Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5265,2,Mod(1,5265)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5265, 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("5265.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5265 = 3^{4} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5265.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: | \(42.0412366642\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} - 8x^{6} + 31x^{5} - x^{4} - 70x^{3} + 66x^{2} - 19x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 585) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.655066\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5265.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.655066 | −0.463201 | −0.231601 | − | 0.972811i | \(-0.574396\pi\) | ||||
−0.231601 | + | 0.972811i | \(0.574396\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.57089 | −0.785445 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.777184 | −0.293748 | −0.146874 | − | 0.989155i | \(-0.546921\pi\) | ||||
−0.146874 | + | 0.989155i | \(0.546921\pi\) | |||||||
\(8\) | 2.33917 | 0.827020 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.655066 | −0.207150 | ||||||||
\(11\) | 4.06797 | 1.22654 | 0.613270 | − | 0.789873i | \(-0.289854\pi\) | ||||
0.613270 | + | 0.789873i | \(0.289854\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0.509106 | 0.136064 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.60947 | 0.402368 | ||||||||
\(17\) | −5.29154 | −1.28339 | −0.641693 | − | 0.766961i | \(-0.721768\pi\) | ||||
−0.641693 | + | 0.766961i | \(0.721768\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.65042 | 1.52571 | 0.762855 | − | 0.646569i | \(-0.223797\pi\) | ||||
0.762855 | + | 0.646569i | \(0.223797\pi\) | |||||||
\(20\) | −1.57089 | −0.351261 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.66479 | −0.568135 | ||||||||
\(23\) | −2.30567 | −0.480765 | −0.240383 | − | 0.970678i | \(-0.577273\pi\) | ||||
−0.240383 | + | 0.970678i | \(0.577273\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0.655066 | 0.128469 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.22087 | 0.230723 | ||||||||
\(29\) | −6.38016 | −1.18477 | −0.592383 | − | 0.805656i | \(-0.701813\pi\) | ||||
−0.592383 | + | 0.805656i | \(0.701813\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.94517 | −1.60660 | −0.803300 | − | 0.595574i | \(-0.796925\pi\) | ||||
−0.803300 | + | 0.595574i | \(0.796925\pi\) | |||||||
\(32\) | −5.73264 | −1.01340 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.46630 | 0.594466 | ||||||||
\(35\) | −0.777184 | −0.131368 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.80592 | −0.461291 | −0.230645 | − | 0.973038i | \(-0.574084\pi\) | ||||
−0.230645 | + | 0.973038i | \(0.574084\pi\) | |||||||
\(38\) | −4.35646 | −0.706711 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.33917 | 0.369855 | ||||||||
\(41\) | −7.60986 | −1.18846 | −0.594231 | − | 0.804295i | \(-0.702543\pi\) | ||||
−0.594231 | + | 0.804295i | \(0.702543\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.84366 | 1.34865 | 0.674323 | − | 0.738437i | \(-0.264436\pi\) | ||||
0.674323 | + | 0.738437i | \(0.264436\pi\) | |||||||
\(44\) | −6.39034 | −0.963379 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.51036 | 0.222691 | ||||||||
\(47\) | 4.08782 | 0.596270 | 0.298135 | − | 0.954524i | \(-0.403635\pi\) | ||||
0.298135 | + | 0.954524i | \(0.403635\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.39599 | −0.913712 | ||||||||
\(50\) | −0.655066 | −0.0926403 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.57089 | 0.217843 | ||||||||
\(53\) | 4.78025 | 0.656618 | 0.328309 | − | 0.944570i | \(-0.393521\pi\) | ||||
0.328309 | + | 0.944570i | \(0.393521\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.06797 | 0.548525 | ||||||||
\(56\) | −1.81796 | −0.242935 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.17942 | 0.548785 | ||||||||
\(59\) | 4.74099 | 0.617224 | 0.308612 | − | 0.951188i | \(-0.400136\pi\) | ||||
0.308612 | + | 0.951188i | \(0.400136\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.3660 | −1.83938 | −0.919688 | − | 0.392651i | \(-0.871558\pi\) | ||||
−0.919688 | + | 0.392651i | \(0.871558\pi\) | |||||||
\(62\) | 5.85967 | 0.744179 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.536314 | 0.0670393 | ||||||||
\(65\) | −1.00000 | −0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.7871 | 1.31785 | 0.658925 | − | 0.752209i | \(-0.271011\pi\) | ||||
0.658925 | + | 0.752209i | \(0.271011\pi\) | |||||||
\(68\) | 8.31242 | 1.00803 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.509106 | 0.0608498 | ||||||||
\(71\) | −0.307776 | −0.0365262 | −0.0182631 | − | 0.999833i | \(-0.505814\pi\) | ||||
−0.0182631 | + | 0.999833i | \(0.505814\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.50636 | −0.878553 | −0.439277 | − | 0.898352i | \(-0.644765\pi\) | ||||
−0.439277 | + | 0.898352i | \(0.644765\pi\) | |||||||
\(74\) | 1.83806 | 0.213670 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −10.4471 | −1.19836 | ||||||||
\(77\) | −3.16156 | −0.360293 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.61897 | 0.857201 | 0.428601 | − | 0.903494i | \(-0.359007\pi\) | ||||
0.428601 | + | 0.903494i | \(0.359007\pi\) | |||||||
\(80\) | 1.60947 | 0.179944 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.98496 | 0.550497 | ||||||||
\(83\) | 12.5297 | 1.37531 | 0.687656 | − | 0.726037i | \(-0.258640\pi\) | ||||
0.687656 | + | 0.726037i | \(0.258640\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.29154 | −0.573948 | ||||||||
\(86\) | −5.79318 | −0.624694 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 9.51567 | 1.01437 | ||||||||
\(89\) | 11.7743 | 1.24807 | 0.624037 | − | 0.781394i | \(-0.285491\pi\) | ||||
0.624037 | + | 0.781394i | \(0.285491\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.777184 | 0.0814710 | ||||||||
\(92\) | 3.62195 | 0.377615 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.67779 | −0.276193 | ||||||||
\(95\) | 6.65042 | 0.682318 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.08536 | −0.617874 | −0.308937 | − | 0.951082i | \(-0.599973\pi\) | ||||
−0.308937 | + | 0.951082i | \(0.599973\pi\) | |||||||
\(98\) | 4.18979 | 0.423233 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.57089 | −0.157089 | ||||||||
\(101\) | −9.35209 | −0.930568 | −0.465284 | − | 0.885162i | \(-0.654048\pi\) | ||||
−0.465284 | + | 0.885162i | \(0.654048\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.21467 | −0.218218 | −0.109109 | − | 0.994030i | \(-0.534800\pi\) | ||||
−0.109109 | + | 0.994030i | \(0.534800\pi\) | |||||||
\(104\) | −2.33917 | −0.229374 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.13138 | −0.304146 | ||||||||
\(107\) | 15.4985 | 1.49830 | 0.749148 | − | 0.662403i | \(-0.230463\pi\) | ||||
0.749148 | + | 0.662403i | \(0.230463\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.88278 | −0.563468 | −0.281734 | − | 0.959493i | \(-0.590910\pi\) | ||||
−0.281734 | + | 0.959493i | \(0.590910\pi\) | |||||||
\(110\) | −2.66479 | −0.254078 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.25085 | −0.118195 | ||||||||
\(113\) | −10.5758 | −0.994888 | −0.497444 | − | 0.867496i | \(-0.665728\pi\) | ||||
−0.497444 | + | 0.867496i | \(0.665728\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.30567 | −0.215005 | ||||||||
\(116\) | 10.0225 | 0.930568 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.10566 | −0.285899 | ||||||||
\(119\) | 4.11250 | 0.376992 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.54841 | 0.504401 | ||||||||
\(122\) | 9.41066 | 0.852001 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 14.0519 | 1.26190 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.4873 | −1.01934 | −0.509668 | − | 0.860371i | \(-0.670232\pi\) | ||||
−0.509668 | + | 0.860371i | \(0.670232\pi\) | |||||||
\(128\) | 11.1140 | 0.982345 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.655066 | 0.0574530 | ||||||||
\(131\) | −12.5793 | −1.09906 | −0.549531 | − | 0.835473i | \(-0.685194\pi\) | ||||
−0.549531 | + | 0.835473i | \(0.685194\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.16860 | −0.448174 | ||||||||
\(134\) | −7.06624 | −0.610430 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −12.3778 | −1.06139 | ||||||||
\(137\) | 1.81204 | 0.154813 | 0.0774067 | − | 0.997000i | \(-0.475336\pi\) | ||||
0.0774067 | + | 0.997000i | \(0.475336\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −20.4105 | −1.73119 | −0.865597 | − | 0.500741i | \(-0.833061\pi\) | ||||
−0.865597 | + | 0.500741i | \(0.833061\pi\) | |||||||
\(140\) | 1.22087 | 0.103182 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.201613 | 0.0169190 | ||||||||
\(143\) | −4.06797 | −0.340181 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.38016 | −0.529843 | ||||||||
\(146\) | 4.91716 | 0.406947 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.40779 | 0.362318 | ||||||||
\(149\) | 0.464119 | 0.0380221 | 0.0190111 | − | 0.999819i | \(-0.493948\pi\) | ||||
0.0190111 | + | 0.999819i | \(0.493948\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.96476 | −0.810921 | −0.405460 | − | 0.914113i | \(-0.632889\pi\) | ||||
−0.405460 | + | 0.914113i | \(0.632889\pi\) | |||||||
\(152\) | 15.5564 | 1.26179 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.07103 | 0.166888 | ||||||||
\(155\) | −8.94517 | −0.718494 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.31971 | −0.743794 | −0.371897 | − | 0.928274i | \(-0.621292\pi\) | ||||
−0.371897 | + | 0.928274i | \(0.621292\pi\) | |||||||
\(158\) | −4.99093 | −0.397057 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −5.73264 | −0.453205 | ||||||||
\(161\) | 1.79193 | 0.141224 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.93727 | 0.700021 | 0.350010 | − | 0.936746i | \(-0.386178\pi\) | ||||
0.350010 | + | 0.936746i | \(0.386178\pi\) | |||||||
\(164\) | 11.9543 | 0.933470 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.20776 | −0.637046 | ||||||||
\(167\) | 16.3450 | 1.26482 | 0.632409 | − | 0.774635i | \(-0.282066\pi\) | ||||
0.632409 | + | 0.774635i | \(0.282066\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 3.46630 | 0.265853 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −13.8924 | −1.05929 | ||||||||
\(173\) | −11.0008 | −0.836374 | −0.418187 | − | 0.908361i | \(-0.637334\pi\) | ||||
−0.418187 | + | 0.908361i | \(0.637334\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.777184 | −0.0587496 | ||||||||
\(176\) | 6.54728 | 0.493520 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −7.71295 | −0.578110 | ||||||||
\(179\) | 2.87227 | 0.214683 | 0.107342 | − | 0.994222i | \(-0.465766\pi\) | ||||
0.107342 | + | 0.994222i | \(0.465766\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.8459 | −0.806169 | −0.403084 | − | 0.915163i | \(-0.632062\pi\) | ||||
−0.403084 | + | 0.915163i | \(0.632062\pi\) | |||||||
\(182\) | −0.509106 | −0.0377375 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.39335 | −0.397603 | ||||||||
\(185\) | −2.80592 | −0.206296 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −21.5258 | −1.57413 | ||||||||
\(188\) | −6.42151 | −0.468337 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.35646 | −0.316051 | ||||||||
\(191\) | −13.8954 | −1.00543 | −0.502716 | − | 0.864452i | \(-0.667666\pi\) | ||||
−0.502716 | + | 0.864452i | \(0.667666\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.7868 | 1.56825 | 0.784123 | − | 0.620606i | \(-0.213113\pi\) | ||||
0.784123 | + | 0.620606i | \(0.213113\pi\) | |||||||
\(194\) | 3.98631 | 0.286200 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 10.0474 | 0.717670 | ||||||||
\(197\) | 3.29282 | 0.234604 | 0.117302 | − | 0.993096i | \(-0.462575\pi\) | ||||
0.117302 | + | 0.993096i | \(0.462575\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.7792 | −1.40211 | −0.701055 | − | 0.713107i | \(-0.747287\pi\) | ||||
−0.701055 | + | 0.713107i | \(0.747287\pi\) | |||||||
\(200\) | 2.33917 | 0.165404 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.12623 | 0.431040 | ||||||||
\(203\) | 4.95856 | 0.348022 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.60986 | −0.531496 | ||||||||
\(206\) | 1.45075 | 0.101079 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.60947 | −0.111597 | ||||||||
\(209\) | 27.0537 | 1.87134 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.42809 | −0.167157 | −0.0835783 | − | 0.996501i | \(-0.526635\pi\) | ||||
−0.0835783 | + | 0.996501i | \(0.526635\pi\) | |||||||
\(212\) | −7.50925 | −0.515737 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −10.1525 | −0.694013 | ||||||||
\(215\) | 8.84366 | 0.603132 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.95204 | 0.471935 | ||||||||
\(218\) | 3.85361 | 0.260999 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6.39034 | −0.430836 | ||||||||
\(221\) | 5.29154 | 0.355947 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.45726 | −0.633305 | −0.316652 | − | 0.948542i | \(-0.602559\pi\) | ||||
−0.316652 | + | 0.948542i | \(0.602559\pi\) | |||||||
\(224\) | 4.45532 | 0.297683 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.92785 | 0.460834 | ||||||||
\(227\) | −24.0821 | −1.59839 | −0.799193 | − | 0.601074i | \(-0.794740\pi\) | ||||
−0.799193 | + | 0.601074i | \(0.794740\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.97401 | 0.659101 | 0.329550 | − | 0.944138i | \(-0.393103\pi\) | ||||
0.329550 | + | 0.944138i | \(0.393103\pi\) | |||||||
\(230\) | 1.51036 | 0.0995905 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −14.9243 | −0.979825 | ||||||||
\(233\) | −18.2730 | −1.19710 | −0.598552 | − | 0.801084i | \(-0.704257\pi\) | ||||
−0.598552 | + | 0.801084i | \(0.704257\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.08782 | 0.266660 | ||||||||
\(236\) | −7.44756 | −0.484795 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.69396 | −0.174623 | ||||||||
\(239\) | 26.5440 | 1.71699 | 0.858495 | − | 0.512822i | \(-0.171400\pi\) | ||||
0.858495 | + | 0.512822i | \(0.171400\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.4187 | 0.928791 | 0.464396 | − | 0.885628i | \(-0.346272\pi\) | ||||
0.464396 | + | 0.885628i | \(0.346272\pi\) | |||||||
\(242\) | −3.63457 | −0.233639 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 22.5674 | 1.44473 | ||||||||
\(245\) | −6.39599 | −0.408625 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.65042 | −0.423156 | ||||||||
\(248\) | −20.9242 | −1.32869 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.655066 | −0.0414300 | ||||||||
\(251\) | −13.7541 | −0.868148 | −0.434074 | − | 0.900877i | \(-0.642924\pi\) | ||||
−0.434074 | + | 0.900877i | \(0.642924\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.37940 | −0.589678 | ||||||||
\(254\) | 7.52496 | 0.472158 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.35300 | −0.522063 | ||||||||
\(257\) | 4.91358 | 0.306500 | 0.153250 | − | 0.988187i | \(-0.451026\pi\) | ||||
0.153250 | + | 0.988187i | \(0.451026\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.18072 | 0.135503 | ||||||||
\(260\) | 1.57089 | 0.0974224 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.24029 | 0.509087 | ||||||||
\(263\) | −26.0723 | −1.60769 | −0.803843 | − | 0.594841i | \(-0.797215\pi\) | ||||
−0.803843 | + | 0.594841i | \(0.797215\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.78025 | 0.293649 | ||||||||
\(266\) | 3.38577 | 0.207595 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −16.9453 | −1.03510 | ||||||||
\(269\) | −29.7277 | −1.81253 | −0.906263 | − | 0.422713i | \(-0.861078\pi\) | ||||
−0.906263 | + | 0.422713i | \(0.861078\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.2980 | 0.868540 | 0.434270 | − | 0.900783i | \(-0.357006\pi\) | ||||
0.434270 | + | 0.900783i | \(0.357006\pi\) | |||||||
\(272\) | −8.51658 | −0.516393 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.18701 | −0.0717098 | ||||||||
\(275\) | 4.06797 | 0.245308 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.87861 | 0.112875 | 0.0564373 | − | 0.998406i | \(-0.482026\pi\) | ||||
0.0564373 | + | 0.998406i | \(0.482026\pi\) | |||||||
\(278\) | 13.3702 | 0.801892 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.81796 | −0.108644 | ||||||||
\(281\) | −3.57185 | −0.213079 | −0.106539 | − | 0.994308i | \(-0.533977\pi\) | ||||
−0.106539 | + | 0.994308i | \(0.533977\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.7483 | −0.817249 | −0.408625 | − | 0.912703i | \(-0.633991\pi\) | ||||
−0.408625 | + | 0.912703i | \(0.633991\pi\) | |||||||
\(284\) | 0.483481 | 0.0286893 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.66479 | 0.157572 | ||||||||
\(287\) | 5.91426 | 0.349108 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.0004 | 0.647081 | ||||||||
\(290\) | 4.17942 | 0.245424 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 11.7917 | 0.690055 | ||||||||
\(293\) | 7.49807 | 0.438042 | 0.219021 | − | 0.975720i | \(-0.429714\pi\) | ||||
0.219021 | + | 0.975720i | \(0.429714\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.74099 | 0.276031 | ||||||||
\(296\) | −6.56352 | −0.381497 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.304028 | −0.0176119 | ||||||||
\(299\) | 2.30567 | 0.133340 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.87315 | −0.396162 | ||||||||
\(302\) | 6.52757 | 0.375619 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 10.7037 | 0.613897 | ||||||||
\(305\) | −14.3660 | −0.822594 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.4113 | −1.05079 | −0.525395 | − | 0.850858i | \(-0.676082\pi\) | ||||
−0.525395 | + | 0.850858i | \(0.676082\pi\) | |||||||
\(308\) | 4.96646 | 0.282991 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 5.85967 | 0.332807 | ||||||||
\(311\) | −17.2648 | −0.978996 | −0.489498 | − | 0.872004i | \(-0.662820\pi\) | ||||
−0.489498 | + | 0.872004i | \(0.662820\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.06061 | −0.512136 | −0.256068 | − | 0.966659i | \(-0.582427\pi\) | ||||
−0.256068 | + | 0.966659i | \(0.582427\pi\) | |||||||
\(314\) | 6.10502 | 0.344526 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −11.9686 | −0.673284 | ||||||||
\(317\) | −8.03887 | −0.451508 | −0.225754 | − | 0.974184i | \(-0.572485\pi\) | ||||
−0.225754 | + | 0.974184i | \(0.572485\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −25.9543 | −1.45316 | ||||||||
\(320\) | 0.536314 | 0.0299809 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.17383 | −0.0654150 | ||||||||
\(323\) | −35.1909 | −1.95808 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.00000 | −0.0554700 | ||||||||
\(326\) | −5.85450 | −0.324251 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −17.8007 | −0.982881 | ||||||||
\(329\) | −3.17699 | −0.175153 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −29.8664 | −1.64161 | −0.820803 | − | 0.571212i | \(-0.806473\pi\) | ||||
−0.820803 | + | 0.571212i | \(0.806473\pi\) | |||||||
\(332\) | −19.6827 | −1.08023 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −10.7071 | −0.585865 | ||||||||
\(335\) | 10.7871 | 0.589361 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.2087 | 1.31873 | 0.659366 | − | 0.751822i | \(-0.270825\pi\) | ||||
0.659366 | + | 0.751822i | \(0.270825\pi\) | |||||||
\(338\) | −0.655066 | −0.0356309 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 8.31242 | 0.450804 | ||||||||
\(341\) | −36.3887 | −1.97056 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.4111 | 0.562149 | ||||||||
\(344\) | 20.6868 | 1.11536 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.20624 | 0.387410 | ||||||||
\(347\) | 22.9143 | 1.23011 | 0.615053 | − | 0.788486i | \(-0.289135\pi\) | ||||
0.615053 | + | 0.788486i | \(0.289135\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.3575 | −0.661481 | −0.330740 | − | 0.943722i | \(-0.607298\pi\) | ||||
−0.330740 | + | 0.943722i | \(0.607298\pi\) | |||||||
\(350\) | 0.509106 | 0.0272129 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −23.3202 | −1.24297 | ||||||||
\(353\) | 27.0380 | 1.43909 | 0.719544 | − | 0.694447i | \(-0.244351\pi\) | ||||
0.719544 | + | 0.694447i | \(0.244351\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.307776 | −0.0163350 | ||||||||
\(356\) | −18.4961 | −0.980294 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.88152 | −0.0994417 | ||||||||
\(359\) | 28.4894 | 1.50361 | 0.751806 | − | 0.659384i | \(-0.229183\pi\) | ||||
0.751806 | + | 0.659384i | \(0.229183\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 25.2280 | 1.32779 | ||||||||
\(362\) | 7.10477 | 0.373418 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.22087 | −0.0639909 | ||||||||
\(365\) | −7.50636 | −0.392901 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −30.3201 | −1.58269 | −0.791347 | − | 0.611367i | \(-0.790620\pi\) | ||||
−0.791347 | + | 0.611367i | \(0.790620\pi\) | |||||||
\(368\) | −3.71091 | −0.193444 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.83806 | 0.0955563 | ||||||||
\(371\) | −3.71514 | −0.192880 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.33620 | −0.483410 | −0.241705 | − | 0.970350i | \(-0.577707\pi\) | ||||
−0.241705 | + | 0.970350i | \(0.577707\pi\) | |||||||
\(374\) | 14.1008 | 0.729137 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.56209 | 0.493127 | ||||||||
\(377\) | 6.38016 | 0.328595 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.5156 | −1.15655 | −0.578274 | − | 0.815843i | \(-0.696274\pi\) | ||||
−0.578274 | + | 0.815843i | \(0.696274\pi\) | |||||||
\(380\) | −10.4471 | −0.535923 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 9.10237 | 0.465718 | ||||||||
\(383\) | 3.03380 | 0.155020 | 0.0775100 | − | 0.996992i | \(-0.475303\pi\) | ||||
0.0775100 | + | 0.996992i | \(0.475303\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.16156 | −0.161128 | ||||||||
\(386\) | −14.2718 | −0.726413 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 9.55942 | 0.485306 | ||||||||
\(389\) | 18.2987 | 0.927782 | 0.463891 | − | 0.885892i | \(-0.346453\pi\) | ||||
0.463891 | + | 0.885892i | \(0.346453\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.2005 | 0.617008 | ||||||||
\(392\) | −14.9613 | −0.755658 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.15701 | −0.108669 | ||||||||
\(395\) | 7.61897 | 0.383352 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −29.4753 | −1.47932 | −0.739661 | − | 0.672980i | \(-0.765014\pi\) | ||||
−0.739661 | + | 0.672980i | \(0.765014\pi\) | |||||||
\(398\) | 12.9567 | 0.649459 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.60947 | 0.0804735 | ||||||||
\(401\) | 27.7675 | 1.38664 | 0.693322 | − | 0.720628i | \(-0.256146\pi\) | ||||
0.693322 | + | 0.720628i | \(0.256146\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.94517 | 0.445591 | ||||||||
\(404\) | 14.6911 | 0.730909 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.24818 | −0.161204 | ||||||||
\(407\) | −11.4144 | −0.565792 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.80833 | −0.484991 | −0.242495 | − | 0.970153i | \(-0.577966\pi\) | ||||
−0.242495 | + | 0.970153i | \(0.577966\pi\) | |||||||
\(410\) | 4.98496 | 0.246190 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.47900 | 0.171398 | ||||||||
\(413\) | −3.68462 | −0.181308 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.5297 | 0.615058 | ||||||||
\(416\) | 5.73264 | 0.281066 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −17.7220 | −0.866809 | ||||||||
\(419\) | −14.4829 | −0.707535 | −0.353768 | − | 0.935333i | \(-0.615100\pi\) | ||||
−0.353768 | + | 0.935333i | \(0.615100\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −35.8224 | −1.74587 | −0.872937 | − | 0.487832i | \(-0.837788\pi\) | ||||
−0.872937 | + | 0.487832i | \(0.837788\pi\) | |||||||
\(422\) | 1.59056 | 0.0774272 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 11.1818 | 0.543037 | ||||||||
\(425\) | −5.29154 | −0.256677 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.1650 | 0.540313 | ||||||||
\(428\) | −24.3464 | −1.17683 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5.79318 | −0.279372 | ||||||||
\(431\) | −7.34712 | −0.353898 | −0.176949 | − | 0.984220i | \(-0.556623\pi\) | ||||
−0.176949 | + | 0.984220i | \(0.556623\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.55302 | −0.314918 | −0.157459 | − | 0.987526i | \(-0.550330\pi\) | ||||
−0.157459 | + | 0.987526i | \(0.550330\pi\) | |||||||
\(434\) | −4.55404 | −0.218601 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.24119 | 0.442573 | ||||||||
\(437\) | −15.3337 | −0.733509 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.71109 | −0.0816657 | −0.0408329 | − | 0.999166i | \(-0.513001\pi\) | ||||
−0.0408329 | + | 0.999166i | \(0.513001\pi\) | |||||||
\(440\) | 9.51567 | 0.453642 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.46630 | −0.164875 | ||||||||
\(443\) | 22.0916 | 1.04960 | 0.524801 | − | 0.851225i | \(-0.324140\pi\) | ||||
0.524801 | + | 0.851225i | \(0.324140\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.7743 | 0.558156 | ||||||||
\(446\) | 6.19512 | 0.293348 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.416815 | −0.0196926 | ||||||||
\(449\) | −35.4082 | −1.67102 | −0.835508 | − | 0.549479i | \(-0.814826\pi\) | ||||
−0.835508 | + | 0.549479i | \(0.814826\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −30.9567 | −1.45770 | ||||||||
\(452\) | 16.6134 | 0.781430 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 15.7754 | 0.740375 | ||||||||
\(455\) | 0.777184 | 0.0364349 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.53430 | −0.118550 | −0.0592748 | − | 0.998242i | \(-0.518879\pi\) | ||||
−0.0592748 | + | 0.998242i | \(0.518879\pi\) | |||||||
\(458\) | −6.53363 | −0.305296 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.62195 | 0.168874 | ||||||||
\(461\) | 2.19744 | 0.102345 | 0.0511724 | − | 0.998690i | \(-0.483704\pi\) | ||||
0.0511724 | + | 0.998690i | \(0.483704\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.4537 | −1.18294 | −0.591468 | − | 0.806329i | \(-0.701451\pi\) | ||||
−0.591468 | + | 0.806329i | \(0.701451\pi\) | |||||||
\(464\) | −10.2687 | −0.476712 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 11.9700 | 0.554500 | ||||||||
\(467\) | 15.4769 | 0.716187 | 0.358093 | − | 0.933686i | \(-0.383427\pi\) | ||||
0.358093 | + | 0.933686i | \(0.383427\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.38353 | −0.387116 | ||||||||
\(470\) | −2.67779 | −0.123517 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 11.0900 | 0.510457 | ||||||||
\(473\) | 35.9758 | 1.65417 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.65042 | 0.305142 | ||||||||
\(476\) | −6.46028 | −0.296106 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −17.3881 | −0.795312 | ||||||||
\(479\) | 9.62232 | 0.439655 | 0.219828 | − | 0.975539i | \(-0.429451\pi\) | ||||
0.219828 | + | 0.975539i | \(0.429451\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.80592 | 0.127939 | ||||||||
\(482\) | −9.44521 | −0.430217 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.71593 | −0.396179 | ||||||||
\(485\) | −6.08536 | −0.276322 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.0963 | −0.910649 | −0.455325 | − | 0.890325i | \(-0.650477\pi\) | ||||
−0.455325 | + | 0.890325i | \(0.650477\pi\) | |||||||
\(488\) | −33.6044 | −1.52120 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4.18979 | 0.189275 | ||||||||
\(491\) | −2.96672 | −0.133886 | −0.0669430 | − | 0.997757i | \(-0.521325\pi\) | ||||
−0.0669430 | + | 0.997757i | \(0.521325\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 33.7609 | 1.52051 | ||||||||
\(494\) | 4.35646 | 0.196006 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −14.3970 | −0.646444 | ||||||||
\(497\) | 0.239198 | 0.0107295 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.9441 | 0.624224 | 0.312112 | − | 0.950045i | \(-0.398964\pi\) | ||||
0.312112 | + | 0.950045i | \(0.398964\pi\) | |||||||
\(500\) | −1.57089 | −0.0702523 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9.00981 | 0.402127 | ||||||||
\(503\) | 25.1391 | 1.12090 | 0.560448 | − | 0.828190i | \(-0.310629\pi\) | ||||
0.560448 | + | 0.828190i | \(0.310629\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.35209 | −0.416162 | ||||||||
\(506\) | 6.14412 | 0.273140 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 18.0453 | 0.800632 | ||||||||
\(509\) | 2.08157 | 0.0922639 | 0.0461320 | − | 0.998935i | \(-0.485311\pi\) | ||||
0.0461320 | + | 0.998935i | \(0.485311\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.83382 | 0.258073 | ||||||||
\(512\) | −16.7562 | −0.740525 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.21871 | −0.141971 | ||||||||
\(515\) | −2.21467 | −0.0975899 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16.6291 | 0.731349 | ||||||||
\(518\) | −1.42851 | −0.0627652 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.33917 | −0.102579 | ||||||||
\(521\) | 16.7112 | 0.732130 | 0.366065 | − | 0.930589i | \(-0.380705\pi\) | ||||
0.366065 | + | 0.930589i | \(0.380705\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 39.1071 | 1.71003 | 0.855016 | − | 0.518602i | \(-0.173547\pi\) | ||||
0.855016 | + | 0.518602i | \(0.173547\pi\) | |||||||
\(524\) | 19.7607 | 0.863252 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 17.0791 | 0.744683 | ||||||||
\(527\) | 47.3337 | 2.06189 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.6839 | −0.768865 | ||||||||
\(530\) | −3.13138 | −0.136018 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8.11929 | 0.352016 | ||||||||
\(533\) | 7.60986 | 0.329620 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.4985 | 0.670058 | ||||||||
\(536\) | 25.2328 | 1.08989 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 19.4736 | 0.839565 | ||||||||
\(539\) | −26.0187 | −1.12070 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.87732 | 0.209692 | 0.104846 | − | 0.994488i | \(-0.466565\pi\) | ||||
0.104846 | + | 0.994488i | \(0.466565\pi\) | |||||||
\(542\) | −9.36611 | −0.402309 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 30.3345 | 1.30058 | ||||||||
\(545\) | −5.88278 | −0.251991 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.9480 | −0.639128 | −0.319564 | − | 0.947565i | \(-0.603537\pi\) | ||||
−0.319564 | + | 0.947565i | \(0.603537\pi\) | |||||||
\(548\) | −2.84652 | −0.121597 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.66479 | −0.113627 | ||||||||
\(551\) | −42.4307 | −1.80761 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.92134 | −0.251801 | ||||||||
\(554\) | −1.23061 | −0.0522836 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 32.0626 | 1.35976 | ||||||||
\(557\) | 23.5505 | 0.997866 | 0.498933 | − | 0.866641i | \(-0.333725\pi\) | ||||
0.498933 | + | 0.866641i | \(0.333725\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.84366 | −0.374047 | ||||||||
\(560\) | −1.25085 | −0.0528583 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.33980 | 0.0986983 | ||||||||
\(563\) | 0.293153 | 0.0123549 | 0.00617747 | − | 0.999981i | \(-0.498034\pi\) | ||||
0.00617747 | + | 0.999981i | \(0.498034\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.5758 | −0.444928 | ||||||||
\(566\) | 9.00601 | 0.378551 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.719938 | −0.0302079 | ||||||||
\(569\) | −33.8631 | −1.41961 | −0.709807 | − | 0.704396i | \(-0.751218\pi\) | ||||
−0.709807 | + | 0.704396i | \(0.751218\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.0309 | −0.921963 | −0.460981 | − | 0.887410i | \(-0.652503\pi\) | ||||
−0.460981 | + | 0.887410i | \(0.652503\pi\) | |||||||
\(572\) | 6.39034 | 0.267193 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.87423 | −0.161707 | ||||||||
\(575\) | −2.30567 | −0.0961531 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.7846 | 0.990165 | 0.495083 | − | 0.868846i | \(-0.335138\pi\) | ||||
0.495083 | + | 0.868846i | \(0.335138\pi\) | |||||||
\(578\) | −7.20597 | −0.299729 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 10.0225 | 0.416163 | ||||||||
\(581\) | −9.73786 | −0.403995 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19.4459 | 0.805369 | ||||||||
\(584\) | −17.5586 | −0.726581 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.91173 | −0.202902 | ||||||||
\(587\) | −11.6973 | −0.482798 | −0.241399 | − | 0.970426i | \(-0.577606\pi\) | ||||
−0.241399 | + | 0.970426i | \(0.577606\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −59.4891 | −2.45121 | ||||||||
\(590\) | −3.10566 | −0.127858 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.51605 | −0.185609 | ||||||||
\(593\) | −14.5999 | −0.599545 | −0.299773 | − | 0.954011i | \(-0.596911\pi\) | ||||
−0.299773 | + | 0.954011i | \(0.596911\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.11250 | 0.168596 | ||||||||
\(596\) | −0.729080 | −0.0298643 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.51036 | −0.0617634 | ||||||||
\(599\) | −17.4884 | −0.714557 | −0.357278 | − | 0.933998i | \(-0.616295\pi\) | ||||
−0.357278 | + | 0.933998i | \(0.616295\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −44.7939 | −1.82718 | −0.913590 | − | 0.406636i | \(-0.866702\pi\) | ||||
−0.913590 | + | 0.406636i | \(0.866702\pi\) | |||||||
\(602\) | 4.50236 | 0.183503 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 15.6535 | 0.636933 | ||||||||
\(605\) | 5.54841 | 0.225575 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −42.3787 | −1.72010 | −0.860050 | − | 0.510209i | \(-0.829568\pi\) | ||||
−0.860050 | + | 0.510209i | \(0.829568\pi\) | |||||||
\(608\) | −38.1245 | −1.54615 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 9.41066 | 0.381026 | ||||||||
\(611\) | −4.08782 | −0.165375 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.73566 | −0.272051 | −0.136025 | − | 0.990705i | \(-0.543433\pi\) | ||||
−0.136025 | + | 0.990705i | \(0.543433\pi\) | |||||||
\(614\) | 12.0606 | 0.486727 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.39542 | −0.297970 | ||||||||
\(617\) | −14.7847 | −0.595211 | −0.297606 | − | 0.954689i | \(-0.596188\pi\) | ||||
−0.297606 | + | 0.954689i | \(0.596188\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 27.3795 | 1.10048 | 0.550239 | − | 0.835008i | \(-0.314537\pi\) | ||||
0.550239 | + | 0.835008i | \(0.314537\pi\) | |||||||
\(620\) | 14.0519 | 0.564337 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 11.3096 | 0.453472 | ||||||||
\(623\) | −9.15080 | −0.366619 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 5.93529 | 0.237222 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 14.6402 | 0.584209 | ||||||||
\(629\) | 14.8476 | 0.592014 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.2458 | 0.766162 | 0.383081 | − | 0.923715i | \(-0.374863\pi\) | ||||
0.383081 | + | 0.923715i | \(0.374863\pi\) | |||||||
\(632\) | 17.8220 | 0.708923 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 5.26599 | 0.209139 | ||||||||
\(635\) | −11.4873 | −0.455861 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.39599 | 0.253418 | ||||||||
\(638\) | 17.0018 | 0.673107 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 11.1140 | 0.439318 | ||||||||
\(641\) | 27.9161 | 1.10262 | 0.551310 | − | 0.834300i | \(-0.314128\pi\) | ||||
0.551310 | + | 0.834300i | \(0.314128\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.24764 | 0.128074 | 0.0640372 | − | 0.997948i | \(-0.479602\pi\) | ||||
0.0640372 | + | 0.997948i | \(0.479602\pi\) | |||||||
\(644\) | −2.81492 | −0.110923 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 23.0524 | 0.906983 | ||||||||
\(647\) | 1.47061 | 0.0578155 | 0.0289077 | − | 0.999582i | \(-0.490797\pi\) | ||||
0.0289077 | + | 0.999582i | \(0.490797\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19.2862 | 0.757050 | ||||||||
\(650\) | 0.655066 | 0.0256938 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −14.0395 | −0.549828 | ||||||||
\(653\) | 2.39978 | 0.0939107 | 0.0469554 | − | 0.998897i | \(-0.485048\pi\) | ||||
0.0469554 | + | 0.998897i | \(0.485048\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.5793 | −0.491515 | ||||||||
\(656\) | −12.2479 | −0.478198 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.08113 | 0.0811311 | ||||||||
\(659\) | 3.50745 | 0.136631 | 0.0683154 | − | 0.997664i | \(-0.478238\pi\) | ||||
0.0683154 | + | 0.997664i | \(0.478238\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.2946 | −0.789369 | −0.394685 | − | 0.918817i | \(-0.629146\pi\) | ||||
−0.394685 | + | 0.918817i | \(0.629146\pi\) | |||||||
\(662\) | 19.5644 | 0.760394 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 29.3090 | 1.13741 | ||||||||
\(665\) | −5.16860 | −0.200430 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.7105 | 0.569595 | ||||||||
\(668\) | −25.6763 | −0.993444 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −7.06624 | −0.272993 | ||||||||
\(671\) | −58.4404 | −2.25607 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.89110 | 0.381274 | 0.190637 | − | 0.981661i | \(-0.438945\pi\) | ||||
0.190637 | + | 0.981661i | \(0.438945\pi\) | |||||||
\(674\) | −15.8583 | −0.610838 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.57089 | −0.0604188 | ||||||||
\(677\) | −8.03421 | −0.308780 | −0.154390 | − | 0.988010i | \(-0.549341\pi\) | ||||
−0.154390 | + | 0.988010i | \(0.549341\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.72944 | 0.181499 | ||||||||
\(680\) | −12.3778 | −0.474667 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 23.8370 | 0.912766 | ||||||||
\(683\) | −0.652224 | −0.0249567 | −0.0124783 | − | 0.999922i | \(-0.503972\pi\) | ||||
−0.0124783 | + | 0.999922i | \(0.503972\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.81204 | 0.0692347 | ||||||||
\(686\) | −6.81998 | −0.260388 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 14.2336 | 0.542651 | ||||||||
\(689\) | −4.78025 | −0.182113 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 41.1289 | 1.56462 | 0.782308 | − | 0.622892i | \(-0.214042\pi\) | ||||
0.782308 | + | 0.622892i | \(0.214042\pi\) | |||||||
\(692\) | 17.2810 | 0.656926 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −15.0104 | −0.569786 | ||||||||
\(695\) | −20.4105 | −0.774214 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 40.2679 | 1.52526 | ||||||||
\(698\) | 8.09496 | 0.306399 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.22087 | 0.0461445 | ||||||||
\(701\) | −28.9154 | −1.09212 | −0.546060 | − | 0.837746i | \(-0.683873\pi\) | ||||
−0.546060 | + | 0.837746i | \(0.683873\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18.6606 | −0.703796 | ||||||||
\(704\) | 2.18171 | 0.0822264 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −17.7117 | −0.666588 | ||||||||
\(707\) | 7.26829 | 0.273352 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −38.2858 | −1.43785 | −0.718927 | − | 0.695086i | \(-0.755366\pi\) | ||||
−0.718927 | + | 0.695086i | \(0.755366\pi\) | |||||||
\(710\) | 0.201613 | 0.00756641 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 27.5421 | 1.03218 | ||||||||
\(713\) | 20.6246 | 0.772398 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.06797 | −0.152134 | ||||||||
\(716\) | −4.51202 | −0.168622 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −18.6624 | −0.696475 | ||||||||
\(719\) | 31.0939 | 1.15961 | 0.579803 | − | 0.814757i | \(-0.303130\pi\) | ||||
0.579803 | + | 0.814757i | \(0.303130\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.72120 | 0.0641009 | ||||||||
\(722\) | −16.5260 | −0.615035 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 17.0377 | 0.633201 | ||||||||
\(725\) | −6.38016 | −0.236953 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23.3504 | −0.866017 | −0.433008 | − | 0.901390i | \(-0.642548\pi\) | ||||
−0.433008 | + | 0.901390i | \(0.642548\pi\) | |||||||
\(728\) | 1.81796 | 0.0673782 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4.91716 | 0.181992 | ||||||||
\(731\) | −46.7966 | −1.73083 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.11626 | 0.0412301 | 0.0206150 | − | 0.999787i | \(-0.493438\pi\) | ||||
0.0206150 | + | 0.999787i | \(0.493438\pi\) | |||||||
\(734\) | 19.8616 | 0.733106 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 13.2176 | 0.487206 | ||||||||
\(737\) | 43.8815 | 1.61640 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.73962 | 0.0639930 | 0.0319965 | − | 0.999488i | \(-0.489813\pi\) | ||||
0.0319965 | + | 0.999488i | \(0.489813\pi\) | |||||||
\(740\) | 4.40779 | 0.162034 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.43366 | 0.0893424 | ||||||||
\(743\) | 27.2753 | 1.00063 | 0.500317 | − | 0.865842i | \(-0.333217\pi\) | ||||
0.500317 | + | 0.865842i | \(0.333217\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.464119 | 0.0170040 | ||||||||
\(746\) | 6.11582 | 0.223916 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 33.8147 | 1.23639 | ||||||||
\(749\) | −12.0452 | −0.440121 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32.6647 | 1.19195 | 0.595977 | − | 0.803002i | \(-0.296765\pi\) | ||||
0.595977 | + | 0.803002i | \(0.296765\pi\) | |||||||
\(752\) | 6.57923 | 0.239920 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −4.17942 | −0.152206 | ||||||||
\(755\) | −9.96476 | −0.362655 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 43.4319 | 1.57856 | 0.789279 | − | 0.614035i | \(-0.210455\pi\) | ||||
0.789279 | + | 0.614035i | \(0.210455\pi\) | |||||||
\(758\) | 14.7492 | 0.535715 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 15.5564 | 0.564291 | ||||||||
\(761\) | −49.4890 | −1.79397 | −0.896987 | − | 0.442058i | \(-0.854249\pi\) | ||||
−0.896987 | + | 0.442058i | \(0.854249\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.57200 | 0.165518 | ||||||||
\(764\) | 21.8281 | 0.789711 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.98734 | −0.0718055 | ||||||||
\(767\) | −4.74099 | −0.171187 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.04054 | −0.326010 | −0.163005 | − | 0.986625i | \(-0.552119\pi\) | ||||
−0.163005 | + | 0.986625i | \(0.552119\pi\) | |||||||
\(770\) | 2.07103 | 0.0746348 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −34.2246 | −1.23177 | ||||||||
\(773\) | 8.64817 | 0.311053 | 0.155527 | − | 0.987832i | \(-0.450293\pi\) | ||||
0.155527 | + | 0.987832i | \(0.450293\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.94517 | −0.321320 | ||||||||
\(776\) | −14.2347 | −0.510995 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −11.9869 | −0.429750 | ||||||||
\(779\) | −50.6088 | −1.81325 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.25202 | −0.0448009 | ||||||||
\(782\) | −7.99215 | −0.285799 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −10.2942 | −0.367648 | ||||||||
\(785\) | −9.31971 | −0.332635 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.3542 | 0.654258 | 0.327129 | − | 0.944980i | \(-0.393919\pi\) | ||||
0.327129 | + | 0.944980i | \(0.393919\pi\) | |||||||
\(788\) | −5.17266 | −0.184268 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −4.99093 | −0.177569 | ||||||||
\(791\) | 8.21935 | 0.292246 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.3660 | 0.510151 | ||||||||
\(794\) | 19.3082 | 0.685224 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 31.0709 | 1.10128 | ||||||||
\(797\) | −14.2529 | −0.504862 | −0.252431 | − | 0.967615i | \(-0.581230\pi\) | ||||
−0.252431 | + | 0.967615i | \(0.581230\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21.6309 | −0.765245 | ||||||||
\(800\) | −5.73264 | −0.202679 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −18.1896 | −0.642295 | ||||||||
\(803\) | −30.5357 | −1.07758 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.79193 | 0.0631572 | ||||||||
\(806\) | −5.85967 | −0.206398 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −21.8761 | −0.769598 | ||||||||
\(809\) | 2.15221 | 0.0756676 | 0.0378338 | − | 0.999284i | \(-0.487954\pi\) | ||||
0.0378338 | + | 0.999284i | \(0.487954\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −30.3748 | −1.06660 | −0.533302 | − | 0.845925i | \(-0.679049\pi\) | ||||
−0.533302 | + | 0.845925i | \(0.679049\pi\) | |||||||
\(812\) | −7.78934 | −0.273352 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 7.47719 | 0.262075 | ||||||||
\(815\) | 8.93727 | 0.313059 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 58.8140 | 2.05764 | ||||||||
\(818\) | 6.42510 | 0.224648 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 11.9543 | 0.417461 | ||||||||
\(821\) | 11.9606 | 0.417428 | 0.208714 | − | 0.977977i | \(-0.433072\pi\) | ||||
0.208714 | + | 0.977977i | \(0.433072\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.88386 | 0.135383 | 0.0676914 | − | 0.997706i | \(-0.478437\pi\) | ||||
0.0676914 | + | 0.997706i | \(0.478437\pi\) | |||||||
\(824\) | −5.18047 | −0.180470 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.41367 | 0.0839822 | ||||||||
\(827\) | 30.4261 | 1.05802 | 0.529010 | − | 0.848615i | \(-0.322563\pi\) | ||||
0.529010 | + | 0.848615i | \(0.322563\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23.8577 | −0.828613 | −0.414307 | − | 0.910137i | \(-0.635976\pi\) | ||||
−0.414307 | + | 0.910137i | \(0.635976\pi\) | |||||||
\(830\) | −8.20776 | −0.284896 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.536314 | −0.0185934 | ||||||||
\(833\) | 33.8446 | 1.17265 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.3450 | 0.565644 | ||||||||
\(836\) | −42.4984 | −1.46984 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 9.48724 | 0.327731 | ||||||||
\(839\) | 19.0333 | 0.657103 | 0.328552 | − | 0.944486i | \(-0.393439\pi\) | ||||
0.328552 | + | 0.944486i | \(0.393439\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.7064 | 0.403671 | ||||||||
\(842\) | 23.4660 | 0.808691 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.81426 | 0.131292 | ||||||||
\(845\) | 1.00000 | 0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.31213 | −0.148167 | ||||||||
\(848\) | 7.69368 | 0.264202 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.46630 | 0.118893 | ||||||||
\(851\) | 6.46953 | 0.221773 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.0527 | 0.720832 | 0.360416 | − | 0.932792i | \(-0.382635\pi\) | ||||
0.360416 | + | 0.932792i | \(0.382635\pi\) | |||||||
\(854\) | −7.31381 | −0.250273 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 36.2536 | 1.23912 | ||||||||
\(857\) | 9.88134 | 0.337540 | 0.168770 | − | 0.985655i | \(-0.446020\pi\) | ||||
0.168770 | + | 0.985655i | \(0.446020\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.82391 | −0.335187 | −0.167594 | − | 0.985856i | \(-0.553600\pi\) | ||||
−0.167594 | + | 0.985856i | \(0.553600\pi\) | |||||||
\(860\) | −13.8924 | −0.473727 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.81285 | 0.163926 | ||||||||
\(863\) | −46.5764 | −1.58548 | −0.792739 | − | 0.609561i | \(-0.791346\pi\) | ||||
−0.792739 | + | 0.609561i | \(0.791346\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.0008 | −0.374038 | ||||||||
\(866\) | 4.29266 | 0.145870 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −10.9209 | −0.370679 | ||||||||
\(869\) | 30.9938 | 1.05139 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.7871 | −0.365506 | ||||||||
\(872\) | −13.7608 | −0.465999 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 10.0446 | 0.339762 | ||||||||
\(875\) | −0.777184 | −0.0262736 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −55.8285 | −1.88520 | −0.942598 | − | 0.333931i | \(-0.891625\pi\) | ||||
−0.942598 | + | 0.333931i | \(0.891625\pi\) | |||||||
\(878\) | 1.12087 | 0.0378277 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 6.54728 | 0.220709 | ||||||||
\(881\) | −1.22939 | −0.0414192 | −0.0207096 | − | 0.999786i | \(-0.506593\pi\) | ||||
−0.0207096 | + | 0.999786i | \(0.506593\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.89957 | −0.198536 | −0.0992681 | − | 0.995061i | \(-0.531650\pi\) | ||||
−0.0992681 | + | 0.995061i | \(0.531650\pi\) | |||||||
\(884\) | −8.31242 | −0.279577 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −14.4714 | −0.486177 | ||||||||
\(887\) | 42.4663 | 1.42588 | 0.712939 | − | 0.701226i | \(-0.247364\pi\) | ||||
0.712939 | + | 0.701226i | \(0.247364\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.92777 | 0.299428 | ||||||||
\(890\) | −7.71295 | −0.258539 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 14.8563 | 0.497426 | ||||||||
\(893\) | 27.1857 | 0.909735 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.87227 | 0.0960094 | ||||||||
\(896\) | −8.63759 | −0.288562 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 23.1947 | 0.774016 | ||||||||
\(899\) | 57.0716 | 1.90345 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −25.2949 | −0.842695 | ||||||||
\(902\) | 20.2787 | 0.675206 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −24.7386 | −0.822793 | ||||||||
\(905\) | −10.8459 | −0.360530 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.1772 | −0.371134 | −0.185567 | − | 0.982632i | \(-0.559412\pi\) | ||||
−0.185567 | + | 0.982632i | \(0.559412\pi\) | |||||||
\(908\) | 37.8304 | 1.25544 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.509106 | −0.0168767 | ||||||||
\(911\) | 28.0289 | 0.928638 | 0.464319 | − | 0.885668i | \(-0.346299\pi\) | ||||
0.464319 | + | 0.885668i | \(0.346299\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 50.9704 | 1.68687 | ||||||||
\(914\) | 1.66013 | 0.0549123 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −15.6681 | −0.517687 | ||||||||
\(917\) | 9.77645 | 0.322847 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 43.1860 | 1.42457 | 0.712287 | − | 0.701888i | \(-0.247659\pi\) | ||||
0.712287 | + | 0.701888i | \(0.247659\pi\) | |||||||
\(920\) | −5.39335 | −0.177813 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.43946 | −0.0474062 | ||||||||
\(923\) | 0.307776 | 0.0101306 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.80592 | −0.0922582 | ||||||||
\(926\) | 16.6739 | 0.547937 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 36.5752 | 1.20064 | ||||||||
\(929\) | 18.3836 | 0.603146 | 0.301573 | − | 0.953443i | \(-0.402488\pi\) | ||||
0.301573 | + | 0.953443i | \(0.402488\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −42.5360 | −1.39406 | ||||||||
\(932\) | 28.7049 | 0.940259 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −10.1384 | −0.331739 | ||||||||
\(935\) | −21.5258 | −0.703970 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.2414 | −0.432579 | −0.216289 | − | 0.976329i | \(-0.569395\pi\) | ||||
−0.216289 | + | 0.976329i | \(0.569395\pi\) | |||||||
\(938\) | 5.49176 | 0.179312 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6.42151 | −0.209447 | ||||||||
\(941\) | −15.3309 | −0.499774 | −0.249887 | − | 0.968275i | \(-0.580394\pi\) | ||||
−0.249887 | + | 0.968275i | \(0.580394\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 17.5458 | 0.571371 | ||||||||
\(944\) | 7.63048 | 0.248351 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −23.5665 | −0.766213 | ||||||||
\(947\) | −44.0956 | −1.43291 | −0.716457 | − | 0.697631i | \(-0.754237\pi\) | ||||
−0.716457 | + | 0.697631i | \(0.754237\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.50636 | 0.243667 | ||||||||
\(950\) | −4.35646 | −0.141342 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 9.61982 | 0.311780 | ||||||||
\(953\) | 23.1623 | 0.750300 | 0.375150 | − | 0.926964i | \(-0.377591\pi\) | ||||
0.375150 | + | 0.926964i | \(0.377591\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.8954 | −0.449643 | ||||||||
\(956\) | −41.6977 | −1.34860 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −6.30325 | −0.203649 | ||||||||
\(959\) | −1.40829 | −0.0454761 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 49.0161 | 1.58116 | ||||||||
\(962\) | −1.83806 | −0.0592615 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −22.6502 | −0.729514 | ||||||||
\(965\) | 21.7868 | 0.701341 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28.8356 | −0.927289 | −0.463644 | − | 0.886021i | \(-0.653458\pi\) | ||||
−0.463644 | + | 0.886021i | \(0.653458\pi\) | |||||||
\(968\) | 12.9786 | 0.417150 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.98631 | 0.127993 | ||||||||
\(971\) | 1.72410 | 0.0553290 | 0.0276645 | − | 0.999617i | \(-0.491193\pi\) | ||||
0.0276645 | + | 0.999617i | \(0.491193\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.8627 | 0.508535 | ||||||||
\(974\) | 13.1644 | 0.421814 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −23.1216 | −0.740105 | ||||||||
\(977\) | −3.18384 | −0.101860 | −0.0509301 | − | 0.998702i | \(-0.516219\pi\) | ||||
−0.0509301 | + | 0.998702i | \(0.516219\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 47.8976 | 1.53081 | ||||||||
\(980\) | 10.0474 | 0.320952 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.94339 | 0.0620162 | ||||||||
\(983\) | −11.7189 | −0.373776 | −0.186888 | − | 0.982381i | \(-0.559840\pi\) | ||||
−0.186888 | + | 0.982381i | \(0.559840\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.29282 | 0.104918 | ||||||||
\(986\) | −22.1156 | −0.704304 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 10.4471 | 0.332365 | ||||||||
\(989\) | −20.3906 | −0.648382 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.8521 | 1.45654 | 0.728271 | − | 0.685290i | \(-0.240324\pi\) | ||||
0.728271 | + | 0.685290i | \(0.240324\pi\) | |||||||
\(992\) | 51.2795 | 1.62812 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −0.156690 | −0.00496992 | ||||||||
\(995\) | −19.7792 | −0.627043 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24.1678 | −0.765402 | −0.382701 | − | 0.923872i | \(-0.625006\pi\) | ||||
−0.382701 | + | 0.923872i | \(0.625006\pi\) | |||||||
\(998\) | −9.13431 | −0.289141 | ||||||||
\(999\) | 0 | 0 |
(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 | 5265.2.a.ba.1.4 | 8 | ||
3.2 | odd | 2 | 5265.2.a.bf.1.5 | 8 | |||
9.2 | odd | 6 | 585.2.i.e.391.4 | yes | 16 | ||
9.4 | even | 3 | 1755.2.i.f.586.5 | 16 | |||
9.5 | odd | 6 | 585.2.i.e.196.4 | ✓ | 16 | ||
9.7 | even | 3 | 1755.2.i.f.1171.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
585.2.i.e.196.4 | ✓ | 16 | 9.5 | odd | 6 | ||
585.2.i.e.391.4 | yes | 16 | 9.2 | odd | 6 | ||
1755.2.i.f.586.5 | 16 | 9.4 | even | 3 | |||
1755.2.i.f.1171.5 | 16 | 9.7 | even | 3 | |||
5265.2.a.ba.1.4 | 8 | 1.1 | even | 1 | trivial | ||
5265.2.a.bf.1.5 | 8 | 3.2 | odd | 2 |