Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1680,2,Mod(1,1680)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1680, 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("1680.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1680.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: | \(13.4148675396\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 840) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1680.1 |
$q$-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 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.65685 | −1.70561 | −0.852803 | − | 0.522233i | \(-0.825099\pi\) | ||||
−0.852803 | + | 0.522233i | \(0.825099\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.65685 | −0.886917 | −0.443459 | − | 0.896295i | \(-0.646249\pi\) | ||||
−0.443459 | + | 0.896295i | \(0.646249\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.65685 | 1.29777 | 0.648886 | − | 0.760886i | \(-0.275235\pi\) | ||||
0.648886 | + | 0.760886i | \(0.275235\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.65685 | 1.17954 | 0.589768 | − | 0.807573i | \(-0.299219\pi\) | ||||
0.589768 | + | 0.807573i | \(0.299219\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.65685 | 0.679061 | 0.339530 | − | 0.940595i | \(-0.389732\pi\) | ||||
0.339530 | + | 0.940595i | \(0.389732\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.65685 | 0.984732 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.6569 | 1.91638 | 0.958188 | − | 0.286141i | \(-0.0923726\pi\) | ||||
0.958188 | + | 0.286141i | \(0.0923726\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.00000 | −0.320256 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.00000 | 0.312348 | 0.156174 | − | 0.987730i | \(-0.450084\pi\) | ||||
0.156174 | + | 0.987730i | \(0.450084\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.65685 | −0.252668 | −0.126334 | − | 0.991988i | \(-0.540321\pi\) | ||||
−0.126334 | + | 0.991988i | \(0.540321\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.34315 | 0.341783 | 0.170891 | − | 0.985290i | \(-0.445335\pi\) | ||||
0.170891 | + | 0.985290i | \(0.445335\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.65685 | 0.512062 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.65685 | −0.502308 | −0.251154 | − | 0.967947i | \(-0.580810\pi\) | ||||
−0.251154 | + | 0.967947i | \(0.580810\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.65685 | −0.762770 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.65685 | −0.749269 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.00000 | 0.520756 | 0.260378 | − | 0.965507i | \(-0.416153\pi\) | ||||
0.260378 | + | 0.965507i | \(0.416153\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.343146 | 0.0439353 | 0.0219677 | − | 0.999759i | \(-0.493007\pi\) | ||||
0.0219677 | + | 0.999759i | \(0.493007\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.00000 | 0.248069 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.65685 | 1.17977 | 0.589886 | − | 0.807486i | \(-0.299173\pi\) | ||||
0.589886 | + | 0.807486i | \(0.299173\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.65685 | −0.681005 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.31371 | 0.867978 | 0.433989 | − | 0.900918i | \(-0.357106\pi\) | ||||
0.433989 | + | 0.900918i | \(0.357106\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.00000 | 0.702247 | 0.351123 | − | 0.936329i | \(-0.385800\pi\) | ||||
0.351123 | + | 0.936329i | \(0.385800\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.65685 | 0.644658 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.3137 | −1.27289 | −0.636446 | − | 0.771321i | \(-0.719596\pi\) | ||||
−0.636446 | + | 0.771321i | \(0.719596\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.00000 | 0.439057 | 0.219529 | − | 0.975606i | \(-0.429548\pi\) | ||||
0.219529 | + | 0.975606i | \(0.429548\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.65685 | −0.396642 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.65685 | −0.392056 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.0000 | −1.48400 | −0.741999 | − | 0.670402i | \(-0.766122\pi\) | ||||
−0.741999 | + | 0.670402i | \(0.766122\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.00000 | −0.209657 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.00000 | 0.414781 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.65685 | 0.580381 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.00000 | 0.609208 | 0.304604 | − | 0.952479i | \(-0.401476\pi\) | ||||
0.304604 | + | 0.952479i | \(0.401476\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.65685 | −0.568535 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.3137 | 1.72278 | 0.861389 | − | 0.507946i | \(-0.169595\pi\) | ||||
0.861389 | + | 0.507946i | \(0.169595\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.00000 | 0.788263 | 0.394132 | − | 0.919054i | \(-0.371045\pi\) | ||||
0.394132 | + | 0.919054i | \(0.371045\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.00000 | 0.0975900 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.34315 | 0.613215 | 0.306608 | − | 0.951836i | \(-0.400806\pi\) | ||||
0.306608 | + | 0.951836i | \(0.400806\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.00000 | −0.191565 | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957826 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.6569 | −1.10642 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.34315 | −0.408569 | −0.204284 | − | 0.978912i | \(-0.565487\pi\) | ||||
−0.204284 | + | 0.978912i | \(0.565487\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.65685 | 0.527504 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.00000 | 0.184900 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.65685 | 0.335223 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 21.0000 | 1.90909 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.00000 | −0.180334 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.3137 | 1.71381 | 0.856907 | − | 0.515471i | \(-0.172383\pi\) | ||||
0.856907 | + | 0.515471i | \(0.172383\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.65685 | 0.145878 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20.0000 | 1.74741 | 0.873704 | − | 0.486458i | \(-0.161711\pi\) | ||||
0.873704 | + | 0.486458i | \(0.161711\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.65685 | −0.490511 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.34315 | −0.371060 | −0.185530 | − | 0.982639i | \(-0.559400\pi\) | ||||
−0.185530 | + | 0.982639i | \(0.559400\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.6569 | 1.15836 | 0.579180 | − | 0.815200i | \(-0.303373\pi\) | ||||
0.579180 | + | 0.815200i | \(0.303373\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.34315 | −0.197328 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −11.3137 | −0.946100 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.65685 | 0.303685 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.9706 | −1.55413 | −0.777065 | − | 0.629421i | \(-0.783292\pi\) | ||||
−0.777065 | + | 0.629421i | \(0.783292\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.0000 | −1.30206 | −0.651031 | − | 0.759051i | \(-0.725663\pi\) | ||||
−0.651031 | + | 0.759051i | \(0.725663\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.65685 | −0.295639 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.00000 | −0.321288 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.0000 | 0.798087 | 0.399043 | − | 0.916932i | \(-0.369342\pi\) | ||||
0.399043 | + | 0.916932i | \(0.369342\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.65685 | 0.290007 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.65685 | −0.445823 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.6569 | 1.38299 | 0.691496 | − | 0.722380i | \(-0.256952\pi\) | ||||
0.691496 | + | 0.722380i | \(0.256952\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.65685 | 0.440386 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.6569 | 1.05680 | 0.528400 | − | 0.848996i | \(-0.322792\pi\) | ||||
0.528400 | + | 0.848996i | \(0.322792\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.65685 | 0.432590 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −21.3137 | −1.62045 | −0.810226 | − | 0.586118i | \(-0.800655\pi\) | ||||
−0.810226 | + | 0.586118i | \(0.800655\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.00000 | −0.300658 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.6569 | −1.02076 | −0.510381 | − | 0.859949i | \(-0.670495\pi\) | ||||
−0.510381 | + | 0.859949i | \(0.670495\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.6569 | 0.866447 | 0.433224 | − | 0.901286i | \(-0.357376\pi\) | ||||
0.433224 | + | 0.901286i | \(0.357376\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.343146 | −0.0253661 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 11.6569 | 0.857029 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 20.6863 | 1.51273 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.3137 | −1.10806 | −0.554031 | − | 0.832496i | \(-0.686911\pi\) | ||||
−0.554031 | + | 0.832496i | \(0.686911\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.3137 | 0.958342 | 0.479171 | − | 0.877722i | \(-0.340937\pi\) | ||||
0.479171 | + | 0.877722i | \(0.340937\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.00000 | −0.143223 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.6569 | −0.830516 | −0.415258 | − | 0.909704i | \(-0.636309\pi\) | ||||
−0.415258 | + | 0.909704i | \(0.636309\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.00000 | 0.283552 | 0.141776 | − | 0.989899i | \(-0.454719\pi\) | ||||
0.141776 | + | 0.989899i | \(0.454719\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.65685 | −0.681142 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.65685 | −0.256661 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.00000 | 0.139686 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.65685 | 0.393179 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −32.0000 | −2.21349 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −26.6274 | −1.83311 | −0.916553 | − | 0.399912i | \(-0.869041\pi\) | ||||
−0.916553 | + | 0.399912i | \(0.869041\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.31371 | −0.501127 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.65685 | −0.112997 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.00000 | 0.271538 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.00000 | −0.405442 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.31371 | −0.491973 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.3137 | 1.29334 | 0.646671 | − | 0.762769i | \(-0.276161\pi\) | ||||
0.646671 | + | 0.762769i | \(0.276161\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 26.6274 | 1.76732 | 0.883662 | − | 0.468126i | \(-0.155071\pi\) | ||||
0.883662 | + | 0.468126i | \(0.155071\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.9706 | 0.989283 | 0.494641 | − | 0.869097i | \(-0.335299\pi\) | ||||
0.494641 | + | 0.869097i | \(0.335299\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.65685 | −0.372194 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.9706 | 0.980754 | 0.490377 | − | 0.871510i | \(-0.336859\pi\) | ||||
0.490377 | + | 0.871510i | \(0.336859\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.34315 | 0.152850 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 11.3137 | 0.734904 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −23.3137 | −1.50804 | −0.754019 | − | 0.656852i | \(-0.771887\pi\) | ||||
−0.754019 | + | 0.656852i | \(0.771887\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.31371 | −0.0846234 | −0.0423117 | − | 0.999104i | \(-0.513472\pi\) | ||||
−0.0423117 | + | 0.999104i | \(0.513472\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.3137 | 0.719874 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.00000 | −0.253490 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.3137 | 0.966593 | 0.483296 | − | 0.875457i | \(-0.339439\pi\) | ||||
0.483296 | + | 0.875457i | \(0.339439\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −32.0000 | −2.01182 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.65685 | 0.229001 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −27.6569 | −1.72519 | −0.862594 | − | 0.505898i | \(-0.831161\pi\) | ||||
−0.862594 | + | 0.505898i | \(0.831161\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.6569 | −0.724322 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.65685 | 0.226354 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −29.6569 | −1.82872 | −0.914360 | − | 0.404902i | \(-0.867306\pi\) | ||||
−0.914360 | + | 0.404902i | \(0.867306\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.65685 | −0.224639 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.0000 | 0.856786 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.00000 | −0.121942 | −0.0609711 | − | 0.998140i | \(-0.519420\pi\) | ||||
−0.0609711 | + | 0.998140i | \(0.519420\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.0000 | −0.728948 | −0.364474 | − | 0.931214i | \(-0.618751\pi\) | ||||
−0.364474 | + | 0.931214i | \(0.618751\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.00000 | 0.121046 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.65685 | −0.341121 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.6569 | −0.940729 | −0.470365 | − | 0.882472i | \(-0.655878\pi\) | ||||
−0.470365 | + | 0.882472i | \(0.655878\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.00000 | −0.239474 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.31371 | −0.555609 | −0.277805 | − | 0.960638i | \(-0.589607\pi\) | ||||
−0.277805 | + | 0.960638i | \(0.589607\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.00000 | 0.237775 | 0.118888 | − | 0.992908i | \(-0.462067\pi\) | ||||
0.118888 | + | 0.992908i | \(0.462067\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.65685 | −0.335083 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.00000 | −0.118056 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.62742 | −0.213377 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.00000 | −0.351726 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 20.6274 | 1.20507 | 0.602533 | − | 0.798094i | \(-0.294158\pi\) | ||||
0.602533 | + | 0.798094i | \(0.294158\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.00000 | 0.232889 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.65685 | 0.328244 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 11.3137 | 0.654289 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.65685 | 0.0954995 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −17.3137 | −0.994647 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.343146 | 0.0196485 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.6274 | −1.06312 | −0.531561 | − | 0.847020i | \(-0.678395\pi\) | ||||
−0.531561 | + | 0.847020i | \(0.678395\pi\) | |||||||
\(308\) | 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 | ||||||||
\(313\) | −29.3137 | −1.65691 | −0.828454 | − | 0.560057i | \(-0.810779\pi\) | ||||
−0.828454 | + | 0.560057i | \(0.810779\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.00000 | −0.0563436 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.6569 | −0.654714 | −0.327357 | − | 0.944901i | \(-0.606158\pi\) | ||||
−0.327357 | + | 0.944901i | \(0.606158\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −20.6863 | −1.15821 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.34315 | −0.354040 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −20.6863 | −1.15102 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.00000 | 0.110940 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.00000 | 0.110600 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.34315 | −0.129182 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.6274 | 1.46358 | 0.731788 | − | 0.681533i | \(-0.238686\pi\) | ||||
0.731788 | + | 0.681533i | \(0.238686\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 11.6569 | 0.638792 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.65685 | 0.527610 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.3137 | 0.725244 | 0.362622 | − | 0.931936i | \(-0.381882\pi\) | ||||
0.362622 | + | 0.931936i | \(0.381882\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.34315 | 0.235887 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 22.6274 | 1.22534 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.65685 | −0.304555 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.65685 | −0.0889446 | −0.0444723 | − | 0.999011i | \(-0.514161\pi\) | ||||
−0.0444723 | + | 0.999011i | \(0.514161\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.3431 | −1.08894 | −0.544472 | − | 0.838779i | \(-0.683270\pi\) | ||||
−0.544472 | + | 0.838779i | \(0.683270\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.00000 | −0.106752 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.02944 | 0.0547914 | 0.0273957 | − | 0.999625i | \(-0.491279\pi\) | ||||
0.0273957 | + | 0.999625i | \(0.491279\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.31371 | 0.388171 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.65685 | −0.193541 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −28.0000 | −1.47778 | −0.738892 | − | 0.673824i | \(-0.764651\pi\) | ||||
−0.738892 | + | 0.673824i | \(0.764651\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.0000 | 0.684211 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −21.0000 | −1.10221 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.00000 | 0.314054 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.6274 | −0.763545 | −0.381772 | − | 0.924256i | \(-0.624686\pi\) | ||||
−0.381772 | + | 0.924256i | \(0.624686\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.00000 | 0.104116 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.65685 | 0.189854 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.6569 | 1.01779 | 0.508897 | − | 0.860828i | \(-0.330054\pi\) | ||||
0.508897 | + | 0.860828i | \(0.330054\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.31371 | 0.376675 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 34.6274 | 1.77869 | 0.889345 | − | 0.457236i | \(-0.151160\pi\) | ||||
0.889345 | + | 0.457236i | \(0.151160\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −19.3137 | −0.989471 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.65685 | 0.289052 | 0.144526 | − | 0.989501i | \(-0.453834\pi\) | ||||
0.144526 | + | 0.989501i | \(0.453834\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.65685 | 0.288300 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.65685 | −0.0842226 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 30.9706 | 1.57027 | 0.785135 | − | 0.619325i | \(-0.212594\pi\) | ||||
0.785135 | + | 0.619325i | \(0.212594\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −20.6863 | −1.04615 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −20.0000 | −1.00887 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −11.3137 | −0.569254 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.31371 | −0.467442 | −0.233721 | − | 0.972304i | \(-0.575090\pi\) | ||||
−0.233721 | + | 0.972304i | \(0.575090\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.65685 | 0.283197 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.3137 | 0.664855 | 0.332427 | − | 0.943129i | \(-0.392132\pi\) | ||||
0.332427 | + | 0.943129i | \(0.392132\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.00000 | −0.398508 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −65.9411 | −3.26858 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.3137 | 1.05390 | 0.526948 | − | 0.849898i | \(-0.323336\pi\) | ||||
0.526948 | + | 0.849898i | \(0.323336\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.34315 | 0.214232 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.00000 | −0.196827 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.00000 | 0.196352 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −13.6569 | −0.668779 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.6274 | −0.910009 | −0.455004 | − | 0.890489i | \(-0.650362\pi\) | ||||
−0.455004 | + | 0.890489i | \(0.650362\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.0000 | −0.487370 | −0.243685 | − | 0.969854i | \(-0.578356\pi\) | ||||
−0.243685 | + | 0.969854i | \(0.578356\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.34315 | 0.113928 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.65685 | −0.177383 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.343146 | −0.0166060 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 11.3137 | 0.546231 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.6863 | −0.803750 | −0.401875 | − | 0.915694i | \(-0.631641\pi\) | ||||
−0.401875 | + | 0.915694i | \(0.631641\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −21.3137 | −1.02427 | −0.512136 | − | 0.858905i | \(-0.671146\pi\) | ||||
−0.512136 | + | 0.858905i | \(0.671146\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.65685 | −0.175333 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 32.0000 | 1.53077 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −23.3137 | −1.11270 | −0.556351 | − | 0.830947i | \(-0.687799\pi\) | ||||
−0.556351 | + | 0.830947i | \(0.687799\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.97056 | 0.236159 | 0.118079 | − | 0.993004i | \(-0.462326\pi\) | ||||
0.118079 | + | 0.993004i | \(0.462326\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.0000 | −0.663664 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 18.9706 | 0.897277 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.31371 | −0.439541 | −0.219771 | − | 0.975552i | \(-0.570531\pi\) | ||||
−0.219771 | + | 0.975552i | \(0.570531\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.3137 | −0.532742 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 16.0000 | 0.751746 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.00000 | −0.0937614 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 34.0000 | 1.59045 | 0.795226 | − | 0.606313i | \(-0.207352\pi\) | ||||
0.795226 | + | 0.606313i | \(0.207352\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.65685 | 0.170687 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −35.9411 | −1.67395 | −0.836973 | − | 0.547245i | \(-0.815677\pi\) | ||||
−0.836973 | + | 0.547245i | \(0.815677\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.00000 | 0.371792 | 0.185896 | − | 0.982569i | \(-0.440481\pi\) | ||||
0.185896 | + | 0.982569i | \(0.440481\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.00000 | 0.185496 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 31.3137 | 1.44903 | 0.724513 | − | 0.689261i | \(-0.242065\pi\) | ||||
0.724513 | + | 0.689261i | \(0.242065\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.65685 | −0.445912 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.0000 | −0.460776 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.37258 | 0.430952 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.65685 | 0.259554 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.65685 | −0.167436 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.6274 | 1.03387 | 0.516937 | − | 0.856024i | \(-0.327072\pi\) | ||||
0.516937 | + | 0.856024i | \(0.327072\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 23.3137 | 1.06301 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.65685 | 0.257396 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.00000 | 0.272446 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −22.6274 | −1.02535 | −0.512673 | − | 0.858584i | \(-0.671345\pi\) | ||||
−0.512673 | + | 0.858584i | \(0.671345\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −17.6569 | −0.798471 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.65685 | −0.255290 | −0.127645 | − | 0.991820i | \(-0.540742\pi\) | ||||
−0.127645 | + | 0.991820i | \(0.540742\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13.3726 | −0.602271 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.65685 | −0.254257 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.31371 | −0.328065 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −34.6274 | −1.55014 | −0.775068 | − | 0.631878i | \(-0.782284\pi\) | ||||
−0.775068 | + | 0.631878i | \(0.782284\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.6569 | −0.610143 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13.6569 | −0.608929 | −0.304465 | − | 0.952524i | \(-0.598478\pi\) | ||||
−0.304465 | + | 0.952524i | \(0.598478\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.3137 | 0.770450 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.00000 | 0.399704 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.0000 | 0.620539 | 0.310270 | − | 0.950649i | \(-0.399581\pi\) | ||||
0.310270 | + | 0.950649i | \(0.399581\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.00000 | −0.265424 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.65685 | −0.249756 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.00000 | 0.352522 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.2548 | −0.582947 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 21.3137 | 0.935568 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 29.3137 | 1.28426 | 0.642128 | − | 0.766597i | \(-0.278052\pi\) | ||||
0.642128 | + | 0.766597i | \(0.278052\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.6274 | −1.16434 | −0.582168 | − | 0.813069i | \(-0.697795\pi\) | ||||
−0.582168 | + | 0.813069i | \(0.697795\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.00000 | 0.0436436 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 14.6274 | 0.637180 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.00000 | 0.391304 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.00000 | 0.173585 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.00000 | 0.173259 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.34315 | 0.274238 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 13.6569 | 0.589337 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.65685 | −0.243658 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.68629 | −0.287466 | −0.143733 | − | 0.989616i | \(-0.545911\pi\) | ||||
−0.143733 | + | 0.989616i | \(0.545911\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11.6569 | −0.500243 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.00000 | −0.0856706 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.2843 | 1.38038 | 0.690188 | − | 0.723630i | \(-0.257528\pi\) | ||||
0.690188 | + | 0.723630i | \(0.257528\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.343146 | 0.0146451 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 20.6863 | 0.881266 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.3137 | 0.481108 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −11.6569 | −0.494806 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.02944 | −0.213104 | −0.106552 | − | 0.994307i | \(-0.533981\pi\) | ||||
−0.106552 | + | 0.994307i | \(0.533981\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.31371 | −0.140155 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −20.6863 | −0.873376 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.00000 | −0.168580 | −0.0842900 | − | 0.996441i | \(-0.526862\pi\) | ||||
−0.0842900 | + | 0.996441i | \(0.526862\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.34315 | −0.182718 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 27.9411 | 1.17135 | 0.585676 | − | 0.810545i | \(-0.300829\pi\) | ||||
0.585676 | + | 0.810545i | \(0.300829\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.00000 | −0.167395 | −0.0836974 | − | 0.996491i | \(-0.526673\pi\) | ||||
−0.0836974 | + | 0.996491i | \(0.526673\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.3137 | 0.639739 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.65685 | 0.235907 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 33.3137 | 1.38687 | 0.693434 | − | 0.720520i | \(-0.256097\pi\) | ||||
0.693434 | + | 0.720520i | \(0.256097\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13.3137 | −0.553299 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.00000 | −0.165948 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20.6863 | 0.856739 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.00000 | 0.0826898 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −28.0000 | −1.15568 | −0.577842 | − | 0.816149i | \(-0.696105\pi\) | ||||
−0.577842 | + | 0.816149i | \(0.696105\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −22.6274 | −0.932346 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.6569 | 0.479499 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.97056 | 0.121986 | 0.0609932 | − | 0.998138i | \(-0.480573\pi\) | ||||
0.0609932 | + | 0.998138i | \(0.480573\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.65685 | 0.149916 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.00000 | −0.163709 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.686292 | −0.0280411 | −0.0140206 | − | 0.999902i | \(-0.504463\pi\) | ||||
−0.0140206 | + | 0.999902i | \(0.504463\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.6274 | 1.00457 | 0.502287 | − | 0.864701i | \(-0.332492\pi\) | ||||
0.502287 | + | 0.864701i | \(0.332492\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.65685 | 0.393258 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 21.0000 | 0.853771 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.9411 | 1.05292 | 0.526459 | − | 0.850201i | \(-0.323519\pi\) | ||||
0.526459 | + | 0.850201i | \(0.323519\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.65685 | 0.148183 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.68629 | 0.189587 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26.9706 | −1.08933 | −0.544665 | − | 0.838653i | \(-0.683343\pi\) | ||||
−0.544665 | + | 0.838653i | \(0.683343\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.00000 | −0.0806478 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 30.9706 | 1.24683 | 0.623414 | − | 0.781892i | \(-0.285745\pi\) | ||||
0.623414 | + | 0.781892i | \(0.285745\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 40.9706 | 1.64675 | 0.823373 | − | 0.567501i | \(-0.192090\pi\) | ||||
0.823373 | + | 0.567501i | \(0.192090\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.65685 | −0.227002 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 14.0000 | 0.560898 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 32.0000 | 1.27796 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −42.6274 | −1.69967 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.6274 | 0.582308 | 0.291154 | − | 0.956676i | \(-0.405961\pi\) | ||||
0.291154 | + | 0.956676i | \(0.405961\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 26.6274 | 1.05834 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 19.3137 | 0.766441 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.00000 | 0.0792429 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.31371 | 0.289326 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 32.6274 | 1.28871 | 0.644353 | − | 0.764728i | \(-0.277127\pi\) | ||||
0.644353 | + | 0.764728i | \(0.277127\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.31371 | −0.288425 | −0.144212 | − | 0.989547i | \(-0.546065\pi\) | ||||
−0.144212 | + | 0.989547i | \(0.546065\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.65685 | 0.0652386 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −13.6569 | −0.536906 | −0.268453 | − | 0.963293i | \(-0.586512\pi\) | ||||
−0.268453 | + | 0.963293i | \(0.586512\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −22.6274 | −0.888204 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.00000 | −0.156772 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.9706 | −0.585843 | −0.292922 | − | 0.956136i | \(-0.594628\pi\) | ||||
−0.292922 | + | 0.956136i | \(0.594628\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20.0000 | 0.781465 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.00000 | 0.234082 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.9706 | 0.661079 | 0.330540 | − | 0.943792i | \(-0.392769\pi\) | ||||
0.330540 | + | 0.943792i | \(0.392769\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −46.2843 | −1.80025 | −0.900125 | − | 0.435632i | \(-0.856525\pi\) | ||||
−0.900125 | + | 0.435632i | \(0.856525\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7.31371 | 0.284041 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.65685 | −0.219363 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20.6863 | 0.800976 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −19.3137 | −0.746711 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.94113 | −0.0749363 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −49.3137 | −1.90090 | −0.950452 | − | 0.310872i | \(-0.899379\pi\) | ||||
−0.950452 | + | 0.310872i | \(0.899379\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 41.3137 | 1.58781 | 0.793907 | − | 0.608039i | \(-0.208043\pi\) | ||||
0.793907 | + | 0.608039i | \(0.208043\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.00000 | −0.230259 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −26.6274 | −1.02036 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −22.3431 | −0.854937 | −0.427468 | − | 0.904030i | \(-0.640594\pi\) | ||||
−0.427468 | + | 0.904030i | \(0.640594\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.34315 | −0.165943 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.9706 | −0.571163 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.31371 | −0.278630 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.97056 | 0.341256 | 0.170628 | − | 0.985335i | \(-0.445420\pi\) | ||||
0.170628 | + | 0.985335i | \(0.445420\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.65685 | 0.214886 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13.6569 | 0.518034 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.31371 | −0.277026 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −14.9706 | −0.566239 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.65685 | 0.138117 | 0.0690587 | − | 0.997613i | \(-0.478000\pi\) | ||||
0.0690587 | + | 0.997613i | \(0.478000\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 65.9411 | 2.48702 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.34315 | −0.0882480 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −17.3137 | −0.651149 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.3137 | 0.650230 | 0.325115 | − | 0.945674i | \(-0.394597\pi\) | ||||
0.325115 | + | 0.945674i | \(0.394597\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −11.3137 | −0.424297 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −22.6274 | −0.847403 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.3137 | −0.423109 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 23.3137 | 0.870666 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −35.3137 | −1.31698 | −0.658490 | − | 0.752590i | \(-0.728804\pi\) | ||||
−0.658490 | + | 0.752590i | \(0.728804\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.00000 | −0.297936 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.31371 | 0.0488573 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.65685 | 0.135812 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.0000 | −0.593407 | −0.296704 | − | 0.954970i | \(-0.595887\pi\) | ||||
−0.296704 | + | 0.954970i | \(0.595887\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.05887 | 0.224096 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.00000 | 0.0738717 | 0.0369358 | − | 0.999318i | \(-0.488240\pi\) | ||||
0.0369358 | + | 0.999318i | \(0.488240\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.00000 | −0.0368856 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −54.6274 | −2.01223 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23.3137 | −0.857609 | −0.428804 | − | 0.903397i | \(-0.641065\pi\) | ||||
−0.428804 | + | 0.903397i | \(0.641065\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −11.3137 | −0.415619 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13.6569 | −0.501021 | −0.250511 | − | 0.968114i | \(-0.580599\pi\) | ||||
−0.250511 | + | 0.968114i | \(0.580599\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.9706 | −0.695028 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.00000 | 0.146352 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.34315 | −0.231774 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.3137 | −0.412843 | −0.206422 | − | 0.978463i | \(-0.566182\pi\) | ||||
−0.206422 | + | 0.978463i | \(0.566182\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −15.3137 | −0.558063 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16.0000 | −0.582300 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 48.9117 | 1.77773 | 0.888863 | − | 0.458174i | \(-0.151496\pi\) | ||||
0.888863 | + | 0.458174i | \(0.151496\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 32.0000 | 1.16153 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31.9411 | −1.15786 | −0.578932 | − | 0.815376i | \(-0.696531\pi\) | ||||
−0.578932 | + | 0.815376i | \(0.696531\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.00000 | 0.0724049 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.65685 | −0.132214 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.00000 | 0.288863 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.9411 | 1.00758 | 0.503791 | − | 0.863825i | \(-0.331938\pi\) | ||||
0.503791 | + | 0.863825i | \(0.331938\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 27.6569 | 0.996037 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14.0000 | 0.503545 | 0.251773 | − | 0.967786i | \(-0.418987\pi\) | ||||
0.251773 | + | 0.967786i | \(0.418987\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.00000 | −0.143684 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 11.6569 | 0.418187 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 11.3137 | 0.405356 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −41.3726 | −1.48043 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.65685 | −0.130685 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.0000 | 0.356915 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.6863 | −0.594802 | −0.297401 | − | 0.954753i | \(-0.596120\pi\) | ||||
−0.297401 | + | 0.954753i | \(0.596120\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 29.6569 | 1.05581 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.34315 | 0.154424 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.686292 | 0.0243709 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.65685 | 0.129695 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17.3137 | 0.613283 | 0.306642 | − | 0.951825i | \(-0.400795\pi\) | ||||
0.306642 | + | 0.951825i | \(0.400795\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.56854 | −0.303133 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.0000 | −0.494666 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −33.9411 | −1.19776 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.65685 | −0.199378 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.00000 | 0.0704033 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.62742 | −0.162691 | −0.0813457 | − | 0.996686i | \(-0.525922\pi\) | ||||
−0.0813457 | + | 0.996686i | \(0.525922\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.6569 | 0.479557 | 0.239779 | − | 0.970828i | \(-0.422925\pi\) | ||||
0.239779 | + | 0.970828i | \(0.422925\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.0000 | 0.420858 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17.6569 | 0.618493 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.37258 | −0.327905 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.00000 | −0.0698857 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −38.2843 | −1.33613 | −0.668065 | − | 0.744103i | \(-0.732877\pi\) | ||||
−0.668065 | + | 0.744103i | \(0.732877\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.65685 | 0.196946 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −30.3431 | −1.05513 | −0.527567 | − | 0.849513i | \(-0.676896\pi\) | ||||
−0.527567 | + | 0.849513i | \(0.676896\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23.6569 | −0.821637 | −0.410818 | − | 0.911717i | \(-0.634757\pi\) | ||||
−0.410818 | + | 0.911717i | \(0.634757\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15.6569 | 0.543130 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.65685 | −0.126702 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13.6569 | 0.472615 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.00000 | 0.138260 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 27.3137 | 0.942974 | 0.471487 | − | 0.881873i | \(-0.343717\pi\) | ||||
0.471487 | + | 0.881873i | \(0.343717\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.6274 | −0.538876 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.31371 | 0.320781 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.00000 | −0.309609 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −21.0000 | −0.721569 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.00000 | −0.137280 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 65.9411 | 2.26043 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 27.9411 | 0.956686 | 0.478343 | − | 0.878173i | \(-0.341238\pi\) | ||||
0.478343 | + | 0.878173i | \(0.341238\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.65685 | 0.193460 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 44.3431 | 1.51473 | 0.757367 | − | 0.652990i | \(-0.226486\pi\) | ||||
0.757367 | + | 0.652990i | \(0.226486\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −48.9706 | −1.67085 | −0.835427 | − | 0.549601i | \(-0.814780\pi\) | ||||
−0.835427 | + | 0.549601i | \(0.814780\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.00000 | 0.0681598 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.3431 | 0.624408 | 0.312204 | − | 0.950015i | \(-0.398933\pi\) | ||||
0.312204 | + | 0.950015i | \(0.398933\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21.3137 | −0.724688 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.62742 | 0.123194 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 64.0000 | 2.17105 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.3137 | 0.654420 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.00000 | 0.203069 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 46.9706 | 1.58608 | 0.793042 | − | 0.609167i | \(-0.208496\pi\) | ||||
0.793042 | + | 0.609167i | \(0.208496\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −20.6274 | −0.695746 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.627417 | 0.0211382 | 0.0105691 | − | 0.999944i | \(-0.496636\pi\) | ||||
0.0105691 | + | 0.999944i | \(0.496636\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33.6569 | −1.13264 | −0.566322 | − | 0.824184i | \(-0.691634\pi\) | ||||
−0.566322 | + | 0.824184i | \(0.691634\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.00000 | −0.134459 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 44.2843 | 1.48692 | 0.743460 | − | 0.668780i | \(-0.233183\pi\) | ||||
0.743460 | + | 0.668780i | \(0.233183\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −19.3137 | −0.647761 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.65685 | −0.189512 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13.2548 | 0.443556 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −13.6569 | −0.456498 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −11.3137 | −0.377754 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −14.6274 | −0.487852 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.3726 | 0.445505 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.65685 | −0.0551367 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 11.6569 | 0.387487 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.9706 | 0.961952 | 0.480976 | − | 0.876734i | \(-0.340282\pi\) | ||||
0.480976 | + | 0.876734i | \(0.340282\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 17.3137 | 0.574259 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29.9411 | 0.991994 | 0.495997 | − | 0.868324i | \(-0.334803\pi\) | ||||
0.495997 | + | 0.868324i | \(0.334803\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −22.6274 | −0.748858 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.343146 | −0.0113440 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −20.0000 | −0.660458 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 41.9411 | 1.38351 | 0.691755 | − | 0.722132i | \(-0.256838\pi\) | ||||
0.691755 | + | 0.722132i | \(0.256838\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 18.6274 | 0.613794 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 14.6274 | 0.481467 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.6569 | 0.383275 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.00000 | 0.262754 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10.6863 | −0.350606 | −0.175303 | − | 0.984515i | \(-0.556090\pi\) | ||||
−0.175303 | + | 0.984515i | \(0.556090\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.65685 | 0.185396 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.00000 | 0.261908 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 20.6863 | 0.676514 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.6863 | 0.871803 | 0.435902 | − | 0.899994i | \(-0.356430\pi\) | ||||
0.435902 | + | 0.899994i | \(0.356430\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 29.3137 | 0.956617 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.0000 | 0.456387 | 0.228193 | − | 0.973616i | \(-0.426718\pi\) | ||||
0.228193 | + | 0.973616i | \(0.426718\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.3137 | 0.368425 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.00000 | 0.0325300 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16.2843 | −0.529168 | −0.264584 | − | 0.964363i | \(-0.585235\pi\) | ||||
−0.264584 | + | 0.964363i | \(0.585235\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.0000 | 0.389536 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.6569 | 0.377999 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.65685 | 0.118457 | 0.0592286 | − | 0.998244i | \(-0.481136\pi\) | ||||
0.0592286 | + | 0.998244i | \(0.481136\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15.3137 | −0.495540 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 20.6863 | 0.668693 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.34315 | 0.140247 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.34315 | 0.204405 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 13.3137 | 0.428583 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −41.9411 | −1.34874 | −0.674368 | − | 0.738396i | \(-0.735584\pi\) | ||||
−0.674368 | + | 0.738396i | \(0.735584\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 20.6863 | 0.664539 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 58.6274 | 1.88144 | 0.940722 | − | 0.339180i | \(-0.110149\pi\) | ||||
0.940722 | + | 0.339180i | \(0.110149\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13.6569 | −0.437819 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.00000 | −0.0640513 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −47.6569 | −1.52468 | −0.762339 | − | 0.647178i | \(-0.775949\pi\) | ||||
−0.762339 | + | 0.647178i | \(0.775949\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 79.1960 | 2.53111 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.00000 | −0.0638551 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 21.6569 | 0.690746 | 0.345373 | − | 0.938465i | \(-0.387752\pi\) | ||||
0.345373 | + | 0.938465i | \(0.387752\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.6569 | −0.371418 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.34315 | 0.0745832 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.37258 | −0.298031 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.3137 | −0.359392 | −0.179696 | − | 0.983722i | \(-0.557511\pi\) | ||||
−0.179696 | + | 0.983722i | \(0.557511\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −26.6274 | −0.844996 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.00000 | 0.126809 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.3137 | −0.548331 | −0.274165 | − | 0.961683i | \(-0.588402\pi\) | ||||
−0.274165 | + | 0.961683i | \(0.588402\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −11.6569 | −0.368807 |
(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 | 1680.2.a.u.1.1 | 2 | ||
3.2 | odd | 2 | 5040.2.a.br.1.2 | 2 | |||
4.3 | odd | 2 | 840.2.a.k.1.2 | ✓ | 2 | ||
5.4 | even | 2 | 8400.2.a.de.1.1 | 2 | |||
8.3 | odd | 2 | 6720.2.a.co.1.1 | 2 | |||
8.5 | even | 2 | 6720.2.a.cu.1.2 | 2 | |||
12.11 | even | 2 | 2520.2.a.v.1.1 | 2 | |||
20.3 | even | 4 | 4200.2.t.u.1849.4 | 4 | |||
20.7 | even | 4 | 4200.2.t.u.1849.2 | 4 | |||
20.19 | odd | 2 | 4200.2.a.bg.1.2 | 2 | |||
28.27 | even | 2 | 5880.2.a.bl.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
840.2.a.k.1.2 | ✓ | 2 | 4.3 | odd | 2 | ||
1680.2.a.u.1.1 | 2 | 1.1 | even | 1 | trivial | ||
2520.2.a.v.1.1 | 2 | 12.11 | even | 2 | |||
4200.2.a.bg.1.2 | 2 | 20.19 | odd | 2 | |||
4200.2.t.u.1849.2 | 4 | 20.7 | even | 4 | |||
4200.2.t.u.1849.4 | 4 | 20.3 | even | 4 | |||
5040.2.a.br.1.2 | 2 | 3.2 | odd | 2 | |||
5880.2.a.bl.1.2 | 2 | 28.27 | even | 2 | |||
6720.2.a.co.1.1 | 2 | 8.3 | odd | 2 | |||
6720.2.a.cu.1.2 | 2 | 8.5 | even | 2 | |||
8400.2.a.de.1.1 | 2 | 5.4 | even | 2 |