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 | 1.1 | ||
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 | \(-0.825557\pi\) | ||||
−0.853553 | + | 0.521005i | \(0.825557\pi\) | |||||||
\(3\) | 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 | \(-0.519890\pi\) | ||||
−0.0624450 | + | 0.998048i | \(0.519890\pi\) | |||||||
\(12\) | 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 | \(-0.699115\pi\) | ||||
−0.585533 | + | 0.810649i | \(0.699115\pi\) | |||||||
\(18\) | 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 | \(-0.472473\pi\) | ||||
0.0863695 | + | 0.996263i | \(0.472473\pi\) | |||||||
\(24\) | 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 | \(-0.378881\pi\) | ||||
0.371391 | + | 0.928477i | \(0.378881\pi\) | |||||||
\(30\) | 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 | \(-0.290648\pi\) | ||||
0.611297 | + | 0.791401i | \(0.290648\pi\) | |||||||
\(42\) | 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 | \(-0.683820\pi\) | ||||
−0.545920 | + | 0.837837i | \(0.683820\pi\) | |||||||
\(48\) | 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 | \(-0.230736\pi\) | ||||
0.748580 | + | 0.663044i | \(0.230736\pi\) | |||||||
\(54\) | 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 | \(-0.361273\pi\) | ||||
0.422156 | + | 0.906523i | \(0.361273\pi\) | |||||||
\(60\) | 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 | \(-0.537866\pi\) | ||||
−0.118678 | + | 0.992933i | \(0.537866\pi\) | |||||||
\(72\) | 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 | \(-0.365247\pi\) | ||||
0.410808 | + | 0.911722i | \(0.365247\pi\) | |||||||
\(84\) | 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 | \(-0.348275\pi\) | ||||
0.458812 | + | 0.888533i | \(0.348275\pi\) | |||||||
\(90\) | 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 | \(-0.0523605\pi\) | ||||
0.986501 | + | 0.163755i | \(0.0523605\pi\) | |||||||
\(102\) | 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 | \(-0.330819\pi\) | ||||
0.506825 | + | 0.862049i | \(0.330819\pi\) | |||||||
\(108\) | 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 | \(-0.541400\pi\) | ||||
−0.129695 | + | 0.991554i | \(0.541400\pi\) | |||||||
\(114\) | 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 | \(-0.677970\pi\) | ||||
−0.530432 | + | 0.847728i | \(0.677970\pi\) | |||||||
\(132\) | 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 | \(-0.382969\pi\) | ||||
0.359437 | + | 0.933169i | \(0.382969\pi\) | |||||||
\(138\) | 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 | \(-0.760049\pi\) | ||||
−0.729075 | + | 0.684434i | \(0.760049\pi\) | |||||||
\(150\) | 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 | \(-0.355779\pi\) | ||||
0.437741 | + | 0.899101i | \(0.355779\pi\) | |||||||
\(168\) | 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 | \(-0.697784\pi\) | ||||
−0.582140 | + | 0.813089i | \(0.697784\pi\) | |||||||
\(174\) | 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 | \(-0.328521\pi\) | ||||
0.513037 | + | 0.858367i | \(0.328521\pi\) | |||||||
\(180\) | 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 | \(-0.241310\pi\) | ||||
0.726146 | + | 0.687541i | \(0.241310\pi\) | |||||||
\(192\) | 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 | \(-0.651981\pi\) | ||||
−0.459525 | + | 0.888165i | \(0.651981\pi\) | |||||||
\(198\) | 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 | \(-0.601931\pi\) | ||||
−0.314780 | + | 0.949165i | \(0.601931\pi\) | |||||||
\(228\) | 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 | \(-0.341793\pi\) | ||||
0.476809 | + | 0.879007i | \(0.341793\pi\) | |||||||
\(234\) | 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 | \(-0.793322\pi\) | ||||
−0.796508 | + | 0.604629i | \(0.793322\pi\) | |||||||
\(240\) | 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 | \(-0.481326\pi\) | ||||
0.0586337 | + | 0.998280i | \(0.481326\pi\) | |||||||
\(252\) | 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 | \(-0.563392\pi\) | ||||
−0.197837 | + | 0.980235i | \(0.563392\pi\) | |||||||
\(258\) | 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 | \(-0.535965\pi\) | ||||
−0.112746 | + | 0.993624i | \(0.535965\pi\) | |||||||
\(264\) | 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 | \(-0.359642\pi\) | ||||
0.426798 | + | 0.904347i | \(0.359642\pi\) | |||||||
\(270\) | 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 | \(-0.808788\pi\) | ||||
−0.824935 | + | 0.565228i | \(0.808788\pi\) | |||||||
\(282\) | 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 | \(-0.318439\pi\) | ||||
0.539961 | + | 0.841690i | \(0.318439\pi\) | |||||||
\(294\) | 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 | \(-0.633308\pi\) | ||||
−0.406663 | + | 0.913578i | \(0.633308\pi\) | |||||||
\(312\) | 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 | \(-0.794082\pi\) | ||||
−0.797951 | + | 0.602723i | \(0.794082\pi\) | |||||||
\(318\) | 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 | \(-0.527130\pi\) | ||||
−0.0851295 | + | 0.996370i | \(0.527130\pi\) | |||||||
\(348\) | 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 | \(-0.744907\pi\) | ||||
−0.695703 | + | 0.718330i | \(0.744907\pi\) | |||||||
\(354\) | 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 | \(-0.773494\pi\) | ||||
−0.757324 | + | 0.653039i | \(0.773494\pi\) | |||||||
\(360\) | 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 | \(-0.585126\pi\) | ||||
−0.264255 | + | 0.964453i | \(0.585126\pi\) | |||||||
\(384\) | 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 | \(-0.355361\pi\) | ||||
0.438920 | + | 0.898526i | \(0.355361\pi\) | |||||||
\(390\) | 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 | \(-0.546252\pi\) | ||||
−0.144794 | + | 0.989462i | \(0.546252\pi\) | |||||||
\(402\) | 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 | \(-0.475316\pi\) | ||||
0.0774707 | + | 0.996995i | \(0.475316\pi\) | |||||||
\(420\) | 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 | \(-0.159538\pi\) | ||||
0.877005 | + | 0.480480i | \(0.159538\pi\) | |||||||
\(432\) | 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 | \(-0.553405\pi\) | ||||
−0.166989 | + | 0.985959i | \(0.553405\pi\) | |||||||
\(444\) | 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 | \(-0.415087\pi\) | ||||
0.263610 | + | 0.964629i | \(0.415087\pi\) | |||||||
\(450\) | 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 | \(-0.397208\pi\) | ||||
0.317346 | + | 0.948310i | \(0.397208\pi\) | |||||||
\(462\) | 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 | \(-0.512205\pi\) | ||||
−0.0383350 | + | 0.999265i | \(0.512205\pi\) | |||||||
\(468\) | 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 | \(-0.296267\pi\) | ||||
0.597232 | + | 0.802068i | \(0.296267\pi\) | |||||||
\(480\) | 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 | \(-0.408028\pi\) | ||||
0.284934 | + | 0.958547i | \(0.408028\pi\) | |||||||
\(492\) | 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 | \(-0.207851\pi\) | ||||
0.794274 | + | 0.607560i | \(0.207851\pi\) | |||||||
\(504\) | 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 | \(-0.530686\pi\) | ||||
−0.0962533 | + | 0.995357i | \(0.530686\pi\) | |||||||
\(510\) | 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 | \(-0.705660\pi\) | ||||
−0.602076 | + | 0.798439i | \(0.705660\pi\) | |||||||
\(522\) | 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 | \(-0.878397\pi\) | ||||
−0.927911 | + | 0.372801i | \(0.878397\pi\) | |||||||
\(558\) | 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 | \(-0.700639\pi\) | ||||
−0.589409 | + | 0.807835i | \(0.700639\pi\) | |||||||
\(564\) | 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 | \(-0.558281\pi\) | ||||
−0.182074 | + | 0.983285i | \(0.558281\pi\) | |||||||
\(570\) | 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 | \(-0.584319\pi\) | ||||
−0.261810 | + | 0.965120i | \(0.584319\pi\) | |||||||
\(588\) | 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 | \(-0.435124\pi\) | ||||
0.202407 | + | 0.979301i | \(0.435124\pi\) | |||||||
\(594\) | 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 | \(-0.533228\pi\) | ||||
−0.104200 | + | 0.994556i | \(0.533228\pi\) | |||||||
\(600\) | 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 | \(-0.666150\pi\) | ||||
−0.498592 | + | 0.866837i | \(0.666150\pi\) | |||||||
\(618\) | 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 | \(-0.496949\pi\) | ||||
0.00958373 | + | 0.999954i | \(0.496949\pi\) | |||||||
\(642\) | 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 | \(-0.334005\pi\) | ||||
0.498171 | + | 0.867079i | \(0.334005\pi\) | |||||||
\(648\) | 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 | \(-0.448701\pi\) | ||||
0.160465 | + | 0.987042i | \(0.448701\pi\) | |||||||
\(654\) | 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 | \(-0.422718\pi\) | ||||
0.240410 | + | 0.970671i | \(0.422718\pi\) | |||||||
\(660\) | 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 | \(-0.585801\pi\) | ||||
−0.266300 | + | 0.963890i | \(0.585801\pi\) | |||||||
\(678\) | 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 | \(-0.404071\pi\) | ||||
0.296827 | + | 0.954931i | \(0.404071\pi\) | |||||||
\(684\) | 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 | \(-0.679784\pi\) | ||||
−0.535253 | + | 0.844692i | \(0.679784\pi\) | |||||||
\(702\) | 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 | \(-0.267348\pi\) | ||||
0.667539 | + | 0.744575i | \(0.267348\pi\) | |||||||
\(720\) | 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 | \(-0.568592\pi\) | ||||
−0.213824 | + | 0.976872i | \(0.568592\pi\) | |||||||
\(744\) | 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 | \(-0.352716\pi\) | ||||
0.446372 | + | 0.894848i | \(0.352716\pi\) | |||||||
\(762\) | 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 | \(-0.208078\pi\) | ||||
0.793841 | + | 0.608125i | \(0.208078\pi\) | |||||||
\(774\) | 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 | \(-0.591454\pi\) | ||||
−0.283375 | + | 0.959009i | \(0.591454\pi\) | |||||||
\(798\) | 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 | \(-0.868264\pi\) | ||||
−0.915575 | + | 0.402147i | \(0.868264\pi\) | |||||||
\(810\) | 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 | \(-0.550364\pi\) | ||||
−0.157565 | + | 0.987509i | \(0.550364\pi\) | |||||||
\(822\) | 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 | \(-0.718736\pi\) | ||||
−0.634359 | + | 0.773039i | \(0.718736\pi\) | |||||||
\(828\) | 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 | \(-0.353083\pi\) | ||||
0.445340 | + | 0.895362i | \(0.353083\pi\) | |||||||
\(840\) | 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 | \(-0.595557\pi\) | ||||
−0.295713 | + | 0.955277i | \(0.595557\pi\) | |||||||
\(858\) | 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 | \(-0.264158\pi\) | ||||
0.674968 | + | 0.737847i | \(0.264158\pi\) | |||||||
\(864\) | 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 | \(-0.415042\pi\) | ||||
0.263746 | + | 0.964592i | \(0.415042\pi\) | |||||||
\(882\) | 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 | \(-0.403573\pi\) | ||||
0.298322 | + | 0.954465i | \(0.403573\pi\) | |||||||
\(888\) | 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 | \(-0.263472\pi\) | ||||
0.676555 | + | 0.736392i | \(0.263472\pi\) | |||||||
\(912\) | 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 | \(-0.552610\pi\) | ||||
−0.164528 | + | 0.986372i | \(0.552610\pi\) | |||||||
\(930\) | 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 | \(-0.519137\pi\) | ||||
−0.0600848 | + | 0.998193i | \(0.519137\pi\) | |||||||
\(942\) | 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 | \(-0.450901\pi\) | ||||
0.153637 | + | 0.988127i | \(0.450901\pi\) | |||||||
\(948\) | 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 | \(-0.231328\pi\) | ||||
0.747345 | + | 0.664436i | \(0.231328\pi\) | |||||||
\(954\) | 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 | \(-0.569272\pi\) | ||||
−0.215909 | + | 0.976413i | \(0.569272\pi\) | |||||||
\(972\) | 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 | \(-0.254840\pi\) | ||||
0.696275 | + | 0.717775i | \(0.254840\pi\) | |||||||
\(978\) | 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 | \(-0.484616\pi\) | ||||
0.0483120 | + | 0.998832i | \(0.484616\pi\) | |||||||
\(984\) | 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.b.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 945.2.a.k.1.2 | yes | 2 | ||
5.4 | even | 2 | 4725.2.a.bg.1.2 | 2 | |||
7.6 | odd | 2 | 6615.2.a.l.1.1 | 2 | |||
15.14 | odd | 2 | 4725.2.a.v.1.1 | 2 | |||
21.20 | even | 2 | 6615.2.a.w.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
945.2.a.b.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
945.2.a.k.1.2 | yes | 2 | 3.2 | odd | 2 | ||
4725.2.a.v.1.1 | 2 | 15.14 | odd | 2 | |||
4725.2.a.bg.1.2 | 2 | 5.4 | even | 2 | |||
6615.2.a.l.1.1 | 2 | 7.6 | odd | 2 | |||
6615.2.a.w.1.2 | 2 | 21.20 | even | 2 |