Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4788,2,Mod(1,4788)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4788, 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("4788.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4788 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4788.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: | \(38.2323724878\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 6x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.28825\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4788.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.70246 | −1.65579 | −0.827895 | − | 0.560883i | \(-0.810462\pi\) | ||||
−0.827895 | + | 0.560883i | \(0.810462\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.57649 | 1.37986 | 0.689932 | − | 0.723874i | \(-0.257640\pi\) | ||||
0.689932 | + | 0.723874i | \(0.257640\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.23607 | −1.45222 | −0.726112 | − | 0.687576i | \(-0.758675\pi\) | ||||
−0.726112 | + | 0.687576i | \(0.758675\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.874032 | 0.211984 | 0.105992 | − | 0.994367i | \(-0.466198\pi\) | ||||
0.105992 | + | 0.994367i | \(0.466198\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.08036 | 0.225271 | 0.112636 | − | 0.993636i | \(-0.464071\pi\) | ||||
0.112636 | + | 0.993636i | \(0.464071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.70820 | 1.74164 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.78282 | 0.888148 | 0.444074 | − | 0.895990i | \(-0.353533\pi\) | ||||
0.444074 | + | 0.895990i | \(0.353533\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.23607 | −1.29964 | −0.649818 | − | 0.760090i | \(-0.725155\pi\) | ||||
−0.649818 | + | 0.760090i | \(0.725155\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.70246 | −0.625830 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.00000 | −0.986394 | −0.493197 | − | 0.869918i | \(-0.664172\pi\) | ||||
−0.493197 | + | 0.869918i | \(0.664172\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.57649 | 0.714728 | 0.357364 | − | 0.933965i | \(-0.383676\pi\) | ||||
0.357364 | + | 0.933965i | \(0.383676\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.1803 | 1.85748 | 0.928742 | − | 0.370726i | \(-0.120891\pi\) | ||||
0.928742 | + | 0.370726i | \(0.120891\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.0270 | −1.46259 | −0.731295 | − | 0.682061i | \(-0.761084\pi\) | ||||
−0.731295 | + | 0.682061i | \(0.761084\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.35931 | 1.28560 | 0.642800 | − | 0.766034i | \(-0.277773\pi\) | ||||
0.642800 | + | 0.766034i | \(0.277773\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −16.9443 | −2.28477 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.6491 | 1.64677 | 0.823387 | − | 0.567480i | \(-0.192082\pi\) | ||||
0.823387 | + | 0.567480i | \(0.192082\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.9443 | −1.40127 | −0.700635 | − | 0.713520i | \(-0.747100\pi\) | ||||
−0.700635 | + | 0.713520i | \(0.747100\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 19.3863 | 2.40458 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.47214 | 0.790697 | 0.395349 | − | 0.918531i | \(-0.370624\pi\) | ||||
0.395349 | + | 0.918531i | \(0.370624\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.206331 | −0.0244870 | −0.0122435 | − | 0.999925i | \(-0.503897\pi\) | ||||
−0.0122435 | + | 0.999925i | \(0.503897\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.4721 | −1.45975 | −0.729877 | − | 0.683579i | \(-0.760422\pi\) | ||||
−0.729877 | + | 0.683579i | \(0.760422\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.57649 | 0.521540 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.9443 | −1.45634 | −0.728172 | − | 0.685394i | \(-0.759630\pi\) | ||||
−0.728172 | + | 0.685394i | \(0.759630\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −16.7642 | −1.84011 | −0.920057 | − | 0.391785i | \(-0.871858\pi\) | ||||
−0.920057 | + | 0.391785i | \(0.871858\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.23607 | −0.351001 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.57649 | 0.485107 | 0.242554 | − | 0.970138i | \(-0.422015\pi\) | ||||
0.242554 | + | 0.970138i | \(0.422015\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.23607 | −0.548889 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.70246 | 0.379864 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.41641 | 0.956091 | 0.478046 | − | 0.878335i | \(-0.341345\pi\) | ||||
0.478046 | + | 0.878335i | \(0.341345\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.9358 | 1.38666 | 0.693332 | − | 0.720618i | \(-0.256142\pi\) | ||||
0.693332 | + | 0.720618i | \(0.256142\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.94427 | 0.487174 | 0.243587 | − | 0.969879i | \(-0.421676\pi\) | ||||
0.243587 | + | 0.969879i | \(0.421676\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.5231 | −1.30733 | −0.653666 | − | 0.756783i | \(-0.726770\pi\) | ||||
−0.653666 | + | 0.756783i | \(0.726770\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.9443 | −1.04827 | −0.524136 | − | 0.851635i | \(-0.675611\pi\) | ||||
−0.524136 | + | 0.851635i | \(0.675611\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.69161 | −0.817638 | −0.408819 | − | 0.912615i | \(-0.634059\pi\) | ||||
−0.408819 | + | 0.912615i | \(0.634059\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.00000 | −0.373002 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.874032 | 0.0801224 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.94427 | 0.904025 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −13.7295 | −1.22800 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.4721 | −1.63914 | −0.819569 | − | 0.572981i | \(-0.805787\pi\) | ||||
−0.819569 | + | 0.572981i | \(0.805787\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.35931 | −0.817727 | −0.408864 | − | 0.912596i | \(-0.634075\pi\) | ||||
−0.408864 | + | 0.912596i | \(0.634075\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.00000 | −0.0867110 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.3060 | 1.56398 | 0.781992 | − | 0.623288i | \(-0.214204\pi\) | ||||
0.781992 | + | 0.623288i | \(0.214204\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.52786 | 0.129592 | 0.0647959 | − | 0.997899i | \(-0.479360\pi\) | ||||
0.0647959 | + | 0.997899i | \(0.479360\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −23.9628 | −2.00387 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −17.7082 | −1.47059 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.40492 | −0.606635 | −0.303317 | − | 0.952890i | \(-0.598094\pi\) | ||||
−0.303317 | + | 0.952890i | \(0.598094\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.9443 | −1.05339 | −0.526695 | − | 0.850054i | \(-0.676569\pi\) | ||||
−0.526695 | + | 0.850054i | \(0.676569\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 26.7912 | 2.15192 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.472136 | 0.0376806 | 0.0188403 | − | 0.999823i | \(-0.494003\pi\) | ||||
0.0188403 | + | 0.999823i | \(0.494003\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.08036 | 0.0851445 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.763932 | 0.0598358 | 0.0299179 | − | 0.999552i | \(-0.490475\pi\) | ||||
0.0299179 | + | 0.999552i | \(0.490475\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.06952 | 0.469673 | 0.234837 | − | 0.972035i | \(-0.424544\pi\) | ||||
0.234837 | + | 0.972035i | \(0.424544\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 14.4164 | 1.10895 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −15.8902 | −1.20811 | −0.604055 | − | 0.796943i | \(-0.706449\pi\) | ||||
−0.604055 | + | 0.796943i | \(0.706449\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.70820 | 0.658278 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −23.0888 | −1.72574 | −0.862868 | − | 0.505429i | \(-0.831334\pi\) | ||||
−0.862868 | + | 0.505429i | \(0.831334\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.8885 | 1.18099 | 0.590493 | − | 0.807043i | \(-0.298933\pi\) | ||||
0.590493 | + | 0.807043i | \(0.298933\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 22.2148 | 1.63326 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.00000 | 0.292509 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.57649 | −0.331143 | −0.165572 | − | 0.986198i | \(-0.552947\pi\) | ||||
−0.165572 | + | 0.986198i | \(0.552947\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.41641 | −0.389882 | −0.194941 | − | 0.980815i | \(-0.562451\pi\) | ||||
−0.194941 | + | 0.980815i | \(0.562451\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.99226 | −0.498178 | −0.249089 | − | 0.968481i | \(-0.580131\pi\) | ||||
−0.249089 | + | 0.968481i | \(0.580131\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.05573 | −0.216615 | −0.108307 | − | 0.994117i | \(-0.534543\pi\) | ||||
−0.108307 | + | 0.994117i | \(0.534543\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.78282 | 0.335688 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −16.9443 | −1.18344 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.57649 | −0.316563 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.4164 | −0.785938 | −0.392969 | − | 0.919552i | \(-0.628552\pi\) | ||||
−0.392969 | + | 0.919552i | \(0.628552\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −45.0972 | −3.07560 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.23607 | −0.491216 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.57649 | −0.307848 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.763932 | −0.0511567 | −0.0255783 | − | 0.999673i | \(-0.508143\pi\) | ||||
−0.0255783 | + | 0.999673i | \(0.508143\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −16.5579 | −1.09899 | −0.549493 | − | 0.835498i | \(-0.685179\pi\) | ||||
−0.549493 | + | 0.835498i | \(0.685179\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 26.3607 | 1.74196 | 0.870981 | − | 0.491316i | \(-0.163484\pi\) | ||||
0.870981 | + | 0.491316i | \(0.163484\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −20.8794 | −1.36785 | −0.683926 | − | 0.729551i | \(-0.739729\pi\) | ||||
−0.683926 | + | 0.729551i | \(0.739729\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 37.1246 | 2.42174 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −23.2951 | −1.50684 | −0.753418 | − | 0.657542i | \(-0.771596\pi\) | ||||
−0.753418 | + | 0.657542i | \(0.771596\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.0000 | −1.41714 | −0.708572 | − | 0.705638i | \(-0.750660\pi\) | ||||
−0.708572 | + | 0.705638i | \(0.750660\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.70246 | −0.236541 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.23607 | 0.333163 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.61435 | 0.606853 | 0.303426 | − | 0.952855i | \(-0.401869\pi\) | ||||
0.303426 | + | 0.952855i | \(0.401869\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.94427 | 0.310844 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −21.1344 | −1.31833 | −0.659164 | − | 0.752000i | \(-0.729090\pi\) | ||||
−0.659164 | + | 0.752000i | \(0.729090\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.00000 | −0.372822 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.82068 | 0.605569 | 0.302785 | − | 0.953059i | \(-0.402084\pi\) | ||||
0.302785 | + | 0.953059i | \(0.402084\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −34.6525 | −2.12868 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.3168 | −0.811940 | −0.405970 | − | 0.913886i | \(-0.633066\pi\) | ||||
−0.405970 | + | 0.913886i | \(0.633066\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.4164 | −0.936480 | −0.468240 | − | 0.883601i | \(-0.655112\pi\) | ||||
−0.468240 | + | 0.883601i | \(0.655112\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 39.8530 | 2.40323 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.2361 | −0.795278 | −0.397639 | − | 0.917542i | \(-0.630170\pi\) | ||||
−0.397639 | + | 0.917542i | \(0.630170\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.5123 | −1.10435 | −0.552175 | − | 0.833728i | \(-0.686202\pi\) | ||||
−0.552175 | + | 0.833728i | \(0.686202\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.47214 | −0.146953 | −0.0734766 | − | 0.997297i | \(-0.523409\pi\) | ||||
−0.0734766 | + | 0.997297i | \(0.523409\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.57649 | 0.270142 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.2361 | −0.955063 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.41577 | 0.141131 | 0.0705653 | − | 0.997507i | \(-0.477520\pi\) | ||||
0.0705653 | + | 0.997507i | \(0.477520\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −46.8328 | −2.72671 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.65685 | −0.327144 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.1803 | 0.702063 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 40.5207 | 2.32021 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.18034 | 0.466877 | 0.233438 | − | 0.972372i | \(-0.425002\pi\) | ||||
0.233438 | + | 0.972372i | \(0.425002\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 27.2526 | 1.54535 | 0.772677 | − | 0.634799i | \(-0.218917\pi\) | ||||
0.772677 | + | 0.634799i | \(0.218917\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −34.3607 | −1.94218 | −0.971090 | − | 0.238713i | \(-0.923275\pi\) | ||||
−0.971090 | + | 0.238713i | \(0.923275\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 24.4242 | 1.37180 | 0.685900 | − | 0.727696i | \(-0.259409\pi\) | ||||
0.685900 | + | 0.727696i | \(0.259409\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 21.8885 | 1.22552 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.874032 | −0.0486324 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −45.5967 | −2.52925 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −10.0270 | −0.552807 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.4164 | 0.847362 | 0.423681 | − | 0.905811i | \(-0.360738\pi\) | ||||
0.423681 | + | 0.905811i | \(0.360738\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −23.9628 | −1.30923 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −35.8885 | −1.95497 | −0.977487 | − | 0.210997i | \(-0.932329\pi\) | ||||
−0.977487 | + | 0.210997i | \(0.932329\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −33.1158 | −1.79332 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −18.9737 | −1.01856 | −0.509280 | − | 0.860601i | \(-0.670088\pi\) | ||||
−0.509280 | + | 0.860601i | \(0.670088\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.4164 | −0.718164 | −0.359082 | − | 0.933306i | \(-0.616910\pi\) | ||||
−0.359082 | + | 0.933306i | \(0.616910\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.6808 | 0.728154 | 0.364077 | − | 0.931369i | \(-0.381385\pi\) | ||||
0.364077 | + | 0.931369i | \(0.381385\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.763932 | 0.0405453 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.7295 | 0.724614 | 0.362307 | − | 0.932059i | \(-0.381989\pi\) | ||||
0.362307 | + | 0.932059i | \(0.381989\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 46.1776 | 2.41704 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −24.3607 | −1.27162 | −0.635809 | − | 0.771847i | \(-0.719333\pi\) | ||||
−0.635809 | + | 0.771847i | \(0.719333\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.35931 | 0.485911 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.9443 | −1.18801 | −0.594005 | − | 0.804462i | \(-0.702454\pi\) | ||||
−0.594005 | + | 0.804462i | \(0.702454\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −25.0432 | −1.28979 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.05573 | −0.362428 | −0.181214 | − | 0.983444i | \(-0.558003\pi\) | ||||
−0.181214 | + | 0.983444i | \(0.558003\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.90879 | 0.199730 | 0.0998649 | − | 0.995001i | \(-0.468159\pi\) | ||||
0.0998649 | + | 0.995001i | \(0.468159\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16.9443 | −0.863560 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.412662 | −0.0209228 | −0.0104614 | − | 0.999945i | \(-0.503330\pi\) | ||||
−0.0104614 | + | 0.999945i | \(0.503330\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.944272 | 0.0477539 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 47.9256 | 2.41140 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 31.8885 | 1.60044 | 0.800220 | − | 0.599706i | \(-0.204716\pi\) | ||||
0.800220 | + | 0.599706i | \(0.204716\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.28980 | −0.164285 | −0.0821423 | − | 0.996621i | \(-0.526176\pi\) | ||||
−0.0821423 | + | 0.996621i | \(0.526176\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 37.8885 | 1.88736 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −27.4589 | −1.36109 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.7082 | 0.578933 | 0.289467 | − | 0.957188i | \(-0.406522\pi\) | ||||
0.289467 | + | 0.957188i | \(0.406522\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12.6491 | 0.622422 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 62.0689 | 3.04684 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.69936 | 0.0830190 | 0.0415095 | − | 0.999138i | \(-0.486783\pi\) | ||||
0.0415095 | + | 0.999138i | \(0.486783\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.3607 | 1.47969 | 0.739844 | − | 0.672778i | \(-0.234899\pi\) | ||||
0.739844 | + | 0.672778i | \(0.234899\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.61125 | 0.369200 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.9443 | −0.529630 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.7534 | 1.04782 | 0.523912 | − | 0.851772i | \(-0.324472\pi\) | ||||
0.523912 | + | 0.851772i | \(0.324472\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.111456 | −0.00535624 | −0.00267812 | − | 0.999996i | \(-0.500852\pi\) | ||||
−0.00267812 | + | 0.999996i | \(0.500852\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.08036 | −0.0516808 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 38.0689 | 1.81693 | 0.908464 | − | 0.417962i | \(-0.137256\pi\) | ||||
0.908464 | + | 0.417962i | \(0.137256\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 35.1189 | 1.66855 | 0.834275 | − | 0.551349i | \(-0.185887\pi\) | ||||
0.834275 | + | 0.551349i | \(0.185887\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16.9443 | −0.803236 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −31.5741 | −1.49007 | −0.745036 | − | 0.667024i | \(-0.767568\pi\) | ||||
−0.745036 | + | 0.667024i | \(0.767568\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20.9443 | 0.986227 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 19.3863 | 0.908845 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −26.7639 | −1.25196 | −0.625982 | − | 0.779838i | \(-0.715302\pi\) | ||||
−0.625982 | + | 0.779838i | \(0.715302\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 40.0593 | 1.86575 | 0.932875 | − | 0.360200i | \(-0.117292\pi\) | ||||
0.932875 | + | 0.360200i | \(0.117292\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.05573 | 0.327907 | 0.163954 | − | 0.986468i | \(-0.447575\pi\) | ||||
0.163954 | + | 0.986468i | \(0.447575\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 21.5958 | 0.999333 | 0.499666 | − | 0.866218i | \(-0.333456\pi\) | ||||
0.499666 | + | 0.866218i | \(0.333456\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.47214 | 0.298855 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 55.7432 | 2.56308 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.70820 | −0.399560 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 24.8369 | 1.13482 | 0.567412 | − | 0.823434i | \(-0.307945\pi\) | ||||
0.567412 | + | 0.823434i | \(0.307945\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 31.4164 | 1.43246 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −34.8639 | −1.58309 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.8328 | −0.490882 | −0.245441 | − | 0.969412i | \(-0.578933\pi\) | ||||
−0.245441 | + | 0.969412i | \(0.578933\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.9814 | −0.540713 | −0.270357 | − | 0.962760i | \(-0.587142\pi\) | ||||
−0.270357 | + | 0.962760i | \(0.587142\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.18034 | 0.188273 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.206331 | −0.00925521 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.0557 | 0.494922 | 0.247461 | − | 0.968898i | \(-0.420404\pi\) | ||||
0.247461 | + | 0.968898i | \(0.420404\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −19.3376 | −0.862222 | −0.431111 | − | 0.902299i | \(-0.641878\pi\) | ||||
−0.431111 | + | 0.902299i | \(0.641878\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −51.5967 | −2.29603 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 21.1344 | 0.936765 | 0.468383 | − | 0.883526i | \(-0.344837\pi\) | ||||
0.468383 | + | 0.883526i | \(0.344837\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.4721 | −0.551735 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −18.3060 | −0.806657 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −45.8885 | −2.01818 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16.3029 | −0.714241 | −0.357121 | − | 0.934058i | \(-0.616242\pi\) | ||||
−0.357121 | + | 0.934058i | \(0.616242\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.2918 | 0.624937 | 0.312468 | − | 0.949928i | \(-0.398844\pi\) | ||||
0.312468 | + | 0.949928i | \(0.398844\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.32456 | −0.275502 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.8328 | −0.949253 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −23.9628 | −1.03794 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 50.0689 | 2.16467 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.57649 | 0.197123 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.4164 | −0.576816 | −0.288408 | − | 0.957508i | \(-0.593126\pi\) | ||||
−0.288408 | + | 0.957508i | \(0.593126\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 40.5207 | 1.73572 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.9443 | −1.06654 | −0.533270 | − | 0.845945i | \(-0.679037\pi\) | ||||
−0.533270 | + | 0.845945i | \(0.679037\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.78282 | −0.203755 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.9443 | −0.550446 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12.2364 | −0.518475 | −0.259237 | − | 0.965814i | \(-0.583471\pi\) | ||||
−0.259237 | + | 0.965814i | \(0.583471\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −63.7771 | −2.69748 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −17.8933 | −0.754113 | −0.377056 | − | 0.926190i | \(-0.623064\pi\) | ||||
−0.377056 | + | 0.926190i | \(0.623064\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 32.1803 | 1.35384 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.4288 | 0.646810 | 0.323405 | − | 0.946261i | \(-0.395172\pi\) | ||||
0.323405 | + | 0.946261i | \(0.395172\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.0557 | 0.630063 | 0.315031 | − | 0.949081i | \(-0.397985\pi\) | ||||
0.315031 | + | 0.949081i | \(0.397985\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.40802 | 0.392342 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.3607 | 0.597843 | 0.298921 | − | 0.954278i | \(-0.403373\pi\) | ||||
0.298921 | + | 0.954278i | \(0.403373\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.7642 | −0.695498 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 42.8328 | 1.77395 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.44742 | 0.142290 | 0.0711451 | − | 0.997466i | \(-0.477335\pi\) | ||||
0.0711451 | + | 0.997466i | \(0.477335\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.23607 | 0.298157 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 25.9172 | 1.06429 | 0.532146 | − | 0.846652i | \(-0.321386\pi\) | ||||
0.532146 | + | 0.846652i | \(0.321386\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.23607 | −0.132666 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.5927 | −0.800534 | −0.400267 | − | 0.916398i | \(-0.631083\pi\) | ||||
−0.400267 | + | 0.916398i | \(0.631083\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.4164 | 0.547267 | 0.273633 | − | 0.961834i | \(-0.411775\pi\) | ||||
0.273633 | + | 0.961834i | \(0.411775\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −36.8183 | −1.49688 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −29.8885 | −1.21314 | −0.606569 | − | 0.795031i | \(-0.707455\pi\) | ||||
−0.606569 | + | 0.795031i | \(0.707455\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 52.5021 | 2.12401 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 37.5967 | 1.51852 | 0.759259 | − | 0.650788i | \(-0.225561\pi\) | ||||
0.759259 | + | 0.650788i | \(0.225561\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −42.2688 | −1.70168 | −0.850839 | − | 0.525427i | \(-0.823906\pi\) | ||||
−0.850839 | + | 0.525427i | \(0.823906\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.52786 | −0.0614100 | −0.0307050 | − | 0.999528i | \(-0.509775\pi\) | ||||
−0.0307050 | + | 0.999528i | \(0.509775\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.57649 | 0.183353 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.29180 | 0.291672 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.24419 | −0.209100 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.1803 | 0.962604 | 0.481302 | − | 0.876555i | \(-0.340164\pi\) | ||||
0.481302 | + | 0.876555i | \(0.340164\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 68.3923 | 2.71407 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.23607 | −0.207461 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.03476 | 0.119866 | 0.0599329 | − | 0.998202i | \(-0.480911\pi\) | ||||
0.0599329 | + | 0.998202i | \(0.480911\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.5279 | 0.533487 | 0.266743 | − | 0.963768i | \(-0.414052\pi\) | ||||
0.266743 | + | 0.963768i | \(0.414052\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −36.9759 | −1.45367 | −0.726836 | − | 0.686811i | \(-0.759010\pi\) | ||||
−0.726836 | + | 0.686811i | \(0.759010\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 57.8885 | 2.27232 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12.6491 | −0.494998 | −0.247499 | − | 0.968888i | \(-0.579609\pi\) | ||||
−0.247499 | + | 0.968888i | \(0.579609\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 34.6525 | 1.35398 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.0084 | 0.857326 | 0.428663 | − | 0.903464i | \(-0.358985\pi\) | ||||
0.428663 | + | 0.903464i | \(0.358985\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.1803 | 1.32946 | 0.664731 | − | 0.747083i | \(-0.268546\pi\) | ||||
0.664731 | + | 0.747083i | \(0.268546\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.70246 | 0.143575 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.16718 | 0.200074 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −50.0864 | −1.93356 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.3050 | 0.744151 | 0.372076 | − | 0.928202i | \(-0.378646\pi\) | ||||
0.372076 | + | 0.928202i | \(0.378646\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −33.2734 | −1.27880 | −0.639401 | − | 0.768874i | \(-0.720818\pi\) | ||||
−0.639401 | + | 0.768874i | \(0.720818\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.41641 | 0.361369 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.461370 | −0.0176538 | −0.00882692 | − | 0.999961i | \(-0.502810\pi\) | ||||
−0.00882692 | + | 0.999961i | \(0.502810\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −67.7771 | −2.58963 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −49.0060 | −1.86698 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −50.2492 | −1.91157 | −0.955785 | − | 0.294065i | \(-0.904992\pi\) | ||||
−0.955785 | + | 0.294065i | \(0.904992\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.65685 | −0.214577 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.00000 | 0.151511 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.99226 | −0.264094 | −0.132047 | − | 0.991243i | \(-0.542155\pi\) | ||||
−0.132047 | + | 0.991243i | \(0.542155\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.00000 | 0.226294 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.9358 | 0.524110 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.29180 | 0.161182 | 0.0805909 | − | 0.996747i | \(-0.474319\pi\) | ||||
0.0805909 | + | 0.996747i | \(0.474319\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.81758 | −0.292771 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 88.7214 | 3.31799 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.03165 | 0.0384742 | 0.0192371 | − | 0.999815i | \(-0.493876\pi\) | ||||
0.0192371 | + | 0.999815i | \(0.493876\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.94427 | 0.184134 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 41.6498 | 1.54683 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.11146 | −0.0783096 | −0.0391548 | − | 0.999233i | \(-0.512467\pi\) | ||||
−0.0391548 | + | 0.999233i | \(0.512467\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.6460 | 0.393757 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.5836 | 0.390914 | 0.195457 | − | 0.980712i | \(-0.437381\pi\) | ||||
0.195457 | + | 0.980712i | \(0.437381\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 29.6197 | 1.09105 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22.0689 | −0.811817 | −0.405909 | − | 0.913914i | \(-0.633045\pi\) | ||||
−0.405909 | + | 0.913914i | \(0.633045\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25.2495 | 0.926315 | 0.463157 | − | 0.886276i | \(-0.346716\pi\) | ||||
0.463157 | + | 0.886276i | \(0.346716\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 27.4164 | 1.00446 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −13.5231 | −0.494125 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.05573 | 0.111505 | 0.0557526 | − | 0.998445i | \(-0.482244\pi\) | ||||
0.0557526 | + | 0.998445i | \(0.482244\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 47.9256 | 1.74419 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.5836 | −0.530050 | −0.265025 | − | 0.964242i | \(-0.585380\pi\) | ||||
−0.265025 | + | 0.964242i | \(0.585380\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.9389 | 0.577785 | 0.288892 | − | 0.957362i | \(-0.406713\pi\) | ||||
0.288892 | + | 0.957362i | \(0.406713\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.9443 | −0.396209 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −66.2316 | −2.39148 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.3050 | 0.696154 | 0.348077 | − | 0.937466i | \(-0.386835\pi\) | ||||
0.348077 | + | 0.937466i | \(0.386835\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −26.3786 | −0.948772 | −0.474386 | − | 0.880317i | \(-0.657330\pi\) | ||||
−0.474386 | + | 0.880317i | \(0.657330\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −63.0132 | −2.26350 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.57649 | −0.163970 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.944272 | −0.0337887 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.74806 | −0.0623911 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.2361 | −0.685692 | −0.342846 | − | 0.939392i | \(-0.611391\pi\) | ||||
−0.342846 | + | 0.939392i | \(0.611391\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.69161 | −0.309038 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 57.3050 | 2.03496 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.40182 | −0.191342 | −0.0956711 | − | 0.995413i | \(-0.530500\pi\) | ||||
−0.0956711 | + | 0.995413i | \(0.530500\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.76393 | −0.310046 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −57.0786 | −2.01426 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.00000 | −0.140981 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −37.4373 | −1.31622 | −0.658112 | − | 0.752920i | \(-0.728645\pi\) | ||||
−0.658112 | + | 0.752920i | \(0.728645\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.944272 | −0.0331579 | −0.0165789 | − | 0.999863i | \(-0.505277\pi\) | ||||
−0.0165789 | + | 0.999863i | \(0.505277\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.82843 | −0.0990755 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12.1803 | −0.426136 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.922740 | −0.0322039 | −0.0161019 | − | 0.999870i | \(-0.505126\pi\) | ||||
−0.0161019 | + | 0.999870i | \(0.505126\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.3475 | 0.883559 | 0.441780 | − | 0.897124i | \(-0.354347\pi\) | ||||
0.441780 | + | 0.897124i | \(0.354347\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.27585 | 0.218233 | 0.109116 | − | 0.994029i | \(-0.465198\pi\) | ||||
0.109116 | + | 0.994029i | \(0.465198\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.58359 | −0.0897319 | −0.0448659 | − | 0.998993i | \(-0.514286\pi\) | ||||
−0.0448659 | + | 0.998993i | \(0.514286\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.874032 | 0.0302834 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −22.4721 | −0.777680 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 36.6119 | 1.26398 | 0.631992 | − | 0.774975i | \(-0.282238\pi\) | ||||
0.631992 | + | 0.774975i | \(0.282238\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.12461 | −0.211194 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −53.3762 | −1.83620 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.94427 | 0.341689 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.48218 | −0.222206 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.5279 | 0.531664 | 0.265832 | − | 0.964019i | \(-0.414353\pi\) | ||||
0.265832 | + | 0.964019i | \(0.414353\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 46.8453 | 1.60020 | 0.800102 | − | 0.599864i | \(-0.204779\pi\) | ||||
0.800102 | + | 0.599864i | \(0.204779\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.58359 | 0.292868 | 0.146434 | − | 0.989220i | \(-0.453220\pi\) | ||||
0.146434 | + | 0.989220i | \(0.453220\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −46.2263 | −1.57356 | −0.786780 | − | 0.617233i | \(-0.788254\pi\) | ||||
−0.786780 | + | 0.617233i | \(0.788254\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 58.8328 | 2.00038 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −59.2393 | −2.00956 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −33.8885 | −1.14827 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −13.7295 | −0.464141 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −24.8328 | −0.838545 | −0.419272 | − | 0.907861i | \(-0.637715\pi\) | ||||
−0.419272 | + | 0.907861i | \(0.637715\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 58.1103 | 1.95778 | 0.978892 | − | 0.204376i | \(-0.0655165\pi\) | ||||
0.978892 | + | 0.204376i | \(0.0655165\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.0000 | 0.807664 | 0.403832 | − | 0.914833i | \(-0.367678\pi\) | ||||
0.403832 | + | 0.914833i | \(0.367678\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20.0540 | 0.673348 | 0.336674 | − | 0.941621i | \(-0.390698\pi\) | ||||
0.336674 | + | 0.941621i | \(0.390698\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.4721 | −0.619536 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.0270 | 0.335541 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 85.4853 | 2.85746 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −34.6088 | −1.15427 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.18034 | 0.272527 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −58.8267 | −1.95547 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.05573 | 0.101464 | 0.0507319 | − | 0.998712i | \(-0.483845\pi\) | ||||
0.0507319 | + | 0.998712i | \(0.483845\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.12133 | −0.269072 | −0.134536 | − | 0.990909i | \(-0.542954\pi\) | ||||
−0.134536 | + | 0.990909i | \(0.542954\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −76.7214 | −2.53911 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.35931 | −0.309072 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.9443 | 0.690888 | 0.345444 | − | 0.938439i | \(-0.387728\pi\) | ||||
0.345444 | + | 0.938439i | \(0.387728\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.08036 | 0.0355606 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −52.2492 | −1.71794 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 50.1351 | 1.64488 | 0.822439 | − | 0.568853i | \(-0.192613\pi\) | ||||
0.822439 | + | 0.568853i | \(0.192613\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.00000 | −0.0327737 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −14.8098 | −0.484333 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −36.8328 | −1.20328 | −0.601638 | − | 0.798769i | \(-0.705485\pi\) | ||||
−0.601638 | + | 0.798769i | \(0.705485\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.65375 | −0.119109 | −0.0595544 | − | 0.998225i | \(-0.518968\pi\) | ||||
−0.0595544 | + | 0.998225i | \(0.518968\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.94427 | 0.161008 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12.3941 | 0.402753 | 0.201377 | − | 0.979514i | \(-0.435458\pi\) | ||||
0.201377 | + | 0.979514i | \(0.435458\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 65.3050 | 2.11989 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −24.5818 | −0.796283 | −0.398141 | − | 0.917324i | \(-0.630345\pi\) | ||||
−0.398141 | + | 0.917324i | \(0.630345\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.9443 | 0.548304 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 18.3060 | 0.591130 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21.3607 | 0.689054 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 20.0540 | 0.645562 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19.2361 | −0.618590 | −0.309295 | − | 0.950966i | \(-0.600093\pi\) | ||||
−0.309295 | + | 0.950966i | \(0.600093\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.65685 | −0.181537 | −0.0907685 | − | 0.995872i | \(-0.528932\pi\) | ||||
−0.0907685 | + | 0.995872i | \(0.528932\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.52786 | 0.0489811 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −7.61125 | −0.243505 | −0.121753 | − | 0.992560i | \(-0.538851\pi\) | ||||
−0.121753 | + | 0.992560i | \(0.538851\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20.9443 | 0.669382 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 32.6057 | 1.03996 | 0.519981 | − | 0.854178i | \(-0.325939\pi\) | ||||
0.519981 | + | 0.854178i | \(0.325939\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 25.8885 | 0.824878 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13.1592 | 0.418438 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36.0000 | 1.14358 | 0.571789 | − | 0.820401i | \(-0.306250\pi\) | ||||
0.571789 | + | 0.820401i | \(0.306250\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.3137 | 0.358669 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −36.4721 | −1.15508 | −0.577542 | − | 0.816361i | \(-0.695988\pi\) | ||||
−0.577542 | + | 0.816361i | \(0.695988\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4788.2.a.r.1.1 | ✓ | 4 | |
3.2 | odd | 2 | inner | 4788.2.a.r.1.4 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4788.2.a.r.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
4788.2.a.r.1.4 | yes | 4 | 3.2 | odd | 2 | inner |