Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7728,2,Mod(1,7728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7728, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7728.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7728 = 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7728.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: | \(61.7083906820\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.39605.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 8x^{2} + 9x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 3864) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(3.57685\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7728.1 |
$q$-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 | ||||||||
\(5\) | 2.57685 | 1.15240 | 0.576201 | − | 0.817308i | \(-0.304535\pi\) | ||||
0.576201 | + | 0.817308i | \(0.304535\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.81840 | −1.45280 | −0.726401 | − | 0.687271i | \(-0.758809\pi\) | ||||
−0.726401 | + | 0.687271i | \(0.758809\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.91214 | 1.36238 | 0.681191 | − | 0.732105i | \(-0.261462\pi\) | ||||
0.681191 | + | 0.732105i | \(0.261462\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.57685 | −0.665339 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.21699 | −1.75038 | −0.875189 | − | 0.483782i | \(-0.839263\pi\) | ||||
−0.875189 | + | 0.483782i | \(0.839263\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.33529 | −0.535753 | −0.267877 | − | 0.963453i | \(-0.586322\pi\) | ||||
−0.267877 | + | 0.963453i | \(0.586322\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.64014 | 0.328029 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.10555 | 0.576687 | 0.288344 | − | 0.957527i | \(-0.406895\pi\) | ||||
0.288344 | + | 0.957527i | \(0.406895\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.21699 | 0.218578 | 0.109289 | − | 0.994010i | \(-0.465143\pi\) | ||||
0.109289 | + | 0.994010i | \(0.465143\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.81840 | 0.838776 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.57685 | 0.435567 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.223858 | 0.0368020 | 0.0184010 | − | 0.999831i | \(-0.494142\pi\) | ||||
0.0184010 | + | 0.999831i | \(0.494142\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.91214 | −0.786572 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.25925 | 1.28988 | 0.644939 | − | 0.764234i | \(-0.276883\pi\) | ||||
0.644939 | + | 0.764234i | \(0.276883\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.31073 | −1.11488 | −0.557438 | − | 0.830219i | \(-0.688216\pi\) | ||||
−0.557438 | + | 0.830219i | \(0.688216\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.57685 | 0.384134 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.11144 | −1.18317 | −0.591587 | − | 0.806241i | \(-0.701498\pi\) | ||||
−0.591587 | + | 0.806241i | \(0.701498\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.21699 | 1.01058 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.13600 | −0.156041 | −0.0780207 | − | 0.996952i | \(-0.524860\pi\) | ||||
−0.0780207 | + | 0.996952i | \(0.524860\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −12.4163 | −1.67421 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.33529 | 0.309317 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.56998 | 1.24591 | 0.622953 | − | 0.782260i | \(-0.285933\pi\) | ||||
0.622953 | + | 0.782260i | \(0.285933\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.1773 | −1.81521 | −0.907607 | − | 0.419821i | \(-0.862093\pi\) | ||||
−0.907607 | + | 0.419821i | \(0.862093\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 12.6578 | 1.57001 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.01770 | −0.735179 | −0.367589 | − | 0.929988i | \(-0.619817\pi\) | ||||
−0.367589 | + | 0.929988i | \(0.619817\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.75158 | 0.563909 | 0.281954 | − | 0.959428i | \(-0.409017\pi\) | ||||
0.281954 | + | 0.959428i | \(0.409017\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.70010 | −1.13531 | −0.567655 | − | 0.823266i | \(-0.692149\pi\) | ||||
−0.567655 | + | 0.823266i | \(0.692149\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.64014 | −0.189387 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.81840 | −0.549108 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.87582 | −0.661081 | −0.330540 | − | 0.943792i | \(-0.607231\pi\) | ||||
−0.330540 | + | 0.943792i | \(0.607231\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.60729 | −0.505716 | −0.252858 | − | 0.967503i | \(-0.581371\pi\) | ||||
−0.252858 | + | 0.967503i | \(0.581371\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −18.5971 | −2.01714 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.10555 | −0.332950 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.95440 | 0.843165 | 0.421582 | − | 0.906790i | \(-0.361475\pi\) | ||||
0.421582 | + | 0.906790i | \(0.361475\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.91214 | 0.514932 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.21699 | −0.126196 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.01770 | −0.617403 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.43497 | −0.450303 | −0.225151 | − | 0.974324i | \(-0.572288\pi\) | ||||
−0.225151 | + | 0.974324i | \(0.572288\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.81840 | −0.484268 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.93318 | 0.391366 | 0.195683 | − | 0.980667i | \(-0.437308\pi\) | ||||
0.195683 | + | 0.980667i | \(0.437308\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.92396 | 0.189573 | 0.0947865 | − | 0.995498i | \(-0.469783\pi\) | ||||
0.0947865 | + | 0.995498i | \(0.469783\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.57685 | −0.251475 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.13012 | 0.205926 | 0.102963 | − | 0.994685i | \(-0.467168\pi\) | ||||
0.102963 | + | 0.994685i | \(0.467168\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.0108 | −1.24621 | −0.623106 | − | 0.782138i | \(-0.714129\pi\) | ||||
−0.623106 | + | 0.782138i | \(0.714129\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.223858 | −0.0212476 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.5431 | −1.08588 | −0.542940 | − | 0.839771i | \(-0.682689\pi\) | ||||
−0.542940 | + | 0.839771i | \(0.682689\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.57685 | 0.240292 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.91214 | 0.454128 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.21699 | −0.661580 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.2170 | 1.11064 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.25925 | −0.744711 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.65784 | −0.774381 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −20.3378 | −1.80469 | −0.902345 | − | 0.431013i | \(-0.858156\pi\) | ||||
−0.902345 | + | 0.431013i | \(0.858156\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.31073 | 0.643674 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.7693 | 1.29040 | 0.645199 | − | 0.764015i | \(-0.276775\pi\) | ||||
0.645199 | + | 0.764015i | \(0.276775\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.33529 | −0.202496 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.57685 | −0.221780 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.4975 | 1.32404 | 0.662019 | − | 0.749487i | \(-0.269700\pi\) | ||||
0.662019 | + | 0.749487i | \(0.269700\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.1291 | −1.36806 | −0.684028 | − | 0.729456i | \(-0.739773\pi\) | ||||
−0.684028 | + | 0.729456i | \(0.739773\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.11144 | 0.683106 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −23.6687 | −1.97927 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.00254 | 0.664575 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14.2583 | −1.16808 | −0.584041 | − | 0.811724i | \(-0.698529\pi\) | ||||
−0.584041 | + | 0.811724i | \(0.698529\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.76197 | −0.143387 | −0.0716937 | − | 0.997427i | \(-0.522840\pi\) | ||||
−0.0716937 | + | 0.997427i | \(0.522840\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.21699 | −0.583459 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.13600 | 0.251890 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.82428 | −0.305211 | −0.152605 | − | 0.988287i | \(-0.548766\pi\) | ||||
−0.152605 | + | 0.988287i | \(0.548766\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.13600 | 0.0900906 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.3943 | 0.892468 | 0.446234 | − | 0.894916i | \(-0.352765\pi\) | ||||
0.446234 | + | 0.894916i | \(0.352765\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 12.4163 | 0.966606 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.33529 | −0.180710 | −0.0903552 | − | 0.995910i | \(-0.528800\pi\) | ||||
−0.0903552 | + | 0.995910i | \(0.528800\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.1291 | 0.856087 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.33529 | −0.178584 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.6765 | 1.03980 | 0.519901 | − | 0.854226i | \(-0.325969\pi\) | ||||
0.519901 | + | 0.854226i | \(0.325969\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.64014 | 0.123983 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.56998 | −0.719324 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −19.2337 | −1.43759 | −0.718797 | − | 0.695220i | \(-0.755307\pi\) | ||||
−0.718797 | + | 0.695220i | \(0.755307\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.28617 | −0.615906 | −0.307953 | − | 0.951402i | \(-0.599644\pi\) | ||||
−0.307953 | + | 0.951402i | \(0.599644\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.1773 | 1.04801 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.576848 | 0.0424107 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 34.7744 | 2.54295 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.3648 | −0.822328 | −0.411164 | − | 0.911561i | \(-0.634878\pi\) | ||||
−0.411164 | + | 0.911561i | \(0.634878\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.2077 | −1.16666 | −0.583328 | − | 0.812236i | \(-0.698250\pi\) | ||||
−0.583328 | + | 0.812236i | \(0.698250\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −12.6578 | −0.906447 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.8784 | 1.13129 | 0.565643 | − | 0.824650i | \(-0.308628\pi\) | ||||
0.565643 | + | 0.824650i | \(0.308628\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.4503 | −0.882575 | −0.441288 | − | 0.897366i | \(-0.645478\pi\) | ||||
−0.441288 | + | 0.897366i | \(0.645478\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.01770 | 0.424456 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.10555 | 0.217967 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 21.2828 | 1.48646 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 11.2524 | 0.778344 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.15958 | 0.148671 | 0.0743357 | − | 0.997233i | \(-0.476316\pi\) | ||||
0.0743357 | + | 0.997233i | \(0.476316\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.75158 | −0.325573 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −18.8386 | −1.28478 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.21699 | 0.0826147 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.70010 | 0.655472 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −35.4509 | −2.38468 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.89110 | 0.260568 | 0.130284 | − | 0.991477i | \(-0.458411\pi\) | ||||
0.130284 | + | 0.991477i | \(0.458411\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.64014 | 0.109343 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.7423 | 1.17760 | 0.588799 | − | 0.808279i | \(-0.299601\pi\) | ||||
0.588799 | + | 0.808279i | \(0.299601\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24.4026 | 1.61257 | 0.806283 | − | 0.591530i | \(-0.201476\pi\) | ||||
0.806283 | + | 0.591530i | \(0.201476\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.81840 | 0.317028 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.9839 | −0.850604 | −0.425302 | − | 0.905051i | \(-0.639832\pi\) | ||||
−0.425302 | + | 0.905051i | \(0.639832\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −20.9019 | −1.36349 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.87582 | 0.381675 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.58532 | 0.296600 | 0.148300 | − | 0.988942i | \(-0.452620\pi\) | ||||
0.148300 | + | 0.988942i | \(0.452620\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.1881 | 1.23601 | 0.618007 | − | 0.786173i | \(-0.287940\pi\) | ||||
0.618007 | + | 0.786173i | \(0.287940\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.57685 | 0.164629 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.4713 | −0.729901 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.60729 | 0.291975 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.4071 | 1.28808 | 0.644041 | − | 0.764991i | \(-0.277257\pi\) | ||||
0.644041 | + | 0.764991i | \(0.277257\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.81840 | −0.302930 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 18.5971 | 1.16459 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.30578 | −0.206209 | −0.103105 | − | 0.994671i | \(-0.532878\pi\) | ||||
−0.103105 | + | 0.994671i | \(0.532878\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.223858 | 0.0139098 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.10555 | 0.192229 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 25.0682 | 1.54577 | 0.772885 | − | 0.634546i | \(-0.218813\pi\) | ||||
0.772885 | + | 0.634546i | \(0.218813\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.92730 | −0.179822 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.95440 | −0.486801 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.5220 | −0.641539 | −0.320770 | − | 0.947157i | \(-0.603942\pi\) | ||||
−0.320770 | + | 0.947157i | \(0.603942\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.0075 | 0.729403 | 0.364701 | − | 0.931124i | \(-0.381171\pi\) | ||||
0.364701 | + | 0.931124i | \(0.381171\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.91214 | −0.297296 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.90287 | −0.476561 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.3310 | 0.921149 | 0.460574 | − | 0.887621i | \(-0.347643\pi\) | ||||
0.460574 | + | 0.887621i | \(0.347643\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.21699 | 0.0728593 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.47463 | −0.386244 | −0.193122 | − | 0.981175i | \(-0.561861\pi\) | ||||
−0.193122 | + | 0.981175i | \(0.561861\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.0531 | −1.19203 | −0.596016 | − | 0.802972i | \(-0.703251\pi\) | ||||
−0.596016 | + | 0.802972i | \(0.703251\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.01770 | 0.356458 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.25925 | 0.487528 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 35.0850 | 2.06382 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.43497 | 0.259982 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.32941 | −0.545030 | −0.272515 | − | 0.962152i | \(-0.587855\pi\) | ||||
−0.272515 | + | 0.962152i | \(0.587855\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 24.6604 | 1.43578 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.81840 | 0.279592 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.91214 | 0.284076 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.31073 | −0.421384 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.93318 | −0.225955 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −36.5327 | −2.09185 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.7070 | −0.839371 | −0.419685 | − | 0.907670i | \(-0.637860\pi\) | ||||
−0.419685 | + | 0.907670i | \(0.637860\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.92396 | −0.109450 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −17.3192 | −0.982082 | −0.491041 | − | 0.871136i | \(-0.663383\pi\) | ||||
−0.491041 | + | 0.871136i | \(0.663383\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −30.5303 | −1.72567 | −0.862836 | − | 0.505484i | \(-0.831314\pi\) | ||||
−0.862836 | + | 0.505484i | \(0.831314\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.57685 | 0.145189 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.0937 | 0.566921 | 0.283460 | − | 0.958984i | \(-0.408518\pi\) | ||||
0.283460 | + | 0.958984i | \(0.408518\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −14.9638 | −0.837812 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.13012 | −0.118892 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 16.8538 | 0.937770 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.05661 | 0.446901 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 13.0108 | 0.719500 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.11144 | −0.447198 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.3632 | −0.569613 | −0.284806 | − | 0.958585i | \(-0.591929\pi\) | ||||
−0.284806 | + | 0.958585i | \(0.591929\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.223858 | 0.0122673 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −15.5067 | −0.847221 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.8798 | −1.51871 | −0.759354 | − | 0.650678i | \(-0.774485\pi\) | ||||
−0.759354 | + | 0.650678i | \(0.774485\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.5431 | 0.626933 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.86395 | −0.317551 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.57685 | −0.138733 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 21.6849 | 1.16411 | 0.582054 | − | 0.813150i | \(-0.302249\pi\) | ||||
0.582054 | + | 0.813150i | \(0.302249\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 29.1038 | 1.55789 | 0.778946 | − | 0.627091i | \(-0.215755\pi\) | ||||
0.778946 | + | 0.627091i | \(0.215755\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.91214 | −0.262191 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −34.6932 | −1.84653 | −0.923267 | − | 0.384158i | \(-0.874492\pi\) | ||||
−0.923267 | + | 0.384158i | \(0.874492\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.2441 | 0.649849 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7.21699 | 0.381964 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.9888 | 0.738301 | 0.369150 | − | 0.929370i | \(-0.379649\pi\) | ||||
0.369150 | + | 0.929370i | \(0.379649\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.5464 | −0.712969 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −12.2170 | −0.641226 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −24.9957 | −1.30833 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −29.1704 | −1.52268 | −0.761341 | − | 0.648351i | \(-0.775459\pi\) | ||||
−0.761341 | + | 0.648351i | \(0.775459\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.25925 | 0.429959 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.13600 | −0.0589781 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.5818 | −0.858573 | −0.429286 | − | 0.903168i | \(-0.641235\pi\) | ||||
−0.429286 | + | 0.903168i | \(0.641235\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.65784 | 0.447089 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 15.2549 | 0.785669 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −36.1331 | −1.85603 | −0.928016 | − | 0.372540i | \(-0.878487\pi\) | ||||
−0.928016 | + | 0.372540i | \(0.878487\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 20.3378 | 1.04194 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.05501 | 0.360494 | 0.180247 | − | 0.983621i | \(-0.442310\pi\) | ||||
0.180247 | + | 0.983621i | \(0.442310\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −12.4163 | −0.632792 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.31073 | −0.371625 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −26.1832 | −1.32754 | −0.663771 | − | 0.747936i | \(-0.731045\pi\) | ||||
−0.663771 | + | 0.747936i | \(0.731045\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.21699 | −0.364979 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −14.7693 | −0.745011 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −15.1411 | −0.761830 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.19924 | 0.311131 | 0.155566 | − | 0.987826i | \(-0.450280\pi\) | ||||
0.155566 | + | 0.987826i | \(0.450280\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.33529 | 0.116911 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.546403 | −0.0272861 | −0.0136430 | − | 0.999907i | \(-0.504343\pi\) | ||||
−0.0136430 | + | 0.999907i | \(0.504343\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.97803 | 0.297787 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.57685 | 0.128045 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.07864 | −0.0534660 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 30.0311 | 1.48494 | 0.742472 | − | 0.669878i | \(-0.233653\pi\) | ||||
0.742472 | + | 0.669878i | \(0.233653\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −15.4975 | −0.764433 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.56998 | 0.470908 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.8723 | −0.582788 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.1291 | 0.789847 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.1022 | −0.884351 | −0.442176 | − | 0.896929i | \(-0.645793\pi\) | ||||
−0.442176 | + | 0.896929i | \(0.645793\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.2549 | 0.646005 | 0.323003 | − | 0.946398i | \(-0.395308\pi\) | ||||
0.323003 | + | 0.946398i | \(0.395308\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.11144 | −0.394392 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11.8369 | −0.574174 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14.1773 | −0.686086 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 23.6687 | 1.14273 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −29.3678 | −1.41460 | −0.707298 | − | 0.706915i | \(-0.750086\pi\) | ||||
−0.707298 | + | 0.706915i | \(0.750086\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.8748 | −0.762896 | −0.381448 | − | 0.924390i | \(-0.624574\pi\) | ||||
−0.381448 | + | 0.924390i | \(0.624574\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.00254 | −0.383692 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.33529 | −0.111712 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.38603 | 0.447971 | 0.223985 | − | 0.974593i | \(-0.428093\pi\) | ||||
0.223985 | + | 0.974593i | \(0.428093\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13.3800 | −0.635701 | −0.317851 | − | 0.948141i | \(-0.602961\pi\) | ||||
−0.317851 | + | 0.948141i | \(0.602961\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 20.4973 | 0.971664 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 14.2583 | 0.674393 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −21.9383 | −1.03533 | −0.517665 | − | 0.855583i | \(-0.673199\pi\) | ||||
−0.517665 | + | 0.855583i | \(0.673199\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −39.7964 | −1.87394 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.76197 | 0.0827847 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 12.6578 | 0.593409 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.1376 | 1.03555 | 0.517777 | − | 0.855516i | \(-0.326760\pi\) | ||||
0.517777 | + | 0.855516i | \(0.326760\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.21699 | 0.336860 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.1006 | −0.517007 | −0.258503 | − | 0.966010i | \(-0.583229\pi\) | ||||
−0.258503 | + | 0.966010i | \(0.583229\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.71873 | 0.405194 | 0.202597 | − | 0.979262i | \(-0.435062\pi\) | ||||
0.202597 | + | 0.979262i | \(0.435062\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.13600 | −0.145428 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.3084 | 0.662113 | 0.331056 | − | 0.943611i | \(-0.392595\pi\) | ||||
0.331056 | + | 0.943611i | \(0.392595\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.01770 | −0.277871 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.82428 | 0.176214 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 35.2260 | 1.61969 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.83022 | −0.175742 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.13600 | −0.0520138 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −37.8738 | −1.73050 | −0.865250 | − | 0.501341i | \(-0.832840\pi\) | ||||
−0.865250 | + | 0.501341i | \(0.832840\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.09962 | 0.0501384 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.00000 | −0.0455016 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −11.4282 | −0.518929 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.2172 | 0.553613 | 0.276807 | − | 0.960926i | \(-0.410724\pi\) | ||||
0.276807 | + | 0.960926i | \(0.410724\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −11.3943 | −0.515266 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 40.4964 | 1.82758 | 0.913789 | − | 0.406189i | \(-0.133143\pi\) | ||||
0.913789 | + | 0.406189i | \(0.133143\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −22.4128 | −1.00942 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −12.4163 | −0.558071 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.75158 | 0.213137 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.00941 | −0.313784 | −0.156892 | − | 0.987616i | \(-0.550147\pi\) | ||||
−0.156892 | + | 0.987616i | \(0.550147\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.33529 | 0.104333 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −31.4905 | −1.40409 | −0.702047 | − | 0.712131i | \(-0.747730\pi\) | ||||
−0.702047 | + | 0.712131i | \(0.747730\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.1352 | 0.451010 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.1291 | −0.494262 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −27.4356 | −1.21606 | −0.608031 | − | 0.793914i | \(-0.708040\pi\) | ||||
−0.608031 | + | 0.793914i | \(0.708040\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.70010 | −0.429107 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.33529 | 0.103106 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.95774 | 0.218464 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 39.0842 | 1.71892 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −13.6765 | −0.600330 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.9579 | −0.611508 | −0.305754 | − | 0.952111i | \(-0.598908\pi\) | ||||
−0.305754 | + | 0.952111i | \(0.598908\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.1046 | 0.747931 | 0.373965 | − | 0.927443i | \(-0.377998\pi\) | ||||
0.373965 | + | 0.927443i | \(0.377998\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.64014 | −0.0715817 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.78301 | −0.382594 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.56998 | 0.415302 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 40.5706 | 1.75731 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.48899 | 0.237310 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 19.2337 | 0.829995 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.81840 | −0.207543 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.9847 | 0.816214 | 0.408107 | − | 0.912934i | \(-0.366189\pi\) | ||||
0.408107 | + | 0.912934i | \(0.366189\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.28617 | 0.355593 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −33.5269 | −1.43614 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.4026 | 0.444781 | 0.222390 | − | 0.974958i | \(-0.428614\pi\) | ||||
0.222390 | + | 0.974958i | \(0.428614\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −14.1773 | −0.605071 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.25238 | −0.308962 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.87582 | −0.249865 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.576848 | −0.0244858 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.972896 | −0.0412229 | −0.0206115 | − | 0.999788i | \(-0.506561\pi\) | ||||
−0.0206115 | + | 0.999788i | \(0.506561\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −35.9113 | −1.51889 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −34.7744 | −1.46817 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 42.0521 | 1.77228 | 0.886142 | − | 0.463413i | \(-0.153375\pi\) | ||||
0.886142 | + | 0.463413i | \(0.153375\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −29.7447 | −1.25137 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.1586 | −0.593559 | −0.296779 | − | 0.954946i | \(-0.595913\pi\) | ||||
−0.296779 | + | 0.954946i | \(0.595913\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.4433 | 0.771830 | 0.385915 | − | 0.922534i | \(-0.373886\pi\) | ||||
0.385915 | + | 0.922534i | \(0.373886\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11.3648 | 0.474772 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.64014 | 0.0683987 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −32.7296 | −1.36255 | −0.681276 | − | 0.732027i | \(-0.738575\pi\) | ||||
−0.681276 | + | 0.732027i | \(0.738575\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 16.2077 | 0.673570 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.60729 | −0.191143 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.47370 | 0.226697 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 12.6578 | 0.523337 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 32.6230 | 1.34650 | 0.673248 | − | 0.739417i | \(-0.264899\pi\) | ||||
0.673248 | + | 0.739417i | \(0.264899\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.84203 | −0.117104 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −15.8784 | −0.653148 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.76197 | −0.154486 | −0.0772429 | − | 0.997012i | \(-0.524612\pi\) | ||||
−0.0772429 | + | 0.997012i | \(0.524612\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −18.5971 | −0.762406 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12.4503 | 0.509555 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.51694 | 0.102840 | 0.0514198 | − | 0.998677i | \(-0.483625\pi\) | ||||
0.0514198 | + | 0.998677i | \(0.483625\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.0330 | −0.613210 | −0.306605 | − | 0.951837i | \(-0.599193\pi\) | ||||
−0.306605 | + | 0.951837i | \(0.599193\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.01770 | −0.245060 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 31.4813 | 1.27990 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.7041 | 0.556231 | 0.278115 | − | 0.960548i | \(-0.410290\pi\) | ||||
0.278115 | + | 0.960548i | \(0.410290\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.10555 | −0.125843 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −39.8445 | −1.61194 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −29.6429 | −1.19726 | −0.598632 | − | 0.801024i | \(-0.704289\pi\) | ||||
−0.598632 | + | 0.801024i | \(0.704289\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −21.2828 | −0.858206 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.6687 | 0.872348 | 0.436174 | − | 0.899862i | \(-0.356333\pi\) | ||||
0.436174 | + | 0.899862i | \(0.356333\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.9815 | −0.441384 | −0.220692 | − | 0.975344i | \(-0.570832\pi\) | ||||
−0.220692 | + | 0.975344i | \(0.570832\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.95440 | 0.318686 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.5106 | −1.22043 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −11.2524 | −0.449377 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.61558 | −0.0644174 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −45.8837 | −1.82660 | −0.913301 | − | 0.407284i | \(-0.866476\pi\) | ||||
−0.913301 | + | 0.407284i | \(0.866476\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.15958 | −0.0858355 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −52.4075 | −2.07973 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.91214 | 0.194626 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.75158 | 0.187970 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.9121 | −0.431004 | −0.215502 | − | 0.976503i | \(-0.569139\pi\) | ||||
−0.215502 | + | 0.976503i | \(0.569139\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.3526 | 1.15755 | 0.578777 | − | 0.815486i | \(-0.303530\pi\) | ||||
0.578777 | + | 0.815486i | \(0.303530\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 18.8386 | 0.741771 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 45.5259 | 1.78981 | 0.894905 | − | 0.446257i | \(-0.147243\pi\) | ||||
0.894905 | + | 0.446257i | \(0.147243\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −46.1120 | −1.81005 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.21699 | −0.0476976 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12.7251 | −0.497971 | −0.248986 | − | 0.968507i | \(-0.580097\pi\) | ||||
−0.248986 | + | 0.968507i | \(0.580097\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 38.0582 | 1.48706 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9.70010 | −0.378437 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.4552 | 0.718913 | 0.359456 | − | 0.933162i | \(-0.382962\pi\) | ||||
0.359456 | + | 0.933162i | \(0.382962\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.3506 | −0.830443 | −0.415222 | − | 0.909720i | \(-0.636296\pi\) | ||||
−0.415222 | + | 0.909720i | \(0.636296\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 35.4509 | 1.37680 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.01770 | −0.233356 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.10555 | 0.120248 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.89110 | −0.150439 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 68.3118 | 2.63715 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.1492 | 0.391224 | 0.195612 | − | 0.980681i | \(-0.437331\pi\) | ||||
0.195612 | + | 0.980681i | \(0.437331\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.64014 | −0.0631291 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −38.4171 | −1.47649 | −0.738244 | − | 0.674533i | \(-0.764345\pi\) | ||||
−0.738244 | + | 0.674533i | \(0.764345\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.43497 | −0.170198 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −17.7423 | −0.679887 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 11.4418 | 0.437810 | 0.218905 | − | 0.975746i | \(-0.429752\pi\) | ||||
0.218905 | + | 0.975746i | \(0.429752\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 39.9346 | 1.52582 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −24.4026 | −0.931015 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.58019 | −0.212588 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 37.3225 | 1.41981 | 0.709907 | − | 0.704295i | \(-0.248737\pi\) | ||||
0.709907 | + | 0.704295i | \(0.248737\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.81840 | −0.183036 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −41.5623 | −1.57655 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −59.6069 | −2.25777 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 12.9839 | 0.491097 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.18165 | −0.157939 | −0.0789694 | − | 0.996877i | \(-0.525163\pi\) | ||||
−0.0789694 | + | 0.996877i | \(0.525163\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.522774 | −0.0197168 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 20.9019 | 0.787212 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.93318 | 0.147922 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27.1435 | 1.01940 | 0.509698 | − | 0.860354i | \(-0.329757\pi\) | ||||
0.509698 | + | 0.860354i | \(0.329757\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.87582 | −0.220360 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.21699 | 0.0455767 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −60.9905 | −2.28092 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.58532 | −0.171242 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 29.7369 | 1.10900 | 0.554500 | − | 0.832184i | \(-0.312910\pi\) | ||||
0.554500 | + | 0.832184i | \(0.312910\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.92396 | 0.0716519 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −19.1881 | −0.713613 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.09355 | 0.189170 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −27.2170 | −1.00942 | −0.504711 | − | 0.863288i | \(-0.668401\pi\) | ||||
−0.504711 | + | 0.863288i | \(0.668401\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 52.7615 | 1.95145 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.0775 | 0.593835 | 0.296917 | − | 0.954903i | \(-0.404041\pi\) | ||||
0.296917 | + | 0.954903i | \(0.404041\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.57685 | −0.0950485 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 28.9957 | 1.06807 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.16786 | −0.337245 | −0.168623 | − | 0.985681i | \(-0.553932\pi\) | ||||
−0.168623 | + | 0.985681i | \(0.553932\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.4713 | 0.421408 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20.4163 | 0.749001 | 0.374500 | − | 0.927227i | \(-0.377814\pi\) | ||||
0.374500 | + | 0.927227i | \(0.377814\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −36.7414 | −1.34610 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.60729 | −0.168572 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.13012 | 0.0778328 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.9249 | 0.471636 | 0.235818 | − | 0.971797i | \(-0.424223\pi\) | ||||
0.235818 | + | 0.971797i | \(0.424223\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −20.4071 | −0.743675 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.54034 | −0.165240 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −42.4953 | −1.54452 | −0.772259 | − | 0.635308i | \(-0.780873\pi\) | ||||
−0.772259 | + | 0.635308i | \(0.780873\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.81840 | 0.174897 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 49.9167 | 1.80948 | 0.904740 | − | 0.425964i | \(-0.140065\pi\) | ||||
0.904740 | + | 0.425964i | \(0.140065\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.0108 | −0.471024 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −18.5971 | −0.672379 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 47.0091 | 1.69740 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.94240 | 0.0700447 | 0.0350224 | − | 0.999387i | \(-0.488850\pi\) | ||||
0.0350224 | + | 0.999387i | \(0.488850\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.30578 | 0.119055 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −29.7576 | −1.07031 | −0.535153 | − | 0.844755i | \(-0.679746\pi\) | ||||
−0.535153 | + | 0.844755i | \(0.679746\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.99604 | 0.0716998 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.223858 | −0.00803086 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −19.2878 | −0.691056 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22.8950 | −0.819248 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.10555 | −0.110983 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.85459 | −0.351726 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.8758 | −0.744141 | −0.372070 | − | 0.928205i | \(-0.621352\pi\) | ||||
−0.372070 | + | 0.928205i | \(0.621352\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −25.0682 | −0.892451 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.5431 | −0.410424 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −69.6408 | −2.47302 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.92730 | 0.103821 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.09486 | −0.215891 | −0.107946 | − | 0.994157i | \(-0.534427\pi\) | ||||
−0.107946 | + | 0.994157i | \(0.534427\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 58.5402 | 2.07100 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.95440 | 0.281055 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 46.7390 | 1.64938 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.57685 | 0.0908219 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.5220 | 0.370393 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.87817 | −0.241824 | −0.120912 | − | 0.992663i | \(-0.538582\pi\) | ||||
−0.120912 | + | 0.992663i | \(0.538582\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.30293 | 0.0457520 | 0.0228760 | − | 0.999738i | \(-0.492718\pi\) | ||||
0.0228760 | + | 0.999738i | \(0.492718\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.0075 | −0.421121 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 29.3613 | 1.02848 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 17.0727 | 0.597298 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.91214 | 0.171644 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 32.1030 | 1.12040 | 0.560201 | − | 0.828357i | \(-0.310724\pi\) | ||||
0.560201 | + | 0.828357i | \(0.310724\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −37.1916 | −1.29642 | −0.648209 | − | 0.761462i | \(-0.724482\pi\) | ||||
−0.648209 | + | 0.761462i | \(0.724482\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.90287 | 0.275143 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.61082 | 0.299428 | 0.149714 | − | 0.988729i | \(-0.452165\pi\) | ||||
0.149714 | + | 0.988729i | \(0.452165\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −52.6544 | −1.82876 | −0.914382 | − | 0.404852i | \(-0.867323\pi\) | ||||
−0.914382 | + | 0.404852i | \(0.867323\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.3310 | −0.531825 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.21699 | −0.250054 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.01770 | −0.208251 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.21699 | −0.0420653 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −49.9387 | −1.72408 | −0.862038 | − | 0.506844i | \(-0.830812\pi\) | ||||
−0.862038 | + | 0.506844i | \(0.830812\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.3555 | −0.667432 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.47463 | 0.222998 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 28.6781 | 0.986556 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12.2170 | 0.419781 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 20.0531 | 0.688220 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.223858 | 0.00767375 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.8513 | −0.679696 | −0.339848 | − | 0.940480i | \(-0.610376\pi\) | ||||
−0.339848 | + | 0.940480i | \(0.610376\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.01770 | −0.205801 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −47.8328 | −1.63394 | −0.816968 | − | 0.576683i | \(-0.804347\pi\) | ||||
−0.816968 | + | 0.576683i | \(0.804347\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.81742 | −0.0961290 | −0.0480645 | − | 0.998844i | \(-0.515305\pi\) | ||||
−0.0480645 | + | 0.998844i | \(0.515305\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.25925 | −0.281474 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19.6840 | −0.670050 | −0.335025 | − | 0.942209i | \(-0.608745\pi\) | ||||
−0.335025 | + | 0.942209i | \(0.608745\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 35.2422 | 1.19827 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −35.0850 | −1.19155 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 28.3120 | 0.960420 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −29.5598 | −1.00159 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.43497 | −0.150101 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −8.65784 | −0.292688 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.5185 | 0.490255 | 0.245127 | − | 0.969491i | \(-0.421170\pi\) | ||||
0.245127 | + | 0.969491i | \(0.421170\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.32941 | 0.314673 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −34.5657 | −1.16455 | −0.582273 | − | 0.812993i | \(-0.697837\pi\) | ||||
−0.582273 | + | 0.812993i | \(0.697837\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28.9929 | −0.975689 | −0.487844 | − | 0.872931i | \(-0.662217\pi\) | ||||
−0.487844 | + | 0.872931i | \(0.662217\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −24.6604 | −0.828950 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −39.5048 | −1.32644 | −0.663221 | − | 0.748424i | \(-0.730811\pi\) | ||||
−0.663221 | + | 0.748424i | \(0.730811\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −20.3378 | −0.682109 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.81840 | −0.161423 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 18.9426 | 0.633889 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −49.5623 | −1.65669 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.91214 | −0.164012 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.77943 | 0.126051 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.19849 | 0.273131 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.31073 | 0.243286 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −21.3522 | −0.709771 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.2911 | 0.806573 | 0.403287 | − | 0.915074i | \(-0.367868\pi\) | ||||
0.403287 | + | 0.915074i | \(0.367868\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.93318 | 0.130455 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33.1064 | 1.09686 | 0.548431 | − | 0.836196i | \(-0.315225\pi\) | ||||
0.548431 | + | 0.836196i | \(0.315225\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 22.1998 | 0.734706 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 36.5327 | 1.20773 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14.7693 | 0.487724 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38.3521 | 1.26512 | 0.632560 | − | 0.774511i | \(-0.282004\pi\) | ||||
0.632560 | + | 0.774511i | \(0.282004\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.7070 | 0.484611 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 23.3404 | 0.768260 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.367159 | 0.0120721 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.92396 | 0.0631910 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20.9805 | 0.688348 | 0.344174 | − | 0.938906i | \(-0.388159\pi\) | ||||
0.344174 | + | 0.938906i | \(0.388159\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.33529 | −0.0765362 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 17.3192 | 0.567005 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 89.6082 | 2.93050 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 49.5054 | 1.61727 | 0.808635 | − | 0.588310i | \(-0.200207\pi\) | ||||
0.808635 | + | 0.588310i | \(0.200207\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 30.5303 | 0.996317 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.2093 | 0.561008 | 0.280504 | − | 0.959853i | \(-0.409498\pi\) | ||||
0.280504 | + | 0.959853i | \(0.409498\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.25925 | 0.268958 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.57685 | −0.0838249 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −57.5167 | −1.86904 | −0.934521 | − | 0.355908i | \(-0.884172\pi\) | ||||
−0.934521 | + | 0.355908i | \(0.884172\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −47.6483 | −1.54673 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10.0937 | −0.327312 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 50.4525 | 1.63432 | 0.817158 | − | 0.576414i | \(-0.195548\pi\) | ||||
0.817158 | + | 0.576414i | \(0.195548\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −29.2854 | −0.947652 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 14.9638 | 0.483711 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 15.4975 | 0.500439 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.5189 | −0.952224 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.13012 | 0.0686421 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −41.7648 | −1.34446 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 35.6769 | 1.14729 | 0.573646 | − | 0.819103i | \(-0.305529\pi\) | ||||
0.573646 | + | 0.819103i | \(0.305529\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −16.8538 | −0.541422 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27.3986 | 0.879264 | 0.439632 | − | 0.898178i | \(-0.355109\pi\) | ||||
0.439632 | + | 0.898178i | \(0.355109\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16.1291 | −0.517076 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −8.05661 | −0.258018 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10.1552 | 0.324893 | 0.162446 | − | 0.986717i | \(-0.448062\pi\) | ||||
0.162446 | + | 0.986717i | \(0.448062\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −38.3275 | −1.22495 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.0108 | −0.415404 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.05153 | 0.129224 | 0.0646119 | − | 0.997910i | \(-0.479419\pi\) | ||||
0.0646119 | + | 0.997910i | \(0.479419\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 40.9161 | 1.30370 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.11144 | 0.258190 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.31073 | −0.232468 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.7787 | −0.564758 | −0.282379 | − | 0.959303i | \(-0.591124\pi\) | ||||
−0.282379 | + | 0.959303i | \(0.591124\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 10.3632 | 0.328866 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −32.0824 | −1.01708 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.6882 | −0.370170 | −0.185085 | − | 0.982723i | \(-0.559256\pi\) | ||||
−0.185085 | + | 0.982723i | \(0.559256\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.223858 | −0.00708255 |
(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 | 7728.2.a.bz.1.4 | 4 | ||
4.3 | odd | 2 | 3864.2.a.t.1.4 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3864.2.a.t.1.4 | ✓ | 4 | 4.3 | odd | 2 | ||
7728.2.a.bz.1.4 | 4 | 1.1 | even | 1 | trivial |