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: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 5 x^{12} - 25 x^{11} + 134 x^{10} + 196 x^{9} - 1151 x^{8} - 801 x^{7} + 4263 x^{6} + 2205 x^{5} - 6840 x^{4} - 3579 x^{3} + 3559 x^{2} + 1839 x - 180 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(4.50145\) 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 | ||||||||
\(5\) | −1.68854 | −0.755140 | −0.377570 | − | 0.925981i | \(-0.623240\pi\) | ||||
−0.377570 | + | 0.925981i | \(0.623240\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 4.50145 | 1.70139 | 0.850694 | − | 0.525661i | \(-0.176182\pi\) | ||||
0.850694 | + | 0.525661i | \(0.176182\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.68854 | −0.533964 | ||||||||
\(11\) | −0.787053 | −0.237305 | −0.118653 | − | 0.992936i | \(-0.537857\pi\) | ||||
−0.118653 | + | 0.992936i | \(0.537857\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 4.50145 | 1.20306 | ||||||||
\(15\) | 1.68854 | 0.435980 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.120738 | −0.0292833 | −0.0146416 | − | 0.999893i | \(-0.504661\pi\) | ||||
−0.0146416 | + | 0.999893i | \(0.504661\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 2.16827 | 0.497436 | 0.248718 | − | 0.968576i | \(-0.419991\pi\) | ||||
0.248718 | + | 0.968576i | \(0.419991\pi\) | |||||||
\(20\) | −1.68854 | −0.377570 | ||||||||
\(21\) | −4.50145 | −0.982297 | ||||||||
\(22\) | −0.787053 | −0.167800 | ||||||||
\(23\) | −4.63632 | −0.966739 | −0.483369 | − | 0.875417i | \(-0.660587\pi\) | ||||
−0.483369 | + | 0.875417i | \(0.660587\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −2.14882 | −0.429764 | ||||||||
\(26\) | 1.00000 | 0.196116 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 4.50145 | 0.850694 | ||||||||
\(29\) | 0.430855 | 0.0800078 | 0.0400039 | − | 0.999200i | \(-0.487263\pi\) | ||||
0.0400039 | + | 0.999200i | \(0.487263\pi\) | |||||||
\(30\) | 1.68854 | 0.308284 | ||||||||
\(31\) | 2.16827 | 0.389433 | 0.194717 | − | 0.980860i | \(-0.437621\pi\) | ||||
0.194717 | + | 0.980860i | \(0.437621\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0.787053 | 0.137008 | ||||||||
\(34\) | −0.120738 | −0.0207064 | ||||||||
\(35\) | −7.60090 | −1.28479 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 5.51041 | 0.905905 | 0.452953 | − | 0.891535i | \(-0.350371\pi\) | ||||
0.452953 | + | 0.891535i | \(0.350371\pi\) | |||||||
\(38\) | 2.16827 | 0.351740 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | −1.68854 | −0.266982 | ||||||||
\(41\) | 10.5241 | 1.64359 | 0.821793 | − | 0.569786i | \(-0.192974\pi\) | ||||
0.821793 | + | 0.569786i | \(0.192974\pi\) | |||||||
\(42\) | −4.50145 | −0.694589 | ||||||||
\(43\) | 2.43028 | 0.370614 | 0.185307 | − | 0.982681i | \(-0.440672\pi\) | ||||
0.185307 | + | 0.982681i | \(0.440672\pi\) | |||||||
\(44\) | −0.787053 | −0.118653 | ||||||||
\(45\) | −1.68854 | −0.251713 | ||||||||
\(46\) | −4.63632 | −0.683588 | ||||||||
\(47\) | 1.33865 | 0.195262 | 0.0976308 | − | 0.995223i | \(-0.468874\pi\) | ||||
0.0976308 | + | 0.995223i | \(0.468874\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 13.2631 | 1.89472 | ||||||||
\(50\) | −2.14882 | −0.303889 | ||||||||
\(51\) | 0.120738 | 0.0169067 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | 8.80373 | 1.20929 | 0.604643 | − | 0.796497i | \(-0.293316\pi\) | ||||
0.604643 | + | 0.796497i | \(0.293316\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 1.32897 | 0.179199 | ||||||||
\(56\) | 4.50145 | 0.601532 | ||||||||
\(57\) | −2.16827 | −0.287195 | ||||||||
\(58\) | 0.430855 | 0.0565741 | ||||||||
\(59\) | −9.51134 | −1.23827 | −0.619135 | − | 0.785284i | \(-0.712517\pi\) | ||||
−0.619135 | + | 0.785284i | \(0.712517\pi\) | |||||||
\(60\) | 1.68854 | 0.217990 | ||||||||
\(61\) | −9.33774 | −1.19558 | −0.597788 | − | 0.801654i | \(-0.703953\pi\) | ||||
−0.597788 | + | 0.801654i | \(0.703953\pi\) | |||||||
\(62\) | 2.16827 | 0.275371 | ||||||||
\(63\) | 4.50145 | 0.567130 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.68854 | −0.209438 | ||||||||
\(66\) | 0.787053 | 0.0968795 | ||||||||
\(67\) | 15.9992 | 1.95462 | 0.977308 | − | 0.211825i | \(-0.0679406\pi\) | ||||
0.977308 | + | 0.211825i | \(0.0679406\pi\) | |||||||
\(68\) | −0.120738 | −0.0146416 | ||||||||
\(69\) | 4.63632 | 0.558147 | ||||||||
\(70\) | −7.60090 | −0.908481 | ||||||||
\(71\) | −14.3213 | −1.69963 | −0.849815 | − | 0.527081i | \(-0.823287\pi\) | ||||
−0.849815 | + | 0.527081i | \(0.823287\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 10.9288 | 1.27912 | 0.639561 | − | 0.768740i | \(-0.279116\pi\) | ||||
0.639561 | + | 0.768740i | \(0.279116\pi\) | |||||||
\(74\) | 5.51041 | 0.640572 | ||||||||
\(75\) | 2.14882 | 0.248125 | ||||||||
\(76\) | 2.16827 | 0.248718 | ||||||||
\(77\) | −3.54288 | −0.403749 | ||||||||
\(78\) | −1.00000 | −0.113228 | ||||||||
\(79\) | −11.7235 | −1.31900 | −0.659501 | − | 0.751704i | \(-0.729232\pi\) | ||||
−0.659501 | + | 0.751704i | \(0.729232\pi\) | |||||||
\(80\) | −1.68854 | −0.188785 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 10.5241 | 1.16219 | ||||||||
\(83\) | 9.92233 | 1.08912 | 0.544558 | − | 0.838723i | \(-0.316697\pi\) | ||||
0.544558 | + | 0.838723i | \(0.316697\pi\) | |||||||
\(84\) | −4.50145 | −0.491149 | ||||||||
\(85\) | 0.203871 | 0.0221130 | ||||||||
\(86\) | 2.43028 | 0.262064 | ||||||||
\(87\) | −0.430855 | −0.0461926 | ||||||||
\(88\) | −0.787053 | −0.0839001 | ||||||||
\(89\) | 4.51314 | 0.478392 | 0.239196 | − | 0.970971i | \(-0.423116\pi\) | ||||
0.239196 | + | 0.970971i | \(0.423116\pi\) | |||||||
\(90\) | −1.68854 | −0.177988 | ||||||||
\(91\) | 4.50145 | 0.471880 | ||||||||
\(92\) | −4.63632 | −0.483369 | ||||||||
\(93\) | −2.16827 | −0.224840 | ||||||||
\(94\) | 1.33865 | 0.138071 | ||||||||
\(95\) | −3.66122 | −0.375634 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 1.26242 | 0.128180 | 0.0640899 | − | 0.997944i | \(-0.479586\pi\) | ||||
0.0640899 | + | 0.997944i | \(0.479586\pi\) | |||||||
\(98\) | 13.2631 | 1.33977 | ||||||||
\(99\) | −0.787053 | −0.0791018 | ||||||||
\(100\) | −2.14882 | −0.214882 | ||||||||
\(101\) | −11.2050 | −1.11494 | −0.557470 | − | 0.830197i | \(-0.688228\pi\) | ||||
−0.557470 | + | 0.830197i | \(0.688228\pi\) | |||||||
\(102\) | 0.120738 | 0.0119548 | ||||||||
\(103\) | 1.00000 | 0.0985329 | ||||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | 7.60090 | 0.741772 | ||||||||
\(106\) | 8.80373 | 0.855094 | ||||||||
\(107\) | 11.8054 | 1.14128 | 0.570638 | − | 0.821202i | \(-0.306696\pi\) | ||||
0.570638 | + | 0.821202i | \(0.306696\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −2.30323 | −0.220609 | −0.110305 | − | 0.993898i | \(-0.535183\pi\) | ||||
−0.110305 | + | 0.993898i | \(0.535183\pi\) | |||||||
\(110\) | 1.32897 | 0.126713 | ||||||||
\(111\) | −5.51041 | −0.523024 | ||||||||
\(112\) | 4.50145 | 0.425347 | ||||||||
\(113\) | 2.92570 | 0.275227 | 0.137614 | − | 0.990486i | \(-0.456057\pi\) | ||||
0.137614 | + | 0.990486i | \(0.456057\pi\) | |||||||
\(114\) | −2.16827 | −0.203077 | ||||||||
\(115\) | 7.82862 | 0.730023 | ||||||||
\(116\) | 0.430855 | 0.0400039 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | −9.51134 | −0.875589 | ||||||||
\(119\) | −0.543496 | −0.0498222 | ||||||||
\(120\) | 1.68854 | 0.154142 | ||||||||
\(121\) | −10.3805 | −0.943686 | ||||||||
\(122\) | −9.33774 | −0.845400 | ||||||||
\(123\) | −10.5241 | −0.948925 | ||||||||
\(124\) | 2.16827 | 0.194717 | ||||||||
\(125\) | 12.0711 | 1.07967 | ||||||||
\(126\) | 4.50145 | 0.401021 | ||||||||
\(127\) | −4.62781 | −0.410652 | −0.205326 | − | 0.978694i | \(-0.565825\pi\) | ||||
−0.205326 | + | 0.978694i | \(0.565825\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −2.43028 | −0.213974 | ||||||||
\(130\) | −1.68854 | −0.148095 | ||||||||
\(131\) | −8.06962 | −0.705046 | −0.352523 | − | 0.935803i | \(-0.614676\pi\) | ||||
−0.352523 | + | 0.935803i | \(0.614676\pi\) | |||||||
\(132\) | 0.787053 | 0.0685041 | ||||||||
\(133\) | 9.76038 | 0.846332 | ||||||||
\(134\) | 15.9992 | 1.38212 | ||||||||
\(135\) | 1.68854 | 0.145327 | ||||||||
\(136\) | −0.120738 | −0.0103532 | ||||||||
\(137\) | −16.1423 | −1.37913 | −0.689563 | − | 0.724226i | \(-0.742197\pi\) | ||||
−0.689563 | + | 0.724226i | \(0.742197\pi\) | |||||||
\(138\) | 4.63632 | 0.394669 | ||||||||
\(139\) | 7.49861 | 0.636024 | 0.318012 | − | 0.948087i | \(-0.396985\pi\) | ||||
0.318012 | + | 0.948087i | \(0.396985\pi\) | |||||||
\(140\) | −7.60090 | −0.642393 | ||||||||
\(141\) | −1.33865 | −0.112734 | ||||||||
\(142\) | −14.3213 | −1.20182 | ||||||||
\(143\) | −0.787053 | −0.0658167 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −0.727518 | −0.0604171 | ||||||||
\(146\) | 10.9288 | 0.904476 | ||||||||
\(147\) | −13.2631 | −1.09392 | ||||||||
\(148\) | 5.51041 | 0.452953 | ||||||||
\(149\) | 4.84346 | 0.396792 | 0.198396 | − | 0.980122i | \(-0.436427\pi\) | ||||
0.198396 | + | 0.980122i | \(0.436427\pi\) | |||||||
\(150\) | 2.14882 | 0.175451 | ||||||||
\(151\) | 20.2437 | 1.64741 | 0.823705 | − | 0.567019i | \(-0.191903\pi\) | ||||
0.823705 | + | 0.567019i | \(0.191903\pi\) | |||||||
\(152\) | 2.16827 | 0.175870 | ||||||||
\(153\) | −0.120738 | −0.00976109 | ||||||||
\(154\) | −3.54288 | −0.285493 | ||||||||
\(155\) | −3.66122 | −0.294077 | ||||||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | −0.819356 | −0.0653917 | −0.0326959 | − | 0.999465i | \(-0.510409\pi\) | ||||
−0.0326959 | + | 0.999465i | \(0.510409\pi\) | |||||||
\(158\) | −11.7235 | −0.932675 | ||||||||
\(159\) | −8.80373 | −0.698181 | ||||||||
\(160\) | −1.68854 | −0.133491 | ||||||||
\(161\) | −20.8702 | −1.64480 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 18.4391 | 1.44426 | 0.722132 | − | 0.691755i | \(-0.243162\pi\) | ||||
0.722132 | + | 0.691755i | \(0.243162\pi\) | |||||||
\(164\) | 10.5241 | 0.821793 | ||||||||
\(165\) | −1.32897 | −0.103460 | ||||||||
\(166\) | 9.92233 | 0.770122 | ||||||||
\(167\) | −7.78642 | −0.602532 | −0.301266 | − | 0.953540i | \(-0.597409\pi\) | ||||
−0.301266 | + | 0.953540i | \(0.597409\pi\) | |||||||
\(168\) | −4.50145 | −0.347295 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0.203871 | 0.0156362 | ||||||||
\(171\) | 2.16827 | 0.165812 | ||||||||
\(172\) | 2.43028 | 0.185307 | ||||||||
\(173\) | −5.22606 | −0.397330 | −0.198665 | − | 0.980067i | \(-0.563661\pi\) | ||||
−0.198665 | + | 0.980067i | \(0.563661\pi\) | |||||||
\(174\) | −0.430855 | −0.0326631 | ||||||||
\(175\) | −9.67282 | −0.731196 | ||||||||
\(176\) | −0.787053 | −0.0593263 | ||||||||
\(177\) | 9.51134 | 0.714916 | ||||||||
\(178\) | 4.51314 | 0.338274 | ||||||||
\(179\) | 8.23133 | 0.615238 | 0.307619 | − | 0.951510i | \(-0.400468\pi\) | ||||
0.307619 | + | 0.951510i | \(0.400468\pi\) | |||||||
\(180\) | −1.68854 | −0.125857 | ||||||||
\(181\) | −23.2659 | −1.72934 | −0.864671 | − | 0.502339i | \(-0.832473\pi\) | ||||
−0.864671 | + | 0.502339i | \(0.832473\pi\) | |||||||
\(182\) | 4.50145 | 0.333670 | ||||||||
\(183\) | 9.33774 | 0.690266 | ||||||||
\(184\) | −4.63632 | −0.341794 | ||||||||
\(185\) | −9.30456 | −0.684085 | ||||||||
\(186\) | −2.16827 | −0.158986 | ||||||||
\(187\) | 0.0950272 | 0.00694908 | ||||||||
\(188\) | 1.33865 | 0.0976308 | ||||||||
\(189\) | −4.50145 | −0.327432 | ||||||||
\(190\) | −3.66122 | −0.265613 | ||||||||
\(191\) | −3.16411 | −0.228947 | −0.114474 | − | 0.993426i | \(-0.536518\pi\) | ||||
−0.114474 | + | 0.993426i | \(0.536518\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −1.32889 | −0.0956557 | −0.0478279 | − | 0.998856i | \(-0.515230\pi\) | ||||
−0.0478279 | + | 0.998856i | \(0.515230\pi\) | |||||||
\(194\) | 1.26242 | 0.0906368 | ||||||||
\(195\) | 1.68854 | 0.120919 | ||||||||
\(196\) | 13.2631 | 0.947362 | ||||||||
\(197\) | 1.46635 | 0.104473 | 0.0522367 | − | 0.998635i | \(-0.483365\pi\) | ||||
0.0522367 | + | 0.998635i | \(0.483365\pi\) | |||||||
\(198\) | −0.787053 | −0.0559334 | ||||||||
\(199\) | 21.4614 | 1.52136 | 0.760680 | − | 0.649127i | \(-0.224866\pi\) | ||||
0.760680 | + | 0.649127i | \(0.224866\pi\) | |||||||
\(200\) | −2.14882 | −0.151945 | ||||||||
\(201\) | −15.9992 | −1.12850 | ||||||||
\(202\) | −11.2050 | −0.788381 | ||||||||
\(203\) | 1.93947 | 0.136124 | ||||||||
\(204\) | 0.120738 | 0.00845335 | ||||||||
\(205\) | −17.7704 | −1.24114 | ||||||||
\(206\) | 1.00000 | 0.0696733 | ||||||||
\(207\) | −4.63632 | −0.322246 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | −1.70655 | −0.118044 | ||||||||
\(210\) | 7.60090 | 0.524512 | ||||||||
\(211\) | 2.00558 | 0.138070 | 0.0690350 | − | 0.997614i | \(-0.478008\pi\) | ||||
0.0690350 | + | 0.997614i | \(0.478008\pi\) | |||||||
\(212\) | 8.80373 | 0.604643 | ||||||||
\(213\) | 14.3213 | 0.981282 | ||||||||
\(214\) | 11.8054 | 0.807003 | ||||||||
\(215\) | −4.10363 | −0.279865 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 9.76038 | 0.662578 | ||||||||
\(218\) | −2.30323 | −0.155994 | ||||||||
\(219\) | −10.9288 | −0.738501 | ||||||||
\(220\) | 1.32897 | 0.0895993 | ||||||||
\(221\) | −0.120738 | −0.00812172 | ||||||||
\(222\) | −5.51041 | −0.369834 | ||||||||
\(223\) | −19.0380 | −1.27488 | −0.637440 | − | 0.770500i | \(-0.720007\pi\) | ||||
−0.637440 | + | 0.770500i | \(0.720007\pi\) | |||||||
\(224\) | 4.50145 | 0.300766 | ||||||||
\(225\) | −2.14882 | −0.143255 | ||||||||
\(226\) | 2.92570 | 0.194615 | ||||||||
\(227\) | 22.5082 | 1.49392 | 0.746960 | − | 0.664869i | \(-0.231513\pi\) | ||||
0.746960 | + | 0.664869i | \(0.231513\pi\) | |||||||
\(228\) | −2.16827 | −0.143597 | ||||||||
\(229\) | 16.8382 | 1.11270 | 0.556349 | − | 0.830949i | \(-0.312202\pi\) | ||||
0.556349 | + | 0.830949i | \(0.312202\pi\) | |||||||
\(230\) | 7.82862 | 0.516204 | ||||||||
\(231\) | 3.54288 | 0.233104 | ||||||||
\(232\) | 0.430855 | 0.0282870 | ||||||||
\(233\) | 14.4896 | 0.949246 | 0.474623 | − | 0.880189i | \(-0.342584\pi\) | ||||
0.474623 | + | 0.880189i | \(0.342584\pi\) | |||||||
\(234\) | 1.00000 | 0.0653720 | ||||||||
\(235\) | −2.26036 | −0.147450 | ||||||||
\(236\) | −9.51134 | −0.619135 | ||||||||
\(237\) | 11.7235 | 0.761526 | ||||||||
\(238\) | −0.543496 | −0.0352296 | ||||||||
\(239\) | 5.77146 | 0.373325 | 0.186663 | − | 0.982424i | \(-0.440233\pi\) | ||||
0.186663 | + | 0.982424i | \(0.440233\pi\) | |||||||
\(240\) | 1.68854 | 0.108995 | ||||||||
\(241\) | 22.2958 | 1.43620 | 0.718100 | − | 0.695940i | \(-0.245012\pi\) | ||||
0.718100 | + | 0.695940i | \(0.245012\pi\) | |||||||
\(242\) | −10.3805 | −0.667287 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −9.33774 | −0.597788 | ||||||||
\(245\) | −22.3953 | −1.43078 | ||||||||
\(246\) | −10.5241 | −0.670991 | ||||||||
\(247\) | 2.16827 | 0.137964 | ||||||||
\(248\) | 2.16827 | 0.137686 | ||||||||
\(249\) | −9.92233 | −0.628802 | ||||||||
\(250\) | 12.0711 | 0.763443 | ||||||||
\(251\) | −5.12799 | −0.323676 | −0.161838 | − | 0.986817i | \(-0.551742\pi\) | ||||
−0.161838 | + | 0.986817i | \(0.551742\pi\) | |||||||
\(252\) | 4.50145 | 0.283565 | ||||||||
\(253\) | 3.64902 | 0.229412 | ||||||||
\(254\) | −4.62781 | −0.290375 | ||||||||
\(255\) | −0.203871 | −0.0127669 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 1.47989 | 0.0923133 | 0.0461566 | − | 0.998934i | \(-0.485303\pi\) | ||||
0.0461566 | + | 0.998934i | \(0.485303\pi\) | |||||||
\(258\) | −2.43028 | −0.151303 | ||||||||
\(259\) | 24.8048 | 1.54130 | ||||||||
\(260\) | −1.68854 | −0.104719 | ||||||||
\(261\) | 0.430855 | 0.0266693 | ||||||||
\(262\) | −8.06962 | −0.498543 | ||||||||
\(263\) | −20.0334 | −1.23532 | −0.617658 | − | 0.786447i | \(-0.711918\pi\) | ||||
−0.617658 | + | 0.786447i | \(0.711918\pi\) | |||||||
\(264\) | 0.787053 | 0.0484397 | ||||||||
\(265\) | −14.8655 | −0.913179 | ||||||||
\(266\) | 9.76038 | 0.598447 | ||||||||
\(267\) | −4.51314 | −0.276200 | ||||||||
\(268\) | 15.9992 | 0.977308 | ||||||||
\(269\) | −2.10282 | −0.128211 | −0.0641057 | − | 0.997943i | \(-0.520419\pi\) | ||||
−0.0641057 | + | 0.997943i | \(0.520419\pi\) | |||||||
\(270\) | 1.68854 | 0.102761 | ||||||||
\(271\) | 28.5103 | 1.73188 | 0.865940 | − | 0.500148i | \(-0.166721\pi\) | ||||
0.865940 | + | 0.500148i | \(0.166721\pi\) | |||||||
\(272\) | −0.120738 | −0.00732082 | ||||||||
\(273\) | −4.50145 | −0.272440 | ||||||||
\(274\) | −16.1423 | −0.975189 | ||||||||
\(275\) | 1.69124 | 0.101985 | ||||||||
\(276\) | 4.63632 | 0.279073 | ||||||||
\(277\) | 19.2633 | 1.15742 | 0.578711 | − | 0.815533i | \(-0.303556\pi\) | ||||
0.578711 | + | 0.815533i | \(0.303556\pi\) | |||||||
\(278\) | 7.49861 | 0.449737 | ||||||||
\(279\) | 2.16827 | 0.129811 | ||||||||
\(280\) | −7.60090 | −0.454240 | ||||||||
\(281\) | 20.9688 | 1.25089 | 0.625446 | − | 0.780267i | \(-0.284917\pi\) | ||||
0.625446 | + | 0.780267i | \(0.284917\pi\) | |||||||
\(282\) | −1.33865 | −0.0797152 | ||||||||
\(283\) | 29.4972 | 1.75343 | 0.876714 | − | 0.481012i | \(-0.159731\pi\) | ||||
0.876714 | + | 0.481012i | \(0.159731\pi\) | |||||||
\(284\) | −14.3213 | −0.849815 | ||||||||
\(285\) | 3.66122 | 0.216872 | ||||||||
\(286\) | −0.787053 | −0.0465394 | ||||||||
\(287\) | 47.3737 | 2.79638 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −16.9854 | −0.999142 | ||||||||
\(290\) | −0.727518 | −0.0427213 | ||||||||
\(291\) | −1.26242 | −0.0740046 | ||||||||
\(292\) | 10.9288 | 0.639561 | ||||||||
\(293\) | −22.5817 | −1.31924 | −0.659619 | − | 0.751600i | \(-0.729282\pi\) | ||||
−0.659619 | + | 0.751600i | \(0.729282\pi\) | |||||||
\(294\) | −13.2631 | −0.773518 | ||||||||
\(295\) | 16.0603 | 0.935067 | ||||||||
\(296\) | 5.51041 | 0.320286 | ||||||||
\(297\) | 0.787053 | 0.0456694 | ||||||||
\(298\) | 4.84346 | 0.280574 | ||||||||
\(299\) | −4.63632 | −0.268125 | ||||||||
\(300\) | 2.14882 | 0.124062 | ||||||||
\(301\) | 10.9398 | 0.630559 | ||||||||
\(302\) | 20.2437 | 1.16489 | ||||||||
\(303\) | 11.2050 | 0.643711 | ||||||||
\(304\) | 2.16827 | 0.124359 | ||||||||
\(305\) | 15.7672 | 0.902826 | ||||||||
\(306\) | −0.120738 | −0.00690213 | ||||||||
\(307\) | −12.4312 | −0.709484 | −0.354742 | − | 0.934964i | \(-0.615431\pi\) | ||||
−0.354742 | + | 0.934964i | \(0.615431\pi\) | |||||||
\(308\) | −3.54288 | −0.201874 | ||||||||
\(309\) | −1.00000 | −0.0568880 | ||||||||
\(310\) | −3.66122 | −0.207944 | ||||||||
\(311\) | −12.2864 | −0.696699 | −0.348349 | − | 0.937365i | \(-0.613258\pi\) | ||||
−0.348349 | + | 0.937365i | \(0.613258\pi\) | |||||||
\(312\) | −1.00000 | −0.0566139 | ||||||||
\(313\) | −17.9396 | −1.01401 | −0.507004 | − | 0.861944i | \(-0.669247\pi\) | ||||
−0.507004 | + | 0.861944i | \(0.669247\pi\) | |||||||
\(314\) | −0.819356 | −0.0462389 | ||||||||
\(315\) | −7.60090 | −0.428262 | ||||||||
\(316\) | −11.7235 | −0.659501 | ||||||||
\(317\) | 31.1119 | 1.74742 | 0.873709 | − | 0.486449i | \(-0.161708\pi\) | ||||
0.873709 | + | 0.486449i | \(0.161708\pi\) | |||||||
\(318\) | −8.80373 | −0.493689 | ||||||||
\(319\) | −0.339106 | −0.0189863 | ||||||||
\(320\) | −1.68854 | −0.0943924 | ||||||||
\(321\) | −11.8054 | −0.658916 | ||||||||
\(322\) | −20.8702 | −1.16305 | ||||||||
\(323\) | −0.261793 | −0.0145666 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −2.14882 | −0.119195 | ||||||||
\(326\) | 18.4391 | 1.02125 | ||||||||
\(327\) | 2.30323 | 0.127369 | ||||||||
\(328\) | 10.5241 | 0.581095 | ||||||||
\(329\) | 6.02585 | 0.332216 | ||||||||
\(330\) | −1.32897 | −0.0731575 | ||||||||
\(331\) | 29.8047 | 1.63821 | 0.819107 | − | 0.573641i | \(-0.194470\pi\) | ||||
0.819107 | + | 0.573641i | \(0.194470\pi\) | |||||||
\(332\) | 9.92233 | 0.544558 | ||||||||
\(333\) | 5.51041 | 0.301968 | ||||||||
\(334\) | −7.78642 | −0.426054 | ||||||||
\(335\) | −27.0154 | −1.47601 | ||||||||
\(336\) | −4.50145 | −0.245574 | ||||||||
\(337\) | −9.10231 | −0.495834 | −0.247917 | − | 0.968781i | \(-0.579746\pi\) | ||||
−0.247917 | + | 0.968781i | \(0.579746\pi\) | |||||||
\(338\) | 1.00000 | 0.0543928 | ||||||||
\(339\) | −2.92570 | −0.158902 | ||||||||
\(340\) | 0.203871 | 0.0110565 | ||||||||
\(341\) | −1.70655 | −0.0924146 | ||||||||
\(342\) | 2.16827 | 0.117247 | ||||||||
\(343\) | 28.1929 | 1.52227 | ||||||||
\(344\) | 2.43028 | 0.131032 | ||||||||
\(345\) | −7.82862 | −0.421479 | ||||||||
\(346\) | −5.22606 | −0.280955 | ||||||||
\(347\) | 7.09876 | 0.381081 | 0.190541 | − | 0.981679i | \(-0.438976\pi\) | ||||
0.190541 | + | 0.981679i | \(0.438976\pi\) | |||||||
\(348\) | −0.430855 | −0.0230963 | ||||||||
\(349\) | −27.6902 | −1.48222 | −0.741111 | − | 0.671382i | \(-0.765701\pi\) | ||||
−0.741111 | + | 0.671382i | \(0.765701\pi\) | |||||||
\(350\) | −9.67282 | −0.517034 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | −0.787053 | −0.0419500 | ||||||||
\(353\) | 36.0299 | 1.91768 | 0.958839 | − | 0.283949i | \(-0.0916448\pi\) | ||||
0.958839 | + | 0.283949i | \(0.0916448\pi\) | |||||||
\(354\) | 9.51134 | 0.505522 | ||||||||
\(355\) | 24.1822 | 1.28346 | ||||||||
\(356\) | 4.51314 | 0.239196 | ||||||||
\(357\) | 0.543496 | 0.0287649 | ||||||||
\(358\) | 8.23133 | 0.435039 | ||||||||
\(359\) | −24.0969 | −1.27178 | −0.635892 | − | 0.771778i | \(-0.719368\pi\) | ||||
−0.635892 | + | 0.771778i | \(0.719368\pi\) | |||||||
\(360\) | −1.68854 | −0.0889940 | ||||||||
\(361\) | −14.2986 | −0.752557 | ||||||||
\(362\) | −23.2659 | −1.22283 | ||||||||
\(363\) | 10.3805 | 0.544837 | ||||||||
\(364\) | 4.50145 | 0.235940 | ||||||||
\(365\) | −18.4538 | −0.965915 | ||||||||
\(366\) | 9.33774 | 0.488092 | ||||||||
\(367\) | 10.2238 | 0.533678 | 0.266839 | − | 0.963741i | \(-0.414021\pi\) | ||||
0.266839 | + | 0.963741i | \(0.414021\pi\) | |||||||
\(368\) | −4.63632 | −0.241685 | ||||||||
\(369\) | 10.5241 | 0.547862 | ||||||||
\(370\) | −9.30456 | −0.483721 | ||||||||
\(371\) | 39.6296 | 2.05746 | ||||||||
\(372\) | −2.16827 | −0.112420 | ||||||||
\(373\) | 30.3725 | 1.57263 | 0.786313 | − | 0.617828i | \(-0.211987\pi\) | ||||
0.786313 | + | 0.617828i | \(0.211987\pi\) | |||||||
\(374\) | 0.0950272 | 0.00491374 | ||||||||
\(375\) | −12.0711 | −0.623349 | ||||||||
\(376\) | 1.33865 | 0.0690354 | ||||||||
\(377\) | 0.430855 | 0.0221902 | ||||||||
\(378\) | −4.50145 | −0.231530 | ||||||||
\(379\) | 28.6696 | 1.47266 | 0.736330 | − | 0.676623i | \(-0.236557\pi\) | ||||
0.736330 | + | 0.676623i | \(0.236557\pi\) | |||||||
\(380\) | −3.66122 | −0.187817 | ||||||||
\(381\) | 4.62781 | 0.237090 | ||||||||
\(382\) | −3.16411 | −0.161890 | ||||||||
\(383\) | 2.20806 | 0.112826 | 0.0564132 | − | 0.998408i | \(-0.482034\pi\) | ||||
0.0564132 | + | 0.998408i | \(0.482034\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 5.98231 | 0.304887 | ||||||||
\(386\) | −1.32889 | −0.0676388 | ||||||||
\(387\) | 2.43028 | 0.123538 | ||||||||
\(388\) | 1.26242 | 0.0640899 | ||||||||
\(389\) | 13.0889 | 0.663634 | 0.331817 | − | 0.943344i | \(-0.392338\pi\) | ||||
0.331817 | + | 0.943344i | \(0.392338\pi\) | |||||||
\(390\) | 1.68854 | 0.0855027 | ||||||||
\(391\) | 0.559780 | 0.0283093 | ||||||||
\(392\) | 13.2631 | 0.669886 | ||||||||
\(393\) | 8.06962 | 0.407058 | ||||||||
\(394\) | 1.46635 | 0.0738738 | ||||||||
\(395\) | 19.7957 | 0.996030 | ||||||||
\(396\) | −0.787053 | −0.0395509 | ||||||||
\(397\) | 18.6996 | 0.938507 | 0.469254 | − | 0.883063i | \(-0.344523\pi\) | ||||
0.469254 | + | 0.883063i | \(0.344523\pi\) | |||||||
\(398\) | 21.4614 | 1.07576 | ||||||||
\(399\) | −9.76038 | −0.488630 | ||||||||
\(400\) | −2.14882 | −0.107441 | ||||||||
\(401\) | 20.9674 | 1.04706 | 0.523532 | − | 0.852006i | \(-0.324614\pi\) | ||||
0.523532 | + | 0.852006i | \(0.324614\pi\) | |||||||
\(402\) | −15.9992 | −0.797968 | ||||||||
\(403\) | 2.16827 | 0.108009 | ||||||||
\(404\) | −11.2050 | −0.557470 | ||||||||
\(405\) | −1.68854 | −0.0839044 | ||||||||
\(406\) | 1.93947 | 0.0962545 | ||||||||
\(407\) | −4.33698 | −0.214976 | ||||||||
\(408\) | 0.120738 | 0.00597742 | ||||||||
\(409\) | 18.3390 | 0.906805 | 0.453403 | − | 0.891306i | \(-0.350210\pi\) | ||||
0.453403 | + | 0.891306i | \(0.350210\pi\) | |||||||
\(410\) | −17.7704 | −0.877616 | ||||||||
\(411\) | 16.1423 | 0.796239 | ||||||||
\(412\) | 1.00000 | 0.0492665 | ||||||||
\(413\) | −42.8148 | −2.10678 | ||||||||
\(414\) | −4.63632 | −0.227863 | ||||||||
\(415\) | −16.7543 | −0.822435 | ||||||||
\(416\) | 1.00000 | 0.0490290 | ||||||||
\(417\) | −7.49861 | −0.367209 | ||||||||
\(418\) | −1.70655 | −0.0834699 | ||||||||
\(419\) | 3.18302 | 0.155501 | 0.0777503 | − | 0.996973i | \(-0.475226\pi\) | ||||
0.0777503 | + | 0.996973i | \(0.475226\pi\) | |||||||
\(420\) | 7.60090 | 0.370886 | ||||||||
\(421\) | 12.8911 | 0.628272 | 0.314136 | − | 0.949378i | \(-0.398285\pi\) | ||||
0.314136 | + | 0.949378i | \(0.398285\pi\) | |||||||
\(422\) | 2.00558 | 0.0976302 | ||||||||
\(423\) | 1.33865 | 0.0650872 | ||||||||
\(424\) | 8.80373 | 0.427547 | ||||||||
\(425\) | 0.259444 | 0.0125849 | ||||||||
\(426\) | 14.3213 | 0.693871 | ||||||||
\(427\) | −42.0334 | −2.03414 | ||||||||
\(428\) | 11.8054 | 0.570638 | ||||||||
\(429\) | 0.787053 | 0.0379993 | ||||||||
\(430\) | −4.10363 | −0.197895 | ||||||||
\(431\) | −24.0805 | −1.15992 | −0.579958 | − | 0.814647i | \(-0.696931\pi\) | ||||
−0.579958 | + | 0.814647i | \(0.696931\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −30.1923 | −1.45095 | −0.725475 | − | 0.688248i | \(-0.758380\pi\) | ||||
−0.725475 | + | 0.688248i | \(0.758380\pi\) | |||||||
\(434\) | 9.76038 | 0.468513 | ||||||||
\(435\) | 0.727518 | 0.0348818 | ||||||||
\(436\) | −2.30323 | −0.110305 | ||||||||
\(437\) | −10.0528 | −0.480891 | ||||||||
\(438\) | −10.9288 | −0.522199 | ||||||||
\(439\) | 5.69015 | 0.271576 | 0.135788 | − | 0.990738i | \(-0.456643\pi\) | ||||
0.135788 | + | 0.990738i | \(0.456643\pi\) | |||||||
\(440\) | 1.32897 | 0.0633563 | ||||||||
\(441\) | 13.2631 | 0.631575 | ||||||||
\(442\) | −0.120738 | −0.00574292 | ||||||||
\(443\) | −12.9170 | −0.613705 | −0.306852 | − | 0.951757i | \(-0.599276\pi\) | ||||
−0.306852 | + | 0.951757i | \(0.599276\pi\) | |||||||
\(444\) | −5.51041 | −0.261512 | ||||||||
\(445\) | −7.62063 | −0.361253 | ||||||||
\(446\) | −19.0380 | −0.901477 | ||||||||
\(447\) | −4.84346 | −0.229088 | ||||||||
\(448\) | 4.50145 | 0.212674 | ||||||||
\(449\) | −21.2531 | −1.00300 | −0.501499 | − | 0.865158i | \(-0.667218\pi\) | ||||
−0.501499 | + | 0.865158i | \(0.667218\pi\) | |||||||
\(450\) | −2.14882 | −0.101296 | ||||||||
\(451\) | −8.28301 | −0.390032 | ||||||||
\(452\) | 2.92570 | 0.137614 | ||||||||
\(453\) | −20.2437 | −0.951132 | ||||||||
\(454\) | 22.5082 | 1.05636 | ||||||||
\(455\) | −7.60090 | −0.356336 | ||||||||
\(456\) | −2.16827 | −0.101539 | ||||||||
\(457\) | 23.2880 | 1.08937 | 0.544683 | − | 0.838642i | \(-0.316650\pi\) | ||||
0.544683 | + | 0.838642i | \(0.316650\pi\) | |||||||
\(458\) | 16.8382 | 0.786797 | ||||||||
\(459\) | 0.120738 | 0.00563557 | ||||||||
\(460\) | 7.82862 | 0.365011 | ||||||||
\(461\) | 18.2701 | 0.850923 | 0.425461 | − | 0.904977i | \(-0.360112\pi\) | ||||
0.425461 | + | 0.904977i | \(0.360112\pi\) | |||||||
\(462\) | 3.54288 | 0.164830 | ||||||||
\(463\) | 22.7042 | 1.05515 | 0.527576 | − | 0.849508i | \(-0.323101\pi\) | ||||
0.527576 | + | 0.849508i | \(0.323101\pi\) | |||||||
\(464\) | 0.430855 | 0.0200020 | ||||||||
\(465\) | 3.66122 | 0.169785 | ||||||||
\(466\) | 14.4896 | 0.671218 | ||||||||
\(467\) | 12.0488 | 0.557553 | 0.278776 | − | 0.960356i | \(-0.410071\pi\) | ||||
0.278776 | + | 0.960356i | \(0.410071\pi\) | |||||||
\(468\) | 1.00000 | 0.0462250 | ||||||||
\(469\) | 72.0197 | 3.32556 | ||||||||
\(470\) | −2.26036 | −0.104263 | ||||||||
\(471\) | 0.819356 | 0.0377539 | ||||||||
\(472\) | −9.51134 | −0.437795 | ||||||||
\(473\) | −1.91276 | −0.0879487 | ||||||||
\(474\) | 11.7235 | 0.538480 | ||||||||
\(475\) | −4.65923 | −0.213780 | ||||||||
\(476\) | −0.543496 | −0.0249111 | ||||||||
\(477\) | 8.80373 | 0.403095 | ||||||||
\(478\) | 5.77146 | 0.263981 | ||||||||
\(479\) | −41.7439 | −1.90733 | −0.953664 | − | 0.300874i | \(-0.902722\pi\) | ||||
−0.953664 | + | 0.300874i | \(0.902722\pi\) | |||||||
\(480\) | 1.68854 | 0.0770711 | ||||||||
\(481\) | 5.51041 | 0.251253 | ||||||||
\(482\) | 22.2958 | 1.01555 | ||||||||
\(483\) | 20.8702 | 0.949625 | ||||||||
\(484\) | −10.3805 | −0.471843 | ||||||||
\(485\) | −2.13166 | −0.0967936 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −34.4976 | −1.56323 | −0.781617 | − | 0.623759i | \(-0.785605\pi\) | ||||
−0.781617 | + | 0.623759i | \(0.785605\pi\) | |||||||
\(488\) | −9.33774 | −0.422700 | ||||||||
\(489\) | −18.4391 | −0.833847 | ||||||||
\(490\) | −22.3953 | −1.01171 | ||||||||
\(491\) | −33.4958 | −1.51165 | −0.755823 | − | 0.654776i | \(-0.772763\pi\) | ||||
−0.755823 | + | 0.654776i | \(0.772763\pi\) | |||||||
\(492\) | −10.5241 | −0.474462 | ||||||||
\(493\) | −0.0520206 | −0.00234289 | ||||||||
\(494\) | 2.16827 | 0.0975553 | ||||||||
\(495\) | 1.32897 | 0.0597329 | ||||||||
\(496\) | 2.16827 | 0.0973584 | ||||||||
\(497\) | −64.4668 | −2.89173 | ||||||||
\(498\) | −9.92233 | −0.444630 | ||||||||
\(499\) | 24.5788 | 1.10030 | 0.550148 | − | 0.835067i | \(-0.314571\pi\) | ||||
0.550148 | + | 0.835067i | \(0.314571\pi\) | |||||||
\(500\) | 12.0711 | 0.539836 | ||||||||
\(501\) | 7.78642 | 0.347872 | ||||||||
\(502\) | −5.12799 | −0.228873 | ||||||||
\(503\) | 14.5933 | 0.650684 | 0.325342 | − | 0.945596i | \(-0.394521\pi\) | ||||
0.325342 | + | 0.945596i | \(0.394521\pi\) | |||||||
\(504\) | 4.50145 | 0.200511 | ||||||||
\(505\) | 18.9201 | 0.841935 | ||||||||
\(506\) | 3.64902 | 0.162219 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | −4.62781 | −0.205326 | ||||||||
\(509\) | 4.91456 | 0.217834 | 0.108917 | − | 0.994051i | \(-0.465262\pi\) | ||||
0.108917 | + | 0.994051i | \(0.465262\pi\) | |||||||
\(510\) | −0.203871 | −0.00902758 | ||||||||
\(511\) | 49.1956 | 2.17628 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −2.16827 | −0.0957316 | ||||||||
\(514\) | 1.47989 | 0.0652753 | ||||||||
\(515\) | −1.68854 | −0.0744061 | ||||||||
\(516\) | −2.43028 | −0.106987 | ||||||||
\(517\) | −1.05359 | −0.0463366 | ||||||||
\(518\) | 24.8048 | 1.08986 | ||||||||
\(519\) | 5.22606 | 0.229399 | ||||||||
\(520\) | −1.68854 | −0.0740475 | ||||||||
\(521\) | −24.3944 | −1.06874 | −0.534368 | − | 0.845252i | \(-0.679450\pi\) | ||||
−0.534368 | + | 0.845252i | \(0.679450\pi\) | |||||||
\(522\) | 0.430855 | 0.0188580 | ||||||||
\(523\) | 23.0303 | 1.00704 | 0.503522 | − | 0.863982i | \(-0.332037\pi\) | ||||
0.503522 | + | 0.863982i | \(0.332037\pi\) | |||||||
\(524\) | −8.06962 | −0.352523 | ||||||||
\(525\) | 9.67282 | 0.422156 | ||||||||
\(526\) | −20.0334 | −0.873500 | ||||||||
\(527\) | −0.261793 | −0.0114039 | ||||||||
\(528\) | 0.787053 | 0.0342521 | ||||||||
\(529\) | −1.50457 | −0.0654162 | ||||||||
\(530\) | −14.8655 | −0.645715 | ||||||||
\(531\) | −9.51134 | −0.412757 | ||||||||
\(532\) | 9.76038 | 0.423166 | ||||||||
\(533\) | 10.5241 | 0.455849 | ||||||||
\(534\) | −4.51314 | −0.195303 | ||||||||
\(535\) | −19.9340 | −0.861822 | ||||||||
\(536\) | 15.9992 | 0.691061 | ||||||||
\(537\) | −8.23133 | −0.355208 | ||||||||
\(538\) | −2.10282 | −0.0906591 | ||||||||
\(539\) | −10.4387 | −0.449628 | ||||||||
\(540\) | 1.68854 | 0.0726633 | ||||||||
\(541\) | 3.05816 | 0.131481 | 0.0657403 | − | 0.997837i | \(-0.479059\pi\) | ||||
0.0657403 | + | 0.997837i | \(0.479059\pi\) | |||||||
\(542\) | 28.5103 | 1.22462 | ||||||||
\(543\) | 23.2659 | 0.998436 | ||||||||
\(544\) | −0.120738 | −0.00517660 | ||||||||
\(545\) | 3.88910 | 0.166591 | ||||||||
\(546\) | −4.50145 | −0.192644 | ||||||||
\(547\) | −41.7413 | −1.78473 | −0.892365 | − | 0.451314i | \(-0.850955\pi\) | ||||
−0.892365 | + | 0.451314i | \(0.850955\pi\) | |||||||
\(548\) | −16.1423 | −0.689563 | ||||||||
\(549\) | −9.33774 | −0.398525 | ||||||||
\(550\) | 1.69124 | 0.0721145 | ||||||||
\(551\) | 0.934213 | 0.0397988 | ||||||||
\(552\) | 4.63632 | 0.197335 | ||||||||
\(553\) | −52.7730 | −2.24413 | ||||||||
\(554\) | 19.2633 | 0.818421 | ||||||||
\(555\) | 9.30456 | 0.394956 | ||||||||
\(556\) | 7.49861 | 0.318012 | ||||||||
\(557\) | −28.4286 | −1.20456 | −0.602278 | − | 0.798286i | \(-0.705740\pi\) | ||||
−0.602278 | + | 0.798286i | \(0.705740\pi\) | |||||||
\(558\) | 2.16827 | 0.0917904 | ||||||||
\(559\) | 2.43028 | 0.102790 | ||||||||
\(560\) | −7.60090 | −0.321196 | ||||||||
\(561\) | −0.0950272 | −0.00401205 | ||||||||
\(562\) | 20.9688 | 0.884514 | ||||||||
\(563\) | 27.2329 | 1.14773 | 0.573865 | − | 0.818950i | \(-0.305444\pi\) | ||||
0.573865 | + | 0.818950i | \(0.305444\pi\) | |||||||
\(564\) | −1.33865 | −0.0563672 | ||||||||
\(565\) | −4.94018 | −0.207835 | ||||||||
\(566\) | 29.4972 | 1.23986 | ||||||||
\(567\) | 4.50145 | 0.189043 | ||||||||
\(568\) | −14.3213 | −0.600910 | ||||||||
\(569\) | −24.6215 | −1.03219 | −0.516094 | − | 0.856532i | \(-0.672614\pi\) | ||||
−0.516094 | + | 0.856532i | \(0.672614\pi\) | |||||||
\(570\) | 3.66122 | 0.153352 | ||||||||
\(571\) | −23.1123 | −0.967222 | −0.483611 | − | 0.875283i | \(-0.660675\pi\) | ||||
−0.483611 | + | 0.875283i | \(0.660675\pi\) | |||||||
\(572\) | −0.787053 | −0.0329083 | ||||||||
\(573\) | 3.16411 | 0.132183 | ||||||||
\(574\) | 47.3737 | 1.97734 | ||||||||
\(575\) | 9.96262 | 0.415470 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −4.71744 | −0.196389 | −0.0981947 | − | 0.995167i | \(-0.531307\pi\) | ||||
−0.0981947 | + | 0.995167i | \(0.531307\pi\) | |||||||
\(578\) | −16.9854 | −0.706500 | ||||||||
\(579\) | 1.32889 | 0.0552269 | ||||||||
\(580\) | −0.727518 | −0.0302085 | ||||||||
\(581\) | 44.6649 | 1.85301 | ||||||||
\(582\) | −1.26242 | −0.0523292 | ||||||||
\(583\) | −6.92900 | −0.286970 | ||||||||
\(584\) | 10.9288 | 0.452238 | ||||||||
\(585\) | −1.68854 | −0.0698127 | ||||||||
\(586\) | −22.5817 | −0.932842 | ||||||||
\(587\) | −7.95453 | −0.328318 | −0.164159 | − | 0.986434i | \(-0.552491\pi\) | ||||
−0.164159 | + | 0.986434i | \(0.552491\pi\) | |||||||
\(588\) | −13.2631 | −0.546960 | ||||||||
\(589\) | 4.70141 | 0.193718 | ||||||||
\(590\) | 16.0603 | 0.661192 | ||||||||
\(591\) | −1.46635 | −0.0603177 | ||||||||
\(592\) | 5.51041 | 0.226476 | ||||||||
\(593\) | −21.3889 | −0.878339 | −0.439169 | − | 0.898404i | \(-0.644727\pi\) | ||||
−0.439169 | + | 0.898404i | \(0.644727\pi\) | |||||||
\(594\) | 0.787053 | 0.0322932 | ||||||||
\(595\) | 0.917717 | 0.0376227 | ||||||||
\(596\) | 4.84346 | 0.198396 | ||||||||
\(597\) | −21.4614 | −0.878358 | ||||||||
\(598\) | −4.63632 | −0.189593 | ||||||||
\(599\) | 3.89261 | 0.159048 | 0.0795238 | − | 0.996833i | \(-0.474660\pi\) | ||||
0.0795238 | + | 0.996833i | \(0.474660\pi\) | |||||||
\(600\) | 2.14882 | 0.0877253 | ||||||||
\(601\) | −46.7978 | −1.90892 | −0.954462 | − | 0.298333i | \(-0.903569\pi\) | ||||
−0.954462 | + | 0.298333i | \(0.903569\pi\) | |||||||
\(602\) | 10.9398 | 0.445872 | ||||||||
\(603\) | 15.9992 | 0.651538 | ||||||||
\(604\) | 20.2437 | 0.823705 | ||||||||
\(605\) | 17.5280 | 0.712615 | ||||||||
\(606\) | 11.2050 | 0.455172 | ||||||||
\(607\) | −28.8775 | −1.17210 | −0.586050 | − | 0.810275i | \(-0.699318\pi\) | ||||
−0.586050 | + | 0.810275i | \(0.699318\pi\) | |||||||
\(608\) | 2.16827 | 0.0879351 | ||||||||
\(609\) | −1.93947 | −0.0785915 | ||||||||
\(610\) | 15.7672 | 0.638395 | ||||||||
\(611\) | 1.33865 | 0.0541558 | ||||||||
\(612\) | −0.120738 | −0.00488055 | ||||||||
\(613\) | 1.52992 | 0.0617930 | 0.0308965 | − | 0.999523i | \(-0.490164\pi\) | ||||
0.0308965 | + | 0.999523i | \(0.490164\pi\) | |||||||
\(614\) | −12.4312 | −0.501681 | ||||||||
\(615\) | 17.7704 | 0.716571 | ||||||||
\(616\) | −3.54288 | −0.142747 | ||||||||
\(617\) | 18.9018 | 0.760956 | 0.380478 | − | 0.924790i | \(-0.375759\pi\) | ||||
0.380478 | + | 0.924790i | \(0.375759\pi\) | |||||||
\(618\) | −1.00000 | −0.0402259 | ||||||||
\(619\) | −29.9232 | −1.20271 | −0.601357 | − | 0.798980i | \(-0.705373\pi\) | ||||
−0.601357 | + | 0.798980i | \(0.705373\pi\) | |||||||
\(620\) | −3.66122 | −0.147038 | ||||||||
\(621\) | 4.63632 | 0.186049 | ||||||||
\(622\) | −12.2864 | −0.492640 | ||||||||
\(623\) | 20.3157 | 0.813931 | ||||||||
\(624\) | −1.00000 | −0.0400320 | ||||||||
\(625\) | −9.63846 | −0.385538 | ||||||||
\(626\) | −17.9396 | −0.717011 | ||||||||
\(627\) | 1.70655 | 0.0681529 | ||||||||
\(628\) | −0.819356 | −0.0326959 | ||||||||
\(629\) | −0.665315 | −0.0265279 | ||||||||
\(630\) | −7.60090 | −0.302827 | ||||||||
\(631\) | 1.87357 | 0.0745858 | 0.0372929 | − | 0.999304i | \(-0.488127\pi\) | ||||
0.0372929 | + | 0.999304i | \(0.488127\pi\) | |||||||
\(632\) | −11.7235 | −0.466338 | ||||||||
\(633\) | −2.00558 | −0.0797147 | ||||||||
\(634\) | 31.1119 | 1.23561 | ||||||||
\(635\) | 7.81426 | 0.310100 | ||||||||
\(636\) | −8.80373 | −0.349091 | ||||||||
\(637\) | 13.2631 | 0.525502 | ||||||||
\(638\) | −0.339106 | −0.0134253 | ||||||||
\(639\) | −14.3213 | −0.566543 | ||||||||
\(640\) | −1.68854 | −0.0667455 | ||||||||
\(641\) | 10.1990 | 0.402835 | 0.201418 | − | 0.979505i | \(-0.435445\pi\) | ||||
0.201418 | + | 0.979505i | \(0.435445\pi\) | |||||||
\(642\) | −11.8054 | −0.465924 | ||||||||
\(643\) | 2.65800 | 0.104821 | 0.0524106 | − | 0.998626i | \(-0.483310\pi\) | ||||
0.0524106 | + | 0.998626i | \(0.483310\pi\) | |||||||
\(644\) | −20.8702 | −0.822399 | ||||||||
\(645\) | 4.10363 | 0.161580 | ||||||||
\(646\) | −0.261793 | −0.0103001 | ||||||||
\(647\) | −44.8081 | −1.76159 | −0.880794 | − | 0.473500i | \(-0.842990\pi\) | ||||
−0.880794 | + | 0.473500i | \(0.842990\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 7.48592 | 0.293848 | ||||||||
\(650\) | −2.14882 | −0.0842837 | ||||||||
\(651\) | −9.76038 | −0.382539 | ||||||||
\(652\) | 18.4391 | 0.722132 | ||||||||
\(653\) | 42.6007 | 1.66709 | 0.833547 | − | 0.552448i | \(-0.186306\pi\) | ||||
0.833547 | + | 0.552448i | \(0.186306\pi\) | |||||||
\(654\) | 2.30323 | 0.0900634 | ||||||||
\(655\) | 13.6259 | 0.532408 | ||||||||
\(656\) | 10.5241 | 0.410896 | ||||||||
\(657\) | 10.9288 | 0.426374 | ||||||||
\(658\) | 6.02585 | 0.234912 | ||||||||
\(659\) | 22.2070 | 0.865063 | 0.432531 | − | 0.901619i | \(-0.357620\pi\) | ||||
0.432531 | + | 0.901619i | \(0.357620\pi\) | |||||||
\(660\) | −1.32897 | −0.0517302 | ||||||||
\(661\) | −3.30680 | −0.128620 | −0.0643098 | − | 0.997930i | \(-0.520485\pi\) | ||||
−0.0643098 | + | 0.997930i | \(0.520485\pi\) | |||||||
\(662\) | 29.8047 | 1.15839 | ||||||||
\(663\) | 0.120738 | 0.00468908 | ||||||||
\(664\) | 9.92233 | 0.385061 | ||||||||
\(665\) | −16.4808 | −0.639099 | ||||||||
\(666\) | 5.51041 | 0.213524 | ||||||||
\(667\) | −1.99758 | −0.0773467 | ||||||||
\(668\) | −7.78642 | −0.301266 | ||||||||
\(669\) | 19.0380 | 0.736053 | ||||||||
\(670\) | −27.0154 | −1.04369 | ||||||||
\(671\) | 7.34930 | 0.283716 | ||||||||
\(672\) | −4.50145 | −0.173647 | ||||||||
\(673\) | 34.7100 | 1.33797 | 0.668987 | − | 0.743274i | \(-0.266728\pi\) | ||||
0.668987 | + | 0.743274i | \(0.266728\pi\) | |||||||
\(674\) | −9.10231 | −0.350608 | ||||||||
\(675\) | 2.14882 | 0.0827082 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −12.5673 | −0.482999 | −0.241500 | − | 0.970401i | \(-0.577639\pi\) | ||||
−0.241500 | + | 0.970401i | \(0.577639\pi\) | |||||||
\(678\) | −2.92570 | −0.112361 | ||||||||
\(679\) | 5.68274 | 0.218084 | ||||||||
\(680\) | 0.203871 | 0.00781811 | ||||||||
\(681\) | −22.5082 | −0.862515 | ||||||||
\(682\) | −1.70655 | −0.0653470 | ||||||||
\(683\) | −26.5155 | −1.01459 | −0.507293 | − | 0.861774i | \(-0.669354\pi\) | ||||
−0.507293 | + | 0.861774i | \(0.669354\pi\) | |||||||
\(684\) | 2.16827 | 0.0829060 | ||||||||
\(685\) | 27.2569 | 1.04143 | ||||||||
\(686\) | 28.1929 | 1.07641 | ||||||||
\(687\) | −16.8382 | −0.642417 | ||||||||
\(688\) | 2.43028 | 0.0926535 | ||||||||
\(689\) | 8.80373 | 0.335395 | ||||||||
\(690\) | −7.82862 | −0.298030 | ||||||||
\(691\) | −20.7887 | −0.790838 | −0.395419 | − | 0.918501i | \(-0.629401\pi\) | ||||
−0.395419 | + | 0.918501i | \(0.629401\pi\) | |||||||
\(692\) | −5.22606 | −0.198665 | ||||||||
\(693\) | −3.54288 | −0.134583 | ||||||||
\(694\) | 7.09876 | 0.269465 | ||||||||
\(695\) | −12.6617 | −0.480287 | ||||||||
\(696\) | −0.430855 | −0.0163315 | ||||||||
\(697\) | −1.27066 | −0.0481296 | ||||||||
\(698\) | −27.6902 | −1.04809 | ||||||||
\(699\) | −14.4896 | −0.548048 | ||||||||
\(700\) | −9.67282 | −0.365598 | ||||||||
\(701\) | 4.46688 | 0.168712 | 0.0843559 | − | 0.996436i | \(-0.473117\pi\) | ||||
0.0843559 | + | 0.996436i | \(0.473117\pi\) | |||||||
\(702\) | −1.00000 | −0.0377426 | ||||||||
\(703\) | 11.9481 | 0.450630 | ||||||||
\(704\) | −0.787053 | −0.0296632 | ||||||||
\(705\) | 2.26036 | 0.0851302 | ||||||||
\(706\) | 36.0299 | 1.35600 | ||||||||
\(707\) | −50.4388 | −1.89695 | ||||||||
\(708\) | 9.51134 | 0.357458 | ||||||||
\(709\) | 25.2271 | 0.947425 | 0.473712 | − | 0.880680i | \(-0.342914\pi\) | ||||
0.473712 | + | 0.880680i | \(0.342914\pi\) | |||||||
\(710\) | 24.1822 | 0.907542 | ||||||||
\(711\) | −11.7235 | −0.439667 | ||||||||
\(712\) | 4.51314 | 0.169137 | ||||||||
\(713\) | −10.0528 | −0.376480 | ||||||||
\(714\) | 0.543496 | 0.0203398 | ||||||||
\(715\) | 1.32897 | 0.0497008 | ||||||||
\(716\) | 8.23133 | 0.307619 | ||||||||
\(717\) | −5.77146 | −0.215539 | ||||||||
\(718\) | −24.0969 | −0.899288 | ||||||||
\(719\) | 36.2789 | 1.35298 | 0.676488 | − | 0.736454i | \(-0.263501\pi\) | ||||
0.676488 | + | 0.736454i | \(0.263501\pi\) | |||||||
\(720\) | −1.68854 | −0.0629283 | ||||||||
\(721\) | 4.50145 | 0.167643 | ||||||||
\(722\) | −14.2986 | −0.532138 | ||||||||
\(723\) | −22.2958 | −0.829190 | ||||||||
\(724\) | −23.2659 | −0.864671 | ||||||||
\(725\) | −0.925831 | −0.0343845 | ||||||||
\(726\) | 10.3805 | 0.385258 | ||||||||
\(727\) | −33.8689 | −1.25613 | −0.628064 | − | 0.778162i | \(-0.716152\pi\) | ||||
−0.628064 | + | 0.778162i | \(0.716152\pi\) | |||||||
\(728\) | 4.50145 | 0.166835 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −18.4538 | −0.683005 | ||||||||
\(731\) | −0.293427 | −0.0108528 | ||||||||
\(732\) | 9.33774 | 0.345133 | ||||||||
\(733\) | 10.9523 | 0.404532 | 0.202266 | − | 0.979331i | \(-0.435169\pi\) | ||||
0.202266 | + | 0.979331i | \(0.435169\pi\) | |||||||
\(734\) | 10.2238 | 0.377367 | ||||||||
\(735\) | 22.3953 | 0.826062 | ||||||||
\(736\) | −4.63632 | −0.170897 | ||||||||
\(737\) | −12.5922 | −0.463841 | ||||||||
\(738\) | 10.5241 | 0.387397 | ||||||||
\(739\) | −14.7262 | −0.541713 | −0.270856 | − | 0.962620i | \(-0.587307\pi\) | ||||
−0.270856 | + | 0.962620i | \(0.587307\pi\) | |||||||
\(740\) | −9.30456 | −0.342042 | ||||||||
\(741\) | −2.16827 | −0.0796535 | ||||||||
\(742\) | 39.6296 | 1.45485 | ||||||||
\(743\) | 47.2952 | 1.73509 | 0.867546 | − | 0.497356i | \(-0.165696\pi\) | ||||
0.867546 | + | 0.497356i | \(0.165696\pi\) | |||||||
\(744\) | −2.16827 | −0.0794928 | ||||||||
\(745\) | −8.17839 | −0.299633 | ||||||||
\(746\) | 30.3725 | 1.11201 | ||||||||
\(747\) | 9.92233 | 0.363039 | ||||||||
\(748\) | 0.0950272 | 0.00347454 | ||||||||
\(749\) | 53.1416 | 1.94175 | ||||||||
\(750\) | −12.0711 | −0.440774 | ||||||||
\(751\) | −26.9359 | −0.982906 | −0.491453 | − | 0.870904i | \(-0.663534\pi\) | ||||
−0.491453 | + | 0.870904i | \(0.663534\pi\) | |||||||
\(752\) | 1.33865 | 0.0488154 | ||||||||
\(753\) | 5.12799 | 0.186874 | ||||||||
\(754\) | 0.430855 | 0.0156908 | ||||||||
\(755\) | −34.1824 | −1.24402 | ||||||||
\(756\) | −4.50145 | −0.163716 | ||||||||
\(757\) | −8.91683 | −0.324088 | −0.162044 | − | 0.986784i | \(-0.551809\pi\) | ||||
−0.162044 | + | 0.986784i | \(0.551809\pi\) | |||||||
\(758\) | 28.6696 | 1.04133 | ||||||||
\(759\) | −3.64902 | −0.132451 | ||||||||
\(760\) | −3.66122 | −0.132807 | ||||||||
\(761\) | 43.1405 | 1.56384 | 0.781921 | − | 0.623377i | \(-0.214240\pi\) | ||||
0.781921 | + | 0.623377i | \(0.214240\pi\) | |||||||
\(762\) | 4.62781 | 0.167648 | ||||||||
\(763\) | −10.3679 | −0.375342 | ||||||||
\(764\) | −3.16411 | −0.114474 | ||||||||
\(765\) | 0.203871 | 0.00737099 | ||||||||
\(766\) | 2.20806 | 0.0797803 | ||||||||
\(767\) | −9.51134 | −0.343434 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 28.1086 | 1.01362 | 0.506812 | − | 0.862057i | \(-0.330824\pi\) | ||||
0.506812 | + | 0.862057i | \(0.330824\pi\) | |||||||
\(770\) | 5.98231 | 0.215587 | ||||||||
\(771\) | −1.47989 | −0.0532971 | ||||||||
\(772\) | −1.32889 | −0.0478279 | ||||||||
\(773\) | −29.6284 | −1.06566 | −0.532830 | − | 0.846223i | \(-0.678871\pi\) | ||||
−0.532830 | + | 0.846223i | \(0.678871\pi\) | |||||||
\(774\) | 2.43028 | 0.0873546 | ||||||||
\(775\) | −4.65923 | −0.167365 | ||||||||
\(776\) | 1.26242 | 0.0453184 | ||||||||
\(777\) | −24.8048 | −0.889868 | ||||||||
\(778\) | 13.0889 | 0.469260 | ||||||||
\(779\) | 22.8191 | 0.817579 | ||||||||
\(780\) | 1.68854 | 0.0604595 | ||||||||
\(781\) | 11.2716 | 0.403331 | ||||||||
\(782\) | 0.559780 | 0.0200177 | ||||||||
\(783\) | −0.430855 | −0.0153975 | ||||||||
\(784\) | 13.2631 | 0.473681 | ||||||||
\(785\) | 1.38352 | 0.0493799 | ||||||||
\(786\) | 8.06962 | 0.287834 | ||||||||
\(787\) | −21.9080 | −0.780935 | −0.390468 | − | 0.920617i | \(-0.627687\pi\) | ||||
−0.390468 | + | 0.920617i | \(0.627687\pi\) | |||||||
\(788\) | 1.46635 | 0.0522367 | ||||||||
\(789\) | 20.0334 | 0.713210 | ||||||||
\(790\) | 19.7957 | 0.704300 | ||||||||
\(791\) | 13.1699 | 0.468268 | ||||||||
\(792\) | −0.787053 | −0.0279667 | ||||||||
\(793\) | −9.33774 | −0.331593 | ||||||||
\(794\) | 18.6996 | 0.663625 | ||||||||
\(795\) | 14.8655 | 0.527224 | ||||||||
\(796\) | 21.4614 | 0.760680 | ||||||||
\(797\) | 38.2469 | 1.35478 | 0.677388 | − | 0.735626i | \(-0.263112\pi\) | ||||
0.677388 | + | 0.735626i | \(0.263112\pi\) | |||||||
\(798\) | −9.76038 | −0.345514 | ||||||||
\(799\) | −0.161626 | −0.00571790 | ||||||||
\(800\) | −2.14882 | −0.0759723 | ||||||||
\(801\) | 4.51314 | 0.159464 | ||||||||
\(802\) | 20.9674 | 0.740385 | ||||||||
\(803\) | −8.60156 | −0.303542 | ||||||||
\(804\) | −15.9992 | −0.564249 | ||||||||
\(805\) | 35.2402 | 1.24205 | ||||||||
\(806\) | 2.16827 | 0.0763742 | ||||||||
\(807\) | 2.10282 | 0.0740229 | ||||||||
\(808\) | −11.2050 | −0.394191 | ||||||||
\(809\) | 42.9302 | 1.50935 | 0.754673 | − | 0.656101i | \(-0.227795\pi\) | ||||
0.754673 | + | 0.656101i | \(0.227795\pi\) | |||||||
\(810\) | −1.68854 | −0.0593294 | ||||||||
\(811\) | 33.9971 | 1.19380 | 0.596900 | − | 0.802316i | \(-0.296399\pi\) | ||||
0.596900 | + | 0.802316i | \(0.296399\pi\) | |||||||
\(812\) | 1.93947 | 0.0680622 | ||||||||
\(813\) | −28.5103 | −0.999901 | ||||||||
\(814\) | −4.33698 | −0.152011 | ||||||||
\(815\) | −31.1353 | −1.09062 | ||||||||
\(816\) | 0.120738 | 0.00422668 | ||||||||
\(817\) | 5.26951 | 0.184357 | ||||||||
\(818\) | 18.3390 | 0.641208 | ||||||||
\(819\) | 4.50145 | 0.157293 | ||||||||
\(820\) | −17.7704 | −0.620568 | ||||||||
\(821\) | 50.2619 | 1.75415 | 0.877077 | − | 0.480350i | \(-0.159490\pi\) | ||||
0.877077 | + | 0.480350i | \(0.159490\pi\) | |||||||
\(822\) | 16.1423 | 0.563026 | ||||||||
\(823\) | 42.3691 | 1.47689 | 0.738447 | − | 0.674311i | \(-0.235559\pi\) | ||||
0.738447 | + | 0.674311i | \(0.235559\pi\) | |||||||
\(824\) | 1.00000 | 0.0348367 | ||||||||
\(825\) | −1.69124 | −0.0588813 | ||||||||
\(826\) | −42.8148 | −1.48972 | ||||||||
\(827\) | −1.76874 | −0.0615050 | −0.0307525 | − | 0.999527i | \(-0.509790\pi\) | ||||
−0.0307525 | + | 0.999527i | \(0.509790\pi\) | |||||||
\(828\) | −4.63632 | −0.161123 | ||||||||
\(829\) | −49.8563 | −1.73158 | −0.865791 | − | 0.500406i | \(-0.833184\pi\) | ||||
−0.865791 | + | 0.500406i | \(0.833184\pi\) | |||||||
\(830\) | −16.7543 | −0.581549 | ||||||||
\(831\) | −19.2633 | −0.668238 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | −1.60136 | −0.0554837 | ||||||||
\(834\) | −7.49861 | −0.259656 | ||||||||
\(835\) | 13.1477 | 0.454995 | ||||||||
\(836\) | −1.70655 | −0.0590221 | ||||||||
\(837\) | −2.16827 | −0.0749465 | ||||||||
\(838\) | 3.18302 | 0.109956 | ||||||||
\(839\) | 9.35636 | 0.323018 | 0.161509 | − | 0.986871i | \(-0.448364\pi\) | ||||
0.161509 | + | 0.986871i | \(0.448364\pi\) | |||||||
\(840\) | 7.60090 | 0.262256 | ||||||||
\(841\) | −28.8144 | −0.993599 | ||||||||
\(842\) | 12.8911 | 0.444255 | ||||||||
\(843\) | −20.9688 | −0.722203 | ||||||||
\(844\) | 2.00558 | 0.0690350 | ||||||||
\(845\) | −1.68854 | −0.0580877 | ||||||||
\(846\) | 1.33865 | 0.0460236 | ||||||||
\(847\) | −46.7275 | −1.60558 | ||||||||
\(848\) | 8.80373 | 0.302321 | ||||||||
\(849\) | −29.4972 | −1.01234 | ||||||||
\(850\) | 0.259444 | 0.00889887 | ||||||||
\(851\) | −25.5480 | −0.875773 | ||||||||
\(852\) | 14.3213 | 0.490641 | ||||||||
\(853\) | 2.09185 | 0.0716237 | 0.0358119 | − | 0.999359i | \(-0.488598\pi\) | ||||
0.0358119 | + | 0.999359i | \(0.488598\pi\) | |||||||
\(854\) | −42.0334 | −1.43835 | ||||||||
\(855\) | −3.66122 | −0.125211 | ||||||||
\(856\) | 11.8054 | 0.403502 | ||||||||
\(857\) | 22.2378 | 0.759627 | 0.379814 | − | 0.925063i | \(-0.375988\pi\) | ||||
0.379814 | + | 0.925063i | \(0.375988\pi\) | |||||||
\(858\) | 0.787053 | 0.0268695 | ||||||||
\(859\) | −20.6629 | −0.705008 | −0.352504 | − | 0.935810i | \(-0.614670\pi\) | ||||
−0.352504 | + | 0.935810i | \(0.614670\pi\) | |||||||
\(860\) | −4.10363 | −0.139933 | ||||||||
\(861\) | −47.3737 | −1.61449 | ||||||||
\(862\) | −24.0805 | −0.820184 | ||||||||
\(863\) | −27.2497 | −0.927590 | −0.463795 | − | 0.885943i | \(-0.653513\pi\) | ||||
−0.463795 | + | 0.885943i | \(0.653513\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 8.82443 | 0.300040 | ||||||||
\(866\) | −30.1923 | −1.02598 | ||||||||
\(867\) | 16.9854 | 0.576855 | ||||||||
\(868\) | 9.76038 | 0.331289 | ||||||||
\(869\) | 9.22705 | 0.313006 | ||||||||
\(870\) | 0.727518 | 0.0246652 | ||||||||
\(871\) | 15.9992 | 0.542113 | ||||||||
\(872\) | −2.30323 | −0.0779972 | ||||||||
\(873\) | 1.26242 | 0.0427266 | ||||||||
\(874\) | −10.0528 | −0.340041 | ||||||||
\(875\) | 54.3375 | 1.83694 | ||||||||
\(876\) | −10.9288 | −0.369251 | ||||||||
\(877\) | 43.1359 | 1.45660 | 0.728298 | − | 0.685260i | \(-0.240312\pi\) | ||||
0.728298 | + | 0.685260i | \(0.240312\pi\) | |||||||
\(878\) | 5.69015 | 0.192033 | ||||||||
\(879\) | 22.5817 | 0.761662 | ||||||||
\(880\) | 1.32897 | 0.0447997 | ||||||||
\(881\) | −11.7335 | −0.395313 | −0.197656 | − | 0.980271i | \(-0.563333\pi\) | ||||
−0.197656 | + | 0.980271i | \(0.563333\pi\) | |||||||
\(882\) | 13.2631 | 0.446591 | ||||||||
\(883\) | −18.8362 | −0.633887 | −0.316944 | − | 0.948444i | \(-0.602657\pi\) | ||||
−0.316944 | + | 0.948444i | \(0.602657\pi\) | |||||||
\(884\) | −0.120738 | −0.00406086 | ||||||||
\(885\) | −16.0603 | −0.539861 | ||||||||
\(886\) | −12.9170 | −0.433955 | ||||||||
\(887\) | −23.3711 | −0.784724 | −0.392362 | − | 0.919811i | \(-0.628342\pi\) | ||||
−0.392362 | + | 0.919811i | \(0.628342\pi\) | |||||||
\(888\) | −5.51041 | −0.184917 | ||||||||
\(889\) | −20.8319 | −0.698679 | ||||||||
\(890\) | −7.62063 | −0.255444 | ||||||||
\(891\) | −0.787053 | −0.0263673 | ||||||||
\(892\) | −19.0380 | −0.637440 | ||||||||
\(893\) | 2.90255 | 0.0971302 | ||||||||
\(894\) | −4.84346 | −0.161990 | ||||||||
\(895\) | −13.8990 | −0.464591 | ||||||||
\(896\) | 4.50145 | 0.150383 | ||||||||
\(897\) | 4.63632 | 0.154802 | ||||||||
\(898\) | −21.2531 | −0.709226 | ||||||||
\(899\) | 0.934213 | 0.0311577 | ||||||||
\(900\) | −2.14882 | −0.0716274 | ||||||||
\(901\) | −1.06294 | −0.0354118 | ||||||||
\(902\) | −8.28301 | −0.275794 | ||||||||
\(903\) | −10.9398 | −0.364053 | ||||||||
\(904\) | 2.92570 | 0.0973075 | ||||||||
\(905\) | 39.2855 | 1.30589 | ||||||||
\(906\) | −20.2437 | −0.672552 | ||||||||
\(907\) | −15.2785 | −0.507315 | −0.253658 | − | 0.967294i | \(-0.581634\pi\) | ||||
−0.253658 | + | 0.967294i | \(0.581634\pi\) | |||||||
\(908\) | 22.5082 | 0.746960 | ||||||||
\(909\) | −11.2050 | −0.371647 | ||||||||
\(910\) | −7.60090 | −0.251967 | ||||||||
\(911\) | 21.8494 | 0.723904 | 0.361952 | − | 0.932197i | \(-0.382110\pi\) | ||||
0.361952 | + | 0.932197i | \(0.382110\pi\) | |||||||
\(912\) | −2.16827 | −0.0717987 | ||||||||
\(913\) | −7.80939 | −0.258453 | ||||||||
\(914\) | 23.2880 | 0.770298 | ||||||||
\(915\) | −15.7672 | −0.521247 | ||||||||
\(916\) | 16.8382 | 0.556349 | ||||||||
\(917\) | −36.3250 | −1.19956 | ||||||||
\(918\) | 0.120738 | 0.00398495 | ||||||||
\(919\) | −17.3501 | −0.572328 | −0.286164 | − | 0.958181i | \(-0.592380\pi\) | ||||
−0.286164 | + | 0.958181i | \(0.592380\pi\) | |||||||
\(920\) | 7.82862 | 0.258102 | ||||||||
\(921\) | 12.4312 | 0.409621 | ||||||||
\(922\) | 18.2701 | 0.601693 | ||||||||
\(923\) | −14.3213 | −0.471393 | ||||||||
\(924\) | 3.54288 | 0.116552 | ||||||||
\(925\) | −11.8409 | −0.389326 | ||||||||
\(926\) | 22.7042 | 0.746105 | ||||||||
\(927\) | 1.00000 | 0.0328443 | ||||||||
\(928\) | 0.430855 | 0.0141435 | ||||||||
\(929\) | −40.3220 | −1.32292 | −0.661461 | − | 0.749979i | \(-0.730063\pi\) | ||||
−0.661461 | + | 0.749979i | \(0.730063\pi\) | |||||||
\(930\) | 3.66122 | 0.120056 | ||||||||
\(931\) | 28.7580 | 0.942504 | ||||||||
\(932\) | 14.4896 | 0.474623 | ||||||||
\(933\) | 12.2864 | 0.402239 | ||||||||
\(934\) | 12.0488 | 0.394249 | ||||||||
\(935\) | −0.160458 | −0.00524752 | ||||||||
\(936\) | 1.00000 | 0.0326860 | ||||||||
\(937\) | 33.5992 | 1.09764 | 0.548819 | − | 0.835941i | \(-0.315078\pi\) | ||||
0.548819 | + | 0.835941i | \(0.315078\pi\) | |||||||
\(938\) | 72.0197 | 2.35153 | ||||||||
\(939\) | 17.9396 | 0.585437 | ||||||||
\(940\) | −2.26036 | −0.0737249 | ||||||||
\(941\) | −21.5286 | −0.701811 | −0.350906 | − | 0.936411i | \(-0.614126\pi\) | ||||
−0.350906 | + | 0.936411i | \(0.614126\pi\) | |||||||
\(942\) | 0.819356 | 0.0266961 | ||||||||
\(943\) | −48.7930 | −1.58892 | ||||||||
\(944\) | −9.51134 | −0.309568 | ||||||||
\(945\) | 7.60090 | 0.247257 | ||||||||
\(946\) | −1.91276 | −0.0621891 | ||||||||
\(947\) | −53.3155 | −1.73252 | −0.866261 | − | 0.499592i | \(-0.833483\pi\) | ||||
−0.866261 | + | 0.499592i | \(0.833483\pi\) | |||||||
\(948\) | 11.7235 | 0.380763 | ||||||||
\(949\) | 10.9288 | 0.354765 | ||||||||
\(950\) | −4.65923 | −0.151165 | ||||||||
\(951\) | −31.1119 | −1.00887 | ||||||||
\(952\) | −0.543496 | −0.0176148 | ||||||||
\(953\) | −23.5990 | −0.764447 | −0.382223 | − | 0.924070i | \(-0.624842\pi\) | ||||
−0.382223 | + | 0.924070i | \(0.624842\pi\) | |||||||
\(954\) | 8.80373 | 0.285031 | ||||||||
\(955\) | 5.34275 | 0.172887 | ||||||||
\(956\) | 5.77146 | 0.186663 | ||||||||
\(957\) | 0.339106 | 0.0109617 | ||||||||
\(958\) | −41.7439 | −1.34868 | ||||||||
\(959\) | −72.6636 | −2.34643 | ||||||||
\(960\) | 1.68854 | 0.0544975 | ||||||||
\(961\) | −26.2986 | −0.848342 | ||||||||
\(962\) | 5.51041 | 0.177663 | ||||||||
\(963\) | 11.8054 | 0.380425 | ||||||||
\(964\) | 22.2958 | 0.718100 | ||||||||
\(965\) | 2.24389 | 0.0722334 | ||||||||
\(966\) | 20.8702 | 0.671486 | ||||||||
\(967\) | 15.5519 | 0.500116 | 0.250058 | − | 0.968231i | \(-0.419550\pi\) | ||||
0.250058 | + | 0.968231i | \(0.419550\pi\) | |||||||
\(968\) | −10.3805 | −0.333643 | ||||||||
\(969\) | 0.261793 | 0.00841001 | ||||||||
\(970\) | −2.13166 | −0.0684434 | ||||||||
\(971\) | −41.5430 | −1.33318 | −0.666589 | − | 0.745426i | \(-0.732246\pi\) | ||||
−0.666589 | + | 0.745426i | \(0.732246\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 33.7546 | 1.08212 | ||||||||
\(974\) | −34.4976 | −1.10537 | ||||||||
\(975\) | 2.14882 | 0.0688174 | ||||||||
\(976\) | −9.33774 | −0.298894 | ||||||||
\(977\) | −12.4419 | −0.398053 | −0.199027 | − | 0.979994i | \(-0.563778\pi\) | ||||
−0.199027 | + | 0.979994i | \(0.563778\pi\) | |||||||
\(978\) | −18.4391 | −0.589619 | ||||||||
\(979\) | −3.55208 | −0.113525 | ||||||||
\(980\) | −22.3953 | −0.715390 | ||||||||
\(981\) | −2.30323 | −0.0735364 | ||||||||
\(982\) | −33.4958 | −1.06890 | ||||||||
\(983\) | −21.3596 | −0.681265 | −0.340632 | − | 0.940197i | \(-0.610641\pi\) | ||||
−0.340632 | + | 0.940197i | \(0.610641\pi\) | |||||||
\(984\) | −10.5241 | −0.335496 | ||||||||
\(985\) | −2.47600 | −0.0788920 | ||||||||
\(986\) | −0.0520206 | −0.00165667 | ||||||||
\(987\) | −6.02585 | −0.191805 | ||||||||
\(988\) | 2.16827 | 0.0689820 | ||||||||
\(989\) | −11.2675 | −0.358287 | ||||||||
\(990\) | 1.32897 | 0.0422375 | ||||||||
\(991\) | −5.35562 | −0.170127 | −0.0850634 | − | 0.996376i | \(-0.527109\pi\) | ||||
−0.0850634 | + | 0.996376i | \(0.527109\pi\) | |||||||
\(992\) | 2.16827 | 0.0688428 | ||||||||
\(993\) | −29.8047 | −0.945823 | ||||||||
\(994\) | −64.4668 | −2.04476 | ||||||||
\(995\) | −36.2386 | −1.14884 | ||||||||
\(996\) | −9.92233 | −0.314401 | ||||||||
\(997\) | −55.2271 | −1.74906 | −0.874530 | − | 0.484972i | \(-0.838830\pi\) | ||||
−0.874530 | + | 0.484972i | \(0.838830\pi\) | |||||||
\(998\) | 24.5788 | 0.778027 | ||||||||
\(999\) | −5.51041 | −0.174341 |
(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.y.1.3 | ✓ | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.y.1.3 | ✓ | 13 | 1.1 | even | 1 | trivial |