Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [920,2,Mod(1,920)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(920, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("920.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 920 = 2^{3} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 920.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: | \(7.34623698596\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.621.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 6x - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.66908\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 920.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.66908 | 1.54099 | 0.770497 | − | 0.637444i | \(-0.220008\pi\) | ||||
0.770497 | + | 0.637444i | \(0.220008\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.66908 | 1.38678 | 0.693391 | − | 0.720562i | \(-0.256116\pi\) | ||||
0.693391 | + | 0.720562i | \(0.256116\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.12398 | 1.37466 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.21417 | −0.366088 | −0.183044 | − | 0.983105i | \(-0.558595\pi\) | ||||
−0.183044 | + | 0.983105i | \(0.558595\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.21417 | 0.614102 | 0.307051 | − | 0.951693i | \(-0.400658\pi\) | ||||
0.307051 | + | 0.951693i | \(0.400658\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.66908 | −0.689153 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.21417 | 0.294481 | 0.147240 | − | 0.989101i | \(-0.452961\pi\) | ||||
0.147240 | + | 0.989101i | \(0.452961\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.57889 | −0.591637 | −0.295819 | − | 0.955244i | \(-0.595592\pi\) | ||||
−0.295819 | + | 0.955244i | \(0.595592\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 9.79306 | 2.13702 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.00000 | 0.577350 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.45490 | 0.270169 | 0.135084 | − | 0.990834i | \(-0.456869\pi\) | ||||
0.135084 | + | 0.990834i | \(0.456869\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.46214 | −1.16063 | −0.580317 | − | 0.814390i | \(-0.697072\pi\) | ||||
−0.580317 | + | 0.814390i | \(0.697072\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.24073 | −0.564139 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.66908 | −0.620188 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.00000 | 0.657596 | 0.328798 | − | 0.944400i | \(-0.393356\pi\) | ||||
0.328798 | + | 0.944400i | \(0.393356\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.90981 | 0.946327 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.9170 | −1.70496 | −0.852478 | − | 0.522763i | \(-0.824901\pi\) | ||||
−0.852478 | + | 0.522763i | \(0.824901\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.90981 | 1.05374 | 0.526868 | − | 0.849947i | \(-0.323366\pi\) | ||||
0.526868 | + | 0.849947i | \(0.323366\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.12398 | −0.614767 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.45490 | 0.795680 | 0.397840 | − | 0.917455i | \(-0.369760\pi\) | ||||
0.397840 | + | 0.917455i | \(0.369760\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.46214 | 0.923163 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.24073 | 0.453793 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.81962 | 0.524665 | 0.262332 | − | 0.964978i | \(-0.415508\pi\) | ||||
0.262332 | + | 0.964978i | \(0.415508\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.21417 | 0.163719 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.88325 | −0.911709 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.24797 | −0.553038 | −0.276519 | − | 0.961008i | \(-0.589181\pi\) | ||||
−0.276519 | + | 0.961008i | \(0.589181\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.78583 | 0.868836 | 0.434418 | − | 0.900711i | \(-0.356954\pi\) | ||||
0.434418 | + | 0.900711i | \(0.356954\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 15.1312 | 1.90635 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.21417 | −0.274635 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.8567 | 1.57070 | 0.785348 | − | 0.619055i | \(-0.212484\pi\) | ||||
0.785348 | + | 0.619055i | \(0.212484\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.66908 | 0.321319 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.91705 | −0.820902 | −0.410451 | − | 0.911883i | \(-0.634629\pi\) | ||||
−0.410451 | + | 0.911883i | \(0.634629\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −15.2214 | −1.78153 | −0.890766 | − | 0.454463i | \(-0.849831\pi\) | ||||
−0.890766 | + | 0.454463i | \(0.849831\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.66908 | 0.308199 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.45490 | −0.507683 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.36471 | −0.484968 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.5861 | −1.71080 | −0.855400 | − | 0.517968i | \(-0.826688\pi\) | ||||
−0.855400 | + | 0.517968i | \(0.826688\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.21417 | −0.131696 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.88325 | 0.416329 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.9098 | −1.15644 | −0.578219 | − | 0.815882i | \(-0.696252\pi\) | ||||
−0.578219 | + | 0.815882i | \(0.696252\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.12398 | 0.851625 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −17.2480 | −1.78853 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.57889 | 0.264588 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.69563 | 0.172165 | 0.0860827 | − | 0.996288i | \(-0.472565\pi\) | ||||
0.0860827 | + | 0.996288i | \(0.472565\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.00724 | −0.503246 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.24797 | −0.223681 | −0.111841 | − | 0.993726i | \(-0.535675\pi\) | ||||
−0.111841 | + | 0.993726i | \(0.535675\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.78583 | −0.274495 | −0.137248 | − | 0.990537i | \(-0.543826\pi\) | ||||
−0.137248 | + | 0.990537i | \(0.543826\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −9.79306 | −0.955705 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.1578 | 1.27201 | 0.636005 | − | 0.771685i | \(-0.280586\pi\) | ||||
0.636005 | + | 0.771685i | \(0.280586\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.42111 | 0.327683 | 0.163842 | − | 0.986487i | \(-0.447611\pi\) | ||||
0.163842 | + | 0.986487i | \(0.447611\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.6763 | 1.01335 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.0000 | −0.940721 | −0.470360 | − | 0.882474i | \(-0.655876\pi\) | ||||
−0.470360 | + | 0.882474i | \(0.655876\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.00000 | −0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.13122 | 0.844182 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.45490 | 0.408380 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.52578 | −0.865980 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −29.1385 | −2.62733 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.9508 | 1.77035 | 0.885175 | − | 0.465258i | \(-0.154038\pi\) | ||||
0.885175 | + | 0.465258i | \(0.154038\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 18.4428 | 1.62380 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.70287 | −0.847744 | −0.423872 | − | 0.905722i | \(-0.639329\pi\) | ||||
−0.423872 | + | 0.905722i | \(0.639329\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.46214 | −0.820472 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.00000 | −0.258199 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.82685 | 0.241514 | 0.120757 | − | 0.992682i | \(-0.461468\pi\) | ||||
0.120757 | + | 0.992682i | \(0.461468\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.36471 | 0.200572 | 0.100286 | − | 0.994959i | \(-0.468024\pi\) | ||||
0.100286 | + | 0.994959i | \(0.468024\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 14.5596 | 1.22614 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.68840 | −0.224815 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.45490 | −0.120823 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 17.2480 | 1.42259 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.9170 | −0.976282 | −0.488141 | − | 0.872765i | \(-0.662325\pi\) | ||||
−0.488141 | + | 0.872765i | \(0.662325\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.57889 | 0.779519 | 0.389759 | − | 0.920917i | \(-0.372558\pi\) | ||||
0.389759 | + | 0.920917i | \(0.372558\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.00724 | 0.404811 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.46214 | 0.519052 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.7439 | −1.49593 | −0.747963 | − | 0.663740i | \(-0.768968\pi\) | ||||
−0.747963 | + | 0.663740i | \(0.768968\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.1949 | 0.808505 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.66908 | 0.289164 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.3188 | −1.51317 | −0.756584 | − | 0.653896i | \(-0.773133\pi\) | ||||
−0.756584 | + | 0.653896i | \(0.773133\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.24073 | 0.252290 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.81962 | −0.140806 | −0.0704031 | − | 0.997519i | \(-0.522429\pi\) | ||||
−0.0704031 | + | 0.997519i | \(0.522429\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.09743 | −0.622879 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −10.6353 | −0.813301 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.9581 | 1.21327 | 0.606635 | − | 0.794981i | \(-0.292519\pi\) | ||||
0.606635 | + | 0.794981i | \(0.292519\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.66908 | 0.277356 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −11.3382 | −0.852228 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.9508 | 1.34171 | 0.670854 | − | 0.741589i | \(-0.265928\pi\) | ||||
0.670854 | + | 0.741589i | \(0.265928\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.33092 | 0.470574 | 0.235287 | − | 0.971926i | \(-0.424397\pi\) | ||||
0.235287 | + | 0.971926i | \(0.424397\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 18.1119 | 1.33887 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.00000 | −0.294086 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.47422 | −0.107806 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 11.0072 | 0.800659 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.1578 | −1.09678 | −0.548389 | − | 0.836223i | \(-0.684759\pi\) | ||||
−0.548389 | + | 0.836223i | \(0.684759\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.9879 | 1.36678 | 0.683390 | − | 0.730053i | \(-0.260505\pi\) | ||||
0.683390 | + | 0.730053i | \(0.260505\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.90981 | −0.423210 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −19.1650 | −1.36545 | −0.682725 | − | 0.730675i | \(-0.739205\pi\) | ||||
−0.682725 | + | 0.730675i | \(0.739205\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.76651 | −0.408777 | −0.204388 | − | 0.978890i | \(-0.565521\pi\) | ||||
−0.204388 | + | 0.978890i | \(0.565521\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 34.3155 | 2.42043 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.33816 | 0.374665 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.9170 | 0.762480 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.12398 | 0.286637 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.13122 | 0.216591 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.4057 | −1.19826 | −0.599130 | − | 0.800652i | \(-0.704487\pi\) | ||||
−0.599130 | + | 0.800652i | \(0.704487\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −18.4621 | −1.26501 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.90981 | −0.471245 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −23.7101 | −1.60955 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −40.6272 | −2.74533 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.68840 | 0.180841 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.6763 | −0.982799 | −0.491399 | − | 0.870934i | \(-0.663514\pi\) | ||||
−0.491399 | + | 0.870934i | \(0.663514\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.12398 | 0.274932 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.4283 | 1.09039 | 0.545194 | − | 0.838310i | \(-0.316456\pi\) | ||||
0.545194 | + | 0.838310i | \(0.316456\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.3526 | 1.27886 | 0.639429 | − | 0.768850i | \(-0.279171\pi\) | ||||
0.639429 | + | 0.768850i | \(0.279171\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −11.8905 | −0.782337 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −19.4549 | −1.27453 | −0.637267 | − | 0.770643i | \(-0.719935\pi\) | ||||
−0.637267 | + | 0.770643i | \(0.719935\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.45490 | −0.355839 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 23.7029 | 1.53321 | 0.766606 | − | 0.642118i | \(-0.221944\pi\) | ||||
0.766606 | + | 0.642118i | \(0.221944\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.233492 | 0.0150405 | 0.00752027 | − | 0.999972i | \(-0.497606\pi\) | ||||
0.00752027 | + | 0.999972i | \(0.497606\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −20.6498 | −1.32468 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.46214 | −0.412851 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.71011 | −0.363325 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −41.6006 | −2.63633 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.7511 | 1.37292 | 0.686460 | − | 0.727168i | \(-0.259164\pi\) | ||||
0.686460 | + | 0.727168i | \(0.259164\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.21417 | −0.0763345 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.24073 | −0.202942 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −16.3116 | −1.01749 | −0.508745 | − | 0.860917i | \(-0.669890\pi\) | ||||
−0.508745 | + | 0.860917i | \(0.669890\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.6763 | 0.911942 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.00000 | 0.371391 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.53786 | −0.156491 | −0.0782455 | − | 0.996934i | \(-0.524932\pi\) | ||||
−0.0782455 | + | 0.996934i | \(0.524932\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.81962 | −0.234637 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −29.1191 | −1.78206 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.54510 | −0.155177 | −0.0775886 | − | 0.996985i | \(-0.524722\pi\) | ||||
−0.0775886 | + | 0.996985i | \(0.524722\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.1795 | 1.46880 | 0.734400 | − | 0.678717i | \(-0.237464\pi\) | ||||
0.734400 | + | 0.678717i | \(0.237464\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 21.6836 | 1.31235 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.21417 | −0.0732175 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −21.2359 | −1.27594 | −0.637970 | − | 0.770061i | \(-0.720226\pi\) | ||||
−0.637970 | + | 0.770061i | \(0.720226\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −26.6498 | −1.59548 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.8872 | −0.828441 | −0.414220 | − | 0.910177i | \(-0.635946\pi\) | ||||
−0.414220 | + | 0.910177i | \(0.635946\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −29.5330 | −1.75556 | −0.877778 | − | 0.479068i | \(-0.840975\pi\) | ||||
−0.877778 | + | 0.479068i | \(0.840975\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.88325 | 0.407729 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −40.0555 | −2.36440 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.5258 | −0.913281 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.52578 | 0.265306 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −24.0821 | −1.40689 | −0.703444 | − | 0.710750i | \(-0.748356\pi\) | ||||
−0.703444 | + | 0.710750i | \(0.748356\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.24797 | 0.247326 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.64252 | −0.211361 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.21417 | 0.128049 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 25.3526 | 1.46130 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.00000 | −0.344691 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.78583 | −0.388555 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.9436 | 1.13824 | 0.569121 | − | 0.822254i | \(-0.307284\pi\) | ||||
0.569121 | + | 0.822254i | \(0.307284\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.43559 | −0.422996 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.97345 | −0.168609 | −0.0843043 | − | 0.996440i | \(-0.526867\pi\) | ||||
−0.0843043 | + | 0.996440i | \(0.526867\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.4887 | 0.875473 | 0.437736 | − | 0.899103i | \(-0.355780\pi\) | ||||
0.437736 | + | 0.899103i | \(0.355780\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −15.1312 | −0.852548 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.82685 | 0.495765 | 0.247883 | − | 0.968790i | \(-0.420265\pi\) | ||||
0.247883 | + | 0.968790i | \(0.420265\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.76651 | −0.0989055 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 35.1191 | 1.96016 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.13122 | −0.174226 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.21417 | 0.122820 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9.13122 | 0.504958 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 20.0145 | 1.10343 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.4018 | 0.956489 | 0.478245 | − | 0.878227i | \(-0.341273\pi\) | ||||
0.478245 | + | 0.878227i | \(0.341273\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 16.4959 | 0.903972 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.8567 | −0.702437 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.9541 | 1.46828 | 0.734142 | − | 0.678995i | \(-0.237584\pi\) | ||||
0.734142 | + | 0.678995i | \(0.237584\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −26.6908 | −1.44964 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.84617 | 0.424894 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.97345 | −0.106556 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.66908 | −0.143698 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.1240 | −0.543484 | −0.271742 | − | 0.962370i | \(-0.587600\pi\) | ||||
−0.271742 | + | 0.962370i | \(0.587600\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.38732 | 0.395434 | 0.197717 | − | 0.980259i | \(-0.436647\pi\) | ||||
0.197717 | + | 0.980259i | \(0.436647\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.64252 | 0.354552 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.8833 | 0.738931 | 0.369466 | − | 0.929244i | \(-0.379541\pi\) | ||||
0.369466 | + | 0.929244i | \(0.379541\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.91705 | 0.367119 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 11.8905 | 0.629312 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.0902 | 0.796430 | 0.398215 | − | 0.917292i | \(-0.369630\pi\) | ||||
0.398215 | + | 0.917292i | \(0.369630\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.3493 | −0.649965 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −25.4251 | −1.33447 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.2214 | 0.796725 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −24.0289 | −1.25430 | −0.627150 | − | 0.778898i | \(-0.715779\pi\) | ||||
−0.627150 | + | 0.778898i | \(0.715779\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −45.0217 | −2.34374 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 14.0145 | 0.727595 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 30.6908 | 1.58911 | 0.794554 | − | 0.607193i | \(-0.207704\pi\) | ||||
0.794554 | + | 0.607193i | \(0.207704\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.66908 | −0.137831 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.22141 | 0.165911 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.07087 | 0.106374 | 0.0531869 | − | 0.998585i | \(-0.483062\pi\) | ||||
0.0531869 | + | 0.998585i | \(0.483062\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 53.2504 | 2.72810 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.58612 | −0.0810472 | −0.0405236 | − | 0.999179i | \(-0.512903\pi\) | ||||
−0.0405236 | + | 0.999179i | \(0.512903\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.45490 | 0.227043 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 28.4959 | 1.44853 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 21.2142 | 1.07560 | 0.537801 | − | 0.843072i | \(-0.319255\pi\) | ||||
0.537801 | + | 0.843072i | \(0.319255\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.21417 | 0.0614035 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −25.8977 | −1.30637 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.93965 | −0.0973485 | −0.0486742 | − | 0.998815i | \(-0.515500\pi\) | ||||
−0.0486742 | + | 0.998815i | \(0.515500\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −25.2552 | −1.26434 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.69893 | −0.284591 | −0.142295 | − | 0.989824i | \(-0.545448\pi\) | ||||
−0.142295 | + | 0.989824i | \(0.545448\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.3083 | −0.712748 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.36471 | 0.216884 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.85670 | −0.240738 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.53786 | 0.174936 | 0.0874679 | − | 0.996167i | \(-0.472122\pi\) | ||||
0.0874679 | + | 0.996167i | \(0.472122\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.54510 | 0.372172 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −15.5861 | −0.766943 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.5861 | 0.765093 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.31160 | 0.309081 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 28.2624 | 1.38071 | 0.690355 | − | 0.723471i | \(-0.257454\pi\) | ||||
0.690355 | + | 0.723471i | \(0.257454\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34.0974 | 1.66181 | 0.830904 | − | 0.556417i | \(-0.187824\pi\) | ||||
0.830904 | + | 0.556417i | \(0.187824\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 22.4959 | 1.09379 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.21417 | 0.0588961 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 24.8977 | 1.20489 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.17554 | −0.346438 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.2850 | −0.639918 | −0.319959 | − | 0.947431i | \(-0.603669\pi\) | ||||
−0.319959 | + | 0.947431i | \(0.603669\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.0603 | 0.531526 | 0.265763 | − | 0.964038i | \(-0.414376\pi\) | ||||
0.265763 | + | 0.964038i | \(0.414376\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.88325 | −0.186188 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.57889 | −0.123365 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.1916 | −0.915963 | −0.457982 | − | 0.888962i | \(-0.651427\pi\) | ||||
−0.457982 | + | 0.888962i | \(0.651427\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 26.6498 | 1.26904 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.2818 | 1.15366 | 0.576831 | − | 0.816864i | \(-0.304289\pi\) | ||||
0.576831 | + | 0.816864i | \(0.304289\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.9098 | 0.517175 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −31.8075 | −1.50444 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.8413 | 0.700406 | 0.350203 | − | 0.936674i | \(-0.386113\pi\) | ||||
0.350203 | + | 0.936674i | \(0.386113\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.2552 | 0.624163 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 25.5668 | 1.20123 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.12398 | −0.380858 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.5861 | 0.729088 | 0.364544 | − | 0.931186i | \(-0.381225\pi\) | ||||
0.364544 | + | 0.931186i | \(0.381225\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.64252 | 0.170019 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.1312 | −0.658157 | −0.329078 | − | 0.944303i | \(-0.606738\pi\) | ||||
−0.329078 | + | 0.944303i | \(0.606738\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.7584 | 1.24357 | 0.621784 | − | 0.783189i | \(-0.286408\pi\) | ||||
0.621784 | + | 0.783189i | \(0.286408\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 17.2480 | 0.799855 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 26.6908 | 1.23510 | 0.617551 | − | 0.786531i | \(-0.288125\pi\) | ||||
0.617551 | + | 0.786531i | \(0.288125\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 47.1722 | 2.17821 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −50.0289 | −2.30521 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.38972 | −0.385760 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.57889 | −0.118327 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 15.7520 | 0.721236 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.90981 | 0.224335 | 0.112167 | − | 0.993689i | \(-0.464221\pi\) | ||||
0.112167 | + | 0.993689i | \(0.464221\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.85670 | 0.403831 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.79306 | 0.445600 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.69563 | −0.0769947 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.7786 | 0.760310 | 0.380155 | − | 0.924923i | \(-0.375871\pi\) | ||||
0.380155 | + | 0.924923i | \(0.375871\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −51.5635 | −2.33178 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 41.4839 | 1.87214 | 0.936070 | − | 0.351814i | \(-0.114435\pi\) | ||||
0.936070 | + | 0.351814i | \(0.114435\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.76651 | 0.0795595 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.00724 | 0.225059 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −25.3792 | −1.13841 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.47751 | −0.289973 | −0.144987 | − | 0.989434i | \(-0.546314\pi\) | ||||
−0.144987 | + | 0.989434i | \(0.546314\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.85670 | −0.216981 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 37.3825 | 1.66680 | 0.833401 | − | 0.552669i | \(-0.186390\pi\) | ||||
0.833401 | + | 0.552669i | \(0.186390\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.24797 | 0.100033 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −21.6127 | −0.959853 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15.0410 | −0.666682 | −0.333341 | − | 0.942806i | \(-0.608176\pi\) | ||||
−0.333341 | + | 0.942806i | \(0.608176\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −55.8486 | −2.47060 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.73666 | −0.341582 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.78583 | 0.122758 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.62321 | −0.291288 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 42.5934 | 1.86964 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.9469 | 0.698646 | 0.349323 | − | 0.937002i | \(-0.386412\pi\) | ||||
0.349323 | + | 0.937002i | \(0.386412\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.8567 | 0.474730 | 0.237365 | − | 0.971420i | \(-0.423716\pi\) | ||||
0.237365 | + | 0.971420i | \(0.423716\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 9.79306 | 0.427404 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.84617 | −0.341785 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −17.5185 | −0.760240 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −24.1722 | −1.04702 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.1578 | −0.568860 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 47.9122 | 2.06756 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.84617 | −0.337958 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −30.3792 | −1.30610 | −0.653052 | − | 0.757313i | \(-0.726512\pi\) | ||||
−0.653052 | + | 0.757313i | \(0.726512\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 16.8977 | 0.725151 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.42111 | −0.146544 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.4090 | 1.21468 | 0.607341 | − | 0.794441i | \(-0.292236\pi\) | ||||
0.607341 | + | 0.794441i | \(0.292236\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 27.9846 | 1.19435 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.75203 | −0.159842 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −10.6763 | −0.453184 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 36.7584 | 1.55750 | 0.778751 | − | 0.627333i | \(-0.215853\pi\) | ||||
0.778751 | + | 0.627333i | \(0.215853\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.2995 | 0.647101 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.93481 | −0.166128 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.03708 | −0.127998 | −0.0639989 | − | 0.997950i | \(-0.520385\pi\) | ||||
−0.0639989 | + | 0.997950i | \(0.520385\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.0000 | 0.420703 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −16.0145 | −0.672545 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −32.2093 | −1.35029 | −0.675143 | − | 0.737687i | \(-0.735918\pi\) | ||||
−0.675143 | + | 0.737687i | \(0.735918\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.7777 | 1.16246 | 0.581230 | − | 0.813739i | \(-0.302572\pi\) | ||||
0.581230 | + | 0.813739i | \(0.302572\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −40.4573 | −1.69013 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.2890 | 0.469967 | 0.234984 | − | 0.971999i | \(-0.424496\pi\) | ||||
0.234984 | + | 0.971999i | \(0.424496\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 50.6803 | 2.10620 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −57.1867 | −2.37251 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.63768 | −0.192073 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −9.13122 | −0.377530 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23.6609 | 0.976592 | 0.488296 | − | 0.872678i | \(-0.337619\pi\) | ||||
0.488296 | + | 0.872678i | \(0.337619\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.6651 | 0.686675 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −51.1529 | −2.10415 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −17.8341 | −0.732358 | −0.366179 | − | 0.930544i | \(-0.619334\pi\) | ||||
−0.366179 | + | 0.930544i | \(0.619334\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.45490 | −0.182633 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −15.3913 | −0.629923 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −23.8308 | −0.973700 | −0.486850 | − | 0.873486i | \(-0.661854\pi\) | ||||
−0.486850 | + | 0.873486i | \(0.661854\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.5297 | 0.511098 | 0.255549 | − | 0.966796i | \(-0.417744\pi\) | ||||
0.255549 | + | 0.966796i | \(0.417744\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 53.0208 | 2.15917 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.52578 | 0.387278 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.1722 | −0.940533 | −0.470266 | − | 0.882525i | \(-0.655842\pi\) | ||||
−0.470266 | + | 0.882525i | \(0.655842\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 14.2480 | 0.577357 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.0781 | 0.488628 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −44.5780 | −1.80049 | −0.900244 | − | 0.435386i | \(-0.856612\pi\) | ||||
−0.900244 | + | 0.435386i | \(0.856612\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 29.1385 | 1.17498 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −32.1385 | −1.29385 | −0.646923 | − | 0.762556i | \(-0.723944\pi\) | ||||
−0.646923 | + | 0.762556i | \(0.723944\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.5708 | 1.26894 | 0.634468 | − | 0.772949i | \(-0.281219\pi\) | ||||
0.634468 | + | 0.772949i | \(0.281219\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.00000 | 0.120386 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −40.0289 | −1.60373 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.35748 | 0.333765 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.85670 | 0.193649 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.0145 | 0.956001 | 0.478001 | − | 0.878360i | \(-0.341362\pi\) | ||||
0.478001 | + | 0.878360i | \(0.341362\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −46.4573 | −1.84651 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −19.9508 | −0.791725 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14.3083 | 0.566916 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −28.5258 | −1.12846 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.4428 | −0.412467 | −0.206233 | − | 0.978503i | \(-0.566121\pi\) | ||||
−0.206233 | + | 0.978503i | \(0.566121\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.39940 | 0.173495 | 0.0867477 | − | 0.996230i | \(-0.472353\pi\) | ||||
0.0867477 | + | 0.996230i | \(0.472353\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −18.4428 | −0.726186 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −23.6498 | −0.929768 | −0.464884 | − | 0.885372i | \(-0.653904\pi\) | ||||
−0.464884 | + | 0.885372i | \(0.653904\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.15777 | 0.202460 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −63.2842 | −2.48030 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 40.9194 | 1.60130 | 0.800651 | − | 0.599131i | \(-0.204487\pi\) | ||||
0.800651 | + | 0.599131i | \(0.204487\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.70287 | 0.379123 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −62.7728 | −2.44900 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 48.8567 | 1.90319 | 0.951593 | − | 0.307360i | \(-0.0994455\pi\) | ||||
0.951593 | + | 0.307360i | \(0.0994455\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.1529 | −0.472694 | −0.236347 | − | 0.971669i | \(-0.575950\pi\) | ||||
−0.236347 | + | 0.971669i | \(0.575950\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7.17554 | 0.278675 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 9.46214 | 0.366926 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.45490 | 0.0563341 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −39.1722 | −1.51449 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.23918 | −0.318070 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.20694 | 0.354901 | 0.177451 | − | 0.984130i | \(-0.443215\pi\) | ||||
0.177451 | + | 0.984130i | \(0.443215\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.00000 | 0.115470 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −39.8196 | −1.53039 | −0.765196 | − | 0.643797i | \(-0.777358\pi\) | ||||
−0.765196 | + | 0.643797i | \(0.777358\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.22141 | 0.238756 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 43.8486 | 1.68028 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.60544 | −0.214486 | −0.107243 | − | 0.994233i | \(-0.534202\pi\) | ||||
−0.107243 | + | 0.994233i | \(0.534202\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.82685 | −0.108009 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 51.6537 | 1.97071 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.45730 | 0.322197 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.84223 | −0.108123 | −0.0540617 | − | 0.998538i | \(-0.517217\pi\) | ||||
−0.0540617 | + | 0.998538i | \(0.517217\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −18.3719 | −0.697893 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.36471 | −0.0896986 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13.2552 | −0.502077 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −51.9267 | −1.96405 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24.4130 | −0.922065 | −0.461033 | − | 0.887383i | \(-0.652521\pi\) | ||||
−0.461033 | + | 0.887383i | \(0.652521\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.3155 | −0.389058 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −14.5596 | −0.548345 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.24797 | −0.310197 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.123983 | 0.00465629 | 0.00232814 | − | 0.999997i | \(-0.499259\pi\) | ||||
0.00232814 | + | 0.999997i | \(0.499259\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.46214 | −0.242009 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.68840 | 0.100540 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 63.2648 | 2.36267 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 47.1569 | 1.75865 | 0.879327 | − | 0.476218i | \(-0.157993\pi\) | ||||
0.879327 | + | 0.476218i | \(0.157993\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.2214 | −0.380665 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.623208 | 0.0231774 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.45490 | 0.0540338 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 43.2962 | 1.60577 | 0.802884 | − | 0.596135i | \(-0.203298\pi\) | ||||
0.802884 | + | 0.596135i | \(0.203298\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −42.0217 | −1.55636 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.38972 | 0.310305 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.5861 | 0.427943 | 0.213972 | − | 0.976840i | \(-0.431360\pi\) | ||||
0.213972 | + | 0.976840i | \(0.431360\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −17.2480 | −0.636201 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −15.6103 | −0.575012 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −30.3792 | −1.11752 | −0.558758 | − | 0.829331i | \(-0.688722\pi\) | ||||
−0.558758 | + | 0.829331i | \(0.688722\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −15.2407 | −0.559882 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35.5708 | 1.30496 | 0.652482 | − | 0.757804i | \(-0.273728\pi\) | ||||
0.652482 | + | 0.757804i | \(0.273728\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.9170 | 0.436607 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −64.2769 | −2.35177 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 48.2769 | 1.76400 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.9774 | −0.911438 | −0.455719 | − | 0.890124i | \(-0.650618\pi\) | ||||
−0.455719 | + | 0.890124i | \(0.650618\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 58.0555 | 2.11566 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.57889 | −0.348611 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.35263 | 0.339927 | 0.169964 | − | 0.985450i | \(-0.445635\pi\) | ||||
0.169964 | + | 0.985450i | \(0.445635\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.24073 | −0.117631 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.1466 | −0.657813 | −0.328907 | − | 0.944362i | \(-0.606680\pi\) | ||||
−0.328907 | + | 0.944362i | \(0.606680\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.5523 | 0.454425 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.00724 | −0.181037 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.40574 | −0.339622 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 44.3445 | 1.59910 | 0.799552 | − | 0.600597i | \(-0.205070\pi\) | ||||
0.799552 | + | 0.600597i | \(0.205070\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −43.5370 | −1.56795 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −10.8036 | −0.388578 | −0.194289 | − | 0.980944i | \(-0.562240\pi\) | ||||
−0.194289 | + | 0.980944i | \(0.562240\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.46214 | −0.232127 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 39.1722 | 1.40530 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 28.1538 | 1.00872 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.39850 | 0.300522 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.36471 | 0.155982 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18.7439 | 0.668998 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −31.7810 | −1.13287 | −0.566435 | − | 0.824107i | \(-0.691678\pi\) | ||||
−0.566435 | + | 0.824107i | \(0.691678\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.77375 | −0.241152 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −36.6908 | −1.30457 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.0250 | 0.533554 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −10.1949 | −0.361574 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 35.0594 | 1.24187 | 0.620935 | − | 0.783862i | \(-0.286753\pi\) | ||||
0.620935 | + | 0.783862i | \(0.286753\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.62321 | 0.234312 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −44.9919 | −1.58971 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 18.4815 | 0.652196 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.66908 | −0.129318 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.79306 | −0.239127 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −51.4911 | −1.81033 | −0.905165 | − | 0.425060i | \(-0.860253\pi\) | ||||
−0.905165 | + | 0.425060i | \(0.860253\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.7705 | −0.694235 | −0.347117 | − | 0.937822i | \(-0.612839\pi\) | ||||
−0.347117 | + | 0.937822i | \(0.612839\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 64.5370 | 2.26341 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 19.3188 | 0.676709 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −17.8196 | −0.623429 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 33.5032 | 1.17070 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31.8486 | 1.11152 | 0.555761 | − | 0.831342i | \(-0.312427\pi\) | ||||
0.555761 | + | 0.831342i | \(0.312427\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.34210 | 0.325645 | 0.162823 | − | 0.986655i | \(-0.447940\pi\) | ||||
0.162823 | + | 0.986655i | \(0.447940\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.24073 | −0.112828 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −30.9243 | −1.07534 | −0.537671 | − | 0.843155i | \(-0.680696\pi\) | ||||
−0.537671 | + | 0.843155i | \(0.680696\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −32.5701 | −1.13121 | −0.565603 | − | 0.824678i | \(-0.691357\pi\) | ||||
−0.565603 | + | 0.824678i | \(0.691357\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −56.6803 | −1.96622 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.84617 | 0.271854 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.81962 | 0.0629704 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −19.3864 | −0.670093 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 48.5635 | 1.67660 | 0.838299 | − | 0.545210i | \(-0.183550\pi\) | ||||
0.838299 | + | 0.545210i | \(0.183550\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.8833 | −0.927009 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −37.0660 | −1.27662 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.09743 | 0.278560 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −34.9508 | −1.20092 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −78.8260 | −2.70530 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.00000 | 0.137118 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −33.6546 | −1.15231 | −0.576156 | − | 0.817340i | \(-0.695448\pi\) | ||||
−0.576156 | + | 0.817340i | \(0.695448\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.6353 | 0.363719 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.4081 | 0.833766 | 0.416883 | − | 0.908960i | \(-0.363122\pi\) | ||||
0.416883 | + | 0.908960i | \(0.363122\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.1394 | −0.380070 | −0.190035 | − | 0.981777i | \(-0.560860\pi\) | ||||
−0.190035 | + | 0.981777i | \(0.560860\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −106.911 | −3.64353 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −15.7173 | −0.535025 | −0.267512 | − | 0.963554i | \(-0.586202\pi\) | ||||
−0.267512 | + | 0.963554i | \(0.586202\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15.9581 | −0.542591 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −41.4395 | −1.40736 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 28.4670 | 0.964567 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.99276 | 0.236669 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.66908 | −0.124038 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −33.2818 | −1.12385 | −0.561923 | − | 0.827190i | \(-0.689938\pi\) | ||||
−0.561923 | + | 0.827190i | \(0.689938\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −64.2769 | −2.16801 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.99187 | 0.302944 | 0.151472 | − | 0.988462i | \(-0.451599\pi\) | ||||
0.151472 | + | 0.988462i | \(0.451599\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 58.5258 | 1.96955 | 0.984775 | − | 0.173836i | \(-0.0556162\pi\) | ||||
0.984775 | + | 0.173836i | \(0.0556162\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 11.3382 | 0.381128 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 32.8220 | 1.10206 | 0.551028 | − | 0.834487i | \(-0.314236\pi\) | ||||
0.551028 | + | 0.834487i | \(0.314236\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 73.2012 | 2.45509 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.29952 | 0.177541 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −14.0676 | −0.470754 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −17.9508 | −0.600030 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.90981 | 0.197323 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.40180 | −0.313567 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.63768 | 0.154504 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 67.6682 | 2.25186 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.33092 | −0.210447 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.3300 | 0.940683 | 0.470341 | − | 0.882484i | \(-0.344131\pi\) | ||||
0.470341 | + | 0.882484i | \(0.344131\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.27058 | −0.307486 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.3382 | 0.508176 | 0.254088 | − | 0.967181i | \(-0.418225\pi\) | ||||
0.254088 | + | 0.967181i | \(0.418225\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.9243 | 0.626302 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −18.1119 | −0.598761 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −35.6006 | −1.17564 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −38.8036 | −1.28001 | −0.640006 | − | 0.768370i | \(-0.721068\pi\) | ||||
−0.640006 | + | 0.768370i | \(0.721068\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 53.2310 | 1.75402 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −15.3155 | −0.504117 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.00000 | 0.131519 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −11.4887 | −0.377338 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.01053 | 0.131581 | 0.0657906 | − | 0.997833i | \(-0.479043\pi\) | ||||
0.0657906 | + | 0.997833i | \(0.479043\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16.6651 | −0.546178 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7.93636 | −0.259825 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.47422 | 0.0482122 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 43.6836 | 1.42708 | 0.713540 | − | 0.700615i | \(-0.247091\pi\) | ||||
0.713540 | + | 0.700615i | \(0.247091\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 41.3406 | 1.34910 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.8534 | −0.810198 | −0.405099 | − | 0.914273i | \(-0.632763\pi\) | ||||
−0.405099 | + | 0.914273i | \(0.632763\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.9170 | −0.355508 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −11.0072 | −0.358065 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −22.1690 | −0.720394 | −0.360197 | − | 0.932876i | \(-0.617291\pi\) | ||||
−0.360197 | + | 0.932876i | \(0.617291\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −33.7029 | −1.09404 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 23.5596 | 0.763971 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 15.9050 | 0.515212 | 0.257606 | − | 0.966250i | \(-0.417066\pi\) | ||||
0.257606 | + | 0.966250i | \(0.417066\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15.1578 | 0.490494 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.71495 | −0.152413 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10.3719 | 0.334928 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.7593 | 0.347073 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 54.2624 | 1.74858 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −18.9879 | −0.611243 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 50.6272 | 1.62806 | 0.814030 | − | 0.580823i | \(-0.197269\pi\) | ||||
0.814030 | + | 0.580823i | \(0.197269\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.35748 | −0.268481 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −52.4009 | −1.68162 | −0.840812 | − | 0.541327i | \(-0.817922\pi\) | ||||
−0.840812 | + | 0.541327i | \(0.817922\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.67632 | 0.278150 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.90981 | 0.189265 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10.5258 | 0.336750 | 0.168375 | − | 0.985723i | \(-0.446148\pi\) | ||||
0.168375 | + | 0.985723i | \(0.446148\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13.2464 | 0.423357 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.1086 | 0.450453 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.44767 | 0.301334 | 0.150667 | − | 0.988585i | \(-0.451858\pi\) | ||||
0.150667 | + | 0.988585i | \(0.451858\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 19.1650 | 0.610648 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 53.4202 | 1.70038 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.90981 | 0.219719 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33.3252 | 1.05861 | 0.529305 | − | 0.848432i | \(-0.322453\pi\) | ||||
0.529305 | + | 0.848432i | \(0.322453\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 46.4468 | 1.47394 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.76651 | 0.182811 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 54.0289 | 1.71111 | 0.855557 | − | 0.517709i | \(-0.173215\pi\) | ||||
0.855557 | + | 0.517709i | \(0.173215\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 12.0000 | 0.379663 |
(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 | 920.2.a.g.1.3 | ✓ | 3 | |
3.2 | odd | 2 | 8280.2.a.bo.1.3 | 3 | |||
4.3 | odd | 2 | 1840.2.a.t.1.1 | 3 | |||
5.2 | odd | 4 | 4600.2.e.r.4049.1 | 6 | |||
5.3 | odd | 4 | 4600.2.e.r.4049.6 | 6 | |||
5.4 | even | 2 | 4600.2.a.y.1.1 | 3 | |||
8.3 | odd | 2 | 7360.2.a.ca.1.3 | 3 | |||
8.5 | even | 2 | 7360.2.a.cb.1.1 | 3 | |||
20.19 | odd | 2 | 9200.2.a.cd.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.2.a.g.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
1840.2.a.t.1.1 | 3 | 4.3 | odd | 2 | |||
4600.2.a.y.1.1 | 3 | 5.4 | even | 2 | |||
4600.2.e.r.4049.1 | 6 | 5.2 | odd | 4 | |||
4600.2.e.r.4049.6 | 6 | 5.3 | odd | 4 | |||
7360.2.a.ca.1.3 | 3 | 8.3 | odd | 2 | |||
7360.2.a.cb.1.1 | 3 | 8.5 | even | 2 | |||
8280.2.a.bo.1.3 | 3 | 3.2 | odd | 2 | |||
9200.2.a.cd.1.3 | 3 | 20.19 | odd | 2 |