Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1815,2,Mod(1,1815)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1815, 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("1815.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1815 = 3 \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1815.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: | \(14.4928479669\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.8112.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 5x^{2} + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.07431\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1815.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.628052 | −0.444099 | −0.222050 | − | 0.975035i | \(-0.571275\pi\) | ||||
−0.222050 | + | 0.975035i | \(0.571275\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.60555 | −0.802776 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0.628052 | 0.256401 | ||||||||
\(7\) | 4.14863 | 1.56803 | 0.784017 | − | 0.620740i | \(-0.213168\pi\) | ||||
0.784017 | + | 0.620740i | \(0.213168\pi\) | |||||||
\(8\) | 2.26447 | 0.800612 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.628052 | −0.198607 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 1.60555 | 0.463483 | ||||||||
\(13\) | 5.40473 | 1.49900 | 0.749501 | − | 0.662003i | \(-0.230293\pi\) | ||||
0.749501 | + | 0.662003i | \(0.230293\pi\) | |||||||
\(14\) | −2.60555 | −0.696363 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 1.78890 | 0.447224 | ||||||||
\(17\) | 4.14863 | 1.00619 | 0.503095 | − | 0.864231i | \(-0.332195\pi\) | ||||
0.503095 | + | 0.864231i | \(0.332195\pi\) | |||||||
\(18\) | −0.628052 | −0.148033 | ||||||||
\(19\) | −1.25610 | −0.288170 | −0.144085 | − | 0.989565i | \(-0.546024\pi\) | ||||
−0.144085 | + | 0.989565i | \(0.546024\pi\) | |||||||
\(20\) | −1.60555 | −0.359012 | ||||||||
\(21\) | −4.14863 | −0.905305 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.21110 | 1.08659 | 0.543295 | − | 0.839542i | \(-0.317177\pi\) | ||||
0.543295 | + | 0.839542i | \(0.317177\pi\) | |||||||
\(24\) | −2.26447 | −0.462233 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −3.39445 | −0.665706 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −6.66083 | −1.25878 | ||||||||
\(29\) | −7.04115 | −1.30751 | −0.653754 | − | 0.756707i | \(-0.726807\pi\) | ||||
−0.653754 | + | 0.756707i | \(0.726807\pi\) | |||||||
\(30\) | 0.628052 | 0.114666 | ||||||||
\(31\) | 4.00000 | 0.718421 | 0.359211 | − | 0.933257i | \(-0.383046\pi\) | ||||
0.359211 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(32\) | −5.65246 | −0.999224 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.60555 | −0.446848 | ||||||||
\(35\) | 4.14863 | 0.701246 | ||||||||
\(36\) | −1.60555 | −0.267592 | ||||||||
\(37\) | −7.21110 | −1.18550 | −0.592749 | − | 0.805387i | \(-0.701957\pi\) | ||||
−0.592749 | + | 0.805387i | \(0.701957\pi\) | |||||||
\(38\) | 0.788897 | 0.127976 | ||||||||
\(39\) | −5.40473 | −0.865449 | ||||||||
\(40\) | 2.26447 | 0.358044 | ||||||||
\(41\) | −9.55336 | −1.49198 | −0.745992 | − | 0.665955i | \(-0.768024\pi\) | ||||
−0.745992 | + | 0.665955i | \(0.768024\pi\) | |||||||
\(42\) | 2.60555 | 0.402045 | ||||||||
\(43\) | 6.66083 | 1.01577 | 0.507884 | − | 0.861426i | \(-0.330428\pi\) | ||||
0.507884 | + | 0.861426i | \(0.330428\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | −3.27284 | −0.482554 | ||||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | −1.78890 | −0.258205 | ||||||||
\(49\) | 10.2111 | 1.45873 | ||||||||
\(50\) | −0.628052 | −0.0888199 | ||||||||
\(51\) | −4.14863 | −0.580924 | ||||||||
\(52\) | −8.67757 | −1.20336 | ||||||||
\(53\) | 11.2111 | 1.53996 | 0.769982 | − | 0.638066i | \(-0.220265\pi\) | ||||
0.769982 | + | 0.638066i | \(0.220265\pi\) | |||||||
\(54\) | 0.628052 | 0.0854670 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 9.39445 | 1.25539 | ||||||||
\(57\) | 1.25610 | 0.166375 | ||||||||
\(58\) | 4.42221 | 0.580664 | ||||||||
\(59\) | −5.21110 | −0.678428 | −0.339214 | − | 0.940709i | \(-0.610161\pi\) | ||||
−0.339214 | + | 0.940709i | \(0.610161\pi\) | |||||||
\(60\) | 1.60555 | 0.207276 | ||||||||
\(61\) | 8.29725 | 1.06235 | 0.531177 | − | 0.847261i | \(-0.321750\pi\) | ||||
0.531177 | + | 0.847261i | \(0.321750\pi\) | |||||||
\(62\) | −2.51221 | −0.319050 | ||||||||
\(63\) | 4.14863 | 0.522678 | ||||||||
\(64\) | −0.0277564 | −0.00346955 | ||||||||
\(65\) | 5.40473 | 0.670374 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.2111 | −1.61399 | −0.806997 | − | 0.590556i | \(-0.798908\pi\) | ||||
−0.806997 | + | 0.590556i | \(0.798908\pi\) | |||||||
\(68\) | −6.66083 | −0.807745 | ||||||||
\(69\) | −5.21110 | −0.627343 | ||||||||
\(70\) | −2.60555 | −0.311423 | ||||||||
\(71\) | 5.21110 | 0.618444 | 0.309222 | − | 0.950990i | \(-0.399931\pi\) | ||||
0.309222 | + | 0.950990i | \(0.399931\pi\) | |||||||
\(72\) | 2.26447 | 0.266871 | ||||||||
\(73\) | −2.89252 | −0.338544 | −0.169272 | − | 0.985569i | \(-0.554142\pi\) | ||||
−0.169272 | + | 0.985569i | \(0.554142\pi\) | |||||||
\(74\) | 4.52894 | 0.526479 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 2.01674 | 0.231336 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.39445 | 0.384346 | ||||||||
\(79\) | −1.25610 | −0.141323 | −0.0706613 | − | 0.997500i | \(-0.522511\pi\) | ||||
−0.0706613 | + | 0.997500i | \(0.522511\pi\) | |||||||
\(80\) | 1.78890 | 0.200005 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 6.00000 | 0.662589 | ||||||||
\(83\) | −13.7020 | −1.50399 | −0.751994 | − | 0.659170i | \(-0.770908\pi\) | ||||
−0.751994 | + | 0.659170i | \(0.770908\pi\) | |||||||
\(84\) | 6.66083 | 0.726756 | ||||||||
\(85\) | 4.14863 | 0.449982 | ||||||||
\(86\) | −4.18335 | −0.451102 | ||||||||
\(87\) | 7.04115 | 0.754891 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.00000 | 0.635999 | 0.317999 | − | 0.948091i | \(-0.396989\pi\) | ||||
0.317999 | + | 0.948091i | \(0.396989\pi\) | |||||||
\(90\) | −0.628052 | −0.0662024 | ||||||||
\(91\) | 22.4222 | 2.35049 | ||||||||
\(92\) | −8.36669 | −0.872288 | ||||||||
\(93\) | −4.00000 | −0.414781 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.25610 | −0.128873 | ||||||||
\(96\) | 5.65246 | 0.576902 | ||||||||
\(97\) | 19.2111 | 1.95059 | 0.975296 | − | 0.220902i | \(-0.0709002\pi\) | ||||
0.975296 | + | 0.220902i | \(0.0709002\pi\) | |||||||
\(98\) | −6.41310 | −0.647821 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.60555 | −0.160555 | ||||||||
\(101\) | −1.25610 | −0.124987 | −0.0624935 | − | 0.998045i | \(-0.519905\pi\) | ||||
−0.0624935 | + | 0.998045i | \(0.519905\pi\) | |||||||
\(102\) | 2.60555 | 0.257988 | ||||||||
\(103\) | 1.21110 | 0.119333 | 0.0596667 | − | 0.998218i | \(-0.480996\pi\) | ||||
0.0596667 | + | 0.998218i | \(0.480996\pi\) | |||||||
\(104\) | 12.2389 | 1.20012 | ||||||||
\(105\) | −4.14863 | −0.404864 | ||||||||
\(106\) | −7.04115 | −0.683897 | ||||||||
\(107\) | 2.89252 | 0.279631 | 0.139815 | − | 0.990178i | \(-0.455349\pi\) | ||||
0.139815 | + | 0.990178i | \(0.455349\pi\) | |||||||
\(108\) | 1.60555 | 0.154494 | ||||||||
\(109\) | −16.5945 | −1.58947 | −0.794733 | − | 0.606960i | \(-0.792389\pi\) | ||||
−0.794733 | + | 0.606960i | \(0.792389\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.21110 | 0.684448 | ||||||||
\(112\) | 7.42147 | 0.701263 | ||||||||
\(113\) | 11.2111 | 1.05465 | 0.527326 | − | 0.849663i | \(-0.323195\pi\) | ||||
0.527326 | + | 0.849663i | \(0.323195\pi\) | |||||||
\(114\) | −0.788897 | −0.0738870 | ||||||||
\(115\) | 5.21110 | 0.485938 | ||||||||
\(116\) | 11.3049 | 1.04964 | ||||||||
\(117\) | 5.40473 | 0.499667 | ||||||||
\(118\) | 3.27284 | 0.301289 | ||||||||
\(119\) | 17.2111 | 1.57774 | ||||||||
\(120\) | −2.26447 | −0.206717 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −5.21110 | −0.471791 | ||||||||
\(123\) | 9.55336 | 0.861397 | ||||||||
\(124\) | −6.42221 | −0.576731 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −2.60555 | −0.232121 | ||||||||
\(127\) | −1.63642 | −0.145209 | −0.0726044 | − | 0.997361i | \(-0.523131\pi\) | ||||
−0.0726044 | + | 0.997361i | \(0.523131\pi\) | |||||||
\(128\) | 11.3224 | 1.00076 | ||||||||
\(129\) | −6.66083 | −0.586454 | ||||||||
\(130\) | −3.39445 | −0.297713 | ||||||||
\(131\) | −5.78505 | −0.505442 | −0.252721 | − | 0.967539i | \(-0.581325\pi\) | ||||
−0.252721 | + | 0.967539i | \(0.581325\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.21110 | −0.451860 | ||||||||
\(134\) | 8.29725 | 0.716774 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 9.39445 | 0.805567 | ||||||||
\(137\) | −16.4222 | −1.40304 | −0.701522 | − | 0.712648i | \(-0.747496\pi\) | ||||
−0.701522 | + | 0.712648i | \(0.747496\pi\) | |||||||
\(138\) | 3.27284 | 0.278603 | ||||||||
\(139\) | 9.55336 | 0.810305 | 0.405153 | − | 0.914249i | \(-0.367218\pi\) | ||||
0.405153 | + | 0.914249i | \(0.367218\pi\) | |||||||
\(140\) | −6.66083 | −0.562943 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.27284 | −0.274651 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.78890 | 0.149075 | ||||||||
\(145\) | −7.04115 | −0.584736 | ||||||||
\(146\) | 1.81665 | 0.150347 | ||||||||
\(147\) | −10.2111 | −0.842198 | ||||||||
\(148\) | 11.5778 | 0.951689 | ||||||||
\(149\) | 22.8750 | 1.87399 | 0.936997 | − | 0.349336i | \(-0.113593\pi\) | ||||
0.936997 | + | 0.349336i | \(0.113593\pi\) | |||||||
\(150\) | 0.628052 | 0.0512802 | ||||||||
\(151\) | 15.3384 | 1.24822 | 0.624111 | − | 0.781336i | \(-0.285461\pi\) | ||||
0.624111 | + | 0.781336i | \(0.285461\pi\) | |||||||
\(152\) | −2.84441 | −0.230712 | ||||||||
\(153\) | 4.14863 | 0.335397 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.00000 | 0.321288 | ||||||||
\(156\) | 8.67757 | 0.694762 | ||||||||
\(157\) | 10.0000 | 0.798087 | 0.399043 | − | 0.916932i | \(-0.369342\pi\) | ||||
0.399043 | + | 0.916932i | \(0.369342\pi\) | |||||||
\(158\) | 0.788897 | 0.0627613 | ||||||||
\(159\) | −11.2111 | −0.889098 | ||||||||
\(160\) | −5.65246 | −0.446866 | ||||||||
\(161\) | 21.6189 | 1.70381 | ||||||||
\(162\) | −0.628052 | −0.0493444 | ||||||||
\(163\) | 13.2111 | 1.03477 | 0.517387 | − | 0.855752i | \(-0.326905\pi\) | ||||
0.517387 | + | 0.855752i | \(0.326905\pi\) | |||||||
\(164\) | 15.3384 | 1.19773 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.60555 | 0.667920 | ||||||||
\(167\) | −19.4870 | −1.50795 | −0.753976 | − | 0.656902i | \(-0.771866\pi\) | ||||
−0.753976 | + | 0.656902i | \(0.771866\pi\) | |||||||
\(168\) | −9.39445 | −0.724797 | ||||||||
\(169\) | 16.2111 | 1.24701 | ||||||||
\(170\) | −2.60555 | −0.199837 | ||||||||
\(171\) | −1.25610 | −0.0960566 | ||||||||
\(172\) | −10.6943 | −0.815433 | ||||||||
\(173\) | −12.4459 | −0.946243 | −0.473121 | − | 0.880997i | \(-0.656873\pi\) | ||||
−0.473121 | + | 0.880997i | \(0.656873\pi\) | |||||||
\(174\) | −4.42221 | −0.335247 | ||||||||
\(175\) | 4.14863 | 0.313607 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.21110 | 0.391690 | ||||||||
\(178\) | −3.76831 | −0.282447 | ||||||||
\(179\) | −22.4222 | −1.67591 | −0.837957 | − | 0.545736i | \(-0.816250\pi\) | ||||
−0.837957 | + | 0.545736i | \(0.816250\pi\) | |||||||
\(180\) | −1.60555 | −0.119671 | ||||||||
\(181\) | 19.2111 | 1.42795 | 0.713975 | − | 0.700171i | \(-0.246893\pi\) | ||||
0.713975 | + | 0.700171i | \(0.246893\pi\) | |||||||
\(182\) | −14.0823 | −1.04385 | ||||||||
\(183\) | −8.29725 | −0.613351 | ||||||||
\(184\) | 11.8004 | 0.869937 | ||||||||
\(185\) | −7.21110 | −0.530171 | ||||||||
\(186\) | 2.51221 | 0.184204 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.14863 | −0.301768 | ||||||||
\(190\) | 0.788897 | 0.0572326 | ||||||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | 0.0277564 | 0.00200314 | ||||||||
\(193\) | 11.1898 | 0.805458 | 0.402729 | − | 0.915319i | \(-0.368062\pi\) | ||||
0.402729 | + | 0.915319i | \(0.368062\pi\) | |||||||
\(194\) | −12.0656 | −0.866257 | ||||||||
\(195\) | −5.40473 | −0.387041 | ||||||||
\(196\) | −16.3944 | −1.17103 | ||||||||
\(197\) | 9.17304 | 0.653552 | 0.326776 | − | 0.945102i | \(-0.394038\pi\) | ||||
0.326776 | + | 0.945102i | \(0.394038\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.00000 | −0.567105 | −0.283552 | − | 0.958957i | \(-0.591513\pi\) | ||||
−0.283552 | + | 0.958957i | \(0.591513\pi\) | |||||||
\(200\) | 2.26447 | 0.160122 | ||||||||
\(201\) | 13.2111 | 0.931839 | ||||||||
\(202\) | 0.788897 | 0.0555066 | ||||||||
\(203\) | −29.2111 | −2.05022 | ||||||||
\(204\) | 6.66083 | 0.466352 | ||||||||
\(205\) | −9.55336 | −0.667235 | ||||||||
\(206\) | −0.760635 | −0.0529959 | ||||||||
\(207\) | 5.21110 | 0.362197 | ||||||||
\(208\) | 9.66851 | 0.670390 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 2.60555 | 0.179800 | ||||||||
\(211\) | 3.76831 | 0.259421 | 0.129711 | − | 0.991552i | \(-0.458595\pi\) | ||||
0.129711 | + | 0.991552i | \(0.458595\pi\) | |||||||
\(212\) | −18.0000 | −1.23625 | ||||||||
\(213\) | −5.21110 | −0.357059 | ||||||||
\(214\) | −1.81665 | −0.124184 | ||||||||
\(215\) | 6.66083 | 0.454265 | ||||||||
\(216\) | −2.26447 | −0.154078 | ||||||||
\(217\) | 16.5945 | 1.12651 | ||||||||
\(218\) | 10.4222 | 0.705881 | ||||||||
\(219\) | 2.89252 | 0.195459 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 22.4222 | 1.50828 | ||||||||
\(222\) | −4.52894 | −0.303963 | ||||||||
\(223\) | −2.42221 | −0.162203 | −0.0811014 | − | 0.996706i | \(-0.525844\pi\) | ||||
−0.0811014 | + | 0.996706i | \(0.525844\pi\) | |||||||
\(224\) | −23.4500 | −1.56682 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −7.04115 | −0.468370 | ||||||||
\(227\) | −2.89252 | −0.191984 | −0.0959918 | − | 0.995382i | \(-0.530602\pi\) | ||||
−0.0959918 | + | 0.995382i | \(0.530602\pi\) | |||||||
\(228\) | −2.01674 | −0.133562 | ||||||||
\(229\) | 10.0000 | 0.660819 | 0.330409 | − | 0.943838i | \(-0.392813\pi\) | ||||
0.330409 | + | 0.943838i | \(0.392813\pi\) | |||||||
\(230\) | −3.27284 | −0.215805 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −15.9445 | −1.04681 | ||||||||
\(233\) | −25.7675 | −1.68809 | −0.844044 | − | 0.536274i | \(-0.819831\pi\) | ||||
−0.844044 | + | 0.536274i | \(0.819831\pi\) | |||||||
\(234\) | −3.39445 | −0.221902 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 8.36669 | 0.544625 | ||||||||
\(237\) | 1.25610 | 0.0815927 | ||||||||
\(238\) | −10.8095 | −0.700673 | ||||||||
\(239\) | −8.29725 | −0.536705 | −0.268352 | − | 0.963321i | \(-0.586479\pi\) | ||||
−0.268352 | + | 0.963321i | \(0.586479\pi\) | |||||||
\(240\) | −1.78890 | −0.115473 | ||||||||
\(241\) | 3.27284 | 0.210822 | 0.105411 | − | 0.994429i | \(-0.466384\pi\) | ||||
0.105411 | + | 0.994429i | \(0.466384\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −13.3217 | −0.852832 | ||||||||
\(245\) | 10.2111 | 0.652363 | ||||||||
\(246\) | −6.00000 | −0.382546 | ||||||||
\(247\) | −6.78890 | −0.431967 | ||||||||
\(248\) | 9.05789 | 0.575176 | ||||||||
\(249\) | 13.7020 | 0.868328 | ||||||||
\(250\) | −0.628052 | −0.0397215 | ||||||||
\(251\) | −27.6333 | −1.74420 | −0.872099 | − | 0.489329i | \(-0.837242\pi\) | ||||
−0.872099 | + | 0.489329i | \(0.837242\pi\) | |||||||
\(252\) | −6.66083 | −0.419593 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 1.02776 | 0.0644872 | ||||||||
\(255\) | −4.14863 | −0.259797 | ||||||||
\(256\) | −7.05551 | −0.440970 | ||||||||
\(257\) | 6.00000 | 0.374270 | 0.187135 | − | 0.982334i | \(-0.440080\pi\) | ||||
0.187135 | + | 0.982334i | \(0.440080\pi\) | |||||||
\(258\) | 4.18335 | 0.260444 | ||||||||
\(259\) | −29.9162 | −1.85890 | ||||||||
\(260\) | −8.67757 | −0.538160 | ||||||||
\(261\) | −7.04115 | −0.435836 | ||||||||
\(262\) | 3.63331 | 0.224466 | ||||||||
\(263\) | 7.91694 | 0.488179 | 0.244090 | − | 0.969753i | \(-0.421511\pi\) | ||||
0.244090 | + | 0.969753i | \(0.421511\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.2111 | 0.688693 | ||||||||
\(266\) | 3.27284 | 0.200671 | ||||||||
\(267\) | −6.00000 | −0.367194 | ||||||||
\(268\) | 21.2111 | 1.29567 | ||||||||
\(269\) | −18.0000 | −1.09748 | −0.548740 | − | 0.835993i | \(-0.684892\pi\) | ||||
−0.548740 | + | 0.835993i | \(0.684892\pi\) | |||||||
\(270\) | 0.628052 | 0.0382220 | ||||||||
\(271\) | 22.8750 | 1.38956 | 0.694779 | − | 0.719223i | \(-0.255502\pi\) | ||||
0.694779 | + | 0.719223i | \(0.255502\pi\) | |||||||
\(272\) | 7.42147 | 0.449993 | ||||||||
\(273\) | −22.4222 | −1.35705 | ||||||||
\(274\) | 10.3140 | 0.623091 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 8.36669 | 0.503616 | ||||||||
\(277\) | 10.4291 | 0.626626 | 0.313313 | − | 0.949650i | \(-0.398561\pi\) | ||||
0.313313 | + | 0.949650i | \(0.398561\pi\) | |||||||
\(278\) | −6.00000 | −0.359856 | ||||||||
\(279\) | 4.00000 | 0.239474 | ||||||||
\(280\) | 9.39445 | 0.561426 | ||||||||
\(281\) | −26.1479 | −1.55985 | −0.779925 | − | 0.625873i | \(-0.784743\pi\) | ||||
−0.779925 | + | 0.625873i | \(0.784743\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −31.5526 | −1.87561 | −0.937803 | − | 0.347167i | \(-0.887144\pi\) | ||||
−0.937803 | + | 0.347167i | \(0.887144\pi\) | |||||||
\(284\) | −8.36669 | −0.496472 | ||||||||
\(285\) | 1.25610 | 0.0744051 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −39.6333 | −2.33948 | ||||||||
\(288\) | −5.65246 | −0.333075 | ||||||||
\(289\) | 0.211103 | 0.0124178 | ||||||||
\(290\) | 4.42221 | 0.259681 | ||||||||
\(291\) | −19.2111 | −1.12617 | ||||||||
\(292\) | 4.64409 | 0.271775 | ||||||||
\(293\) | −20.7431 | −1.21183 | −0.605913 | − | 0.795531i | \(-0.707192\pi\) | ||||
−0.605913 | + | 0.795531i | \(0.707192\pi\) | |||||||
\(294\) | 6.41310 | 0.374020 | ||||||||
\(295\) | −5.21110 | −0.303402 | ||||||||
\(296\) | −16.3293 | −0.949124 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −14.3667 | −0.832240 | ||||||||
\(299\) | 28.1646 | 1.62880 | ||||||||
\(300\) | 1.60555 | 0.0926965 | ||||||||
\(301\) | 27.6333 | 1.59276 | ||||||||
\(302\) | −9.63331 | −0.554335 | ||||||||
\(303\) | 1.25610 | 0.0721612 | ||||||||
\(304\) | −2.24704 | −0.128877 | ||||||||
\(305\) | 8.29725 | 0.475099 | ||||||||
\(306\) | −2.60555 | −0.148949 | ||||||||
\(307\) | −7.42147 | −0.423566 | −0.211783 | − | 0.977317i | \(-0.567927\pi\) | ||||
−0.211783 | + | 0.977317i | \(0.567927\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.21110 | −0.0688972 | ||||||||
\(310\) | −2.51221 | −0.142684 | ||||||||
\(311\) | 6.78890 | 0.384963 | 0.192482 | − | 0.981301i | \(-0.438346\pi\) | ||||
0.192482 | + | 0.981301i | \(0.438346\pi\) | |||||||
\(312\) | −12.2389 | −0.692889 | ||||||||
\(313\) | 15.2111 | 0.859782 | 0.429891 | − | 0.902881i | \(-0.358552\pi\) | ||||
0.429891 | + | 0.902881i | \(0.358552\pi\) | |||||||
\(314\) | −6.28052 | −0.354430 | ||||||||
\(315\) | 4.14863 | 0.233749 | ||||||||
\(316\) | 2.01674 | 0.113450 | ||||||||
\(317\) | −11.2111 | −0.629678 | −0.314839 | − | 0.949145i | \(-0.601951\pi\) | ||||
−0.314839 | + | 0.949145i | \(0.601951\pi\) | |||||||
\(318\) | 7.04115 | 0.394848 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −0.0277564 | −0.00155163 | ||||||||
\(321\) | −2.89252 | −0.161445 | ||||||||
\(322\) | −13.5778 | −0.756661 | ||||||||
\(323\) | −5.21110 | −0.289954 | ||||||||
\(324\) | −1.60555 | −0.0891973 | ||||||||
\(325\) | 5.40473 | 0.299800 | ||||||||
\(326\) | −8.29725 | −0.459542 | ||||||||
\(327\) | 16.5945 | 0.917678 | ||||||||
\(328\) | −21.6333 | −1.19450 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.00000 | 0.439720 | 0.219860 | − | 0.975531i | \(-0.429440\pi\) | ||||
0.219860 | + | 0.975531i | \(0.429440\pi\) | |||||||
\(332\) | 21.9992 | 1.20736 | ||||||||
\(333\) | −7.21110 | −0.395166 | ||||||||
\(334\) | 12.2389 | 0.669681 | ||||||||
\(335\) | −13.2111 | −0.721800 | ||||||||
\(336\) | −7.42147 | −0.404874 | ||||||||
\(337\) | 8.67757 | 0.472697 | 0.236349 | − | 0.971668i | \(-0.424049\pi\) | ||||
0.236349 | + | 0.971668i | \(0.424049\pi\) | |||||||
\(338\) | −10.1814 | −0.553796 | ||||||||
\(339\) | −11.2111 | −0.608904 | ||||||||
\(340\) | −6.66083 | −0.361234 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0.788897 | 0.0426587 | ||||||||
\(343\) | 13.3217 | 0.719302 | ||||||||
\(344\) | 15.0833 | 0.813235 | ||||||||
\(345\) | −5.21110 | −0.280556 | ||||||||
\(346\) | 7.81665 | 0.420226 | ||||||||
\(347\) | 29.5359 | 1.58557 | 0.792784 | − | 0.609503i | \(-0.208631\pi\) | ||||
0.792784 | + | 0.609503i | \(0.208631\pi\) | |||||||
\(348\) | −11.3049 | −0.606008 | ||||||||
\(349\) | −13.3217 | −0.713092 | −0.356546 | − | 0.934278i | \(-0.616046\pi\) | ||||
−0.356546 | + | 0.934278i | \(0.616046\pi\) | |||||||
\(350\) | −2.60555 | −0.139273 | ||||||||
\(351\) | −5.40473 | −0.288483 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.7889 | 0.680684 | 0.340342 | − | 0.940302i | \(-0.389457\pi\) | ||||
0.340342 | + | 0.940302i | \(0.389457\pi\) | |||||||
\(354\) | −3.27284 | −0.173950 | ||||||||
\(355\) | 5.21110 | 0.276577 | ||||||||
\(356\) | −9.63331 | −0.510564 | ||||||||
\(357\) | −17.2111 | −0.910908 | ||||||||
\(358\) | 14.0823 | 0.744273 | ||||||||
\(359\) | 15.8339 | 0.835680 | 0.417840 | − | 0.908521i | \(-0.362787\pi\) | ||||
0.417840 | + | 0.908521i | \(0.362787\pi\) | |||||||
\(360\) | 2.26447 | 0.119348 | ||||||||
\(361\) | −17.4222 | −0.916958 | ||||||||
\(362\) | −12.0656 | −0.634152 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −36.0000 | −1.88691 | ||||||||
\(365\) | −2.89252 | −0.151402 | ||||||||
\(366\) | 5.21110 | 0.272389 | ||||||||
\(367\) | 18.4222 | 0.961631 | 0.480816 | − | 0.876822i | \(-0.340341\pi\) | ||||
0.480816 | + | 0.876822i | \(0.340341\pi\) | |||||||
\(368\) | 9.32213 | 0.485950 | ||||||||
\(369\) | −9.55336 | −0.497328 | ||||||||
\(370\) | 4.52894 | 0.235449 | ||||||||
\(371\) | 46.5107 | 2.41471 | ||||||||
\(372\) | 6.42221 | 0.332976 | ||||||||
\(373\) | −7.91694 | −0.409923 | −0.204962 | − | 0.978770i | \(-0.565707\pi\) | ||||
−0.204962 | + | 0.978770i | \(0.565707\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −38.0555 | −1.95996 | ||||||||
\(378\) | 2.60555 | 0.134015 | ||||||||
\(379\) | −14.4222 | −0.740819 | −0.370409 | − | 0.928869i | \(-0.620783\pi\) | ||||
−0.370409 | + | 0.928869i | \(0.620783\pi\) | |||||||
\(380\) | 2.01674 | 0.103456 | ||||||||
\(381\) | 1.63642 | 0.0838364 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.21110 | −0.266275 | −0.133137 | − | 0.991098i | \(-0.542505\pi\) | ||||
−0.133137 | + | 0.991098i | \(0.542505\pi\) | |||||||
\(384\) | −11.3224 | −0.577792 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.02776 | −0.357703 | ||||||||
\(387\) | 6.66083 | 0.338589 | ||||||||
\(388\) | −30.8444 | −1.56589 | ||||||||
\(389\) | 18.0000 | 0.912636 | 0.456318 | − | 0.889817i | \(-0.349168\pi\) | ||||
0.456318 | + | 0.889817i | \(0.349168\pi\) | |||||||
\(390\) | 3.39445 | 0.171885 | ||||||||
\(391\) | 21.6189 | 1.09332 | ||||||||
\(392\) | 23.1228 | 1.16788 | ||||||||
\(393\) | 5.78505 | 0.291817 | ||||||||
\(394\) | −5.76114 | −0.290242 | ||||||||
\(395\) | −1.25610 | −0.0632014 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.6333 | −0.684236 | −0.342118 | − | 0.939657i | \(-0.611144\pi\) | ||||
−0.342118 | + | 0.939657i | \(0.611144\pi\) | |||||||
\(398\) | 5.02441 | 0.251851 | ||||||||
\(399\) | 5.21110 | 0.260881 | ||||||||
\(400\) | 1.78890 | 0.0894449 | ||||||||
\(401\) | 28.4222 | 1.41934 | 0.709669 | − | 0.704536i | \(-0.248845\pi\) | ||||
0.709669 | + | 0.704536i | \(0.248845\pi\) | |||||||
\(402\) | −8.29725 | −0.413829 | ||||||||
\(403\) | 21.6189 | 1.07692 | ||||||||
\(404\) | 2.01674 | 0.100336 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 18.3461 | 0.910501 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −9.39445 | −0.465095 | ||||||||
\(409\) | −7.53662 | −0.372662 | −0.186331 | − | 0.982487i | \(-0.559660\pi\) | ||||
−0.186331 | + | 0.982487i | \(0.559660\pi\) | |||||||
\(410\) | 6.00000 | 0.296319 | ||||||||
\(411\) | 16.4222 | 0.810048 | ||||||||
\(412\) | −1.94449 | −0.0957980 | ||||||||
\(413\) | −21.6189 | −1.06380 | ||||||||
\(414\) | −3.27284 | −0.160851 | ||||||||
\(415\) | −13.7020 | −0.672604 | ||||||||
\(416\) | −30.5500 | −1.49784 | ||||||||
\(417\) | −9.55336 | −0.467830 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.0000 | −0.586238 | −0.293119 | − | 0.956076i | \(-0.594693\pi\) | ||||
−0.293119 | + | 0.956076i | \(0.594693\pi\) | |||||||
\(420\) | 6.66083 | 0.325015 | ||||||||
\(421\) | 39.2111 | 1.91103 | 0.955516 | − | 0.294939i | \(-0.0952993\pi\) | ||||
0.955516 | + | 0.294939i | \(0.0952993\pi\) | |||||||
\(422\) | −2.36669 | −0.115209 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 25.3872 | 1.23291 | ||||||||
\(425\) | 4.14863 | 0.201238 | ||||||||
\(426\) | 3.27284 | 0.158570 | ||||||||
\(427\) | 34.4222 | 1.66581 | ||||||||
\(428\) | −4.64409 | −0.224481 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.18335 | −0.201739 | ||||||||
\(431\) | −2.51221 | −0.121009 | −0.0605044 | − | 0.998168i | \(-0.519271\pi\) | ||||
−0.0605044 | + | 0.998168i | \(0.519271\pi\) | |||||||
\(432\) | −1.78890 | −0.0860684 | ||||||||
\(433\) | −4.78890 | −0.230140 | −0.115070 | − | 0.993357i | \(-0.536709\pi\) | ||||
−0.115070 | + | 0.993357i | \(0.536709\pi\) | |||||||
\(434\) | −10.4222 | −0.500282 | ||||||||
\(435\) | 7.04115 | 0.337597 | ||||||||
\(436\) | 26.6433 | 1.27598 | ||||||||
\(437\) | −6.54568 | −0.313122 | ||||||||
\(438\) | −1.81665 | −0.0868031 | ||||||||
\(439\) | 2.01674 | 0.0962536 | 0.0481268 | − | 0.998841i | \(-0.484675\pi\) | ||||
0.0481268 | + | 0.998841i | \(0.484675\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 10.2111 | 0.486243 | ||||||||
\(442\) | −14.0823 | −0.669827 | ||||||||
\(443\) | 27.6333 | 1.31290 | 0.656449 | − | 0.754370i | \(-0.272058\pi\) | ||||
0.656449 | + | 0.754370i | \(0.272058\pi\) | |||||||
\(444\) | −11.5778 | −0.549458 | ||||||||
\(445\) | 6.00000 | 0.284427 | ||||||||
\(446\) | 1.52127 | 0.0720342 | ||||||||
\(447\) | −22.8750 | −1.08195 | ||||||||
\(448\) | −0.115151 | −0.00544037 | ||||||||
\(449\) | 16.4222 | 0.775012 | 0.387506 | − | 0.921867i | \(-0.373337\pi\) | ||||
0.387506 | + | 0.921867i | \(0.373337\pi\) | |||||||
\(450\) | −0.628052 | −0.0296066 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −18.0000 | −0.846649 | ||||||||
\(453\) | −15.3384 | −0.720661 | ||||||||
\(454\) | 1.81665 | 0.0852598 | ||||||||
\(455\) | 22.4222 | 1.05117 | ||||||||
\(456\) | 2.84441 | 0.133202 | ||||||||
\(457\) | −2.13189 | −0.0997255 | −0.0498628 | − | 0.998756i | \(-0.515878\pi\) | ||||
−0.0498628 | + | 0.998756i | \(0.515878\pi\) | |||||||
\(458\) | −6.28052 | −0.293469 | ||||||||
\(459\) | −4.14863 | −0.193641 | ||||||||
\(460\) | −8.36669 | −0.390099 | ||||||||
\(461\) | 6.28052 | 0.292513 | 0.146256 | − | 0.989247i | \(-0.453278\pi\) | ||||
0.146256 | + | 0.989247i | \(0.453278\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.4222 | −1.22794 | −0.613972 | − | 0.789328i | \(-0.710429\pi\) | ||||
−0.613972 | + | 0.789328i | \(0.710429\pi\) | |||||||
\(464\) | −12.5959 | −0.584750 | ||||||||
\(465\) | −4.00000 | −0.185496 | ||||||||
\(466\) | 16.1833 | 0.749679 | ||||||||
\(467\) | −17.2111 | −0.796435 | −0.398217 | − | 0.917291i | \(-0.630371\pi\) | ||||
−0.398217 | + | 0.917291i | \(0.630371\pi\) | |||||||
\(468\) | −8.67757 | −0.401121 | ||||||||
\(469\) | −54.8079 | −2.53080 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.0000 | −0.460776 | ||||||||
\(472\) | −11.8004 | −0.543157 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −0.788897 | −0.0362353 | ||||||||
\(475\) | −1.25610 | −0.0576340 | ||||||||
\(476\) | −27.6333 | −1.26657 | ||||||||
\(477\) | 11.2111 | 0.513321 | ||||||||
\(478\) | 5.21110 | 0.238350 | ||||||||
\(479\) | 3.27284 | 0.149540 | 0.0747700 | − | 0.997201i | \(-0.476178\pi\) | ||||
0.0747700 | + | 0.997201i | \(0.476178\pi\) | |||||||
\(480\) | 5.65246 | 0.257998 | ||||||||
\(481\) | −38.9741 | −1.77706 | ||||||||
\(482\) | −2.05551 | −0.0936260 | ||||||||
\(483\) | −21.6189 | −0.983695 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 19.2111 | 0.872331 | ||||||||
\(486\) | 0.628052 | 0.0284890 | ||||||||
\(487\) | −1.21110 | −0.0548803 | −0.0274401 | − | 0.999623i | \(-0.508736\pi\) | ||||
−0.0274401 | + | 0.999623i | \(0.508736\pi\) | |||||||
\(488\) | 18.7889 | 0.850533 | ||||||||
\(489\) | −13.2111 | −0.597427 | ||||||||
\(490\) | −6.41310 | −0.289714 | ||||||||
\(491\) | −40.7256 | −1.83792 | −0.918961 | − | 0.394348i | \(-0.870970\pi\) | ||||
−0.918961 | + | 0.394348i | \(0.870970\pi\) | |||||||
\(492\) | −15.3384 | −0.691509 | ||||||||
\(493\) | −29.2111 | −1.31560 | ||||||||
\(494\) | 4.26378 | 0.191836 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.15559 | 0.321295 | ||||||||
\(497\) | 21.6189 | 0.969741 | ||||||||
\(498\) | −8.60555 | −0.385624 | ||||||||
\(499\) | 14.4222 | 0.645627 | 0.322813 | − | 0.946463i | \(-0.395371\pi\) | ||||
0.322813 | + | 0.946463i | \(0.395371\pi\) | |||||||
\(500\) | −1.60555 | −0.0718024 | ||||||||
\(501\) | 19.4870 | 0.870616 | ||||||||
\(502\) | 17.3551 | 0.774598 | ||||||||
\(503\) | 18.7264 | 0.834969 | 0.417484 | − | 0.908684i | \(-0.362912\pi\) | ||||
0.417484 | + | 0.908684i | \(0.362912\pi\) | |||||||
\(504\) | 9.39445 | 0.418462 | ||||||||
\(505\) | −1.25610 | −0.0558959 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −16.2111 | −0.719960 | ||||||||
\(508\) | 2.62736 | 0.116570 | ||||||||
\(509\) | 16.4222 | 0.727901 | 0.363951 | − | 0.931418i | \(-0.381428\pi\) | ||||
0.363951 | + | 0.931418i | \(0.381428\pi\) | |||||||
\(510\) | 2.60555 | 0.115376 | ||||||||
\(511\) | −12.0000 | −0.530849 | ||||||||
\(512\) | −18.2135 | −0.804930 | ||||||||
\(513\) | 1.25610 | 0.0554583 | ||||||||
\(514\) | −3.76831 | −0.166213 | ||||||||
\(515\) | 1.21110 | 0.0533676 | ||||||||
\(516\) | 10.6943 | 0.470791 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 18.7889 | 0.825537 | ||||||||
\(519\) | 12.4459 | 0.546313 | ||||||||
\(520\) | 12.2389 | 0.536709 | ||||||||
\(521\) | 7.57779 | 0.331989 | 0.165995 | − | 0.986127i | \(-0.446917\pi\) | ||||
0.165995 | + | 0.986127i | \(0.446917\pi\) | |||||||
\(522\) | 4.42221 | 0.193555 | ||||||||
\(523\) | −25.7675 | −1.12674 | −0.563368 | − | 0.826206i | \(-0.690495\pi\) | ||||
−0.563368 | + | 0.826206i | \(0.690495\pi\) | |||||||
\(524\) | 9.28819 | 0.405756 | ||||||||
\(525\) | −4.14863 | −0.181061 | ||||||||
\(526\) | −4.97224 | −0.216800 | ||||||||
\(527\) | 16.5945 | 0.722868 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.15559 | 0.180678 | ||||||||
\(530\) | −7.04115 | −0.305848 | ||||||||
\(531\) | −5.21110 | −0.226143 | ||||||||
\(532\) | 8.36669 | 0.362742 | ||||||||
\(533\) | −51.6333 | −2.23649 | ||||||||
\(534\) | 3.76831 | 0.163071 | ||||||||
\(535\) | 2.89252 | 0.125055 | ||||||||
\(536\) | −29.9162 | −1.29218 | ||||||||
\(537\) | 22.4222 | 0.967590 | ||||||||
\(538\) | 11.3049 | 0.487390 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.60555 | 0.0690919 | ||||||||
\(541\) | 33.1890 | 1.42691 | 0.713454 | − | 0.700703i | \(-0.247130\pi\) | ||||
0.713454 | + | 0.700703i | \(0.247130\pi\) | |||||||
\(542\) | −14.3667 | −0.617102 | ||||||||
\(543\) | −19.2111 | −0.824427 | ||||||||
\(544\) | −23.4500 | −1.00541 | ||||||||
\(545\) | −16.5945 | −0.710831 | ||||||||
\(546\) | 14.0823 | 0.602667 | ||||||||
\(547\) | −25.7675 | −1.10174 | −0.550870 | − | 0.834591i | \(-0.685704\pi\) | ||||
−0.550870 | + | 0.834591i | \(0.685704\pi\) | |||||||
\(548\) | 26.3667 | 1.12633 | ||||||||
\(549\) | 8.29725 | 0.354118 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.84441 | 0.376785 | ||||||||
\(552\) | −11.8004 | −0.502258 | ||||||||
\(553\) | −5.21110 | −0.221599 | ||||||||
\(554\) | −6.55004 | −0.278284 | ||||||||
\(555\) | 7.21110 | 0.306094 | ||||||||
\(556\) | −15.3384 | −0.650493 | ||||||||
\(557\) | −3.38799 | −0.143554 | −0.0717769 | − | 0.997421i | \(-0.522867\pi\) | ||||
−0.0717769 | + | 0.997421i | \(0.522867\pi\) | |||||||
\(558\) | −2.51221 | −0.106350 | ||||||||
\(559\) | 36.0000 | 1.52264 | ||||||||
\(560\) | 7.42147 | 0.313614 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 16.4222 | 0.692729 | ||||||||
\(563\) | 22.7599 | 0.959214 | 0.479607 | − | 0.877483i | \(-0.340779\pi\) | ||||
0.479607 | + | 0.877483i | \(0.340779\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.2111 | 0.471655 | ||||||||
\(566\) | 19.8167 | 0.832956 | ||||||||
\(567\) | 4.14863 | 0.174226 | ||||||||
\(568\) | 11.8004 | 0.495134 | ||||||||
\(569\) | −1.25610 | −0.0526586 | −0.0263293 | − | 0.999653i | \(-0.508382\pi\) | ||||
−0.0263293 | + | 0.999653i | \(0.508382\pi\) | |||||||
\(570\) | −0.788897 | −0.0330433 | ||||||||
\(571\) | −31.1723 | −1.30452 | −0.652260 | − | 0.757996i | \(-0.726179\pi\) | ||||
−0.652260 | + | 0.757996i | \(0.726179\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 24.8918 | 1.03896 | ||||||||
\(575\) | 5.21110 | 0.217318 | ||||||||
\(576\) | −0.0277564 | −0.00115652 | ||||||||
\(577\) | 11.5778 | 0.481990 | 0.240995 | − | 0.970526i | \(-0.422526\pi\) | ||||
0.240995 | + | 0.970526i | \(0.422526\pi\) | |||||||
\(578\) | −0.132583 | −0.00551474 | ||||||||
\(579\) | −11.1898 | −0.465031 | ||||||||
\(580\) | 11.3049 | 0.469412 | ||||||||
\(581\) | −56.8444 | −2.35830 | ||||||||
\(582\) | 12.0656 | 0.500134 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −6.55004 | −0.271043 | ||||||||
\(585\) | 5.40473 | 0.223458 | ||||||||
\(586\) | 13.0278 | 0.538172 | ||||||||
\(587\) | 17.2111 | 0.710378 | 0.355189 | − | 0.934794i | \(-0.384416\pi\) | ||||
0.355189 | + | 0.934794i | \(0.384416\pi\) | |||||||
\(588\) | 16.3944 | 0.676096 | ||||||||
\(589\) | −5.02441 | −0.207027 | ||||||||
\(590\) | 3.27284 | 0.134741 | ||||||||
\(591\) | −9.17304 | −0.377328 | ||||||||
\(592\) | −12.8999 | −0.530184 | ||||||||
\(593\) | −9.93367 | −0.407927 | −0.203964 | − | 0.978978i | \(-0.565382\pi\) | ||||
−0.203964 | + | 0.978978i | \(0.565382\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 17.2111 | 0.705586 | ||||||||
\(596\) | −36.7270 | −1.50440 | ||||||||
\(597\) | 8.00000 | 0.327418 | ||||||||
\(598\) | −17.6888 | −0.723350 | ||||||||
\(599\) | 12.0000 | 0.490307 | 0.245153 | − | 0.969484i | \(-0.421162\pi\) | ||||
0.245153 | + | 0.969484i | \(0.421162\pi\) | |||||||
\(600\) | −2.26447 | −0.0924467 | ||||||||
\(601\) | −43.9985 | −1.79474 | −0.897368 | − | 0.441284i | \(-0.854523\pi\) | ||||
−0.897368 | + | 0.441284i | \(0.854523\pi\) | |||||||
\(602\) | −17.3551 | −0.707343 | ||||||||
\(603\) | −13.2111 | −0.537998 | ||||||||
\(604\) | −24.6266 | −1.00204 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.788897 | −0.0320468 | ||||||||
\(607\) | −18.2309 | −0.739970 | −0.369985 | − | 0.929038i | \(-0.620637\pi\) | ||||
−0.369985 | + | 0.929038i | \(0.620637\pi\) | |||||||
\(608\) | 7.10008 | 0.287946 | ||||||||
\(609\) | 29.2111 | 1.18369 | ||||||||
\(610\) | −5.21110 | −0.210991 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −6.66083 | −0.269248 | ||||||||
\(613\) | 41.8666 | 1.69098 | 0.845488 | − | 0.533995i | \(-0.179310\pi\) | ||||
0.845488 | + | 0.533995i | \(0.179310\pi\) | |||||||
\(614\) | 4.66106 | 0.188105 | ||||||||
\(615\) | 9.55336 | 0.385229 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.7889 | 0.997963 | 0.498982 | − | 0.866613i | \(-0.333707\pi\) | ||||
0.498982 | + | 0.866613i | \(0.333707\pi\) | |||||||
\(618\) | 0.760635 | 0.0305972 | ||||||||
\(619\) | 8.00000 | 0.321547 | 0.160774 | − | 0.986991i | \(-0.448601\pi\) | ||||
0.160774 | + | 0.986991i | \(0.448601\pi\) | |||||||
\(620\) | −6.42221 | −0.257922 | ||||||||
\(621\) | −5.21110 | −0.209114 | ||||||||
\(622\) | −4.26378 | −0.170962 | ||||||||
\(623\) | 24.8918 | 0.997267 | ||||||||
\(624\) | −9.66851 | −0.387050 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −9.55336 | −0.381829 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −16.0555 | −0.640685 | ||||||||
\(629\) | −29.9162 | −1.19284 | ||||||||
\(630\) | −2.60555 | −0.103808 | ||||||||
\(631\) | −28.8444 | −1.14828 | −0.574139 | − | 0.818758i | \(-0.694663\pi\) | ||||
−0.574139 | + | 0.818758i | \(0.694663\pi\) | |||||||
\(632\) | −2.84441 | −0.113145 | ||||||||
\(633\) | −3.76831 | −0.149777 | ||||||||
\(634\) | 7.04115 | 0.279640 | ||||||||
\(635\) | −1.63642 | −0.0649394 | ||||||||
\(636\) | 18.0000 | 0.713746 | ||||||||
\(637\) | 55.1882 | 2.18664 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.21110 | 0.206148 | ||||||||
\(640\) | 11.3224 | 0.447556 | ||||||||
\(641\) | 6.00000 | 0.236986 | 0.118493 | − | 0.992955i | \(-0.462194\pi\) | ||||
0.118493 | + | 0.992955i | \(0.462194\pi\) | |||||||
\(642\) | 1.81665 | 0.0716976 | ||||||||
\(643\) | −0.366692 | −0.0144609 | −0.00723047 | − | 0.999974i | \(-0.502302\pi\) | ||||
−0.00723047 | + | 0.999974i | \(0.502302\pi\) | |||||||
\(644\) | −34.7103 | −1.36778 | ||||||||
\(645\) | −6.66083 | −0.262270 | ||||||||
\(646\) | 3.27284 | 0.128768 | ||||||||
\(647\) | 5.21110 | 0.204870 | 0.102435 | − | 0.994740i | \(-0.467337\pi\) | ||||
0.102435 | + | 0.994740i | \(0.467337\pi\) | |||||||
\(648\) | 2.26447 | 0.0889569 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −3.39445 | −0.133141 | ||||||||
\(651\) | −16.5945 | −0.650390 | ||||||||
\(652\) | −21.2111 | −0.830691 | ||||||||
\(653\) | 4.42221 | 0.173054 | 0.0865271 | − | 0.996249i | \(-0.472423\pi\) | ||||
0.0865271 | + | 0.996249i | \(0.472423\pi\) | |||||||
\(654\) | −10.4222 | −0.407540 | ||||||||
\(655\) | −5.78505 | −0.226040 | ||||||||
\(656\) | −17.0900 | −0.667251 | ||||||||
\(657\) | −2.89252 | −0.112848 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −33.1890 | −1.29286 | −0.646430 | − | 0.762973i | \(-0.723739\pi\) | ||||
−0.646430 | + | 0.762973i | \(0.723739\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.8444 | 1.19971 | 0.599854 | − | 0.800109i | \(-0.295225\pi\) | ||||
0.599854 | + | 0.800109i | \(0.295225\pi\) | |||||||
\(662\) | −5.02441 | −0.195279 | ||||||||
\(663\) | −22.4222 | −0.870806 | ||||||||
\(664\) | −31.0278 | −1.20411 | ||||||||
\(665\) | −5.21110 | −0.202078 | ||||||||
\(666\) | 4.52894 | 0.175493 | ||||||||
\(667\) | −36.6922 | −1.42073 | ||||||||
\(668\) | 31.2874 | 1.21055 | ||||||||
\(669\) | 2.42221 | 0.0936479 | ||||||||
\(670\) | 8.29725 | 0.320551 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 23.4500 | 0.904602 | ||||||||
\(673\) | −15.4536 | −0.595691 | −0.297845 | − | 0.954614i | \(-0.596268\pi\) | ||||
−0.297845 | + | 0.954614i | \(0.596268\pi\) | |||||||
\(674\) | −5.44996 | −0.209925 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | −26.0278 | −1.00107 | ||||||||
\(677\) | 3.38799 | 0.130211 | 0.0651056 | − | 0.997878i | \(-0.479262\pi\) | ||||
0.0651056 | + | 0.997878i | \(0.479262\pi\) | |||||||
\(678\) | 7.04115 | 0.270414 | ||||||||
\(679\) | 79.6997 | 3.05859 | ||||||||
\(680\) | 9.39445 | 0.360261 | ||||||||
\(681\) | 2.89252 | 0.110842 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −36.0000 | −1.37750 | −0.688751 | − | 0.724998i | \(-0.741841\pi\) | ||||
−0.688751 | + | 0.724998i | \(0.741841\pi\) | |||||||
\(684\) | 2.01674 | 0.0771119 | ||||||||
\(685\) | −16.4222 | −0.627460 | ||||||||
\(686\) | −8.36669 | −0.319442 | ||||||||
\(687\) | −10.0000 | −0.381524 | ||||||||
\(688\) | 11.9155 | 0.454276 | ||||||||
\(689\) | 60.5930 | 2.30841 | ||||||||
\(690\) | 3.27284 | 0.124595 | ||||||||
\(691\) | 9.57779 | 0.364356 | 0.182178 | − | 0.983266i | \(-0.441685\pi\) | ||||
0.182178 | + | 0.983266i | \(0.441685\pi\) | |||||||
\(692\) | 19.9825 | 0.759621 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −18.5500 | −0.704150 | ||||||||
\(695\) | 9.55336 | 0.362379 | ||||||||
\(696\) | 15.9445 | 0.604374 | ||||||||
\(697\) | −39.6333 | −1.50122 | ||||||||
\(698\) | 8.36669 | 0.316684 | ||||||||
\(699\) | 25.7675 | 0.974618 | ||||||||
\(700\) | −6.66083 | −0.251756 | ||||||||
\(701\) | 7.04115 | 0.265941 | 0.132970 | − | 0.991120i | \(-0.457549\pi\) | ||||
0.132970 | + | 0.991120i | \(0.457549\pi\) | |||||||
\(702\) | 3.39445 | 0.128115 | ||||||||
\(703\) | 9.05789 | 0.341625 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.03209 | −0.302292 | ||||||||
\(707\) | −5.21110 | −0.195984 | ||||||||
\(708\) | −8.36669 | −0.314440 | ||||||||
\(709\) | −5.63331 | −0.211563 | −0.105782 | − | 0.994389i | \(-0.533734\pi\) | ||||
−0.105782 | + | 0.994389i | \(0.533734\pi\) | |||||||
\(710\) | −3.27284 | −0.122828 | ||||||||
\(711\) | −1.25610 | −0.0471075 | ||||||||
\(712\) | 13.5868 | 0.509188 | ||||||||
\(713\) | 20.8444 | 0.780629 | ||||||||
\(714\) | 10.8095 | 0.404534 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 36.0000 | 1.34538 | ||||||||
\(717\) | 8.29725 | 0.309867 | ||||||||
\(718\) | −9.94449 | −0.371125 | ||||||||
\(719\) | −10.4222 | −0.388683 | −0.194341 | − | 0.980934i | \(-0.562257\pi\) | ||||
−0.194341 | + | 0.980934i | \(0.562257\pi\) | |||||||
\(720\) | 1.78890 | 0.0666683 | ||||||||
\(721\) | 5.02441 | 0.187119 | ||||||||
\(722\) | 10.9420 | 0.407221 | ||||||||
\(723\) | −3.27284 | −0.121718 | ||||||||
\(724\) | −30.8444 | −1.14632 | ||||||||
\(725\) | −7.04115 | −0.261502 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21.5778 | −0.800276 | −0.400138 | − | 0.916455i | \(-0.631038\pi\) | ||||
−0.400138 | + | 0.916455i | \(0.631038\pi\) | |||||||
\(728\) | 50.7745 | 1.88183 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 1.81665 | 0.0672374 | ||||||||
\(731\) | 27.6333 | 1.02205 | ||||||||
\(732\) | 13.3217 | 0.492383 | ||||||||
\(733\) | 16.2142 | 0.598885 | 0.299442 | − | 0.954114i | \(-0.403199\pi\) | ||||
0.299442 | + | 0.954114i | \(0.403199\pi\) | |||||||
\(734\) | −11.5701 | −0.427060 | ||||||||
\(735\) | −10.2111 | −0.376642 | ||||||||
\(736\) | −29.4556 | −1.08575 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 6.00000 | 0.220863 | ||||||||
\(739\) | −42.7424 | −1.57230 | −0.786152 | − | 0.618034i | \(-0.787930\pi\) | ||||
−0.786152 | + | 0.618034i | \(0.787930\pi\) | |||||||
\(740\) | 11.5778 | 0.425608 | ||||||||
\(741\) | 6.78890 | 0.249396 | ||||||||
\(742\) | −29.2111 | −1.07237 | ||||||||
\(743\) | 33.5693 | 1.23154 | 0.615770 | − | 0.787926i | \(-0.288845\pi\) | ||||
0.615770 | + | 0.787926i | \(0.288845\pi\) | |||||||
\(744\) | −9.05789 | −0.332078 | ||||||||
\(745\) | 22.8750 | 0.838076 | ||||||||
\(746\) | 4.97224 | 0.182047 | ||||||||
\(747\) | −13.7020 | −0.501329 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.0000 | 0.438470 | ||||||||
\(750\) | 0.628052 | 0.0229332 | ||||||||
\(751\) | 36.8444 | 1.34447 | 0.672236 | − | 0.740337i | \(-0.265334\pi\) | ||||
0.672236 | + | 0.740337i | \(0.265334\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 27.6333 | 1.00701 | ||||||||
\(754\) | 23.9008 | 0.870417 | ||||||||
\(755\) | 15.3384 | 0.558222 | ||||||||
\(756\) | 6.66083 | 0.242252 | ||||||||
\(757\) | 20.4222 | 0.742258 | 0.371129 | − | 0.928581i | \(-0.378971\pi\) | ||||
0.371129 | + | 0.928581i | \(0.378971\pi\) | |||||||
\(758\) | 9.05789 | 0.328997 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.84441 | −0.103178 | ||||||||
\(761\) | 26.9085 | 0.975432 | 0.487716 | − | 0.873002i | \(-0.337830\pi\) | ||||
0.487716 | + | 0.873002i | \(0.337830\pi\) | |||||||
\(762\) | −1.02776 | −0.0372317 | ||||||||
\(763\) | −68.8444 | −2.49233 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.14863 | 0.149994 | ||||||||
\(766\) | 3.27284 | 0.118253 | ||||||||
\(767\) | −28.1646 | −1.01696 | ||||||||
\(768\) | 7.05551 | 0.254594 | ||||||||
\(769\) | −10.8095 | −0.389799 | −0.194900 | − | 0.980823i | \(-0.562438\pi\) | ||||
−0.194900 | + | 0.980823i | \(0.562438\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.00000 | −0.216085 | ||||||||
\(772\) | −17.9658 | −0.646602 | ||||||||
\(773\) | 42.0000 | 1.51064 | 0.755318 | − | 0.655359i | \(-0.227483\pi\) | ||||
0.755318 | + | 0.655359i | \(0.227483\pi\) | |||||||
\(774\) | −4.18335 | −0.150367 | ||||||||
\(775\) | 4.00000 | 0.143684 | ||||||||
\(776\) | 43.5030 | 1.56167 | ||||||||
\(777\) | 29.9162 | 1.07324 | ||||||||
\(778\) | −11.3049 | −0.405301 | ||||||||
\(779\) | 12.0000 | 0.429945 | ||||||||
\(780\) | 8.67757 | 0.310707 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −13.5778 | −0.485541 | ||||||||
\(783\) | 7.04115 | 0.251630 | ||||||||
\(784\) | 18.2666 | 0.652379 | ||||||||
\(785\) | 10.0000 | 0.356915 | ||||||||
\(786\) | −3.63331 | −0.129596 | ||||||||
\(787\) | 6.66083 | 0.237433 | 0.118717 | − | 0.992928i | \(-0.462122\pi\) | ||||
0.118717 | + | 0.992928i | \(0.462122\pi\) | |||||||
\(788\) | −14.7278 | −0.524656 | ||||||||
\(789\) | −7.91694 | −0.281850 | ||||||||
\(790\) | 0.788897 | 0.0280677 | ||||||||
\(791\) | 46.5107 | 1.65373 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 44.8444 | 1.59247 | ||||||||
\(794\) | 8.56242 | 0.303869 | ||||||||
\(795\) | −11.2111 | −0.397617 | ||||||||
\(796\) | 12.8444 | 0.455258 | ||||||||
\(797\) | 54.4777 | 1.92970 | 0.964850 | − | 0.262802i | \(-0.0846465\pi\) | ||||
0.964850 | + | 0.262802i | \(0.0846465\pi\) | |||||||
\(798\) | −3.27284 | −0.115857 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −5.65246 | −0.199845 | ||||||||
\(801\) | 6.00000 | 0.212000 | ||||||||
\(802\) | −17.8506 | −0.630327 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −21.2111 | −0.748058 | ||||||||
\(805\) | 21.6189 | 0.761967 | ||||||||
\(806\) | −13.5778 | −0.478257 | ||||||||
\(807\) | 18.0000 | 0.633630 | ||||||||
\(808\) | −2.84441 | −0.100066 | ||||||||
\(809\) | −12.0656 | −0.424203 | −0.212101 | − | 0.977248i | \(-0.568031\pi\) | ||||
−0.212101 | + | 0.977248i | \(0.568031\pi\) | |||||||
\(810\) | −0.628052 | −0.0220675 | ||||||||
\(811\) | −51.8003 | −1.81895 | −0.909477 | − | 0.415755i | \(-0.863517\pi\) | ||||
−0.909477 | + | 0.415755i | \(0.863517\pi\) | |||||||
\(812\) | 46.8999 | 1.64586 | ||||||||
\(813\) | −22.8750 | −0.802262 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13.2111 | 0.462765 | ||||||||
\(816\) | −7.42147 | −0.259803 | ||||||||
\(817\) | −8.36669 | −0.292714 | ||||||||
\(818\) | 4.73338 | 0.165499 | ||||||||
\(819\) | 22.4222 | 0.783495 | ||||||||
\(820\) | 15.3384 | 0.535640 | ||||||||
\(821\) | 37.7180 | 1.31637 | 0.658183 | − | 0.752858i | \(-0.271325\pi\) | ||||
0.658183 | + | 0.752858i | \(0.271325\pi\) | |||||||
\(822\) | −10.3140 | −0.359742 | ||||||||
\(823\) | 4.36669 | 0.152213 | 0.0761067 | − | 0.997100i | \(-0.475751\pi\) | ||||
0.0761067 | + | 0.997100i | \(0.475751\pi\) | |||||||
\(824\) | 2.74251 | 0.0955398 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 13.5778 | 0.472432 | ||||||||
\(827\) | −13.7020 | −0.476465 | −0.238232 | − | 0.971208i | \(-0.576568\pi\) | ||||
−0.238232 | + | 0.971208i | \(0.576568\pi\) | |||||||
\(828\) | −8.36669 | −0.290763 | ||||||||
\(829\) | −36.0555 | −1.25226 | −0.626130 | − | 0.779719i | \(-0.715362\pi\) | ||||
−0.626130 | + | 0.779719i | \(0.715362\pi\) | |||||||
\(830\) | 8.60555 | 0.298703 | ||||||||
\(831\) | −10.4291 | −0.361783 | ||||||||
\(832\) | −0.150016 | −0.00520086 | ||||||||
\(833\) | 42.3621 | 1.46776 | ||||||||
\(834\) | 6.00000 | 0.207763 | ||||||||
\(835\) | −19.4870 | −0.674376 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.00000 | −0.138260 | ||||||||
\(838\) | 7.53662 | 0.260348 | ||||||||
\(839\) | −30.7889 | −1.06295 | −0.531475 | − | 0.847074i | \(-0.678362\pi\) | ||||
−0.531475 | + | 0.847074i | \(0.678362\pi\) | |||||||
\(840\) | −9.39445 | −0.324139 | ||||||||
\(841\) | 20.5778 | 0.709579 | ||||||||
\(842\) | −24.6266 | −0.848688 | ||||||||
\(843\) | 26.1479 | 0.900580 | ||||||||
\(844\) | −6.05021 | −0.208257 | ||||||||
\(845\) | 16.2111 | 0.557679 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 20.0555 | 0.688709 | ||||||||
\(849\) | 31.5526 | 1.08288 | ||||||||
\(850\) | −2.60555 | −0.0893697 | ||||||||
\(851\) | −37.5778 | −1.28815 | ||||||||
\(852\) | 8.36669 | 0.286638 | ||||||||
\(853\) | −19.4870 | −0.667223 | −0.333612 | − | 0.942711i | \(-0.608267\pi\) | ||||
−0.333612 | + | 0.942711i | \(0.608267\pi\) | |||||||
\(854\) | −21.6189 | −0.739784 | ||||||||
\(855\) | −1.25610 | −0.0429578 | ||||||||
\(856\) | 6.55004 | 0.223876 | ||||||||
\(857\) | −40.6105 | −1.38723 | −0.693614 | − | 0.720347i | \(-0.743983\pi\) | ||||
−0.693614 | + | 0.720347i | \(0.743983\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32.0000 | 1.09183 | 0.545913 | − | 0.837842i | \(-0.316183\pi\) | ||||
0.545913 | + | 0.837842i | \(0.316183\pi\) | |||||||
\(860\) | −10.6943 | −0.364673 | ||||||||
\(861\) | 39.6333 | 1.35070 | ||||||||
\(862\) | 1.57779 | 0.0537399 | ||||||||
\(863\) | −15.6333 | −0.532164 | −0.266082 | − | 0.963950i | \(-0.585729\pi\) | ||||
−0.266082 | + | 0.963950i | \(0.585729\pi\) | |||||||
\(864\) | 5.65246 | 0.192301 | ||||||||
\(865\) | −12.4459 | −0.423173 | ||||||||
\(866\) | 3.00767 | 0.102205 | ||||||||
\(867\) | −0.211103 | −0.00716942 | ||||||||
\(868\) | −26.6433 | −0.904334 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −4.42221 | −0.149927 | ||||||||
\(871\) | −71.4024 | −2.41938 | ||||||||
\(872\) | −37.5778 | −1.27254 | ||||||||
\(873\) | 19.2111 | 0.650197 | ||||||||
\(874\) | 4.11103 | 0.139058 | ||||||||
\(875\) | 4.14863 | 0.140249 | ||||||||
\(876\) | −4.64409 | −0.156909 | ||||||||
\(877\) | 13.7020 | 0.462683 | 0.231342 | − | 0.972873i | \(-0.425689\pi\) | ||||
0.231342 | + | 0.972873i | \(0.425689\pi\) | |||||||
\(878\) | −1.26662 | −0.0427462 | ||||||||
\(879\) | 20.7431 | 0.699649 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −49.2666 | −1.65983 | −0.829917 | − | 0.557887i | \(-0.811612\pi\) | ||||
−0.829917 | + | 0.557887i | \(0.811612\pi\) | |||||||
\(882\) | −6.41310 | −0.215940 | ||||||||
\(883\) | −6.42221 | −0.216124 | −0.108062 | − | 0.994144i | \(-0.534465\pi\) | ||||
−0.108062 | + | 0.994144i | \(0.534465\pi\) | |||||||
\(884\) | −36.0000 | −1.21081 | ||||||||
\(885\) | 5.21110 | 0.175169 | ||||||||
\(886\) | −17.3551 | −0.583057 | ||||||||
\(887\) | −38.5937 | −1.29585 | −0.647926 | − | 0.761704i | \(-0.724363\pi\) | ||||
−0.647926 | + | 0.761704i | \(0.724363\pi\) | |||||||
\(888\) | 16.3293 | 0.547977 | ||||||||
\(889\) | −6.78890 | −0.227692 | ||||||||
\(890\) | −3.76831 | −0.126314 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.88897 | 0.130212 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 14.3667 | 0.480494 | ||||||||
\(895\) | −22.4222 | −0.749492 | ||||||||
\(896\) | 46.9722 | 1.56923 | ||||||||
\(897\) | −28.1646 | −0.940389 | ||||||||
\(898\) | −10.3140 | −0.344182 | ||||||||
\(899\) | −28.1646 | −0.939342 | ||||||||
\(900\) | −1.60555 | −0.0535184 | ||||||||
\(901\) | 46.5107 | 1.54950 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −27.6333 | −0.919579 | ||||||||
\(904\) | 25.3872 | 0.844367 | ||||||||
\(905\) | 19.2111 | 0.638599 | ||||||||
\(906\) | 9.63331 | 0.320045 | ||||||||
\(907\) | −14.4222 | −0.478881 | −0.239441 | − | 0.970911i | \(-0.576964\pi\) | ||||
−0.239441 | + | 0.970911i | \(0.576964\pi\) | |||||||
\(908\) | 4.64409 | 0.154120 | ||||||||
\(909\) | −1.25610 | −0.0416623 | ||||||||
\(910\) | −14.0823 | −0.466824 | ||||||||
\(911\) | 10.4222 | 0.345303 | 0.172652 | − | 0.984983i | \(-0.444767\pi\) | ||||
0.172652 | + | 0.984983i | \(0.444767\pi\) | |||||||
\(912\) | 2.24704 | 0.0744069 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 1.33894 | 0.0442881 | ||||||||
\(915\) | −8.29725 | −0.274299 | ||||||||
\(916\) | −16.0555 | −0.530489 | ||||||||
\(917\) | −24.0000 | −0.792550 | ||||||||
\(918\) | 2.60555 | 0.0859960 | ||||||||
\(919\) | 18.6112 | 0.613928 | 0.306964 | − | 0.951721i | \(-0.400687\pi\) | ||||
0.306964 | + | 0.951721i | \(0.400687\pi\) | |||||||
\(920\) | 11.8004 | 0.389048 | ||||||||
\(921\) | 7.42147 | 0.244546 | ||||||||
\(922\) | −3.94449 | −0.129905 | ||||||||
\(923\) | 28.1646 | 0.927049 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.21110 | −0.237100 | ||||||||
\(926\) | 16.5945 | 0.545329 | ||||||||
\(927\) | 1.21110 | 0.0397778 | ||||||||
\(928\) | 39.7998 | 1.30649 | ||||||||
\(929\) | 16.4222 | 0.538795 | 0.269398 | − | 0.963029i | \(-0.413175\pi\) | ||||
0.269398 | + | 0.963029i | \(0.413175\pi\) | |||||||
\(930\) | 2.51221 | 0.0823785 | ||||||||
\(931\) | −12.8262 | −0.420362 | ||||||||
\(932\) | 41.3711 | 1.35516 | ||||||||
\(933\) | −6.78890 | −0.222259 | ||||||||
\(934\) | 10.8095 | 0.353696 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 12.2389 | 0.400040 | ||||||||
\(937\) | 10.4291 | 0.340705 | 0.170353 | − | 0.985383i | \(-0.445509\pi\) | ||||
0.170353 | + | 0.985383i | \(0.445509\pi\) | |||||||
\(938\) | 34.4222 | 1.12392 | ||||||||
\(939\) | −15.2111 | −0.496396 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.28052 | −0.204739 | −0.102369 | − | 0.994746i | \(-0.532642\pi\) | ||||
−0.102369 | + | 0.994746i | \(0.532642\pi\) | |||||||
\(942\) | 6.28052 | 0.204630 | ||||||||
\(943\) | −49.7835 | −1.62117 | ||||||||
\(944\) | −9.32213 | −0.303409 | ||||||||
\(945\) | −4.14863 | −0.134955 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.57779 | −0.0512714 | −0.0256357 | − | 0.999671i | \(-0.508161\pi\) | ||||
−0.0256357 | + | 0.999671i | \(0.508161\pi\) | |||||||
\(948\) | −2.01674 | −0.0655006 | ||||||||
\(949\) | −15.6333 | −0.507479 | ||||||||
\(950\) | 0.788897 | 0.0255952 | ||||||||
\(951\) | 11.2111 | 0.363545 | ||||||||
\(952\) | 38.9741 | 1.26316 | ||||||||
\(953\) | −34.8254 | −1.12811 | −0.564053 | − | 0.825738i | \(-0.690759\pi\) | ||||
−0.564053 | + | 0.825738i | \(0.690759\pi\) | |||||||
\(954\) | −7.04115 | −0.227966 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 13.3217 | 0.430853 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.05551 | −0.0664106 | ||||||||
\(959\) | −68.1296 | −2.20002 | ||||||||
\(960\) | 0.0277564 | 0.000895833 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 24.4777 | 0.789193 | ||||||||
\(963\) | 2.89252 | 0.0932103 | ||||||||
\(964\) | −5.25471 | −0.169243 | ||||||||
\(965\) | 11.1898 | 0.360212 | ||||||||
\(966\) | 13.5778 | 0.436858 | ||||||||
\(967\) | −13.2065 | −0.424693 | −0.212346 | − | 0.977194i | \(-0.568111\pi\) | ||||
−0.212346 | + | 0.977194i | \(0.568111\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.21110 | 0.167405 | ||||||||
\(970\) | −12.0656 | −0.387402 | ||||||||
\(971\) | −58.4222 | −1.87486 | −0.937429 | − | 0.348177i | \(-0.886801\pi\) | ||||
−0.937429 | + | 0.348177i | \(0.886801\pi\) | |||||||
\(972\) | 1.60555 | 0.0514981 | ||||||||
\(973\) | 39.6333 | 1.27059 | ||||||||
\(974\) | 0.760635 | 0.0243723 | ||||||||
\(975\) | −5.40473 | −0.173090 | ||||||||
\(976\) | 14.8429 | 0.475111 | ||||||||
\(977\) | −30.0000 | −0.959785 | −0.479893 | − | 0.877327i | \(-0.659324\pi\) | ||||
−0.479893 | + | 0.877327i | \(0.659324\pi\) | |||||||
\(978\) | 8.29725 | 0.265317 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −16.3944 | −0.523701 | ||||||||
\(981\) | −16.5945 | −0.529822 | ||||||||
\(982\) | 25.5778 | 0.816220 | ||||||||
\(983\) | 26.0555 | 0.831042 | 0.415521 | − | 0.909584i | \(-0.363599\pi\) | ||||
0.415521 | + | 0.909584i | \(0.363599\pi\) | |||||||
\(984\) | 21.6333 | 0.689645 | ||||||||
\(985\) | 9.17304 | 0.292277 | ||||||||
\(986\) | 18.3461 | 0.584258 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 10.8999 | 0.346773 | ||||||||
\(989\) | 34.7103 | 1.10372 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.00000 | 0.127064 | 0.0635321 | − | 0.997980i | \(-0.479763\pi\) | ||||
0.0635321 | + | 0.997980i | \(0.479763\pi\) | |||||||
\(992\) | −22.6099 | −0.717864 | ||||||||
\(993\) | −8.00000 | −0.253872 | ||||||||
\(994\) | −13.5778 | −0.430662 | ||||||||
\(995\) | −8.00000 | −0.253617 | ||||||||
\(996\) | −21.9992 | −0.697072 | ||||||||
\(997\) | 30.2965 | 0.959499 | 0.479750 | − | 0.877405i | \(-0.340727\pi\) | ||||
0.479750 | + | 0.877405i | \(0.340727\pi\) | |||||||
\(998\) | −9.05789 | −0.286722 | ||||||||
\(999\) | 7.21110 | 0.228149 |
(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 | 1815.2.a.s.1.2 | ✓ | 4 | |
3.2 | odd | 2 | 5445.2.a.bo.1.3 | 4 | |||
5.4 | even | 2 | 9075.2.a.dc.1.3 | 4 | |||
11.10 | odd | 2 | inner | 1815.2.a.s.1.3 | yes | 4 | |
33.32 | even | 2 | 5445.2.a.bo.1.2 | 4 | |||
55.54 | odd | 2 | 9075.2.a.dc.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1815.2.a.s.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
1815.2.a.s.1.3 | yes | 4 | 11.10 | odd | 2 | inner | |
5445.2.a.bo.1.2 | 4 | 33.32 | even | 2 | |||
5445.2.a.bo.1.3 | 4 | 3.2 | odd | 2 | |||
9075.2.a.dc.1.2 | 4 | 55.54 | odd | 2 | |||
9075.2.a.dc.1.3 | 4 | 5.4 | even | 2 |