Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [945,2,Mod(1,945)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(945, 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("945.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 945 = 3^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 945.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: | \(7.54586299101\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 945.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.41421 | 1.70711 | 0.853553 | − | 0.521005i | \(-0.174443\pi\) | ||||
0.853553 | + | 0.521005i | \(0.174443\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.82843 | 1.91421 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 4.41421 | 1.56066 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.41421 | 0.763441 | ||||||||
\(11\) | 0.414214 | 0.124890 | 0.0624450 | − | 0.998048i | \(-0.480110\pi\) | ||||
0.0624450 | + | 0.998048i | \(0.480110\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.41421 | 0.669582 | 0.334791 | − | 0.942292i | \(-0.391334\pi\) | ||||
0.334791 | + | 0.942292i | \(0.391334\pi\) | |||||||
\(14\) | −2.41421 | −0.645226 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | 4.82843 | 1.17107 | 0.585533 | − | 0.810649i | \(-0.300885\pi\) | ||||
0.585533 | + | 0.810649i | \(0.300885\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.58579 | 0.363804 | 0.181902 | − | 0.983317i | \(-0.441775\pi\) | ||||
0.181902 | + | 0.983317i | \(0.441775\pi\) | |||||||
\(20\) | 3.82843 | 0.856062 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −0.828427 | −0.172739 | −0.0863695 | − | 0.996263i | \(-0.527527\pi\) | ||||
−0.0863695 | + | 0.996263i | \(0.527527\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 5.82843 | 1.14305 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.82843 | −0.723505 | ||||||||
\(29\) | −4.00000 | −0.742781 | −0.371391 | − | 0.928477i | \(-0.621119\pi\) | ||||
−0.371391 | + | 0.928477i | \(0.621119\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.00000 | 1.07763 | 0.538816 | − | 0.842424i | \(-0.318872\pi\) | ||||
0.538816 | + | 0.842424i | \(0.318872\pi\) | |||||||
\(32\) | −1.58579 | −0.280330 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 11.6569 | 1.99913 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.48528 | −1.39497 | −0.697486 | − | 0.716599i | \(-0.745698\pi\) | ||||
−0.697486 | + | 0.716599i | \(0.745698\pi\) | |||||||
\(38\) | 3.82843 | 0.621053 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.41421 | 0.697948 | ||||||||
\(41\) | −7.82843 | −1.22259 | −0.611297 | − | 0.791401i | \(-0.709352\pi\) | ||||
−0.611297 | + | 0.791401i | \(0.709352\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.65685 | −1.01516 | −0.507580 | − | 0.861604i | \(-0.669460\pi\) | ||||
−0.507580 | + | 0.861604i | \(0.669460\pi\) | |||||||
\(44\) | 1.58579 | 0.239066 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.00000 | −0.294884 | ||||||||
\(47\) | 7.48528 | 1.09184 | 0.545920 | − | 0.837837i | \(-0.316180\pi\) | ||||
0.545920 | + | 0.837837i | \(0.316180\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 2.41421 | 0.341421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 9.24264 | 1.28172 | ||||||||
\(53\) | −10.8995 | −1.49716 | −0.748580 | − | 0.663044i | \(-0.769264\pi\) | ||||
−0.748580 | + | 0.663044i | \(0.769264\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.414214 | 0.0558525 | ||||||||
\(56\) | −4.41421 | −0.589874 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −9.65685 | −1.26801 | ||||||||
\(59\) | −6.48528 | −0.844312 | −0.422156 | − | 0.906523i | \(-0.638727\pi\) | ||||
−0.422156 | + | 0.906523i | \(0.638727\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.48528 | −1.08643 | −0.543214 | − | 0.839594i | \(-0.682793\pi\) | ||||
−0.543214 | + | 0.839594i | \(0.682793\pi\) | |||||||
\(62\) | 14.4853 | 1.83963 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −9.82843 | −1.22855 | ||||||||
\(65\) | 2.41421 | 0.299446 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.82843 | 0.956395 | 0.478197 | − | 0.878252i | \(-0.341290\pi\) | ||||
0.478197 | + | 0.878252i | \(0.341290\pi\) | |||||||
\(68\) | 18.4853 | 2.24167 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.41421 | −0.288554 | ||||||||
\(71\) | 2.00000 | 0.237356 | 0.118678 | − | 0.992933i | \(-0.462134\pi\) | ||||
0.118678 | + | 0.992933i | \(0.462134\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.07107 | −0.242400 | −0.121200 | − | 0.992628i | \(-0.538674\pi\) | ||||
−0.121200 | + | 0.992628i | \(0.538674\pi\) | |||||||
\(74\) | −20.4853 | −2.38137 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.07107 | 0.696399 | ||||||||
\(77\) | −0.414214 | −0.0472040 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.8284 | 1.66833 | 0.834164 | − | 0.551516i | \(-0.185951\pi\) | ||||
0.834164 | + | 0.551516i | \(0.185951\pi\) | |||||||
\(80\) | 3.00000 | 0.335410 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −18.8995 | −2.08710 | ||||||||
\(83\) | −7.48528 | −0.821616 | −0.410808 | − | 0.911722i | \(-0.634753\pi\) | ||||
−0.410808 | + | 0.911722i | \(0.634753\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.82843 | 0.523716 | ||||||||
\(86\) | −16.0711 | −1.73299 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.82843 | 0.194911 | ||||||||
\(89\) | −8.65685 | −0.917625 | −0.458812 | − | 0.888533i | \(-0.651725\pi\) | ||||
−0.458812 | + | 0.888533i | \(0.651725\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.41421 | −0.253078 | ||||||||
\(92\) | −3.17157 | −0.330659 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 18.0711 | 1.86389 | ||||||||
\(95\) | 1.58579 | 0.162698 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.1421 | 1.43592 | 0.717958 | − | 0.696086i | \(-0.245077\pi\) | ||||
0.717958 | + | 0.696086i | \(0.245077\pi\) | |||||||
\(98\) | 2.41421 | 0.243872 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.82843 | 0.382843 | ||||||||
\(101\) | −19.8284 | −1.97300 | −0.986501 | − | 0.163755i | \(-0.947640\pi\) | ||||
−0.986501 | + | 0.163755i | \(0.947640\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.8284 | 1.06696 | 0.533478 | − | 0.845814i | \(-0.320885\pi\) | ||||
0.533478 | + | 0.845814i | \(0.320885\pi\) | |||||||
\(104\) | 10.6569 | 1.04499 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −26.3137 | −2.55581 | ||||||||
\(107\) | −10.4853 | −1.01365 | −0.506825 | − | 0.862049i | \(-0.669181\pi\) | ||||
−0.506825 | + | 0.862049i | \(0.669181\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.48528 | 0.333829 | 0.166915 | − | 0.985971i | \(-0.446620\pi\) | ||||
0.166915 | + | 0.985971i | \(0.446620\pi\) | |||||||
\(110\) | 1.00000 | 0.0953463 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.00000 | −0.283473 | ||||||||
\(113\) | 2.75736 | 0.259391 | 0.129695 | − | 0.991554i | \(-0.458600\pi\) | ||||
0.129695 | + | 0.991554i | \(0.458600\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.828427 | −0.0772512 | ||||||||
\(116\) | −15.3137 | −1.42184 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −15.6569 | −1.44133 | ||||||||
\(119\) | −4.82843 | −0.442621 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8284 | −0.984402 | ||||||||
\(122\) | −20.4853 | −1.85465 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 22.9706 | 2.06282 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.6569 | 1.47806 | 0.739028 | − | 0.673674i | \(-0.235285\pi\) | ||||
0.739028 | + | 0.673674i | \(0.235285\pi\) | |||||||
\(128\) | −20.5563 | −1.81694 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5.82843 | 0.511187 | ||||||||
\(131\) | 12.1421 | 1.06086 | 0.530432 | − | 0.847728i | \(-0.322030\pi\) | ||||
0.530432 | + | 0.847728i | \(0.322030\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.58579 | −0.137505 | ||||||||
\(134\) | 18.8995 | 1.63267 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 21.3137 | 1.82764 | ||||||||
\(137\) | −8.41421 | −0.718875 | −0.359437 | − | 0.933169i | \(-0.617031\pi\) | ||||
−0.359437 | + | 0.933169i | \(0.617031\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 21.3137 | 1.80781 | 0.903903 | − | 0.427738i | \(-0.140690\pi\) | ||||
0.903903 | + | 0.427738i | \(0.140690\pi\) | |||||||
\(140\) | −3.82843 | −0.323561 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.82843 | 0.405193 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.00000 | −0.332182 | ||||||||
\(146\) | −5.00000 | −0.413803 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −32.4853 | −2.67027 | ||||||||
\(149\) | 17.7990 | 1.45815 | 0.729075 | − | 0.684434i | \(-0.239951\pi\) | ||||
0.729075 | + | 0.684434i | \(0.239951\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −23.3137 | −1.89724 | −0.948621 | − | 0.316414i | \(-0.897521\pi\) | ||||
−0.948621 | + | 0.316414i | \(0.897521\pi\) | |||||||
\(152\) | 7.00000 | 0.567775 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.00000 | −0.0805823 | ||||||||
\(155\) | 6.00000 | 0.481932 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.8284 | 1.18344 | 0.591719 | − | 0.806145i | \(-0.298450\pi\) | ||||
0.591719 | + | 0.806145i | \(0.298450\pi\) | |||||||
\(158\) | 35.7990 | 2.84801 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.58579 | −0.125367 | ||||||||
\(161\) | 0.828427 | 0.0652892 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.34315 | 0.496834 | 0.248417 | − | 0.968653i | \(-0.420090\pi\) | ||||
0.248417 | + | 0.968653i | \(0.420090\pi\) | |||||||
\(164\) | −29.9706 | −2.34031 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −18.0711 | −1.40259 | ||||||||
\(167\) | −11.3137 | −0.875481 | −0.437741 | − | 0.899101i | \(-0.644221\pi\) | ||||
−0.437741 | + | 0.899101i | \(0.644221\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.17157 | −0.551659 | ||||||||
\(170\) | 11.6569 | 0.894040 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −25.4853 | −1.94323 | ||||||||
\(173\) | 15.3137 | 1.16428 | 0.582140 | − | 0.813089i | \(-0.302216\pi\) | ||||
0.582140 | + | 0.813089i | \(0.302216\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 1.24264 | 0.0936676 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −20.8995 | −1.56648 | ||||||||
\(179\) | −13.7279 | −1.02607 | −0.513037 | − | 0.858367i | \(-0.671479\pi\) | ||||
−0.513037 | + | 0.858367i | \(0.671479\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.65685 | 0.420471 | 0.210235 | − | 0.977651i | \(-0.432577\pi\) | ||||
0.210235 | + | 0.977651i | \(0.432577\pi\) | |||||||
\(182\) | −5.82843 | −0.432032 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.65685 | −0.269587 | ||||||||
\(185\) | −8.48528 | −0.623850 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.00000 | 0.146254 | ||||||||
\(188\) | 28.6569 | 2.09002 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.82843 | 0.277743 | ||||||||
\(191\) | −20.0711 | −1.45229 | −0.726146 | − | 0.687541i | \(-0.758690\pi\) | ||||
−0.726146 | + | 0.687541i | \(0.758690\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.51472 | −0.396958 | −0.198479 | − | 0.980105i | \(-0.563600\pi\) | ||||
−0.198479 | + | 0.980105i | \(0.563600\pi\) | |||||||
\(194\) | 34.1421 | 2.45126 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.82843 | 0.273459 | ||||||||
\(197\) | 12.8995 | 0.919051 | 0.459525 | − | 0.888165i | \(-0.348019\pi\) | ||||
0.459525 | + | 0.888165i | \(0.348019\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.41421 | −0.171139 | −0.0855695 | − | 0.996332i | \(-0.527271\pi\) | ||||
−0.0855695 | + | 0.996332i | \(0.527271\pi\) | |||||||
\(200\) | 4.41421 | 0.312132 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −47.8701 | −3.36813 | ||||||||
\(203\) | 4.00000 | 0.280745 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.82843 | −0.546761 | ||||||||
\(206\) | 26.1421 | 1.82141 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 7.24264 | 0.502187 | ||||||||
\(209\) | 0.656854 | 0.0454356 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.48528 | 0.171094 | 0.0855469 | − | 0.996334i | \(-0.472736\pi\) | ||||
0.0855469 | + | 0.996334i | \(0.472736\pi\) | |||||||
\(212\) | −41.7279 | −2.86589 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −25.3137 | −1.73041 | ||||||||
\(215\) | −6.65685 | −0.453994 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.00000 | −0.407307 | ||||||||
\(218\) | 8.41421 | 0.569882 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.58579 | 0.106914 | ||||||||
\(221\) | 11.6569 | 0.784125 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.65685 | −0.378811 | −0.189405 | − | 0.981899i | \(-0.560656\pi\) | ||||
−0.189405 | + | 0.981899i | \(0.560656\pi\) | |||||||
\(224\) | 1.58579 | 0.105955 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.65685 | 0.442807 | ||||||||
\(227\) | 9.48528 | 0.629560 | 0.314780 | − | 0.949165i | \(-0.398069\pi\) | ||||
0.314780 | + | 0.949165i | \(0.398069\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.34315 | 0.419167 | 0.209583 | − | 0.977791i | \(-0.432789\pi\) | ||||
0.209583 | + | 0.977791i | \(0.432789\pi\) | |||||||
\(230\) | −2.00000 | −0.131876 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −17.6569 | −1.15923 | ||||||||
\(233\) | −14.5563 | −0.953618 | −0.476809 | − | 0.879007i | \(-0.658207\pi\) | ||||
−0.476809 | + | 0.879007i | \(0.658207\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.48528 | 0.488286 | ||||||||
\(236\) | −24.8284 | −1.61619 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −11.6569 | −0.755602 | ||||||||
\(239\) | 24.6274 | 1.59302 | 0.796508 | − | 0.604629i | \(-0.206678\pi\) | ||||
0.796508 | + | 0.604629i | \(0.206678\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.7990 | −1.01770 | −0.508851 | − | 0.860854i | \(-0.669930\pi\) | ||||
−0.508851 | + | 0.860854i | \(0.669930\pi\) | |||||||
\(242\) | −26.1421 | −1.68048 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −32.4853 | −2.07966 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.82843 | 0.243597 | ||||||||
\(248\) | 26.4853 | 1.68182 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.41421 | 0.152688 | ||||||||
\(251\) | −1.85786 | −0.117267 | −0.0586337 | − | 0.998280i | \(-0.518674\pi\) | ||||
−0.0586337 | + | 0.998280i | \(0.518674\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.343146 | −0.0215734 | ||||||||
\(254\) | 40.2132 | 2.52320 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −29.9706 | −1.87316 | ||||||||
\(257\) | 6.34315 | 0.395675 | 0.197837 | − | 0.980235i | \(-0.436608\pi\) | ||||
0.197837 | + | 0.980235i | \(0.436608\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.48528 | 0.527250 | ||||||||
\(260\) | 9.24264 | 0.573204 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 29.3137 | 1.81101 | ||||||||
\(263\) | 3.65685 | 0.225491 | 0.112746 | − | 0.993624i | \(-0.464035\pi\) | ||||
0.112746 | + | 0.993624i | \(0.464035\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.8995 | −0.669551 | ||||||||
\(266\) | −3.82843 | −0.234736 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 29.9706 | 1.83074 | ||||||||
\(269\) | −14.0000 | −0.853595 | −0.426798 | − | 0.904347i | \(-0.640358\pi\) | ||||
−0.426798 | + | 0.904347i | \(0.640358\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.7574 | 0.774954 | 0.387477 | − | 0.921879i | \(-0.373347\pi\) | ||||
0.387477 | + | 0.921879i | \(0.373347\pi\) | |||||||
\(272\) | 14.4853 | 0.878299 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −20.3137 | −1.22720 | ||||||||
\(275\) | 0.414214 | 0.0249780 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.34315 | −0.260954 | −0.130477 | − | 0.991451i | \(-0.541651\pi\) | ||||
−0.130477 | + | 0.991451i | \(0.541651\pi\) | |||||||
\(278\) | 51.4558 | 3.08612 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4.41421 | −0.263800 | ||||||||
\(281\) | 27.6569 | 1.64987 | 0.824935 | − | 0.565228i | \(-0.191212\pi\) | ||||
0.824935 | + | 0.565228i | \(0.191212\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.4853 | −0.742173 | −0.371086 | − | 0.928598i | \(-0.621015\pi\) | ||||
−0.371086 | + | 0.928598i | \(0.621015\pi\) | |||||||
\(284\) | 7.65685 | 0.454351 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.41421 | 0.142755 | ||||||||
\(287\) | 7.82843 | 0.462097 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.31371 | 0.371395 | ||||||||
\(290\) | −9.65685 | −0.567070 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −7.92893 | −0.464006 | ||||||||
\(293\) | −18.4853 | −1.07992 | −0.539961 | − | 0.841690i | \(-0.681561\pi\) | ||||
−0.539961 | + | 0.841690i | \(0.681561\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.48528 | −0.377588 | ||||||||
\(296\) | −37.4558 | −2.17708 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 42.9706 | 2.48922 | ||||||||
\(299\) | −2.00000 | −0.115663 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.65685 | 0.383695 | ||||||||
\(302\) | −56.2843 | −3.23880 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.75736 | 0.272853 | ||||||||
\(305\) | −8.48528 | −0.485866 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.4853 | −0.826719 | −0.413359 | − | 0.910568i | \(-0.635645\pi\) | ||||
−0.413359 | + | 0.910568i | \(0.635645\pi\) | |||||||
\(308\) | −1.58579 | −0.0903586 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 14.4853 | 0.822709 | ||||||||
\(311\) | 14.3431 | 0.813325 | 0.406663 | − | 0.913578i | \(-0.366692\pi\) | ||||
0.406663 | + | 0.913578i | \(0.366692\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 27.3848 | 1.54788 | 0.773940 | − | 0.633259i | \(-0.218283\pi\) | ||||
0.773940 | + | 0.633259i | \(0.218283\pi\) | |||||||
\(314\) | 35.7990 | 2.02025 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 56.7696 | 3.19354 | ||||||||
\(317\) | 28.4142 | 1.59590 | 0.797951 | − | 0.602723i | \(-0.205918\pi\) | ||||
0.797951 | + | 0.602723i | \(0.205918\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.65685 | −0.0927660 | ||||||||
\(320\) | −9.82843 | −0.549426 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.00000 | 0.111456 | ||||||||
\(323\) | 7.65685 | 0.426039 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.41421 | 0.133916 | ||||||||
\(326\) | 15.3137 | 0.848148 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −34.5563 | −1.90806 | ||||||||
\(329\) | −7.48528 | −0.412677 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.00000 | 0.329790 | 0.164895 | − | 0.986311i | \(-0.447272\pi\) | ||||
0.164895 | + | 0.986311i | \(0.447272\pi\) | |||||||
\(332\) | −28.6569 | −1.57275 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −27.3137 | −1.49454 | ||||||||
\(335\) | 7.82843 | 0.427713 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.6274 | 1.55943 | 0.779717 | − | 0.626132i | \(-0.215363\pi\) | ||||
0.779717 | + | 0.626132i | \(0.215363\pi\) | |||||||
\(338\) | −17.3137 | −0.941742 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 18.4853 | 1.00251 | ||||||||
\(341\) | 2.48528 | 0.134586 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −29.3848 | −1.58432 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 36.9706 | 1.98755 | ||||||||
\(347\) | 3.17157 | 0.170259 | 0.0851295 | − | 0.996370i | \(-0.472870\pi\) | ||||
0.0851295 | + | 0.996370i | \(0.472870\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −25.7990 | −1.38099 | −0.690494 | − | 0.723338i | \(-0.742607\pi\) | ||||
−0.690494 | + | 0.723338i | \(0.742607\pi\) | |||||||
\(350\) | −2.41421 | −0.129045 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.656854 | −0.0350104 | ||||||||
\(353\) | 26.1421 | 1.39141 | 0.695703 | − | 0.718330i | \(-0.255093\pi\) | ||||
0.695703 | + | 0.718330i | \(0.255093\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.00000 | 0.106149 | ||||||||
\(356\) | −33.1421 | −1.75653 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −33.1421 | −1.75162 | ||||||||
\(359\) | 28.6985 | 1.51465 | 0.757324 | − | 0.653039i | \(-0.226506\pi\) | ||||
0.757324 | + | 0.653039i | \(0.226506\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.4853 | −0.867646 | ||||||||
\(362\) | 13.6569 | 0.717788 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −9.24264 | −0.484446 | ||||||||
\(365\) | −2.07107 | −0.108405 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 26.0000 | 1.35719 | 0.678594 | − | 0.734513i | \(-0.262589\pi\) | ||||
0.678594 | + | 0.734513i | \(0.262589\pi\) | |||||||
\(368\) | −2.48528 | −0.129554 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −20.4853 | −1.06498 | ||||||||
\(371\) | 10.8995 | 0.565874 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.9706 | 0.982259 | 0.491129 | − | 0.871087i | \(-0.336584\pi\) | ||||
0.491129 | + | 0.871087i | \(0.336584\pi\) | |||||||
\(374\) | 4.82843 | 0.249672 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 33.0416 | 1.70399 | ||||||||
\(377\) | −9.65685 | −0.497353 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.2843 | 1.14467 | 0.572333 | − | 0.820021i | \(-0.306038\pi\) | ||||
0.572333 | + | 0.820021i | \(0.306038\pi\) | |||||||
\(380\) | 6.07107 | 0.311439 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −48.4558 | −2.47922 | ||||||||
\(383\) | 10.3431 | 0.528510 | 0.264255 | − | 0.964453i | \(-0.414874\pi\) | ||||
0.264255 | + | 0.964453i | \(0.414874\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.414214 | −0.0211103 | ||||||||
\(386\) | −13.3137 | −0.677650 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 54.1421 | 2.74865 | ||||||||
\(389\) | −17.3137 | −0.877840 | −0.438920 | − | 0.898526i | \(-0.644639\pi\) | ||||
−0.438920 | + | 0.898526i | \(0.644639\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.00000 | −0.202289 | ||||||||
\(392\) | 4.41421 | 0.222951 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 31.1421 | 1.56892 | ||||||||
\(395\) | 14.8284 | 0.746099 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.8284 | 0.744217 | 0.372109 | − | 0.928189i | \(-0.378635\pi\) | ||||
0.372109 | + | 0.928189i | \(0.378635\pi\) | |||||||
\(398\) | −5.82843 | −0.292153 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.00000 | 0.150000 | ||||||||
\(401\) | 5.79899 | 0.289588 | 0.144794 | − | 0.989462i | \(-0.453748\pi\) | ||||
0.144794 | + | 0.989462i | \(0.453748\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.4853 | 0.721563 | ||||||||
\(404\) | −75.9117 | −3.77675 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 9.65685 | 0.479262 | ||||||||
\(407\) | −3.51472 | −0.174218 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.31371 | −0.163852 | −0.0819262 | − | 0.996638i | \(-0.526107\pi\) | ||||
−0.0819262 | + | 0.996638i | \(0.526107\pi\) | |||||||
\(410\) | −18.8995 | −0.933380 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 41.4558 | 2.04238 | ||||||||
\(413\) | 6.48528 | 0.319120 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.48528 | −0.367438 | ||||||||
\(416\) | −3.82843 | −0.187704 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.58579 | 0.0775634 | ||||||||
\(419\) | −3.17157 | −0.154941 | −0.0774707 | − | 0.996995i | \(-0.524684\pi\) | ||||
−0.0774707 | + | 0.996995i | \(0.524684\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.00000 | −0.341159 | −0.170580 | − | 0.985344i | \(-0.554564\pi\) | ||||
−0.170580 | + | 0.985344i | \(0.554564\pi\) | |||||||
\(422\) | 6.00000 | 0.292075 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −48.1127 | −2.33656 | ||||||||
\(425\) | 4.82843 | 0.234213 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.48528 | 0.410632 | ||||||||
\(428\) | −40.1421 | −1.94034 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −16.0711 | −0.775016 | ||||||||
\(431\) | −36.4142 | −1.75401 | −0.877005 | − | 0.480480i | \(-0.840462\pi\) | ||||
−0.877005 | + | 0.480480i | \(0.840462\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −29.8701 | −1.43546 | −0.717732 | − | 0.696320i | \(-0.754820\pi\) | ||||
−0.717732 | + | 0.696320i | \(0.754820\pi\) | |||||||
\(434\) | −14.4853 | −0.695316 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 13.3431 | 0.639021 | ||||||||
\(437\) | −1.31371 | −0.0628432 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.7574 | 0.513421 | 0.256710 | − | 0.966488i | \(-0.417361\pi\) | ||||
0.256710 | + | 0.966488i | \(0.417361\pi\) | |||||||
\(440\) | 1.82843 | 0.0871668 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 28.1421 | 1.33858 | ||||||||
\(443\) | 7.02944 | 0.333979 | 0.166989 | − | 0.985959i | \(-0.446595\pi\) | ||||
0.166989 | + | 0.985959i | \(0.446595\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.65685 | −0.410374 | ||||||||
\(446\) | −13.6569 | −0.646671 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 9.82843 | 0.464350 | ||||||||
\(449\) | −11.1716 | −0.527219 | −0.263610 | − | 0.964629i | \(-0.584913\pi\) | ||||
−0.263610 | + | 0.964629i | \(0.584913\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.24264 | −0.152690 | ||||||||
\(452\) | 10.5563 | 0.496529 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 22.8995 | 1.07473 | ||||||||
\(455\) | −2.41421 | −0.113180 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −30.1421 | −1.40999 | −0.704995 | − | 0.709212i | \(-0.749051\pi\) | ||||
−0.704995 | + | 0.709212i | \(0.749051\pi\) | |||||||
\(458\) | 15.3137 | 0.715563 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3.17157 | −0.147875 | ||||||||
\(461\) | −13.6274 | −0.634692 | −0.317346 | − | 0.948310i | \(-0.602792\pi\) | ||||
−0.317346 | + | 0.948310i | \(0.602792\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.6569 | 1.05295 | 0.526477 | − | 0.850190i | \(-0.323513\pi\) | ||||
0.526477 | + | 0.850190i | \(0.323513\pi\) | |||||||
\(464\) | −12.0000 | −0.557086 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −35.1421 | −1.62793 | ||||||||
\(467\) | 1.65685 | 0.0766701 | 0.0383350 | − | 0.999265i | \(-0.487795\pi\) | ||||
0.0383350 | + | 0.999265i | \(0.487795\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.82843 | −0.361483 | ||||||||
\(470\) | 18.0711 | 0.833556 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −28.6274 | −1.31768 | ||||||||
\(473\) | −2.75736 | −0.126784 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.58579 | 0.0727609 | ||||||||
\(476\) | −18.4853 | −0.847271 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 59.4558 | 2.71945 | ||||||||
\(479\) | −26.1421 | −1.19446 | −0.597232 | − | 0.802068i | \(-0.703733\pi\) | ||||
−0.597232 | + | 0.802068i | \(0.703733\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.4853 | −0.934048 | ||||||||
\(482\) | −38.1421 | −1.73733 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −41.4558 | −1.88436 | ||||||||
\(485\) | 14.1421 | 0.642161 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 30.3137 | 1.37365 | 0.686823 | − | 0.726825i | \(-0.259005\pi\) | ||||
0.686823 | + | 0.726825i | \(0.259005\pi\) | |||||||
\(488\) | −37.4558 | −1.69555 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.41421 | 0.109063 | ||||||||
\(491\) | −12.6274 | −0.569867 | −0.284934 | − | 0.958547i | \(-0.591972\pi\) | ||||
−0.284934 | + | 0.958547i | \(0.591972\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −19.3137 | −0.869846 | ||||||||
\(494\) | 9.24264 | 0.415846 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 18.0000 | 0.808224 | ||||||||
\(497\) | −2.00000 | −0.0897123 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.201010 | 0.00899845 | 0.00449922 | − | 0.999990i | \(-0.498568\pi\) | ||||
0.00449922 | + | 0.999990i | \(0.498568\pi\) | |||||||
\(500\) | 3.82843 | 0.171212 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4.48528 | −0.200188 | ||||||||
\(503\) | −35.6274 | −1.58855 | −0.794274 | − | 0.607560i | \(-0.792149\pi\) | ||||
−0.794274 | + | 0.607560i | \(0.792149\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −19.8284 | −0.882353 | ||||||||
\(506\) | −0.828427 | −0.0368281 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 63.7696 | 2.82932 | ||||||||
\(509\) | 4.34315 | 0.192507 | 0.0962533 | − | 0.995357i | \(-0.469314\pi\) | ||||
0.0962533 | + | 0.995357i | \(0.469314\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.07107 | 0.0916186 | ||||||||
\(512\) | −31.2426 | −1.38074 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 15.3137 | 0.675459 | ||||||||
\(515\) | 10.8284 | 0.477158 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.10051 | 0.136360 | ||||||||
\(518\) | 20.4853 | 0.900072 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 10.6569 | 0.467334 | ||||||||
\(521\) | 27.4853 | 1.20415 | 0.602076 | − | 0.798439i | \(-0.294340\pi\) | ||||
0.602076 | + | 0.798439i | \(0.294340\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.1716 | 0.925768 | 0.462884 | − | 0.886419i | \(-0.346815\pi\) | ||||
0.462884 | + | 0.886419i | \(0.346815\pi\) | |||||||
\(524\) | 46.4853 | 2.03072 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.82843 | 0.384938 | ||||||||
\(527\) | 28.9706 | 1.26198 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.3137 | −0.970161 | ||||||||
\(530\) | −26.3137 | −1.14299 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −6.07107 | −0.263214 | ||||||||
\(533\) | −18.8995 | −0.818628 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.4853 | −0.453318 | ||||||||
\(536\) | 34.5563 | 1.49261 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −33.7990 | −1.45718 | ||||||||
\(539\) | 0.414214 | 0.0178414 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −27.6274 | −1.18780 | −0.593898 | − | 0.804541i | \(-0.702412\pi\) | ||||
−0.593898 | + | 0.804541i | \(0.702412\pi\) | |||||||
\(542\) | 30.7990 | 1.32293 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −7.65685 | −0.328285 | ||||||||
\(545\) | 3.48528 | 0.149293 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −40.2843 | −1.72243 | −0.861216 | − | 0.508240i | \(-0.830296\pi\) | ||||
−0.861216 | + | 0.508240i | \(0.830296\pi\) | |||||||
\(548\) | −32.2132 | −1.37608 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.00000 | 0.0426401 | ||||||||
\(551\) | −6.34315 | −0.270227 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14.8284 | −0.630569 | ||||||||
\(554\) | −10.4853 | −0.445477 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 81.5980 | 3.46053 | ||||||||
\(557\) | 43.7990 | 1.85582 | 0.927911 | − | 0.372801i | \(-0.121603\pi\) | ||||
0.927911 | + | 0.372801i | \(0.121603\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16.0711 | −0.679734 | ||||||||
\(560\) | −3.00000 | −0.126773 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 66.7696 | 2.81650 | ||||||||
\(563\) | 27.9706 | 1.17882 | 0.589409 | − | 0.807835i | \(-0.299361\pi\) | ||||
0.589409 | + | 0.807835i | \(0.299361\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.75736 | 0.116003 | ||||||||
\(566\) | −30.1421 | −1.26697 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.82843 | 0.370433 | ||||||||
\(569\) | 8.68629 | 0.364148 | 0.182074 | − | 0.983285i | \(-0.441719\pi\) | ||||
0.182074 | + | 0.983285i | \(0.441719\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −43.7990 | −1.83293 | −0.916465 | − | 0.400114i | \(-0.868970\pi\) | ||||
−0.916465 | + | 0.400114i | \(0.868970\pi\) | |||||||
\(572\) | 3.82843 | 0.160075 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 18.8995 | 0.788850 | ||||||||
\(575\) | −0.828427 | −0.0345478 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.72792 | 0.238457 | 0.119228 | − | 0.992867i | \(-0.461958\pi\) | ||||
0.119228 | + | 0.992867i | \(0.461958\pi\) | |||||||
\(578\) | 15.2426 | 0.634010 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −15.3137 | −0.635867 | ||||||||
\(581\) | 7.48528 | 0.310542 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.51472 | −0.186981 | ||||||||
\(584\) | −9.14214 | −0.378304 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −44.6274 | −1.84354 | ||||||||
\(587\) | 12.6863 | 0.523619 | 0.261810 | − | 0.965120i | \(-0.415681\pi\) | ||||
0.261810 | + | 0.965120i | \(0.415681\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.51472 | 0.392047 | ||||||||
\(590\) | −15.6569 | −0.644582 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −25.4558 | −1.04623 | ||||||||
\(593\) | −9.85786 | −0.404814 | −0.202407 | − | 0.979301i | \(-0.564876\pi\) | ||||
−0.202407 | + | 0.979301i | \(0.564876\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.82843 | −0.197946 | ||||||||
\(596\) | 68.1421 | 2.79121 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.82843 | −0.197449 | ||||||||
\(599\) | 5.10051 | 0.208401 | 0.104200 | − | 0.994556i | \(-0.466772\pi\) | ||||
0.104200 | + | 0.994556i | \(0.466772\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.6274 | 1.00457 | 0.502287 | − | 0.864701i | \(-0.332492\pi\) | ||||
0.502287 | + | 0.864701i | \(0.332492\pi\) | |||||||
\(602\) | 16.0711 | 0.655008 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −89.2548 | −3.63173 | ||||||||
\(605\) | −10.8284 | −0.440238 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 40.4853 | 1.64325 | 0.821623 | − | 0.570031i | \(-0.193069\pi\) | ||||
0.821623 | + | 0.570031i | \(0.193069\pi\) | |||||||
\(608\) | −2.51472 | −0.101985 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −20.4853 | −0.829425 | ||||||||
\(611\) | 18.0711 | 0.731077 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 37.9411 | 1.53243 | 0.766214 | − | 0.642586i | \(-0.222138\pi\) | ||||
0.766214 | + | 0.642586i | \(0.222138\pi\) | |||||||
\(614\) | −34.9706 | −1.41130 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.82843 | −0.0736694 | ||||||||
\(617\) | 24.7696 | 0.997185 | 0.498592 | − | 0.866837i | \(-0.333850\pi\) | ||||
0.498592 | + | 0.866837i | \(0.333850\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −26.2132 | −1.05360 | −0.526799 | − | 0.849990i | \(-0.676608\pi\) | ||||
−0.526799 | + | 0.849990i | \(0.676608\pi\) | |||||||
\(620\) | 22.9706 | 0.922520 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 34.6274 | 1.38843 | ||||||||
\(623\) | 8.65685 | 0.346830 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 66.1127 | 2.64239 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 56.7696 | 2.26535 | ||||||||
\(629\) | −40.9706 | −1.63360 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.37258 | 0.0546417 | 0.0273208 | − | 0.999627i | \(-0.491302\pi\) | ||||
0.0273208 | + | 0.999627i | \(0.491302\pi\) | |||||||
\(632\) | 65.4558 | 2.60369 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 68.5980 | 2.72437 | ||||||||
\(635\) | 16.6569 | 0.661007 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.41421 | 0.0956546 | ||||||||
\(638\) | −4.00000 | −0.158362 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −20.5563 | −0.812561 | ||||||||
\(641\) | −0.485281 | −0.0191675 | −0.00958373 | − | 0.999954i | \(-0.503051\pi\) | ||||
−0.00958373 | + | 0.999954i | \(0.503051\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.7696 | 1.13456 | 0.567280 | − | 0.823525i | \(-0.307996\pi\) | ||||
0.567280 | + | 0.823525i | \(0.307996\pi\) | |||||||
\(644\) | 3.17157 | 0.124977 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 18.4853 | 0.727294 | ||||||||
\(647\) | −25.3431 | −0.996342 | −0.498171 | − | 0.867079i | \(-0.665995\pi\) | ||||
−0.498171 | + | 0.867079i | \(0.665995\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.68629 | −0.105446 | ||||||||
\(650\) | 5.82843 | 0.228610 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 24.2843 | 0.951045 | ||||||||
\(653\) | −8.20101 | −0.320930 | −0.160465 | − | 0.987042i | \(-0.551299\pi\) | ||||
−0.160465 | + | 0.987042i | \(0.551299\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.1421 | 0.474432 | ||||||||
\(656\) | −23.4853 | −0.916946 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −18.0711 | −0.704484 | ||||||||
\(659\) | −12.3431 | −0.480821 | −0.240410 | − | 0.970671i | \(-0.577282\pi\) | ||||
−0.240410 | + | 0.970671i | \(0.577282\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.20101 | −0.318982 | −0.159491 | − | 0.987199i | \(-0.550985\pi\) | ||||
−0.159491 | + | 0.987199i | \(0.550985\pi\) | |||||||
\(662\) | 14.4853 | 0.562986 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −33.0416 | −1.28226 | ||||||||
\(665\) | −1.58579 | −0.0614942 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.31371 | 0.128307 | ||||||||
\(668\) | −43.3137 | −1.67586 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 18.8995 | 0.730151 | ||||||||
\(671\) | −3.51472 | −0.135684 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.17157 | 0.122255 | 0.0611276 | − | 0.998130i | \(-0.480530\pi\) | ||||
0.0611276 | + | 0.998130i | \(0.480530\pi\) | |||||||
\(674\) | 69.1127 | 2.66212 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −27.4558 | −1.05599 | ||||||||
\(677\) | 13.8579 | 0.532601 | 0.266300 | − | 0.963890i | \(-0.414199\pi\) | ||||
0.266300 | + | 0.963890i | \(0.414199\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14.1421 | −0.542725 | ||||||||
\(680\) | 21.3137 | 0.817343 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 6.00000 | 0.229752 | ||||||||
\(683\) | −15.5147 | −0.593654 | −0.296827 | − | 0.954931i | \(-0.595929\pi\) | ||||
−0.296827 | + | 0.954931i | \(0.595929\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.41421 | −0.321491 | ||||||||
\(686\) | −2.41421 | −0.0921751 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −19.9706 | −0.761371 | ||||||||
\(689\) | −26.3137 | −1.00247 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.5563 | 1.08633 | 0.543167 | − | 0.839624i | \(-0.317225\pi\) | ||||
0.543167 | + | 0.839624i | \(0.317225\pi\) | |||||||
\(692\) | 58.6274 | 2.22868 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.65685 | 0.290650 | ||||||||
\(695\) | 21.3137 | 0.808475 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −37.7990 | −1.43174 | ||||||||
\(698\) | −62.2843 | −2.35749 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.82843 | −0.144701 | ||||||||
\(701\) | 28.3431 | 1.07051 | 0.535253 | − | 0.844692i | \(-0.320216\pi\) | ||||
0.535253 | + | 0.844692i | \(0.320216\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13.4558 | −0.507497 | ||||||||
\(704\) | −4.07107 | −0.153434 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 63.1127 | 2.37528 | ||||||||
\(707\) | 19.8284 | 0.745725 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.62742 | 0.0611189 | 0.0305595 | − | 0.999533i | \(-0.490271\pi\) | ||||
0.0305595 | + | 0.999533i | \(0.490271\pi\) | |||||||
\(710\) | 4.82843 | 0.181208 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −38.2132 | −1.43210 | ||||||||
\(713\) | −4.97056 | −0.186149 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.00000 | 0.0373979 | ||||||||
\(716\) | −52.5563 | −1.96412 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 69.2843 | 2.58567 | ||||||||
\(719\) | −35.7990 | −1.33508 | −0.667539 | − | 0.744575i | \(-0.732652\pi\) | ||||
−0.667539 | + | 0.744575i | \(0.732652\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.8284 | −0.403272 | ||||||||
\(722\) | −39.7990 | −1.48117 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 21.6569 | 0.804871 | ||||||||
\(725\) | −4.00000 | −0.148556 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 48.0833 | 1.78331 | 0.891655 | − | 0.452716i | \(-0.149545\pi\) | ||||
0.891655 | + | 0.452716i | \(0.149545\pi\) | |||||||
\(728\) | −10.6569 | −0.394969 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5.00000 | −0.185058 | ||||||||
\(731\) | −32.1421 | −1.18882 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −41.2426 | −1.52333 | −0.761666 | − | 0.647970i | \(-0.775618\pi\) | ||||
−0.761666 | + | 0.647970i | \(0.775618\pi\) | |||||||
\(734\) | 62.7696 | 2.31687 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.31371 | 0.0484239 | ||||||||
\(737\) | 3.24264 | 0.119444 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −35.1716 | −1.29381 | −0.646904 | − | 0.762572i | \(-0.723936\pi\) | ||||
−0.646904 | + | 0.762572i | \(0.723936\pi\) | |||||||
\(740\) | −32.4853 | −1.19418 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 26.3137 | 0.966007 | ||||||||
\(743\) | 11.6569 | 0.427649 | 0.213824 | − | 0.976872i | \(-0.431408\pi\) | ||||
0.213824 | + | 0.976872i | \(0.431408\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.7990 | 0.652105 | ||||||||
\(746\) | 45.7990 | 1.67682 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 7.65685 | 0.279962 | ||||||||
\(749\) | 10.4853 | 0.383124 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.8284 | −0.760040 | −0.380020 | − | 0.924978i | \(-0.624083\pi\) | ||||
−0.380020 | + | 0.924978i | \(0.624083\pi\) | |||||||
\(752\) | 22.4558 | 0.818880 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −23.3137 | −0.849035 | ||||||||
\(755\) | −23.3137 | −0.848473 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −38.4853 | −1.39877 | −0.699386 | − | 0.714744i | \(-0.746543\pi\) | ||||
−0.699386 | + | 0.714744i | \(0.746543\pi\) | |||||||
\(758\) | 53.7990 | 1.95407 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 7.00000 | 0.253917 | ||||||||
\(761\) | −24.6274 | −0.892743 | −0.446372 | − | 0.894848i | \(-0.647284\pi\) | ||||
−0.446372 | + | 0.894848i | \(0.647284\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.48528 | −0.126176 | ||||||||
\(764\) | −76.8406 | −2.78000 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24.9706 | 0.902223 | ||||||||
\(767\) | −15.6569 | −0.565336 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 46.7696 | 1.68655 | 0.843277 | − | 0.537480i | \(-0.180624\pi\) | ||||
0.843277 | + | 0.537480i | \(0.180624\pi\) | |||||||
\(770\) | −1.00000 | −0.0360375 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −21.1127 | −0.759863 | ||||||||
\(773\) | −44.1421 | −1.58768 | −0.793841 | − | 0.608125i | \(-0.791922\pi\) | ||||
−0.793841 | + | 0.608125i | \(0.791922\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.00000 | 0.215526 | ||||||||
\(776\) | 62.4264 | 2.24098 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −41.7990 | −1.49857 | ||||||||
\(779\) | −12.4142 | −0.444785 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.828427 | 0.0296435 | ||||||||
\(782\) | −9.65685 | −0.345328 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.00000 | 0.107143 | ||||||||
\(785\) | 14.8284 | 0.529249 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.79899 | 0.135419 | 0.0677097 | − | 0.997705i | \(-0.478431\pi\) | ||||
0.0677097 | + | 0.997705i | \(0.478431\pi\) | |||||||
\(788\) | 49.3848 | 1.75926 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 35.7990 | 1.27367 | ||||||||
\(791\) | −2.75736 | −0.0980404 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20.4853 | −0.727454 | ||||||||
\(794\) | 35.7990 | 1.27046 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.24264 | −0.327597 | ||||||||
\(797\) | 16.0000 | 0.566749 | 0.283375 | − | 0.959009i | \(-0.408546\pi\) | ||||
0.283375 | + | 0.959009i | \(0.408546\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 36.1421 | 1.27862 | ||||||||
\(800\) | −1.58579 | −0.0560660 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 14.0000 | 0.494357 | ||||||||
\(803\) | −0.857864 | −0.0302734 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.828427 | 0.0291982 | ||||||||
\(806\) | 34.9706 | 1.23179 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −87.5269 | −3.07919 | ||||||||
\(809\) | 52.0833 | 1.83115 | 0.915575 | − | 0.402147i | \(-0.131736\pi\) | ||||
0.915575 | + | 0.402147i | \(0.131736\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.3848 | −0.680692 | −0.340346 | − | 0.940300i | \(-0.610544\pi\) | ||||
−0.340346 | + | 0.940300i | \(0.610544\pi\) | |||||||
\(812\) | 15.3137 | 0.537406 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −8.48528 | −0.297409 | ||||||||
\(815\) | 6.34315 | 0.222191 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.5563 | −0.369320 | ||||||||
\(818\) | −8.00000 | −0.279713 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −29.9706 | −1.04662 | ||||||||
\(821\) | 9.02944 | 0.315130 | 0.157565 | − | 0.987509i | \(-0.449636\pi\) | ||||
0.157565 | + | 0.987509i | \(0.449636\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 29.2843 | 1.02079 | 0.510393 | − | 0.859941i | \(-0.329500\pi\) | ||||
0.510393 | + | 0.859941i | \(0.329500\pi\) | |||||||
\(824\) | 47.7990 | 1.66516 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 15.6569 | 0.544772 | ||||||||
\(827\) | 36.4853 | 1.26872 | 0.634359 | − | 0.773039i | \(-0.281264\pi\) | ||||
0.634359 | + | 0.773039i | \(0.281264\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.1716 | −0.735319 | −0.367660 | − | 0.929960i | \(-0.619841\pi\) | ||||
−0.367660 | + | 0.929960i | \(0.619841\pi\) | |||||||
\(830\) | −18.0711 | −0.627256 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −23.7279 | −0.822618 | ||||||||
\(833\) | 4.82843 | 0.167295 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.3137 | −0.391527 | ||||||||
\(836\) | 2.51472 | 0.0869734 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −7.65685 | −0.264502 | ||||||||
\(839\) | −25.7990 | −0.890680 | −0.445340 | − | 0.895362i | \(-0.646917\pi\) | ||||
−0.445340 | + | 0.895362i | \(0.646917\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.0000 | −0.448276 | ||||||||
\(842\) | −16.8995 | −0.582395 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 9.51472 | 0.327510 | ||||||||
\(845\) | −7.17157 | −0.246710 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.8284 | 0.372069 | ||||||||
\(848\) | −32.6985 | −1.12287 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 11.6569 | 0.399827 | ||||||||
\(851\) | 7.02944 | 0.240966 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.48528 | −0.153573 | −0.0767866 | − | 0.997048i | \(-0.524466\pi\) | ||||
−0.0767866 | + | 0.997048i | \(0.524466\pi\) | |||||||
\(854\) | 20.4853 | 0.700992 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −46.2843 | −1.58196 | ||||||||
\(857\) | 17.3137 | 0.591425 | 0.295713 | − | 0.955277i | \(-0.404443\pi\) | ||||
0.295713 | + | 0.955277i | \(0.404443\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −38.3553 | −1.30867 | −0.654334 | − | 0.756206i | \(-0.727051\pi\) | ||||
−0.654334 | + | 0.756206i | \(0.727051\pi\) | |||||||
\(860\) | −25.4853 | −0.869041 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −87.9117 | −2.99428 | ||||||||
\(863\) | −39.6569 | −1.34994 | −0.674968 | − | 0.737847i | \(-0.735842\pi\) | ||||
−0.674968 | + | 0.737847i | \(0.735842\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.3137 | 0.520682 | ||||||||
\(866\) | −72.1127 | −2.45049 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −22.9706 | −0.779672 | ||||||||
\(869\) | 6.14214 | 0.208358 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.8995 | 0.640385 | ||||||||
\(872\) | 15.3848 | 0.520994 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3.17157 | −0.107280 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −34.8284 | −1.17607 | −0.588036 | − | 0.808835i | \(-0.700099\pi\) | ||||
−0.588036 | + | 0.808835i | \(0.700099\pi\) | |||||||
\(878\) | 25.9706 | 0.876464 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.24264 | 0.0418894 | ||||||||
\(881\) | −15.6569 | −0.527493 | −0.263746 | − | 0.964592i | \(-0.584958\pi\) | ||||
−0.263746 | + | 0.964592i | \(0.584958\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.34315 | 0.0788531 | 0.0394266 | − | 0.999222i | \(-0.487447\pi\) | ||||
0.0394266 | + | 0.999222i | \(0.487447\pi\) | |||||||
\(884\) | 44.6274 | 1.50098 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16.9706 | 0.570137 | ||||||||
\(887\) | −17.7696 | −0.596643 | −0.298322 | − | 0.954465i | \(-0.596427\pi\) | ||||
−0.298322 | + | 0.954465i | \(0.596427\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16.6569 | −0.558653 | ||||||||
\(890\) | −20.8995 | −0.700553 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −21.6569 | −0.725125 | ||||||||
\(893\) | 11.8701 | 0.397216 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −13.7279 | −0.458874 | ||||||||
\(896\) | 20.5563 | 0.686739 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −26.9706 | −0.900019 | ||||||||
\(899\) | −24.0000 | −0.800445 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −52.6274 | −1.75327 | ||||||||
\(902\) | −7.82843 | −0.260658 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 12.1716 | 0.404820 | ||||||||
\(905\) | 5.65685 | 0.188040 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26.5147 | −0.880407 | −0.440203 | − | 0.897898i | \(-0.645094\pi\) | ||||
−0.440203 | + | 0.897898i | \(0.645094\pi\) | |||||||
\(908\) | 36.3137 | 1.20511 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −5.82843 | −0.193210 | ||||||||
\(911\) | −40.8406 | −1.35311 | −0.676555 | − | 0.736392i | \(-0.736528\pi\) | ||||
−0.676555 | + | 0.736392i | \(0.736528\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.10051 | −0.102612 | ||||||||
\(914\) | −72.7696 | −2.40700 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 24.2843 | 0.802375 | ||||||||
\(917\) | −12.1421 | −0.400969 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36.7696 | 1.21292 | 0.606458 | − | 0.795116i | \(-0.292590\pi\) | ||||
0.606458 | + | 0.795116i | \(0.292590\pi\) | |||||||
\(920\) | −3.65685 | −0.120563 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −32.8995 | −1.08349 | ||||||||
\(923\) | 4.82843 | 0.158930 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.48528 | −0.278994 | ||||||||
\(926\) | 54.6985 | 1.79750 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.34315 | 0.208224 | ||||||||
\(929\) | 10.0294 | 0.329055 | 0.164528 | − | 0.986372i | \(-0.447390\pi\) | ||||
0.164528 | + | 0.986372i | \(0.447390\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.58579 | 0.0519721 | ||||||||
\(932\) | −55.7279 | −1.82543 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4.00000 | 0.130884 | ||||||||
\(935\) | 2.00000 | 0.0654070 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.8995 | 0.617420 | 0.308710 | − | 0.951156i | \(-0.400103\pi\) | ||||
0.308710 | + | 0.951156i | \(0.400103\pi\) | |||||||
\(938\) | −18.8995 | −0.617090 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 28.6569 | 0.934684 | ||||||||
\(941\) | 3.68629 | 0.120170 | 0.0600848 | − | 0.998193i | \(-0.480863\pi\) | ||||
0.0600848 | + | 0.998193i | \(0.480863\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.48528 | 0.211190 | ||||||||
\(944\) | −19.4558 | −0.633234 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.65685 | −0.216433 | ||||||||
\(947\) | −9.45584 | −0.307274 | −0.153637 | − | 0.988127i | \(-0.549099\pi\) | ||||
−0.153637 | + | 0.988127i | \(0.549099\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.00000 | −0.162307 | ||||||||
\(950\) | 3.82843 | 0.124211 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −21.3137 | −0.690781 | ||||||||
\(953\) | −46.1421 | −1.49469 | −0.747345 | − | 0.664436i | \(-0.768672\pi\) | ||||
−0.747345 | + | 0.664436i | \(0.768672\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −20.0711 | −0.649485 | ||||||||
\(956\) | 94.2843 | 3.04937 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −63.1127 | −2.03908 | ||||||||
\(959\) | 8.41421 | 0.271709 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | −49.4558 | −1.59452 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −60.4853 | −1.94810 | ||||||||
\(965\) | −5.51472 | −0.177525 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.8284 | 0.444692 | 0.222346 | − | 0.974968i | \(-0.428629\pi\) | ||||
0.222346 | + | 0.974968i | \(0.428629\pi\) | |||||||
\(968\) | −47.7990 | −1.53632 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 34.1421 | 1.09624 | ||||||||
\(971\) | 13.4558 | 0.431819 | 0.215909 | − | 0.976413i | \(-0.430728\pi\) | ||||
0.215909 | + | 0.976413i | \(0.430728\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −21.3137 | −0.683286 | ||||||||
\(974\) | 73.1838 | 2.34496 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −25.4558 | −0.814822 | ||||||||
\(977\) | −43.5269 | −1.39255 | −0.696275 | − | 0.717775i | \(-0.745160\pi\) | ||||
−0.696275 | + | 0.717775i | \(0.745160\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.58579 | −0.114602 | ||||||||
\(980\) | 3.82843 | 0.122295 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −30.4853 | −0.972824 | ||||||||
\(983\) | −3.02944 | −0.0966240 | −0.0483120 | − | 0.998832i | \(-0.515384\pi\) | ||||
−0.0483120 | + | 0.998832i | \(0.515384\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.8995 | 0.411012 | ||||||||
\(986\) | −46.6274 | −1.48492 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 14.6569 | 0.466297 | ||||||||
\(989\) | 5.51472 | 0.175358 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.1716 | 0.736069 | 0.368035 | − | 0.929812i | \(-0.380031\pi\) | ||||
0.368035 | + | 0.929812i | \(0.380031\pi\) | |||||||
\(992\) | −9.51472 | −0.302093 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.82843 | −0.153148 | ||||||||
\(995\) | −2.41421 | −0.0765357 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −31.5147 | −0.998081 | −0.499041 | − | 0.866579i | \(-0.666314\pi\) | ||||
−0.499041 | + | 0.866579i | \(0.666314\pi\) | |||||||
\(998\) | 0.485281 | 0.0153613 | ||||||||
\(999\) | 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 | 945.2.a.k.1.2 | yes | 2 | |
3.2 | odd | 2 | 945.2.a.b.1.1 | ✓ | 2 | ||
5.4 | even | 2 | 4725.2.a.v.1.1 | 2 | |||
7.6 | odd | 2 | 6615.2.a.w.1.2 | 2 | |||
15.14 | odd | 2 | 4725.2.a.bg.1.2 | 2 | |||
21.20 | even | 2 | 6615.2.a.l.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
945.2.a.b.1.1 | ✓ | 2 | 3.2 | odd | 2 | ||
945.2.a.k.1.2 | yes | 2 | 1.1 | even | 1 | trivial | |
4725.2.a.v.1.1 | 2 | 5.4 | even | 2 | |||
4725.2.a.bg.1.2 | 2 | 15.14 | odd | 2 | |||
6615.2.a.l.1.1 | 2 | 21.20 | even | 2 | |||
6615.2.a.w.1.2 | 2 | 7.6 | odd | 2 |