Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9800,2,Mod(1,9800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("9800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9800.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: | \(78.2533939809\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 18x^{6} + 85x^{4} - 38x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.87509\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9800.1 |
$q$-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 | ||||||||
\(3\) | −2.87509 | −1.65994 | −0.829968 | − | 0.557811i | \(-0.811641\pi\) | ||||
−0.829968 | + | 0.557811i | \(0.811641\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.26617 | 1.75539 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.08223 | −0.627815 | −0.313908 | − | 0.949453i | \(-0.601638\pi\) | ||||
−0.313908 | + | 0.949453i | \(0.601638\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.695629 | −0.192933 | −0.0964664 | − | 0.995336i | \(-0.530754\pi\) | ||||
−0.0964664 | + | 0.995336i | \(0.530754\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.15651 | −0.523030 | −0.261515 | − | 0.965199i | \(-0.584222\pi\) | ||||
−0.261515 | + | 0.965199i | \(0.584222\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.21273 | 1.88413 | 0.942065 | − | 0.335430i | \(-0.108882\pi\) | ||||
0.942065 | + | 0.335430i | \(0.108882\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.33216 | 1.52886 | 0.764431 | − | 0.644706i | \(-0.223020\pi\) | ||||
0.764431 | + | 0.644706i | \(0.223020\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −6.51544 | −1.25390 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.18394 | 0.405547 | 0.202773 | − | 0.979226i | \(-0.435004\pi\) | ||||
0.202773 | + | 0.979226i | \(0.435004\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.88299 | 1.41583 | 0.707913 | − | 0.706300i | \(-0.249637\pi\) | ||||
0.707913 | + | 0.706300i | \(0.249637\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.98660 | 1.04213 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.78360 | 0.293222 | 0.146611 | − | 0.989194i | \(-0.453163\pi\) | ||||
0.146611 | + | 0.989194i | \(0.453163\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.00000 | 0.320256 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.48384 | −0.231736 | −0.115868 | − | 0.993265i | \(-0.536965\pi\) | ||||
−0.115868 | + | 0.993265i | \(0.536965\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.216400 | 0.0330007 | 0.0165003 | − | 0.999864i | \(-0.494748\pi\) | ||||
0.0165003 | + | 0.999864i | \(0.494748\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.6672 | −1.70183 | −0.850916 | − | 0.525302i | \(-0.823952\pi\) | ||||
−0.850916 | + | 0.525302i | \(0.823952\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.20017 | 0.868197 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.14823 | 0.432442 | 0.216221 | − | 0.976344i | \(-0.430627\pi\) | ||||
0.216221 | + | 0.976344i | \(0.430627\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −23.6124 | −3.12754 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.4791 | −1.62464 | −0.812319 | − | 0.583213i | \(-0.801795\pi\) | ||||
−0.812319 | + | 0.583213i | \(0.801795\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.84519 | 0.876436 | 0.438218 | − | 0.898869i | \(-0.355610\pi\) | ||||
0.438218 | + | 0.898869i | \(0.355610\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.1320 | 1.60433 | 0.802164 | − | 0.597104i | \(-0.203682\pi\) | ||||
0.802164 | + | 0.597104i | \(0.203682\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −21.0807 | −2.53781 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.3159 | 1.22428 | 0.612138 | − | 0.790751i | \(-0.290310\pi\) | ||||
0.612138 | + | 0.790751i | \(0.290310\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.5652 | −1.70473 | −0.852365 | − | 0.522948i | \(-0.824832\pi\) | ||||
−0.852365 | + | 0.522948i | \(0.824832\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.9318 | 1.22993 | 0.614963 | − | 0.788556i | \(-0.289171\pi\) | ||||
0.614963 | + | 0.788556i | \(0.289171\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.93400 | 0.326000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.74396 | −0.191425 | −0.0957123 | − | 0.995409i | \(-0.530513\pi\) | ||||
−0.0957123 | + | 0.995409i | \(0.530513\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.27902 | −0.673182 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.5700 | −1.22642 | −0.613209 | − | 0.789921i | \(-0.710122\pi\) | ||||
−0.613209 | + | 0.789921i | \(0.710122\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −22.6643 | −2.35018 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.14764 | −0.319595 | −0.159797 | − | 0.987150i | \(-0.551084\pi\) | ||||
−0.159797 | + | 0.987150i | \(0.551084\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −10.9654 | −1.10206 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.2338 | 1.31681 | 0.658406 | − | 0.752663i | \(-0.271231\pi\) | ||||
0.658406 | + | 0.752663i | \(0.271231\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.13113 | 0.111454 | 0.0557269 | − | 0.998446i | \(-0.482252\pi\) | ||||
0.0557269 | + | 0.998446i | \(0.482252\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.3646 | 1.38868 | 0.694340 | − | 0.719647i | \(-0.255696\pi\) | ||||
0.694340 | + | 0.719647i | \(0.255696\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.4642 | 1.67276 | 0.836381 | − | 0.548148i | \(-0.184667\pi\) | ||||
0.836381 | + | 0.548148i | \(0.184667\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.12802 | −0.486730 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.09846 | −0.479623 | −0.239811 | − | 0.970820i | \(-0.577086\pi\) | ||||
−0.239811 | + | 0.970820i | \(0.577086\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.66330 | −0.338672 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.66433 | −0.605848 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.26617 | 0.384667 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.4479 | −1.28205 | −0.641023 | − | 0.767522i | \(-0.721490\pi\) | ||||
−0.641023 | + | 0.767522i | \(0.721490\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.622170 | −0.0547791 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.2989 | −0.899816 | −0.449908 | − | 0.893075i | \(-0.648543\pi\) | ||||
−0.449908 | + | 0.893075i | \(0.648543\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.84960 | 0.243457 | 0.121729 | − | 0.992563i | \(-0.461156\pi\) | ||||
0.121729 | + | 0.992563i | \(0.461156\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.53195 | 0.723670 | 0.361835 | − | 0.932242i | \(-0.382150\pi\) | ||||
0.361835 | + | 0.932242i | \(0.382150\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 33.5442 | 2.82493 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.44846 | 0.121126 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.6124 | −1.52479 | −0.762393 | − | 0.647114i | \(-0.775976\pi\) | ||||
−0.762393 | + | 0.647114i | \(0.775976\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.248863 | 0.0202522 | 0.0101261 | − | 0.999949i | \(-0.496777\pi\) | ||||
0.0101261 | + | 0.999949i | \(0.496777\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −11.3565 | −0.918122 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.11009 | −0.328021 | −0.164011 | − | 0.986459i | \(-0.552443\pi\) | ||||
−0.164011 | + | 0.986459i | \(0.552443\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.05144 | −0.717826 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.5302 | 1.29474 | 0.647371 | − | 0.762175i | \(-0.275869\pi\) | ||||
0.647371 | + | 0.762175i | \(0.275869\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.2893 | −0.950978 | −0.475489 | − | 0.879722i | \(-0.657729\pi\) | ||||
−0.475489 | + | 0.879722i | \(0.657729\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.5161 | −0.962777 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 43.2496 | 3.30738 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.07132 | −0.689680 | −0.344840 | − | 0.938662i | \(-0.612067\pi\) | ||||
−0.344840 | + | 0.938662i | \(0.612067\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 35.8785 | 2.69680 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.78360 | 0.357543 | 0.178772 | − | 0.983891i | \(-0.442788\pi\) | ||||
0.178772 | + | 0.983891i | \(0.442788\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.3915 | 1.36703 | 0.683514 | − | 0.729938i | \(-0.260451\pi\) | ||||
0.683514 | + | 0.729938i | \(0.260451\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −19.6806 | −1.45483 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.49035 | 0.328367 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.1158 | 1.38317 | 0.691584 | − | 0.722296i | \(-0.256913\pi\) | ||||
0.691584 | + | 0.722296i | \(0.256913\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.7952 | −1.56886 | −0.784428 | − | 0.620220i | \(-0.787043\pi\) | ||||
−0.784428 | + | 0.620220i | \(0.787043\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.76496 | 0.125748 | 0.0628742 | − | 0.998021i | \(-0.479973\pi\) | ||||
0.0628742 | + | 0.998021i | \(0.479973\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.61261 | 0.468756 | 0.234378 | − | 0.972146i | \(-0.424695\pi\) | ||||
0.234378 | + | 0.972146i | \(0.424695\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −37.7557 | −2.66308 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 38.6124 | 2.68375 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −17.1008 | −1.18289 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.7000 | −0.874307 | −0.437153 | − | 0.899387i | \(-0.644013\pi\) | ||||
−0.437153 | + | 0.899387i | \(0.644013\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −29.6593 | −2.03222 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 41.8764 | 2.82974 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.50013 | 0.100910 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 28.0354 | 1.87739 | 0.938696 | − | 0.344747i | \(-0.112035\pi\) | ||||
0.938696 | + | 0.344747i | \(0.112035\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −23.6832 | −1.57191 | −0.785955 | − | 0.618284i | \(-0.787828\pi\) | ||||
−0.785955 | + | 0.618284i | \(0.787828\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.4956 | −0.957896 | −0.478948 | − | 0.877843i | \(-0.658982\pi\) | ||||
−0.478948 | + | 0.877843i | \(0.658982\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.7998 | −0.838545 | −0.419272 | − | 0.907860i | \(-0.637715\pi\) | ||||
−0.419272 | + | 0.907860i | \(0.637715\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −31.4300 | −2.04160 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −30.3773 | −1.96495 | −0.982474 | − | 0.186402i | \(-0.940317\pi\) | ||||
−0.982474 | + | 0.186402i | \(0.940317\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.82122 | 0.310562 | 0.155281 | − | 0.987870i | \(-0.450372\pi\) | ||||
0.155281 | + | 0.987870i | \(0.450372\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.1108 | 0.712757 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.71302 | −0.363511 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.01405 | 0.317753 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.1118 | 0.827609 | 0.413804 | − | 0.910366i | \(-0.364200\pi\) | ||||
0.413804 | + | 0.910366i | \(0.364200\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −15.2672 | −0.959843 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.4468 | 0.963542 | 0.481771 | − | 0.876297i | \(-0.339994\pi\) | ||||
0.481771 | + | 0.876297i | \(0.339994\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 11.5010 | 0.711892 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.81606 | −0.358634 | −0.179317 | − | 0.983791i | \(-0.557389\pi\) | ||||
−0.179317 | + | 0.983791i | \(0.557389\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 33.2648 | 2.03577 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.22682 | 0.562569 | 0.281285 | − | 0.959624i | \(-0.409240\pi\) | ||||
0.281285 | + | 0.959624i | \(0.409240\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.8232 | 0.961189 | 0.480595 | − | 0.876943i | \(-0.340421\pi\) | ||||
0.480595 | + | 0.876943i | \(0.340421\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.43521 | −0.0862332 | −0.0431166 | − | 0.999070i | \(-0.513729\pi\) | ||||
−0.0431166 | + | 0.999070i | \(0.513729\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 41.5131 | 2.48532 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.6124 | −0.871702 | −0.435851 | − | 0.900019i | \(-0.643552\pi\) | ||||
−0.435851 | + | 0.900019i | \(0.643552\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.08833 | −0.540245 | −0.270123 | − | 0.962826i | \(-0.587064\pi\) | ||||
−0.270123 | + | 0.962826i | \(0.587064\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.3495 | −0.726439 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.04977 | 0.530507 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.30657 | −0.368434 | −0.184217 | − | 0.982886i | \(-0.558975\pi\) | ||||
−0.184217 | + | 0.982886i | \(0.558975\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 13.5666 | 0.787216 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.10047 | −0.294968 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −38.0484 | −2.18583 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.0515 | −0.973179 | −0.486590 | − | 0.873631i | \(-0.661759\pi\) | ||||
−0.486590 | + | 0.873631i | \(0.661759\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.25211 | −0.185006 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.6542 | 0.604145 | 0.302072 | − | 0.953285i | \(-0.402322\pi\) | ||||
0.302072 | + | 0.953285i | \(0.402322\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.93447 | −0.109343 | −0.0546713 | − | 0.998504i | \(-0.517411\pi\) | ||||
−0.0546713 | + | 0.998504i | \(0.517411\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.9643 | 0.840478 | 0.420239 | − | 0.907413i | \(-0.361946\pi\) | ||||
0.420239 | + | 0.907413i | \(0.361946\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.54746 | −0.254609 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −41.2996 | −2.30512 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −17.7108 | −0.985458 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −50.2111 | −2.77668 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.2816 | 0.949880 | 0.474940 | − | 0.880018i | \(-0.342470\pi\) | ||||
0.474940 | + | 0.880018i | \(0.342470\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.39273 | 0.514719 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −31.6124 | −1.72204 | −0.861018 | − | 0.508574i | \(-0.830173\pi\) | ||||
−0.861018 | + | 0.508574i | \(0.830173\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.6586 | 0.796143 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −16.4142 | −0.888877 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 21.9178 | 1.17661 | 0.588304 | − | 0.808640i | \(-0.299796\pi\) | ||||
0.588304 | + | 0.808640i | \(0.299796\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.9581 | −1.06833 | −0.534167 | − | 0.845379i | \(-0.679374\pi\) | ||||
−0.534167 | + | 0.845379i | \(0.679374\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.53233 | 0.241918 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 31.9656 | 1.70135 | 0.850677 | − | 0.525688i | \(-0.176192\pi\) | ||||
0.850677 | + | 0.525688i | \(0.176192\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.65161 | 0.403836 | 0.201918 | − | 0.979402i | \(-0.435282\pi\) | ||||
0.201918 | + | 0.979402i | \(0.435282\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 48.4490 | 2.54995 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 19.1606 | 1.00567 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.3591 | 1.11494 | 0.557469 | − | 0.830198i | \(-0.311773\pi\) | ||||
0.557469 | + | 0.830198i | \(0.311773\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.81412 | −0.406787 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.8483 | 0.561702 | 0.280851 | − | 0.959751i | \(-0.409383\pi\) | ||||
0.280851 | + | 0.959751i | \(0.409383\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.51921 | −0.0782433 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.4339 | 1.10098 | 0.550492 | − | 0.834840i | \(-0.314440\pi\) | ||||
0.550492 | + | 0.834840i | \(0.314440\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 41.5391 | 2.12811 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 17.6203 | 0.900354 | 0.450177 | − | 0.892939i | \(-0.351361\pi\) | ||||
0.450177 | + | 0.892939i | \(0.351361\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.13960 | 0.0579290 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −20.5129 | −1.04004 | −0.520021 | − | 0.854153i | \(-0.674076\pi\) | ||||
−0.520021 | + | 0.854153i | \(0.674076\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −15.8119 | −0.799641 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 29.6102 | 1.49364 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.2079 | 0.713075 | 0.356538 | − | 0.934281i | \(-0.383957\pi\) | ||||
0.356538 | + | 0.934281i | \(0.383957\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 28.0833 | 1.40241 | 0.701207 | − | 0.712958i | \(-0.252645\pi\) | ||||
0.701207 | + | 0.712958i | \(0.252645\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.48364 | −0.273159 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.71386 | −0.184089 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.58915 | −0.424706 | −0.212353 | − | 0.977193i | \(-0.568113\pi\) | ||||
−0.212353 | + | 0.977193i | \(0.568113\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.19286 | −0.404124 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −24.5302 | −1.20125 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.872956 | −0.0426467 | −0.0213233 | − | 0.999773i | \(-0.506788\pi\) | ||||
−0.0213233 | + | 0.999773i | \(0.506788\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.3159 | 1.18509 | 0.592543 | − | 0.805539i | \(-0.298124\pi\) | ||||
0.592543 | + | 0.805539i | \(0.298124\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −61.4412 | −2.98738 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.16446 | −0.201062 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −31.9770 | −1.54028 | −0.770139 | − | 0.637876i | \(-0.779813\pi\) | ||||
−0.770139 | + | 0.637876i | \(0.779813\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.36468 | −0.353924 | −0.176962 | − | 0.984218i | \(-0.556627\pi\) | ||||
−0.176962 | + | 0.984218i | \(0.556627\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 60.2171 | 2.88057 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.3073 | −0.635121 | −0.317561 | − | 0.948238i | \(-0.602864\pi\) | ||||
−0.317561 | + | 0.948238i | \(0.602864\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.75114 | 0.415779 | 0.207890 | − | 0.978152i | \(-0.433341\pi\) | ||||
0.207890 | + | 0.978152i | \(0.433341\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 53.5123 | 2.53105 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.2129 | 1.09548 | 0.547742 | − | 0.836647i | \(-0.315488\pi\) | ||||
0.547742 | + | 0.836647i | \(0.315488\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.08968 | 0.145488 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.715504 | −0.0336173 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.1980 | 0.804488 | 0.402244 | − | 0.915532i | \(-0.368230\pi\) | ||||
0.402244 | + | 0.915532i | \(0.368230\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 14.0506 | 0.655826 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.52073 | 0.0708273 | 0.0354136 | − | 0.999373i | \(-0.488725\pi\) | ||||
0.0354136 | + | 0.999373i | \(0.488725\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.6968 | 0.590070 | 0.295035 | − | 0.955486i | \(-0.404669\pi\) | ||||
0.295035 | + | 0.955486i | \(0.404669\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.97440 | −0.230188 | −0.115094 | − | 0.993355i | \(-0.536717\pi\) | ||||
−0.115094 | + | 0.993355i | \(0.536717\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.8169 | 0.544494 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.450594 | −0.0207183 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 16.5791 | 0.759104 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 30.8363 | 1.40895 | 0.704474 | − | 0.709730i | \(-0.251183\pi\) | ||||
0.704474 | + | 0.709730i | \(0.251183\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.24072 | −0.0565722 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −36.8253 | −1.66871 | −0.834356 | − | 0.551226i | \(-0.814160\pi\) | ||||
−0.834356 | + | 0.551226i | \(0.814160\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −47.5257 | −2.14919 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.94806 | −0.358691 | −0.179345 | − | 0.983786i | \(-0.557398\pi\) | ||||
−0.179345 | + | 0.983786i | \(0.557398\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.70968 | −0.212113 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.92858 | −0.0863349 | −0.0431675 | − | 0.999068i | \(-0.513745\pi\) | ||||
−0.0431675 | + | 0.999068i | \(0.513745\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 35.3330 | 1.57856 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 35.5389 | 1.58460 | 0.792301 | − | 0.610130i | \(-0.208883\pi\) | ||||
0.792301 | + | 0.610130i | \(0.208883\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 35.9850 | 1.59815 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.4039 | 0.682767 | 0.341384 | − | 0.939924i | \(-0.389105\pi\) | ||||
0.341384 | + | 0.939924i | \(0.389105\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −53.5096 | −2.36251 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 24.2937 | 1.06844 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 26.0809 | 1.14482 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.97708 | −0.349482 | −0.174741 | − | 0.984614i | \(-0.555909\pi\) | ||||
−0.174741 | + | 0.984614i | \(0.555909\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.86412 | 0.431328 | 0.215664 | − | 0.976468i | \(-0.430808\pi\) | ||||
0.215664 | + | 0.976468i | \(0.430808\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −16.9997 | −0.740520 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 30.7606 | 1.33742 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −65.7169 | −2.85187 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.03220 | 0.0447095 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −13.7533 | −0.593499 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.6191 | 0.585533 | 0.292766 | − | 0.956184i | \(-0.405424\pi\) | ||||
0.292766 | + | 0.956184i | \(0.405424\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −52.8772 | −2.26918 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 39.8299 | 1.70300 | 0.851501 | − | 0.524353i | \(-0.175693\pi\) | ||||
0.851501 | + | 0.524353i | \(0.175693\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 36.0479 | 1.53849 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 17.9361 | 0.764103 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −32.5799 | −1.38046 | −0.690228 | − | 0.723592i | \(-0.742490\pi\) | ||||
−0.690228 | + | 0.723592i | \(0.742490\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.150534 | −0.00636692 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.9102 | −0.545068 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.6233 | −0.658445 | −0.329222 | − | 0.944252i | \(-0.606787\pi\) | ||||
−0.329222 | + | 0.944252i | \(0.606787\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.32891 | −0.391088 | −0.195544 | − | 0.980695i | \(-0.562647\pi\) | ||||
−0.195544 | + | 0.980695i | \(0.562647\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.88073 | −0.287949 | −0.143975 | − | 0.989581i | \(-0.545988\pi\) | ||||
−0.143975 | + | 0.989581i | \(0.545988\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −54.9596 | −2.29597 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.5238 | 1.02094 | 0.510470 | − | 0.859896i | \(-0.329472\pi\) | ||||
0.510470 | + | 0.859896i | \(0.329472\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 62.6634 | 2.60420 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.55532 | −0.271494 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.2462 | 0.546730 | 0.273365 | − | 0.961910i | \(-0.411863\pi\) | ||||
0.273365 | + | 0.961910i | \(0.411863\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 64.7409 | 2.66760 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.07443 | −0.208734 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 29.8957 | 1.22767 | 0.613834 | − | 0.789435i | \(-0.289626\pi\) | ||||
0.613834 | + | 0.789435i | \(0.289626\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −19.0119 | −0.778104 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25.4317 | 1.03911 | 0.519555 | − | 0.854437i | \(-0.326098\pi\) | ||||
0.519555 | + | 0.854437i | \(0.326098\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.815755 | 0.0332754 | 0.0166377 | − | 0.999862i | \(-0.494704\pi\) | ||||
0.0166377 | + | 0.999862i | \(0.494704\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 69.1553 | 2.81622 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.49506 | −0.344804 | −0.172402 | − | 0.985027i | \(-0.555153\pi\) | ||||
−0.172402 | + | 0.985027i | \(0.555153\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.11603 | 0.328339 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 28.7972 | 1.16311 | 0.581553 | − | 0.813508i | \(-0.302445\pi\) | ||||
0.581553 | + | 0.813508i | \(0.302445\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20.1934 | 0.812956 | 0.406478 | − | 0.913661i | \(-0.366757\pi\) | ||||
0.406478 | + | 0.913661i | \(0.366757\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −30.8868 | −1.24145 | −0.620723 | − | 0.784030i | \(-0.713161\pi\) | ||||
−0.620723 | + | 0.784030i | \(0.713161\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −47.7723 | −1.91703 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 49.1664 | 1.96352 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.84635 | −0.153364 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.0638 | −0.838537 | −0.419269 | − | 0.907862i | \(-0.637713\pi\) | ||||
−0.419269 | + | 0.907862i | \(0.637713\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 36.5138 | 1.45129 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 54.3254 | 2.14908 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27.1287 | 1.07152 | 0.535760 | − | 0.844370i | \(-0.320025\pi\) | ||||
0.535760 | + | 0.844370i | \(0.320025\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.3862 | 0.527901 | 0.263951 | − | 0.964536i | \(-0.414974\pi\) | ||||
0.263951 | + | 0.964536i | \(0.414974\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11.8982 | −0.467768 | −0.233884 | − | 0.972265i | \(-0.575144\pi\) | ||||
−0.233884 | + | 0.972265i | \(0.575144\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 25.9843 | 1.01997 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 27.1252 | 1.06149 | 0.530746 | − | 0.847531i | \(-0.321912\pi\) | ||||
0.530746 | + | 0.847531i | \(0.321912\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −76.7028 | −2.99246 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 32.0463 | 1.24834 | 0.624172 | − | 0.781287i | \(-0.285436\pi\) | ||||
0.624172 | + | 0.781287i | \(0.285436\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.5074 | 0.603166 | 0.301583 | − | 0.953440i | \(-0.402485\pi\) | ||||
0.301583 | + | 0.953440i | \(0.402485\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.31302 | −0.167504 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.0130 | 0.620025 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −80.6045 | −3.11635 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.2532 | −0.550240 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.0833 | 1.04398 | 0.521992 | − | 0.852950i | \(-0.325189\pi\) | ||||
0.521992 | + | 0.852950i | \(0.325189\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.32000 | 0.319764 | 0.159882 | − | 0.987136i | \(-0.448889\pi\) | ||||
0.159882 | + | 0.987136i | \(0.448889\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 68.0914 | 2.60927 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13.8288 | −0.529144 | −0.264572 | − | 0.964366i | \(-0.585231\pi\) | ||||
−0.264572 | + | 0.964366i | \(0.585231\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 41.6762 | 1.59005 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.19000 | −0.0834323 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −43.3621 | −1.64957 | −0.824785 | − | 0.565446i | \(-0.808704\pi\) | ||||
−0.824785 | + | 0.565446i | \(0.808704\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.19991 | 0.121205 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 36.8007 | 1.39193 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.76821 | −0.255632 | −0.127816 | − | 0.991798i | \(-0.540797\pi\) | ||||
−0.127816 | + | 0.991798i | \(0.540797\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.6482 | 0.552469 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.46981 | −0.355646 | −0.177823 | − | 0.984062i | \(-0.556905\pi\) | ||||
−0.177823 | + | 0.984062i | \(0.556905\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 57.5688 | 2.15900 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 57.7993 | 2.16460 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 87.3377 | 3.26169 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −36.2805 | −1.35303 | −0.676517 | − | 0.736427i | \(-0.736511\pi\) | ||||
−0.676517 | + | 0.736427i | \(0.736511\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −13.8615 | −0.515514 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.7840 | 1.21589 | 0.607945 | − | 0.793979i | \(-0.291994\pi\) | ||||
0.607945 | + | 0.793979i | \(0.291994\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −40.7466 | −1.50913 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.466669 | −0.0172604 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.0673 | 1.29524 | 0.647620 | − | 0.761964i | \(-0.275764\pi\) | ||||
0.647620 | + | 0.761964i | \(0.275764\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −27.3438 | −1.00722 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.97105 | 0.0725062 | 0.0362531 | − | 0.999343i | \(-0.488458\pi\) | ||||
0.0362531 | + | 0.999343i | \(0.488458\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.4255 | 0.603405 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −26.3124 | −0.965309 | −0.482655 | − | 0.875811i | \(-0.660327\pi\) | ||||
−0.482655 | + | 0.875811i | \(0.660327\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.18399 | −0.336025 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 35.0278 | 1.27818 | 0.639092 | − | 0.769130i | \(-0.279310\pi\) | ||||
0.639092 | + | 0.769130i | \(0.279310\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −37.6976 | −1.37378 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.1958 | 0.406919 | 0.203459 | − | 0.979083i | \(-0.434782\pi\) | ||||
0.203459 | + | 0.979083i | \(0.434782\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 43.8947 | 1.59328 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 43.4437 | 1.57483 | 0.787417 | − | 0.616421i | \(-0.211418\pi\) | ||||
0.787417 | + | 0.616421i | \(0.211418\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.68082 | 0.313446 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32.3819 | 1.16772 | 0.583861 | − | 0.811853i | \(-0.301541\pi\) | ||||
0.583861 | + | 0.811853i | \(0.301541\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −44.4109 | −1.59942 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −42.0334 | −1.51183 | −0.755917 | − | 0.654667i | \(-0.772809\pi\) | ||||
−0.755917 | + | 0.654667i | \(0.772809\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −12.1863 | −0.436621 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −21.4801 | −0.768619 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −14.2293 | −0.508514 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.1451 | 0.468571 | 0.234285 | − | 0.972168i | \(-0.424725\pi\) | ||||
0.234285 | + | 0.972168i | \(0.424725\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16.7217 | 0.595309 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.76171 | −0.169093 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 56.1776 | 1.98991 | 0.994956 | − | 0.100309i | \(-0.0319832\pi\) | ||||
0.994956 | + | 0.100309i | \(0.0319832\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25.1604 | 0.890110 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −60.9295 | −2.15284 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 30.3281 | 1.07026 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −26.5280 | −0.933829 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −14.0195 | −0.492899 | −0.246449 | − | 0.969156i | \(-0.579264\pi\) | ||||
−0.246449 | + | 0.969156i | \(0.579264\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.0241 | 0.387110 | 0.193555 | − | 0.981089i | \(-0.437998\pi\) | ||||
0.193555 | + | 0.981089i | \(0.437998\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −45.4931 | −1.59551 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.77724 | 0.0621776 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −37.6965 | −1.31562 | −0.657809 | − | 0.753185i | \(-0.728517\pi\) | ||||
−0.657809 | + | 0.753185i | \(0.728517\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 53.1931 | 1.85420 | 0.927098 | − | 0.374818i | \(-0.122295\pi\) | ||||
0.927098 | + | 0.374818i | \(0.122295\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34.3451 | 1.19430 | 0.597149 | − | 0.802130i | \(-0.296300\pi\) | ||||
0.597149 | + | 0.802130i | \(0.296300\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33.0640 | 1.14836 | 0.574179 | − | 0.818730i | \(-0.305321\pi\) | ||||
0.574179 | + | 0.818730i | \(0.305321\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.12635 | 0.143142 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −51.3611 | −1.77530 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.04312 | −0.139584 | −0.0697920 | − | 0.997562i | \(-0.522234\pi\) | ||||
−0.0697920 | + | 0.997562i | \(0.522234\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.2304 | −0.835532 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 42.0120 | 1.44697 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 26.1298 | 0.896773 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13.0776 | 0.448296 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 41.1970 | 1.41056 | 0.705279 | − | 0.708930i | \(-0.250822\pi\) | ||||
0.705279 | + | 0.708930i | \(0.250822\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13.5978 | −0.464492 | −0.232246 | − | 0.972657i | \(-0.574607\pi\) | ||||
−0.232246 | + | 0.972657i | \(0.574607\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −52.8276 | −1.80245 | −0.901227 | − | 0.433348i | \(-0.857332\pi\) | ||||
−0.901227 | + | 0.433348i | \(0.857332\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −11.8810 | −0.404434 | −0.202217 | − | 0.979341i | \(-0.564815\pi\) | ||||
−0.202217 | + | 0.979341i | \(0.564815\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 35.5059 | 1.20584 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −22.7626 | −0.772167 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.13500 | −0.309528 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −16.5760 | −0.561013 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.31509 | −0.145710 | −0.0728551 | − | 0.997343i | \(-0.523211\pi\) | ||||
−0.0728551 | + | 0.997343i | \(0.523211\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 18.1320 | 0.611577 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.411033 | 0.0138481 | 0.00692403 | − | 0.999976i | \(-0.497796\pi\) | ||||
0.00692403 | + | 0.999976i | \(0.497796\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −38.8610 | −1.30778 | −0.653888 | − | 0.756591i | \(-0.726863\pi\) | ||||
−0.653888 | + | 0.756591i | \(0.726863\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 17.7530 | 0.596089 | 0.298044 | − | 0.954552i | \(-0.403666\pi\) | ||||
0.298044 | + | 0.954552i | \(0.403666\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.10926 | −0.204668 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −95.8194 | −3.20647 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 14.6643 | 0.489628 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17.2159 | 0.574184 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.78918 | −0.226180 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20.9997 | −0.697285 | −0.348642 | − | 0.937256i | \(-0.613357\pi\) | ||||
−0.348642 | + | 0.937256i | \(0.613357\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 69.6914 | 2.31152 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.8994 | −0.361112 | −0.180556 | − | 0.983565i | \(-0.557790\pi\) | ||||
−0.180556 | + | 0.983565i | \(0.557790\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.63133 | 0.120179 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −42.0060 | −1.38565 | −0.692824 | − | 0.721106i | \(-0.743634\pi\) | ||||
−0.692824 | + | 0.721106i | \(0.743634\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 49.0246 | 1.61542 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.17607 | −0.236203 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.95673 | 0.195645 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.08833 | −0.134134 | −0.0670669 | − | 0.997748i | \(-0.521364\pi\) | ||||
−0.0670669 | + | 0.997748i | \(0.521364\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −30.6319 | −1.00284 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −47.3538 | −1.54698 | −0.773490 | − | 0.633808i | \(-0.781491\pi\) | ||||
−0.773490 | + | 0.633808i | \(0.781491\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.56177 | 0.181502 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.9278 | 0.421433 | 0.210717 | − | 0.977547i | \(-0.432420\pi\) | ||||
0.210717 | + | 0.977547i | \(0.432420\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.8797 | −0.354292 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 42.6989 | 1.38753 | 0.693764 | − | 0.720202i | \(-0.255951\pi\) | ||||
0.693764 | + | 0.720202i | \(0.255951\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.1320 | 0.328898 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −43.0237 | −1.39514 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −13.8193 | −0.447651 | −0.223826 | − | 0.974629i | \(-0.571855\pi\) | ||||
−0.223826 | + | 0.974629i | \(0.571855\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 13.0744 | 0.422634 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 31.1415 | 1.00456 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 75.6465 | 2.43767 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.8612 | 0.799484 | 0.399742 | − | 0.916628i | \(-0.369100\pi\) | ||||
0.399742 | + | 0.916628i | \(0.369100\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 50.9203 | 1.63580 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11.0871 | 0.355801 | 0.177901 | − | 0.984048i | \(-0.443069\pi\) | ||||
0.177901 | + | 0.984048i | \(0.443069\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 20.0917 | 0.642790 | 0.321395 | − | 0.946945i | \(-0.395848\pi\) | ||||
0.321395 | + | 0.946945i | \(0.395848\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24.0914 | 0.769964 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 91.9691 | 2.93635 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.12683 | −0.163520 | −0.0817602 | − | 0.996652i | \(-0.526054\pi\) | ||||
−0.0817602 | + | 0.996652i | \(0.526054\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.58668 | 0.0504535 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −48.1082 | −1.52821 | −0.764103 | − | 0.645094i | \(-0.776818\pi\) | ||||
−0.764103 | + | 0.645094i | \(0.776818\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −49.6861 | −1.57674 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.78201 | 0.309799 | 0.154900 | − | 0.987930i | \(-0.450495\pi\) | ||||
0.154900 | + | 0.987930i | \(0.450495\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −11.6209 | −0.367670 |
(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 | 9800.2.a.cz.1.2 | ✓ | 8 | |
5.4 | even | 2 | 9800.2.a.da.1.7 | yes | 8 | ||
7.6 | odd | 2 | inner | 9800.2.a.cz.1.7 | yes | 8 | |
35.34 | odd | 2 | 9800.2.a.da.1.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9800.2.a.cz.1.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
9800.2.a.cz.1.7 | yes | 8 | 7.6 | odd | 2 | inner | |
9800.2.a.da.1.2 | yes | 8 | 35.34 | odd | 2 | ||
9800.2.a.da.1.7 | yes | 8 | 5.4 | even | 2 |