\(563\) | −35.2147 | −1.48412 | −0.742061 | − | 0.670332i | \(-0.766152\pi\) | ||||
−0.742061 | + | 0.670332i | \(0.766152\pi\) | |||||||
\(564\) | −2.17246 | −0.0914770 | ||||||||
\(565\) | −22.9225 | −0.964355 | ||||||||
\(566\) | 1.20280 | 0.0505576 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.88388 | 0.330800 | ||||||||
\(569\) | −45.4576 | −1.90568 | −0.952841 | − | 0.303469i | \(-0.901855\pi\) | ||||
−0.952841 | + | 0.303469i | \(0.901855\pi\) | |||||||
\(570\) | 9.86332 | 0.413129 | ||||||||
\(571\) | −29.2916 | −1.22582 | −0.612908 | − | 0.790154i | \(-0.710000\pi\) | ||||
−0.612908 | + | 0.790154i | \(0.710000\pi\) | |||||||
\(572\) | 3.72335 | 0.155681 | ||||||||
\(573\) | −11.9405 | −0.498821 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −48.6292 | −2.02798 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 40.7604 | 1.69688 | 0.848439 | − | 0.529293i | \(-0.177543\pi\) | ||||
0.848439 | + | 0.529293i | \(0.177543\pi\) | |||||||
\(578\) | 10.2519 | 0.426422 | ||||||||
\(579\) | −21.9610 | −0.912670 | ||||||||
\(580\) | 20.1384 | 0.836204 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −11.6807 | −0.484181 | ||||||||
\(583\) | −15.5355 | −0.643415 | ||||||||
\(584\) | −13.2641 | −0.548872 | ||||||||
\(585\) | −4.16053 | −0.172017 | ||||||||
\(586\) | 6.25610 | 0.258437 | ||||||||
\(587\) | −13.1642 | −0.543345 | −0.271672 | − | 0.962390i | \(-0.587577\pi\) | ||||
−0.271672 | + | 0.962390i | \(0.587577\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.538207 | 0.0221764 | ||||||||
\(590\) | 31.3735 | 1.29162 | ||||||||
\(591\) | 0.823213 | 0.0338624 | ||||||||
\(592\) | 1.04352 | 0.0428886 | ||||||||
\(593\) | −1.12689 | −0.0462757 | −0.0231379 | − | 0.999732i | \(-0.507366\pi\) | ||||
−0.0231379 | + | 0.999732i | \(0.507366\pi\) | |||||||
\(594\) | 3.72335 | 0.152771 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −13.1495 | −0.538624 | ||||||||
\(597\) | −13.9951 | −0.572780 | ||||||||
\(598\) | 3.95037 | 0.161543 | ||||||||
\(599\) | −41.4981 | −1.69557 | −0.847783 | − | 0.530343i | \(-0.822063\pi\) | ||||
−0.847783 | + | 0.530343i | \(0.822063\pi\) | |||||||
\(600\) | 12.3100 | 0.502555 | ||||||||
\(601\) | 28.7564 | 1.17300 | 0.586500 | − | 0.809949i | \(-0.300505\pi\) | ||||
0.586500 | + | 0.809949i | \(0.300505\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.56370 | −0.267295 | ||||||||
\(604\) | −17.4041 | −0.708161 | ||||||||
\(605\) | −11.9130 | −0.484330 | ||||||||
\(606\) | −14.9562 | −0.607554 | ||||||||
\(607\) | 36.7788 | 1.49280 | 0.746402 | − | 0.665495i | \(-0.231780\pi\) | ||||
0.746402 | + | 0.665495i | \(0.231780\pi\) | |||||||
\(608\) | 2.37069 | 0.0961441 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −51.8091 | −2.09769 | ||||||||
\(611\) | 2.17246 | 0.0878883 | ||||||||
\(612\) | −2.59771 | −0.105006 | ||||||||
\(613\) | −18.9197 | −0.764159 | −0.382079 | − | 0.924129i | \(-0.624792\pi\) | ||||
−0.382079 | + | 0.924129i | \(0.624792\pi\) | |||||||
\(614\) | 23.2145 | 0.936859 | ||||||||
\(615\) | −9.81370 | −0.395727 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 40.1670 | 1.61706 | 0.808531 | − | 0.588454i | \(-0.200263\pi\) | ||||
0.808531 | + | 0.588454i | \(0.200263\pi\) | |||||||
\(618\) | 6.32600 | 0.254469 | ||||||||
\(619\) | 13.7199 | 0.551450 | 0.275725 | − | 0.961237i | \(-0.411082\pi\) | ||||
0.275725 | + | 0.961237i | \(0.411082\pi\) | |||||||
\(620\) | 0.944547 | 0.0379339 | ||||||||
\(621\) | 3.95037 | 0.158523 | ||||||||
\(622\) | 3.79162 | 0.152030 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.00000 | −0.0400320 | ||||||||
\(625\) | 64.9865 | 2.59946 | ||||||||
\(626\) | −1.62260 | −0.0648521 | ||||||||
\(627\) | 8.82690 | 0.352512 | ||||||||
\(628\) | 23.7013 | 0.945783 | ||||||||
\(629\) | −2.71078 | −0.108086 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.8728 | −0.472649 | −0.236325 | − | 0.971674i | \(-0.575943\pi\) | ||||
−0.236325 | + | 0.971674i | \(0.575943\pi\) | |||||||
\(632\) | 12.3379 | 0.490777 | ||||||||
\(633\) | −25.2420 | −1.00328 | ||||||||
\(634\) | 18.5719 | 0.737586 | ||||||||
\(635\) | −58.4476 | −2.31942 | ||||||||
\(636\) | 4.17246 | 0.165449 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 18.0223 | 0.713511 | ||||||||
\(639\) | −7.88388 | −0.311881 | ||||||||
\(640\) | 4.16053 | 0.164459 | ||||||||
\(641\) | −7.77475 | −0.307084 | −0.153542 | − | 0.988142i | \(-0.549068\pi\) | ||||
−0.153542 | + | 0.988142i | \(0.549068\pi\) | |||||||
\(642\) | 18.7617 | 0.740464 | ||||||||
\(643\) | −34.6722 | −1.36734 | −0.683669 | − | 0.729793i | \(-0.739617\pi\) | ||||
−0.683669 | + | 0.729793i | \(0.739617\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 33.0778 | 1.30244 | ||||||||
\(646\) | −6.15837 | −0.242298 | ||||||||
\(647\) | 18.0528 | 0.709727 | 0.354864 | − | 0.934918i | \(-0.384527\pi\) | ||||
0.354864 | + | 0.934918i | \(0.384527\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 28.0768 | 1.10211 | ||||||||
\(650\) | −12.3100 | −0.482839 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.06408 | 0.119999 | ||||||||
\(653\) | 48.9089 | 1.91395 | 0.956976 | − | 0.290167i | \(-0.0937110\pi\) | ||||
0.956976 | + | 0.290167i | \(0.0937110\pi\) | |||||||
\(654\) | −14.1709 | −0.554127 | ||||||||
\(655\) | −62.3403 | −2.43584 | ||||||||
\(656\) | −2.35876 | −0.0920941 | ||||||||
\(657\) | 13.2641 | 0.517481 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.13695 | −0.316971 | −0.158485 | − | 0.987361i | \(-0.550661\pi\) | ||||
−0.158485 | + | 0.987361i | \(0.550661\pi\) | |||||||
\(660\) | 15.4911 | 0.602991 | ||||||||
\(661\) | 3.48275 | 0.135463 | 0.0677317 | − | 0.997704i | \(-0.478424\pi\) | ||||
0.0677317 | + | 0.997704i | \(0.478424\pi\) | |||||||
\(662\) | 31.3289 | 1.21763 | ||||||||
\(663\) | 2.59771 | 0.100887 | ||||||||
\(664\) | 17.9779 | 0.697678 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.04352 | −0.0404358 | ||||||||
\(667\) | 19.1212 | 0.740376 | ||||||||
\(668\) | 9.92488 | 0.384005 | ||||||||
\(669\) | −26.4969 | −1.02443 | ||||||||
\(670\) | −27.3085 | −1.05502 | ||||||||
\(671\) | −46.3651 | −1.78990 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.1771 | 0.623580 | 0.311790 | − | 0.950151i | \(-0.399072\pi\) | ||||
0.311790 | + | 0.950151i | \(0.399072\pi\) | |||||||
\(674\) | −18.4577 | −0.710966 | ||||||||
\(675\) | −12.3100 | −0.473813 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −31.8903 | −1.22564 | −0.612822 | − | 0.790221i | \(-0.709966\pi\) | ||||
−0.612822 | + | 0.790221i | \(0.709966\pi\) | |||||||
\(678\) | 5.50950 | 0.211591 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −10.8079 | −0.414463 | ||||||||
\(681\) | −6.78210 | −0.259891 | ||||||||
\(682\) | 0.845296 | 0.0323680 | ||||||||
\(683\) | −28.1675 | −1.07780 | −0.538900 | − | 0.842370i | \(-0.681160\pi\) | ||||
−0.538900 | + | 0.842370i | \(0.681160\pi\) | |||||||
\(684\) | −2.37069 | −0.0906455 | ||||||||
\(685\) | −60.1809 | −2.29940 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.90774 | 0.378004 | ||||||||
\(688\) | 7.95037 | 0.303105 | ||||||||
\(689\) | −4.17246 | −0.158958 | ||||||||
\(690\) | 16.4357 | 0.625695 | ||||||||
\(691\) | 11.4467 | 0.435453 | 0.217726 | − | 0.976010i | \(-0.430136\pi\) | ||||
0.217726 | + | 0.976010i | \(0.430136\pi\) | |||||||
\(692\) | 14.1590 | 0.538245 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.75001 | −0.180308 | ||||||||
\(695\) | −39.0815 | −1.48244 | ||||||||
\(696\) | −4.84035 | −0.183473 | ||||||||
\(697\) | 6.12739 | 0.232091 | ||||||||
\(698\) | 25.4433 | 0.963041 | ||||||||
\(699\) | 2.38603 | 0.0902479 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.5971 | 1.30671 | 0.653356 | − | 0.757051i | \(-0.273360\pi\) | ||||
0.653356 | + | 0.757051i | \(0.273360\pi\) | |||||||
\(702\) | 1.00000 | 0.0377426 | ||||||||
\(703\) | −2.47387 | −0.0933039 | ||||||||
\(704\) | 3.72335 | 0.140329 | ||||||||
\(705\) | 9.03858 | 0.340413 | ||||||||
\(706\) | 24.1382 | 0.908452 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −7.54073 | −0.283398 | ||||||||
\(709\) | 10.2153 | 0.383645 | 0.191823 | − | 0.981430i | \(-0.438560\pi\) | ||||
0.191823 | + | 0.981430i | \(0.438560\pi\) | |||||||
\(710\) | −32.8011 | −1.23100 | ||||||||
\(711\) | −12.3379 | −0.462709 | ||||||||
\(712\) | 4.79594 | 0.179736 | ||||||||
\(713\) | 0.896836 | 0.0335868 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15.4911 | −0.579335 | ||||||||
\(716\) | −10.8609 | −0.405891 | ||||||||
\(717\) | −2.68108 | −0.100127 | ||||||||
\(718\) | −31.0282 | −1.15796 | ||||||||
\(719\) | 36.0598 | 1.34480 | 0.672401 | − | 0.740187i | \(-0.265263\pi\) | ||||
0.672401 | + | 0.740187i | \(0.265263\pi\) | |||||||
\(720\) | −4.16053 | −0.155054 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 13.3798 | 0.497946 | ||||||||
\(723\) | −17.8327 | −0.663206 | ||||||||
\(724\) | 16.8523 | 0.626310 | ||||||||
\(725\) | −59.5849 | −2.21293 | ||||||||
\(726\) | 2.86332 | 0.106268 | ||||||||
\(727\) | 38.9895 | 1.44604 | 0.723020 | − | 0.690827i | \(-0.242753\pi\) | ||||
0.723020 | + | 0.690827i | \(0.242753\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 55.1856 | 2.04251 | ||||||||
\(731\) | −20.6528 | −0.763871 | ||||||||
\(732\) | 12.4525 | 0.460259 | ||||||||
\(733\) | 26.2509 | 0.969598 | 0.484799 | − | 0.874625i | \(-0.338893\pi\) | ||||
0.484799 | + | 0.874625i | \(0.338893\pi\) | |||||||
\(734\) | 7.08794 | 0.261620 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.95037 | 0.145613 | ||||||||
\(737\) | −24.4390 | −0.900220 | ||||||||
\(738\) | 2.35876 | 0.0868272 | ||||||||
\(739\) | −7.60750 | −0.279846 | −0.139923 | − | 0.990162i | \(-0.544686\pi\) | ||||
−0.139923 | + | 0.990162i | \(0.544686\pi\) | |||||||
\(740\) | −4.34162 | −0.159601 | ||||||||
\(741\) | 2.37069 | 0.0870894 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −17.4657 | −0.640755 | −0.320378 | − | 0.947290i | \(-0.603810\pi\) | ||||
−0.320378 | + | 0.947290i | \(0.603810\pi\) | |||||||
\(744\) | −0.227026 | −0.00832316 | ||||||||
\(745\) | 54.7089 | 2.00438 | ||||||||
\(746\) | −20.7994 | −0.761519 | ||||||||
\(747\) | −17.9779 | −0.657778 | ||||||||
\(748\) | −9.67220 | −0.353650 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −30.4136 | −1.11055 | ||||||||
\(751\) | 22.8569 | 0.834062 | 0.417031 | − | 0.908892i | \(-0.363071\pi\) | ||||
0.417031 | + | 0.908892i | \(0.363071\pi\) | |||||||
\(752\) | 2.17246 | 0.0792214 | ||||||||
\(753\) | −0.317763 | −0.0115799 | ||||||||
\(754\) | 4.84035 | 0.176275 | ||||||||
\(755\) | 72.4101 | 2.63527 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.0156 | 1.23632 | 0.618159 | − | 0.786053i | \(-0.287879\pi\) | ||||
0.618159 | + | 0.786053i | \(0.287879\pi\) | |||||||
\(758\) | 5.16294 | 0.187527 | ||||||||
\(759\) | 14.7086 | 0.533889 | ||||||||
\(760\) | −9.86332 | −0.357780 | ||||||||
\(761\) | −22.2357 | −0.806042 | −0.403021 | − | 0.915191i | \(-0.632040\pi\) | ||||
−0.403021 | + | 0.915191i | \(0.632040\pi\) | |||||||
\(762\) | 14.0481 | 0.508909 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 11.9405 | 0.431992 | ||||||||
\(765\) | 10.8079 | 0.390759 | ||||||||
\(766\) | 11.4685 | 0.414374 | ||||||||
\(767\) | 7.54073 | 0.272280 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 23.2897 | 0.839848 | 0.419924 | − | 0.907559i | \(-0.362057\pi\) | ||||
0.419924 | + | 0.907559i | \(0.362057\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.13299 | −0.0768177 | ||||||||
\(772\) | 21.9610 | 0.790395 | ||||||||
\(773\) | 42.6813 | 1.53514 | 0.767570 | − | 0.640965i | \(-0.221466\pi\) | ||||
0.767570 | + | 0.640965i | \(0.221466\pi\) | |||||||
\(774\) | −7.95037 | −0.285770 | ||||||||
\(775\) | −2.79469 | −0.100388 | ||||||||
\(776\) | 11.6807 | 0.419313 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −34.3796 | −1.23257 | ||||||||
\(779\) | 5.59189 | 0.200350 | ||||||||
\(780\) | 4.16053 | 0.148971 | ||||||||
\(781\) | −29.3544 | −1.05038 | ||||||||
\(782\) | −10.2619 | −0.366966 | ||||||||
\(783\) | 4.84035 | 0.172980 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −98.6099 | −3.51954 | ||||||||
\(786\) | 14.9837 | 0.534452 | ||||||||
\(787\) | −28.2476 | −1.00692 | −0.503459 | − | 0.864019i | \(-0.667939\pi\) | ||||
−0.503459 | + | 0.864019i | \(0.667939\pi\) | |||||||
\(788\) | −0.823213 | −0.0293257 | ||||||||
\(789\) | 6.29898 | 0.224250 | ||||||||
\(790\) | −51.3323 | −1.82632 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −3.72335 | −0.132303 | ||||||||
\(793\) | −12.4525 | −0.442202 | ||||||||
\(794\) | 17.2916 | 0.613657 | ||||||||
\(795\) | −17.3596 | −0.615683 | ||||||||
\(796\) | 13.9951 | 0.496042 | ||||||||
\(797\) | −43.9384 | −1.55638 | −0.778189 | − | 0.628030i | \(-0.783862\pi\) | ||||
−0.778189 | + | 0.628030i | \(0.783862\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.64343 | −0.199650 | ||||||||
\(800\) | −12.3100 | −0.435225 | ||||||||
\(801\) | −4.79594 | −0.169456 | ||||||||
\(802\) | −12.4541 | −0.439768 | ||||||||
\(803\) | 49.3868 | 1.74282 | ||||||||
\(804\) | 6.56370 | 0.231484 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.227026 | 0.00799664 | ||||||||
\(807\) | −5.76077 | −0.202789 | ||||||||
\(808\) | 14.9562 | 0.526157 | ||||||||
\(809\) | 11.0235 | 0.387565 | 0.193783 | − | 0.981044i | \(-0.437924\pi\) | ||||
0.193783 | + | 0.981044i | \(0.437924\pi\) | |||||||
\(810\) | 4.16053 | 0.146186 | ||||||||
\(811\) | −6.13107 | −0.215291 | −0.107646 | − | 0.994189i | \(-0.534331\pi\) | ||||
−0.107646 | + | 0.994189i | \(0.534331\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −19.0793 | −0.669141 | ||||||||
\(814\) | −3.88541 | −0.136183 | ||||||||
\(815\) | −12.7482 | −0.446550 | ||||||||
\(816\) | 2.59771 | 0.0909382 | ||||||||
\(817\) | −18.8479 | −0.659403 | ||||||||
\(818\) | 29.8651 | 1.04421 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9.81370 | 0.342709 | ||||||||
\(821\) | 29.1728 | 1.01814 | 0.509069 | − | 0.860726i | \(-0.329990\pi\) | ||||
0.509069 | + | 0.860726i | \(0.329990\pi\) | |||||||
\(822\) | 14.4647 | 0.504515 | ||||||||
\(823\) | 14.3636 | 0.500682 | 0.250341 | − | 0.968158i | \(-0.419457\pi\) | ||||
0.250341 | + | 0.968158i | \(0.419457\pi\) | |||||||
\(824\) | −6.32600 | −0.220377 | ||||||||
\(825\) | −45.8345 | −1.59575 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.4855 | 1.26873 | 0.634363 | − | 0.773035i | \(-0.281262\pi\) | ||||
0.634363 | + | 0.773035i | \(0.281262\pi\) | |||||||
\(828\) | −3.95037 | −0.137285 | ||||||||
\(829\) | −50.3312 | −1.74807 | −0.874037 | − | 0.485859i | \(-0.838507\pi\) | ||||
−0.874037 | + | 0.485859i | \(0.838507\pi\) | |||||||
\(830\) | −74.7977 | −2.59627 | ||||||||
\(831\) | −15.6204 | −0.541866 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 9.39338 | 0.325266 | ||||||||
\(835\) | −41.2928 | −1.42900 | ||||||||
\(836\) | −8.82690 | −0.305285 | ||||||||
\(837\) | 0.227026 | 0.00784715 | ||||||||
\(838\) | −32.4084 | −1.11953 | ||||||||
\(839\) | −11.3613 | −0.392235 | −0.196118 | − | 0.980580i | \(-0.562833\pi\) | ||||
−0.196118 | + | 0.980580i | \(0.562833\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.57096 | −0.192102 | ||||||||
\(842\) | −29.5732 | −1.01916 | ||||||||
\(843\) | −10.9926 | −0.378607 | ||||||||
\(844\) | 25.2420 | 0.868865 | ||||||||
\(845\) | −4.16053 | −0.143127 | ||||||||
\(846\) | −2.17246 | −0.0746907 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −4.17246 | −0.143283 | ||||||||
\(849\) | 1.20280 | 0.0412801 | ||||||||
\(850\) | 31.9779 | 1.09683 | ||||||||
\(851\) | −4.12231 | −0.141311 | ||||||||
\(852\) | 7.88388 | 0.270097 | ||||||||
\(853\) | 23.5576 | 0.806597 | 0.403298 | − | 0.915068i | \(-0.367864\pi\) | ||||
0.403298 | + | 0.915068i | \(0.367864\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9.86332 | 0.337319 | ||||||||
\(856\) | −18.7617 | −0.641260 | ||||||||
\(857\) | 30.5642 | 1.04405 | 0.522027 | − | 0.852929i | \(-0.325176\pi\) | ||||
0.522027 | + | 0.852929i | \(0.325176\pi\) | |||||||
\(858\) | 3.72335 | 0.127113 | ||||||||
\(859\) | −2.02946 | −0.0692442 | −0.0346221 | − | 0.999400i | \(-0.511023\pi\) | ||||
−0.0346221 | + | 0.999400i | \(0.511023\pi\) | |||||||
\(860\) | −33.0778 | −1.12794 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −19.9147 | −0.678298 | ||||||||
\(863\) | 24.8805 | 0.846941 | 0.423470 | − | 0.905910i | \(-0.360812\pi\) | ||||
0.423470 | + | 0.905910i | \(0.360812\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −58.9090 | −2.00297 | ||||||||
\(866\) | −4.56154 | −0.155008 | ||||||||
\(867\) | 10.2519 | 0.348172 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −45.9384 | −1.55835 | ||||||||
\(870\) | 20.1384 | 0.682757 | ||||||||
\(871\) | −6.56370 | −0.222403 | ||||||||
\(872\) | 14.1709 | 0.479888 | ||||||||
\(873\) | −11.6807 | −0.395332 | ||||||||
\(874\) | −9.36511 | −0.316779 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −13.2641 | −0.448152 | ||||||||
\(877\) | 39.2704 | 1.32607 | 0.663034 | − | 0.748590i | \(-0.269269\pi\) | ||||
0.663034 | + | 0.748590i | \(0.269269\pi\) | |||||||
\(878\) | 2.09376 | 0.0706611 | ||||||||
\(879\) | 6.25610 | 0.211013 | ||||||||
\(880\) | −15.4911 | −0.522205 | ||||||||
\(881\) | 24.5107 | 0.825785 | 0.412893 | − | 0.910780i | \(-0.364518\pi\) | ||||
0.412893 | + | 0.910780i | \(0.364518\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.2935 | −0.716585 | −0.358292 | − | 0.933609i | \(-0.616641\pi\) | ||||
−0.358292 | + | 0.933609i | \(0.616641\pi\) | |||||||
\(884\) | −2.59771 | −0.0873706 | ||||||||
\(885\) | 31.3735 | 1.05461 | ||||||||
\(886\) | 15.2686 | 0.512960 | ||||||||
\(887\) | −51.4264 | −1.72673 | −0.863365 | − | 0.504581i | \(-0.831647\pi\) | ||||
−0.863365 | + | 0.504581i | \(0.831647\pi\) | |||||||
\(888\) | 1.04352 | 0.0350184 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −19.9537 | −0.668849 | ||||||||
\(891\) | 3.72335 | 0.124737 | ||||||||
\(892\) | 26.4969 | 0.887183 | ||||||||
\(893\) | −5.15022 | −0.172346 | ||||||||
\(894\) | −13.1495 | −0.439785 | ||||||||
\(895\) | 45.1872 | 1.51044 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.95037 | 0.131899 | ||||||||
\(898\) | −26.3992 | −0.880953 | ||||||||
\(899\) | 1.09888 | 0.0366499 | ||||||||
\(900\) | 12.3100 | 0.410334 | ||||||||
\(901\) | 10.8389 | 0.361095 | ||||||||
\(902\) | 8.78249 | 0.292425 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.50950 | −0.183243 | ||||||||
\(905\) | −70.1145 | −2.33068 | ||||||||
\(906\) | −17.4041 | −0.578211 | ||||||||
\(907\) | −42.5421 | −1.41259 | −0.706294 | − | 0.707918i | \(-0.749634\pi\) | ||||
−0.706294 | + | 0.707918i | \(0.749634\pi\) | |||||||
\(908\) | 6.78210 | 0.225072 | ||||||||
\(909\) | −14.9562 | −0.496066 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.4712 | 0.744503 | 0.372251 | − | 0.928132i | \(-0.378586\pi\) | ||||
0.372251 | + | 0.928132i | \(0.378586\pi\) | |||||||
\(912\) | 2.37069 | 0.0785013 | ||||||||
\(913\) | −66.9381 | −2.21533 | ||||||||
\(914\) | −6.42553 | −0.212538 | ||||||||
\(915\) | −51.8091 | −1.71276 | ||||||||
\(916\) | −9.90774 | −0.327361 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −2.59771 | −0.0857373 | ||||||||
\(919\) | −31.8137 | −1.04944 | −0.524719 | − | 0.851276i | \(-0.675829\pi\) | ||||
−0.524719 | + | 0.851276i | \(0.675829\pi\) | |||||||
\(920\) | −16.4357 | −0.541868 | ||||||||
\(921\) | 23.2145 | 0.764942 | ||||||||
\(922\) | −25.7009 | −0.846413 | ||||||||
\(923\) | −7.88388 | −0.259501 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12.8458 | 0.422368 | ||||||||
\(926\) | −6.83910 | −0.224747 | ||||||||
\(927\) | 6.32600 | 0.207773 | ||||||||
\(928\) | 4.84035 | 0.158892 | ||||||||
\(929\) | 46.4610 | 1.52434 | 0.762168 | − | 0.647379i | \(-0.224135\pi\) | ||||
0.762168 | + | 0.647379i | \(0.224135\pi\) | |||||||
\(930\) | 0.944547 | 0.0309729 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −2.38603 | −0.0781570 | ||||||||
\(933\) | 3.79162 | 0.124132 | ||||||||
\(934\) | 12.7472 | 0.417102 | ||||||||
\(935\) | 40.2415 | 1.31604 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | 54.1421 | 1.76875 | 0.884373 | − | 0.466781i | \(-0.154586\pi\) | ||||
0.884373 | + | 0.466781i | \(0.154586\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.62260 | −0.0529515 | ||||||||
\(940\) | −9.03858 | −0.294806 | ||||||||
\(941\) | 33.0607 | 1.07775 | 0.538873 | − | 0.842387i | \(-0.318850\pi\) | ||||
0.538873 | + | 0.842387i | \(0.318850\pi\) | |||||||
\(942\) | 23.7013 | 0.772229 | ||||||||
\(943\) | 9.31799 | 0.303435 | ||||||||
\(944\) | 7.54073 | 0.245430 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −29.6020 | −0.962444 | ||||||||
\(947\) | −2.10510 | −0.0684065 | −0.0342033 | − | 0.999415i | \(-0.510889\pi\) | ||||
−0.0342033 | + | 0.999415i | \(0.510889\pi\) | |||||||
\(948\) | 12.3379 | 0.400717 | ||||||||
\(949\) | 13.2641 | 0.430570 | ||||||||
\(950\) | 29.1832 | 0.946829 | ||||||||
\(951\) | 18.5719 | 0.602237 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21.1158 | −0.684006 | −0.342003 | − | 0.939699i | \(-0.611105\pi\) | ||||
−0.342003 | + | 0.939699i | \(0.611105\pi\) | |||||||
\(954\) | 4.17246 | 0.135088 | ||||||||
\(955\) | −49.6788 | −1.60757 | ||||||||
\(956\) | 2.68108 | 0.0867122 | ||||||||
\(957\) | 18.0223 | 0.582579 | ||||||||
\(958\) | −6.61800 | −0.213818 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 4.16053 | 0.134281 | ||||||||
\(961\) | −30.9485 | −0.998337 | ||||||||
\(962\) | −1.04352 | −0.0336446 | ||||||||
\(963\) | 18.7617 | 0.604586 | ||||||||
\(964\) | 17.8327 | 0.574353 | ||||||||
\(965\) | −91.3696 | −2.94129 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.3967 | −0.655914 | −0.327957 | − | 0.944693i | \(-0.606360\pi\) | ||||
−0.327957 | + | 0.944693i | \(0.606360\pi\) | |||||||
\(968\) | −2.86332 | −0.0920307 | ||||||||
\(969\) | −6.15837 | −0.197835 | ||||||||
\(970\) | −48.5980 | −1.56039 | ||||||||
\(971\) | 12.6373 | 0.405550 | 0.202775 | − | 0.979225i | \(-0.435004\pi\) | ||||
0.202775 | + | 0.979225i | \(0.435004\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 32.2292 | 1.03269 | ||||||||
\(975\) | −12.3100 | −0.394236 | ||||||||
\(976\) | −12.4525 | −0.398596 | ||||||||
\(977\) | −42.9921 | −1.37544 | −0.687720 | − | 0.725976i | \(-0.741388\pi\) | ||||
−0.687720 | + | 0.725976i | \(0.741388\pi\) | |||||||
\(978\) | 3.06408 | 0.0979785 | ||||||||
\(979\) | −17.8570 | −0.570711 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.1709 | −0.452443 | ||||||||
\(982\) | −17.5511 | −0.560079 | ||||||||
\(983\) | −25.8231 | −0.823630 | −0.411815 | − | 0.911268i | \(-0.635105\pi\) | ||||
−0.411815 | + | 0.911268i | \(0.635105\pi\) | |||||||
\(984\) | −2.35876 | −0.0751945 | ||||||||
\(985\) | 3.42500 | 0.109130 | ||||||||
\(986\) | −12.5739 | −0.400433 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.37069 | −0.0754217 | ||||||||
\(989\) | −31.4070 | −0.998683 | ||||||||
\(990\) | 15.4911 | 0.492340 | ||||||||
\(991\) | −40.0018 | −1.27070 | −0.635349 | − | 0.772225i | \(-0.719144\pi\) | ||||
−0.635349 | + | 0.772225i | \(0.719144\pi\) | |||||||
\(992\) | 0.227026 | 0.00720807 | ||||||||
\(993\) | 31.3289 | 0.994194 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −58.2269 | −1.84592 | ||||||||
\(996\) | 17.9779 | 0.569652 | ||||||||
\(997\) | −10.6586 | −0.337561 | −0.168781 | − | 0.985654i | \(-0.553983\pi\) | ||||
−0.168781 | + | 0.985654i | \(0.553983\pi\) | |||||||
\(998\) | 14.7304 | 0.466284 | ||||||||
\(999\) | −1.04352 | −0.0330157 |
(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 | 3822.2.a.bx.1.1 | ✓ | 4 | |
7.6 | odd | 2 | 3822.2.a.by.1.4 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3822.2.a.bx.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
3822.2.a.by.1.4 | yes | 4 | 7.6 | odd | 2 |