Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8280,2,Mod(1,8280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8280, 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("8280.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8280 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8280.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: | \(66.1161328736\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.568.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.76156\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8280.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.761557 | −0.287842 | −0.143921 | − | 0.989589i | \(-0.545971\pi\) | ||||
−0.143921 | + | 0.989589i | \(0.545971\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.86464 | −0.863722 | −0.431861 | − | 0.901940i | \(-0.642143\pi\) | ||||
−0.431861 | + | 0.901940i | \(0.642143\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.864641 | 0.239808 | 0.119904 | − | 0.992785i | \(-0.461741\pi\) | ||||
0.119904 | + | 0.992785i | \(0.461741\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.761557 | 0.184705 | 0.0923524 | − | 0.995726i | \(-0.470561\pi\) | ||||
0.0923524 | + | 0.995726i | \(0.470561\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.38776 | 1.46545 | 0.732726 | − | 0.680524i | \(-0.238248\pi\) | ||||
0.732726 | + | 0.680524i | \(0.238248\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.62620 | −0.301977 | −0.150989 | − | 0.988535i | \(-0.548246\pi\) | ||||
−0.150989 | + | 0.988535i | \(0.548246\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.62620 | −0.651284 | −0.325642 | − | 0.945493i | \(-0.605580\pi\) | ||||
−0.325642 | + | 0.945493i | \(0.605580\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.761557 | 0.128727 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.76156 | 0.453997 | 0.226999 | − | 0.973895i | \(-0.427109\pi\) | ||||
0.226999 | + | 0.973895i | \(0.427109\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.62620 | −1.19101 | −0.595506 | − | 0.803351i | \(-0.703048\pi\) | ||||
−0.595506 | + | 0.803351i | \(0.703048\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.72928 | 0.263713 | 0.131856 | − | 0.991269i | \(-0.457906\pi\) | ||||
0.131856 | + | 0.991269i | \(0.457906\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.3878 | −1.51521 | −0.757605 | − | 0.652713i | \(-0.773631\pi\) | ||||
−0.757605 | + | 0.652713i | \(0.773631\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.42003 | −0.917147 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.761557 | 0.104608 | 0.0523040 | − | 0.998631i | \(-0.483344\pi\) | ||||
0.0523040 | + | 0.998631i | \(0.483344\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.86464 | 0.386268 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.35548 | 0.436846 | 0.218423 | − | 0.975854i | \(-0.429909\pi\) | ||||
0.218423 | + | 0.975854i | \(0.429909\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.11704 | −0.271059 | −0.135529 | − | 0.990773i | \(-0.543274\pi\) | ||||
−0.135529 | + | 0.990773i | \(0.543274\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.864641 | −0.107246 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.74324 | −0.945987 | −0.472993 | − | 0.881066i | \(-0.656827\pi\) | ||||
−0.472993 | + | 0.881066i | \(0.656827\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.9248 | 1.65257 | 0.826286 | − | 0.563250i | \(-0.190449\pi\) | ||||
0.826286 | + | 0.563250i | \(0.190449\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.92919 | 0.576918 | 0.288459 | − | 0.957492i | \(-0.406857\pi\) | ||||
0.288459 | + | 0.957492i | \(0.406857\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.18159 | 0.248615 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.5048 | 1.18188 | 0.590941 | − | 0.806715i | \(-0.298757\pi\) | ||||
0.590941 | + | 0.806715i | \(0.298757\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.490839 | 0.0538766 | 0.0269383 | − | 0.999637i | \(-0.491424\pi\) | ||||
0.0269383 | + | 0.999637i | \(0.491424\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.761557 | −0.0826025 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.7755 | 1.77820 | 0.889100 | − | 0.457712i | \(-0.151331\pi\) | ||||
0.889100 | + | 0.457712i | \(0.151331\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.658473 | −0.0690268 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.38776 | −0.655370 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.77551 | 0.687949 | 0.343974 | − | 0.938979i | \(-0.388227\pi\) | ||||
0.343974 | + | 0.938979i | \(0.388227\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.89692 | −0.785773 | −0.392886 | − | 0.919587i | \(-0.628523\pi\) | ||||
−0.392886 | + | 0.919587i | \(0.628523\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.8401 | 1.65930 | 0.829650 | − | 0.558283i | \(-0.188540\pi\) | ||||
0.829650 | + | 0.558283i | \(0.188540\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.74324 | −0.748567 | −0.374283 | − | 0.927314i | \(-0.622111\pi\) | ||||
−0.374283 | + | 0.927314i | \(0.622111\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.593923 | 0.0568875 | 0.0284437 | − | 0.999595i | \(-0.490945\pi\) | ||||
0.0284437 | + | 0.999595i | \(0.490945\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −20.7895 | −1.95571 | −0.977854 | − | 0.209288i | \(-0.932886\pi\) | ||||
−0.977854 | + | 0.209288i | \(0.932886\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.00000 | −0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.579969 | −0.0531657 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.79383 | −0.253985 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.6864 | 1.30321 | 0.651603 | − | 0.758560i | \(-0.274097\pi\) | ||||
0.651603 | + | 0.758560i | \(0.274097\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.72928 | 0.675310 | 0.337655 | − | 0.941270i | \(-0.390366\pi\) | ||||
0.337655 | + | 0.941270i | \(0.390366\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.86464 | −0.421818 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.98168 | 0.254742 | 0.127371 | − | 0.991855i | \(-0.459346\pi\) | ||||
0.127371 | + | 0.991855i | \(0.459346\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.8603 | −1.68453 | −0.842263 | − | 0.539067i | \(-0.818777\pi\) | ||||
−0.842263 | + | 0.539067i | \(0.818777\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.47689 | −0.207128 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.62620 | 0.135048 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.92919 | −0.403815 | −0.201908 | − | 0.979405i | \(-0.564714\pi\) | ||||
−0.201908 | + | 0.979405i | \(0.564714\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.25240 | 0.590192 | 0.295096 | − | 0.955468i | \(-0.404648\pi\) | ||||
0.295096 | + | 0.955468i | \(0.404648\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.62620 | 0.291263 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.2663 | −1.05877 | −0.529385 | − | 0.848382i | \(-0.677577\pi\) | ||||
−0.529385 | + | 0.848382i | \(0.677577\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.761557 | −0.0600191 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.0279 | −1.25540 | −0.627701 | − | 0.778454i | \(-0.716004\pi\) | ||||
−0.627701 | + | 0.778454i | \(0.716004\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −19.7047 | −1.52480 | −0.762398 | − | 0.647109i | \(-0.775978\pi\) | ||||
−0.762398 | + | 0.647109i | \(0.775978\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.2524 | −0.942492 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.7572 | 0.893882 | 0.446941 | − | 0.894563i | \(-0.352513\pi\) | ||||
0.446941 | + | 0.894563i | \(0.352513\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.761557 | −0.0575683 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20.8401 | −1.55766 | −0.778830 | − | 0.627235i | \(-0.784186\pi\) | ||||
−0.778830 | + | 0.627235i | \(0.784186\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −26.0279 | −1.93464 | −0.967320 | − | 0.253560i | \(-0.918398\pi\) | ||||
−0.967320 | + | 0.253560i | \(0.918398\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.76156 | −0.203034 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.18159 | −0.159534 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.40608 | −0.391170 | −0.195585 | − | 0.980687i | \(-0.562661\pi\) | ||||
−0.195585 | + | 0.980687i | \(0.562661\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.7476 | −0.773629 | −0.386815 | − | 0.922157i | \(-0.626425\pi\) | ||||
−0.386815 | + | 0.922157i | \(0.626425\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.9634 | −1.13734 | −0.568671 | − | 0.822565i | \(-0.692542\pi\) | ||||
−0.568671 | + | 0.822565i | \(0.692542\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.20617 | −0.298167 | −0.149084 | − | 0.988825i | \(-0.547632\pi\) | ||||
−0.149084 | + | 0.988825i | \(0.547632\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.23844 | 0.0869216 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.62620 | 0.532637 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −18.2986 | −1.26574 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.4017 | 1.12914 | 0.564570 | − | 0.825385i | \(-0.309042\pi\) | ||||
0.564570 | + | 0.825385i | \(0.309042\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.72928 | −0.117936 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.76156 | 0.187467 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.658473 | 0.0442937 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.7755 | 0.989441 | 0.494721 | − | 0.869052i | \(-0.335270\pi\) | ||||
0.494721 | + | 0.869052i | \(0.335270\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.54144 | −0.301426 | −0.150713 | − | 0.988578i | \(-0.548157\pi\) | ||||
−0.150713 | + | 0.988578i | \(0.548157\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 27.3449 | 1.80700 | 0.903499 | − | 0.428589i | \(-0.140989\pi\) | ||||
0.903499 | + | 0.428589i | \(0.140989\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.0279 | 1.18105 | 0.590524 | − | 0.807020i | \(-0.298921\pi\) | ||||
0.590524 | + | 0.807020i | \(0.298921\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.3878 | 0.677622 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.81404 | −0.570133 | −0.285067 | − | 0.958508i | \(-0.592016\pi\) | ||||
−0.285067 | + | 0.958508i | \(0.592016\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.6864 | −1.46136 | −0.730679 | − | 0.682721i | \(-0.760796\pi\) | ||||
−0.730679 | + | 0.682721i | \(0.760796\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.42003 | 0.410161 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.52311 | 0.351427 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.7293 | −0.740346 | −0.370173 | − | 0.928963i | \(-0.620702\pi\) | ||||
−0.370173 | + | 0.928963i | \(0.620702\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.86464 | −0.180098 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −21.9109 | −1.36676 | −0.683381 | − | 0.730062i | \(-0.739491\pi\) | ||||
−0.683381 | + | 0.730062i | \(0.739491\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.10308 | −0.130679 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −27.9773 | −1.72515 | −0.862577 | − | 0.505925i | \(-0.831151\pi\) | ||||
−0.862577 | + | 0.505925i | \(0.831151\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.761557 | −0.0467821 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.21386 | −0.0740105 | −0.0370053 | − | 0.999315i | \(-0.511782\pi\) | ||||
−0.0370053 | + | 0.999315i | \(0.511782\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −22.7003 | −1.37895 | −0.689474 | − | 0.724311i | \(-0.742158\pi\) | ||||
−0.689474 | + | 0.724311i | \(0.742158\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.86464 | −0.172744 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.52311 | 0.331852 | 0.165926 | − | 0.986138i | \(-0.446939\pi\) | ||||
0.165926 | + | 0.986138i | \(0.446939\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.3511 | −1.45267 | −0.726333 | − | 0.687343i | \(-0.758777\pi\) | ||||
−0.726333 | + | 0.687343i | \(0.758777\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.9956 | 0.891398 | 0.445699 | − | 0.895183i | \(-0.352955\pi\) | ||||
0.445699 | + | 0.895183i | \(0.352955\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.80779 | 0.342823 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.4200 | −0.965884 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −24.5833 | −1.43617 | −0.718086 | − | 0.695955i | \(-0.754981\pi\) | ||||
−0.718086 | + | 0.695955i | \(0.754981\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.35548 | −0.195364 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.864641 | 0.0500035 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.31695 | −0.0759076 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.11704 | 0.121221 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 30.1816 | 1.72255 | 0.861277 | − | 0.508136i | \(-0.169665\pi\) | ||||
0.861277 | + | 0.508136i | \(0.169665\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.0741 | −1.08159 | −0.540797 | − | 0.841153i | \(-0.681877\pi\) | ||||
−0.540797 | + | 0.841153i | \(0.681877\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.3955 | −1.32239 | −0.661195 | − | 0.750214i | \(-0.729950\pi\) | ||||
−0.661195 | + | 0.750214i | \(0.729950\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.4985 | 0.982816 | 0.491408 | − | 0.870930i | \(-0.336482\pi\) | ||||
0.491408 | + | 0.870930i | \(0.336482\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.65847 | 0.260824 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.86464 | 0.270676 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.864641 | 0.0479616 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.91087 | 0.436140 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.07518 | 0.114062 | 0.0570310 | − | 0.998372i | \(-0.481837\pi\) | ||||
0.0570310 | + | 0.998372i | \(0.481837\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.74324 | 0.423058 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.02791 | 0.110467 | 0.0552336 | − | 0.998473i | \(-0.482410\pi\) | ||||
0.0552336 | + | 0.998473i | \(0.482410\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.3878 | 0.562528 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.2201 | 0.551835 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.1676 | −0.544261 | −0.272130 | − | 0.962260i | \(-0.587728\pi\) | ||||
−0.272130 | + | 0.962260i | \(0.587728\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.9937 | −0.585138 | −0.292569 | − | 0.956244i | \(-0.594510\pi\) | ||||
−0.292569 | + | 0.956244i | \(0.594510\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.9248 | −0.739053 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −31.9109 | −1.68419 | −0.842096 | − | 0.539328i | \(-0.818678\pi\) | ||||
−0.842096 | + | 0.539328i | \(0.818678\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 21.8034 | 1.14755 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.92919 | −0.258006 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.2663 | 1.42329 | 0.711646 | − | 0.702538i | \(-0.247950\pi\) | ||||
0.711646 | + | 0.702538i | \(0.247950\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.579969 | −0.0301105 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −32.6743 | −1.69181 | −0.845906 | − | 0.533332i | \(-0.820940\pi\) | ||||
−0.845906 | + | 0.533332i | \(0.820940\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.40608 | −0.0724167 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.6339 | −1.16263 | −0.581313 | − | 0.813680i | \(-0.697461\pi\) | ||||
−0.581313 | + | 0.813680i | \(0.697461\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.46293 | −0.432436 | −0.216218 | − | 0.976345i | \(-0.569372\pi\) | ||||
−0.216218 | + | 0.976345i | \(0.569372\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.18159 | −0.111184 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 35.7851 | 1.81438 | 0.907188 | − | 0.420725i | \(-0.138224\pi\) | ||||
0.907188 | + | 0.420725i | \(0.138224\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.761557 | 0.0385136 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.5048 | −0.528553 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.5972 | 1.43525 | 0.717627 | − | 0.696427i | \(-0.245228\pi\) | ||||
0.717627 | + | 0.696427i | \(0.245228\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.0279066 | 0.00139359 | 0.000696795 | − | 1.00000i | \(-0.499778\pi\) | ||||
0.000696795 | 1.00000i | \(0.499778\pi\) | ||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.13536 | −0.156183 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.91087 | −0.392127 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.65410 | 0.279577 | 0.139789 | − | 0.990181i | \(-0.455358\pi\) | ||||
0.139789 | + | 0.990181i | \(0.455358\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.55539 | −0.125743 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.490839 | −0.0240943 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.54769 | −0.271023 | −0.135511 | − | 0.990776i | \(-0.543268\pi\) | ||||
−0.135511 | + | 0.990776i | \(0.543268\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.0033 | 0.974903 | 0.487451 | − | 0.873150i | \(-0.337927\pi\) | ||||
0.487451 | + | 0.873150i | \(0.337927\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.761557 | 0.0369409 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.61224 | 0.0780220 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.58767 | −0.365485 | −0.182742 | − | 0.983161i | \(-0.558497\pi\) | ||||
−0.182742 | + | 0.983161i | \(0.558497\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.19221 | −0.201465 | −0.100732 | − | 0.994914i | \(-0.532119\pi\) | ||||
−0.100732 | + | 0.994914i | \(0.532119\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.38776 | 0.305568 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.4769 | −0.500034 | −0.250017 | − | 0.968241i | \(-0.580436\pi\) | ||||
−0.250017 | + | 0.968241i | \(0.580436\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 29.6681 | 1.40957 | 0.704786 | − | 0.709420i | \(-0.251043\pi\) | ||||
0.704786 | + | 0.709420i | \(0.251043\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16.7755 | −0.795235 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.81404 | −0.415960 | −0.207980 | − | 0.978133i | \(-0.566689\pi\) | ||||
−0.207980 | + | 0.978133i | \(0.566689\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21.8463 | 1.02870 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.658473 | 0.0308697 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.4725 | −0.910886 | −0.455443 | − | 0.890265i | \(-0.650519\pi\) | ||||
−0.455443 | + | 0.890265i | \(0.650519\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.98168 | −0.325169 | −0.162585 | − | 0.986695i | \(-0.551983\pi\) | ||||
−0.162585 | + | 0.986695i | \(0.551983\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −40.9850 | −1.90473 | −0.952367 | − | 0.304953i | \(-0.901359\pi\) | ||||
−0.952367 | + | 0.304953i | \(0.901359\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.09683 | 0.328402 | 0.164201 | − | 0.986427i | \(-0.447495\pi\) | ||||
0.164201 | + | 0.986427i | \(0.447495\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.89692 | 0.272294 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.95377 | −0.227775 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.38776 | 0.293090 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19.7326 | 0.901606 | 0.450803 | − | 0.892623i | \(-0.351138\pi\) | ||||
0.450803 | + | 0.892623i | \(0.351138\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.38776 | 0.108872 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.77551 | −0.307660 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.04290 | 0.137887 | 0.0689435 | − | 0.997621i | \(-0.478037\pi\) | ||||
0.0689435 | + | 0.997621i | \(0.478037\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.8420 | 1.03084 | 0.515421 | − | 0.856937i | \(-0.327635\pi\) | ||||
0.515421 | + | 0.856937i | \(0.327635\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.23844 | −0.0557767 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10.6045 | −0.475679 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.57997 | −0.384092 | −0.192046 | − | 0.981386i | \(-0.561512\pi\) | ||||
−0.192046 | + | 0.981386i | \(0.561512\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.4138 | 0.553503 | 0.276751 | − | 0.960942i | \(-0.410742\pi\) | ||||
0.276751 | + | 0.960942i | \(0.410742\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.89692 | 0.351408 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −40.5606 | −1.79782 | −0.898909 | − | 0.438136i | \(-0.855639\pi\) | ||||
−0.898909 | + | 0.438136i | \(0.855639\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.75386 | −0.166061 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −16.8401 | −0.742062 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 29.7572 | 1.30872 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −33.2557 | −1.45696 | −0.728480 | − | 0.685067i | \(-0.759773\pi\) | ||||
−0.728480 | + | 0.685067i | \(0.759773\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.34485 | −0.408622 | −0.204311 | − | 0.978906i | \(-0.565495\pi\) | ||||
−0.204311 | + | 0.978906i | \(0.565495\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.76156 | −0.120295 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.59392 | −0.285614 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.74324 | 0.334769 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 18.3911 | 0.792160 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.5327 | 0.538823 | 0.269411 | − | 0.963025i | \(-0.413171\pi\) | ||||
0.269411 | + | 0.963025i | \(0.413171\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.593923 | −0.0254409 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.9634 | 1.11011 | 0.555056 | − | 0.831813i | \(-0.312697\pi\) | ||||
0.555056 | + | 0.831813i | \(0.312697\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.3878 | −0.442533 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.00000 | −0.340195 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.11515 | −0.174364 | −0.0871822 | − | 0.996192i | \(-0.527786\pi\) | ||||
−0.0871822 | + | 0.996192i | \(0.527786\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.49521 | 0.0632405 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.7616 | −0.453546 | −0.226773 | − | 0.973948i | \(-0.572817\pi\) | ||||
−0.226773 | + | 0.973948i | \(0.572817\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 20.7895 | 0.874619 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11.2524 | −0.471725 | −0.235862 | − | 0.971786i | \(-0.575791\pi\) | ||||
−0.235862 | + | 0.971786i | \(0.575791\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 38.2866 | 1.60224 | 0.801121 | − | 0.598502i | \(-0.204237\pi\) | ||||
0.801121 | + | 0.598502i | \(0.204237\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −43.9913 | −1.83138 | −0.915690 | − | 0.401885i | \(-0.868355\pi\) | ||||
−0.915690 | + | 0.401885i | \(0.868355\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.373802 | −0.0155079 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.18159 | −0.0903521 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18.8401 | −0.777613 | −0.388806 | − | 0.921320i | \(-0.627112\pi\) | ||||
−0.388806 | + | 0.921320i | \(0.627112\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −23.1633 | −0.954426 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7.81841 | −0.321064 | −0.160532 | − | 0.987031i | \(-0.551321\pi\) | ||||
−0.160532 | + | 0.987031i | \(0.551321\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.579969 | 0.0237764 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17.6281 | 0.720264 | 0.360132 | − | 0.932901i | \(-0.382732\pi\) | ||||
0.360132 | + | 0.932901i | \(0.382732\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.40171 | 0.0979677 | 0.0489839 | − | 0.998800i | \(-0.484402\pi\) | ||||
0.0489839 | + | 0.998800i | \(0.484402\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.79383 | 0.113585 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.9475 | 0.484935 | 0.242467 | − | 0.970160i | \(-0.422043\pi\) | ||||
0.242467 | + | 0.970160i | \(0.422043\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.98168 | −0.363360 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.234074 | 0.00945416 | 0.00472708 | − | 0.999989i | \(-0.498495\pi\) | ||||
0.00472708 | + | 0.999989i | \(0.498495\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.1835 | 0.571005 | 0.285503 | − | 0.958378i | \(-0.407839\pi\) | ||||
0.285503 | + | 0.958378i | \(0.407839\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.129102 | 0.00518903 | 0.00259452 | − | 0.999997i | \(-0.499174\pi\) | ||||
0.00259452 | + | 0.999997i | \(0.499174\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.7755 | −0.511840 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.10308 | 0.0838554 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.6035 | −0.621166 | −0.310583 | − | 0.950546i | \(-0.600524\pi\) | ||||
−0.310583 | + | 0.950546i | \(0.600524\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −14.6864 | −0.582811 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.55102 | −0.219939 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.6218 | 0.419537 | 0.209769 | − | 0.977751i | \(-0.432729\pi\) | ||||
0.209769 | + | 0.977751i | \(0.432729\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.82611 | 0.348068 | 0.174034 | − | 0.984740i | \(-0.444320\pi\) | ||||
0.174034 | + | 0.984740i | \(0.444320\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.49853 | −0.294798 | −0.147399 | − | 0.989077i | \(-0.547090\pi\) | ||||
−0.147399 | + | 0.989077i | \(0.547090\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.61224 | −0.377314 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.34153 | −0.209030 | −0.104515 | − | 0.994523i | \(-0.533329\pi\) | ||||
−0.104515 | + | 0.994523i | \(0.533329\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.72928 | −0.302008 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −35.6402 | −1.38834 | −0.694172 | − | 0.719810i | \(-0.744229\pi\) | ||||
−0.694172 | + | 0.719810i | \(0.744229\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −33.5144 | −1.30356 | −0.651779 | − | 0.758409i | \(-0.725977\pi\) | ||||
−0.651779 | + | 0.758409i | \(0.725977\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.86464 | 0.188643 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.62620 | −0.0629666 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.06455 | 0.234119 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.0525 | −1.08134 | −0.540672 | − | 0.841234i | \(-0.681830\pi\) | ||||
−0.540672 | + | 0.841234i | \(0.681830\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −32.7616 | −1.25913 | −0.629564 | − | 0.776948i | \(-0.716767\pi\) | ||||
−0.629564 | + | 0.776948i | \(0.716767\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.15994 | −0.198020 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.88296 | 0.301633 | 0.150817 | − | 0.988562i | \(-0.451810\pi\) | ||||
0.150817 | + | 0.988562i | \(0.451810\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.98168 | −0.113924 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.658473 | 0.0250858 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.4277 | −0.396689 | −0.198345 | − | 0.980132i | \(-0.563557\pi\) | ||||
−0.198345 | + | 0.980132i | \(0.563557\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 19.8603 | 0.753343 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.80779 | −0.219986 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.5294 | −0.548767 | −0.274383 | − | 0.961620i | \(-0.588474\pi\) | ||||
−0.274383 | + | 0.961620i | \(0.588474\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.6402 | 0.665311 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.01395 | 0.226178 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −35.9754 | −1.35109 | −0.675543 | − | 0.737321i | \(-0.736091\pi\) | ||||
−0.675543 | + | 0.737321i | \(0.736091\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.62620 | −0.135802 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.47689 | 0.0926303 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 26.4942 | 0.988066 | 0.494033 | − | 0.869443i | \(-0.335522\pi\) | ||||
0.494033 | + | 0.869443i | \(0.335522\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.8247 | −0.477616 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.62620 | −0.0603955 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.2018 | 0.786331 | 0.393166 | − | 0.919468i | \(-0.371380\pi\) | ||||
0.393166 | + | 0.919468i | \(0.371380\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.31695 | 0.0487090 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.74324 | 0.138260 | 0.0691298 | − | 0.997608i | \(-0.477978\pi\) | ||||
0.0691298 | + | 0.997608i | \(0.477978\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 22.1816 | 0.817069 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.1493 | 0.925132 | 0.462566 | − | 0.886585i | \(-0.346929\pi\) | ||||
0.462566 | + | 0.886585i | \(0.346929\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.0925 | −0.517002 | −0.258501 | − | 0.966011i | \(-0.583229\pi\) | ||||
−0.258501 | + | 0.966011i | \(0.583229\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.92919 | 0.180592 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.89692 | 0.215469 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.6681 | 0.936641 | 0.468320 | − | 0.883559i | \(-0.344859\pi\) | ||||
0.468320 | + | 0.883559i | \(0.344859\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.25240 | −0.263942 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.2201 | 0.807604 | 0.403802 | − | 0.914846i | \(-0.367688\pi\) | ||||
0.403802 | + | 0.914846i | \(0.367688\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23.4200 | −0.848975 | −0.424488 | − | 0.905434i | \(-0.639546\pi\) | ||||
−0.424488 | + | 0.905434i | \(0.639546\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.452306 | −0.0163746 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.90129 | 0.104759 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.7634 | −0.532383 | −0.266192 | − | 0.963920i | \(-0.585765\pi\) | ||||
−0.266192 | + | 0.963920i | \(0.585765\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 22.3632 | 0.804348 | 0.402174 | − | 0.915563i | \(-0.368255\pi\) | ||||
0.402174 | + | 0.915563i | \(0.368255\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.62620 | −0.130257 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −48.7143 | −1.74537 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −39.8896 | −1.42736 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13.2663 | 0.473496 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.72491 | −0.311010 | −0.155505 | − | 0.987835i | \(-0.549700\pi\) | ||||
−0.155505 | + | 0.987835i | \(0.549700\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.8324 | 0.562934 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.83048 | −0.0650021 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12.8386 | −0.454767 | −0.227384 | − | 0.973805i | \(-0.573017\pi\) | ||||
−0.227384 | + | 0.973805i | \(0.573017\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.91087 | −0.279866 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −14.1204 | −0.498297 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.761557 | 0.0268414 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.18596 | 0.112012 | 0.0560061 | − | 0.998430i | \(-0.482163\pi\) | ||||
0.0560061 | + | 0.998430i | \(0.482163\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.4663 | 1.21027 | 0.605137 | − | 0.796121i | \(-0.293118\pi\) | ||||
0.605137 | + | 0.796121i | \(0.293118\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 16.0279 | 0.561433 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.0462 | 0.386459 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.4219 | 0.677830 | 0.338915 | − | 0.940817i | \(-0.389940\pi\) | ||||
0.338915 | + | 0.940817i | \(0.389940\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32.5327 | 1.13402 | 0.567009 | − | 0.823711i | \(-0.308100\pi\) | ||||
0.567009 | + | 0.823711i | \(0.308100\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 32.1835 | 1.11913 | 0.559565 | − | 0.828787i | \(-0.310968\pi\) | ||||
0.559565 | + | 0.828787i | \(0.310968\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −46.6637 | −1.62070 | −0.810348 | − | 0.585948i | \(-0.800722\pi\) | ||||
−0.810348 | + | 0.585948i | \(0.800722\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.88922 | −0.169401 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19.7047 | 0.681909 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −15.2524 | −0.526571 | −0.263286 | − | 0.964718i | \(-0.584806\pi\) | ||||
−0.263286 | + | 0.964718i | \(0.584806\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.3555 | −0.908810 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.2524 | 0.421495 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.12766 | 0.0731074 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.76156 | 0.0946650 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.2986 | 0.900448 | 0.450224 | − | 0.892916i | \(-0.351344\pi\) | ||||
0.450224 | + | 0.892916i | \(0.351344\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 23.7293 | 0.810577 | 0.405288 | − | 0.914189i | \(-0.367171\pi\) | ||||
0.405288 | + | 0.914189i | \(0.367171\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.3834 | 1.13903 | 0.569513 | − | 0.821982i | \(-0.307132\pi\) | ||||
0.569513 | + | 0.821982i | \(0.307132\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.38150 | −0.115108 | −0.0575538 | − | 0.998342i | \(-0.518330\pi\) | ||||
−0.0575538 | + | 0.998342i | \(0.518330\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.7572 | −0.399756 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −30.0925 | −1.02082 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.69512 | −0.226855 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.761557 | 0.0257453 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.65515 | 0.224728 | 0.112364 | − | 0.993667i | \(-0.464158\pi\) | ||||
0.112364 | + | 0.993667i | \(0.464158\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.9205 | 0.570065 | 0.285032 | − | 0.958518i | \(-0.407996\pi\) | ||||
0.285032 | + | 0.958518i | \(0.407996\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.7509 | 0.361798 | 0.180899 | − | 0.983502i | \(-0.442099\pi\) | ||||
0.180899 | + | 0.983502i | \(0.442099\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 53.7572 | 1.80499 | 0.902495 | − | 0.430701i | \(-0.141734\pi\) | ||||
0.902495 | + | 0.430701i | \(0.141734\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.1845 | −0.375117 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −66.3544 | −2.22047 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.8401 | 0.696606 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.89692 | 0.196673 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.579969 | 0.0193216 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 26.0279 | 0.865197 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 51.1526 | 1.69850 | 0.849248 | − | 0.527995i | \(-0.177056\pi\) | ||||
0.849248 | + | 0.527995i | \(0.177056\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.9046 | 0.825127 | 0.412563 | − | 0.910929i | \(-0.364634\pi\) | ||||
0.412563 | + | 0.910929i | \(0.364634\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.40608 | −0.0465344 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.88629 | −0.194382 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −20.4923 | −0.675978 | −0.337989 | − | 0.941150i | \(-0.609747\pi\) | ||||
−0.337989 | + | 0.941150i | \(0.609747\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.0400 | 0.396300 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.76156 | 0.0907994 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.97979 | 0.0977637 | 0.0488819 | − | 0.998805i | \(-0.484434\pi\) | ||||
0.0488819 | + | 0.998805i | \(0.484434\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −41.0096 | −1.34403 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.18159 | 0.0713456 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 41.1512 | 1.34435 | 0.672176 | − | 0.740392i | \(-0.265360\pi\) | ||||
0.672176 | + | 0.740392i | \(0.265360\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 22.1170 | 0.720995 | 0.360497 | − | 0.932760i | \(-0.382607\pi\) | ||||
0.360497 | + | 0.932760i | \(0.382607\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.62620 | −0.248343 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 51.3361 | 1.66820 | 0.834100 | − | 0.551614i | \(-0.185988\pi\) | ||||
0.834100 | + | 0.551614i | \(0.185988\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.26198 | 0.138350 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −54.0558 | −1.75104 | −0.875520 | − | 0.483182i | \(-0.839481\pi\) | ||||
−0.875520 | + | 0.483182i | \(0.839481\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.40608 | 0.174937 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.27072 | −0.0733253 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.8507 | −0.575829 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10.7476 | 0.345978 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.0033 | −0.386001 | −0.193000 | − | 0.981199i | \(-0.561822\pi\) | ||||
−0.193000 | + | 0.981199i | \(0.561822\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24.0646 | 0.772268 | 0.386134 | − | 0.922443i | \(-0.373810\pi\) | ||||
0.386134 | + | 0.922443i | \(0.373810\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.1247 | 0.484877 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −43.3222 | −1.38600 | −0.692999 | − | 0.720938i | \(-0.743711\pi\) | ||||
−0.692999 | + | 0.720938i | \(0.743711\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −48.0558 | −1.53587 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 59.3867 | 1.89414 | 0.947071 | − | 0.321024i | \(-0.104027\pi\) | ||||
0.947071 | + | 0.321024i | \(0.104027\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15.9634 | 0.508635 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.72928 | 0.0549880 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.0260 | 0.826744 | 0.413372 | − | 0.910562i | \(-0.364351\pi\) | ||||
0.413372 | + | 0.910562i | \(0.364351\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.20617 | 0.133344 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 34.5048 | 1.09278 | 0.546389 | − | 0.837532i | \(-0.316002\pi\) | ||||
0.546389 | + | 0.837532i | \(0.316002\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8280.2.a.bk.1.1 | ✓ | 3 | |
3.2 | odd | 2 | 8280.2.a.bp.1.1 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8280.2.a.bk.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
8280.2.a.bp.1.1 | yes | 3 | 3.2 | odd | 2 |