Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4704,2,Mod(1,4704)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4704, 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("4704.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4704 = 2^{5} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4704.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: | \(37.5616291108\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.2624.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 3x^{2} + 2x + 1 \) |
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 | \(-0.360409\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4704.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.13503 | −0.954815 | −0.477408 | − | 0.878682i | \(-0.658424\pi\) | ||||
−0.477408 | + | 0.878682i | \(0.658424\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.298573 | −0.0900231 | −0.0450116 | − | 0.998986i | \(-0.514332\pi\) | ||||
−0.0450116 | + | 0.998986i | \(0.514332\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.43361 | 1.78436 | 0.892181 | − | 0.451679i | \(-0.149175\pi\) | ||||
0.892181 | + | 0.451679i | \(0.149175\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.13503 | −0.551263 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.11564 | 0.270583 | 0.135291 | − | 0.990806i | \(-0.456803\pi\) | ||||
0.135291 | + | 0.990806i | \(0.456803\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.01939 | −0.233864 | −0.116932 | − | 0.993140i | \(-0.537306\pi\) | ||||
−0.116932 | + | 0.993140i | \(0.537306\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.29857 | 0.896314 | 0.448157 | − | 0.893955i | \(-0.352080\pi\) | ||||
0.448157 | + | 0.893955i | \(0.352080\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.441637 | −0.0883275 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.422246 | −0.0784091 | −0.0392045 | − | 0.999231i | \(-0.512482\pi\) | ||||
−0.0392045 | + | 0.999231i | \(0.512482\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.6762 | −1.91751 | −0.958755 | − | 0.284233i | \(-0.908261\pi\) | ||||
−0.958755 | + | 0.284233i | \(0.908261\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.298573 | −0.0519749 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.65685 | −0.929981 | −0.464991 | − | 0.885316i | \(-0.653942\pi\) | ||||
−0.464991 | + | 0.885316i | \(0.653942\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.43361 | 1.03020 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.32600 | 1.30030 | 0.650151 | − | 0.759805i | \(-0.274706\pi\) | ||||
0.650151 | + | 0.759805i | \(0.274706\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.09849 | 1.08251 | 0.541255 | − | 0.840859i | \(-0.317949\pi\) | ||||
0.541255 | + | 0.840859i | \(0.317949\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.13503 | −0.318272 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.11788 | 1.18411 | 0.592057 | − | 0.805896i | \(-0.298316\pi\) | ||||
0.592057 | + | 0.805896i | \(0.298316\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.11564 | 0.156221 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.44164 | −0.472745 | −0.236373 | − | 0.971662i | \(-0.575959\pi\) | ||||
−0.236373 | + | 0.971662i | \(0.575959\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.637463 | 0.0859555 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.01939 | −0.135022 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.46103 | 0.841154 | 0.420577 | − | 0.907257i | \(-0.361828\pi\) | ||||
0.420577 | + | 0.907257i | \(0.361828\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.83646 | 0.747282 | 0.373641 | − | 0.927573i | \(-0.378109\pi\) | ||||
0.373641 | + | 0.927573i | \(0.378109\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −13.7360 | −1.70374 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.05971 | −0.618142 | −0.309071 | − | 0.951039i | \(-0.600018\pi\) | ||||
−0.309071 | + | 0.951039i | \(0.600018\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.29857 | 0.517487 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.35828 | −0.161198 | −0.0805992 | − | 0.996747i | \(-0.525683\pi\) | ||||
−0.0805992 | + | 0.996747i | \(0.525683\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.85585 | −0.334252 | −0.167126 | − | 0.985936i | \(-0.553449\pi\) | ||||
−0.167126 | + | 0.985936i | \(0.553449\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.441637 | −0.0509959 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.69564 | −0.865827 | −0.432913 | − | 0.901436i | \(-0.642514\pi\) | ||||
−0.432913 | + | 0.901436i | \(0.642514\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.03878 | 0.662843 | 0.331421 | − | 0.943483i | \(-0.392472\pi\) | ||||
0.331421 | + | 0.943483i | \(0.392472\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.38193 | −0.258356 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.422246 | −0.0452695 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.3696 | 1.62918 | 0.814589 | − | 0.580038i | \(-0.196962\pi\) | ||||
0.814589 | + | 0.580038i | \(0.196962\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.6762 | −1.10708 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.17643 | 0.223297 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.512705 | −0.0520573 | −0.0260287 | − | 0.999661i | \(-0.508286\pi\) | ||||
−0.0260287 | + | 0.999661i | \(0.508286\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.298573 | −0.0300077 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.96346 | −0.493883 | −0.246941 | − | 0.969030i | \(-0.579425\pi\) | ||||
−0.246941 | + | 0.969030i | \(0.579425\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.48195 | −0.934285 | −0.467142 | − | 0.884182i | \(-0.654716\pi\) | ||||
−0.467142 | + | 0.884182i | \(0.654716\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.8387 | 1.62786 | 0.813929 | − | 0.580964i | \(-0.197324\pi\) | ||||
0.813929 | + | 0.580964i | \(0.197324\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.09849 | 0.296782 | 0.148391 | − | 0.988929i | \(-0.452591\pi\) | ||||
0.148391 | + | 0.988929i | \(0.452591\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.65685 | −0.536925 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.31371 | 0.876160 | 0.438080 | − | 0.898936i | \(-0.355659\pi\) | ||||
0.438080 | + | 0.898936i | \(0.355659\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.17759 | −0.855815 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.43361 | 0.594787 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9109 | −0.991896 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.32600 | 0.750730 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.6181 | 1.03915 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.1373 | −1.52069 | −0.760344 | − | 0.649521i | \(-0.774969\pi\) | ||||
−0.760344 | + | 0.649521i | \(0.774969\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.09849 | 0.624987 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.1582 | 1.41175 | 0.705874 | − | 0.708337i | \(-0.250554\pi\) | ||||
0.705874 | + | 0.708337i | \(0.250554\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.13503 | −0.183754 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 21.7747 | 1.86034 | 0.930171 | − | 0.367127i | \(-0.119659\pi\) | ||||
0.930171 | + | 0.367127i | \(0.119659\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.3137 | 1.29889 | 0.649446 | − | 0.760408i | \(-0.275001\pi\) | ||||
0.649446 | + | 0.760408i | \(0.275001\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.11788 | 0.683649 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.92090 | −0.160634 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.901508 | 0.0748662 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.87207 | −0.317212 | −0.158606 | − | 0.987342i | \(-0.550700\pi\) | ||||
−0.158606 | + | 0.987342i | \(0.550700\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.75535 | 0.386985 | 0.193492 | − | 0.981102i | \(-0.438019\pi\) | ||||
0.193492 | + | 0.981102i | \(0.438019\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.11564 | 0.0901942 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 22.7941 | 1.83087 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.5482 | 0.921644 | 0.460822 | − | 0.887493i | \(-0.347555\pi\) | ||||
0.460822 | + | 0.887493i | \(0.347555\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.44164 | −0.272940 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.9109 | 0.932930 | 0.466465 | − | 0.884540i | \(-0.345527\pi\) | ||||
0.466465 | + | 0.884540i | \(0.345527\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.637463 | 0.0496264 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −15.2734 | −1.18189 | −0.590945 | − | 0.806712i | \(-0.701245\pi\) | ||||
−0.590945 | + | 0.806712i | \(0.701245\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 28.3913 | 2.18394 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.01939 | −0.0779548 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.00710 | −0.304654 | −0.152327 | − | 0.988330i | \(-0.548677\pi\) | ||||
−0.152327 | + | 0.988330i | \(0.548677\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.46103 | 0.485641 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20.7496 | −1.55089 | −0.775447 | − | 0.631412i | \(-0.782476\pi\) | ||||
−0.775447 | + | 0.631412i | \(0.782476\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.7246 | 1.61478 | 0.807388 | − | 0.590021i | \(-0.200880\pi\) | ||||
0.807388 | + | 0.590021i | \(0.200880\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.83646 | 0.431443 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 12.0776 | 0.887960 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.333100 | −0.0243587 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.6720 | −1.49577 | −0.747886 | − | 0.663827i | \(-0.768931\pi\) | ||||
−0.747886 | + | 0.663827i | \(0.768931\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.5998 | 1.12290 | 0.561450 | − | 0.827510i | \(-0.310244\pi\) | ||||
0.561450 | + | 0.827510i | \(0.310244\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −13.7360 | −0.983652 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 25.6386 | 1.82668 | 0.913338 | − | 0.407202i | \(-0.133496\pi\) | ||||
0.913338 | + | 0.407202i | \(0.133496\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.88327 | 0.204390 | 0.102195 | − | 0.994764i | \(-0.467413\pi\) | ||||
0.102195 | + | 0.994764i | \(0.467413\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.05971 | −0.356884 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −17.7763 | −1.24155 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.29857 | 0.298771 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.304363 | 0.0210532 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −24.5401 | −1.68941 | −0.844706 | − | 0.535230i | \(-0.820225\pi\) | ||||
−0.844706 | + | 0.535230i | \(0.820225\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.35828 | −0.0930679 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −15.1555 | −1.03360 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.85585 | −0.192981 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.17759 | 0.482817 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.5080 | 1.37332 | 0.686659 | − | 0.726980i | \(-0.259077\pi\) | ||||
0.686659 | + | 0.726980i | \(0.259077\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.441637 | −0.0294425 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.6972 | 0.909113 | 0.454557 | − | 0.890718i | \(-0.349798\pi\) | ||||
0.454557 | + | 0.890718i | \(0.349798\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.4175 | 1.08490 | 0.542451 | − | 0.840088i | \(-0.317496\pi\) | ||||
0.542451 | + | 0.840088i | \(0.317496\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.8915 | −0.713523 | −0.356762 | − | 0.934195i | \(-0.616119\pi\) | ||||
−0.356762 | + | 0.934195i | \(0.616119\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −17.3319 | −1.13061 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.69564 | −0.499885 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.29857 | 0.278052 | 0.139026 | − | 0.990289i | \(-0.455603\pi\) | ||||
0.139026 | + | 0.990289i | \(0.455603\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.12808 | 0.459160 | 0.229580 | − | 0.973290i | \(-0.426265\pi\) | ||||
0.229580 | + | 0.973290i | \(0.426265\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.55836 | −0.417299 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.03878 | 0.382692 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.9690 | −1.19731 | −0.598657 | − | 0.801005i | \(-0.704299\pi\) | ||||
−0.598657 | + | 0.801005i | \(0.704299\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.28344 | −0.0806890 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.38193 | −0.149162 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.4842 | 1.27777 | 0.638885 | − | 0.769303i | \(-0.279396\pi\) | ||||
0.638885 | + | 0.769303i | \(0.279396\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.422246 | −0.0261364 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 23.5553 | 1.45248 | 0.726240 | − | 0.687441i | \(-0.241266\pi\) | ||||
0.726240 | + | 0.687441i | \(0.241266\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.34801 | 0.451384 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.3696 | 0.940607 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.9086 | 0.787052 | 0.393526 | − | 0.919313i | \(-0.371255\pi\) | ||||
0.393526 | + | 0.919313i | \(0.371255\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.8705 | −1.20705 | −0.603525 | − | 0.797344i | \(-0.706237\pi\) | ||||
−0.603525 | + | 0.797344i | \(0.706237\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.131861 | 0.00795151 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25.9884 | 1.56149 | 0.780746 | − | 0.624848i | \(-0.214839\pi\) | ||||
0.780746 | + | 0.624848i | \(0.214839\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.6762 | −0.639170 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.6553 | −1.17254 | −0.586269 | − | 0.810116i | \(-0.699404\pi\) | ||||
−0.586269 | + | 0.810116i | \(0.699404\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.0582 | 1.13289 | 0.566445 | − | 0.824099i | \(-0.308318\pi\) | ||||
0.566445 | + | 0.824099i | \(0.308318\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.17643 | 0.128921 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.7553 | −0.926785 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.512705 | −0.0300553 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.84890 | 0.458538 | 0.229269 | − | 0.973363i | \(-0.426366\pi\) | ||||
0.229269 | + | 0.973363i | \(0.426366\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.7945 | −0.803147 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.298573 | −0.0173250 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 27.6553 | 1.59935 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.96346 | −0.285143 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −12.4610 | −0.713516 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.5301 | 1.51415 | 0.757076 | − | 0.653327i | \(-0.226627\pi\) | ||||
0.757076 | + | 0.653327i | \(0.226627\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.48195 | −0.539410 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.726608 | −0.0412022 | −0.0206011 | − | 0.999788i | \(-0.506558\pi\) | ||||
−0.0206011 | + | 0.999788i | \(0.506558\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.1259 | 0.854967 | 0.427484 | − | 0.904023i | \(-0.359400\pi\) | ||||
0.427484 | + | 0.904023i | \(0.359400\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −19.9496 | −1.12048 | −0.560242 | − | 0.828329i | \(-0.689292\pi\) | ||||
−0.560242 | + | 0.828329i | \(0.689292\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.126071 | 0.00705863 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 16.8387 | 0.939845 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.13727 | −0.0632797 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.84132 | −0.157608 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.09849 | 0.171347 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.1943 | −0.945084 | −0.472542 | − | 0.881308i | \(-0.656663\pi\) | ||||
−0.472542 | + | 0.881308i | \(0.656663\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.65685 | −0.309994 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10.8026 | 0.590211 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.0388 | 0.546847 | 0.273424 | − | 0.961894i | \(-0.411844\pi\) | ||||
0.273424 | + | 0.961894i | \(0.411844\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.31371 | 0.505851 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.18764 | 0.172620 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −9.17759 | −0.494105 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.41799 | −0.129804 | −0.0649022 | − | 0.997892i | \(-0.520674\pi\) | ||||
−0.0649022 | + | 0.997892i | \(0.520674\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.26689 | −0.335459 | −0.167730 | − | 0.985833i | \(-0.553644\pi\) | ||||
−0.167730 | + | 0.985833i | \(0.553644\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.43361 | 0.343400 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.3099 | −0.548742 | −0.274371 | − | 0.961624i | \(-0.588470\pi\) | ||||
−0.274371 | + | 0.961624i | \(0.588470\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.89997 | 0.153915 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 17.8984 | 0.944642 | 0.472321 | − | 0.881427i | \(-0.343416\pi\) | ||||
0.472321 | + | 0.881427i | \(0.343416\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.9608 | −0.945307 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.9109 | −0.572671 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.09733 | 0.319149 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.0415 | −1.20276 | −0.601378 | − | 0.798965i | \(-0.705381\pi\) | ||||
−0.601378 | + | 0.798965i | \(0.705381\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.32600 | 0.433434 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.68898 | 0.191008 | 0.0955042 | − | 0.995429i | \(-0.469554\pi\) | ||||
0.0955042 | + | 0.995429i | \(0.469554\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.6181 | 0.599955 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.71656 | −0.139910 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.76386 | −0.450169 | −0.225085 | − | 0.974339i | \(-0.572266\pi\) | ||||
−0.225085 | + | 0.974339i | \(0.572266\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −17.1373 | −0.877969 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −21.7665 | −1.11222 | −0.556109 | − | 0.831109i | \(-0.687706\pi\) | ||||
−0.556109 | + | 0.831109i | \(0.687706\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.09849 | 0.360837 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.38346 | 0.323654 | 0.161827 | − | 0.986819i | \(-0.448261\pi\) | ||||
0.161827 | + | 0.986819i | \(0.448261\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.79566 | 0.242527 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 16.1582 | 0.815073 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 16.4304 | 0.826705 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.53210 | 0.277648 | 0.138824 | − | 0.990317i | \(-0.455668\pi\) | ||||
0.138824 | + | 0.990317i | \(0.455668\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.5778 | −0.777916 | −0.388958 | − | 0.921256i | \(-0.627165\pi\) | ||||
−0.388958 | + | 0.921256i | \(0.627165\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −68.6867 | −3.42153 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.13503 | −0.106091 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.68898 | 0.0837198 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.8625 | −0.833797 | −0.416899 | − | 0.908953i | \(-0.636883\pi\) | ||||
−0.416899 | + | 0.908953i | \(0.636883\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 21.7747 | 1.07407 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.8930 | −0.632892 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 15.3137 | 0.749916 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −27.8942 | −1.36272 | −0.681359 | − | 0.731949i | \(-0.738611\pi\) | ||||
−0.681359 | + | 0.731949i | \(0.738611\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −31.6774 | −1.54386 | −0.771931 | − | 0.635706i | \(-0.780709\pi\) | ||||
−0.771931 | + | 0.635706i | \(0.780709\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.11788 | 0.394705 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.492709 | −0.0238999 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.92090 | −0.0927419 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 24.8066 | 1.19489 | 0.597445 | − | 0.801910i | \(-0.296183\pi\) | ||||
0.597445 | + | 0.801910i | \(0.296183\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.4918 | 0.648374 | 0.324187 | − | 0.945993i | \(-0.394909\pi\) | ||||
0.324187 | + | 0.945993i | \(0.394909\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.901508 | 0.0432240 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.38193 | −0.209616 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −35.3137 | −1.68543 | −0.842716 | − | 0.538359i | \(-0.819044\pi\) | ||||
−0.842716 | + | 0.538359i | \(0.819044\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −30.4385 | −1.44618 | −0.723089 | − | 0.690755i | \(-0.757279\pi\) | ||||
−0.723089 | + | 0.690755i | \(0.757279\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −32.8147 | −1.55556 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.87207 | −0.183143 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.0000 | −0.849473 | −0.424736 | − | 0.905317i | \(-0.639633\pi\) | ||||
−0.424736 | + | 0.905317i | \(0.639633\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.48592 | −0.117057 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.75535 | 0.223426 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.1943 | 0.710759 | 0.355379 | − | 0.934722i | \(-0.384352\pi\) | ||||
0.355379 | + | 0.934722i | \(0.384352\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.11564 | 0.0520736 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 38.3935 | 1.78816 | 0.894082 | − | 0.447903i | \(-0.147829\pi\) | ||||
0.894082 | + | 0.447903i | \(0.147829\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.59984 | 0.260247 | 0.130123 | − | 0.991498i | \(-0.458463\pi\) | ||||
0.130123 | + | 0.991498i | \(0.458463\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 22.7941 | 1.05705 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −23.9717 | −1.10928 | −0.554639 | − | 0.832091i | \(-0.687144\pi\) | ||||
−0.554639 | + | 0.832091i | \(0.687144\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.5482 | 0.532111 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.11942 | −0.0974509 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.450201 | 0.0206567 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.44164 | −0.157582 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.23461 | 0.239175 | 0.119588 | − | 0.992824i | \(-0.461843\pi\) | ||||
0.119588 | + | 0.992824i | \(0.461843\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −36.3940 | −1.65942 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.09464 | 0.0497051 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.2447 | −0.509544 | −0.254772 | − | 0.967001i | \(-0.582000\pi\) | ||||
−0.254772 | + | 0.967001i | \(0.582000\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 11.9109 | 0.538627 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.5250 | −0.610374 | −0.305187 | − | 0.952292i | \(-0.598719\pi\) | ||||
−0.305187 | + | 0.952292i | \(0.598719\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.471075 | −0.0212161 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.637463 | 0.0286518 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.87207 | 0.441935 | 0.220967 | − | 0.975281i | \(-0.429079\pi\) | ||||
0.220967 | + | 0.975281i | \(0.429079\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15.2734 | −0.682365 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −39.0415 | −1.74077 | −0.870387 | − | 0.492369i | \(-0.836131\pi\) | ||||
−0.870387 | + | 0.492369i | \(0.836131\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.5971 | 0.471567 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 28.3913 | 1.26090 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −24.2202 | −1.07354 | −0.536770 | − | 0.843729i | \(-0.680356\pi\) | ||||
−0.536770 | + | 0.843729i | \(0.680356\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.01939 | −0.0450072 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 20.2443 | 0.892069 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.42378 | −0.106598 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.00710 | −0.175892 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22.1638 | −0.971012 | −0.485506 | − | 0.874233i | \(-0.661365\pi\) | ||||
−0.485506 | + | 0.874233i | \(0.661365\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 35.8053 | 1.56566 | 0.782829 | − | 0.622237i | \(-0.213776\pi\) | ||||
0.782829 | + | 0.622237i | \(0.213776\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −11.9109 | −0.518845 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.52227 | −0.196620 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.46103 | 0.280385 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 53.5662 | 2.32021 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −35.9512 | −1.55430 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −20.7496 | −0.895409 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.7941 | 0.550063 | 0.275031 | − | 0.961435i | \(-0.411312\pi\) | ||||
0.275031 | + | 0.961435i | \(0.411312\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 21.7246 | 0.932292 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.61538 | −0.283372 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.9675 | 1.23856 | 0.619280 | − | 0.785170i | \(-0.287424\pi\) | ||||
0.619280 | + | 0.785170i | \(0.287424\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.83646 | 0.249094 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.430434 | 0.0183371 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 12.0776 | 0.512664 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.75265 | 0.413233 | 0.206617 | − | 0.978422i | \(-0.433755\pi\) | ||||
0.206617 | + | 0.978422i | \(0.433755\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 45.6689 | 1.93159 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.333100 | −0.0140635 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.6192 | −0.447547 | −0.223774 | − | 0.974641i | \(-0.571838\pi\) | ||||
−0.223774 | + | 0.974641i | \(0.571838\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −19.8851 | −0.836571 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 37.1660 | 1.55808 | 0.779040 | − | 0.626974i | \(-0.215707\pi\) | ||||
0.779040 | + | 0.626974i | \(0.215707\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23.6956 | −0.991632 | −0.495816 | − | 0.868428i | \(-0.665131\pi\) | ||||
−0.495816 | + | 0.868428i | \(0.665131\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −20.6720 | −0.863585 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.89841 | −0.0791692 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.84465 | 0.409838 | 0.204919 | − | 0.978779i | \(-0.434307\pi\) | ||||
0.204919 | + | 0.978779i | \(0.434307\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 15.5998 | 0.648307 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.02758 | 0.0425580 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −13.7360 | −0.567912 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 30.4610 | 1.25726 | 0.628631 | − | 0.777704i | \(-0.283616\pi\) | ||||
0.628631 | + | 0.777704i | \(0.283616\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.8833 | 0.448438 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 25.6386 | 1.05463 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10.0720 | −0.413607 | −0.206804 | − | 0.978382i | \(-0.566306\pi\) | ||||
−0.206804 | + | 0.978382i | \(0.566306\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.88327 | 0.118005 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 31.7220 | 1.29612 | 0.648062 | − | 0.761587i | \(-0.275580\pi\) | ||||
0.648062 | + | 0.761587i | \(0.275580\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.7533 | 1.21366 | 0.606832 | − | 0.794830i | \(-0.292440\pi\) | ||||
0.606832 | + | 0.794830i | \(0.292440\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.05971 | −0.206047 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 23.2950 | 0.947077 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17.6247 | −0.715366 | −0.357683 | − | 0.933843i | \(-0.616433\pi\) | ||||
−0.357683 | + | 0.933843i | \(0.616433\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 52.2273 | 2.11289 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.7068 | 0.513224 | 0.256612 | − | 0.966514i | \(-0.417394\pi\) | ||||
0.256612 | + | 0.966514i | \(0.417394\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −17.7763 | −0.716808 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −40.7386 | −1.64008 | −0.820038 | − | 0.572309i | \(-0.806048\pi\) | ||||
−0.820038 | + | 0.572309i | \(0.806048\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −46.9407 | −1.88671 | −0.943354 | − | 0.331788i | \(-0.892348\pi\) | ||||
−0.943354 | + | 0.331788i | \(0.892348\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.29857 | 0.172496 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.5968 | −0.903871 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.304363 | 0.0121551 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.31102 | −0.251637 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27.4804 | −1.09398 | −0.546989 | − | 0.837140i | \(-0.684226\pi\) | ||||
−0.546989 | + | 0.837140i | \(0.684226\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −24.5401 | −0.975383 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 36.5886 | 1.45198 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.35828 | −0.0537328 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −48.6580 | −1.92188 | −0.960938 | − | 0.276764i | \(-0.910738\pi\) | ||||
−0.960938 | + | 0.276764i | \(0.910738\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.6856 | 0.697452 | 0.348726 | − | 0.937225i | \(-0.386614\pi\) | ||||
0.348726 | + | 0.937225i | \(0.386614\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −15.1555 | −0.596748 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.04032 | 0.158841 | 0.0794206 | − | 0.996841i | \(-0.474693\pi\) | ||||
0.0794206 | + | 0.996841i | \(0.474693\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.92909 | −0.0757233 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 30.9690 | 1.21191 | 0.605956 | − | 0.795498i | \(-0.292791\pi\) | ||||
0.605956 | + | 0.795498i | \(0.292791\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −34.4983 | −1.34796 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.85585 | −0.111417 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.81815 | 0.187689 | 0.0938443 | − | 0.995587i | \(-0.470084\pi\) | ||||
0.0938443 | + | 0.995587i | \(0.470084\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.38324 | −0.170488 | −0.0852442 | − | 0.996360i | \(-0.527167\pi\) | ||||
−0.0852442 | + | 0.996360i | \(0.527167\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7.17759 | 0.278755 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.81505 | −0.0702792 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 20.5080 | 0.792885 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.74261 | −0.0672727 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.67471 | −0.334386 | −0.167193 | − | 0.985924i | \(-0.553470\pi\) | ||||
−0.167193 | + | 0.985924i | \(0.553470\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.441637 | −0.0169986 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.04103 | 0.0400099 | 0.0200049 | − | 0.999800i | \(-0.493632\pi\) | ||||
0.0200049 | + | 0.999800i | \(0.493632\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.6972 | 0.524877 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 35.7220 | 1.36686 | 0.683432 | − | 0.730014i | \(-0.260487\pi\) | ||||
0.683432 | + | 0.730014i | \(0.260487\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −46.4898 | −1.77628 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.4175 | 0.626368 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −22.1421 | −0.843548 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.9221 | −0.643745 | −0.321873 | − | 0.946783i | \(-0.604312\pi\) | ||||
−0.321873 | + | 0.946783i | \(0.604312\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −32.6953 | −1.24020 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.28882 | 0.351839 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10.8915 | −0.411953 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22.2052 | −0.838678 | −0.419339 | − | 0.907830i | \(-0.637738\pi\) | ||||
−0.419339 | + | 0.907830i | \(0.637738\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.76655 | 0.217490 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −17.3319 | −0.652759 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.35435 | −0.276198 | −0.138099 | − | 0.990418i | \(-0.544099\pi\) | ||||
−0.138099 | + | 0.990418i | \(0.544099\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.69564 | −0.288609 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −45.8926 | −1.71869 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.10118 | 0.153376 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.29857 | 0.160533 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −27.5495 | −1.02742 | −0.513711 | − | 0.857963i | \(-0.671730\pi\) | ||||
−0.513711 | + | 0.857963i | \(0.671730\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.12808 | 0.265096 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.186480 | 0.00692568 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.9321 | −0.553801 | −0.276901 | − | 0.960899i | \(-0.589307\pi\) | ||||
−0.276901 | + | 0.960899i | \(0.589307\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.91937 | 0.292908 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 42.4684 | 1.56860 | 0.784302 | − | 0.620379i | \(-0.213021\pi\) | ||||
0.784302 | + | 0.620379i | \(0.213021\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.51069 | 0.0556470 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.83329 | −0.288152 | −0.144076 | − | 0.989567i | \(-0.546021\pi\) | ||||
−0.144076 | + | 0.989567i | \(0.546021\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.55836 | −0.240927 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −30.4064 | −1.11550 | −0.557752 | − | 0.830008i | \(-0.688336\pi\) | ||||
−0.557752 | + | 0.830008i | \(0.688336\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.26700 | 0.302879 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.03878 | 0.220948 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −28.2843 | −1.03211 | −0.516054 | − | 0.856556i | \(-0.672600\pi\) | ||||
−0.516054 | + | 0.856556i | \(0.672600\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −18.9690 | −0.691270 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10.1528 | −0.369499 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19.5289 | −0.709791 | −0.354895 | − | 0.934906i | \(-0.615484\pi\) | ||||
−0.354895 | + | 0.934906i | \(0.615484\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.28344 | −0.0465858 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34.0746 | 1.23520 | 0.617602 | − | 0.786491i | \(-0.288104\pi\) | ||||
0.617602 | + | 0.786491i | \(0.288104\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.38193 | −0.0861188 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 41.5677 | 1.50092 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.3523 | −1.02241 | −0.511206 | − | 0.859458i | \(-0.670801\pi\) | ||||
−0.511206 | + | 0.859458i | \(0.670801\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20.4842 | 0.737720 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.96615 | 0.0707175 | 0.0353588 | − | 0.999375i | \(-0.488743\pi\) | ||||
0.0353588 | + | 0.999375i | \(0.488743\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.71503 | 0.169369 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.48745 | −0.304094 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.405546 | 0.0145116 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.422246 | −0.0150898 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −24.6557 | −0.880000 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.39165 | −0.0852531 | −0.0426266 | − | 0.999091i | \(-0.513573\pi\) | ||||
−0.0426266 | + | 0.999091i | \(0.513573\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 23.5553 | 0.838590 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 37.5495 | 1.33342 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.34801 | 0.260607 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −30.2674 | −1.07213 | −0.536064 | − | 0.844177i | \(-0.680089\pi\) | ||||
−0.536064 | + | 0.844177i | \(0.680089\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.05664 | 0.320401 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.3696 | 0.543060 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.852680 | 0.0300904 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12.9086 | 0.454405 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 28.7692 | 1.01147 | 0.505736 | − | 0.862688i | \(-0.331221\pi\) | ||||
0.505736 | + | 0.862688i | \(0.331221\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 51.6270 | 1.81287 | 0.906435 | − | 0.422345i | \(-0.138793\pi\) | ||||
0.906435 | + | 0.422345i | \(0.138793\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −19.8705 | −0.696890 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −25.4301 | −0.890776 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.23614 | −0.253161 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 44.1885 | 1.54219 | 0.771094 | − | 0.636721i | \(-0.219710\pi\) | ||||
0.771094 | + | 0.636721i | \(0.219710\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −33.8151 | −1.17872 | −0.589359 | − | 0.807871i | \(-0.700620\pi\) | ||||
−0.589359 | + | 0.807871i | \(0.700620\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.131861 | 0.00459081 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 48.0748 | 1.67173 | 0.835863 | − | 0.548938i | \(-0.184968\pi\) | ||||
0.835863 | + | 0.548938i | \(0.184968\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.26203 | −0.321684 | −0.160842 | − | 0.986980i | \(-0.551421\pi\) | ||||
−0.160842 | + | 0.986980i | \(0.551421\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 25.9884 | 0.901528 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 32.6092 | 1.12849 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10.6762 | −0.369025 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18.1567 | −0.626838 | −0.313419 | − | 0.949615i | \(-0.601474\pi\) | ||||
−0.313419 | + | 0.949615i | \(0.601474\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.8217 | −0.993852 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −19.6553 | −0.676965 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −60.6163 | −2.08526 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 19.0582 | 0.654075 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −24.3164 | −0.833555 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −40.7652 | −1.39577 | −0.697886 | − | 0.716208i | \(-0.745876\pi\) | ||||
−0.697886 | + | 0.716208i | \(0.745876\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.17643 | 0.0744325 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.0559 | 0.411823 | 0.205911 | − | 0.978571i | \(-0.433984\pi\) | ||||
0.205911 | + | 0.978571i | \(0.433984\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.25247 | −0.145092 | −0.0725461 | − | 0.997365i | \(-0.523112\pi\) | ||||
−0.0725461 | + | 0.997365i | \(0.523112\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 11.3280 | 0.385610 | 0.192805 | − | 0.981237i | \(-0.438242\pi\) | ||||
0.192805 | + | 0.981237i | \(0.438242\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.55529 | 0.290889 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −15.7553 | −0.535080 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.29771 | 0.0779444 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −32.5522 | −1.10299 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.512705 | −0.0173524 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 31.6871 | 1.07000 | 0.534999 | − | 0.844853i | \(-0.320312\pi\) | ||||
0.534999 | + | 0.844853i | \(0.320312\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.84890 | 0.264737 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.2690 | −0.817643 | −0.408821 | − | 0.912614i | \(-0.634060\pi\) | ||||
−0.408821 | + | 0.912614i | \(0.634060\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −47.1439 | −1.58652 | −0.793260 | − | 0.608883i | \(-0.791618\pi\) | ||||
−0.793260 | + | 0.608883i | \(0.791618\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −13.7945 | −0.463697 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14.6647 | 0.492391 | 0.246196 | − | 0.969220i | \(-0.420819\pi\) | ||||
0.246196 | + | 0.969220i | \(0.420819\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.298573 | −0.0100026 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.27530 | −0.276922 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 44.3010 | 1.48082 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 27.6553 | 0.923384 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.50800 | 0.150350 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.83963 | −0.127917 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −46.3827 | −1.54181 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.99149 | 0.132535 | 0.0662676 | − | 0.997802i | \(-0.478891\pi\) | ||||
0.0662676 | + | 0.997802i | \(0.478891\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.96346 | −0.164628 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.9260 | 0.627046 | 0.313523 | − | 0.949581i | \(-0.398491\pi\) | ||||
0.313523 | + | 0.949581i | \(0.398491\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.80302 | −0.0596711 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −12.4610 | −0.411949 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 46.4898 | 1.53356 | 0.766778 | − | 0.641912i | \(-0.221859\pi\) | ||||
0.766778 | + | 0.641912i | \(0.221859\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 26.5301 | 0.874196 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.73865 | −0.287636 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.49828 | 0.0821429 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9.48195 | −0.311428 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 28.7221 | 0.942343 | 0.471171 | − | 0.882042i | \(-0.343831\pi\) | ||||
0.471171 | + | 0.882042i | \(0.343831\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.726608 | −0.0237881 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.711179 | 0.0232581 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21.2560 | −0.694404 | −0.347202 | − | 0.937790i | \(-0.612868\pi\) | ||||
−0.347202 | + | 0.937790i | \(0.612868\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 15.1259 | 0.493616 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19.4100 | 0.632747 | 0.316373 | − | 0.948635i | \(-0.397535\pi\) | ||||
0.316373 | + | 0.948635i | \(0.397535\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 35.7899 | 1.16548 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27.6123 | 0.897279 | 0.448639 | − | 0.893713i | \(-0.351909\pi\) | ||||
0.448639 | + | 0.893713i | \(0.351909\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18.3734 | −0.596426 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −19.9496 | −0.646911 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.5080 | 0.469960 | 0.234980 | − | 0.972000i | \(-0.424497\pi\) | ||||
0.234980 | + | 0.972000i | \(0.424497\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 44.1354 | 1.42819 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.126071 | 0.00407530 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 82.9822 | 2.67685 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16.8387 | 0.542620 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −33.3062 | −1.07216 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −56.8449 | −1.82801 | −0.914005 | − | 0.405703i | \(-0.867027\pi\) | ||||
−0.914005 | + | 0.405703i | \(0.867027\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.13727 | −0.0365345 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10.1970 | −0.327237 | −0.163618 | − | 0.986524i | \(-0.552317\pi\) | ||||
−0.163618 | + | 0.986524i | \(0.552317\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.84132 | −0.0909951 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −8.53628 | −0.273100 | −0.136550 | − | 0.990633i | \(-0.543601\pi\) | ||||
−0.136550 | + | 0.990633i | \(0.543601\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.58896 | −0.146664 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.09849 | 0.0989272 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −38.1970 | −1.21829 | −0.609147 | − | 0.793057i | \(-0.708488\pi\) | ||||
−0.609147 | + | 0.793057i | \(0.708488\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −54.7393 | −1.74414 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 30.5134 | 0.970269 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.8810 | 1.45746 | 0.728730 | − | 0.684802i | \(-0.240111\pi\) | ||||
0.728730 | + | 0.684802i | \(0.240111\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −17.1943 | −0.545644 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.15588 | −0.195155 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −35.0749 | −1.11083 | −0.555417 | − | 0.831572i | \(-0.687441\pi\) | ||||
−0.555417 | + | 0.831572i | \(0.687441\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.65685 | −0.178975 |
(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 | 4704.2.a.bz.1.1 | yes | 4 | |
4.3 | odd | 2 | 4704.2.a.bx.1.1 | yes | 4 | ||
7.6 | odd | 2 | 4704.2.a.bw.1.4 | ✓ | 4 | ||
8.3 | odd | 2 | 9408.2.a.em.1.4 | 4 | |||
8.5 | even | 2 | 9408.2.a.ek.1.4 | 4 | |||
28.27 | even | 2 | 4704.2.a.by.1.4 | yes | 4 | ||
56.13 | odd | 2 | 9408.2.a.en.1.1 | 4 | |||
56.27 | even | 2 | 9408.2.a.el.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4704.2.a.bw.1.4 | ✓ | 4 | 7.6 | odd | 2 | ||
4704.2.a.bx.1.1 | yes | 4 | 4.3 | odd | 2 | ||
4704.2.a.by.1.4 | yes | 4 | 28.27 | even | 2 | ||
4704.2.a.bz.1.1 | yes | 4 | 1.1 | even | 1 | trivial | |
9408.2.a.ek.1.4 | 4 | 8.5 | even | 2 | |||
9408.2.a.el.1.1 | 4 | 56.27 | even | 2 | |||
9408.2.a.em.1.4 | 4 | 8.3 | odd | 2 | |||
9408.2.a.en.1.1 | 4 | 56.13 | odd | 2 |