Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1792,2,Mod(1,1792)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1792, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1792.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1792 = 2^{8} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1792.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: | \(14.3091920422\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 896) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1792.1 |
$q$-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 | ||||||||
\(3\) | −1.23607 | −0.713644 | −0.356822 | − | 0.934172i | \(-0.616140\pi\) | ||||
−0.356822 | + | 0.934172i | \(0.616140\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.23607 | −0.552786 | −0.276393 | − | 0.961045i | \(-0.589139\pi\) | ||||
−0.276393 | + | 0.961045i | \(0.589139\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.47214 | −0.490712 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.00000 | 1.20605 | 0.603023 | − | 0.797724i | \(-0.293963\pi\) | ||||
0.603023 | + | 0.797724i | \(0.293963\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.23607 | 0.342824 | 0.171412 | − | 0.985199i | \(-0.445167\pi\) | ||||
0.171412 | + | 0.985199i | \(0.445167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.52786 | 0.394493 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.00000 | −0.485071 | −0.242536 | − | 0.970143i | \(-0.577979\pi\) | ||||
−0.242536 | + | 0.970143i | \(0.577979\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.23607 | 0.283573 | 0.141787 | − | 0.989897i | \(-0.454715\pi\) | ||||
0.141787 | + | 0.989897i | \(0.454715\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.23607 | 0.269732 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.47214 | −1.34953 | −0.674767 | − | 0.738031i | \(-0.735756\pi\) | ||||
−0.674767 | + | 0.738031i | \(0.735756\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.47214 | −0.694427 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.52786 | 1.06384 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.52786 | −0.283717 | −0.141859 | − | 0.989887i | \(-0.545308\pi\) | ||||
−0.141859 | + | 0.989887i | \(0.545308\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.94427 | −0.860687 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.23607 | 0.208934 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.47214 | −1.06401 | −0.532006 | − | 0.846740i | \(-0.678562\pi\) | ||||
−0.532006 | + | 0.846740i | \(0.678562\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.52786 | −0.244654 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.00000 | −0.312348 | −0.156174 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156174 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.94427 | 1.36399 | 0.681994 | − | 0.731357i | \(-0.261113\pi\) | ||||
0.681994 | + | 0.731357i | \(0.261113\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.81966 | 0.271259 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.9443 | 1.88812 | 0.944058 | − | 0.329779i | \(-0.106974\pi\) | ||||
0.944058 | + | 0.329779i | \(0.106974\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.47214 | 0.346168 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.94427 | 1.22859 | 0.614295 | − | 0.789076i | \(-0.289440\pi\) | ||||
0.614295 | + | 0.789076i | \(0.289440\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.94427 | −0.666685 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.52786 | −0.202371 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.23607 | 1.20243 | 0.601217 | − | 0.799086i | \(-0.294683\pi\) | ||||
0.601217 | + | 0.799086i | \(0.294683\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.23607 | −0.158262 | −0.0791311 | − | 0.996864i | \(-0.525215\pi\) | ||||
−0.0791311 | + | 0.996864i | \(0.525215\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.47214 | 0.185472 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.52786 | −0.189508 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.52786 | 0.186658 | 0.0933292 | − | 0.995635i | \(-0.470249\pi\) | ||||
0.0933292 | + | 0.995635i | \(0.470249\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.00000 | 0.963087 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.94427 | 0.586777 | 0.293389 | − | 0.955993i | \(-0.405217\pi\) | ||||
0.293389 | + | 0.955993i | \(0.405217\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.9443 | 1.74909 | 0.874547 | − | 0.484940i | \(-0.161159\pi\) | ||||
0.874547 | + | 0.484940i | \(0.161159\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.29180 | 0.495574 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.00000 | −0.455842 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.94427 | −0.556274 | −0.278137 | − | 0.960541i | \(-0.589717\pi\) | ||||
−0.278137 | + | 0.960541i | \(0.589717\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.41641 | −0.268490 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.23607 | 1.01379 | 0.506895 | − | 0.862008i | \(-0.330793\pi\) | ||||
0.506895 | + | 0.862008i | \(0.330793\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.47214 | 0.268141 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.88854 | 0.202473 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.00000 | 0.212000 | 0.106000 | − | 0.994366i | \(-0.466196\pi\) | ||||
0.106000 | + | 0.994366i | \(0.466196\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.23607 | −0.129575 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.52786 | −0.156756 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.9443 | 1.11122 | 0.555611 | − | 0.831442i | \(-0.312484\pi\) | ||||
0.555611 | + | 0.831442i | \(0.312484\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.88854 | −0.591821 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.1803 | −1.41100 | −0.705498 | − | 0.708712i | \(-0.749277\pi\) | ||||
−0.705498 | + | 0.708712i | \(0.749277\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.00000 | 0.788263 | 0.394132 | − | 0.919054i | \(-0.371045\pi\) | ||||
0.394132 | + | 0.919054i | \(0.371045\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.52786 | −0.149104 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.52786 | 0.921093 | 0.460547 | − | 0.887635i | \(-0.347653\pi\) | ||||
0.460547 | + | 0.887635i | \(0.347653\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.52786 | −0.146343 | −0.0731714 | − | 0.997319i | \(-0.523312\pi\) | ||||
−0.0731714 | + | 0.997319i | \(0.523312\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.00000 | 0.759326 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.4164 | 1.26211 | 0.631055 | − | 0.775738i | \(-0.282622\pi\) | ||||
0.631055 | + | 0.775738i | \(0.282622\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.00000 | 0.746004 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.81966 | −0.168228 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.00000 | 0.183340 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | 0.454545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.47214 | 0.222905 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.4721 | 0.936656 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.4164 | −1.72293 | −0.861464 | − | 0.507819i | \(-0.830452\pi\) | ||||
−0.861464 | + | 0.507819i | \(0.830452\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −11.0557 | −0.973403 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.1803 | 1.23894 | 0.619471 | − | 0.785020i | \(-0.287347\pi\) | ||||
0.619471 | + | 0.785020i | \(0.287347\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.23607 | −0.107181 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.83282 | −0.588075 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.0000 | −0.854358 | −0.427179 | − | 0.904167i | \(-0.640493\pi\) | ||||
−0.427179 | + | 0.904167i | \(0.640493\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.2361 | −1.46194 | −0.730972 | − | 0.682407i | \(-0.760933\pi\) | ||||
−0.730972 | + | 0.682407i | \(0.760933\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −16.0000 | −1.34744 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.94427 | 0.413461 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.88854 | 0.156835 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.23607 | −0.101949 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.9443 | −1.38813 | −0.694064 | − | 0.719913i | \(-0.744182\pi\) | ||||
−0.694064 | + | 0.719913i | \(0.744182\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.47214 | 0.526695 | 0.263347 | − | 0.964701i | \(-0.415173\pi\) | ||||
0.263347 | + | 0.964701i | \(0.415173\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.94427 | 0.238030 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.1803 | 1.77018 | 0.885092 | − | 0.465416i | \(-0.154095\pi\) | ||||
0.885092 | + | 0.465416i | \(0.154095\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −11.0557 | −0.876776 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.47214 | 0.510076 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.0000 | 0.939913 | 0.469956 | − | 0.882690i | \(-0.344270\pi\) | ||||
0.469956 | + | 0.882690i | \(0.344270\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.11146 | 0.475776 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.94427 | −0.382599 | −0.191300 | − | 0.981532i | \(-0.561270\pi\) | ||||
−0.191300 | + | 0.981532i | \(0.561270\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.4721 | −0.882472 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.81966 | −0.139153 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.70820 | −0.281930 | −0.140965 | − | 0.990015i | \(-0.545020\pi\) | ||||
−0.140965 | + | 0.990015i | \(0.545020\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.47214 | 0.262469 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −11.4164 | −0.858110 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.47214 | 0.483750 | 0.241875 | − | 0.970307i | \(-0.422238\pi\) | ||||
0.241875 | + | 0.970307i | \(0.422238\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 25.2361 | 1.87578 | 0.937891 | − | 0.346930i | \(-0.112776\pi\) | ||||
0.937891 | + | 0.346930i | \(0.112776\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.52786 | 0.112943 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.00000 | 0.588172 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.00000 | −0.585018 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.52786 | −0.402093 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.8885 | −1.29437 | −0.647185 | − | 0.762333i | \(-0.724054\pi\) | ||||
−0.647185 | + | 0.762333i | \(0.724054\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.4721 | 0.897764 | 0.448882 | − | 0.893591i | \(-0.351822\pi\) | ||||
0.448882 | + | 0.893591i | \(0.351822\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.88854 | 0.135241 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.00000 | 0.284988 | 0.142494 | − | 0.989796i | \(-0.454488\pi\) | ||||
0.142494 | + | 0.989796i | \(0.454488\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.0000 | 1.70131 | 0.850657 | − | 0.525720i | \(-0.176204\pi\) | ||||
0.850657 | + | 0.525720i | \(0.176204\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.88854 | −0.133208 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.52786 | 0.107235 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.47214 | 0.172661 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.52786 | 0.662232 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.94427 | 0.342002 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.4164 | 0.785938 | 0.392969 | − | 0.919552i | \(-0.371448\pi\) | ||||
0.392969 | + | 0.919552i | \(0.371448\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.11146 | −0.418750 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.0557 | −0.753994 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −18.4721 | −1.24823 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.47214 | −0.166294 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −28.9443 | −1.93825 | −0.969126 | − | 0.246566i | \(-0.920698\pi\) | ||||
−0.969126 | + | 0.246566i | \(0.920698\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.11146 | 0.340764 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.70820 | −0.246122 | −0.123061 | − | 0.992399i | \(-0.539271\pi\) | ||||
−0.123061 | + | 0.992399i | \(0.539271\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.6525 | −1.62908 | −0.814541 | − | 0.580106i | \(-0.803011\pi\) | ||||
−0.814541 | + | 0.580106i | \(0.803011\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.94427 | 0.325309 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 19.8885 | 1.30294 | 0.651471 | − | 0.758674i | \(-0.274152\pi\) | ||||
0.651471 | + | 0.758674i | \(0.274152\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −16.0000 | −1.04372 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.11146 | 0.396982 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.52786 | 0.616306 | 0.308153 | − | 0.951337i | \(-0.400289\pi\) | ||||
0.308153 | + | 0.951337i | \(0.400289\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.9443 | −0.962645 | −0.481323 | − | 0.876544i | \(-0.659843\pi\) | ||||
−0.481323 | + | 0.876544i | \(0.659843\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.5967 | −0.872232 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.23607 | −0.0789695 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.52786 | 0.0972157 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −11.4164 | −0.723485 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.6525 | 1.05109 | 0.525547 | − | 0.850764i | \(-0.323861\pi\) | ||||
0.525547 | + | 0.850764i | \(0.323861\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −25.8885 | −1.62760 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.05573 | −0.191357 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.88854 | −0.492074 | −0.246037 | − | 0.969260i | \(-0.579128\pi\) | ||||
−0.246037 | + | 0.969260i | \(0.579128\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.47214 | 0.402159 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.24922 | 0.139223 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 20.9443 | 1.29148 | 0.645740 | − | 0.763558i | \(-0.276549\pi\) | ||||
0.645740 | + | 0.763558i | \(0.276549\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.0557 | −0.679148 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.47214 | −0.151292 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 27.1246 | 1.65382 | 0.826908 | − | 0.562337i | \(-0.190097\pi\) | ||||
0.826908 | + | 0.562337i | \(0.190097\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.05573 | −0.185622 | −0.0928111 | − | 0.995684i | \(-0.529585\pi\) | ||||
−0.0928111 | + | 0.995684i | \(0.529585\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.52786 | 0.0924705 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −13.8885 | −0.837511 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.0000 | 1.20168 | 0.600842 | − | 0.799368i | \(-0.294832\pi\) | ||||
0.600842 | + | 0.799368i | \(0.294832\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.00000 | −0.357930 | −0.178965 | − | 0.983855i | \(-0.557275\pi\) | ||||
−0.178965 | + | 0.983855i | \(0.557275\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −24.6525 | −1.46544 | −0.732719 | − | 0.680532i | \(-0.761749\pi\) | ||||
−0.732719 | + | 0.680532i | \(0.761749\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.88854 | 0.111868 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.00000 | 0.118056 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.5279 | −0.793017 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 27.7082 | 1.61873 | 0.809365 | − | 0.587306i | \(-0.199811\pi\) | ||||
0.809365 | + | 0.587306i | \(0.199811\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.4164 | −0.664689 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 22.1115 | 1.28304 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.00000 | −0.462652 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.94427 | −0.515539 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 17.5279 | 1.00695 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.52786 | 0.0874852 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −21.5967 | −1.23259 | −0.616296 | − | 0.787515i | \(-0.711367\pi\) | ||||
−0.616296 | + | 0.787515i | \(0.711367\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.88854 | −0.562540 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.00000 | −0.453638 | −0.226819 | − | 0.973937i | \(-0.572833\pi\) | ||||
−0.226819 | + | 0.973937i | \(0.572833\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.88854 | 0.445887 | 0.222943 | − | 0.974831i | \(-0.428433\pi\) | ||||
0.222943 | + | 0.974831i | \(0.428433\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.81966 | −0.102526 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −21.8885 | −1.22938 | −0.614692 | − | 0.788768i | \(-0.710720\pi\) | ||||
−0.614692 | + | 0.788768i | \(0.710720\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.11146 | −0.342176 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −11.7771 | −0.657333 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.47214 | −0.137553 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.29180 | −0.238066 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.88854 | 0.104437 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.9443 | −0.713641 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.05573 | −0.387818 | −0.193909 | − | 0.981020i | \(-0.562117\pi\) | ||||
−0.193909 | + | 0.981020i | \(0.562117\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.52786 | 0.522124 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.88854 | −0.103182 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.41641 | −0.512944 | −0.256472 | − | 0.966552i | \(-0.582560\pi\) | ||||
−0.256472 | + | 0.966552i | \(0.582560\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −16.5836 | −0.900697 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −9.88854 | −0.532381 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.0557 | 0.808234 | 0.404117 | − | 0.914707i | \(-0.367579\pi\) | ||||
0.404117 | + | 0.914707i | \(0.367579\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.29180 | 0.229735 | 0.114867 | − | 0.993381i | \(-0.463356\pi\) | ||||
0.114867 | + | 0.993381i | \(0.463356\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.83282 | 0.364709 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −17.0557 | −0.907785 | −0.453892 | − | 0.891056i | \(-0.649965\pi\) | ||||
−0.453892 | + | 0.891056i | \(0.649965\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.11146 | −0.324362 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.47214 | −0.130839 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.41641 | 0.180311 | 0.0901556 | − | 0.995928i | \(-0.471264\pi\) | ||||
0.0901556 | + | 0.995928i | \(0.471264\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.4721 | −0.919586 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.18034 | −0.324384 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −18.4721 | −0.966876 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.9443 | 1.51088 | 0.755439 | − | 0.655219i | \(-0.227423\pi\) | ||||
0.755439 | + | 0.655219i | \(0.227423\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.94427 | 0.153273 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.94427 | −0.464363 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −32.9443 | −1.70579 | −0.852895 | − | 0.522083i | \(-0.825155\pi\) | ||||
−0.852895 | + | 0.522083i | \(0.825155\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12.9443 | −0.668439 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.88854 | −0.0972650 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −37.8885 | −1.94620 | −0.973102 | − | 0.230375i | \(-0.926005\pi\) | ||||
−0.973102 | + | 0.230375i | \(0.926005\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 24.0000 | 1.22956 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.05573 | 0.156140 | 0.0780702 | − | 0.996948i | \(-0.475124\pi\) | ||||
0.0780702 | + | 0.996948i | \(0.475124\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.94427 | 0.251983 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −13.1672 | −0.669326 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 19.4164 | 0.984451 | 0.492225 | − | 0.870468i | \(-0.336184\pi\) | ||||
0.492225 | + | 0.870468i | \(0.336184\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.9443 | 0.654620 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −17.5279 | −0.884164 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.11146 | 0.307501 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.12461 | 0.156820 | 0.0784099 | − | 0.996921i | \(-0.475016\pi\) | ||||
0.0784099 | + | 0.996921i | \(0.475016\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.52786 | 0.0764889 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.472136 | −0.0235773 | −0.0117887 | − | 0.999931i | \(-0.503753\pi\) | ||||
−0.0117887 | + | 0.999931i | \(0.503753\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.98684 | 0.148417 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −25.8885 | −1.28325 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.9443 | −0.738947 | −0.369473 | − | 0.929241i | \(-0.620462\pi\) | ||||
−0.369473 | + | 0.929241i | \(0.620462\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.3607 | 0.609707 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.23607 | −0.454477 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.4164 | −0.560409 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 21.3050 | 1.04331 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.18034 | −0.301929 | −0.150965 | − | 0.988539i | \(-0.548238\pi\) | ||||
−0.150965 | + | 0.988539i | \(0.548238\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.0000 | −0.584844 | −0.292422 | − | 0.956289i | \(-0.594461\pi\) | ||||
−0.292422 | + | 0.956289i | \(0.594461\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −19.0557 | −0.926521 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.94427 | 0.336847 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.23607 | 0.0598175 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.11146 | −0.295064 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 32.3607 | 1.55876 | 0.779380 | − | 0.626552i | \(-0.215534\pi\) | ||||
0.779380 | + | 0.626552i | \(0.215534\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.0000 | 0.672797 | 0.336399 | − | 0.941720i | \(-0.390791\pi\) | ||||
0.336399 | + | 0.941720i | \(0.390791\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.33437 | −0.111924 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.00000 | −0.382692 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.9443 | 0.999616 | 0.499808 | − | 0.866136i | \(-0.333404\pi\) | ||||
0.499808 | + | 0.866136i | \(0.333404\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.47214 | −0.0701017 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.3607 | 1.15741 | 0.578705 | − | 0.815537i | \(-0.303558\pi\) | ||||
0.578705 | + | 0.815537i | \(0.303558\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.47214 | −0.117190 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 20.9443 | 0.990630 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.8885 | 1.12737 | 0.563685 | − | 0.825990i | \(-0.309383\pi\) | ||||
0.563685 | + | 0.825990i | \(0.309383\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.00000 | −0.376705 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.00000 | −0.375873 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.52786 | 0.0716274 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.4721 | 0.957646 | 0.478823 | − | 0.877911i | \(-0.341064\pi\) | ||||
0.478823 | + | 0.877911i | \(0.341064\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −11.0557 | −0.516037 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 40.0689 | 1.86619 | 0.933097 | − | 0.359625i | \(-0.117095\pi\) | ||||
0.933097 | + | 0.359625i | \(0.117095\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.88854 | 0.0877681 | 0.0438840 | − | 0.999037i | \(-0.486027\pi\) | ||||
0.0438840 | + | 0.999037i | \(0.486027\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −24.6525 | −1.14078 | −0.570390 | − | 0.821374i | \(-0.693208\pi\) | ||||
−0.570390 | + | 0.821374i | \(0.693208\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.52786 | −0.0705502 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −27.4164 | −1.26328 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 35.7771 | 1.64503 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.29180 | −0.196921 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13.1672 | −0.602884 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16.0000 | −0.731059 | −0.365529 | − | 0.930800i | \(-0.619112\pi\) | ||||
−0.365529 | + | 0.930800i | \(0.619112\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.00000 | −0.364769 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −8.00000 | −0.364013 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −13.5279 | −0.614269 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −22.4721 | −1.01831 | −0.509155 | − | 0.860675i | \(-0.670042\pi\) | ||||
−0.509155 | + | 0.860675i | \(0.670042\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −14.8328 | −0.670763 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.4721 | 0.653118 | 0.326559 | − | 0.945177i | \(-0.394111\pi\) | ||||
0.326559 | + | 0.945177i | \(0.394111\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.05573 | 0.137623 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.27864 | 0.327151 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.94427 | −0.221781 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.3607 | −1.09053 | −0.545267 | − | 0.838262i | \(-0.683572\pi\) | ||||
−0.545267 | + | 0.838262i | \(0.683572\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.11146 | 0.273040 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −11.0557 | −0.492951 | −0.246475 | − | 0.969149i | \(-0.579272\pi\) | ||||
−0.246475 | + | 0.969149i | \(0.579272\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.5279 | 0.779980 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 14.1803 | 0.629771 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.652476 | −0.0289205 | −0.0144602 | − | 0.999895i | \(-0.504603\pi\) | ||||
−0.0144602 | + | 0.999895i | \(0.504603\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.9443 | −0.661096 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.83282 | 0.301676 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.88854 | −0.435741 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 51.7771 | 2.27715 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.58359 | 0.201197 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.9443 | 1.18045 | 0.590225 | − | 0.807239i | \(-0.299039\pi\) | ||||
0.590225 | + | 0.807239i | \(0.299039\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.81966 | −0.0795682 | −0.0397841 | − | 0.999208i | \(-0.512667\pi\) | ||||
−0.0397841 | + | 0.999208i | \(0.512667\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.29180 | −0.187309 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.8885 | 0.821241 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −13.5967 | −0.590049 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.47214 | −0.107080 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.7771 | −0.509168 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.00000 | −0.345225 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.00000 | 0.172292 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.944272 | −0.0405974 | −0.0202987 | − | 0.999794i | \(-0.506462\pi\) | ||||
−0.0202987 | + | 0.999794i | \(0.506462\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −31.1935 | −1.33864 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.88854 | 0.0808963 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −34.8328 | −1.48934 | −0.744672 | − | 0.667431i | \(-0.767394\pi\) | ||||
−0.744672 | + | 0.667431i | \(0.767394\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.81966 | 0.0776612 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.88854 | −0.0804547 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.94427 | 0.210252 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.88854 | −0.419745 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.88854 | −0.249506 | −0.124753 | − | 0.992188i | \(-0.539814\pi\) | ||||
−0.124753 | + | 0.992188i | \(0.539814\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.0557 | 0.467607 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.88854 | 0.417495 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 42.5410 | 1.79289 | 0.896445 | − | 0.443155i | \(-0.146141\pi\) | ||||
0.896445 | + | 0.443155i | \(0.146141\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16.5836 | −0.697677 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.41641 | 0.101480 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.5836 | −0.611376 | −0.305688 | − | 0.952132i | \(-0.598886\pi\) | ||||
−0.305688 | + | 0.952132i | \(0.598886\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −31.7771 | −1.32983 | −0.664915 | − | 0.746919i | \(-0.731532\pi\) | ||||
−0.664915 | + | 0.746919i | \(0.731532\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 22.1115 | 0.923719 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 22.4721 | 0.937153 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20.8328 | −0.867281 | −0.433641 | − | 0.901086i | \(-0.642771\pi\) | ||||
−0.433641 | + | 0.901086i | \(0.642771\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −15.4164 | −0.640684 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.23607 | −0.383177 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 35.7771 | 1.48174 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.24922 | 0.0929940 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14.7639 | 0.609373 | 0.304686 | − | 0.952453i | \(-0.401448\pi\) | ||||
0.304686 | + | 0.952453i | \(0.401448\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.94427 | −0.203380 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.00000 | 0.0821302 | 0.0410651 | − | 0.999156i | \(-0.486925\pi\) | ||||
0.0410651 | + | 0.999156i | \(0.486925\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.47214 | −0.101348 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −29.6656 | −1.21413 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.0000 | −0.980613 | −0.490307 | − | 0.871550i | \(-0.663115\pi\) | ||||
−0.490307 | + | 0.871550i | \(0.663115\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.11146 | −0.167710 | −0.0838549 | − | 0.996478i | \(-0.526723\pi\) | ||||
−0.0838549 | + | 0.996478i | \(0.526723\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.24922 | −0.0915955 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.18034 | −0.251267 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.88854 | 0.401364 | 0.200682 | − | 0.979656i | \(-0.435684\pi\) | ||||
0.200682 | + | 0.979656i | \(0.435684\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.88854 | −0.0765277 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16.0000 | 0.647291 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.4721 | 0.584524 | 0.292262 | − | 0.956338i | \(-0.405592\pi\) | ||||
0.292262 | + | 0.956338i | \(0.405592\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.05573 | −0.123219 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23.5279 | −0.947196 | −0.473598 | − | 0.880741i | \(-0.657045\pi\) | ||||
−0.473598 | + | 0.880741i | \(0.657045\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.81966 | −0.394685 | −0.197343 | − | 0.980335i | \(-0.563231\pi\) | ||||
−0.197343 | + | 0.980335i | \(0.563231\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −35.7771 | −1.43569 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.00000 | −0.0801283 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.41641 | 0.176656 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.11146 | −0.244068 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12.9443 | 0.516122 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.8885 | 0.712132 | 0.356066 | − | 0.934461i | \(-0.384118\pi\) | ||||
0.356066 | + | 0.934461i | \(0.384118\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.1115 | −0.560880 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 24.0000 | 0.952411 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.23607 | 0.0489748 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.27864 | −0.287939 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.3607 | −0.409222 | −0.204611 | − | 0.978843i | \(-0.565593\pi\) | ||||
−0.204611 | + | 0.978843i | \(0.565593\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.5410 | 1.04668 | 0.523338 | − | 0.852125i | \(-0.324687\pi\) | ||||
0.523338 | + | 0.852125i | \(0.324687\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 13.6656 | 0.538084 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17.8885 | −0.703271 | −0.351636 | − | 0.936137i | \(-0.614374\pi\) | ||||
−0.351636 | + | 0.936137i | \(0.614374\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 36.9443 | 1.45019 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12.5836 | −0.492434 | −0.246217 | − | 0.969215i | \(-0.579188\pi\) | ||||
−0.246217 | + | 0.969215i | \(0.579188\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17.5279 | −0.684870 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −22.0000 | −0.858302 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 42.8328 | 1.66853 | 0.834265 | − | 0.551364i | \(-0.185892\pi\) | ||||
0.834265 | + | 0.551364i | \(0.185892\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.7639 | 0.885414 | 0.442707 | − | 0.896666i | \(-0.354018\pi\) | ||||
0.442707 | + | 0.896666i | \(0.354018\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.05573 | 0.118675 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.52786 | 0.0592480 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.88854 | 0.382886 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 35.7771 | 1.38322 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.94427 | −0.190872 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.8885 | −0.458270 | −0.229135 | − | 0.973395i | \(-0.573590\pi\) | ||||
−0.229135 | + | 0.973395i | \(0.573590\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −19.1935 | −0.738758 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19.1246 | 0.735019 | 0.367509 | − | 0.930020i | \(-0.380211\pi\) | ||||
0.367509 | + | 0.930020i | \(0.380211\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.9443 | −0.420003 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.58359 | 0.175644 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 30.4721 | 1.16598 | 0.582992 | − | 0.812478i | \(-0.301882\pi\) | ||||
0.582992 | + | 0.812478i | \(0.301882\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.3607 | 0.472277 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 30.4721 | 1.16258 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 11.0557 | 0.421190 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.2918 | 0.771936 | 0.385968 | − | 0.922512i | \(-0.373867\pi\) | ||||
0.385968 | + | 0.922512i | \(0.373867\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.88854 | 0.223687 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 21.3050 | 0.808143 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.00000 | 0.151511 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −24.5836 | −0.929837 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.3607 | −0.617934 | −0.308967 | − | 0.951073i | \(-0.599983\pi\) | ||||
−0.308967 | + | 0.951073i | \(0.599983\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.00000 | −0.301726 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 19.7771 | 0.744848 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14.1803 | 0.533307 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.47214 | −0.243066 | −0.121533 | − | 0.992587i | \(-0.538781\pi\) | ||||
−0.121533 | + | 0.992587i | \(0.538781\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.27864 | 0.272970 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.11146 | −0.228556 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −11.7771 | −0.439823 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19.0557 | −0.710659 | −0.355329 | − | 0.934741i | \(-0.615631\pi\) | ||||
−0.355329 | + | 0.934741i | \(0.615631\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.00000 | −0.297936 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 18.4721 | 0.686986 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.30495 | 0.197021 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.8328 | 0.550119 | 0.275059 | − | 0.961427i | \(-0.411302\pi\) | ||||
0.275059 | + | 0.961427i | \(0.411302\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 24.0557 | 0.890953 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.8885 | −0.661632 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −32.0689 | −1.18449 | −0.592246 | − | 0.805757i | \(-0.701758\pi\) | ||||
−0.592246 | + | 0.805757i | \(0.701758\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.52786 | 0.0563561 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.11146 | 0.225118 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 21.8885 | 0.805183 | 0.402592 | − | 0.915380i | \(-0.368110\pi\) | ||||
0.402592 | + | 0.915380i | \(0.368110\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.88854 | −0.0693774 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25.5279 | 0.936527 | 0.468263 | − | 0.883589i | \(-0.344880\pi\) | ||||
0.468263 | + | 0.883589i | \(0.344880\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20.9443 | 0.767339 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −13.5967 | −0.497479 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.52786 | −0.348141 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.3607 | 0.597010 | 0.298505 | − | 0.954408i | \(-0.403512\pi\) | ||||
0.298505 | + | 0.954408i | \(0.403512\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −20.5836 | −0.750108 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.00000 | −0.291150 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −43.4164 | −1.57800 | −0.788998 | − | 0.614396i | \(-0.789400\pi\) | ||||
−0.788998 | + | 0.614396i | \(0.789400\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 32.0000 | 1.16153 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27.8885 | −1.01096 | −0.505479 | − | 0.862839i | \(-0.668684\pi\) | ||||
−0.505479 | + | 0.862839i | \(0.668684\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.52786 | 0.0553124 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.63932 | −0.131580 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.4164 | 0.412223 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.0557 | 0.615045 | 0.307523 | − | 0.951541i | \(-0.400500\pi\) | ||||
0.307523 | + | 0.951541i | \(0.400500\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.75078 | 0.351166 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.1246 | −0.400124 | −0.200062 | − | 0.979783i | \(-0.564114\pi\) | ||||
−0.200062 | + | 0.979783i | \(0.564114\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.00000 | −0.286998 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.47214 | −0.0885735 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 19.7771 | 0.707680 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.44582 | −0.301829 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −27.4164 | −0.978534 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.87539 | −0.173789 | −0.0868944 | − | 0.996218i | \(-0.527694\pi\) | ||||
−0.0868944 | + | 0.996218i | \(0.527694\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −25.8885 | −0.921657 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13.4164 | −0.477033 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.52786 | −0.0542560 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 13.6656 | 0.484670 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 33.2361 | 1.17728 | 0.588641 | − | 0.808395i | \(-0.299663\pi\) | ||||
0.588641 | + | 0.808395i | \(0.299663\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −25.8885 | −0.915871 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.94427 | −0.104031 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 59.7771 | 2.10949 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.00000 | −0.281963 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −33.5279 | −1.18024 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.41641 | −0.190431 | −0.0952154 | − | 0.995457i | \(-0.530354\pi\) | ||||
−0.0952154 | + | 0.995457i | \(0.530354\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.1246 | 0.952474 | 0.476237 | − | 0.879317i | \(-0.342000\pi\) | ||||
0.476237 | + | 0.879317i | \(0.342000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.77709 | 0.132468 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −14.8328 | −0.519571 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.0557 | 0.386791 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.81966 | 0.0635841 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.00000 | 0.139601 | 0.0698005 | − | 0.997561i | \(-0.477764\pi\) | ||||
0.0698005 | + | 0.997561i | \(0.477764\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 30.8328 | 1.07476 | 0.537382 | − | 0.843339i | \(-0.319413\pi\) | ||||
0.537382 | + | 0.843339i | \(0.319413\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 17.1672 | 0.597685 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 35.4164 | 1.23155 | 0.615775 | − | 0.787922i | \(-0.288843\pi\) | ||||
0.615775 | + | 0.787922i | \(0.288843\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −27.1246 | −0.942077 | −0.471038 | − | 0.882113i | \(-0.656121\pi\) | ||||
−0.471038 | + | 0.882113i | \(0.656121\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −24.7214 | −0.857574 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.00000 | −0.0692959 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.11146 | 0.211496 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 40.0000 | 1.38095 | 0.690477 | − | 0.723355i | \(-0.257401\pi\) | ||||
0.690477 | + | 0.723355i | \(0.257401\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.6656 | −0.919505 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.41641 | 0.255435 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 14.1803 | 0.487819 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.00000 | −0.171802 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 30.4721 | 1.04580 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 41.8885 | 1.43592 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33.2361 | 1.13798 | 0.568991 | − | 0.822344i | \(-0.307334\pi\) | ||||
0.568991 | + | 0.822344i | \(0.307334\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.24922 | 0.0769218 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −56.8328 | −1.94137 | −0.970686 | − | 0.240351i | \(-0.922737\pi\) | ||||
−0.970686 | + | 0.240351i | \(0.922737\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30.1803 | −1.02974 | −0.514870 | − | 0.857268i | \(-0.672160\pi\) | ||||
−0.514870 | + | 0.857268i | \(0.672160\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.47214 | −0.0842502 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 33.8885 | 1.15358 | 0.576790 | − | 0.816893i | \(-0.304305\pi\) | ||||
0.576790 | + | 0.816893i | \(0.304305\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.58359 | 0.155847 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.0689 | 0.545728 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −19.7771 | −0.670892 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.88854 | 0.0639909 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −16.1115 | −0.545290 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.4721 | −0.354023 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.360680 | −0.0121793 | −0.00608965 | − | 0.999981i | \(-0.501938\pi\) | ||||
−0.00608965 | + | 0.999981i | \(0.501938\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −34.2492 | −1.15520 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.8328 | −0.701875 | −0.350938 | − | 0.936399i | \(-0.614137\pi\) | ||||
−0.350938 | + | 0.936399i | \(0.614137\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 38.4721 | 1.29469 | 0.647345 | − | 0.762197i | \(-0.275879\pi\) | ||||
0.647345 | + | 0.762197i | \(0.275879\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 14.1115 | 0.474351 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14.8328 | −0.498037 | −0.249019 | − | 0.968499i | \(-0.580108\pi\) | ||||
−0.249019 | + | 0.968499i | \(0.580108\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19.4164 | 0.651205 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.66563 | −0.323811 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 16.0000 | 0.535420 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.00000 | −0.267411 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.88854 | 0.330169 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17.8885 | −0.595954 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 11.0557 | 0.367912 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −31.1935 | −1.03691 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 35.4164 | 1.17598 | 0.587991 | − | 0.808867i | \(-0.299919\pi\) | ||||
0.587991 | + | 0.808867i | \(0.299919\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 20.8754 | 0.692393 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −54.4721 | −1.80474 | −0.902371 | − | 0.430960i | \(-0.858175\pi\) | ||||
−0.902371 | + | 0.430960i | \(0.858175\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 36.9443 | 1.22268 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.88854 | −0.0624333 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −14.1803 | −0.468276 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 46.8328 | 1.54487 | 0.772436 | − | 0.635093i | \(-0.219038\pi\) | ||||
0.772436 | + | 0.635093i | \(0.219038\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 26.6950 | 0.879632 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.11146 | 0.201161 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 22.4721 | 0.738879 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −11.7771 | −0.386810 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −27.8885 | −0.914993 | −0.457497 | − | 0.889211i | \(-0.651254\pi\) | ||||
−0.457497 | + | 0.889211i | \(0.651254\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.23607 | 0.0405105 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 9.88854 | 0.323736 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.88854 | 0.323390 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26.9443 | −0.880231 | −0.440115 | − | 0.897941i | \(-0.645063\pi\) | ||||
−0.440115 | + | 0.897941i | \(0.645063\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.75078 | −0.318205 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.652476 | 0.0212701 | 0.0106351 | − | 0.999943i | \(-0.496615\pi\) | ||||
0.0106351 | + | 0.999943i | \(0.496615\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.9443 | 0.421523 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 6.83282 | 0.222272 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 39.0557 | 1.26914 | 0.634570 | − | 0.772865i | \(-0.281177\pi\) | ||||
0.634570 | + | 0.772865i | \(0.281177\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18.4721 | 0.599631 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 27.0557 | 0.877342 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31.8885 | 1.03297 | 0.516486 | − | 0.856296i | \(-0.327240\pi\) | ||||
0.516486 | + | 0.856296i | \(0.327240\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22.1115 | 0.715510 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.55418 | 0.244192 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10.0000 | 0.322917 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.0263 | −0.451992 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −15.4164 | −0.496272 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.5836 | −0.404661 | −0.202331 | − | 0.979317i | \(-0.564852\pi\) | ||||
−0.202331 | + | 0.979317i | \(0.564852\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.05573 | 0.0981641 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15.3475 | 0.492525 | 0.246263 | − | 0.969203i | \(-0.420797\pi\) | ||||
0.246263 | + | 0.969203i | \(0.420797\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17.2361 | 0.552563 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.30495 | 0.169894 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18.0000 | −0.575871 | −0.287936 | − | 0.957650i | \(-0.592969\pi\) | ||||
−0.287936 | + | 0.957650i | \(0.592969\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.00000 | 0.255681 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.24922 | 0.0718122 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −27.7771 | −0.885952 | −0.442976 | − | 0.896534i | \(-0.646077\pi\) | ||||
−0.442976 | + | 0.896534i | \(0.646077\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.94427 | −0.157538 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 16.0000 | 0.509286 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −57.8885 | −1.84075 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30.8328 | 0.979437 | 0.489718 | − | 0.871881i | \(-0.337100\pi\) | ||||
0.489718 | + | 0.871881i | \(0.337100\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.72136 | 0.276764 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −29.6656 | −0.940464 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 30.7639 | 0.974304 | 0.487152 | − | 0.873317i | \(-0.338036\pi\) | ||||
0.487152 | + | 0.873317i | \(0.338036\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −35.7771 | −1.13194 |
(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 | 1792.2.a.t.1.1 | 2 | ||
4.3 | odd | 2 | 1792.2.a.l.1.2 | 2 | |||
8.3 | odd | 2 | 1792.2.a.r.1.1 | 2 | |||
8.5 | even | 2 | 1792.2.a.j.1.2 | 2 | |||
16.3 | odd | 4 | 896.2.b.e.449.3 | yes | 4 | ||
16.5 | even | 4 | 896.2.b.g.449.3 | yes | 4 | ||
16.11 | odd | 4 | 896.2.b.e.449.2 | ✓ | 4 | ||
16.13 | even | 4 | 896.2.b.g.449.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
896.2.b.e.449.2 | ✓ | 4 | 16.11 | odd | 4 | ||
896.2.b.e.449.3 | yes | 4 | 16.3 | odd | 4 | ||
896.2.b.g.449.2 | yes | 4 | 16.13 | even | 4 | ||
896.2.b.g.449.3 | yes | 4 | 16.5 | even | 4 | ||
1792.2.a.j.1.2 | 2 | 8.5 | even | 2 | |||
1792.2.a.l.1.2 | 2 | 4.3 | odd | 2 | |||
1792.2.a.r.1.1 | 2 | 8.3 | odd | 2 | |||
1792.2.a.t.1.1 | 2 | 1.1 | even | 1 | trivial |