Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5520,2,Mod(1,5520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5520, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("5520.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5520 = 2^{4} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5520.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: | \(44.0774219157\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{33}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2760) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.37228\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5520.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.37228 | −1.27460 | −0.637301 | − | 0.770615i | \(-0.719949\pi\) | ||||
−0.637301 | + | 0.770615i | \(0.719949\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.00000 | −1.20605 | −0.603023 | − | 0.797724i | \(-0.706037\pi\) | ||||
−0.603023 | + | 0.797724i | \(0.706037\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.74456 | 1.31590 | 0.657952 | − | 0.753059i | \(-0.271423\pi\) | ||||
0.657952 | + | 0.753059i | \(0.271423\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.37228 | 1.30297 | 0.651485 | − | 0.758662i | \(-0.274146\pi\) | ||||
0.651485 | + | 0.758662i | \(0.274146\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.00000 | −0.917663 | −0.458831 | − | 0.888523i | \(-0.651732\pi\) | ||||
−0.458831 | + | 0.888523i | \(0.651732\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.37228 | −0.735892 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.37228 | −0.997608 | −0.498804 | − | 0.866715i | \(-0.666227\pi\) | ||||
−0.498804 | + | 0.866715i | \(0.666227\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.37228 | −0.605680 | −0.302840 | − | 0.953041i | \(-0.597935\pi\) | ||||
−0.302840 | + | 0.953041i | \(0.597935\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.00000 | −0.696311 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.37228 | −0.570020 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.37228 | −0.883198 | −0.441599 | − | 0.897213i | \(-0.645589\pi\) | ||||
−0.441599 | + | 0.897213i | \(0.645589\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.74456 | 0.759738 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.11684 | −1.26764 | −0.633819 | − | 0.773481i | \(-0.718514\pi\) | ||||
−0.633819 | + | 0.773481i | \(0.718514\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.00000 | 0.609994 | 0.304997 | − | 0.952353i | \(-0.401344\pi\) | ||||
0.304997 | + | 0.952353i | \(0.401344\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.74456 | 0.983796 | 0.491898 | − | 0.870653i | \(-0.336303\pi\) | ||||
0.491898 | + | 0.870653i | \(0.336303\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.37228 | 0.624612 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.37228 | 0.752270 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.37228 | 0.188497 | 0.0942487 | − | 0.995549i | \(-0.469955\pi\) | ||||
0.0942487 | + | 0.995549i | \(0.469955\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.00000 | −0.539360 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.00000 | −0.529813 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.62772 | −1.12323 | −0.561617 | − | 0.827398i | \(-0.689820\pi\) | ||||
−0.561617 | + | 0.827398i | \(0.689820\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.00000 | −0.256074 | −0.128037 | − | 0.991769i | \(-0.540868\pi\) | ||||
−0.128037 | + | 0.991769i | \(0.540868\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.37228 | −0.424868 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.74456 | 0.588491 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15.3723 | −1.87802 | −0.939012 | − | 0.343886i | \(-0.888257\pi\) | ||||
−0.939012 | + | 0.343886i | \(0.888257\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.37228 | −0.400216 | −0.200108 | − | 0.979774i | \(-0.564129\pi\) | ||||
−0.200108 | + | 0.979774i | \(0.564129\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.7446 | −1.49164 | −0.745819 | − | 0.666149i | \(-0.767942\pi\) | ||||
−0.745819 | + | 0.666149i | \(0.767942\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 13.4891 | 1.53723 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.4891 | 1.51765 | 0.758823 | − | 0.651297i | \(-0.225775\pi\) | ||||
0.758823 | + | 0.651297i | \(0.225775\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.8614 | 1.41172 | 0.705861 | − | 0.708350i | \(-0.250560\pi\) | ||||
0.705861 | + | 0.708350i | \(0.250560\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.37228 | 0.582706 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.37228 | −0.575969 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.74456 | −0.502923 | −0.251461 | − | 0.967867i | \(-0.580911\pi\) | ||||
−0.251461 | + | 0.967867i | \(0.580911\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −16.0000 | −1.67726 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.37228 | −0.349689 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.00000 | −0.410391 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.4891 | 1.57268 | 0.786341 | − | 0.617792i | \(-0.211973\pi\) | ||||
0.786341 | + | 0.617792i | \(0.211973\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.00000 | −0.402015 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.3723 | −1.33059 | −0.665296 | − | 0.746580i | \(-0.731695\pi\) | ||||
−0.665296 | + | 0.746580i | \(0.731695\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.00000 | 0.788263 | 0.394132 | − | 0.919054i | \(-0.371045\pi\) | ||||
0.394132 | + | 0.919054i | \(0.371045\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.37228 | −0.329101 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.37228 | 0.712705 | 0.356353 | − | 0.934352i | \(-0.384020\pi\) | ||||
0.356353 | + | 0.934352i | \(0.384020\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.74456 | 0.454447 | 0.227223 | − | 0.973843i | \(-0.427035\pi\) | ||||
0.227223 | + | 0.973843i | \(0.427035\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.37228 | −0.509914 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.11684 | −0.763568 | −0.381784 | − | 0.924251i | \(-0.624690\pi\) | ||||
−0.381784 | + | 0.924251i | \(0.624690\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.00000 | −0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.74456 | 0.438635 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −18.1168 | −1.66077 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | 0.454545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.11684 | −0.731871 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.25544 | −0.111402 | −0.0557010 | − | 0.998447i | \(-0.517739\pi\) | ||||
−0.0557010 | + | 0.998447i | \(0.517739\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.00000 | 0.352180 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.00000 | 0.349482 | 0.174741 | − | 0.984614i | \(-0.444091\pi\) | ||||
0.174741 | + | 0.984614i | \(0.444091\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13.4891 | 1.16966 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.4891 | −0.981582 | −0.490791 | − | 0.871277i | \(-0.663292\pi\) | ||||
−0.490791 | + | 0.871277i | \(0.663292\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.62772 | −0.731794 | −0.365897 | − | 0.930655i | \(-0.619238\pi\) | ||||
−0.365897 | + | 0.930655i | \(0.619238\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.74456 | 0.567995 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −18.9783 | −1.58704 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.37228 | −0.446144 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.37228 | 0.360620 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.48913 | 0.285840 | 0.142920 | − | 0.989734i | \(-0.454351\pi\) | ||||
0.142920 | + | 0.989734i | \(0.454351\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.0000 | −1.30206 | −0.651031 | − | 0.759051i | \(-0.725663\pi\) | ||||
−0.651031 | + | 0.759051i | \(0.725663\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.37228 | 0.434323 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.37228 | −0.270868 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.6060 | −1.40511 | −0.702555 | − | 0.711630i | \(-0.747957\pi\) | ||||
−0.702555 | + | 0.711630i | \(0.747957\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.37228 | 0.108829 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.37228 | 0.265773 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.25544 | −0.411638 | −0.205819 | − | 0.978590i | \(-0.565986\pi\) | ||||
−0.205819 | + | 0.978590i | \(0.565986\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.00000 | −0.311400 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.25544 | −0.0971487 | −0.0485743 | − | 0.998820i | \(-0.515468\pi\) | ||||
−0.0485743 | + | 0.998820i | \(0.515468\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.51087 | 0.731606 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.00000 | −0.305888 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.2337 | −1.08217 | −0.541084 | − | 0.840969i | \(-0.681986\pi\) | ||||
−0.541084 | + | 0.840969i | \(0.681986\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.37228 | −0.254921 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.62772 | −0.648499 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.48913 | −0.709251 | −0.354625 | − | 0.935009i | \(-0.615392\pi\) | ||||
−0.354625 | + | 0.935009i | \(0.615392\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.2337 | −1.05798 | −0.528991 | − | 0.848628i | \(-0.677429\pi\) | ||||
−0.528991 | + | 0.848628i | \(0.677429\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.00000 | −0.147844 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.37228 | −0.394978 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −21.4891 | −1.57144 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.37228 | −0.245297 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.2337 | −1.46406 | −0.732029 | − | 0.681273i | \(-0.761427\pi\) | ||||
−0.732029 | + | 0.681273i | \(0.761427\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −20.7446 | −1.49323 | −0.746613 | − | 0.665258i | \(-0.768321\pi\) | ||||
−0.746613 | + | 0.665258i | \(0.768321\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.74456 | 0.339765 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.4891 | 0.818566 | 0.409283 | − | 0.912407i | \(-0.365779\pi\) | ||||
0.409283 | + | 0.912407i | \(0.365779\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.25544 | −0.0889956 | −0.0444978 | − | 0.999009i | \(-0.514169\pi\) | ||||
−0.0444978 | + | 0.999009i | \(0.514169\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −15.3723 | −1.08428 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 18.1168 | 1.27155 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.11684 | −0.566905 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.0000 | 1.10674 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.8614 | −1.43616 | −0.718079 | − | 0.695961i | \(-0.754978\pi\) | ||||
−0.718079 | + | 0.695961i | \(0.754978\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.37228 | −0.231065 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.00000 | 0.272798 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.3723 | 0.772001 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.7446 | −0.861198 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 25.4891 | 1.71458 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.2554 | −1.15551 | −0.577755 | − | 0.816210i | \(-0.696071\pi\) | ||||
−0.577755 | + | 0.816210i | \(0.696071\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.0000 | −0.796468 | −0.398234 | − | 0.917284i | \(-0.630377\pi\) | ||||
−0.398234 | + | 0.917284i | \(0.630377\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 28.7446 | 1.89949 | 0.949747 | − | 0.313018i | \(-0.101340\pi\) | ||||
0.949747 | + | 0.313018i | \(0.101340\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 13.4891 | 0.887519 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −26.2337 | −1.71863 | −0.859313 | − | 0.511450i | \(-0.829109\pi\) | ||||
−0.859313 | + | 0.511450i | \(0.829109\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.74456 | 0.439967 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.4891 | 0.876213 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.3723 | 0.735612 | 0.367806 | − | 0.929903i | \(-0.380109\pi\) | ||||
0.367806 | + | 0.929903i | \(0.380109\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.25544 | −0.467364 | −0.233682 | − | 0.972313i | \(-0.575077\pi\) | ||||
−0.233682 | + | 0.972313i | \(0.575077\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.37228 | 0.279335 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −18.9783 | −1.20756 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.8614 | 0.815059 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.7446 | 1.18315 | 0.591573 | − | 0.806251i | \(-0.298507\pi\) | ||||
0.591573 | + | 0.806251i | \(0.298507\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.00000 | 0.251478 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.37228 | 0.336425 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.4891 | −0.716672 | −0.358336 | − | 0.933593i | \(-0.616656\pi\) | ||||
−0.358336 | + | 0.933593i | \(0.616656\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 18.1168 | 1.12573 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.37228 | −0.332536 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.861407 | −0.0531166 | −0.0265583 | − | 0.999647i | \(-0.508455\pi\) | ||||
−0.0265583 | + | 0.999647i | \(0.508455\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.37228 | 0.0842986 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.74456 | −0.290363 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.8614 | 0.906116 | 0.453058 | − | 0.891481i | \(-0.350333\pi\) | ||||
0.453058 | + | 0.891481i | \(0.350333\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.88316 | 0.357376 | 0.178688 | − | 0.983906i | \(-0.442815\pi\) | ||||
0.178688 | + | 0.983906i | \(0.442815\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −16.0000 | −0.968364 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.00000 | −0.241209 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.0000 | 1.32185 | 0.660926 | − | 0.750451i | \(-0.270164\pi\) | ||||
0.660926 | + | 0.750451i | \(0.270164\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.37228 | −0.201893 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.2337 | 1.32635 | 0.663175 | − | 0.748464i | \(-0.269208\pi\) | ||||
0.663175 | + | 0.748464i | \(0.269208\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.627719 | −0.0373140 | −0.0186570 | − | 0.999826i | \(-0.505939\pi\) | ||||
−0.0186570 | + | 0.999826i | \(0.505939\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.00000 | −0.236940 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 27.3723 | 1.61573 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.8614 | 0.697730 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 15.4891 | 0.907989 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −18.8614 | −1.10190 | −0.550948 | − | 0.834540i | \(-0.685734\pi\) | ||||
−0.550948 | + | 0.834540i | \(0.685734\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.62772 | −0.502325 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.00000 | −0.232104 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.74456 | −0.274385 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.4891 | −0.777500 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −13.3723 | −0.768217 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.00000 | −0.114520 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.00000 | 0.228292 | 0.114146 | − | 0.993464i | \(-0.463587\pi\) | ||||
0.114146 | + | 0.993464i | \(0.463587\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.00000 | 0.455104 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.00000 | −0.453638 | −0.226819 | − | 0.973937i | \(-0.572833\pi\) | ||||
−0.226819 | + | 0.973937i | \(0.572833\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.86141 | 0.161736 | 0.0808681 | − | 0.996725i | \(-0.474231\pi\) | ||||
0.0808681 | + | 0.996725i | \(0.474231\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.37228 | −0.190007 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.51087 | 0.478018 | 0.239009 | − | 0.971017i | \(-0.423177\pi\) | ||||
0.239009 | + | 0.971017i | \(0.423177\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 21.4891 | 1.20316 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.37228 | 0.411481 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −21.4891 | −1.19569 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.74456 | 0.263181 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.74456 | 0.262375 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −22.7446 | −1.25395 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.88316 | −0.103508 | −0.0517538 | − | 0.998660i | \(-0.516481\pi\) | ||||
−0.0517538 | + | 0.998660i | \(0.516481\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.37228 | −0.294399 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −15.3723 | −0.839877 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.4891 | −1.49743 | −0.748714 | − | 0.662893i | \(-0.769328\pi\) | ||||
−0.748714 | + | 0.662893i | \(0.769328\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.11684 | −0.440846 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.4891 | 0.730477 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.86141 | 0.478471 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.00000 | −0.0538382 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.00000 | −0.214731 | −0.107366 | − | 0.994220i | \(-0.534242\pi\) | ||||
−0.107366 | + | 0.994220i | \(0.534242\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.11684 | −0.220370 | −0.110185 | − | 0.993911i | \(-0.535144\pi\) | ||||
−0.110185 | + | 0.993911i | \(0.535144\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.74456 | 0.253246 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.0000 | −0.745145 | −0.372572 | − | 0.928003i | \(-0.621524\pi\) | ||||
−0.372572 | + | 0.928003i | \(0.621524\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.37228 | −0.178982 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −18.1168 | −0.958845 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 25.7228 | 1.35760 | 0.678799 | − | 0.734324i | \(-0.262501\pi\) | ||||
0.678799 | + | 0.734324i | \(0.262501\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | −0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.00000 | 0.262432 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.7446 | −0.667081 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 24.8614 | 1.29775 | 0.648877 | − | 0.760893i | \(-0.275239\pi\) | ||||
0.648877 | + | 0.760893i | \(0.275239\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.11684 | −0.422546 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.62772 | −0.240259 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.0000 | −0.517780 | −0.258890 | − | 0.965907i | \(-0.583357\pi\) | ||||
−0.258890 | + | 0.965907i | \(0.583357\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −25.4891 | −1.31276 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.48913 | −0.487424 | −0.243712 | − | 0.969848i | \(-0.578365\pi\) | ||||
−0.243712 | + | 0.969848i | \(0.578365\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.25544 | −0.0643180 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 18.1168 | 0.925727 | 0.462864 | − | 0.886429i | \(-0.346822\pi\) | ||||
0.462864 | + | 0.886429i | \(0.346822\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.4891 | 0.687469 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.00000 | 0.203331 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.48913 | 0.176906 | 0.0884528 | − | 0.996080i | \(-0.471808\pi\) | ||||
0.0884528 | + | 0.996080i | \(0.471808\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.37228 | −0.271688 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.00000 | 0.201773 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 13.4891 | 0.678712 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 34.2337 | 1.71814 | 0.859070 | − | 0.511859i | \(-0.171043\pi\) | ||||
0.859070 | + | 0.511859i | \(0.171043\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 13.4891 | 0.675301 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.4891 | 1.17299 | 0.586495 | − | 0.809953i | \(-0.300507\pi\) | ||||
0.586495 | + | 0.809953i | \(0.300507\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16.0000 | −0.797017 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 21.4891 | 1.06518 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.6277 | 0.723294 | 0.361647 | − | 0.932315i | \(-0.382215\pi\) | ||||
0.361647 | + | 0.932315i | \(0.382215\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.4891 | −0.566717 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 29.0951 | 1.43168 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.8614 | 0.631342 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.62772 | −0.422501 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.0000 | −0.586238 | −0.293119 | − | 0.956076i | \(-0.594693\pi\) | ||||
−0.293119 | + | 0.956076i | \(0.594693\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.25544 | −0.158660 | −0.0793302 | − | 0.996848i | \(-0.525278\pi\) | ||||
−0.0793302 | + | 0.996848i | \(0.525278\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.74456 | 0.327932 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.37228 | 0.260594 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.74456 | 0.326392 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −18.9783 | −0.916279 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 32.0000 | 1.54139 | 0.770693 | − | 0.637207i | \(-0.219910\pi\) | ||||
0.770693 | + | 0.637207i | \(0.219910\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.0951 | 1.49433 | 0.747167 | − | 0.664636i | \(-0.231413\pi\) | ||||
0.747167 | + | 0.664636i | \(0.231413\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.37228 | −0.257581 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.00000 | 0.191346 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −26.9783 | −1.28760 | −0.643801 | − | 0.765193i | \(-0.722643\pi\) | ||||
−0.643801 | + | 0.765193i | \(0.722643\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.37228 | 0.208204 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 21.2554 | 1.00988 | 0.504938 | − | 0.863156i | \(-0.331515\pi\) | ||||
0.504938 | + | 0.863156i | \(0.331515\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.74456 | −0.224914 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.48913 | 0.165030 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.86141 | −0.323810 | −0.161905 | − | 0.986806i | \(-0.551764\pi\) | ||||
−0.161905 | + | 0.986806i | \(0.551764\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 32.4674 | 1.52883 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −16.0000 | −0.751746 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −16.0000 | −0.750092 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −37.6060 | −1.75913 | −0.879567 | − | 0.475776i | \(-0.842167\pi\) | ||||
−0.879567 | + | 0.475776i | \(0.842167\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.37228 | 0.250757 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −34.4674 | −1.60531 | −0.802653 | − | 0.596446i | \(-0.796579\pi\) | ||||
−0.802653 | + | 0.596446i | \(0.796579\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.00000 | 0.371792 | 0.185896 | − | 0.982569i | \(-0.440481\pi\) | ||||
0.185896 | + | 0.982569i | \(0.440481\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.37228 | −0.156386 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 42.3505 | 1.95975 | 0.979874 | − | 0.199615i | \(-0.0639691\pi\) | ||||
0.979874 | + | 0.199615i | \(0.0639691\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 51.8397 | 2.39373 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.6060 | −0.811240 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −16.0000 | −0.735681 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.00000 | −0.183533 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.37228 | 0.0628324 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 33.7228 | 1.54083 | 0.770417 | − | 0.637540i | \(-0.220048\pi\) | ||||
0.770417 | + | 0.637540i | \(0.220048\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −25.4891 | −1.16220 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.37228 | 0.153444 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 15.4891 | 0.703325 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −33.7228 | −1.52813 | −0.764063 | − | 0.645141i | \(-0.776798\pi\) | ||||
−0.764063 | + | 0.645141i | \(0.776798\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.25544 | −0.237659 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.6277 | 0.750398 | 0.375199 | − | 0.926944i | \(-0.377574\pi\) | ||||
0.375199 | + | 0.926944i | \(0.377574\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −28.8614 | −1.29985 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.00000 | −0.179787 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11.3723 | 0.510117 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −43.6060 | −1.95207 | −0.976036 | − | 0.217611i | \(-0.930174\pi\) | ||||
−0.976036 | + | 0.217611i | \(0.930174\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.25544 | −0.0560888 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 28.6277 | 1.27645 | 0.638223 | − | 0.769851i | \(-0.279670\pi\) | ||||
0.638223 | + | 0.769851i | \(0.279670\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.3723 | −0.595059 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.51087 | 0.422393 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −20.9783 | −0.929845 | −0.464922 | − | 0.885351i | \(-0.653918\pi\) | ||||
−0.464922 | + | 0.885351i | \(0.653918\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 42.9783 | 1.90125 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.00000 | −0.176604 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.00000 | 0.352522 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −26.9783 | −1.18650 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −14.2337 | −0.624790 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.2337 | 0.974076 | 0.487038 | − | 0.873381i | \(-0.338077\pi\) | ||||
0.487038 | + | 0.873381i | \(0.338077\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −38.9783 | −1.70440 | −0.852200 | − | 0.523216i | \(-0.824732\pi\) | ||||
−0.852200 | + | 0.523216i | \(0.824732\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.37228 | −0.147178 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −18.1168 | −0.789182 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.62772 | −0.374411 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −38.5109 | −1.66809 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.37228 | 0.318732 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.48913 | −0.409486 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −17.4891 | −0.753310 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.0000 | 0.601907 | 0.300954 | − | 0.953639i | \(-0.402695\pi\) | ||||
0.300954 | + | 0.953639i | \(0.402695\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −14.2337 | −0.610826 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.74456 | 0.203235 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.00000 | 0.171028 | 0.0855138 | − | 0.996337i | \(-0.472747\pi\) | ||||
0.0855138 | + | 0.996337i | \(0.472747\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.00000 | −0.0853579 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21.4891 | 0.915468 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −45.4891 | −1.93439 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.37228 | −0.228041 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 36.3505 | 1.54022 | 0.770111 | − | 0.637910i | \(-0.220201\pi\) | ||||
0.770111 | + | 0.637910i | \(0.220201\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 18.9783 | 0.802694 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −21.4891 | −0.907272 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.37228 | −0.310705 | −0.155352 | − | 0.987859i | \(-0.549651\pi\) | ||||
−0.155352 | + | 0.987859i | \(0.549651\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.11684 | −0.341478 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.37228 | −0.141623 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.510875 | −0.0214170 | −0.0107085 | − | 0.999943i | \(-0.503409\pi\) | ||||
−0.0107085 | + | 0.999943i | \(0.503409\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.233688 | −0.00977954 | −0.00488977 | − | 0.999988i | \(-0.501556\pi\) | ||||
−0.00488977 | + | 0.999988i | \(0.501556\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −20.2337 | −0.845274 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.00000 | −0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.25544 | −0.302048 | −0.151024 | − | 0.988530i | \(-0.548257\pi\) | ||||
−0.151024 | + | 0.988530i | \(0.548257\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −20.7446 | −0.862115 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −43.3723 | −1.79939 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.48913 | −0.227336 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.74456 | 0.196164 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −24.2337 | −1.00023 | −0.500116 | − | 0.865959i | \(-0.666709\pi\) | ||||
−0.500116 | + | 0.865959i | \(0.666709\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.4891 | 0.555810 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.4891 | 0.472599 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.9783 | 0.532953 | 0.266476 | − | 0.963841i | \(-0.414141\pi\) | ||||
0.266476 | + | 0.963841i | \(0.414141\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −18.1168 | −0.742718 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.25544 | −0.0513816 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.5109 | 0.429463 | 0.214731 | − | 0.976673i | \(-0.431112\pi\) | ||||
0.214731 | + | 0.976673i | \(0.431112\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.8614 | 0.769373 | 0.384686 | − | 0.923047i | \(-0.374310\pi\) | ||||
0.384686 | + | 0.923047i | \(0.374310\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −15.3723 | −0.626008 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.00000 | 0.203279 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 33.2554 | 1.34980 | 0.674898 | − | 0.737911i | \(-0.264187\pi\) | ||||
0.674898 | + | 0.737911i | \(0.264187\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 18.1168 | 0.734132 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 32.0000 | 1.29458 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −39.4891 | −1.59495 | −0.797475 | − | 0.603351i | \(-0.793832\pi\) | ||||
−0.797475 | + | 0.603351i | \(0.793832\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.11684 | −0.327303 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.3505 | −0.819282 | −0.409641 | − | 0.912247i | \(-0.634346\pi\) | ||||
−0.409641 | + | 0.912247i | \(0.634346\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −38.9783 | −1.56667 | −0.783334 | − | 0.621601i | \(-0.786483\pi\) | ||||
−0.783334 | + | 0.621601i | \(0.786483\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16.0000 | 0.641026 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 16.0000 | 0.638978 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −28.8614 | −1.15078 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.2554 | 0.686928 | 0.343464 | − | 0.939166i | \(-0.388400\pi\) | ||||
0.343464 | + | 0.939166i | \(0.388400\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −20.8614 | −0.829166 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.25544 | −0.0498205 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 20.7446 | 0.821929 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.37228 | −0.133405 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 43.7228 | 1.72695 | 0.863474 | − | 0.504394i | \(-0.168284\pi\) | ||||
0.863474 | + | 0.504394i | \(0.168284\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −47.3723 | −1.86818 | −0.934090 | − | 0.357037i | \(-0.883787\pi\) | ||||
−0.934090 | + | 0.357037i | \(0.883787\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.00000 | 0.157500 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.4891 | 0.844825 | 0.422412 | − | 0.906404i | \(-0.361183\pi\) | ||||
0.422412 | + | 0.906404i | \(0.361183\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 34.5109 | 1.35467 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.3723 | 0.445715 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.2337 | 0.400475 | 0.200238 | − | 0.979747i | \(-0.435829\pi\) | ||||
0.200238 | + | 0.979747i | \(0.435829\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.00000 | 0.156293 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −12.7446 | −0.497213 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.9783 | −0.895106 | −0.447553 | − | 0.894258i | \(-0.647704\pi\) | ||||
−0.447553 | + | 0.894258i | \(0.647704\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.0000 | 0.855701 | 0.427850 | − | 0.903850i | \(-0.359271\pi\) | ||||
0.427850 | + | 0.903850i | \(0.359271\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 25.4891 | 0.989916 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 13.4891 | 0.523086 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.37228 | 0.208016 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −17.2554 | −0.667134 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.00000 | 0.308837 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.5109 | −0.636447 | −0.318224 | − | 0.948016i | \(-0.603086\pi\) | ||||
−0.318224 | + | 0.948016i | \(0.603086\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 40.1168 | 1.54182 | 0.770908 | − | 0.636947i | \(-0.219803\pi\) | ||||
0.770908 | + | 0.636947i | \(0.219803\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −52.2337 | −2.00454 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.0000 | −0.459841 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32.2337 | 1.23339 | 0.616694 | − | 0.787203i | \(-0.288472\pi\) | ||||
0.616694 | + | 0.787203i | \(0.288472\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.4891 | −0.438977 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 28.7446 | 1.09667 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.51087 | 0.248045 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.48913 | 0.0566490 | 0.0283245 | − | 0.999599i | \(-0.490983\pi\) | ||||
0.0283245 | + | 0.999599i | \(0.490983\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 13.4891 | 0.512409 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.62772 | −0.327268 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −43.6060 | −1.65169 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −26.2337 | −0.992249 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −39.9565 | −1.50914 | −0.754568 | − | 0.656222i | \(-0.772154\pi\) | ||||
−0.754568 | + | 0.656222i | \(0.772154\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 21.4891 | 0.810478 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.74456 | 0.254015 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 45.0951 | 1.69598 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20.9783 | −0.787855 | −0.393927 | − | 0.919142i | \(-0.628884\pi\) | ||||
−0.393927 | + | 0.919142i | \(0.628884\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.4891 | 0.505882 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.37228 | 0.126293 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −18.9783 | −0.709746 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 11.3723 | 0.424706 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −29.0951 | −1.08506 | −0.542532 | − | 0.840035i | \(-0.682534\pi\) | ||||
−0.542532 | + | 0.840035i | \(0.682534\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −26.9783 | −1.00472 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7.25544 | −0.269833 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.37228 | −0.199522 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.37228 | 0.125071 | 0.0625355 | − | 0.998043i | \(-0.480081\pi\) | ||||
0.0625355 | + | 0.998043i | \(0.480081\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 21.4891 | 0.794804 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.116844 | 0.00431573 | 0.00215787 | − | 0.999998i | \(-0.499313\pi\) | ||||
0.00215787 | + | 0.999998i | \(0.499313\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.37228 | 0.161274 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 61.4891 | 2.26498 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −39.3723 | −1.44833 | −0.724166 | − | 0.689625i | \(-0.757775\pi\) | ||||
−0.724166 | + | 0.689625i | \(0.757775\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −18.9783 | −0.697183 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −34.9783 | −1.28323 | −0.641614 | − | 0.767028i | \(-0.721735\pi\) | ||||
−0.641614 | + | 0.767028i | \(0.721735\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.48913 | 0.127832 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.8614 | 0.470574 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −24.8614 | −0.908416 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.0000 | 0.583848 | 0.291924 | − | 0.956441i | \(-0.405705\pi\) | ||||
0.291924 | + | 0.956441i | \(0.405705\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 18.7446 | 0.683090 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16.0000 | −0.582300 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25.6060 | −0.930665 | −0.465332 | − | 0.885136i | \(-0.654065\pi\) | ||||
−0.465332 | + | 0.885136i | \(0.654065\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.00000 | 0.145191 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 45.8397 | 1.66169 | 0.830843 | − | 0.556507i | \(-0.187859\pi\) | ||||
0.830843 | + | 0.556507i | \(0.187859\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.0000 | −0.579239 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.37228 | 0.194235 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −40.9348 | −1.47807 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.5109 | 0.739641 | 0.369821 | − | 0.929103i | \(-0.379419\pi\) | ||||
0.369821 | + | 0.929103i | \(0.379419\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.4891 | −0.413771 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.97825 | −0.179055 | −0.0895276 | − | 0.995984i | \(-0.528536\pi\) | ||||
−0.0895276 | + | 0.995984i | \(0.528536\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.37228 | −0.121136 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 18.1168 | 0.649938 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 32.4674 | 1.16326 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.4891 | 0.482679 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.37228 | −0.191990 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −17.6060 | −0.628384 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.627719 | 0.0223758 | 0.0111879 | − | 0.999937i | \(-0.496439\pi\) | ||||
0.0111879 | + | 0.999937i | \(0.496439\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.861407 | −0.0306669 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 27.3723 | 0.973246 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.48913 | −0.336969 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.37228 | 0.0486698 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16.1168 | 0.570888 | 0.285444 | − | 0.958395i | \(-0.407859\pi\) | ||||
0.285444 | + | 0.958395i | \(0.407859\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 36.2337 | 1.28186 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.74456 | −0.167641 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 50.9783 | 1.79898 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.37228 | 0.118857 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14.8614 | 0.523146 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 30.6277 | 1.07681 | 0.538407 | − | 0.842685i | \(-0.319026\pi\) | ||||
0.538407 | + | 0.842685i | \(0.319026\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.8832 | −0.627963 | −0.313981 | − | 0.949429i | \(-0.601663\pi\) | ||||
−0.313981 | + | 0.949429i | \(0.601663\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.88316 | 0.206331 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.25544 | −0.184090 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.0000 | −0.559769 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −16.0000 | −0.559085 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.97825 | 0.313343 | 0.156672 | − | 0.987651i | \(-0.449924\pi\) | ||||
0.156672 | + | 0.987651i | \(0.449924\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.9783 | 0.382678 | 0.191339 | − | 0.981524i | \(-0.438717\pi\) | ||||
0.191339 | + | 0.981524i | \(0.438717\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.00000 | −0.139262 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 43.6060 | 1.51633 | 0.758164 | − | 0.652064i | \(-0.226097\pi\) | ||||
0.758164 | + | 0.652064i | \(0.226097\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 43.0951 | 1.49675 | 0.748377 | − | 0.663273i | \(-0.230833\pi\) | ||||
0.748377 | + | 0.663273i | \(0.230833\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 22.0000 | 0.763172 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 23.4891 | 0.813850 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.25544 | −0.0434462 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.37228 | −0.116563 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14.7446 | −0.509039 | −0.254519 | − | 0.967068i | \(-0.581917\pi\) | ||||
−0.254519 | + | 0.967068i | \(0.581917\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.138593 | −0.00477908 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 22.2337 | 0.765769 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.51087 | 0.327184 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −16.8614 | −0.579365 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.627719 | −0.0215432 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.37228 | 0.184159 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32.9783 | 1.12915 | 0.564577 | − | 0.825380i | \(-0.309039\pi\) | ||||
0.564577 | + | 0.825380i | \(0.309039\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.00000 | −0.136797 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 50.4674 | 1.72393 | 0.861966 | − | 0.506965i | \(-0.169233\pi\) | ||||
0.861966 | + | 0.506965i | \(0.169233\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27.6060 | 0.941904 | 0.470952 | − | 0.882159i | \(-0.343911\pi\) | ||||
0.470952 | + | 0.882159i | \(0.343911\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 27.3723 | 0.932845 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.74456 | 0.229588 | 0.114794 | − | 0.993389i | \(-0.463379\pi\) | ||||
0.114794 | + | 0.993389i | \(0.463379\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.2337 | −0.483960 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 11.8614 | 0.402834 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −53.9565 | −1.83035 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −72.9348 | −2.47130 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 15.4891 | 0.524227 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.37228 | −0.114004 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.5109 | −0.692603 | −0.346302 | − | 0.938123i | \(-0.612563\pi\) | ||||
−0.346302 | + | 0.938123i | \(0.612563\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −18.8614 | −0.636179 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.0000 | −0.741199 | −0.370599 | − | 0.928793i | \(-0.620848\pi\) | ||||
−0.370599 | + | 0.928793i | \(0.620848\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 51.2119 | 1.72342 | 0.861709 | − | 0.507402i | \(-0.169394\pi\) | ||||
0.861709 | + | 0.507402i | \(0.169394\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.62772 | −0.290018 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 25.7228 | 0.863688 | 0.431844 | − | 0.901948i | \(-0.357863\pi\) | ||||
0.431844 | + | 0.901948i | \(0.357863\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.23369 | 0.141993 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.00000 | −0.134005 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −26.9783 | −0.902793 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.48913 | −0.317186 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.74456 | −0.158416 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 18.1168 | 0.604231 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.37228 | 0.245606 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −13.4891 | −0.448890 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −14.2337 | −0.473144 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.62772 | 0.286479 | 0.143239 | − | 0.989688i | \(-0.454248\pi\) | ||||
0.143239 | + | 0.989688i | \(0.454248\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13.3723 | −0.443531 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 56.4674 | 1.87085 | 0.935424 | − | 0.353528i | \(-0.115018\pi\) | ||||
0.935424 | + | 0.353528i | \(0.115018\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −51.4456 | −1.70260 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.00000 | −0.0661180 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −13.4891 | −0.445450 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37.4891 | −1.23665 | −0.618326 | − | 0.785922i | \(-0.712189\pi\) | ||||
−0.618326 | + | 0.785922i | \(0.712189\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.00000 | 0.131804 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −16.0000 | −0.526646 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.37228 | −0.176640 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.00000 | 0.262754 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 33.6060 | 1.10258 | 0.551288 | − | 0.834315i | \(-0.314137\pi\) | ||||
0.551288 | + | 0.834315i | \(0.314137\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17.4891 | −0.573183 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.00000 | −0.261908 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −21.4891 | −0.702770 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34.4674 | 1.12600 | 0.563000 | − | 0.826457i | \(-0.309647\pi\) | ||||
0.563000 | + | 0.826457i | \(0.309647\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.86141 | 0.0933785 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.9783 | −0.423079 | −0.211539 | − | 0.977369i | \(-0.567848\pi\) | ||||
−0.211539 | + | 0.977369i | \(0.567848\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.11684 | 0.264321 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.37228 | −0.109700 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −54.9783 | −1.78655 | −0.893277 | − | 0.449508i | \(-0.851599\pi\) | ||||
−0.893277 | + | 0.449508i | \(0.851599\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −60.4674 | −1.96285 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.51087 | 0.275984 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 15.4891 | 0.501742 | 0.250871 | − | 0.968021i | \(-0.419283\pi\) | ||||
0.250871 | + | 0.968021i | \(0.419283\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −20.2337 | −0.654747 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 21.4891 | 0.694645 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 38.7446 | 1.25113 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.6277 | −0.633152 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.37228 | 0.237568 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −20.7446 | −0.667791 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.7663 | −0.378379 | −0.189190 | − | 0.981941i | \(-0.560586\pi\) | ||||
−0.189190 | + | 0.981941i | \(0.560586\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −21.4891 | −0.690330 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.48913 | −0.0477883 | −0.0238942 | − | 0.999714i | \(-0.507606\pi\) | ||||
−0.0238942 | + | 0.999714i | \(0.507606\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 29.0951 | 0.932746 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.74456 | 0.151948 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 30.6277 | 0.979868 | 0.489934 | − | 0.871760i | \(-0.337021\pi\) | ||||
0.489934 | + | 0.871760i | \(0.337021\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.9783 | 0.606548 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.74456 | 0.151482 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 48.8614 | 1.55844 | 0.779218 | − | 0.626752i | \(-0.215616\pi\) | ||||
0.779218 | + | 0.626752i | \(0.215616\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.4891 | 0.366074 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −22.7446 | −0.723967 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.00000 | −0.127193 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 42.1168 | 1.33789 | 0.668943 | − | 0.743314i | \(-0.266747\pi\) | ||||
0.668943 | + | 0.743314i | \(0.266747\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.88316 | −0.0597602 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.25544 | −0.0398000 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −46.2337 | −1.46424 | −0.732118 | − | 0.681178i | \(-0.761468\pi\) | ||||
−0.732118 | + | 0.681178i | \(0.761468\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.37228 | −0.169971 |
(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 | 5520.2.a.bq.1.1 | 2 | ||
4.3 | odd | 2 | 2760.2.a.o.1.2 | ✓ | 2 | ||
12.11 | even | 2 | 8280.2.a.z.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2760.2.a.o.1.2 | ✓ | 2 | 4.3 | odd | 2 | ||
5520.2.a.bq.1.1 | 2 | 1.1 | even | 1 | trivial | ||
8280.2.a.z.1.2 | 2 | 12.11 | even | 2 |