Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [464,2,Mod(1,464)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(464, 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("464.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 464 = 2^{4} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 464.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: | \(3.70505865379\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.568.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 232) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.76156\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 464.1 |
$q$-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 | 0 | ||||||||
\(3\) | −2.76156 | −1.59439 | −0.797193 | − | 0.603725i | \(-0.793683\pi\) | ||||
−0.797193 | + | 0.603725i | \(0.793683\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.62620 | −0.727258 | −0.363629 | − | 0.931544i | \(-0.618462\pi\) | ||||
−0.363629 | + | 0.931544i | \(0.618462\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.62620 | 1.54207 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.49084 | −1.35404 | −0.677019 | − | 0.735965i | \(-0.736729\pi\) | ||||
−0.677019 | + | 0.735965i | \(0.736729\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.103084 | 0.0285903 | 0.0142951 | − | 0.999898i | \(-0.495450\pi\) | ||||
0.0142951 | + | 0.999898i | \(0.495450\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.49084 | 1.15953 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.00000 | 0.485071 | 0.242536 | − | 0.970143i | \(-0.422021\pi\) | ||||
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.25240 | 1.66381 | 0.831907 | − | 0.554915i | \(-0.187249\pi\) | ||||
0.831907 | + | 0.554915i | \(0.187249\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.52311 | 1.15165 | 0.575824 | − | 0.817573i | \(-0.304681\pi\) | ||||
0.575824 | + | 0.817573i | \(0.304681\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.35548 | −0.471096 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.49084 | −0.864262 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.76156 | 1.21441 | 0.607206 | − | 0.794545i | \(-0.292290\pi\) | ||||
0.607206 | + | 0.794545i | \(0.292290\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 12.4017 | 2.15886 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.25240 | 0.863489 | 0.431744 | − | 0.901996i | \(-0.357898\pi\) | ||||
0.431744 | + | 0.901996i | \(0.357898\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.284672 | −0.0455839 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.79383 | 0.904845 | 0.452422 | − | 0.891804i | \(-0.350560\pi\) | ||||
0.452422 | + | 0.891804i | \(0.350560\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.0140 | 1.52711 | 0.763557 | − | 0.645741i | \(-0.223451\pi\) | ||||
0.763557 | + | 0.645741i | \(0.223451\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7.52311 | −1.12148 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.5371 | −1.68285 | −0.841427 | − | 0.540371i | \(-0.818284\pi\) | ||||
−0.841427 | + | 0.540371i | \(0.818284\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.00000 | −1.00000 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.52311 | −0.773391 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.14931 | −0.982034 | −0.491017 | − | 0.871150i | \(-0.663375\pi\) | ||||
−0.491017 | + | 0.871150i | \(0.663375\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.30299 | 0.984735 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −20.0279 | −2.65276 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.52311 | 0.198293 | 0.0991463 | − | 0.995073i | \(-0.468389\pi\) | ||||
0.0991463 | + | 0.995073i | \(0.468389\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.04623 | 1.15825 | 0.579125 | − | 0.815238i | \(-0.303394\pi\) | ||||
0.579125 | + | 0.815238i | \(0.303394\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.167635 | −0.0207925 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15.0462 | −1.83819 | −0.919095 | − | 0.394037i | \(-0.871078\pi\) | ||||
−0.919095 | + | 0.394037i | \(0.871078\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −15.2524 | −1.83617 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.0279 | 1.42745 | 0.713725 | − | 0.700426i | \(-0.247007\pi\) | ||||
0.713725 | + | 0.700426i | \(0.247007\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.79383 | −0.209952 | −0.104976 | − | 0.994475i | \(-0.533477\pi\) | ||||
−0.104976 | + | 0.994475i | \(0.533477\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.50479 | 0.751109 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.98605 | 0.223448 | 0.111724 | − | 0.993739i | \(-0.464363\pi\) | ||||
0.111724 | + | 0.993739i | \(0.464363\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.47689 | −0.164098 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.47689 | −0.710931 | −0.355465 | − | 0.934689i | \(-0.615678\pi\) | ||||
−0.355465 | + | 0.934689i | \(0.615678\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.25240 | −0.352772 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.76156 | −0.296070 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.7110 | 1.34736 | 0.673680 | − | 0.739024i | \(-0.264713\pi\) | ||||
0.673680 | + | 0.739024i | \(0.264713\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −18.6724 | −1.93624 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −11.7938 | −1.21002 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.25240 | 0.127162 | 0.0635808 | − | 0.997977i | \(-0.479748\pi\) | ||||
0.0635808 | + | 0.997977i | \(0.479748\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −20.7755 | −2.08802 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.2986 | 1.62177 | 0.810887 | − | 0.585203i | \(-0.198985\pi\) | ||||
0.810887 | + | 0.585203i | \(0.198985\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.52311 | 0.544209 | 0.272104 | − | 0.962268i | \(-0.412280\pi\) | ||||
0.272104 | + | 0.962268i | \(0.412280\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.541436 | −0.0523426 | −0.0261713 | − | 0.999657i | \(-0.508332\pi\) | ||||
−0.0261713 | + | 0.999657i | \(0.508332\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.9248 | 1.52532 | 0.762661 | − | 0.646799i | \(-0.223893\pi\) | ||||
0.762661 | + | 0.646799i | \(0.223893\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −14.5048 | −1.37673 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.5048 | −1.17635 | −0.588176 | − | 0.808733i | \(-0.700154\pi\) | ||||
−0.588176 | + | 0.808733i | \(0.700154\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.98168 | −0.837546 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.476886 | 0.0440881 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.16763 | 0.833421 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −16.0000 | −1.44267 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.9615 | 1.06987 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.206167 | 0.0182944 | 0.00914720 | − | 0.999958i | \(-0.497088\pi\) | ||||
0.00914720 | + | 0.999958i | \(0.497088\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −27.6541 | −2.43481 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.2524 | −1.33261 | −0.666304 | − | 0.745680i | \(-0.732125\pi\) | ||||
−0.666304 | + | 0.745680i | \(0.732125\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 7.30299 | 0.628542 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.25240 | −0.448742 | −0.224371 | − | 0.974504i | \(-0.572033\pi\) | ||||
−0.224371 | + | 0.974504i | \(0.572033\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.5693 | 1.06612 | 0.533059 | − | 0.846078i | \(-0.321042\pi\) | ||||
0.533059 | + | 0.846078i | \(0.321042\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 31.8603 | 2.68312 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.462932 | −0.0387123 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.62620 | −0.135048 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 19.3309 | 1.59439 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.309251 | −0.0253348 | −0.0126674 | − | 0.999920i | \(-0.504032\pi\) | ||||
−0.0126674 | + | 0.999920i | \(0.504032\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.4586 | 0.932485 | 0.466242 | − | 0.884657i | \(-0.345607\pi\) | ||||
0.466242 | + | 0.884657i | \(0.345607\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 9.25240 | 0.748012 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.9956 | −0.883190 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.2524 | 1.05766 | 0.528828 | − | 0.848729i | \(-0.322632\pi\) | ||||
0.528828 | + | 0.848729i | \(0.322632\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 19.7432 | 1.56574 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.17389 | 0.248598 | 0.124299 | − | 0.992245i | \(-0.460332\pi\) | ||||
0.124299 | + | 0.992245i | \(0.460332\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −20.1676 | −1.57005 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.0279 | 0.930747 | 0.465374 | − | 0.885114i | \(-0.345920\pi\) | ||||
0.465374 | + | 0.885114i | \(0.345920\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9894 | −0.999183 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 33.5510 | 2.56571 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.5048 | 0.950722 | 0.475361 | − | 0.879791i | \(-0.342318\pi\) | ||||
0.475361 | + | 0.879791i | \(0.342318\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.20617 | −0.316155 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.02791 | −0.600034 | −0.300017 | − | 0.953934i | \(-0.596992\pi\) | ||||
−0.300017 | + | 0.953934i | \(0.596992\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.9248 | −0.886365 | −0.443183 | − | 0.896431i | \(-0.646151\pi\) | ||||
−0.443183 | + | 0.896431i | \(0.646151\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −24.9817 | −1.84670 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.54144 | −0.627979 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.98168 | −0.656805 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.71096 | −0.485588 | −0.242794 | − | 0.970078i | \(-0.578064\pi\) | ||||
−0.242794 | + | 0.970078i | \(0.578064\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.2986 | 0.885274 | 0.442637 | − | 0.896701i | \(-0.354043\pi\) | ||||
0.442637 | + | 0.896701i | \(0.354043\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.462932 | 0.0331513 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.50479 | 0.320953 | 0.160477 | − | 0.987040i | \(-0.448697\pi\) | ||||
0.160477 | + | 0.987040i | \(0.448697\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.4586 | 1.37938 | 0.689690 | − | 0.724104i | \(-0.257747\pi\) | ||||
0.689690 | + | 0.724104i | \(0.257747\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 41.5510 | 2.93078 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.42192 | −0.658055 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 25.5510 | 1.77592 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −32.5693 | −2.25287 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.77988 | −0.122532 | −0.0612660 | − | 0.998121i | \(-0.519514\pi\) | ||||
−0.0612660 | + | 0.998121i | \(0.519514\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −33.2158 | −2.27591 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −16.2847 | −1.11061 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.95377 | 0.334745 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.206167 | 0.0138683 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −26.5327 | −1.77676 | −0.888380 | − | 0.459108i | \(-0.848169\pi\) | ||||
−0.888380 | + | 0.459108i | \(0.848169\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −10.8969 | −0.726461 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.39401 | 0.358013 | 0.179007 | − | 0.983848i | \(-0.442712\pi\) | ||||
0.179007 | + | 0.983848i | \(0.442712\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.2986 | 1.07704 | 0.538522 | − | 0.842612i | \(-0.318983\pi\) | ||||
0.538522 | + | 0.842612i | \(0.318983\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.64452 | 0.566321 | 0.283161 | − | 0.959072i | \(-0.408617\pi\) | ||||
0.283161 | + | 0.959072i | \(0.408617\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 18.7616 | 1.22387 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.48458 | −0.356262 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.5231 | −0.874738 | −0.437369 | − | 0.899282i | \(-0.644090\pi\) | ||||
−0.437369 | + | 0.899282i | \(0.644090\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.30925 | 0.535246 | 0.267623 | − | 0.963524i | \(-0.413762\pi\) | ||||
0.267623 | + | 0.963524i | \(0.413762\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 17.5510 | 1.12590 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 11.3834 | 0.727258 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.747604 | 0.0475689 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 17.8863 | 1.13350 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.7432 | 1.24618 | 0.623091 | − | 0.782149i | \(-0.285877\pi\) | ||||
0.623091 | + | 0.782149i | \(0.285877\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −24.8034 | −1.55938 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8.98168 | 0.562454 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 21.4200 | 1.33614 | 0.668072 | − | 0.744096i | \(-0.267120\pi\) | ||||
0.668072 | + | 0.744096i | \(0.267120\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.62620 | 0.286354 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.2847 | −0.757505 | −0.378753 | − | 0.925498i | \(-0.623647\pi\) | ||||
−0.378753 | + | 0.925498i | \(0.623647\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.6262 | 0.714192 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −35.1020 | −2.14821 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −22.5972 | −1.37778 | −0.688889 | − | 0.724867i | \(-0.741901\pi\) | ||||
−0.688889 | + | 0.724867i | \(0.741901\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.7432 | 1.44230 | 0.721149 | − | 0.692780i | \(-0.243614\pi\) | ||||
0.721149 | + | 0.692780i | \(0.243614\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.5781 | 0.637882 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.58767 | −0.0953936 | −0.0476968 | − | 0.998862i | \(-0.515188\pi\) | ||||
−0.0476968 | + | 0.998862i | \(0.515188\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 31.2803 | 1.87270 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.8969 | −1.18695 | −0.593475 | − | 0.804852i | \(-0.702245\pi\) | ||||
−0.593475 | + | 0.804852i | \(0.702245\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.9817 | −1.24723 | −0.623616 | − | 0.781731i | \(-0.714337\pi\) | ||||
−0.623616 | + | 0.781731i | \(0.714337\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 32.5693 | 1.92924 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.45856 | −0.202745 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.50479 | 0.263173 | 0.131586 | − | 0.991305i | \(-0.457993\pi\) | ||||
0.131586 | + | 0.991305i | \(0.457993\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.47689 | −0.144210 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 20.1676 | 1.17024 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.569343 | 0.0329260 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −45.0096 | −2.58573 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −14.7110 | −0.842347 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.60162 | 0.547993 | 0.273997 | − | 0.961731i | \(-0.411654\pi\) | ||||
0.273997 | + | 0.961731i | \(0.411654\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.2524 | −0.867679 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 30.2986 | 1.71808 | 0.859039 | − | 0.511911i | \(-0.171062\pi\) | ||||
0.859039 | + | 0.511911i | \(0.171062\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.37380 | 0.134175 | 0.0670876 | − | 0.997747i | \(-0.478629\pi\) | ||||
0.0670876 | + | 0.997747i | \(0.478629\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.5510 | −0.648770 | −0.324385 | − | 0.945925i | \(-0.605157\pi\) | ||||
−0.324385 | + | 0.945925i | \(0.605157\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.49084 | −0.251439 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.49521 | 0.0834544 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.5048 | 0.807068 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.242812 | −0.0134688 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −43.9773 | −2.43195 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.3126 | 0.676761 | 0.338380 | − | 0.941009i | \(-0.390121\pi\) | ||||
0.338380 | + | 0.941009i | \(0.390121\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 24.2986 | 1.33156 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 24.4681 | 1.33684 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.95377 | 0.378796 | 0.189398 | − | 0.981900i | \(-0.439346\pi\) | ||||
0.189398 | + | 0.981900i | \(0.439346\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 34.5327 | 1.87556 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −30.3651 | −1.64436 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 24.8034 | 1.33537 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.4402 | 0.882558 | 0.441279 | − | 0.897370i | \(-0.354525\pi\) | ||||
0.441279 | + | 0.897370i | \(0.354525\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.9431 | 1.22812 | 0.614059 | − | 0.789260i | \(-0.289536\pi\) | ||||
0.614059 | + | 0.789260i | \(0.289536\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.462932 | −0.0247095 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.09246 | 0.430718 | 0.215359 | − | 0.976535i | \(-0.430908\pi\) | ||||
0.215359 | + | 0.976535i | \(0.430908\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −19.5598 | −1.03812 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −20.5187 | −1.08294 | −0.541469 | − | 0.840721i | \(-0.682132\pi\) | ||||
−0.541469 | + | 0.840721i | \(0.682132\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 33.5972 | 1.76828 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −25.3169 | −1.32880 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.91713 | 0.152689 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.75719 | −0.0917245 | −0.0458622 | − | 0.998948i | \(-0.514604\pi\) | ||||
−0.0458622 | + | 0.998948i | \(0.514604\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 26.8034 | 1.39533 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 28.1310 | 1.45657 | 0.728284 | − | 0.685276i | \(-0.240318\pi\) | ||||
0.728284 | + | 0.685276i | \(0.240318\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −33.0323 | −1.70578 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.103084 | 0.00530908 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.8034 | −1.27407 | −0.637033 | − | 0.770837i | \(-0.719839\pi\) | ||||
−0.637033 | + | 0.770837i | \(0.719839\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.569343 | −0.0291683 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −30.5048 | −1.55872 | −0.779361 | − | 0.626575i | \(-0.784456\pi\) | ||||
−0.779361 | + | 0.626575i | \(0.784456\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 46.3265 | 2.35491 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −32.8401 | −1.66506 | −0.832529 | − | 0.553982i | \(-0.813108\pi\) | ||||
−0.832529 | + | 0.553982i | \(0.813108\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.0462 | 0.558632 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 42.1204 | 2.12469 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.22971 | −0.162504 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −28.3372 | −1.42220 | −0.711101 | − | 0.703090i | \(-0.751803\pi\) | ||||
−0.711101 | + | 0.703090i | \(0.751803\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.94315 | −0.346724 | −0.173362 | − | 0.984858i | \(-0.555463\pi\) | ||||
−0.173362 | + | 0.984858i | \(0.555463\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.697006 | 0.0347204 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.40171 | 0.119342 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −23.5877 | −1.16920 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −39.1387 | −1.93528 | −0.967642 | − | 0.252328i | \(-0.918804\pi\) | ||||
−0.967642 | + | 0.252328i | \(0.918804\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.5048 | 0.715469 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.5327 | 0.517030 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −34.7110 | −1.69980 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.6156 | −0.762871 | −0.381435 | − | 0.924396i | \(-0.624570\pi\) | ||||
−0.381435 | + | 0.924396i | \(0.624570\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.50479 | −0.414498 | −0.207249 | − | 0.978288i | \(-0.566451\pi\) | ||||
−0.207249 | + | 0.978288i | \(0.566451\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −53.3728 | −2.59507 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.71096 | −0.228515 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.27841 | 0.0617224 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.60599 | 0.318199 | 0.159100 | − | 0.987263i | \(-0.449141\pi\) | ||||
0.159100 | + | 0.987263i | \(0.449141\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.20617 | −0.106022 | −0.0530108 | − | 0.998594i | \(-0.516882\pi\) | ||||
−0.0530108 | + | 0.998594i | \(0.516882\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.49084 | 0.215319 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 40.0558 | 1.91613 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.44024 | −0.211921 | −0.105961 | − | 0.994370i | \(-0.533792\pi\) | ||||
−0.105961 | + | 0.994370i | \(0.533792\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −32.3834 | −1.54207 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 21.7572 | 1.03372 | 0.516858 | − | 0.856071i | \(-0.327102\pi\) | ||||
0.516858 | + | 0.856071i | \(0.327102\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −20.6705 | −0.979877 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.854015 | 0.0403935 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −34.5972 | −1.63275 | −0.816373 | − | 0.577526i | \(-0.804018\pi\) | ||||
−0.816373 | + | 0.577526i | \(0.804018\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −26.0192 | −1.22519 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −31.6435 | −1.48674 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −28.0925 | −1.31411 | −0.657055 | − | 0.753843i | \(-0.728198\pi\) | ||||
−0.657055 | + | 0.753843i | \(0.728198\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −8.98168 | −0.419229 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.91713 | −0.415312 | −0.207656 | − | 0.978202i | \(-0.566583\pi\) | ||||
−0.207656 | + | 0.978202i | \(0.566583\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.55976 | −0.165436 | −0.0827180 | − | 0.996573i | \(-0.526360\pi\) | ||||
−0.0827180 | + | 0.996573i | \(0.526360\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 30.3651 | 1.40815 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.0968 | 0.513500 | 0.256750 | − | 0.966478i | \(-0.417348\pi\) | ||||
0.256750 | + | 0.966478i | \(0.417348\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −36.5972 | −1.68631 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −44.9711 | −2.06777 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −17.0829 | −0.783816 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −33.0741 | −1.51436 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.77988 | 0.264089 | 0.132045 | − | 0.991244i | \(-0.457846\pi\) | ||||
0.132045 | + | 0.991244i | \(0.457846\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.541436 | 0.0246874 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.03664 | −0.0924792 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.0462 | −0.500552 | −0.250276 | − | 0.968174i | \(-0.580521\pi\) | ||||
−0.250276 | + | 0.968174i | \(0.580521\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.76488 | −0.396362 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.03228 | 0.407621 | 0.203810 | − | 0.979010i | \(-0.434667\pi\) | ||||
0.203810 | + | 0.979010i | \(0.434667\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.00000 | 0.0900755 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 33.7851 | 1.51853 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 39.6156 | 1.77344 | 0.886718 | − | 0.462310i | \(-0.152979\pi\) | ||||
0.886718 | + | 0.462310i | \(0.152979\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −33.2158 | −1.48397 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 26.7895 | 1.19448 | 0.597242 | − | 0.802061i | \(-0.296263\pi\) | ||||
0.597242 | + | 0.802061i | \(0.296263\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −26.5048 | −1.17945 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 35.8709 | 1.59308 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.1127 | −0.758506 | −0.379253 | − | 0.925293i | \(-0.623819\pi\) | ||||
−0.379253 | + | 0.925293i | \(0.623819\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −32.5693 | −1.43797 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.98168 | −0.395780 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 51.8111 | 2.27865 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −34.5327 | −1.51582 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.5896 | 0.858234 | 0.429117 | − | 0.903249i | \(-0.358825\pi\) | ||||
0.429117 | + | 0.903249i | \(0.358825\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.0462 | −0.657926 | −0.328963 | − | 0.944343i | \(-0.606699\pi\) | ||||
−0.328963 | + | 0.944343i | \(0.606699\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 13.5231 | 0.589076 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.50479 | 0.326295 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.04623 | 0.305780 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.597250 | 0.0258698 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.880483 | 0.0380666 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 22.1695 | 0.956686 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 31.4359 | 1.35404 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.2158 | 1.34207 | 0.671035 | − | 0.741426i | \(-0.265850\pi\) | ||||
0.671035 | + | 0.741426i | \(0.265850\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 32.9311 | 1.41321 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −25.8969 | −1.10930 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.5048 | −0.449152 | −0.224576 | − | 0.974457i | \(-0.572100\pi\) | ||||
−0.224576 | + | 0.974457i | \(0.572100\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 41.8496 | 1.78610 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.25240 | 0.308962 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 23.5877 | 1.00124 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 27.6801 | 1.17284 | 0.586422 | − | 0.810006i | \(-0.300536\pi\) | ||||
0.586422 | + | 0.810006i | \(0.300536\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.03228 | 0.0436606 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 24.8034 | 1.04720 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13.6508 | −0.575312 | −0.287656 | − | 0.957734i | \(-0.592876\pi\) | ||||
−0.287656 | + | 0.957734i | \(0.592876\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 20.3353 | 0.855511 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 27.1387 | 1.13771 | 0.568856 | − | 0.822437i | \(-0.307386\pi\) | ||||
0.568856 | + | 0.822437i | \(0.307386\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.9634 | −0.919138 | −0.459569 | − | 0.888142i | \(-0.651996\pi\) | ||||
−0.459569 | + | 0.888142i | \(0.651996\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 18.5327 | 0.774215 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.0096 | −0.542537 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.5414 | −0.438846 | −0.219423 | − | 0.975630i | \(-0.570417\pi\) | ||||
−0.219423 | + | 0.975630i | \(0.570417\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −33.9634 | −1.41147 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 32.1064 | 1.32971 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.775511 | −0.0320634 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14.9450 | −0.616848 | −0.308424 | − | 0.951249i | \(-0.599801\pi\) | ||||
−0.308424 | + | 0.951249i | \(0.599801\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 49.0375 | 2.02055 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.4402 | −0.511723 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 24.8015 | 1.01848 | 0.509238 | − | 0.860626i | \(-0.329927\pi\) | ||||
0.509238 | + | 0.860626i | \(0.329927\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −53.7359 | −2.19927 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.4446 | 0.549332 | 0.274666 | − | 0.961540i | \(-0.411433\pi\) | ||||
0.274666 | + | 0.961540i | \(0.411433\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.2524 | 1.03007 | 0.515033 | − | 0.857170i | \(-0.327780\pi\) | ||||
0.515033 | + | 0.857170i | \(0.327780\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −69.6068 | −2.83461 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −14.9084 | −0.606112 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.78946 | 0.113221 | 0.0566104 | − | 0.998396i | \(-0.481971\pi\) | ||||
0.0566104 | + | 0.998396i | \(0.481971\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.18928 | −0.0481133 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −43.1772 | −1.74391 | −0.871956 | − | 0.489585i | \(-0.837148\pi\) | ||||
−0.871956 | + | 0.489585i | \(0.837148\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 26.0192 | 1.04919 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.7476 | 0.432682 | 0.216341 | − | 0.976318i | \(-0.430588\pi\) | ||||
0.216341 | + | 0.976318i | \(0.430588\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −30.3771 | −1.22096 | −0.610480 | − | 0.792032i | \(-0.709023\pi\) | ||||
−0.610480 | + | 0.792032i | \(0.709023\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −24.8034 | −0.995327 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.67432 | −0.306973 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 89.9421 | 3.59194 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.5048 | 0.418853 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.5231 | 0.538347 | 0.269173 | − | 0.963092i | \(-0.413250\pi\) | ||||
0.269173 | + | 0.963092i | \(0.413250\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.91524 | 0.195363 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.335269 | −0.0133047 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.721586 | −0.0285903 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 55.6435 | 2.20122 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.6339 | −0.656999 | −0.328500 | − | 0.944504i | \(-0.606543\pi\) | ||||
−0.328500 | + | 0.944504i | \(0.606543\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.9538 | −0.984081 | −0.492040 | − | 0.870572i | \(-0.663749\pi\) | ||||
−0.492040 | + | 0.870572i | \(0.663749\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 44.9711 | 1.77073 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10.0646 | −0.395678 | −0.197839 | − | 0.980234i | \(-0.563392\pi\) | ||||
−0.197839 | + | 0.980234i | \(0.563392\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.84006 | −0.268496 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 42.2620 | 1.65384 | 0.826920 | − | 0.562320i | \(-0.190091\pi\) | ||||
0.826920 | + | 0.562320i | \(0.190091\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 24.8034 | 0.969150 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.29862 | −0.323760 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 43.3867 | 1.69011 | 0.845053 | − | 0.534682i | \(-0.179569\pi\) | ||||
0.845053 | + | 0.534682i | \(0.179569\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.0924575 | −0.00359618 | −0.00179809 | − | 0.999998i | \(-0.500572\pi\) | ||||
−0.00179809 | + | 0.999998i | \(0.500572\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.569343 | −0.0221115 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.52311 | 0.213856 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 73.2716 | 2.83284 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −40.6252 | −1.56832 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.86027 | 0.0717082 | 0.0358541 | − | 0.999357i | \(-0.488585\pi\) | ||||
0.0358541 | + | 0.999357i | \(0.488585\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 10.5781 | 0.407151 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11.1387 | −0.428094 | −0.214047 | − | 0.976823i | \(-0.568665\pi\) | ||||
−0.214047 | + | 0.976823i | \(0.568665\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.8959 | −0.570811 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.54144 | 0.326829 | 0.163414 | − | 0.986558i | \(-0.447749\pi\) | ||||
0.163414 | + | 0.986558i | \(0.447749\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.54144 | 0.326352 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −45.0096 | −1.71722 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.736978 | −0.0280766 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.5972 | 0.935723 | 0.467862 | − | 0.883802i | \(-0.345025\pi\) | ||||
0.467862 | + | 0.883802i | \(0.345025\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −20.4402 | −0.775343 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.5877 | 0.438914 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −23.8723 | −0.902935 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.56165 | 0.134522 | 0.0672608 | − | 0.997735i | \(-0.478574\pi\) | ||||
0.0672608 | + | 0.997735i | \(0.478574\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 38.0925 | 1.43668 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −51.8111 | −1.95132 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.3651 | −0.915049 | −0.457525 | − | 0.889197i | \(-0.651264\pi\) | ||||
−0.457525 | + | 0.889197i | \(0.651264\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.18785 | 0.344571 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 37.3449 | 1.39858 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.752820 | 0.0281539 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 37.3449 | 1.39467 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.89881 | −0.294576 | −0.147288 | − | 0.989094i | \(-0.547054\pi\) | ||||
−0.147288 | + | 0.989094i | \(0.547054\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −22.9465 | −0.853388 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.35548 | −0.0874803 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −33.8130 | −1.25405 | −0.627027 | − | 0.778997i | \(-0.715729\pi\) | ||||
−0.627027 | + | 0.778997i | \(0.715729\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −44.0375 | −1.63102 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 20.0279 | 0.740759 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 45.7205 | 1.68873 | 0.844363 | − | 0.535771i | \(-0.179979\pi\) | ||||
0.844363 | + | 0.535771i | \(0.179979\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −31.4359 | −1.15953 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 67.5702 | 2.48898 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.28467 | 0.304757 | 0.152378 | − | 0.988322i | \(-0.451307\pi\) | ||||
0.152378 | + | 0.988322i | \(0.451307\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.06455 | −0.0758432 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.70138 | 0.0624174 | 0.0312087 | − | 0.999513i | \(-0.490064\pi\) | ||||
0.0312087 | + | 0.999513i | \(0.490064\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.502904 | 0.0184250 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −29.9634 | −1.09630 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.4277 | −0.380513 | −0.190257 | − | 0.981734i | \(-0.560932\pi\) | ||||
−0.190257 | + | 0.981734i | \(0.560932\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −54.5221 | −1.98689 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −18.6339 | −0.678157 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −45.9267 | −1.66923 | −0.834617 | − | 0.550830i | \(-0.814311\pi\) | ||||
−0.834617 | + | 0.550830i | \(0.814311\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 68.4961 | 2.48625 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.58767 | 0.0575528 | 0.0287764 | − | 0.999586i | \(-0.490839\pi\) | ||||
0.0287764 | + | 0.999586i | \(0.490839\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −15.0462 | −0.543998 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.157008 | 0.00566924 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.37569 | −0.302035 | −0.151018 | − | 0.988531i | \(-0.548255\pi\) | ||||
−0.151018 | + | 0.988531i | \(0.548255\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −59.1526 | −2.13033 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10.2062 | 0.367090 | 0.183545 | − | 0.983011i | \(-0.441243\pi\) | ||||
0.183545 | + | 0.983011i | \(0.441243\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15.9267 | −0.572104 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 42.0192 | 1.50549 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −54.0154 | −1.93282 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.49084 | −0.160489 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21.5510 | −0.769189 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −26.6618 | −0.950391 | −0.475195 | − | 0.879880i | \(-0.657623\pi\) | ||||
−0.475195 | + | 0.879880i | \(0.657623\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 33.9248 | 1.20776 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.932519 | 0.0331147 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −32.1064 | −1.13870 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 25.0462 | 0.887183 | 0.443591 | − | 0.896229i | \(-0.353704\pi\) | ||||
0.443591 | + | 0.896229i | \(0.353704\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −23.0741 | −0.816304 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 58.8034 | 2.07772 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.05581 | 0.284283 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 62.4036 | 2.19671 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 32.1695 | 1.13102 | 0.565510 | − | 0.824741i | \(-0.308679\pi\) | ||||
0.565510 | + | 0.824741i | \(0.308679\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −26.5048 | −0.930709 | −0.465355 | − | 0.885124i | \(-0.654073\pi\) | ||||
−0.465355 | + | 0.885124i | \(0.654073\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −65.5683 | −2.29958 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.16138 | −0.180795 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 72.6252 | 2.54083 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 27.2051 | 0.949465 | 0.474733 | − | 0.880130i | \(-0.342545\pi\) | ||||
0.474733 | + | 0.880130i | \(0.342545\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.61850 | −0.300422 | −0.150211 | − | 0.988654i | \(-0.547995\pi\) | ||||
−0.150211 | + | 0.988654i | \(0.547995\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −29.2120 | −1.01703 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 37.8636 | 1.31665 | 0.658323 | − | 0.752735i | \(-0.271266\pi\) | ||||
0.658323 | + | 0.752735i | \(0.271266\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −51.9634 | −1.80476 | −0.902381 | − | 0.430939i | \(-0.858182\pi\) | ||||
−0.902381 | + | 0.430939i | \(0.858182\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.38443 | 0.152094 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −14.0000 | −0.485071 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −19.5598 | −0.676893 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −30.3651 | −1.04957 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −32.0785 | −1.10747 | −0.553736 | − | 0.832692i | \(-0.686799\pi\) | ||||
−0.553736 | + | 0.832692i | \(0.686799\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 54.9465 | 1.89246 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 21.1233 | 0.726663 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 57.9421 | 1.98857 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 29.0096 | 0.994436 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −40.5048 | −1.38686 | −0.693429 | − | 0.720525i | \(-0.743901\pi\) | ||||
−0.693429 | + | 0.720525i | \(0.743901\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −54.5606 | −1.86593 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 31.3834 | 1.07204 | 0.536018 | − | 0.844207i | \(-0.319928\pi\) | ||||
0.536018 | + | 0.844207i | \(0.319928\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −32.5187 | −1.10953 | −0.554763 | − | 0.832009i | \(-0.687191\pi\) | ||||
−0.554763 | + | 0.832009i | \(0.687191\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 46.4036 | 1.57960 | 0.789798 | − | 0.613367i | \(-0.210185\pi\) | ||||
0.789798 | + | 0.613367i | \(0.210185\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −20.3353 | −0.691420 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 35.9002 | 1.21924 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.91902 | −0.302557 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.55102 | −0.0525543 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.79383 | 0.196092 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −47.1493 | −1.59212 | −0.796060 | − | 0.605218i | \(-0.793086\pi\) | ||||
−0.796060 | + | 0.605218i | \(0.793086\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −12.4402 | −0.419599 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.95377 | −0.0995151 | −0.0497575 | − | 0.998761i | \(-0.515845\pi\) | ||||
−0.0497575 | + | 0.998761i | \(0.515845\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.6339 | 0.492470 | 0.246235 | − | 0.969210i | \(-0.420807\pi\) | ||||
0.246235 | + | 0.969210i | \(0.420807\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.84006 | 0.229926 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 33.3955 | 1.12131 | 0.560655 | − | 0.828050i | \(-0.310549\pi\) | ||||
0.560655 | + | 0.828050i | \(0.310549\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.63246 | 0.222196 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −83.6714 | −2.79996 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.0550 | 0.436379 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.57227 | −0.0524967 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.76156 | 0.225511 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.2986 | −0.476356 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 19.3921 | 0.644616 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.25240 | −0.240812 | −0.120406 | − | 0.992725i | \(-0.538420\pi\) | ||||
−0.120406 | + | 0.992725i | \(0.538420\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 75.4007 | 2.50088 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.6604 | 0.485719 | 0.242860 | − | 0.970061i | \(-0.421915\pi\) | ||||
0.242860 | + | 0.970061i | \(0.421915\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 29.0867 | 0.962628 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 40.6252 | 1.34303 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 42.1204 | 1.38942 | 0.694711 | − | 0.719289i | \(-0.255532\pi\) | ||||
0.694711 | + | 0.719289i | \(0.255532\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −26.5154 | −0.873713 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.23988 | 0.0408112 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.3719 | −0.406786 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 25.5510 | 0.839206 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −41.5144 | −1.36204 | −0.681021 | − | 0.732264i | \(-0.738464\pi\) | ||||
−0.681021 | + | 0.732264i | \(0.738464\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −50.7668 | −1.66381 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −83.6714 | −2.73928 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 14.6060 | 0.477667 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −43.4219 | −1.41853 | −0.709266 | − | 0.704941i | \(-0.750974\pi\) | ||||
−0.709266 | + | 0.704941i | \(0.750974\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.55539 | −0.213927 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.0848 | −0.426551 | −0.213276 | − | 0.976992i | \(-0.568413\pi\) | ||||
−0.213276 | + | 0.976992i | \(0.568413\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 32.0000 | 1.04206 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −49.9128 | −1.62195 | −0.810973 | − | 0.585083i | \(-0.801062\pi\) | ||||
−0.810973 | + | 0.585083i | \(0.801062\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.184915 | −0.00600259 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 31.8988 | 1.03439 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 39.6175 | 1.28334 | 0.641668 | − | 0.766983i | \(-0.278243\pi\) | ||||
0.641668 | + | 0.766983i | \(0.278243\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.9133 | 0.353148 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 12.4017 | 0.400890 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.7187 | 0.474795 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.50479 | −0.0807158 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −20.0000 | −0.643823 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 37.6574 | 1.21098 | 0.605491 | − | 0.795852i | \(-0.292977\pi\) | ||||
0.605491 | + | 0.795852i | \(0.292977\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −40.0558 | −1.28678 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.15994 | 0.293956 | 0.146978 | − | 0.989140i | \(-0.453045\pi\) | ||||
0.146978 | + | 0.989140i | \(0.453045\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.670538 | 0.0214744 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 45.4758 | 1.45490 | 0.727451 | − | 0.686160i | \(-0.240705\pi\) | ||||
0.727451 | + | 0.686160i | \(0.240705\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −57.0829 | −1.82438 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 73.6714 | 2.35215 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −27.9494 | −0.891447 | −0.445724 | − | 0.895171i | \(-0.647054\pi\) | ||||
−0.445724 | + | 0.895171i | \(0.647054\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.32568 | −0.233416 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 55.3082 | 1.75870 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.1108 | −0.416478 | −0.208239 | − | 0.978078i | \(-0.566773\pi\) | ||||
−0.208239 | + | 0.978078i | \(0.566773\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −34.0019 | −1.07902 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −31.6435 | −1.00317 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.8401 | 0.913374 | 0.456687 | − | 0.889627i | \(-0.349036\pi\) | ||||
0.456687 | + | 0.889627i | \(0.349036\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −23.5877 | −0.746281 |
(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 | 464.2.a.j.1.1 | 3 | ||
3.2 | odd | 2 | 4176.2.a.bu.1.3 | 3 | |||
4.3 | odd | 2 | 232.2.a.d.1.3 | ✓ | 3 | ||
8.3 | odd | 2 | 1856.2.a.x.1.1 | 3 | |||
8.5 | even | 2 | 1856.2.a.y.1.3 | 3 | |||
12.11 | even | 2 | 2088.2.a.s.1.3 | 3 | |||
20.19 | odd | 2 | 5800.2.a.p.1.1 | 3 | |||
116.115 | odd | 2 | 6728.2.a.j.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
232.2.a.d.1.3 | ✓ | 3 | 4.3 | odd | 2 | ||
464.2.a.j.1.1 | 3 | 1.1 | even | 1 | trivial | ||
1856.2.a.x.1.1 | 3 | 8.3 | odd | 2 | |||
1856.2.a.y.1.3 | 3 | 8.5 | even | 2 | |||
2088.2.a.s.1.3 | 3 | 12.11 | even | 2 | |||
4176.2.a.bu.1.3 | 3 | 3.2 | odd | 2 | |||
5800.2.a.p.1.1 | 3 | 20.19 | odd | 2 | |||
6728.2.a.j.1.1 | 3 | 116.115 | odd | 2 |