Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.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: | \(64.1518129839\) |
Analytic rank: | \(0\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 5 x^{10} - 31 x^{9} + 168 x^{8} + 300 x^{7} - 1928 x^{6} - 736 x^{5} + 8532 x^{4} - 2065 x^{3} - 10494 x^{2} + 4024 x + 576 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(0.542814\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.542814 | 0.242754 | 0.121377 | − | 0.992607i | \(-0.461269\pi\) | ||||
0.121377 | + | 0.992607i | \(0.461269\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 3.05565 | 1.15493 | 0.577463 | − | 0.816417i | \(-0.304043\pi\) | ||||
0.577463 | + | 0.816417i | \(0.304043\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.542814 | 0.171653 | ||||||||
\(11\) | 0.632985 | 0.190852 | 0.0954261 | − | 0.995437i | \(-0.469579\pi\) | ||||
0.0954261 | + | 0.995437i | \(0.469579\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 3.05565 | 0.816656 | ||||||||
\(15\) | 0.542814 | 0.140154 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.75403 | 0.667951 | 0.333976 | − | 0.942582i | \(-0.391610\pi\) | ||||
0.333976 | + | 0.942582i | \(0.391610\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 2.05565 | 0.471598 | 0.235799 | − | 0.971802i | \(-0.424229\pi\) | ||||
0.235799 | + | 0.971802i | \(0.424229\pi\) | |||||||
\(20\) | 0.542814 | 0.121377 | ||||||||
\(21\) | 3.05565 | 0.666797 | ||||||||
\(22\) | 0.632985 | 0.134953 | ||||||||
\(23\) | 6.49267 | 1.35382 | 0.676908 | − | 0.736068i | \(-0.263320\pi\) | ||||
0.676908 | + | 0.736068i | \(0.263320\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −4.70535 | −0.941071 | ||||||||
\(26\) | 1.00000 | 0.196116 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 3.05565 | 0.577463 | ||||||||
\(29\) | −1.48269 | −0.275329 | −0.137665 | − | 0.990479i | \(-0.543960\pi\) | ||||
−0.137665 | + | 0.990479i | \(0.543960\pi\) | |||||||
\(30\) | 0.542814 | 0.0991037 | ||||||||
\(31\) | −2.05565 | −0.369205 | −0.184602 | − | 0.982813i | \(-0.559100\pi\) | ||||
−0.184602 | + | 0.982813i | \(0.559100\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0.632985 | 0.110189 | ||||||||
\(34\) | 2.75403 | 0.472313 | ||||||||
\(35\) | 1.65865 | 0.280362 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −0.518334 | −0.0852135 | −0.0426068 | − | 0.999092i | \(-0.513566\pi\) | ||||
−0.0426068 | + | 0.999092i | \(0.513566\pi\) | |||||||
\(38\) | 2.05565 | 0.333470 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 0.542814 | 0.0858264 | ||||||||
\(41\) | 2.61666 | 0.408654 | 0.204327 | − | 0.978903i | \(-0.434499\pi\) | ||||
0.204327 | + | 0.978903i | \(0.434499\pi\) | |||||||
\(42\) | 3.05565 | 0.471496 | ||||||||
\(43\) | 2.49072 | 0.379831 | 0.189915 | − | 0.981800i | \(-0.439179\pi\) | ||||
0.189915 | + | 0.981800i | \(0.439179\pi\) | |||||||
\(44\) | 0.632985 | 0.0954261 | ||||||||
\(45\) | 0.542814 | 0.0809179 | ||||||||
\(46\) | 6.49267 | 0.957292 | ||||||||
\(47\) | 2.09567 | 0.305685 | 0.152843 | − | 0.988251i | \(-0.451157\pi\) | ||||
0.152843 | + | 0.988251i | \(0.451157\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 2.33697 | 0.333853 | ||||||||
\(50\) | −4.70535 | −0.665437 | ||||||||
\(51\) | 2.75403 | 0.385642 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | −12.6644 | −1.73959 | −0.869795 | − | 0.493413i | \(-0.835749\pi\) | ||||
−0.869795 | + | 0.493413i | \(0.835749\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0.343593 | 0.0463301 | ||||||||
\(56\) | 3.05565 | 0.408328 | ||||||||
\(57\) | 2.05565 | 0.272277 | ||||||||
\(58\) | −1.48269 | −0.194687 | ||||||||
\(59\) | 0.846439 | 0.110197 | 0.0550985 | − | 0.998481i | \(-0.482453\pi\) | ||||
0.0550985 | + | 0.998481i | \(0.482453\pi\) | |||||||
\(60\) | 0.542814 | 0.0700769 | ||||||||
\(61\) | −11.2974 | −1.44648 | −0.723241 | − | 0.690596i | \(-0.757348\pi\) | ||||
−0.723241 | + | 0.690596i | \(0.757348\pi\) | |||||||
\(62\) | −2.05565 | −0.261067 | ||||||||
\(63\) | 3.05565 | 0.384975 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.542814 | 0.0673277 | ||||||||
\(66\) | 0.632985 | 0.0779151 | ||||||||
\(67\) | 12.0004 | 1.46608 | 0.733039 | − | 0.680187i | \(-0.238101\pi\) | ||||
0.733039 | + | 0.680187i | \(0.238101\pi\) | |||||||
\(68\) | 2.75403 | 0.333976 | ||||||||
\(69\) | 6.49267 | 0.781626 | ||||||||
\(70\) | 1.65865 | 0.198246 | ||||||||
\(71\) | 3.24887 | 0.385570 | 0.192785 | − | 0.981241i | \(-0.438248\pi\) | ||||
0.192785 | + | 0.981241i | \(0.438248\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 12.2886 | 1.43827 | 0.719136 | − | 0.694869i | \(-0.244538\pi\) | ||||
0.719136 | + | 0.694869i | \(0.244538\pi\) | |||||||
\(74\) | −0.518334 | −0.0602551 | ||||||||
\(75\) | −4.70535 | −0.543327 | ||||||||
\(76\) | 2.05565 | 0.235799 | ||||||||
\(77\) | 1.93418 | 0.220420 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | 10.0724 | 1.13323 | 0.566615 | − | 0.823983i | \(-0.308253\pi\) | ||||
0.566615 | + | 0.823983i | \(0.308253\pi\) | |||||||
\(80\) | 0.542814 | 0.0606884 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.61666 | 0.288962 | ||||||||
\(83\) | 4.86110 | 0.533575 | 0.266787 | − | 0.963755i | \(-0.414038\pi\) | ||||
0.266787 | + | 0.963755i | \(0.414038\pi\) | |||||||
\(84\) | 3.05565 | 0.333398 | ||||||||
\(85\) | 1.49493 | 0.162148 | ||||||||
\(86\) | 2.49072 | 0.268581 | ||||||||
\(87\) | −1.48269 | −0.158961 | ||||||||
\(88\) | 0.632985 | 0.0674765 | ||||||||
\(89\) | −9.35113 | −0.991218 | −0.495609 | − | 0.868546i | \(-0.665055\pi\) | ||||
−0.495609 | + | 0.868546i | \(0.665055\pi\) | |||||||
\(90\) | 0.542814 | 0.0572176 | ||||||||
\(91\) | 3.05565 | 0.320319 | ||||||||
\(92\) | 6.49267 | 0.676908 | ||||||||
\(93\) | −2.05565 | −0.213161 | ||||||||
\(94\) | 2.09567 | 0.216152 | ||||||||
\(95\) | 1.11583 | 0.114482 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −7.29369 | −0.740563 | −0.370281 | − | 0.928920i | \(-0.620739\pi\) | ||||
−0.370281 | + | 0.928920i | \(0.620739\pi\) | |||||||
\(98\) | 2.33697 | 0.236070 | ||||||||
\(99\) | 0.632985 | 0.0636174 | ||||||||
\(100\) | −4.70535 | −0.470535 | ||||||||
\(101\) | −15.2641 | −1.51884 | −0.759420 | − | 0.650601i | \(-0.774517\pi\) | ||||
−0.759420 | + | 0.650601i | \(0.774517\pi\) | |||||||
\(102\) | 2.75403 | 0.272690 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | 1.65865 | 0.161867 | ||||||||
\(106\) | −12.6644 | −1.23008 | ||||||||
\(107\) | −17.5531 | −1.69692 | −0.848462 | − | 0.529256i | \(-0.822471\pi\) | ||||
−0.848462 | + | 0.529256i | \(0.822471\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −8.80317 | −0.843191 | −0.421596 | − | 0.906784i | \(-0.638530\pi\) | ||||
−0.421596 | + | 0.906784i | \(0.638530\pi\) | |||||||
\(110\) | 0.343593 | 0.0327603 | ||||||||
\(111\) | −0.518334 | −0.0491980 | ||||||||
\(112\) | 3.05565 | 0.288731 | ||||||||
\(113\) | −1.00999 | −0.0950122 | −0.0475061 | − | 0.998871i | \(-0.515127\pi\) | ||||
−0.0475061 | + | 0.998871i | \(0.515127\pi\) | |||||||
\(114\) | 2.05565 | 0.192529 | ||||||||
\(115\) | 3.52431 | 0.328644 | ||||||||
\(116\) | −1.48269 | −0.137665 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 0.846439 | 0.0779211 | ||||||||
\(119\) | 8.41535 | 0.771434 | ||||||||
\(120\) | 0.542814 | 0.0495519 | ||||||||
\(121\) | −10.5993 | −0.963575 | ||||||||
\(122\) | −11.2974 | −1.02282 | ||||||||
\(123\) | 2.61666 | 0.235936 | ||||||||
\(124\) | −2.05565 | −0.184602 | ||||||||
\(125\) | −5.26820 | −0.471202 | ||||||||
\(126\) | 3.05565 | 0.272219 | ||||||||
\(127\) | −1.73086 | −0.153589 | −0.0767943 | − | 0.997047i | \(-0.524468\pi\) | ||||
−0.0767943 | + | 0.997047i | \(0.524468\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 2.49072 | 0.219296 | ||||||||
\(130\) | 0.542814 | 0.0476079 | ||||||||
\(131\) | 8.42898 | 0.736443 | 0.368222 | − | 0.929738i | \(-0.379967\pi\) | ||||
0.368222 | + | 0.929738i | \(0.379967\pi\) | |||||||
\(132\) | 0.632985 | 0.0550943 | ||||||||
\(133\) | 6.28133 | 0.544660 | ||||||||
\(134\) | 12.0004 | 1.03667 | ||||||||
\(135\) | 0.542814 | 0.0467180 | ||||||||
\(136\) | 2.75403 | 0.236157 | ||||||||
\(137\) | 8.45316 | 0.722202 | 0.361101 | − | 0.932527i | \(-0.382401\pi\) | ||||
0.361101 | + | 0.932527i | \(0.382401\pi\) | |||||||
\(138\) | 6.49267 | 0.552693 | ||||||||
\(139\) | −3.12795 | −0.265310 | −0.132655 | − | 0.991162i | \(-0.542350\pi\) | ||||
−0.132655 | + | 0.991162i | \(0.542350\pi\) | |||||||
\(140\) | 1.65865 | 0.140181 | ||||||||
\(141\) | 2.09567 | 0.176487 | ||||||||
\(142\) | 3.24887 | 0.272639 | ||||||||
\(143\) | 0.632985 | 0.0529329 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −0.804826 | −0.0668371 | ||||||||
\(146\) | 12.2886 | 1.01701 | ||||||||
\(147\) | 2.33697 | 0.192750 | ||||||||
\(148\) | −0.518334 | −0.0426068 | ||||||||
\(149\) | 9.04546 | 0.741033 | 0.370517 | − | 0.928826i | \(-0.379181\pi\) | ||||
0.370517 | + | 0.928826i | \(0.379181\pi\) | |||||||
\(150\) | −4.70535 | −0.384191 | ||||||||
\(151\) | −18.2754 | −1.48723 | −0.743617 | − | 0.668605i | \(-0.766892\pi\) | ||||
−0.743617 | + | 0.668605i | \(0.766892\pi\) | |||||||
\(152\) | 2.05565 | 0.166735 | ||||||||
\(153\) | 2.75403 | 0.222650 | ||||||||
\(154\) | 1.93418 | 0.155861 | ||||||||
\(155\) | −1.11583 | −0.0896258 | ||||||||
\(156\) | 1.00000 | 0.0800641 | ||||||||
\(157\) | 15.5277 | 1.23925 | 0.619624 | − | 0.784899i | \(-0.287285\pi\) | ||||
0.619624 | + | 0.784899i | \(0.287285\pi\) | |||||||
\(158\) | 10.0724 | 0.801315 | ||||||||
\(159\) | −12.6644 | −1.00435 | ||||||||
\(160\) | 0.542814 | 0.0429132 | ||||||||
\(161\) | 19.8393 | 1.56356 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 15.4871 | 1.21305 | 0.606524 | − | 0.795066i | \(-0.292564\pi\) | ||||
0.606524 | + | 0.795066i | \(0.292564\pi\) | |||||||
\(164\) | 2.61666 | 0.204327 | ||||||||
\(165\) | 0.343593 | 0.0267487 | ||||||||
\(166\) | 4.86110 | 0.377294 | ||||||||
\(167\) | 8.73179 | 0.675686 | 0.337843 | − | 0.941202i | \(-0.390303\pi\) | ||||
0.337843 | + | 0.941202i | \(0.390303\pi\) | |||||||
\(168\) | 3.05565 | 0.235748 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 1.49493 | 0.114656 | ||||||||
\(171\) | 2.05565 | 0.157199 | ||||||||
\(172\) | 2.49072 | 0.189915 | ||||||||
\(173\) | 21.1049 | 1.60457 | 0.802287 | − | 0.596939i | \(-0.203616\pi\) | ||||
0.802287 | + | 0.596939i | \(0.203616\pi\) | |||||||
\(174\) | −1.48269 | −0.112403 | ||||||||
\(175\) | −14.3779 | −1.08687 | ||||||||
\(176\) | 0.632985 | 0.0477131 | ||||||||
\(177\) | 0.846439 | 0.0636223 | ||||||||
\(178\) | −9.35113 | −0.700897 | ||||||||
\(179\) | 8.18560 | 0.611820 | 0.305910 | − | 0.952060i | \(-0.401039\pi\) | ||||
0.305910 | + | 0.952060i | \(0.401039\pi\) | |||||||
\(180\) | 0.542814 | 0.0404589 | ||||||||
\(181\) | 6.24534 | 0.464212 | 0.232106 | − | 0.972690i | \(-0.425438\pi\) | ||||
0.232106 | + | 0.972690i | \(0.425438\pi\) | |||||||
\(182\) | 3.05565 | 0.226500 | ||||||||
\(183\) | −11.2974 | −0.835126 | ||||||||
\(184\) | 6.49267 | 0.478646 | ||||||||
\(185\) | −0.281358 | −0.0206859 | ||||||||
\(186\) | −2.05565 | −0.150727 | ||||||||
\(187\) | 1.74326 | 0.127480 | ||||||||
\(188\) | 2.09567 | 0.152843 | ||||||||
\(189\) | 3.05565 | 0.222266 | ||||||||
\(190\) | 1.11583 | 0.0809510 | ||||||||
\(191\) | −21.2265 | −1.53590 | −0.767950 | − | 0.640510i | \(-0.778723\pi\) | ||||
−0.767950 | + | 0.640510i | \(0.778723\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −9.87884 | −0.711094 | −0.355547 | − | 0.934658i | \(-0.615705\pi\) | ||||
−0.355547 | + | 0.934658i | \(0.615705\pi\) | |||||||
\(194\) | −7.29369 | −0.523657 | ||||||||
\(195\) | 0.542814 | 0.0388717 | ||||||||
\(196\) | 2.33697 | 0.166927 | ||||||||
\(197\) | −17.5032 | −1.24705 | −0.623526 | − | 0.781803i | \(-0.714301\pi\) | ||||
−0.623526 | + | 0.781803i | \(0.714301\pi\) | |||||||
\(198\) | 0.632985 | 0.0449843 | ||||||||
\(199\) | −26.7000 | −1.89272 | −0.946358 | − | 0.323120i | \(-0.895268\pi\) | ||||
−0.946358 | + | 0.323120i | \(0.895268\pi\) | |||||||
\(200\) | −4.70535 | −0.332719 | ||||||||
\(201\) | 12.0004 | 0.846440 | ||||||||
\(202\) | −15.2641 | −1.07398 | ||||||||
\(203\) | −4.53058 | −0.317985 | ||||||||
\(204\) | 2.75403 | 0.192821 | ||||||||
\(205\) | 1.42036 | 0.0992022 | ||||||||
\(206\) | −1.00000 | −0.0696733 | ||||||||
\(207\) | 6.49267 | 0.451272 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | 1.30119 | 0.0900054 | ||||||||
\(210\) | 1.65865 | 0.114457 | ||||||||
\(211\) | 14.8379 | 1.02148 | 0.510742 | − | 0.859734i | \(-0.329371\pi\) | ||||
0.510742 | + | 0.859734i | \(0.329371\pi\) | |||||||
\(212\) | −12.6644 | −0.869795 | ||||||||
\(213\) | 3.24887 | 0.222609 | ||||||||
\(214\) | −17.5531 | −1.19991 | ||||||||
\(215\) | 1.35200 | 0.0922053 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −6.28133 | −0.426404 | ||||||||
\(218\) | −8.80317 | −0.596226 | ||||||||
\(219\) | 12.2886 | 0.830387 | ||||||||
\(220\) | 0.343593 | 0.0231650 | ||||||||
\(221\) | 2.75403 | 0.185256 | ||||||||
\(222\) | −0.518334 | −0.0347883 | ||||||||
\(223\) | −14.8504 | −0.994453 | −0.497227 | − | 0.867621i | \(-0.665648\pi\) | ||||
−0.497227 | + | 0.867621i | \(0.665648\pi\) | |||||||
\(224\) | 3.05565 | 0.204164 | ||||||||
\(225\) | −4.70535 | −0.313690 | ||||||||
\(226\) | −1.00999 | −0.0671838 | ||||||||
\(227\) | 7.10596 | 0.471639 | 0.235820 | − | 0.971797i | \(-0.424223\pi\) | ||||
0.235820 | + | 0.971797i | \(0.424223\pi\) | |||||||
\(228\) | 2.05565 | 0.136138 | ||||||||
\(229\) | 2.94089 | 0.194340 | 0.0971698 | − | 0.995268i | \(-0.469021\pi\) | ||||
0.0971698 | + | 0.995268i | \(0.469021\pi\) | |||||||
\(230\) | 3.52431 | 0.232386 | ||||||||
\(231\) | 1.93418 | 0.127260 | ||||||||
\(232\) | −1.48269 | −0.0973435 | ||||||||
\(233\) | 8.07222 | 0.528829 | 0.264414 | − | 0.964409i | \(-0.414821\pi\) | ||||
0.264414 | + | 0.964409i | \(0.414821\pi\) | |||||||
\(234\) | 1.00000 | 0.0653720 | ||||||||
\(235\) | 1.13756 | 0.0742062 | ||||||||
\(236\) | 0.846439 | 0.0550985 | ||||||||
\(237\) | 10.0724 | 0.654271 | ||||||||
\(238\) | 8.41535 | 0.545486 | ||||||||
\(239\) | 4.41447 | 0.285548 | 0.142774 | − | 0.989755i | \(-0.454398\pi\) | ||||
0.142774 | + | 0.989755i | \(0.454398\pi\) | |||||||
\(240\) | 0.542814 | 0.0350385 | ||||||||
\(241\) | −3.99479 | −0.257327 | −0.128664 | − | 0.991688i | \(-0.541069\pi\) | ||||
−0.128664 | + | 0.991688i | \(0.541069\pi\) | |||||||
\(242\) | −10.5993 | −0.681351 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −11.2974 | −0.723241 | ||||||||
\(245\) | 1.26854 | 0.0810441 | ||||||||
\(246\) | 2.61666 | 0.166832 | ||||||||
\(247\) | 2.05565 | 0.130798 | ||||||||
\(248\) | −2.05565 | −0.130534 | ||||||||
\(249\) | 4.86110 | 0.308060 | ||||||||
\(250\) | −5.26820 | −0.333190 | ||||||||
\(251\) | −3.11912 | −0.196877 | −0.0984386 | − | 0.995143i | \(-0.531385\pi\) | ||||
−0.0984386 | + | 0.995143i | \(0.531385\pi\) | |||||||
\(252\) | 3.05565 | 0.192488 | ||||||||
\(253\) | 4.10977 | 0.258379 | ||||||||
\(254\) | −1.73086 | −0.108604 | ||||||||
\(255\) | 1.49493 | 0.0936160 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 0.0449774 | 0.00280561 | 0.00140281 | − | 0.999999i | \(-0.499553\pi\) | ||||
0.00140281 | + | 0.999999i | \(0.499553\pi\) | |||||||
\(258\) | 2.49072 | 0.155065 | ||||||||
\(259\) | −1.58384 | −0.0984153 | ||||||||
\(260\) | 0.542814 | 0.0336639 | ||||||||
\(261\) | −1.48269 | −0.0917764 | ||||||||
\(262\) | 8.42898 | 0.520744 | ||||||||
\(263\) | 28.7094 | 1.77030 | 0.885148 | − | 0.465309i | \(-0.154057\pi\) | ||||
0.885148 | + | 0.465309i | \(0.154057\pi\) | |||||||
\(264\) | 0.632985 | 0.0389576 | ||||||||
\(265\) | −6.87441 | −0.422292 | ||||||||
\(266\) | 6.28133 | 0.385133 | ||||||||
\(267\) | −9.35113 | −0.572280 | ||||||||
\(268\) | 12.0004 | 0.733039 | ||||||||
\(269\) | 13.4485 | 0.819971 | 0.409985 | − | 0.912092i | \(-0.365534\pi\) | ||||
0.409985 | + | 0.912092i | \(0.365534\pi\) | |||||||
\(270\) | 0.542814 | 0.0330346 | ||||||||
\(271\) | −8.93755 | −0.542917 | −0.271459 | − | 0.962450i | \(-0.587506\pi\) | ||||
−0.271459 | + | 0.962450i | \(0.587506\pi\) | |||||||
\(272\) | 2.75403 | 0.166988 | ||||||||
\(273\) | 3.05565 | 0.184936 | ||||||||
\(274\) | 8.45316 | 0.510674 | ||||||||
\(275\) | −2.97842 | −0.179605 | ||||||||
\(276\) | 6.49267 | 0.390813 | ||||||||
\(277\) | 8.96300 | 0.538534 | 0.269267 | − | 0.963066i | \(-0.413219\pi\) | ||||
0.269267 | + | 0.963066i | \(0.413219\pi\) | |||||||
\(278\) | −3.12795 | −0.187602 | ||||||||
\(279\) | −2.05565 | −0.123068 | ||||||||
\(280\) | 1.65865 | 0.0991231 | ||||||||
\(281\) | 5.60492 | 0.334362 | 0.167181 | − | 0.985926i | \(-0.446534\pi\) | ||||
0.167181 | + | 0.985926i | \(0.446534\pi\) | |||||||
\(282\) | 2.09567 | 0.124796 | ||||||||
\(283\) | 13.6111 | 0.809096 | 0.404548 | − | 0.914517i | \(-0.367429\pi\) | ||||
0.404548 | + | 0.914517i | \(0.367429\pi\) | |||||||
\(284\) | 3.24887 | 0.192785 | ||||||||
\(285\) | 1.11583 | 0.0660962 | ||||||||
\(286\) | 0.632985 | 0.0374292 | ||||||||
\(287\) | 7.99559 | 0.471965 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −9.41529 | −0.553841 | ||||||||
\(290\) | −0.804826 | −0.0472610 | ||||||||
\(291\) | −7.29369 | −0.427564 | ||||||||
\(292\) | 12.2886 | 0.719136 | ||||||||
\(293\) | −17.7380 | −1.03627 | −0.518133 | − | 0.855300i | \(-0.673373\pi\) | ||||
−0.518133 | + | 0.855300i | \(0.673373\pi\) | |||||||
\(294\) | 2.33697 | 0.136295 | ||||||||
\(295\) | 0.459459 | 0.0267507 | ||||||||
\(296\) | −0.518334 | −0.0301275 | ||||||||
\(297\) | 0.632985 | 0.0367295 | ||||||||
\(298\) | 9.04546 | 0.523990 | ||||||||
\(299\) | 6.49267 | 0.375481 | ||||||||
\(300\) | −4.70535 | −0.271664 | ||||||||
\(301\) | 7.61075 | 0.438676 | ||||||||
\(302\) | −18.2754 | −1.05163 | ||||||||
\(303\) | −15.2641 | −0.876902 | ||||||||
\(304\) | 2.05565 | 0.117899 | ||||||||
\(305\) | −6.13237 | −0.351138 | ||||||||
\(306\) | 2.75403 | 0.157438 | ||||||||
\(307\) | 6.26775 | 0.357719 | 0.178860 | − | 0.983875i | \(-0.442759\pi\) | ||||
0.178860 | + | 0.983875i | \(0.442759\pi\) | |||||||
\(308\) | 1.93418 | 0.110210 | ||||||||
\(309\) | −1.00000 | −0.0568880 | ||||||||
\(310\) | −1.11583 | −0.0633750 | ||||||||
\(311\) | 24.8115 | 1.40693 | 0.703466 | − | 0.710729i | \(-0.251635\pi\) | ||||
0.703466 | + | 0.710729i | \(0.251635\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | −26.4684 | −1.49608 | −0.748040 | − | 0.663653i | \(-0.769005\pi\) | ||||
−0.748040 | + | 0.663653i | \(0.769005\pi\) | |||||||
\(314\) | 15.5277 | 0.876281 | ||||||||
\(315\) | 1.65865 | 0.0934541 | ||||||||
\(316\) | 10.0724 | 0.566615 | ||||||||
\(317\) | 24.8381 | 1.39505 | 0.697524 | − | 0.716561i | \(-0.254285\pi\) | ||||
0.697524 | + | 0.716561i | \(0.254285\pi\) | |||||||
\(318\) | −12.6644 | −0.710185 | ||||||||
\(319\) | −0.938523 | −0.0525472 | ||||||||
\(320\) | 0.542814 | 0.0303442 | ||||||||
\(321\) | −17.5531 | −0.979720 | ||||||||
\(322\) | 19.8393 | 1.10560 | ||||||||
\(323\) | 5.66132 | 0.315004 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −4.70535 | −0.261006 | ||||||||
\(326\) | 15.4871 | 0.857754 | ||||||||
\(327\) | −8.80317 | −0.486817 | ||||||||
\(328\) | 2.61666 | 0.144481 | ||||||||
\(329\) | 6.40363 | 0.353044 | ||||||||
\(330\) | 0.343593 | 0.0189142 | ||||||||
\(331\) | 24.3920 | 1.34071 | 0.670354 | − | 0.742041i | \(-0.266142\pi\) | ||||
0.670354 | + | 0.742041i | \(0.266142\pi\) | |||||||
\(332\) | 4.86110 | 0.266787 | ||||||||
\(333\) | −0.518334 | −0.0284045 | ||||||||
\(334\) | 8.73179 | 0.477782 | ||||||||
\(335\) | 6.51396 | 0.355896 | ||||||||
\(336\) | 3.05565 | 0.166699 | ||||||||
\(337\) | −28.4373 | −1.54908 | −0.774539 | − | 0.632527i | \(-0.782018\pi\) | ||||
−0.774539 | + | 0.632527i | \(0.782018\pi\) | |||||||
\(338\) | 1.00000 | 0.0543928 | ||||||||
\(339\) | −1.00999 | −0.0548553 | ||||||||
\(340\) | 1.49493 | 0.0810738 | ||||||||
\(341\) | −1.30119 | −0.0704636 | ||||||||
\(342\) | 2.05565 | 0.111157 | ||||||||
\(343\) | −14.2486 | −0.769350 | ||||||||
\(344\) | 2.49072 | 0.134291 | ||||||||
\(345\) | 3.52431 | 0.189743 | ||||||||
\(346\) | 21.1049 | 1.13461 | ||||||||
\(347\) | 3.72720 | 0.200087 | 0.100043 | − | 0.994983i | \(-0.468102\pi\) | ||||
0.100043 | + | 0.994983i | \(0.468102\pi\) | |||||||
\(348\) | −1.48269 | −0.0794807 | ||||||||
\(349\) | −18.4589 | −0.988081 | −0.494040 | − | 0.869439i | \(-0.664481\pi\) | ||||
−0.494040 | + | 0.869439i | \(0.664481\pi\) | |||||||
\(350\) | −14.3779 | −0.768531 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 0.632985 | 0.0337382 | ||||||||
\(353\) | −10.9773 | −0.584262 | −0.292131 | − | 0.956378i | \(-0.594364\pi\) | ||||
−0.292131 | + | 0.956378i | \(0.594364\pi\) | |||||||
\(354\) | 0.846439 | 0.0449877 | ||||||||
\(355\) | 1.76353 | 0.0935985 | ||||||||
\(356\) | −9.35113 | −0.495609 | ||||||||
\(357\) | 8.41535 | 0.445388 | ||||||||
\(358\) | 8.18560 | 0.432622 | ||||||||
\(359\) | 17.8262 | 0.940829 | 0.470415 | − | 0.882446i | \(-0.344104\pi\) | ||||
0.470415 | + | 0.882446i | \(0.344104\pi\) | |||||||
\(360\) | 0.542814 | 0.0286088 | ||||||||
\(361\) | −14.7743 | −0.777596 | ||||||||
\(362\) | 6.24534 | 0.328248 | ||||||||
\(363\) | −10.5993 | −0.556321 | ||||||||
\(364\) | 3.05565 | 0.160159 | ||||||||
\(365\) | 6.67042 | 0.349146 | ||||||||
\(366\) | −11.2974 | −0.590523 | ||||||||
\(367\) | 3.69689 | 0.192976 | 0.0964880 | − | 0.995334i | \(-0.469239\pi\) | ||||
0.0964880 | + | 0.995334i | \(0.469239\pi\) | |||||||
\(368\) | 6.49267 | 0.338454 | ||||||||
\(369\) | 2.61666 | 0.136218 | ||||||||
\(370\) | −0.281358 | −0.0146271 | ||||||||
\(371\) | −38.6979 | −2.00910 | ||||||||
\(372\) | −2.05565 | −0.106580 | ||||||||
\(373\) | 17.8883 | 0.926222 | 0.463111 | − | 0.886300i | \(-0.346733\pi\) | ||||
0.463111 | + | 0.886300i | \(0.346733\pi\) | |||||||
\(374\) | 1.74326 | 0.0901420 | ||||||||
\(375\) | −5.26820 | −0.272049 | ||||||||
\(376\) | 2.09567 | 0.108076 | ||||||||
\(377\) | −1.48269 | −0.0763626 | ||||||||
\(378\) | 3.05565 | 0.157165 | ||||||||
\(379\) | −29.0777 | −1.49362 | −0.746812 | − | 0.665035i | \(-0.768416\pi\) | ||||
−0.746812 | + | 0.665035i | \(0.768416\pi\) | |||||||
\(380\) | 1.11583 | 0.0572410 | ||||||||
\(381\) | −1.73086 | −0.0886744 | ||||||||
\(382\) | −21.2265 | −1.08604 | ||||||||
\(383\) | 9.42500 | 0.481595 | 0.240797 | − | 0.970575i | \(-0.422591\pi\) | ||||
0.240797 | + | 0.970575i | \(0.422591\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 1.04990 | 0.0535078 | ||||||||
\(386\) | −9.87884 | −0.502820 | ||||||||
\(387\) | 2.49072 | 0.126610 | ||||||||
\(388\) | −7.29369 | −0.370281 | ||||||||
\(389\) | −23.4042 | −1.18664 | −0.593319 | − | 0.804967i | \(-0.702183\pi\) | ||||
−0.593319 | + | 0.804967i | \(0.702183\pi\) | |||||||
\(390\) | 0.542814 | 0.0274864 | ||||||||
\(391\) | 17.8810 | 0.904283 | ||||||||
\(392\) | 2.33697 | 0.118035 | ||||||||
\(393\) | 8.42898 | 0.425186 | ||||||||
\(394\) | −17.5032 | −0.881799 | ||||||||
\(395\) | 5.46742 | 0.275096 | ||||||||
\(396\) | 0.632985 | 0.0318087 | ||||||||
\(397\) | −10.8257 | −0.543325 | −0.271663 | − | 0.962393i | \(-0.587573\pi\) | ||||
−0.271663 | + | 0.962393i | \(0.587573\pi\) | |||||||
\(398\) | −26.7000 | −1.33835 | ||||||||
\(399\) | 6.28133 | 0.314460 | ||||||||
\(400\) | −4.70535 | −0.235268 | ||||||||
\(401\) | −2.98820 | −0.149223 | −0.0746117 | − | 0.997213i | \(-0.523772\pi\) | ||||
−0.0746117 | + | 0.997213i | \(0.523772\pi\) | |||||||
\(402\) | 12.0004 | 0.598524 | ||||||||
\(403\) | −2.05565 | −0.102399 | ||||||||
\(404\) | −15.2641 | −0.759420 | ||||||||
\(405\) | 0.542814 | 0.0269726 | ||||||||
\(406\) | −4.53058 | −0.224849 | ||||||||
\(407\) | −0.328098 | −0.0162632 | ||||||||
\(408\) | 2.75403 | 0.136345 | ||||||||
\(409\) | −25.2550 | −1.24878 | −0.624391 | − | 0.781112i | \(-0.714653\pi\) | ||||
−0.624391 | + | 0.781112i | \(0.714653\pi\) | |||||||
\(410\) | 1.42036 | 0.0701466 | ||||||||
\(411\) | 8.45316 | 0.416964 | ||||||||
\(412\) | −1.00000 | −0.0492665 | ||||||||
\(413\) | 2.58642 | 0.127269 | ||||||||
\(414\) | 6.49267 | 0.319097 | ||||||||
\(415\) | 2.63867 | 0.129527 | ||||||||
\(416\) | 1.00000 | 0.0490290 | ||||||||
\(417\) | −3.12795 | −0.153177 | ||||||||
\(418\) | 1.30119 | 0.0636435 | ||||||||
\(419\) | −1.20744 | −0.0589873 | −0.0294937 | − | 0.999565i | \(-0.509389\pi\) | ||||
−0.0294937 | + | 0.999565i | \(0.509389\pi\) | |||||||
\(420\) | 1.65865 | 0.0809336 | ||||||||
\(421\) | 13.8740 | 0.676179 | 0.338089 | − | 0.941114i | \(-0.390219\pi\) | ||||
0.338089 | + | 0.941114i | \(0.390219\pi\) | |||||||
\(422\) | 14.8379 | 0.722298 | ||||||||
\(423\) | 2.09567 | 0.101895 | ||||||||
\(424\) | −12.6644 | −0.615038 | ||||||||
\(425\) | −12.9587 | −0.628590 | ||||||||
\(426\) | 3.24887 | 0.157408 | ||||||||
\(427\) | −34.5208 | −1.67058 | ||||||||
\(428\) | −17.5531 | −0.848462 | ||||||||
\(429\) | 0.632985 | 0.0305608 | ||||||||
\(430\) | 1.35200 | 0.0651990 | ||||||||
\(431\) | −11.8762 | −0.572055 | −0.286027 | − | 0.958221i | \(-0.592335\pi\) | ||||
−0.286027 | + | 0.958221i | \(0.592335\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 39.6312 | 1.90455 | 0.952277 | − | 0.305234i | \(-0.0987346\pi\) | ||||
0.952277 | + | 0.305234i | \(0.0987346\pi\) | |||||||
\(434\) | −6.28133 | −0.301513 | ||||||||
\(435\) | −0.804826 | −0.0385884 | ||||||||
\(436\) | −8.80317 | −0.421596 | ||||||||
\(437\) | 13.3466 | 0.638456 | ||||||||
\(438\) | 12.2886 | 0.587172 | ||||||||
\(439\) | −18.7402 | −0.894421 | −0.447210 | − | 0.894429i | \(-0.647582\pi\) | ||||
−0.447210 | + | 0.894429i | \(0.647582\pi\) | |||||||
\(440\) | 0.343593 | 0.0163802 | ||||||||
\(441\) | 2.33697 | 0.111284 | ||||||||
\(442\) | 2.75403 | 0.130996 | ||||||||
\(443\) | −1.45204 | −0.0689887 | −0.0344943 | − | 0.999405i | \(-0.510982\pi\) | ||||
−0.0344943 | + | 0.999405i | \(0.510982\pi\) | |||||||
\(444\) | −0.518334 | −0.0245990 | ||||||||
\(445\) | −5.07592 | −0.240622 | ||||||||
\(446\) | −14.8504 | −0.703185 | ||||||||
\(447\) | 9.04546 | 0.427836 | ||||||||
\(448\) | 3.05565 | 0.144366 | ||||||||
\(449\) | −31.2014 | −1.47249 | −0.736243 | − | 0.676717i | \(-0.763402\pi\) | ||||
−0.736243 | + | 0.676717i | \(0.763402\pi\) | |||||||
\(450\) | −4.70535 | −0.221812 | ||||||||
\(451\) | 1.65631 | 0.0779925 | ||||||||
\(452\) | −1.00999 | −0.0475061 | ||||||||
\(453\) | −18.2754 | −0.858655 | ||||||||
\(454\) | 7.10596 | 0.333499 | ||||||||
\(455\) | 1.65865 | 0.0777585 | ||||||||
\(456\) | 2.05565 | 0.0962644 | ||||||||
\(457\) | −4.40435 | −0.206027 | −0.103013 | − | 0.994680i | \(-0.532848\pi\) | ||||
−0.103013 | + | 0.994680i | \(0.532848\pi\) | |||||||
\(458\) | 2.94089 | 0.137419 | ||||||||
\(459\) | 2.75403 | 0.128547 | ||||||||
\(460\) | 3.52431 | 0.164322 | ||||||||
\(461\) | 18.3876 | 0.856394 | 0.428197 | − | 0.903685i | \(-0.359149\pi\) | ||||
0.428197 | + | 0.903685i | \(0.359149\pi\) | |||||||
\(462\) | 1.93418 | 0.0899861 | ||||||||
\(463\) | −10.6320 | −0.494110 | −0.247055 | − | 0.969001i | \(-0.579463\pi\) | ||||
−0.247055 | + | 0.969001i | \(0.579463\pi\) | |||||||
\(464\) | −1.48269 | −0.0688323 | ||||||||
\(465\) | −1.11583 | −0.0517455 | ||||||||
\(466\) | 8.07222 | 0.373938 | ||||||||
\(467\) | 6.28660 | 0.290909 | 0.145455 | − | 0.989365i | \(-0.453536\pi\) | ||||
0.145455 | + | 0.989365i | \(0.453536\pi\) | |||||||
\(468\) | 1.00000 | 0.0462250 | ||||||||
\(469\) | 36.6689 | 1.69321 | ||||||||
\(470\) | 1.13756 | 0.0524717 | ||||||||
\(471\) | 15.5277 | 0.715480 | ||||||||
\(472\) | 0.846439 | 0.0389605 | ||||||||
\(473\) | 1.57659 | 0.0724916 | ||||||||
\(474\) | 10.0724 | 0.462639 | ||||||||
\(475\) | −9.67254 | −0.443807 | ||||||||
\(476\) | 8.41535 | 0.385717 | ||||||||
\(477\) | −12.6644 | −0.579863 | ||||||||
\(478\) | 4.41447 | 0.201913 | ||||||||
\(479\) | 1.22227 | 0.0558471 | 0.0279236 | − | 0.999610i | \(-0.491110\pi\) | ||||
0.0279236 | + | 0.999610i | \(0.491110\pi\) | |||||||
\(480\) | 0.542814 | 0.0247759 | ||||||||
\(481\) | −0.518334 | −0.0236340 | ||||||||
\(482\) | −3.99479 | −0.181958 | ||||||||
\(483\) | 19.8393 | 0.902720 | ||||||||
\(484\) | −10.5993 | −0.481788 | ||||||||
\(485\) | −3.95912 | −0.179774 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 1.80937 | 0.0819903 | 0.0409951 | − | 0.999159i | \(-0.486947\pi\) | ||||
0.0409951 | + | 0.999159i | \(0.486947\pi\) | |||||||
\(488\) | −11.2974 | −0.511408 | ||||||||
\(489\) | 15.4871 | 0.700353 | ||||||||
\(490\) | 1.26854 | 0.0573068 | ||||||||
\(491\) | −20.4058 | −0.920902 | −0.460451 | − | 0.887685i | \(-0.652312\pi\) | ||||
−0.460451 | + | 0.887685i | \(0.652312\pi\) | |||||||
\(492\) | 2.61666 | 0.117968 | ||||||||
\(493\) | −4.08339 | −0.183907 | ||||||||
\(494\) | 2.05565 | 0.0924879 | ||||||||
\(495\) | 0.343593 | 0.0154434 | ||||||||
\(496\) | −2.05565 | −0.0923012 | ||||||||
\(497\) | 9.92740 | 0.445305 | ||||||||
\(498\) | 4.86110 | 0.217831 | ||||||||
\(499\) | 25.4883 | 1.14101 | 0.570506 | − | 0.821293i | \(-0.306747\pi\) | ||||
0.570506 | + | 0.821293i | \(0.306747\pi\) | |||||||
\(500\) | −5.26820 | −0.235601 | ||||||||
\(501\) | 8.73179 | 0.390107 | ||||||||
\(502\) | −3.11912 | −0.139213 | ||||||||
\(503\) | −10.1064 | −0.450623 | −0.225311 | − | 0.974287i | \(-0.572340\pi\) | ||||
−0.225311 | + | 0.974287i | \(0.572340\pi\) | |||||||
\(504\) | 3.05565 | 0.136109 | ||||||||
\(505\) | −8.28558 | −0.368704 | ||||||||
\(506\) | 4.10977 | 0.182701 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | −1.73086 | −0.0767943 | ||||||||
\(509\) | 24.7866 | 1.09865 | 0.549323 | − | 0.835610i | \(-0.314886\pi\) | ||||
0.549323 | + | 0.835610i | \(0.314886\pi\) | |||||||
\(510\) | 1.49493 | 0.0661965 | ||||||||
\(511\) | 37.5496 | 1.66110 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 2.05565 | 0.0907590 | ||||||||
\(514\) | 0.0449774 | 0.00198387 | ||||||||
\(515\) | −0.542814 | −0.0239192 | ||||||||
\(516\) | 2.49072 | 0.109648 | ||||||||
\(517\) | 1.32653 | 0.0583407 | ||||||||
\(518\) | −1.58384 | −0.0695901 | ||||||||
\(519\) | 21.1049 | 0.926401 | ||||||||
\(520\) | 0.542814 | 0.0238039 | ||||||||
\(521\) | −7.43893 | −0.325905 | −0.162953 | − | 0.986634i | \(-0.552102\pi\) | ||||
−0.162953 | + | 0.986634i | \(0.552102\pi\) | |||||||
\(522\) | −1.48269 | −0.0648957 | ||||||||
\(523\) | −39.1467 | −1.71177 | −0.855883 | − | 0.517169i | \(-0.826986\pi\) | ||||
−0.855883 | + | 0.517169i | \(0.826986\pi\) | |||||||
\(524\) | 8.42898 | 0.368222 | ||||||||
\(525\) | −14.3779 | −0.627503 | ||||||||
\(526\) | 28.7094 | 1.25179 | ||||||||
\(527\) | −5.66132 | −0.246611 | ||||||||
\(528\) | 0.632985 | 0.0275471 | ||||||||
\(529\) | 19.1548 | 0.832817 | ||||||||
\(530\) | −6.87441 | −0.298605 | ||||||||
\(531\) | 0.846439 | 0.0367323 | ||||||||
\(532\) | 6.28133 | 0.272330 | ||||||||
\(533\) | 2.61666 | 0.113340 | ||||||||
\(534\) | −9.35113 | −0.404663 | ||||||||
\(535\) | −9.52807 | −0.411934 | ||||||||
\(536\) | 12.0004 | 0.518337 | ||||||||
\(537\) | 8.18560 | 0.353235 | ||||||||
\(538\) | 13.4485 | 0.579807 | ||||||||
\(539\) | 1.47927 | 0.0637166 | ||||||||
\(540\) | 0.542814 | 0.0233590 | ||||||||
\(541\) | −18.0899 | −0.777746 | −0.388873 | − | 0.921291i | \(-0.627135\pi\) | ||||
−0.388873 | + | 0.921291i | \(0.627135\pi\) | |||||||
\(542\) | −8.93755 | −0.383901 | ||||||||
\(543\) | 6.24534 | 0.268013 | ||||||||
\(544\) | 2.75403 | 0.118078 | ||||||||
\(545\) | −4.77848 | −0.204688 | ||||||||
\(546\) | 3.05565 | 0.130770 | ||||||||
\(547\) | 16.3919 | 0.700867 | 0.350434 | − | 0.936588i | \(-0.386034\pi\) | ||||
0.350434 | + | 0.936588i | \(0.386034\pi\) | |||||||
\(548\) | 8.45316 | 0.361101 | ||||||||
\(549\) | −11.2974 | −0.482160 | ||||||||
\(550\) | −2.97842 | −0.127000 | ||||||||
\(551\) | −3.04789 | −0.129845 | ||||||||
\(552\) | 6.49267 | 0.276347 | ||||||||
\(553\) | 30.7776 | 1.30880 | ||||||||
\(554\) | 8.96300 | 0.380801 | ||||||||
\(555\) | −0.281358 | −0.0119430 | ||||||||
\(556\) | −3.12795 | −0.132655 | ||||||||
\(557\) | −5.32319 | −0.225551 | −0.112775 | − | 0.993621i | \(-0.535974\pi\) | ||||
−0.112775 | + | 0.993621i | \(0.535974\pi\) | |||||||
\(558\) | −2.05565 | −0.0870224 | ||||||||
\(559\) | 2.49072 | 0.105346 | ||||||||
\(560\) | 1.65865 | 0.0700906 | ||||||||
\(561\) | 1.74326 | 0.0736006 | ||||||||
\(562\) | 5.60492 | 0.236429 | ||||||||
\(563\) | −9.15521 | −0.385846 | −0.192923 | − | 0.981214i | \(-0.561797\pi\) | ||||
−0.192923 | + | 0.981214i | \(0.561797\pi\) | |||||||
\(564\) | 2.09567 | 0.0882437 | ||||||||
\(565\) | −0.548238 | −0.0230645 | ||||||||
\(566\) | 13.6111 | 0.572117 | ||||||||
\(567\) | 3.05565 | 0.128325 | ||||||||
\(568\) | 3.24887 | 0.136320 | ||||||||
\(569\) | 13.9289 | 0.583929 | 0.291964 | − | 0.956429i | \(-0.405691\pi\) | ||||
0.291964 | + | 0.956429i | \(0.405691\pi\) | |||||||
\(570\) | 1.11583 | 0.0467371 | ||||||||
\(571\) | −37.2016 | −1.55684 | −0.778420 | − | 0.627744i | \(-0.783978\pi\) | ||||
−0.778420 | + | 0.627744i | \(0.783978\pi\) | |||||||
\(572\) | 0.632985 | 0.0264664 | ||||||||
\(573\) | −21.2265 | −0.886752 | ||||||||
\(574\) | 7.99559 | 0.333730 | ||||||||
\(575\) | −30.5503 | −1.27404 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −3.84309 | −0.159990 | −0.0799950 | − | 0.996795i | \(-0.525490\pi\) | ||||
−0.0799950 | + | 0.996795i | \(0.525490\pi\) | |||||||
\(578\) | −9.41529 | −0.391625 | ||||||||
\(579\) | −9.87884 | −0.410551 | ||||||||
\(580\) | −0.804826 | −0.0334186 | ||||||||
\(581\) | 14.8538 | 0.616239 | ||||||||
\(582\) | −7.29369 | −0.302333 | ||||||||
\(583\) | −8.01638 | −0.332005 | ||||||||
\(584\) | 12.2886 | 0.508506 | ||||||||
\(585\) | 0.542814 | 0.0224426 | ||||||||
\(586\) | −17.7380 | −0.732751 | ||||||||
\(587\) | 38.2646 | 1.57935 | 0.789675 | − | 0.613526i | \(-0.210249\pi\) | ||||
0.789675 | + | 0.613526i | \(0.210249\pi\) | |||||||
\(588\) | 2.33697 | 0.0963751 | ||||||||
\(589\) | −4.22568 | −0.174116 | ||||||||
\(590\) | 0.459459 | 0.0189156 | ||||||||
\(591\) | −17.5032 | −0.719986 | ||||||||
\(592\) | −0.518334 | −0.0213034 | ||||||||
\(593\) | 34.1185 | 1.40108 | 0.700539 | − | 0.713614i | \(-0.252943\pi\) | ||||
0.700539 | + | 0.713614i | \(0.252943\pi\) | |||||||
\(594\) | 0.632985 | 0.0259717 | ||||||||
\(595\) | 4.56797 | 0.187268 | ||||||||
\(596\) | 9.04546 | 0.370517 | ||||||||
\(597\) | −26.7000 | −1.09276 | ||||||||
\(598\) | 6.49267 | 0.265505 | ||||||||
\(599\) | −16.2920 | −0.665671 | −0.332836 | − | 0.942985i | \(-0.608005\pi\) | ||||
−0.332836 | + | 0.942985i | \(0.608005\pi\) | |||||||
\(600\) | −4.70535 | −0.192095 | ||||||||
\(601\) | 25.1192 | 1.02463 | 0.512317 | − | 0.858796i | \(-0.328787\pi\) | ||||
0.512317 | + | 0.858796i | \(0.328787\pi\) | |||||||
\(602\) | 7.61075 | 0.310191 | ||||||||
\(603\) | 12.0004 | 0.488692 | ||||||||
\(604\) | −18.2754 | −0.743617 | ||||||||
\(605\) | −5.75346 | −0.233911 | ||||||||
\(606\) | −15.2641 | −0.620063 | ||||||||
\(607\) | 13.5665 | 0.550646 | 0.275323 | − | 0.961352i | \(-0.411215\pi\) | ||||
0.275323 | + | 0.961352i | \(0.411215\pi\) | |||||||
\(608\) | 2.05565 | 0.0833675 | ||||||||
\(609\) | −4.53058 | −0.183589 | ||||||||
\(610\) | −6.13237 | −0.248292 | ||||||||
\(611\) | 2.09567 | 0.0847818 | ||||||||
\(612\) | 2.75403 | 0.111325 | ||||||||
\(613\) | −10.3604 | −0.418452 | −0.209226 | − | 0.977867i | \(-0.567095\pi\) | ||||
−0.209226 | + | 0.977867i | \(0.567095\pi\) | |||||||
\(614\) | 6.26775 | 0.252946 | ||||||||
\(615\) | 1.42036 | 0.0572744 | ||||||||
\(616\) | 1.93418 | 0.0779303 | ||||||||
\(617\) | 4.53975 | 0.182763 | 0.0913817 | − | 0.995816i | \(-0.470872\pi\) | ||||
0.0913817 | + | 0.995816i | \(0.470872\pi\) | |||||||
\(618\) | −1.00000 | −0.0402259 | ||||||||
\(619\) | −14.5122 | −0.583293 | −0.291647 | − | 0.956526i | \(-0.594203\pi\) | ||||
−0.291647 | + | 0.956526i | \(0.594203\pi\) | |||||||
\(620\) | −1.11583 | −0.0448129 | ||||||||
\(621\) | 6.49267 | 0.260542 | ||||||||
\(622\) | 24.8115 | 0.994851 | ||||||||
\(623\) | −28.5737 | −1.14478 | ||||||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | 20.6671 | 0.826685 | ||||||||
\(626\) | −26.4684 | −1.05789 | ||||||||
\(627\) | 1.30119 | 0.0519647 | ||||||||
\(628\) | 15.5277 | 0.619624 | ||||||||
\(629\) | −1.42751 | −0.0569185 | ||||||||
\(630\) | 1.65865 | 0.0660820 | ||||||||
\(631\) | 9.81313 | 0.390654 | 0.195327 | − | 0.980738i | \(-0.437423\pi\) | ||||
0.195327 | + | 0.980738i | \(0.437423\pi\) | |||||||
\(632\) | 10.0724 | 0.400657 | ||||||||
\(633\) | 14.8379 | 0.589754 | ||||||||
\(634\) | 24.8381 | 0.986449 | ||||||||
\(635\) | −0.939532 | −0.0372842 | ||||||||
\(636\) | −12.6644 | −0.502176 | ||||||||
\(637\) | 2.33697 | 0.0925942 | ||||||||
\(638\) | −0.938523 | −0.0371565 | ||||||||
\(639\) | 3.24887 | 0.128523 | ||||||||
\(640\) | 0.542814 | 0.0214566 | ||||||||
\(641\) | 8.38545 | 0.331205 | 0.165603 | − | 0.986193i | \(-0.447043\pi\) | ||||
0.165603 | + | 0.986193i | \(0.447043\pi\) | |||||||
\(642\) | −17.5531 | −0.692766 | ||||||||
\(643\) | 3.02004 | 0.119099 | 0.0595495 | − | 0.998225i | \(-0.481034\pi\) | ||||
0.0595495 | + | 0.998225i | \(0.481034\pi\) | |||||||
\(644\) | 19.8393 | 0.781778 | ||||||||
\(645\) | 1.35200 | 0.0532348 | ||||||||
\(646\) | 5.66132 | 0.222742 | ||||||||
\(647\) | 4.43260 | 0.174264 | 0.0871318 | − | 0.996197i | \(-0.472230\pi\) | ||||
0.0871318 | + | 0.996197i | \(0.472230\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 0.535784 | 0.0210313 | ||||||||
\(650\) | −4.70535 | −0.184559 | ||||||||
\(651\) | −6.28133 | −0.246185 | ||||||||
\(652\) | 15.4871 | 0.606524 | ||||||||
\(653\) | −0.274241 | −0.0107319 | −0.00536595 | − | 0.999986i | \(-0.501708\pi\) | ||||
−0.00536595 | + | 0.999986i | \(0.501708\pi\) | |||||||
\(654\) | −8.80317 | −0.344231 | ||||||||
\(655\) | 4.57536 | 0.178774 | ||||||||
\(656\) | 2.61666 | 0.102163 | ||||||||
\(657\) | 12.2886 | 0.479424 | ||||||||
\(658\) | 6.40363 | 0.249640 | ||||||||
\(659\) | 47.4429 | 1.84811 | 0.924057 | − | 0.382256i | \(-0.124853\pi\) | ||||
0.924057 | + | 0.382256i | \(0.124853\pi\) | |||||||
\(660\) | 0.343593 | 0.0133743 | ||||||||
\(661\) | −33.6301 | −1.30806 | −0.654029 | − | 0.756469i | \(-0.726923\pi\) | ||||
−0.654029 | + | 0.756469i | \(0.726923\pi\) | |||||||
\(662\) | 24.3920 | 0.948024 | ||||||||
\(663\) | 2.75403 | 0.106958 | ||||||||
\(664\) | 4.86110 | 0.188647 | ||||||||
\(665\) | 3.40959 | 0.132218 | ||||||||
\(666\) | −0.518334 | −0.0200850 | ||||||||
\(667\) | −9.62664 | −0.372745 | ||||||||
\(668\) | 8.73179 | 0.337843 | ||||||||
\(669\) | −14.8504 | −0.574148 | ||||||||
\(670\) | 6.51396 | 0.251656 | ||||||||
\(671\) | −7.15107 | −0.276064 | ||||||||
\(672\) | 3.05565 | 0.117874 | ||||||||
\(673\) | −30.9360 | −1.19249 | −0.596247 | − | 0.802801i | \(-0.703342\pi\) | ||||
−0.596247 | + | 0.802801i | \(0.703342\pi\) | |||||||
\(674\) | −28.4373 | −1.09536 | ||||||||
\(675\) | −4.70535 | −0.181109 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 7.31704 | 0.281217 | 0.140608 | − | 0.990065i | \(-0.455094\pi\) | ||||
0.140608 | + | 0.990065i | \(0.455094\pi\) | |||||||
\(678\) | −1.00999 | −0.0387886 | ||||||||
\(679\) | −22.2869 | −0.855295 | ||||||||
\(680\) | 1.49493 | 0.0573278 | ||||||||
\(681\) | 7.10596 | 0.272301 | ||||||||
\(682\) | −1.30119 | −0.0498253 | ||||||||
\(683\) | 43.4758 | 1.66356 | 0.831778 | − | 0.555108i | \(-0.187323\pi\) | ||||
0.831778 | + | 0.555108i | \(0.187323\pi\) | |||||||
\(684\) | 2.05565 | 0.0785996 | ||||||||
\(685\) | 4.58849 | 0.175317 | ||||||||
\(686\) | −14.2486 | −0.544013 | ||||||||
\(687\) | 2.94089 | 0.112202 | ||||||||
\(688\) | 2.49072 | 0.0949577 | ||||||||
\(689\) | −12.6644 | −0.482475 | ||||||||
\(690\) | 3.52431 | 0.134168 | ||||||||
\(691\) | 0.441434 | 0.0167929 | 0.00839646 | − | 0.999965i | \(-0.497327\pi\) | ||||
0.00839646 | + | 0.999965i | \(0.497327\pi\) | |||||||
\(692\) | 21.1049 | 0.802287 | ||||||||
\(693\) | 1.93418 | 0.0734734 | ||||||||
\(694\) | 3.72720 | 0.141483 | ||||||||
\(695\) | −1.69790 | −0.0644049 | ||||||||
\(696\) | −1.48269 | −0.0562013 | ||||||||
\(697\) | 7.20638 | 0.272961 | ||||||||
\(698\) | −18.4589 | −0.698679 | ||||||||
\(699\) | 8.07222 | 0.305319 | ||||||||
\(700\) | −14.3779 | −0.543433 | ||||||||
\(701\) | −25.8603 | −0.976731 | −0.488365 | − | 0.872639i | \(-0.662407\pi\) | ||||
−0.488365 | + | 0.872639i | \(0.662407\pi\) | |||||||
\(702\) | 1.00000 | 0.0377426 | ||||||||
\(703\) | −1.06551 | −0.0401865 | ||||||||
\(704\) | 0.632985 | 0.0238565 | ||||||||
\(705\) | 1.13756 | 0.0428430 | ||||||||
\(706\) | −10.9773 | −0.413136 | ||||||||
\(707\) | −46.6418 | −1.75415 | ||||||||
\(708\) | 0.846439 | 0.0318111 | ||||||||
\(709\) | −17.9601 | −0.674507 | −0.337254 | − | 0.941414i | \(-0.609498\pi\) | ||||
−0.337254 | + | 0.941414i | \(0.609498\pi\) | |||||||
\(710\) | 1.76353 | 0.0661841 | ||||||||
\(711\) | 10.0724 | 0.377743 | ||||||||
\(712\) | −9.35113 | −0.350448 | ||||||||
\(713\) | −13.3466 | −0.499835 | ||||||||
\(714\) | 8.41535 | 0.314937 | ||||||||
\(715\) | 0.343593 | 0.0128496 | ||||||||
\(716\) | 8.18560 | 0.305910 | ||||||||
\(717\) | 4.41447 | 0.164861 | ||||||||
\(718\) | 17.8262 | 0.665267 | ||||||||
\(719\) | −38.0909 | −1.42055 | −0.710276 | − | 0.703924i | \(-0.751430\pi\) | ||||
−0.710276 | + | 0.703924i | \(0.751430\pi\) | |||||||
\(720\) | 0.542814 | 0.0202295 | ||||||||
\(721\) | −3.05565 | −0.113798 | ||||||||
\(722\) | −14.7743 | −0.549843 | ||||||||
\(723\) | −3.99479 | −0.148568 | ||||||||
\(724\) | 6.24534 | 0.232106 | ||||||||
\(725\) | 6.97659 | 0.259104 | ||||||||
\(726\) | −10.5993 | −0.393378 | ||||||||
\(727\) | −11.9914 | −0.444736 | −0.222368 | − | 0.974963i | \(-0.571379\pi\) | ||||
−0.222368 | + | 0.974963i | \(0.571379\pi\) | |||||||
\(728\) | 3.05565 | 0.113250 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 6.67042 | 0.246883 | ||||||||
\(731\) | 6.85952 | 0.253709 | ||||||||
\(732\) | −11.2974 | −0.417563 | ||||||||
\(733\) | −19.4540 | −0.718550 | −0.359275 | − | 0.933232i | \(-0.616976\pi\) | ||||
−0.359275 | + | 0.933232i | \(0.616976\pi\) | |||||||
\(734\) | 3.69689 | 0.136455 | ||||||||
\(735\) | 1.26854 | 0.0467908 | ||||||||
\(736\) | 6.49267 | 0.239323 | ||||||||
\(737\) | 7.59605 | 0.279804 | ||||||||
\(738\) | 2.61666 | 0.0963207 | ||||||||
\(739\) | −25.2685 | −0.929515 | −0.464758 | − | 0.885438i | \(-0.653859\pi\) | ||||
−0.464758 | + | 0.885438i | \(0.653859\pi\) | |||||||
\(740\) | −0.281358 | −0.0103429 | ||||||||
\(741\) | 2.05565 | 0.0755160 | ||||||||
\(742\) | −38.6979 | −1.42065 | ||||||||
\(743\) | −7.19524 | −0.263968 | −0.131984 | − | 0.991252i | \(-0.542135\pi\) | ||||
−0.131984 | + | 0.991252i | \(0.542135\pi\) | |||||||
\(744\) | −2.05565 | −0.0753636 | ||||||||
\(745\) | 4.91000 | 0.179888 | ||||||||
\(746\) | 17.8883 | 0.654938 | ||||||||
\(747\) | 4.86110 | 0.177858 | ||||||||
\(748\) | 1.74326 | 0.0637400 | ||||||||
\(749\) | −53.6361 | −1.95982 | ||||||||
\(750\) | −5.26820 | −0.192367 | ||||||||
\(751\) | 30.5362 | 1.11428 | 0.557140 | − | 0.830418i | \(-0.311899\pi\) | ||||
0.557140 | + | 0.830418i | \(0.311899\pi\) | |||||||
\(752\) | 2.09567 | 0.0764213 | ||||||||
\(753\) | −3.11912 | −0.113667 | ||||||||
\(754\) | −1.48269 | −0.0539965 | ||||||||
\(755\) | −9.92016 | −0.361032 | ||||||||
\(756\) | 3.05565 | 0.111133 | ||||||||
\(757\) | 3.23081 | 0.117426 | 0.0587129 | − | 0.998275i | \(-0.481300\pi\) | ||||
0.0587129 | + | 0.998275i | \(0.481300\pi\) | |||||||
\(758\) | −29.0777 | −1.05615 | ||||||||
\(759\) | 4.10977 | 0.149175 | ||||||||
\(760\) | 1.11583 | 0.0404755 | ||||||||
\(761\) | −28.5912 | −1.03643 | −0.518214 | − | 0.855251i | \(-0.673403\pi\) | ||||
−0.518214 | + | 0.855251i | \(0.673403\pi\) | |||||||
\(762\) | −1.73086 | −0.0627023 | ||||||||
\(763\) | −26.8994 | −0.973823 | ||||||||
\(764\) | −21.2265 | −0.767950 | ||||||||
\(765\) | 1.49493 | 0.0540492 | ||||||||
\(766\) | 9.42500 | 0.340539 | ||||||||
\(767\) | 0.846439 | 0.0305632 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 49.1119 | 1.77102 | 0.885511 | − | 0.464619i | \(-0.153809\pi\) | ||||
0.885511 | + | 0.464619i | \(0.153809\pi\) | |||||||
\(770\) | 1.04990 | 0.0378357 | ||||||||
\(771\) | 0.0449774 | 0.00161982 | ||||||||
\(772\) | −9.87884 | −0.355547 | ||||||||
\(773\) | 31.4008 | 1.12941 | 0.564704 | − | 0.825294i | \(-0.308990\pi\) | ||||
0.564704 | + | 0.825294i | \(0.308990\pi\) | |||||||
\(774\) | 2.49072 | 0.0895270 | ||||||||
\(775\) | 9.67254 | 0.347448 | ||||||||
\(776\) | −7.29369 | −0.261828 | ||||||||
\(777\) | −1.58384 | −0.0568201 | ||||||||
\(778\) | −23.4042 | −0.839080 | ||||||||
\(779\) | 5.37893 | 0.192720 | ||||||||
\(780\) | 0.542814 | 0.0194358 | ||||||||
\(781\) | 2.05649 | 0.0735869 | ||||||||
\(782\) | 17.8810 | 0.639425 | ||||||||
\(783\) | −1.48269 | −0.0529871 | ||||||||
\(784\) | 2.33697 | 0.0834633 | ||||||||
\(785\) | 8.42867 | 0.300832 | ||||||||
\(786\) | 8.42898 | 0.300652 | ||||||||
\(787\) | 35.2321 | 1.25589 | 0.627944 | − | 0.778259i | \(-0.283897\pi\) | ||||
0.627944 | + | 0.778259i | \(0.283897\pi\) | |||||||
\(788\) | −17.5032 | −0.623526 | ||||||||
\(789\) | 28.7094 | 1.02208 | ||||||||
\(790\) | 5.46742 | 0.194522 | ||||||||
\(791\) | −3.08618 | −0.109732 | ||||||||
\(792\) | 0.632985 | 0.0224922 | ||||||||
\(793\) | −11.2974 | −0.401182 | ||||||||
\(794\) | −10.8257 | −0.384189 | ||||||||
\(795\) | −6.87441 | −0.243810 | ||||||||
\(796\) | −26.7000 | −0.946358 | ||||||||
\(797\) | 3.39691 | 0.120325 | 0.0601623 | − | 0.998189i | \(-0.480838\pi\) | ||||
0.0601623 | + | 0.998189i | \(0.480838\pi\) | |||||||
\(798\) | 6.28133 | 0.222357 | ||||||||
\(799\) | 5.77156 | 0.204183 | ||||||||
\(800\) | −4.70535 | −0.166359 | ||||||||
\(801\) | −9.35113 | −0.330406 | ||||||||
\(802\) | −2.98820 | −0.105517 | ||||||||
\(803\) | 7.77851 | 0.274498 | ||||||||
\(804\) | 12.0004 | 0.423220 | ||||||||
\(805\) | 10.7690 | 0.379559 | ||||||||
\(806\) | −2.05565 | −0.0724070 | ||||||||
\(807\) | 13.4485 | 0.473410 | ||||||||
\(808\) | −15.2641 | −0.536991 | ||||||||
\(809\) | −13.9946 | −0.492023 | −0.246011 | − | 0.969267i | \(-0.579120\pi\) | ||||
−0.246011 | + | 0.969267i | \(0.579120\pi\) | |||||||
\(810\) | 0.542814 | 0.0190725 | ||||||||
\(811\) | −43.2608 | −1.51909 | −0.759546 | − | 0.650453i | \(-0.774579\pi\) | ||||
−0.759546 | + | 0.650453i | \(0.774579\pi\) | |||||||
\(812\) | −4.53058 | −0.158992 | ||||||||
\(813\) | −8.93755 | −0.313453 | ||||||||
\(814\) | −0.328098 | −0.0114998 | ||||||||
\(815\) | 8.40663 | 0.294472 | ||||||||
\(816\) | 2.75403 | 0.0964105 | ||||||||
\(817\) | 5.12003 | 0.179127 | ||||||||
\(818\) | −25.2550 | −0.883022 | ||||||||
\(819\) | 3.05565 | 0.106773 | ||||||||
\(820\) | 1.42036 | 0.0496011 | ||||||||
\(821\) | 42.8319 | 1.49485 | 0.747423 | − | 0.664349i | \(-0.231291\pi\) | ||||
0.747423 | + | 0.664349i | \(0.231291\pi\) | |||||||
\(822\) | 8.45316 | 0.294838 | ||||||||
\(823\) | 20.1546 | 0.702545 | 0.351273 | − | 0.936273i | \(-0.385749\pi\) | ||||
0.351273 | + | 0.936273i | \(0.385749\pi\) | |||||||
\(824\) | −1.00000 | −0.0348367 | ||||||||
\(825\) | −2.97842 | −0.103695 | ||||||||
\(826\) | 2.58642 | 0.0899930 | ||||||||
\(827\) | 30.2332 | 1.05131 | 0.525656 | − | 0.850697i | \(-0.323820\pi\) | ||||
0.525656 | + | 0.850697i | \(0.323820\pi\) | |||||||
\(828\) | 6.49267 | 0.225636 | ||||||||
\(829\) | −13.4789 | −0.468140 | −0.234070 | − | 0.972220i | \(-0.575204\pi\) | ||||
−0.234070 | + | 0.972220i | \(0.575204\pi\) | |||||||
\(830\) | 2.63867 | 0.0915896 | ||||||||
\(831\) | 8.96300 | 0.310923 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | 6.43610 | 0.222998 | ||||||||
\(834\) | −3.12795 | −0.108312 | ||||||||
\(835\) | 4.73973 | 0.164025 | ||||||||
\(836\) | 1.30119 | 0.0450027 | ||||||||
\(837\) | −2.05565 | −0.0710535 | ||||||||
\(838\) | −1.20744 | −0.0417103 | ||||||||
\(839\) | 23.6608 | 0.816861 | 0.408430 | − | 0.912790i | \(-0.366076\pi\) | ||||
0.408430 | + | 0.912790i | \(0.366076\pi\) | |||||||
\(840\) | 1.65865 | 0.0572287 | ||||||||
\(841\) | −26.8016 | −0.924194 | ||||||||
\(842\) | 13.8740 | 0.478130 | ||||||||
\(843\) | 5.60492 | 0.193044 | ||||||||
\(844\) | 14.8379 | 0.510742 | ||||||||
\(845\) | 0.542814 | 0.0186734 | ||||||||
\(846\) | 2.09567 | 0.0720507 | ||||||||
\(847\) | −32.3878 | −1.11286 | ||||||||
\(848\) | −12.6644 | −0.434898 | ||||||||
\(849\) | 13.6111 | 0.467132 | ||||||||
\(850\) | −12.9587 | −0.444480 | ||||||||
\(851\) | −3.36537 | −0.115363 | ||||||||
\(852\) | 3.24887 | 0.111304 | ||||||||
\(853\) | 42.1021 | 1.44155 | 0.720774 | − | 0.693170i | \(-0.243787\pi\) | ||||
0.720774 | + | 0.693170i | \(0.243787\pi\) | |||||||
\(854\) | −34.5208 | −1.18128 | ||||||||
\(855\) | 1.11583 | 0.0381607 | ||||||||
\(856\) | −17.5531 | −0.599953 | ||||||||
\(857\) | −4.41287 | −0.150741 | −0.0753704 | − | 0.997156i | \(-0.524014\pi\) | ||||
−0.0753704 | + | 0.997156i | \(0.524014\pi\) | |||||||
\(858\) | 0.632985 | 0.0216098 | ||||||||
\(859\) | −11.8602 | −0.404665 | −0.202333 | − | 0.979317i | \(-0.564852\pi\) | ||||
−0.202333 | + | 0.979317i | \(0.564852\pi\) | |||||||
\(860\) | 1.35200 | 0.0461027 | ||||||||
\(861\) | 7.99559 | 0.272489 | ||||||||
\(862\) | −11.8762 | −0.404504 | ||||||||
\(863\) | 21.0952 | 0.718088 | 0.359044 | − | 0.933321i | \(-0.383103\pi\) | ||||
0.359044 | + | 0.933321i | \(0.383103\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 11.4560 | 0.389516 | ||||||||
\(866\) | 39.6312 | 1.34672 | ||||||||
\(867\) | −9.41529 | −0.319760 | ||||||||
\(868\) | −6.28133 | −0.213202 | ||||||||
\(869\) | 6.37566 | 0.216279 | ||||||||
\(870\) | −0.804826 | −0.0272861 | ||||||||
\(871\) | 12.0004 | 0.406617 | ||||||||
\(872\) | −8.80317 | −0.298113 | ||||||||
\(873\) | −7.29369 | −0.246854 | ||||||||
\(874\) | 13.3466 | 0.451457 | ||||||||
\(875\) | −16.0977 | −0.544203 | ||||||||
\(876\) | 12.2886 | 0.415194 | ||||||||
\(877\) | −15.0715 | −0.508927 | −0.254464 | − | 0.967082i | \(-0.581899\pi\) | ||||
−0.254464 | + | 0.967082i | \(0.581899\pi\) | |||||||
\(878\) | −18.7402 | −0.632451 | ||||||||
\(879\) | −17.7380 | −0.598289 | ||||||||
\(880\) | 0.343593 | 0.0115825 | ||||||||
\(881\) | −20.9867 | −0.707061 | −0.353530 | − | 0.935423i | \(-0.615019\pi\) | ||||
−0.353530 | + | 0.935423i | \(0.615019\pi\) | |||||||
\(882\) | 2.33697 | 0.0786900 | ||||||||
\(883\) | 42.6118 | 1.43400 | 0.717000 | − | 0.697073i | \(-0.245515\pi\) | ||||
0.717000 | + | 0.697073i | \(0.245515\pi\) | |||||||
\(884\) | 2.75403 | 0.0926282 | ||||||||
\(885\) | 0.459459 | 0.0154445 | ||||||||
\(886\) | −1.45204 | −0.0487824 | ||||||||
\(887\) | 11.4372 | 0.384023 | 0.192011 | − | 0.981393i | \(-0.438499\pi\) | ||||
0.192011 | + | 0.981393i | \(0.438499\pi\) | |||||||
\(888\) | −0.518334 | −0.0173941 | ||||||||
\(889\) | −5.28888 | −0.177383 | ||||||||
\(890\) | −5.07592 | −0.170145 | ||||||||
\(891\) | 0.632985 | 0.0212058 | ||||||||
\(892\) | −14.8504 | −0.497227 | ||||||||
\(893\) | 4.30796 | 0.144160 | ||||||||
\(894\) | 9.04546 | 0.302526 | ||||||||
\(895\) | 4.44325 | 0.148522 | ||||||||
\(896\) | 3.05565 | 0.102082 | ||||||||
\(897\) | 6.49267 | 0.216784 | ||||||||
\(898\) | −31.2014 | −1.04121 | ||||||||
\(899\) | 3.04789 | 0.101653 | ||||||||
\(900\) | −4.70535 | −0.156845 | ||||||||
\(901\) | −34.8782 | −1.16196 | ||||||||
\(902\) | 1.65631 | 0.0551490 | ||||||||
\(903\) | 7.61075 | 0.253270 | ||||||||
\(904\) | −1.00999 | −0.0335919 | ||||||||
\(905\) | 3.39006 | 0.112689 | ||||||||
\(906\) | −18.2754 | −0.607161 | ||||||||
\(907\) | −57.8074 | −1.91946 | −0.959732 | − | 0.280919i | \(-0.909361\pi\) | ||||
−0.959732 | + | 0.280919i | \(0.909361\pi\) | |||||||
\(908\) | 7.10596 | 0.235820 | ||||||||
\(909\) | −15.2641 | −0.506280 | ||||||||
\(910\) | 1.65865 | 0.0549836 | ||||||||
\(911\) | 40.3706 | 1.33754 | 0.668769 | − | 0.743471i | \(-0.266822\pi\) | ||||
0.668769 | + | 0.743471i | \(0.266822\pi\) | |||||||
\(912\) | 2.05565 | 0.0680692 | ||||||||
\(913\) | 3.07700 | 0.101834 | ||||||||
\(914\) | −4.40435 | −0.145683 | ||||||||
\(915\) | −6.13237 | −0.202730 | ||||||||
\(916\) | 2.94089 | 0.0971698 | ||||||||
\(917\) | 25.7560 | 0.850537 | ||||||||
\(918\) | 2.75403 | 0.0908967 | ||||||||
\(919\) | −6.88287 | −0.227045 | −0.113522 | − | 0.993535i | \(-0.536213\pi\) | ||||
−0.113522 | + | 0.993535i | \(0.536213\pi\) | |||||||
\(920\) | 3.52431 | 0.116193 | ||||||||
\(921\) | 6.26775 | 0.206529 | ||||||||
\(922\) | 18.3876 | 0.605562 | ||||||||
\(923\) | 3.24887 | 0.106938 | ||||||||
\(924\) | 1.93418 | 0.0636298 | ||||||||
\(925\) | 2.43894 | 0.0801919 | ||||||||
\(926\) | −10.6320 | −0.349389 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | −1.48269 | −0.0486718 | ||||||||
\(929\) | −53.6348 | −1.75970 | −0.879850 | − | 0.475252i | \(-0.842357\pi\) | ||||
−0.879850 | + | 0.475252i | \(0.842357\pi\) | |||||||
\(930\) | −1.11583 | −0.0365896 | ||||||||
\(931\) | 4.80399 | 0.157444 | ||||||||
\(932\) | 8.07222 | 0.264414 | ||||||||
\(933\) | 24.8115 | 0.812292 | ||||||||
\(934\) | 6.28660 | 0.205704 | ||||||||
\(935\) | 0.946267 | 0.0309462 | ||||||||
\(936\) | 1.00000 | 0.0326860 | ||||||||
\(937\) | −47.5909 | −1.55473 | −0.777364 | − | 0.629051i | \(-0.783444\pi\) | ||||
−0.777364 | + | 0.629051i | \(0.783444\pi\) | |||||||
\(938\) | 36.6689 | 1.19728 | ||||||||
\(939\) | −26.4684 | −0.863763 | ||||||||
\(940\) | 1.13756 | 0.0371031 | ||||||||
\(941\) | −59.9987 | −1.95590 | −0.977952 | − | 0.208831i | \(-0.933034\pi\) | ||||
−0.977952 | + | 0.208831i | \(0.933034\pi\) | |||||||
\(942\) | 15.5277 | 0.505921 | ||||||||
\(943\) | 16.9891 | 0.553242 | ||||||||
\(944\) | 0.846439 | 0.0275493 | ||||||||
\(945\) | 1.65865 | 0.0539558 | ||||||||
\(946\) | 1.57659 | 0.0512593 | ||||||||
\(947\) | −29.0066 | −0.942587 | −0.471293 | − | 0.881976i | \(-0.656213\pi\) | ||||
−0.471293 | + | 0.881976i | \(0.656213\pi\) | |||||||
\(948\) | 10.0724 | 0.327135 | ||||||||
\(949\) | 12.2886 | 0.398905 | ||||||||
\(950\) | −9.67254 | −0.313819 | ||||||||
\(951\) | 24.8381 | 0.805432 | ||||||||
\(952\) | 8.41535 | 0.272743 | ||||||||
\(953\) | −0.708339 | −0.0229454 | −0.0114727 | − | 0.999934i | \(-0.503652\pi\) | ||||
−0.0114727 | + | 0.999934i | \(0.503652\pi\) | |||||||
\(954\) | −12.6644 | −0.410025 | ||||||||
\(955\) | −11.5221 | −0.372845 | ||||||||
\(956\) | 4.41447 | 0.142774 | ||||||||
\(957\) | −0.938523 | −0.0303381 | ||||||||
\(958\) | 1.22227 | 0.0394899 | ||||||||
\(959\) | 25.8299 | 0.834090 | ||||||||
\(960\) | 0.542814 | 0.0175192 | ||||||||
\(961\) | −26.7743 | −0.863688 | ||||||||
\(962\) | −0.518334 | −0.0167117 | ||||||||
\(963\) | −17.5531 | −0.565641 | ||||||||
\(964\) | −3.99479 | −0.128664 | ||||||||
\(965\) | −5.36237 | −0.172621 | ||||||||
\(966\) | 19.8393 | 0.638319 | ||||||||
\(967\) | 27.6094 | 0.887859 | 0.443929 | − | 0.896062i | \(-0.353584\pi\) | ||||
0.443929 | + | 0.896062i | \(0.353584\pi\) | |||||||
\(968\) | −10.5993 | −0.340675 | ||||||||
\(969\) | 5.66132 | 0.181868 | ||||||||
\(970\) | −3.95912 | −0.127120 | ||||||||
\(971\) | −0.295774 | −0.00949185 | −0.00474592 | − | 0.999989i | \(-0.501511\pi\) | ||||
−0.00474592 | + | 0.999989i | \(0.501511\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −9.55792 | −0.306413 | ||||||||
\(974\) | 1.80937 | 0.0579759 | ||||||||
\(975\) | −4.70535 | −0.150692 | ||||||||
\(976\) | −11.2974 | −0.361620 | ||||||||
\(977\) | −42.2062 | −1.35030 | −0.675148 | − | 0.737683i | \(-0.735920\pi\) | ||||
−0.675148 | + | 0.737683i | \(0.735920\pi\) | |||||||
\(978\) | 15.4871 | 0.495224 | ||||||||
\(979\) | −5.91913 | −0.189176 | ||||||||
\(980\) | 1.26854 | 0.0405220 | ||||||||
\(981\) | −8.80317 | −0.281064 | ||||||||
\(982\) | −20.4058 | −0.651176 | ||||||||
\(983\) | 38.8764 | 1.23996 | 0.619982 | − | 0.784616i | \(-0.287140\pi\) | ||||
0.619982 | + | 0.784616i | \(0.287140\pi\) | |||||||
\(984\) | 2.61666 | 0.0834161 | ||||||||
\(985\) | −9.50098 | −0.302726 | ||||||||
\(986\) | −4.08339 | −0.130042 | ||||||||
\(987\) | 6.40363 | 0.203830 | ||||||||
\(988\) | 2.05565 | 0.0653988 | ||||||||
\(989\) | 16.1714 | 0.514221 | ||||||||
\(990\) | 0.343593 | 0.0109201 | ||||||||
\(991\) | −22.1102 | −0.702353 | −0.351177 | − | 0.936309i | \(-0.614218\pi\) | ||||
−0.351177 | + | 0.936309i | \(0.614218\pi\) | |||||||
\(992\) | −2.05565 | −0.0652668 | ||||||||
\(993\) | 24.3920 | 0.774058 | ||||||||
\(994\) | 9.92740 | 0.314878 | ||||||||
\(995\) | −14.4931 | −0.459464 | ||||||||
\(996\) | 4.86110 | 0.154030 | ||||||||
\(997\) | −17.8364 | −0.564885 | −0.282442 | − | 0.959284i | \(-0.591145\pi\) | ||||
−0.282442 | + | 0.959284i | \(0.591145\pi\) | |||||||
\(998\) | 25.4883 | 0.806818 | ||||||||
\(999\) | −0.518334 | −0.0163993 |
(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 | 8034.2.a.v.1.6 | ✓ | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.v.1.6 | ✓ | 11 | 1.1 | even | 1 | trivial |