Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7800,2,Mod(1,7800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7800, 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("7800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7800 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7800.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: | \(62.2833135766\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{33}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1560) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.37228\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7800.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.37228 | 0.896638 | 0.448319 | − | 0.893874i | \(-0.352023\pi\) | ||||
0.448319 | + | 0.893874i | \(0.352023\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.37228 | 0.715270 | 0.357635 | − | 0.933862i | \(-0.383583\pi\) | ||||
0.357635 | + | 0.933862i | \(0.383583\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.37228 | −1.06043 | −0.530217 | − | 0.847862i | \(-0.677890\pi\) | ||||
−0.530217 | + | 0.847862i | \(0.677890\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.74456 | 1.08848 | 0.544239 | − | 0.838930i | \(-0.316819\pi\) | ||||
0.544239 | + | 0.838930i | \(0.316819\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.37228 | 0.517674 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.37228 | 1.32871 | 0.664356 | − | 0.747416i | \(-0.268706\pi\) | ||||
0.664356 | + | 0.747416i | \(0.268706\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.74456 | −0.852149 | −0.426074 | − | 0.904688i | \(-0.640104\pi\) | ||||
−0.426074 | + | 0.904688i | \(0.640104\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.37228 | 0.412961 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.372281 | 0.0612027 | 0.0306013 | − | 0.999532i | \(-0.490258\pi\) | ||||
0.0306013 | + | 0.999532i | \(0.490258\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.37228 | 0.682836 | 0.341418 | − | 0.939912i | \(-0.389093\pi\) | ||||
0.341418 | + | 0.939912i | \(0.389093\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.00000 | 0.609994 | 0.304997 | − | 0.952353i | \(-0.401344\pi\) | ||||
0.304997 | + | 0.952353i | \(0.401344\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.7446 | 1.85899 | 0.929493 | − | 0.368840i | \(-0.120245\pi\) | ||||
0.929493 | + | 0.368840i | \(0.120245\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.37228 | −0.196040 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.37228 | −0.612242 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.62772 | 0.498305 | 0.249153 | − | 0.968464i | \(-0.419848\pi\) | ||||
0.249153 | + | 0.968464i | \(0.419848\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.74456 | 0.628433 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.00000 | −1.04151 | −0.520756 | − | 0.853706i | \(-0.674350\pi\) | ||||
−0.520756 | + | 0.853706i | \(0.674350\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.11684 | −1.16729 | −0.583646 | − | 0.812008i | \(-0.698374\pi\) | ||||
−0.583646 | + | 0.812008i | \(0.698374\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.37228 | 0.298879 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.00000 | 0.488678 | 0.244339 | − | 0.969690i | \(-0.421429\pi\) | ||||
0.244339 | + | 0.969690i | \(0.421429\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.37228 | 0.767133 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.62772 | −0.667887 | −0.333944 | − | 0.942593i | \(-0.608380\pi\) | ||||
−0.333944 | + | 0.942593i | \(0.608380\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.48913 | −0.876536 | −0.438268 | − | 0.898844i | \(-0.644408\pi\) | ||||
−0.438268 | + | 0.898844i | \(0.644408\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.62772 | 0.641338 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.8614 | 1.33451 | 0.667256 | − | 0.744828i | \(-0.267469\pi\) | ||||
0.667256 | + | 0.744828i | \(0.267469\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.0000 | 1.31717 | 0.658586 | − | 0.752506i | \(-0.271155\pi\) | ||||
0.658586 | + | 0.752506i | \(0.271155\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.00000 | −0.214423 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.62772 | 0.808537 | 0.404268 | − | 0.914640i | \(-0.367526\pi\) | ||||
0.404268 | + | 0.914640i | \(0.367526\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.37228 | 0.248683 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.74456 | −0.491988 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.37228 | −0.850076 | −0.425038 | − | 0.905175i | \(-0.639739\pi\) | ||||
−0.425038 | + | 0.905175i | \(0.639739\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.37228 | 0.238423 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.74456 | −0.671109 | −0.335555 | − | 0.942021i | \(-0.608924\pi\) | ||||
−0.335555 | + | 0.942021i | \(0.608924\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.00000 | 0.394132 | 0.197066 | − | 0.980390i | \(-0.436859\pi\) | ||||
0.197066 | + | 0.980390i | \(0.436859\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.3723 | 1.38942 | 0.694710 | − | 0.719290i | \(-0.255533\pi\) | ||||
0.694710 | + | 0.719290i | \(0.255533\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.74456 | −0.262881 | −0.131441 | − | 0.991324i | \(-0.541960\pi\) | ||||
−0.131441 | + | 0.991324i | \(0.541960\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.372281 | 0.0353354 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −10.3723 | −0.950825 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.37228 | −0.488389 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.37228 | 0.394235 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.2337 | −1.61798 | −0.808989 | − | 0.587824i | \(-0.799985\pi\) | ||||
−0.808989 | + | 0.587824i | \(0.799985\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.00000 | 0.352180 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.25544 | −0.633911 | −0.316955 | − | 0.948440i | \(-0.602661\pi\) | ||||
−0.316955 | + | 0.948440i | \(0.602661\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.2554 | 0.975970 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.4891 | 0.981582 | 0.490791 | − | 0.871277i | \(-0.336708\pi\) | ||||
0.490791 | + | 0.871277i | \(0.336708\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.62772 | 0.138061 | 0.0690306 | − | 0.997615i | \(-0.478009\pi\) | ||||
0.0690306 | + | 0.997615i | \(0.478009\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.7446 | 1.07329 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.37228 | 0.198380 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.37228 | −0.113184 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.62772 | 0.624887 | 0.312444 | − | 0.949936i | \(-0.398852\pi\) | ||||
0.312444 | + | 0.949936i | \(0.398852\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.37228 | −0.353478 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.00000 | −0.159617 | −0.0798087 | − | 0.996810i | \(-0.525431\pi\) | ||||
−0.0798087 | + | 0.996810i | \(0.525431\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.62772 | 0.287697 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 15.1168 | 1.19137 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.37228 | 0.499116 | 0.249558 | − | 0.968360i | \(-0.419715\pi\) | ||||
0.249558 | + | 0.968360i | \(0.419715\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.74456 | 0.362826 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.4891 | 1.17762 | 0.588808 | − | 0.808273i | \(-0.299597\pi\) | ||||
0.588808 | + | 0.808273i | \(0.299597\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.00000 | −0.601317 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.2337 | −0.764902 | −0.382451 | − | 0.923976i | \(-0.624920\pi\) | ||||
−0.382451 | + | 0.923976i | \(0.624920\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.372281 | 0.0276715 | 0.0138357 | − | 0.999904i | \(-0.495596\pi\) | ||||
0.0138357 | + | 0.999904i | \(0.495596\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.11684 | −0.673936 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.3723 | −0.758496 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.37228 | 0.172558 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.00000 | −0.578860 | −0.289430 | − | 0.957199i | \(-0.593466\pi\) | ||||
−0.289430 | + | 0.957199i | \(0.593466\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.62772 | −0.261129 | −0.130564 | − | 0.991440i | \(-0.541679\pi\) | ||||
−0.130564 | + | 0.991440i | \(0.541679\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −24.2337 | −1.72658 | −0.863289 | − | 0.504709i | \(-0.831600\pi\) | ||||
−0.863289 | + | 0.504709i | \(0.831600\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.48913 | −0.105561 | −0.0527806 | − | 0.998606i | \(-0.516808\pi\) | ||||
−0.0527806 | + | 0.998606i | \(0.516808\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.00000 | 0.282138 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.74456 | −0.333003 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.37228 | 0.442904 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 11.2554 | 0.778555 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.9783 | −1.58189 | −0.790944 | − | 0.611889i | \(-0.790410\pi\) | ||||
−0.790944 | + | 0.611889i | \(0.790410\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.62772 | −0.385605 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.2554 | −0.764069 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.48913 | −0.506068 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.37228 | −0.294111 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 26.9783 | 1.80660 | 0.903299 | − | 0.429012i | \(-0.141138\pi\) | ||||
0.903299 | + | 0.429012i | \(0.141138\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.25544 | 0.481560 | 0.240780 | − | 0.970580i | \(-0.422597\pi\) | ||||
0.240780 | + | 0.970580i | \(0.422597\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.00000 | 0.132164 | 0.0660819 | − | 0.997814i | \(-0.478950\pi\) | ||||
0.0660819 | + | 0.997814i | \(0.478950\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.62772 | 0.370277 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 24.3723 | 1.59668 | 0.798341 | − | 0.602206i | \(-0.205711\pi\) | ||||
0.798341 | + | 0.602206i | \(0.205711\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 11.8614 | 0.770481 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 29.3505 | 1.89853 | 0.949264 | − | 0.314480i | \(-0.101830\pi\) | ||||
0.949264 | + | 0.314480i | \(0.101830\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.9783 | 1.35133 | 0.675664 | − | 0.737210i | \(-0.263857\pi\) | ||||
0.675664 | + | 0.737210i | \(0.263857\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.74456 | 0.301889 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.0000 | 0.760469 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.48913 | −0.346471 | −0.173235 | − | 0.984880i | \(-0.555422\pi\) | ||||
−0.173235 | + | 0.984880i | \(0.555422\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.1168 | 0.950388 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.0000 | −0.623783 | −0.311891 | − | 0.950118i | \(-0.600963\pi\) | ||||
−0.311891 | + | 0.950118i | \(0.600963\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.883156 | 0.0548766 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.00000 | −0.123797 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.48913 | −0.338474 | −0.169237 | − | 0.985575i | \(-0.554130\pi\) | ||||
−0.169237 | + | 0.985575i | \(0.554130\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.62772 | 0.466809 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.25544 | 0.0765454 | 0.0382727 | − | 0.999267i | \(-0.487814\pi\) | ||||
0.0382727 | + | 0.999267i | \(0.487814\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 28.7446 | 1.74611 | 0.873054 | − | 0.487624i | \(-0.162136\pi\) | ||||
0.873054 | + | 0.487624i | \(0.162136\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.37228 | 0.143577 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.9783 | −1.26046 | −0.630230 | − | 0.776408i | \(-0.717040\pi\) | ||||
−0.630230 | + | 0.776408i | \(0.717040\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.74456 | −0.284050 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −32.9783 | −1.96732 | −0.983659 | − | 0.180043i | \(-0.942376\pi\) | ||||
−0.983659 | + | 0.180043i | \(0.942376\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.0000 | −1.18888 | −0.594438 | − | 0.804141i | \(-0.702626\pi\) | ||||
−0.594438 | + | 0.804141i | \(0.702626\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.3723 | 0.612256 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.11684 | 0.124520 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.37228 | −0.490792 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 26.7446 | 1.56243 | 0.781217 | − | 0.624260i | \(-0.214599\pi\) | ||||
0.781217 | + | 0.624260i | \(0.214599\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.37228 | 0.137654 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.37228 | 0.368519 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.48913 | 0.546944 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.74456 | −0.387465 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.62772 | −0.549483 | −0.274741 | − | 0.961518i | \(-0.588592\pi\) | ||||
−0.274741 | + | 0.961518i | \(0.588592\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.00000 | 0.227552 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.00000 | 0.339140 | 0.169570 | − | 0.985518i | \(-0.445762\pi\) | ||||
0.169570 | + | 0.985518i | \(0.445762\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.2337 | −0.911775 | −0.455887 | − | 0.890037i | \(-0.650678\pi\) | ||||
−0.455887 | + | 0.890037i | \(0.650678\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.74456 | −0.265645 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.3723 | 0.802183 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −20.7446 | −1.15426 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.74456 | −0.151775 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 30.2337 | 1.66684 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.48913 | 0.0818497 | 0.0409249 | − | 0.999162i | \(-0.486970\pi\) | ||||
0.0409249 | + | 0.999162i | \(0.486970\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.372281 | 0.0204009 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.2337 | −0.884305 | −0.442153 | − | 0.896940i | \(-0.645785\pi\) | ||||
−0.442153 | + | 0.896940i | \(0.645785\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.00000 | 0.325875 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.2554 | −0.609516 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.8614 | −1.07242 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.86141 | 0.422022 | 0.211011 | − | 0.977484i | \(-0.432324\pi\) | ||||
0.211011 | + | 0.977484i | \(0.432324\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 32.2337 | 1.72543 | 0.862715 | − | 0.505691i | \(-0.168762\pi\) | ||||
0.862715 | + | 0.505691i | \(0.168762\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.0000 | −0.745145 | −0.372572 | − | 0.928003i | \(-0.621524\pi\) | ||||
−0.372572 | + | 0.928003i | \(0.621524\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −10.3723 | −0.548959 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.00000 | 0.422224 | 0.211112 | − | 0.977462i | \(-0.432292\pi\) | ||||
0.211112 | + | 0.977462i | \(0.432292\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.51087 | 0.184783 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.37228 | −0.281972 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.4891 | −0.704127 | −0.352063 | − | 0.935976i | \(-0.614520\pi\) | ||||
−0.352063 | + | 0.935976i | \(0.614520\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.37228 | 0.227612 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.60597 | 0.446800 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.7446 | 1.38478 | 0.692390 | − | 0.721523i | \(-0.256558\pi\) | ||||
0.692390 | + | 0.721523i | \(0.256558\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.00000 | −0.103005 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.25544 | 0.167221 | 0.0836103 | − | 0.996499i | \(-0.473355\pi\) | ||||
0.0836103 | + | 0.996499i | \(0.473355\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −18.2337 | −0.934140 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −20.7446 | −1.06000 | −0.529999 | − | 0.847998i | \(-0.677808\pi\) | ||||
−0.529999 | + | 0.847998i | \(0.677808\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.00000 | 0.203331 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.23369 | −0.417465 | −0.208732 | − | 0.977973i | \(-0.566934\pi\) | ||||
−0.208732 | + | 0.977973i | \(0.566934\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −27.8614 | −1.40901 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.25544 | −0.365988 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.3505 | 1.37268 | 0.686342 | − | 0.727279i | \(-0.259215\pi\) | ||||
0.686342 | + | 0.727279i | \(0.259215\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 11.2554 | 0.563477 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.0000 | 0.499376 | 0.249688 | − | 0.968326i | \(-0.419672\pi\) | ||||
0.249688 | + | 0.968326i | \(0.419672\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.74456 | −0.236343 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.883156 | 0.0437764 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −32.9783 | −1.63067 | −0.815335 | − | 0.578990i | \(-0.803447\pi\) | ||||
−0.815335 | + | 0.578990i | \(0.803447\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.4891 | 0.566717 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −18.9783 | −0.933859 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.62772 | 0.0797097 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.23369 | 0.109123 | 0.0545614 | − | 0.998510i | \(-0.482624\pi\) | ||||
0.0545614 | + | 0.998510i | \(0.482624\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.7228 | −1.44860 | −0.724301 | − | 0.689484i | \(-0.757837\pi\) | ||||
−0.724301 | + | 0.689484i | \(0.757837\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 12.7446 | 0.619662 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −21.6277 | −1.04664 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.37228 | 0.114535 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −26.9783 | −1.29950 | −0.649748 | − | 0.760149i | \(-0.725126\pi\) | ||||
−0.649748 | + | 0.760149i | \(0.725126\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.2337 | 1.35682 | 0.678412 | − | 0.734681i | \(-0.262668\pi\) | ||||
0.678412 | + | 0.734681i | \(0.262668\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 30.2337 | 1.44627 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 40.6060 | 1.93802 | 0.969009 | − | 0.247027i | \(-0.0794537\pi\) | ||||
0.969009 | + | 0.247027i | \(0.0794537\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.37228 | −0.0653467 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 33.3505 | 1.58453 | 0.792266 | − | 0.610176i | \(-0.208901\pi\) | ||||
0.792266 | + | 0.610176i | \(0.208901\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.62772 | 0.360779 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.37228 | 0.206341 | 0.103170 | − | 0.994664i | \(-0.467101\pi\) | ||||
0.103170 | + | 0.994664i | \(0.467101\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.3723 | 0.488412 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.8832 | −1.07043 | −0.535214 | − | 0.844716i | \(-0.679769\pi\) | ||||
−0.535214 | + | 0.844716i | \(0.679769\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.37228 | −0.204081 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 31.3505 | 1.46014 | 0.730070 | − | 0.683372i | \(-0.239487\pi\) | ||||
0.730070 | + | 0.683372i | \(0.239487\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.60597 | −0.399953 | −0.199977 | − | 0.979801i | \(-0.564087\pi\) | ||||
−0.199977 | + | 0.979801i | \(0.564087\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 41.3505 | 1.91347 | 0.956737 | − | 0.290953i | \(-0.0939725\pi\) | ||||
0.956737 | + | 0.290953i | \(0.0939725\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.48913 | 0.438167 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.00000 | −0.0921551 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.48913 | 0.436310 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.62772 | 0.166102 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 31.1168 | 1.42176 | 0.710882 | − | 0.703311i | \(-0.248296\pi\) | ||||
0.710882 | + | 0.703311i | \(0.248296\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.372281 | 0.0169746 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 15.1168 | 0.687840 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.1168 | 0.685010 | 0.342505 | − | 0.939516i | \(-0.388725\pi\) | ||||
0.342505 | + | 0.939516i | \(0.388725\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.37228 | 0.288165 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.0000 | 0.541552 | 0.270776 | − | 0.962642i | \(-0.412720\pi\) | ||||
0.270776 | + | 0.962642i | \(0.412720\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.74456 | 0.393835 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −13.3505 | −0.598853 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.25544 | −0.145733 | −0.0728667 | − | 0.997342i | \(-0.523215\pi\) | ||||
−0.0728667 | + | 0.997342i | \(0.523215\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −22.9783 | −1.02455 | −0.512275 | − | 0.858822i | \(-0.671197\pi\) | ||||
−0.512275 | + | 0.858822i | \(0.671197\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.13859 | 0.272088 | 0.136044 | − | 0.990703i | \(-0.456561\pi\) | ||||
0.136044 | + | 0.990703i | \(0.456561\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −17.7663 | −0.785935 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.74456 | 0.209478 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 30.2337 | 1.32968 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 15.4891 | 0.679897 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.510875 | 0.0223818 | 0.0111909 | − | 0.999937i | \(-0.496438\pi\) | ||||
0.0111909 | + | 0.999937i | \(0.496438\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −28.0000 | −1.22435 | −0.612177 | − | 0.790721i | \(-0.709706\pi\) | ||||
−0.612177 | + | 0.790721i | \(0.709706\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 20.7446 | 0.903647 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.6060 | 0.765477 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.00000 | −0.347170 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.37228 | 0.189385 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −10.2337 | −0.441616 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.25544 | −0.140222 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.510875 | 0.0219642 | 0.0109821 | − | 0.999940i | \(-0.496504\pi\) | ||||
0.0109821 | + | 0.999940i | \(0.496504\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.372281 | 0.0159761 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 38.9783 | 1.66659 | 0.833295 | − | 0.552829i | \(-0.186452\pi\) | ||||
0.833295 | + | 0.552829i | \(0.186452\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.11684 | −0.389097 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.48913 | −0.404250 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 28.1386 | 1.19657 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 32.9783 | 1.39733 | 0.698667 | − | 0.715447i | \(-0.253777\pi\) | ||||
0.698667 | + | 0.715447i | \(0.253777\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.00000 | 0.169182 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.3723 | −0.437918 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.1168 | −0.805679 | −0.402839 | − | 0.915271i | \(-0.631977\pi\) | ||||
−0.402839 | + | 0.915271i | \(0.631977\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.37228 | 0.0996265 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 33.7228 | 1.41373 | 0.706867 | − | 0.707347i | \(-0.250108\pi\) | ||||
0.706867 | + | 0.707347i | \(0.250108\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.3505 | 0.726097 | 0.363049 | − | 0.931770i | \(-0.381736\pi\) | ||||
0.363049 | + | 0.931770i | \(0.381736\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.00000 | −0.334205 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.8832 | −0.952638 | −0.476319 | − | 0.879272i | \(-0.658029\pi\) | ||||
−0.476319 | + | 0.879272i | \(0.658029\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.62772 | −0.150763 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 28.4674 | 1.18103 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.60597 | 0.356423 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.74456 | −0.360927 | −0.180463 | − | 0.983582i | \(-0.557760\pi\) | ||||
−0.180463 | + | 0.983582i | \(0.557760\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −22.5109 | −0.927544 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −24.2337 | −0.996841 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22.7446 | 0.934007 | 0.467004 | − | 0.884255i | \(-0.345333\pi\) | ||||
0.467004 | + | 0.884255i | \(0.345333\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.48913 | −0.0609458 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17.4891 | −0.714586 | −0.357293 | − | 0.933992i | \(-0.616300\pi\) | ||||
−0.357293 | + | 0.933992i | \(0.616300\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.60597 | 0.106300 | 0.0531499 | − | 0.998587i | \(-0.483074\pi\) | ||||
0.0531499 | + | 0.998587i | \(0.483074\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.00000 | 0.162893 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −28.0000 | −1.13648 | −0.568242 | − | 0.822861i | \(-0.692376\pi\) | ||||
−0.568242 | + | 0.822861i | \(0.692376\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.74456 | −0.192259 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.7446 | 0.515590 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.8614 | −0.559857 | −0.279928 | − | 0.960021i | \(-0.590311\pi\) | ||||
−0.279928 | + | 0.960021i | \(0.590311\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.4674 | 0.904502 | 0.452251 | − | 0.891891i | \(-0.350621\pi\) | ||||
0.452251 | + | 0.891891i | \(0.350621\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.7228 | −0.631953 | −0.315977 | − | 0.948767i | \(-0.602332\pi\) | ||||
−0.315977 | + | 0.948767i | \(0.602332\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.37228 | 0.255711 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 18.0951 | 0.724965 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 11.2554 | 0.449499 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.62772 | −0.0649014 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −41.4891 | −1.65166 | −0.825828 | − | 0.563922i | \(-0.809292\pi\) | ||||
−0.825828 | + | 0.563922i | \(0.809292\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −22.9783 | −0.913303 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.37228 | −0.0543718 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.62772 | −0.222629 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.2337 | −0.483202 | −0.241601 | − | 0.970376i | \(-0.577672\pi\) | ||||
−0.241601 | + | 0.970376i | \(0.577672\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.1168 | −0.438406 | −0.219203 | − | 0.975679i | \(-0.570346\pi\) | ||||
−0.219203 | + | 0.975679i | \(0.570346\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −23.8614 | −0.938089 | −0.469044 | − | 0.883175i | \(-0.655402\pi\) | ||||
−0.469044 | + | 0.883175i | \(0.655402\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −18.9783 | −0.744961 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −11.2554 | −0.441135 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 30.0000 | 1.17399 | 0.586995 | − | 0.809590i | \(-0.300311\pi\) | ||||
0.586995 | + | 0.809590i | \(0.300311\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7.48913 | −0.292179 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −37.4891 | −1.46037 | −0.730184 | − | 0.683250i | \(-0.760566\pi\) | ||||
−0.730184 | + | 0.683250i | \(0.760566\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.233688 | 0.00908941 | 0.00454470 | − | 0.999990i | \(-0.498553\pi\) | ||||
0.00454470 | + | 0.999990i | \(0.498553\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.37228 | −0.169805 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.7446 | −0.493471 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 26.9783 | 1.04304 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −21.6277 | −0.834929 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31.4891 | 1.21382 | 0.606908 | − | 0.794772i | \(-0.292410\pi\) | ||||
0.606908 | + | 0.794772i | \(0.292410\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.6277 | 0.446890 | 0.223445 | − | 0.974717i | \(-0.428270\pi\) | ||||
0.223445 | + | 0.974717i | \(0.428270\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −19.8614 | −0.762211 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.25544 | 0.278029 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −46.9783 | −1.79757 | −0.898786 | − | 0.438387i | \(-0.855550\pi\) | ||||
−0.898786 | + | 0.438387i | \(0.855550\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.00000 | 0.0763048 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.62772 | 0.138205 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.7228 | 0.902458 | 0.451229 | − | 0.892408i | \(-0.350986\pi\) | ||||
0.451229 | + | 0.892408i | \(0.350986\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.62772 | 0.213779 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −19.1168 | −0.724102 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 24.3723 | 0.921844 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.25544 | −0.198495 | −0.0992476 | − | 0.995063i | \(-0.531644\pi\) | ||||
−0.0992476 | + | 0.995063i | \(0.531644\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.76631 | 0.0666177 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −16.0000 | −0.601742 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −50.7446 | −1.90575 | −0.952876 | − | 0.303360i | \(-0.901892\pi\) | ||||
−0.952876 | + | 0.303360i | \(0.901892\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.8614 | 0.444838 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −30.2337 | −1.13226 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 29.3505 | 1.09612 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.02175 | 0.187280 | 0.0936398 | − | 0.995606i | \(-0.470150\pi\) | ||||
0.0936398 | + | 0.995606i | \(0.470150\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.48913 | 0.353393 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 20.9783 | 0.780190 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.744563 | −0.0276143 | −0.0138072 | − | 0.999905i | \(-0.504395\pi\) | ||||
−0.0138072 | + | 0.999905i | \(0.504395\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.4891 | −0.646859 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20.0951 | −0.742229 | −0.371115 | − | 0.928587i | \(-0.621024\pi\) | ||||
−0.371115 | + | 0.928587i | \(0.621024\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.48913 | 0.349536 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.23369 | −0.229310 | −0.114655 | − | 0.993405i | \(-0.536576\pi\) | ||||
−0.114655 | + | 0.993405i | \(0.536576\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.74456 | 0.174296 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −22.2337 | −0.815675 | −0.407837 | − | 0.913055i | \(-0.633717\pi\) | ||||
−0.407837 | + | 0.913055i | \(0.633717\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.0000 | 0.439057 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 34.0951 | 1.24581 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.8614 | −0.724753 | −0.362377 | − | 0.932032i | \(-0.618035\pi\) | ||||
−0.362377 | + | 0.932032i | \(0.618035\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5.48913 | −0.200035 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 50.7446 | 1.84434 | 0.922171 | − | 0.386782i | \(-0.126413\pi\) | ||||
0.922171 | + | 0.386782i | \(0.126413\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 15.1168 | 0.548707 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23.4891 | −0.851480 | −0.425740 | − | 0.904846i | \(-0.639986\pi\) | ||||
−0.425740 | + | 0.904846i | \(0.639986\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.51087 | −0.235709 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.00000 | −0.288863 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.2337 | −1.01813 | −0.509066 | − | 0.860727i | \(-0.670009\pi\) | ||||
−0.509066 | + | 0.860727i | \(0.670009\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.0000 | −0.360141 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.25544 | −0.189025 | −0.0945125 | − | 0.995524i | \(-0.530129\pi\) | ||||
−0.0945125 | + | 0.995524i | \(0.530129\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.883156 | 0.0316830 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 20.7446 | 0.743251 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.3505 | −0.477720 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.00000 | −0.0714742 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −38.9783 | −1.38942 | −0.694712 | − | 0.719288i | \(-0.744468\pi\) | ||||
−0.694712 | + | 0.719288i | \(0.744468\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.48913 | −0.195418 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14.2337 | 0.506092 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.11684 | −0.323749 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16.3723 | 0.579936 | 0.289968 | − | 0.957036i | \(-0.406355\pi\) | ||||
0.289968 | + | 0.957036i | \(0.406355\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −55.7228 | −1.97133 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.62772 | 0.269512 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −17.7663 | −0.626960 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.25544 | 0.0441935 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −34.4674 | −1.21181 | −0.605904 | − | 0.795538i | \(-0.707189\pi\) | ||||
−0.605904 | + | 0.795538i | \(0.707189\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.51087 | 0.228628 | 0.114314 | − | 0.993445i | \(-0.463533\pi\) | ||||
0.114314 | + | 0.993445i | \(0.463533\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 28.7446 | 1.00812 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18.9783 | 0.663965 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.37228 | 0.0828942 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −24.0951 | −0.840925 | −0.420462 | − | 0.907310i | \(-0.638132\pi\) | ||||
−0.420462 | + | 0.907310i | \(0.638132\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 44.0000 | 1.53374 | 0.766872 | − | 0.641800i | \(-0.221812\pi\) | ||||
0.766872 | + | 0.641800i | \(0.221812\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.23369 | −0.0776729 | −0.0388365 | − | 0.999246i | \(-0.512365\pi\) | ||||
−0.0388365 | + | 0.999246i | \(0.512365\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24.9783 | 0.867531 | 0.433765 | − | 0.901026i | \(-0.357185\pi\) | ||||
0.433765 | + | 0.901026i | \(0.357185\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −20.9783 | −0.727727 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.00000 | 0.207888 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.74456 | −0.163996 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.62772 | −0.194290 | −0.0971452 | − | 0.995270i | \(-0.530971\pi\) | ||||
−0.0971452 | + | 0.995270i | \(0.530971\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −32.9783 | −1.13583 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.7446 | −0.437908 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −20.0000 | −0.686398 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.37228 | 0.0813208 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.1168 | 0.723027 | 0.361513 | − | 0.932367i | \(-0.382260\pi\) | ||||
0.361513 | + | 0.932367i | \(0.382260\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −18.6060 | −0.635568 | −0.317784 | − | 0.948163i | \(-0.602939\pi\) | ||||
−0.317784 | + | 0.948163i | \(0.602939\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.8832 | −0.439568 | −0.219784 | − | 0.975549i | \(-0.570535\pi\) | ||||
−0.219784 | + | 0.975549i | \(0.570535\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10.3723 | 0.353486 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −35.2554 | −1.20011 | −0.600055 | − | 0.799959i | \(-0.704854\pi\) | ||||
−0.600055 | + | 0.799959i | \(0.704854\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.11684 | 0.0718918 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 28.1386 | 0.954536 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.00000 | 0.135535 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.37228 | −0.283359 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32.9783 | 1.11360 | 0.556798 | − | 0.830648i | \(-0.312030\pi\) | ||||
0.556798 | + | 0.830648i | \(0.312030\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 26.7446 | 0.902072 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.0000 | 0.606435 | 0.303218 | − | 0.952921i | \(-0.401939\pi\) | ||||
0.303218 | + | 0.952921i | \(0.401939\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −38.9783 | −1.31172 | −0.655861 | − | 0.754881i | \(-0.727694\pi\) | ||||
−0.655861 | + | 0.754881i | \(0.727694\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.35053 | −0.0453464 | −0.0226732 | − | 0.999743i | \(-0.507218\pi\) | ||||
−0.0226732 | + | 0.999743i | \(0.507218\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −43.2554 | −1.45074 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.37228 | 0.0794744 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 60.4674 | 2.02346 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.37228 | 0.212764 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.48913 | 0.316480 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.8614 | −0.528420 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.48913 | 0.315778 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −48.7446 | −1.61854 | −0.809268 | − | 0.587439i | \(-0.800136\pi\) | ||||
−0.809268 | + | 0.587439i | \(0.800136\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.74456 | −0.223703 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.0000 | −0.795155 | −0.397578 | − | 0.917568i | \(-0.630149\pi\) | ||||
−0.397578 | + | 0.917568i | \(0.630149\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 28.4674 | 0.942133 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −17.2119 | −0.568388 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −20.1386 | −0.664311 | −0.332155 | − | 0.943225i | \(-0.607776\pi\) | ||||
−0.332155 | + | 0.943225i | \(0.607776\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.62772 | −0.317244 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.62772 | −0.185239 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.00000 | 0.131377 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 50.6060 | 1.66033 | 0.830164 | − | 0.557519i | \(-0.188247\pi\) | ||||
0.830164 | + | 0.557519i | \(0.188247\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.51087 | −0.213385 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19.4891 | −0.636682 | −0.318341 | − | 0.947976i | \(-0.603126\pi\) | ||||
−0.318341 | + | 0.947976i | \(0.603126\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.00000 | 0.195803 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31.6277 | 1.03103 | 0.515517 | − | 0.856879i | \(-0.327600\pi\) | ||||
0.515517 | + | 0.856879i | \(0.327600\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 27.8614 | 0.907292 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.02175 | 0.0332024 | 0.0166012 | − | 0.999862i | \(-0.494715\pi\) | ||||
0.0166012 | + | 0.999862i | \(0.494715\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.48913 | −0.243107 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −16.2337 | −0.526413 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.64947 | 0.280184 | 0.140092 | − | 0.990139i | \(-0.455260\pi\) | ||||
0.140092 | + | 0.990139i | \(0.455260\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.74456 | −0.153370 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 27.2554 | 0.880124 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.48913 | −0.273843 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 14.3723 | 0.463140 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.9783 | 0.353037 | 0.176518 | − | 0.984297i | \(-0.443517\pi\) | ||||
0.176518 | + | 0.984297i | \(0.443517\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −20.7446 | −0.666411 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 29.4891 | 0.946351 | 0.473176 | − | 0.880968i | \(-0.343108\pi\) | ||||
0.473176 | + | 0.880968i | \(0.343108\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.86141 | 0.123791 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −49.2554 | −1.57582 | −0.787911 | − | 0.615790i | \(-0.788837\pi\) | ||||
−0.787911 | + | 0.615790i | \(0.788837\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.0951 | 0.578322 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.74456 | −0.0876271 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 17.4891 | 0.557816 | 0.278908 | − | 0.960318i | \(-0.410027\pi\) | ||||
0.278908 | + | 0.960318i | \(0.410027\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 30.2337 | 0.962349 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 25.4891 | 0.810507 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.6060 | 0.781634 | 0.390817 | − | 0.920468i | \(-0.372192\pi\) | ||||
0.390817 | + | 0.920468i | \(0.372192\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.48913 | 0.0472560 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −33.7228 | −1.06801 | −0.534006 | − | 0.845481i | \(-0.679314\pi\) | ||||
−0.534006 | + | 0.845481i | \(0.679314\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.372281 | 0.0117785 |
(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 | 7800.2.a.bb.1.2 | 2 | ||
5.4 | even | 2 | 1560.2.a.n.1.1 | ✓ | 2 | ||
15.14 | odd | 2 | 4680.2.a.bf.1.1 | 2 | |||
20.19 | odd | 2 | 3120.2.a.bd.1.2 | 2 | |||
60.59 | even | 2 | 9360.2.a.co.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1560.2.a.n.1.1 | ✓ | 2 | 5.4 | even | 2 | ||
3120.2.a.bd.1.2 | 2 | 20.19 | odd | 2 | |||
4680.2.a.bf.1.1 | 2 | 15.14 | odd | 2 | |||
7800.2.a.bb.1.2 | 2 | 1.1 | even | 1 | trivial | ||
9360.2.a.co.1.2 | 2 | 60.59 | even | 2 |