Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4334,2,Mod(1,4334)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4334, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4334.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4334 = 2 \cdot 11 \cdot 197 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4334.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: | \(34.6071642360\) |
Analytic rank: | \(1\) |
Dimension: | \(17\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{17} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{17} - 7 x^{16} - 7 x^{15} + 137 x^{14} - 98 x^{13} - 1048 x^{12} + 1313 x^{11} + 4085 x^{10} - 6021 x^{9} - 8879 x^{8} + 13530 x^{7} + 11150 x^{6} - 15676 x^{5} - 8037 x^{4} + \cdots - 400 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(1.31815\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4334.1 |
$q$-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 | ||||||||
\(3\) | −1.31815 | −0.761032 | −0.380516 | − | 0.924774i | \(-0.624254\pi\) | ||||
−0.380516 | + | 0.924774i | \(0.624254\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.46276 | 0.654167 | 0.327084 | − | 0.944995i | \(-0.393934\pi\) | ||||
0.327084 | + | 0.944995i | \(0.393934\pi\) | |||||||
\(6\) | −1.31815 | −0.538131 | ||||||||
\(7\) | −4.53584 | −1.71439 | −0.857194 | − | 0.514994i | \(-0.827794\pi\) | ||||
−0.857194 | + | 0.514994i | \(0.827794\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.26249 | −0.420830 | ||||||||
\(10\) | 1.46276 | 0.462566 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −1.31815 | −0.380516 | ||||||||
\(13\) | 4.66998 | 1.29522 | 0.647610 | − | 0.761972i | \(-0.275769\pi\) | ||||
0.647610 | + | 0.761972i | \(0.275769\pi\) | |||||||
\(14\) | −4.53584 | −1.21226 | ||||||||
\(15\) | −1.92814 | −0.497842 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.59877 | 0.630296 | 0.315148 | − | 0.949043i | \(-0.397946\pi\) | ||||
0.315148 | + | 0.949043i | \(0.397946\pi\) | |||||||
\(18\) | −1.26249 | −0.297572 | ||||||||
\(19\) | −0.0248218 | −0.00569451 | −0.00284725 | − | 0.999996i | \(-0.500906\pi\) | ||||
−0.00284725 | + | 0.999996i | \(0.500906\pi\) | |||||||
\(20\) | 1.46276 | 0.327084 | ||||||||
\(21\) | 5.97891 | 1.30470 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | 3.39725 | 0.708375 | 0.354188 | − | 0.935174i | \(-0.384757\pi\) | ||||
0.354188 | + | 0.935174i | \(0.384757\pi\) | |||||||
\(24\) | −1.31815 | −0.269066 | ||||||||
\(25\) | −2.86033 | −0.572065 | ||||||||
\(26\) | 4.66998 | 0.915859 | ||||||||
\(27\) | 5.61859 | 1.08130 | ||||||||
\(28\) | −4.53584 | −0.857194 | ||||||||
\(29\) | −3.84555 | −0.714101 | −0.357050 | − | 0.934085i | \(-0.616218\pi\) | ||||
−0.357050 | + | 0.934085i | \(0.616218\pi\) | |||||||
\(30\) | −1.92814 | −0.352028 | ||||||||
\(31\) | −3.79582 | −0.681750 | −0.340875 | − | 0.940109i | \(-0.610723\pi\) | ||||
−0.340875 | + | 0.940109i | \(0.610723\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 1.31815 | 0.229460 | ||||||||
\(34\) | 2.59877 | 0.445686 | ||||||||
\(35\) | −6.63486 | −1.12150 | ||||||||
\(36\) | −1.26249 | −0.210415 | ||||||||
\(37\) | −2.61721 | −0.430267 | −0.215133 | − | 0.976585i | \(-0.569019\pi\) | ||||
−0.215133 | + | 0.976585i | \(0.569019\pi\) | |||||||
\(38\) | −0.0248218 | −0.00402662 | ||||||||
\(39\) | −6.15572 | −0.985704 | ||||||||
\(40\) | 1.46276 | 0.231283 | ||||||||
\(41\) | 5.88709 | 0.919409 | 0.459704 | − | 0.888072i | \(-0.347955\pi\) | ||||
0.459704 | + | 0.888072i | \(0.347955\pi\) | |||||||
\(42\) | 5.97891 | 0.922566 | ||||||||
\(43\) | 3.42657 | 0.522548 | 0.261274 | − | 0.965265i | \(-0.415857\pi\) | ||||
0.261274 | + | 0.965265i | \(0.415857\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | −1.84672 | −0.275293 | ||||||||
\(46\) | 3.39725 | 0.500897 | ||||||||
\(47\) | −1.04331 | −0.152183 | −0.0760913 | − | 0.997101i | \(-0.524244\pi\) | ||||
−0.0760913 | + | 0.997101i | \(0.524244\pi\) | |||||||
\(48\) | −1.31815 | −0.190258 | ||||||||
\(49\) | 13.5739 | 1.93913 | ||||||||
\(50\) | −2.86033 | −0.404511 | ||||||||
\(51\) | −3.42557 | −0.479675 | ||||||||
\(52\) | 4.66998 | 0.647610 | ||||||||
\(53\) | −10.7672 | −1.47899 | −0.739494 | − | 0.673163i | \(-0.764935\pi\) | ||||
−0.739494 | + | 0.673163i | \(0.764935\pi\) | |||||||
\(54\) | 5.61859 | 0.764593 | ||||||||
\(55\) | −1.46276 | −0.197239 | ||||||||
\(56\) | −4.53584 | −0.606128 | ||||||||
\(57\) | 0.0327187 | 0.00433370 | ||||||||
\(58\) | −3.84555 | −0.504946 | ||||||||
\(59\) | −7.61960 | −0.991987 | −0.495994 | − | 0.868326i | \(-0.665196\pi\) | ||||
−0.495994 | + | 0.868326i | \(0.665196\pi\) | |||||||
\(60\) | −1.92814 | −0.248921 | ||||||||
\(61\) | 4.98477 | 0.638235 | 0.319117 | − | 0.947715i | \(-0.396614\pi\) | ||||
0.319117 | + | 0.947715i | \(0.396614\pi\) | |||||||
\(62\) | −3.79582 | −0.482070 | ||||||||
\(63\) | 5.72646 | 0.721466 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 6.83107 | 0.847290 | ||||||||
\(66\) | 1.31815 | 0.162253 | ||||||||
\(67\) | −13.9019 | −1.69839 | −0.849196 | − | 0.528077i | \(-0.822913\pi\) | ||||
−0.849196 | + | 0.528077i | \(0.822913\pi\) | |||||||
\(68\) | 2.59877 | 0.315148 | ||||||||
\(69\) | −4.47807 | −0.539096 | ||||||||
\(70\) | −6.63486 | −0.793018 | ||||||||
\(71\) | −8.51955 | −1.01109 | −0.505543 | − | 0.862802i | \(-0.668708\pi\) | ||||
−0.505543 | + | 0.862802i | \(0.668708\pi\) | |||||||
\(72\) | −1.26249 | −0.148786 | ||||||||
\(73\) | −6.22555 | −0.728646 | −0.364323 | − | 0.931273i | \(-0.618700\pi\) | ||||
−0.364323 | + | 0.931273i | \(0.618700\pi\) | |||||||
\(74\) | −2.61721 | −0.304245 | ||||||||
\(75\) | 3.77033 | 0.435360 | ||||||||
\(76\) | −0.0248218 | −0.00284725 | ||||||||
\(77\) | 4.53584 | 0.516907 | ||||||||
\(78\) | −6.15572 | −0.696998 | ||||||||
\(79\) | −3.75592 | −0.422574 | −0.211287 | − | 0.977424i | \(-0.567766\pi\) | ||||
−0.211287 | + | 0.977424i | \(0.567766\pi\) | |||||||
\(80\) | 1.46276 | 0.163542 | ||||||||
\(81\) | −3.61865 | −0.402072 | ||||||||
\(82\) | 5.88709 | 0.650120 | ||||||||
\(83\) | −13.1972 | −1.44858 | −0.724289 | − | 0.689497i | \(-0.757832\pi\) | ||||
−0.724289 | + | 0.689497i | \(0.757832\pi\) | |||||||
\(84\) | 5.97891 | 0.652352 | ||||||||
\(85\) | 3.80139 | 0.412319 | ||||||||
\(86\) | 3.42657 | 0.369497 | ||||||||
\(87\) | 5.06900 | 0.543454 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | 14.2555 | 1.51108 | 0.755542 | − | 0.655100i | \(-0.227374\pi\) | ||||
0.755542 | + | 0.655100i | \(0.227374\pi\) | |||||||
\(90\) | −1.84672 | −0.194662 | ||||||||
\(91\) | −21.1823 | −2.22051 | ||||||||
\(92\) | 3.39725 | 0.354188 | ||||||||
\(93\) | 5.00345 | 0.518834 | ||||||||
\(94\) | −1.04331 | −0.107609 | ||||||||
\(95\) | −0.0363084 | −0.00372516 | ||||||||
\(96\) | −1.31815 | −0.134533 | ||||||||
\(97\) | −17.1275 | −1.73904 | −0.869518 | − | 0.493902i | \(-0.835570\pi\) | ||||
−0.869518 | + | 0.493902i | \(0.835570\pi\) | |||||||
\(98\) | 13.5739 | 1.37117 | ||||||||
\(99\) | 1.26249 | 0.126885 | ||||||||
\(100\) | −2.86033 | −0.286033 | ||||||||
\(101\) | −3.10944 | −0.309400 | −0.154700 | − | 0.987961i | \(-0.549441\pi\) | ||||
−0.154700 | + | 0.987961i | \(0.549441\pi\) | |||||||
\(102\) | −3.42557 | −0.339182 | ||||||||
\(103\) | 4.19477 | 0.413323 | 0.206661 | − | 0.978413i | \(-0.433740\pi\) | ||||
0.206661 | + | 0.978413i | \(0.433740\pi\) | |||||||
\(104\) | 4.66998 | 0.457929 | ||||||||
\(105\) | 8.74572 | 0.853495 | ||||||||
\(106\) | −10.7672 | −1.04580 | ||||||||
\(107\) | −0.684451 | −0.0661683 | −0.0330842 | − | 0.999453i | \(-0.510533\pi\) | ||||
−0.0330842 | + | 0.999453i | \(0.510533\pi\) | |||||||
\(108\) | 5.61859 | 0.540649 | ||||||||
\(109\) | −18.5080 | −1.77275 | −0.886373 | − | 0.462971i | \(-0.846783\pi\) | ||||
−0.886373 | + | 0.462971i | \(0.846783\pi\) | |||||||
\(110\) | −1.46276 | −0.139469 | ||||||||
\(111\) | 3.44987 | 0.327447 | ||||||||
\(112\) | −4.53584 | −0.428597 | ||||||||
\(113\) | −3.74038 | −0.351865 | −0.175933 | − | 0.984402i | \(-0.556294\pi\) | ||||
−0.175933 | + | 0.984402i | \(0.556294\pi\) | |||||||
\(114\) | 0.0327187 | 0.00306439 | ||||||||
\(115\) | 4.96937 | 0.463396 | ||||||||
\(116\) | −3.84555 | −0.357050 | ||||||||
\(117\) | −5.89580 | −0.545067 | ||||||||
\(118\) | −7.61960 | −0.701441 | ||||||||
\(119\) | −11.7876 | −1.08057 | ||||||||
\(120\) | −1.92814 | −0.176014 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 4.98477 | 0.451300 | ||||||||
\(123\) | −7.76005 | −0.699700 | ||||||||
\(124\) | −3.79582 | −0.340875 | ||||||||
\(125\) | −11.4978 | −1.02839 | ||||||||
\(126\) | 5.72646 | 0.510153 | ||||||||
\(127\) | −14.0597 | −1.24759 | −0.623796 | − | 0.781587i | \(-0.714410\pi\) | ||||
−0.623796 | + | 0.781587i | \(0.714410\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −4.51673 | −0.397676 | ||||||||
\(130\) | 6.83107 | 0.599125 | ||||||||
\(131\) | −5.96454 | −0.521124 | −0.260562 | − | 0.965457i | \(-0.583908\pi\) | ||||
−0.260562 | + | 0.965457i | \(0.583908\pi\) | |||||||
\(132\) | 1.31815 | 0.114730 | ||||||||
\(133\) | 0.112588 | 0.00976259 | ||||||||
\(134\) | −13.9019 | −1.20095 | ||||||||
\(135\) | 8.21866 | 0.707349 | ||||||||
\(136\) | 2.59877 | 0.222843 | ||||||||
\(137\) | −13.2498 | −1.13201 | −0.566003 | − | 0.824403i | \(-0.691511\pi\) | ||||
−0.566003 | + | 0.824403i | \(0.691511\pi\) | |||||||
\(138\) | −4.47807 | −0.381199 | ||||||||
\(139\) | 9.15392 | 0.776425 | 0.388213 | − | 0.921570i | \(-0.373093\pi\) | ||||
0.388213 | + | 0.921570i | \(0.373093\pi\) | |||||||
\(140\) | −6.63486 | −0.560748 | ||||||||
\(141\) | 1.37524 | 0.115816 | ||||||||
\(142\) | −8.51955 | −0.714945 | ||||||||
\(143\) | −4.66998 | −0.390523 | ||||||||
\(144\) | −1.26249 | −0.105207 | ||||||||
\(145\) | −5.62513 | −0.467141 | ||||||||
\(146\) | −6.22555 | −0.515230 | ||||||||
\(147\) | −17.8924 | −1.47574 | ||||||||
\(148\) | −2.61721 | −0.215133 | ||||||||
\(149\) | 12.5013 | 1.02415 | 0.512073 | − | 0.858942i | \(-0.328878\pi\) | ||||
0.512073 | + | 0.858942i | \(0.328878\pi\) | |||||||
\(150\) | 3.77033 | 0.307846 | ||||||||
\(151\) | −11.5610 | −0.940822 | −0.470411 | − | 0.882447i | \(-0.655894\pi\) | ||||
−0.470411 | + | 0.882447i | \(0.655894\pi\) | |||||||
\(152\) | −0.0248218 | −0.00201331 | ||||||||
\(153\) | −3.28093 | −0.265247 | ||||||||
\(154\) | 4.53584 | 0.365509 | ||||||||
\(155\) | −5.55239 | −0.445979 | ||||||||
\(156\) | −6.15572 | −0.492852 | ||||||||
\(157\) | 10.4405 | 0.833242 | 0.416621 | − | 0.909080i | \(-0.363214\pi\) | ||||
0.416621 | + | 0.909080i | \(0.363214\pi\) | |||||||
\(158\) | −3.75592 | −0.298805 | ||||||||
\(159\) | 14.1927 | 1.12556 | ||||||||
\(160\) | 1.46276 | 0.115642 | ||||||||
\(161\) | −15.4094 | −1.21443 | ||||||||
\(162\) | −3.61865 | −0.284308 | ||||||||
\(163\) | 18.9201 | 1.48194 | 0.740969 | − | 0.671540i | \(-0.234367\pi\) | ||||
0.740969 | + | 0.671540i | \(0.234367\pi\) | |||||||
\(164\) | 5.88709 | 0.459704 | ||||||||
\(165\) | 1.92814 | 0.150105 | ||||||||
\(166\) | −13.1972 | −1.02430 | ||||||||
\(167\) | 1.16959 | 0.0905053 | 0.0452526 | − | 0.998976i | \(-0.485591\pi\) | ||||
0.0452526 | + | 0.998976i | \(0.485591\pi\) | |||||||
\(168\) | 5.97891 | 0.461283 | ||||||||
\(169\) | 8.80872 | 0.677594 | ||||||||
\(170\) | 3.80139 | 0.291553 | ||||||||
\(171\) | 0.0313372 | 0.00239642 | ||||||||
\(172\) | 3.42657 | 0.261274 | ||||||||
\(173\) | 1.58761 | 0.120703 | 0.0603517 | − | 0.998177i | \(-0.480778\pi\) | ||||
0.0603517 | + | 0.998177i | \(0.480778\pi\) | |||||||
\(174\) | 5.06900 | 0.384280 | ||||||||
\(175\) | 12.9740 | 0.980742 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 10.0437 | 0.754934 | ||||||||
\(178\) | 14.2555 | 1.06850 | ||||||||
\(179\) | 2.59384 | 0.193873 | 0.0969363 | − | 0.995291i | \(-0.469096\pi\) | ||||
0.0969363 | + | 0.995291i | \(0.469096\pi\) | |||||||
\(180\) | −1.84672 | −0.137647 | ||||||||
\(181\) | 10.5987 | 0.787798 | 0.393899 | − | 0.919154i | \(-0.371126\pi\) | ||||
0.393899 | + | 0.919154i | \(0.371126\pi\) | |||||||
\(182\) | −21.1823 | −1.57014 | ||||||||
\(183\) | −6.57066 | −0.485717 | ||||||||
\(184\) | 3.39725 | 0.250448 | ||||||||
\(185\) | −3.82836 | −0.281467 | ||||||||
\(186\) | 5.00345 | 0.366871 | ||||||||
\(187\) | −2.59877 | −0.190041 | ||||||||
\(188\) | −1.04331 | −0.0760913 | ||||||||
\(189\) | −25.4850 | −1.85376 | ||||||||
\(190\) | −0.0363084 | −0.00263409 | ||||||||
\(191\) | −15.8379 | −1.14599 | −0.572997 | − | 0.819558i | \(-0.694219\pi\) | ||||
−0.572997 | + | 0.819558i | \(0.694219\pi\) | |||||||
\(192\) | −1.31815 | −0.0951290 | ||||||||
\(193\) | 27.5855 | 1.98565 | 0.992826 | − | 0.119572i | \(-0.0381523\pi\) | ||||
0.992826 | + | 0.119572i | \(0.0381523\pi\) | |||||||
\(194\) | −17.1275 | −1.22968 | ||||||||
\(195\) | −9.00435 | −0.644815 | ||||||||
\(196\) | 13.5739 | 0.969563 | ||||||||
\(197\) | 1.00000 | 0.0712470 | ||||||||
\(198\) | 1.26249 | 0.0897212 | ||||||||
\(199\) | −9.49262 | −0.672914 | −0.336457 | − | 0.941699i | \(-0.609229\pi\) | ||||
−0.336457 | + | 0.941699i | \(0.609229\pi\) | |||||||
\(200\) | −2.86033 | −0.202256 | ||||||||
\(201\) | 18.3248 | 1.29253 | ||||||||
\(202\) | −3.10944 | −0.218779 | ||||||||
\(203\) | 17.4428 | 1.22425 | ||||||||
\(204\) | −3.42557 | −0.239838 | ||||||||
\(205\) | 8.61141 | 0.601447 | ||||||||
\(206\) | 4.19477 | 0.292263 | ||||||||
\(207\) | −4.28899 | −0.298105 | ||||||||
\(208\) | 4.66998 | 0.323805 | ||||||||
\(209\) | 0.0248218 | 0.00171696 | ||||||||
\(210\) | 8.74572 | 0.603512 | ||||||||
\(211\) | −4.54282 | −0.312741 | −0.156370 | − | 0.987698i | \(-0.549979\pi\) | ||||
−0.156370 | + | 0.987698i | \(0.549979\pi\) | |||||||
\(212\) | −10.7672 | −0.739494 | ||||||||
\(213\) | 11.2300 | 0.769468 | ||||||||
\(214\) | −0.684451 | −0.0467881 | ||||||||
\(215\) | 5.01226 | 0.341834 | ||||||||
\(216\) | 5.61859 | 0.382296 | ||||||||
\(217\) | 17.2173 | 1.16878 | ||||||||
\(218\) | −18.5080 | −1.25352 | ||||||||
\(219\) | 8.20619 | 0.554523 | ||||||||
\(220\) | −1.46276 | −0.0986194 | ||||||||
\(221\) | 12.1362 | 0.816371 | ||||||||
\(222\) | 3.44987 | 0.231540 | ||||||||
\(223\) | −21.7748 | −1.45815 | −0.729074 | − | 0.684435i | \(-0.760049\pi\) | ||||
−0.729074 | + | 0.684435i | \(0.760049\pi\) | |||||||
\(224\) | −4.53584 | −0.303064 | ||||||||
\(225\) | 3.61113 | 0.240742 | ||||||||
\(226\) | −3.74038 | −0.248806 | ||||||||
\(227\) | −4.31094 | −0.286127 | −0.143064 | − | 0.989714i | \(-0.545695\pi\) | ||||
−0.143064 | + | 0.989714i | \(0.545695\pi\) | |||||||
\(228\) | 0.0327187 | 0.00216685 | ||||||||
\(229\) | 19.2818 | 1.27418 | 0.637088 | − | 0.770791i | \(-0.280139\pi\) | ||||
0.637088 | + | 0.770791i | \(0.280139\pi\) | |||||||
\(230\) | 4.96937 | 0.327670 | ||||||||
\(231\) | −5.97891 | −0.393383 | ||||||||
\(232\) | −3.84555 | −0.252473 | ||||||||
\(233\) | −11.2994 | −0.740251 | −0.370126 | − | 0.928982i | \(-0.620685\pi\) | ||||
−0.370126 | + | 0.928982i | \(0.620685\pi\) | |||||||
\(234\) | −5.89580 | −0.385421 | ||||||||
\(235\) | −1.52612 | −0.0995528 | ||||||||
\(236\) | −7.61960 | −0.495994 | ||||||||
\(237\) | 4.95086 | 0.321593 | ||||||||
\(238\) | −11.7876 | −0.764079 | ||||||||
\(239\) | −3.22286 | −0.208470 | −0.104235 | − | 0.994553i | \(-0.533239\pi\) | ||||
−0.104235 | + | 0.994553i | \(0.533239\pi\) | |||||||
\(240\) | −1.92814 | −0.124461 | ||||||||
\(241\) | 7.88943 | 0.508203 | 0.254101 | − | 0.967178i | \(-0.418220\pi\) | ||||
0.254101 | + | 0.967178i | \(0.418220\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | −12.0858 | −0.775307 | ||||||||
\(244\) | 4.98477 | 0.319117 | ||||||||
\(245\) | 19.8554 | 1.26851 | ||||||||
\(246\) | −7.76005 | −0.494763 | ||||||||
\(247\) | −0.115917 | −0.00737564 | ||||||||
\(248\) | −3.79582 | −0.241035 | ||||||||
\(249\) | 17.3958 | 1.10241 | ||||||||
\(250\) | −11.4978 | −0.727184 | ||||||||
\(251\) | −8.33299 | −0.525974 | −0.262987 | − | 0.964799i | \(-0.584708\pi\) | ||||
−0.262987 | + | 0.964799i | \(0.584708\pi\) | |||||||
\(252\) | 5.72646 | 0.360733 | ||||||||
\(253\) | −3.39725 | −0.213583 | ||||||||
\(254\) | −14.0597 | −0.882181 | ||||||||
\(255\) | −5.01079 | −0.313788 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 7.27548 | 0.453832 | 0.226916 | − | 0.973914i | \(-0.427136\pi\) | ||||
0.226916 | + | 0.973914i | \(0.427136\pi\) | |||||||
\(258\) | −4.51673 | −0.281199 | ||||||||
\(259\) | 11.8713 | 0.737644 | ||||||||
\(260\) | 6.83107 | 0.423645 | ||||||||
\(261\) | 4.85497 | 0.300515 | ||||||||
\(262\) | −5.96454 | −0.368490 | ||||||||
\(263\) | −20.7703 | −1.28075 | −0.640377 | − | 0.768061i | \(-0.721222\pi\) | ||||
−0.640377 | + | 0.768061i | \(0.721222\pi\) | |||||||
\(264\) | 1.31815 | 0.0811263 | ||||||||
\(265\) | −15.7499 | −0.967506 | ||||||||
\(266\) | 0.112588 | 0.00690320 | ||||||||
\(267\) | −18.7909 | −1.14998 | ||||||||
\(268\) | −13.9019 | −0.849196 | ||||||||
\(269\) | 21.8670 | 1.33326 | 0.666628 | − | 0.745390i | \(-0.267737\pi\) | ||||
0.666628 | + | 0.745390i | \(0.267737\pi\) | |||||||
\(270\) | 8.21866 | 0.500172 | ||||||||
\(271\) | −12.8608 | −0.781239 | −0.390620 | − | 0.920552i | \(-0.627739\pi\) | ||||
−0.390620 | + | 0.920552i | \(0.627739\pi\) | |||||||
\(272\) | 2.59877 | 0.157574 | ||||||||
\(273\) | 27.9214 | 1.68988 | ||||||||
\(274\) | −13.2498 | −0.800450 | ||||||||
\(275\) | 2.86033 | 0.172484 | ||||||||
\(276\) | −4.47807 | −0.269548 | ||||||||
\(277\) | −7.99167 | −0.480173 | −0.240087 | − | 0.970751i | \(-0.577176\pi\) | ||||
−0.240087 | + | 0.970751i | \(0.577176\pi\) | |||||||
\(278\) | 9.15392 | 0.549016 | ||||||||
\(279\) | 4.79219 | 0.286901 | ||||||||
\(280\) | −6.63486 | −0.396509 | ||||||||
\(281\) | −16.3440 | −0.975000 | −0.487500 | − | 0.873123i | \(-0.662091\pi\) | ||||
−0.487500 | + | 0.873123i | \(0.662091\pi\) | |||||||
\(282\) | 1.37524 | 0.0818941 | ||||||||
\(283\) | 6.23927 | 0.370886 | 0.185443 | − | 0.982655i | \(-0.440628\pi\) | ||||
0.185443 | + | 0.982655i | \(0.440628\pi\) | |||||||
\(284\) | −8.51955 | −0.505543 | ||||||||
\(285\) | 0.0478597 | 0.00283497 | ||||||||
\(286\) | −4.66998 | −0.276142 | ||||||||
\(287\) | −26.7029 | −1.57622 | ||||||||
\(288\) | −1.26249 | −0.0743929 | ||||||||
\(289\) | −10.2464 | −0.602728 | ||||||||
\(290\) | −5.62513 | −0.330319 | ||||||||
\(291\) | 22.5766 | 1.32346 | ||||||||
\(292\) | −6.22555 | −0.364323 | ||||||||
\(293\) | 19.8379 | 1.15894 | 0.579470 | − | 0.814993i | \(-0.303259\pi\) | ||||
0.579470 | + | 0.814993i | \(0.303259\pi\) | |||||||
\(294\) | −17.8924 | −1.04350 | ||||||||
\(295\) | −11.1457 | −0.648926 | ||||||||
\(296\) | −2.61721 | −0.152122 | ||||||||
\(297\) | −5.61859 | −0.326023 | ||||||||
\(298\) | 12.5013 | 0.724180 | ||||||||
\(299\) | 15.8651 | 0.917501 | ||||||||
\(300\) | 3.77033 | 0.217680 | ||||||||
\(301\) | −15.5424 | −0.895849 | ||||||||
\(302\) | −11.5610 | −0.665262 | ||||||||
\(303\) | 4.09869 | 0.235464 | ||||||||
\(304\) | −0.0248218 | −0.00142363 | ||||||||
\(305\) | 7.29154 | 0.417512 | ||||||||
\(306\) | −3.28093 | −0.187558 | ||||||||
\(307\) | 30.5600 | 1.74415 | 0.872076 | − | 0.489371i | \(-0.162774\pi\) | ||||
0.872076 | + | 0.489371i | \(0.162774\pi\) | |||||||
\(308\) | 4.53584 | 0.258454 | ||||||||
\(309\) | −5.52932 | −0.314552 | ||||||||
\(310\) | −5.55239 | −0.315355 | ||||||||
\(311\) | −15.7508 | −0.893148 | −0.446574 | − | 0.894747i | \(-0.647356\pi\) | ||||
−0.446574 | + | 0.894747i | \(0.647356\pi\) | |||||||
\(312\) | −6.15572 | −0.348499 | ||||||||
\(313\) | 27.8952 | 1.57673 | 0.788364 | − | 0.615209i | \(-0.210928\pi\) | ||||
0.788364 | + | 0.615209i | \(0.210928\pi\) | |||||||
\(314\) | 10.4405 | 0.589191 | ||||||||
\(315\) | 8.37645 | 0.471959 | ||||||||
\(316\) | −3.75592 | −0.211287 | ||||||||
\(317\) | −16.8081 | −0.944040 | −0.472020 | − | 0.881588i | \(-0.656475\pi\) | ||||
−0.472020 | + | 0.881588i | \(0.656475\pi\) | |||||||
\(318\) | 14.1927 | 0.795890 | ||||||||
\(319\) | 3.84555 | 0.215310 | ||||||||
\(320\) | 1.46276 | 0.0817709 | ||||||||
\(321\) | 0.902206 | 0.0503562 | ||||||||
\(322\) | −15.4094 | −0.858732 | ||||||||
\(323\) | −0.0645062 | −0.00358922 | ||||||||
\(324\) | −3.61865 | −0.201036 | ||||||||
\(325\) | −13.3577 | −0.740950 | ||||||||
\(326\) | 18.9201 | 1.04789 | ||||||||
\(327\) | 24.3963 | 1.34912 | ||||||||
\(328\) | 5.88709 | 0.325060 | ||||||||
\(329\) | 4.73230 | 0.260900 | ||||||||
\(330\) | 1.92814 | 0.106140 | ||||||||
\(331\) | −5.46500 | −0.300384 | −0.150192 | − | 0.988657i | \(-0.547989\pi\) | ||||
−0.150192 | + | 0.988657i | \(0.547989\pi\) | |||||||
\(332\) | −13.1972 | −0.724289 | ||||||||
\(333\) | 3.30420 | 0.181069 | ||||||||
\(334\) | 1.16959 | 0.0639969 | ||||||||
\(335\) | −20.3352 | −1.11103 | ||||||||
\(336\) | 5.97891 | 0.326176 | ||||||||
\(337\) | −9.06460 | −0.493780 | −0.246890 | − | 0.969044i | \(-0.579409\pi\) | ||||
−0.246890 | + | 0.969044i | \(0.579409\pi\) | |||||||
\(338\) | 8.80872 | 0.479131 | ||||||||
\(339\) | 4.93037 | 0.267781 | ||||||||
\(340\) | 3.80139 | 0.206159 | ||||||||
\(341\) | 3.79582 | 0.205555 | ||||||||
\(342\) | 0.0313372 | 0.00169452 | ||||||||
\(343\) | −29.8181 | −1.61003 | ||||||||
\(344\) | 3.42657 | 0.184748 | ||||||||
\(345\) | −6.55035 | −0.352659 | ||||||||
\(346\) | 1.58761 | 0.0853502 | ||||||||
\(347\) | −20.4406 | −1.09731 | −0.548655 | − | 0.836049i | \(-0.684860\pi\) | ||||
−0.548655 | + | 0.836049i | \(0.684860\pi\) | |||||||
\(348\) | 5.06900 | 0.271727 | ||||||||
\(349\) | −21.3694 | −1.14388 | −0.571939 | − | 0.820296i | \(-0.693809\pi\) | ||||
−0.571939 | + | 0.820296i | \(0.693809\pi\) | |||||||
\(350\) | 12.9740 | 0.693489 | ||||||||
\(351\) | 26.2387 | 1.40052 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | 14.5443 | 0.774117 | 0.387058 | − | 0.922055i | \(-0.373491\pi\) | ||||
0.387058 | + | 0.922055i | \(0.373491\pi\) | |||||||
\(354\) | 10.0437 | 0.533819 | ||||||||
\(355\) | −12.4621 | −0.661419 | ||||||||
\(356\) | 14.2555 | 0.755542 | ||||||||
\(357\) | 15.5378 | 0.822350 | ||||||||
\(358\) | 2.59384 | 0.137089 | ||||||||
\(359\) | −5.04096 | −0.266052 | −0.133026 | − | 0.991113i | \(-0.542469\pi\) | ||||
−0.133026 | + | 0.991113i | \(0.542469\pi\) | |||||||
\(360\) | −1.84672 | −0.0973308 | ||||||||
\(361\) | −18.9994 | −0.999968 | ||||||||
\(362\) | 10.5987 | 0.557057 | ||||||||
\(363\) | −1.31815 | −0.0691848 | ||||||||
\(364\) | −21.1823 | −1.11025 | ||||||||
\(365\) | −9.10651 | −0.476656 | ||||||||
\(366\) | −6.57066 | −0.343454 | ||||||||
\(367\) | 0.931053 | 0.0486006 | 0.0243003 | − | 0.999705i | \(-0.492264\pi\) | ||||
0.0243003 | + | 0.999705i | \(0.492264\pi\) | |||||||
\(368\) | 3.39725 | 0.177094 | ||||||||
\(369\) | −7.43239 | −0.386915 | ||||||||
\(370\) | −3.82836 | −0.199027 | ||||||||
\(371\) | 48.8383 | 2.53556 | ||||||||
\(372\) | 5.00345 | 0.259417 | ||||||||
\(373\) | 9.53258 | 0.493578 | 0.246789 | − | 0.969069i | \(-0.420624\pi\) | ||||
0.246789 | + | 0.969069i | \(0.420624\pi\) | |||||||
\(374\) | −2.59877 | −0.134379 | ||||||||
\(375\) | 15.1558 | 0.782641 | ||||||||
\(376\) | −1.04331 | −0.0538046 | ||||||||
\(377\) | −17.9586 | −0.924917 | ||||||||
\(378\) | −25.4850 | −1.31081 | ||||||||
\(379\) | −25.5474 | −1.31228 | −0.656141 | − | 0.754638i | \(-0.727812\pi\) | ||||
−0.656141 | + | 0.754638i | \(0.727812\pi\) | |||||||
\(380\) | −0.0363084 | −0.00186258 | ||||||||
\(381\) | 18.5327 | 0.949458 | ||||||||
\(382\) | −15.8379 | −0.810340 | ||||||||
\(383\) | 4.42112 | 0.225909 | 0.112954 | − | 0.993600i | \(-0.463969\pi\) | ||||
0.112954 | + | 0.993600i | \(0.463969\pi\) | |||||||
\(384\) | −1.31815 | −0.0672664 | ||||||||
\(385\) | 6.63486 | 0.338144 | ||||||||
\(386\) | 27.5855 | 1.40407 | ||||||||
\(387\) | −4.32601 | −0.219904 | ||||||||
\(388\) | −17.1275 | −0.869518 | ||||||||
\(389\) | 26.6493 | 1.35117 | 0.675586 | − | 0.737281i | \(-0.263891\pi\) | ||||
0.675586 | + | 0.737281i | \(0.263891\pi\) | |||||||
\(390\) | −9.00435 | −0.455953 | ||||||||
\(391\) | 8.82868 | 0.446486 | ||||||||
\(392\) | 13.5739 | 0.685585 | ||||||||
\(393\) | 7.86213 | 0.396592 | ||||||||
\(394\) | 1.00000 | 0.0503793 | ||||||||
\(395\) | −5.49402 | −0.276434 | ||||||||
\(396\) | 1.26249 | 0.0634425 | ||||||||
\(397\) | 33.9654 | 1.70468 | 0.852338 | − | 0.522992i | \(-0.175184\pi\) | ||||
0.852338 | + | 0.522992i | \(0.175184\pi\) | |||||||
\(398\) | −9.49262 | −0.475822 | ||||||||
\(399\) | −0.148407 | −0.00742965 | ||||||||
\(400\) | −2.86033 | −0.143016 | ||||||||
\(401\) | 19.9873 | 0.998119 | 0.499059 | − | 0.866568i | \(-0.333679\pi\) | ||||
0.499059 | + | 0.866568i | \(0.333679\pi\) | |||||||
\(402\) | 18.3248 | 0.913958 | ||||||||
\(403\) | −17.7264 | −0.883016 | ||||||||
\(404\) | −3.10944 | −0.154700 | ||||||||
\(405\) | −5.29323 | −0.263023 | ||||||||
\(406\) | 17.4428 | 0.865673 | ||||||||
\(407\) | 2.61721 | 0.129730 | ||||||||
\(408\) | −3.42557 | −0.169591 | ||||||||
\(409\) | −13.2776 | −0.656533 | −0.328266 | − | 0.944585i | \(-0.606464\pi\) | ||||
−0.328266 | + | 0.944585i | \(0.606464\pi\) | |||||||
\(410\) | 8.61141 | 0.425287 | ||||||||
\(411\) | 17.4652 | 0.861494 | ||||||||
\(412\) | 4.19477 | 0.206661 | ||||||||
\(413\) | 34.5613 | 1.70065 | ||||||||
\(414\) | −4.28899 | −0.210792 | ||||||||
\(415\) | −19.3043 | −0.947612 | ||||||||
\(416\) | 4.66998 | 0.228965 | ||||||||
\(417\) | −12.0662 | −0.590885 | ||||||||
\(418\) | 0.0248218 | 0.00121407 | ||||||||
\(419\) | 12.0765 | 0.589977 | 0.294989 | − | 0.955501i | \(-0.404684\pi\) | ||||
0.294989 | + | 0.955501i | \(0.404684\pi\) | |||||||
\(420\) | 8.74572 | 0.426748 | ||||||||
\(421\) | 5.00005 | 0.243687 | 0.121844 | − | 0.992549i | \(-0.461119\pi\) | ||||
0.121844 | + | 0.992549i | \(0.461119\pi\) | |||||||
\(422\) | −4.54282 | −0.221141 | ||||||||
\(423\) | 1.31717 | 0.0640429 | ||||||||
\(424\) | −10.7672 | −0.522901 | ||||||||
\(425\) | −7.43334 | −0.360570 | ||||||||
\(426\) | 11.2300 | 0.544096 | ||||||||
\(427\) | −22.6102 | −1.09418 | ||||||||
\(428\) | −0.684451 | −0.0330842 | ||||||||
\(429\) | 6.15572 | 0.297201 | ||||||||
\(430\) | 5.01226 | 0.241713 | ||||||||
\(431\) | 21.5480 | 1.03793 | 0.518964 | − | 0.854796i | \(-0.326318\pi\) | ||||
0.518964 | + | 0.854796i | \(0.326318\pi\) | |||||||
\(432\) | 5.61859 | 0.270324 | ||||||||
\(433\) | 28.9405 | 1.39079 | 0.695397 | − | 0.718626i | \(-0.255229\pi\) | ||||
0.695397 | + | 0.718626i | \(0.255229\pi\) | |||||||
\(434\) | 17.2173 | 0.826455 | ||||||||
\(435\) | 7.41474 | 0.355510 | ||||||||
\(436\) | −18.5080 | −0.886373 | ||||||||
\(437\) | −0.0843257 | −0.00403385 | ||||||||
\(438\) | 8.20619 | 0.392107 | ||||||||
\(439\) | 5.31799 | 0.253814 | 0.126907 | − | 0.991915i | \(-0.459495\pi\) | ||||
0.126907 | + | 0.991915i | \(0.459495\pi\) | |||||||
\(440\) | −1.46276 | −0.0697345 | ||||||||
\(441\) | −17.1369 | −0.816042 | ||||||||
\(442\) | 12.1362 | 0.577262 | ||||||||
\(443\) | −4.59279 | −0.218210 | −0.109105 | − | 0.994030i | \(-0.534798\pi\) | ||||
−0.109105 | + | 0.994030i | \(0.534798\pi\) | |||||||
\(444\) | 3.44987 | 0.163723 | ||||||||
\(445\) | 20.8525 | 0.988502 | ||||||||
\(446\) | −21.7748 | −1.03107 | ||||||||
\(447\) | −16.4785 | −0.779408 | ||||||||
\(448\) | −4.53584 | −0.214299 | ||||||||
\(449\) | −31.4568 | −1.48454 | −0.742269 | − | 0.670102i | \(-0.766250\pi\) | ||||
−0.742269 | + | 0.670102i | \(0.766250\pi\) | |||||||
\(450\) | 3.61113 | 0.170230 | ||||||||
\(451\) | −5.88709 | −0.277212 | ||||||||
\(452\) | −3.74038 | −0.175933 | ||||||||
\(453\) | 15.2391 | 0.715996 | ||||||||
\(454\) | −4.31094 | −0.202322 | ||||||||
\(455\) | −30.9847 | −1.45258 | ||||||||
\(456\) | 0.0327187 | 0.00153220 | ||||||||
\(457\) | −42.5459 | −1.99021 | −0.995106 | − | 0.0988167i | \(-0.968494\pi\) | ||||
−0.995106 | + | 0.0988167i | \(0.968494\pi\) | |||||||
\(458\) | 19.2818 | 0.900979 | ||||||||
\(459\) | 14.6014 | 0.681537 | ||||||||
\(460\) | 4.96937 | 0.231698 | ||||||||
\(461\) | −33.8876 | −1.57830 | −0.789152 | − | 0.614198i | \(-0.789480\pi\) | ||||
−0.789152 | + | 0.614198i | \(0.789480\pi\) | |||||||
\(462\) | −5.97891 | −0.278164 | ||||||||
\(463\) | −17.2341 | −0.800936 | −0.400468 | − | 0.916311i | \(-0.631152\pi\) | ||||
−0.400468 | + | 0.916311i | \(0.631152\pi\) | |||||||
\(464\) | −3.84555 | −0.178525 | ||||||||
\(465\) | 7.31886 | 0.339404 | ||||||||
\(466\) | −11.2994 | −0.523437 | ||||||||
\(467\) | −26.4443 | −1.22370 | −0.611849 | − | 0.790975i | \(-0.709574\pi\) | ||||
−0.611849 | + | 0.790975i | \(0.709574\pi\) | |||||||
\(468\) | −5.89580 | −0.272534 | ||||||||
\(469\) | 63.0571 | 2.91170 | ||||||||
\(470\) | −1.52612 | −0.0703945 | ||||||||
\(471\) | −13.7621 | −0.634124 | ||||||||
\(472\) | −7.61960 | −0.350720 | ||||||||
\(473\) | −3.42657 | −0.157554 | ||||||||
\(474\) | 4.95086 | 0.227400 | ||||||||
\(475\) | 0.0709984 | 0.00325763 | ||||||||
\(476\) | −11.7876 | −0.540286 | ||||||||
\(477\) | 13.5935 | 0.622402 | ||||||||
\(478\) | −3.22286 | −0.147410 | ||||||||
\(479\) | −18.2359 | −0.833220 | −0.416610 | − | 0.909085i | \(-0.636782\pi\) | ||||
−0.416610 | + | 0.909085i | \(0.636782\pi\) | |||||||
\(480\) | −1.92814 | −0.0880069 | ||||||||
\(481\) | −12.2223 | −0.557290 | ||||||||
\(482\) | 7.88943 | 0.359354 | ||||||||
\(483\) | 20.3118 | 0.924220 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −25.0535 | −1.13762 | ||||||||
\(486\) | −12.0858 | −0.548225 | ||||||||
\(487\) | 39.2794 | 1.77992 | 0.889960 | − | 0.456038i | \(-0.150732\pi\) | ||||
0.889960 | + | 0.456038i | \(0.150732\pi\) | |||||||
\(488\) | 4.98477 | 0.225650 | ||||||||
\(489\) | −24.9395 | −1.12780 | ||||||||
\(490\) | 19.8554 | 0.896974 | ||||||||
\(491\) | 28.5260 | 1.28736 | 0.643680 | − | 0.765295i | \(-0.277407\pi\) | ||||
0.643680 | + | 0.765295i | \(0.277407\pi\) | |||||||
\(492\) | −7.76005 | −0.349850 | ||||||||
\(493\) | −9.99372 | −0.450095 | ||||||||
\(494\) | −0.115917 | −0.00521536 | ||||||||
\(495\) | 1.84672 | 0.0830040 | ||||||||
\(496\) | −3.79582 | −0.170438 | ||||||||
\(497\) | 38.6434 | 1.73339 | ||||||||
\(498\) | 17.3958 | 0.779524 | ||||||||
\(499\) | 33.4415 | 1.49705 | 0.748525 | − | 0.663107i | \(-0.230763\pi\) | ||||
0.748525 | + | 0.663107i | \(0.230763\pi\) | |||||||
\(500\) | −11.4978 | −0.514197 | ||||||||
\(501\) | −1.54169 | −0.0688774 | ||||||||
\(502\) | −8.33299 | −0.371920 | ||||||||
\(503\) | −34.0731 | −1.51924 | −0.759621 | − | 0.650366i | \(-0.774616\pi\) | ||||
−0.759621 | + | 0.650366i | \(0.774616\pi\) | |||||||
\(504\) | 5.72646 | 0.255077 | ||||||||
\(505\) | −4.54837 | −0.202400 | ||||||||
\(506\) | −3.39725 | −0.151026 | ||||||||
\(507\) | −11.6112 | −0.515671 | ||||||||
\(508\) | −14.0597 | −0.623796 | ||||||||
\(509\) | −33.7263 | −1.49489 | −0.747446 | − | 0.664322i | \(-0.768720\pi\) | ||||
−0.747446 | + | 0.664322i | \(0.768720\pi\) | |||||||
\(510\) | −5.01079 | −0.221882 | ||||||||
\(511\) | 28.2381 | 1.24918 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −0.139463 | −0.00615745 | ||||||||
\(514\) | 7.27548 | 0.320908 | ||||||||
\(515\) | 6.13595 | 0.270382 | ||||||||
\(516\) | −4.51673 | −0.198838 | ||||||||
\(517\) | 1.04331 | 0.0458848 | ||||||||
\(518\) | 11.8713 | 0.521593 | ||||||||
\(519\) | −2.09270 | −0.0918592 | ||||||||
\(520\) | 6.83107 | 0.299562 | ||||||||
\(521\) | 19.2060 | 0.841430 | 0.420715 | − | 0.907193i | \(-0.361779\pi\) | ||||
0.420715 | + | 0.907193i | \(0.361779\pi\) | |||||||
\(522\) | 4.85497 | 0.212496 | ||||||||
\(523\) | 8.98858 | 0.393043 | 0.196522 | − | 0.980499i | \(-0.437035\pi\) | ||||
0.196522 | + | 0.980499i | \(0.437035\pi\) | |||||||
\(524\) | −5.96454 | −0.260562 | ||||||||
\(525\) | −17.1016 | −0.746376 | ||||||||
\(526\) | −20.7703 | −0.905629 | ||||||||
\(527\) | −9.86449 | −0.429704 | ||||||||
\(528\) | 1.31815 | 0.0573650 | ||||||||
\(529\) | −11.4587 | −0.498205 | ||||||||
\(530\) | −15.7499 | −0.684130 | ||||||||
\(531\) | 9.61966 | 0.417458 | ||||||||
\(532\) | 0.112588 | 0.00488130 | ||||||||
\(533\) | 27.4926 | 1.19084 | ||||||||
\(534\) | −18.7909 | −0.813161 | ||||||||
\(535\) | −1.00119 | −0.0432852 | ||||||||
\(536\) | −13.9019 | −0.600473 | ||||||||
\(537\) | −3.41906 | −0.147543 | ||||||||
\(538\) | 21.8670 | 0.942755 | ||||||||
\(539\) | −13.5739 | −0.584669 | ||||||||
\(540\) | 8.21866 | 0.353675 | ||||||||
\(541\) | −24.9312 | −1.07188 | −0.535938 | − | 0.844257i | \(-0.680042\pi\) | ||||
−0.535938 | + | 0.844257i | \(0.680042\pi\) | |||||||
\(542\) | −12.8608 | −0.552420 | ||||||||
\(543\) | −13.9707 | −0.599540 | ||||||||
\(544\) | 2.59877 | 0.111422 | ||||||||
\(545\) | −27.0728 | −1.15967 | ||||||||
\(546\) | 27.9214 | 1.19492 | ||||||||
\(547\) | 4.51435 | 0.193020 | 0.0965098 | − | 0.995332i | \(-0.469232\pi\) | ||||
0.0965098 | + | 0.995332i | \(0.469232\pi\) | |||||||
\(548\) | −13.2498 | −0.566003 | ||||||||
\(549\) | −6.29323 | −0.268588 | ||||||||
\(550\) | 2.86033 | 0.121965 | ||||||||
\(551\) | 0.0954534 | 0.00406645 | ||||||||
\(552\) | −4.47807 | −0.190599 | ||||||||
\(553\) | 17.0363 | 0.724457 | ||||||||
\(554\) | −7.99167 | −0.339534 | ||||||||
\(555\) | 5.04634 | 0.214205 | ||||||||
\(556\) | 9.15392 | 0.388213 | ||||||||
\(557\) | 0.450981 | 0.0191087 | 0.00955433 | − | 0.999954i | \(-0.496959\pi\) | ||||
0.00955433 | + | 0.999954i | \(0.496959\pi\) | |||||||
\(558\) | 4.79219 | 0.202870 | ||||||||
\(559\) | 16.0020 | 0.676814 | ||||||||
\(560\) | −6.63486 | −0.280374 | ||||||||
\(561\) | 3.42557 | 0.144628 | ||||||||
\(562\) | −16.3440 | −0.689429 | ||||||||
\(563\) | −12.6290 | −0.532247 | −0.266124 | − | 0.963939i | \(-0.585743\pi\) | ||||
−0.266124 | + | 0.963939i | \(0.585743\pi\) | |||||||
\(564\) | 1.37524 | 0.0579079 | ||||||||
\(565\) | −5.47128 | −0.230179 | ||||||||
\(566\) | 6.23927 | 0.262256 | ||||||||
\(567\) | 16.4136 | 0.689308 | ||||||||
\(568\) | −8.51955 | −0.357473 | ||||||||
\(569\) | −10.4797 | −0.439331 | −0.219665 | − | 0.975575i | \(-0.570497\pi\) | ||||
−0.219665 | + | 0.975575i | \(0.570497\pi\) | |||||||
\(570\) | 0.0478597 | 0.00200462 | ||||||||
\(571\) | −12.0789 | −0.505487 | −0.252744 | − | 0.967533i | \(-0.581333\pi\) | ||||
−0.252744 | + | 0.967533i | \(0.581333\pi\) | |||||||
\(572\) | −4.66998 | −0.195262 | ||||||||
\(573\) | 20.8767 | 0.872138 | ||||||||
\(574\) | −26.7029 | −1.11456 | ||||||||
\(575\) | −9.71724 | −0.405237 | ||||||||
\(576\) | −1.26249 | −0.0526037 | ||||||||
\(577\) | −33.6728 | −1.40182 | −0.700908 | − | 0.713251i | \(-0.747222\pi\) | ||||
−0.700908 | + | 0.713251i | \(0.747222\pi\) | |||||||
\(578\) | −10.2464 | −0.426193 | ||||||||
\(579\) | −36.3618 | −1.51114 | ||||||||
\(580\) | −5.62513 | −0.233571 | ||||||||
\(581\) | 59.8603 | 2.48342 | ||||||||
\(582\) | 22.5766 | 0.935829 | ||||||||
\(583\) | 10.7672 | 0.445932 | ||||||||
\(584\) | −6.22555 | −0.257615 | ||||||||
\(585\) | −8.62416 | −0.356565 | ||||||||
\(586\) | 19.8379 | 0.819495 | ||||||||
\(587\) | 22.6738 | 0.935848 | 0.467924 | − | 0.883769i | \(-0.345002\pi\) | ||||
0.467924 | + | 0.883769i | \(0.345002\pi\) | |||||||
\(588\) | −17.8924 | −0.737869 | ||||||||
\(589\) | 0.0942191 | 0.00388223 | ||||||||
\(590\) | −11.1457 | −0.458860 | ||||||||
\(591\) | −1.31815 | −0.0542213 | ||||||||
\(592\) | −2.61721 | −0.107567 | ||||||||
\(593\) | 2.49682 | 0.102532 | 0.0512660 | − | 0.998685i | \(-0.483674\pi\) | ||||
0.0512660 | + | 0.998685i | \(0.483674\pi\) | |||||||
\(594\) | −5.61859 | −0.230533 | ||||||||
\(595\) | −17.2425 | −0.706874 | ||||||||
\(596\) | 12.5013 | 0.512073 | ||||||||
\(597\) | 12.5127 | 0.512109 | ||||||||
\(598\) | 15.8651 | 0.648771 | ||||||||
\(599\) | 22.7518 | 0.929615 | 0.464808 | − | 0.885412i | \(-0.346123\pi\) | ||||
0.464808 | + | 0.885412i | \(0.346123\pi\) | |||||||
\(600\) | 3.77033 | 0.153923 | ||||||||
\(601\) | −1.79248 | −0.0731170 | −0.0365585 | − | 0.999332i | \(-0.511640\pi\) | ||||
−0.0365585 | + | 0.999332i | \(0.511640\pi\) | |||||||
\(602\) | −15.5424 | −0.633461 | ||||||||
\(603\) | 17.5511 | 0.714734 | ||||||||
\(604\) | −11.5610 | −0.470411 | ||||||||
\(605\) | 1.46276 | 0.0594698 | ||||||||
\(606\) | 4.09869 | 0.166498 | ||||||||
\(607\) | 34.7467 | 1.41033 | 0.705163 | − | 0.709045i | \(-0.250874\pi\) | ||||
0.705163 | + | 0.709045i | \(0.250874\pi\) | |||||||
\(608\) | −0.0248218 | −0.00100666 | ||||||||
\(609\) | −22.9922 | −0.931691 | ||||||||
\(610\) | 7.29154 | 0.295226 | ||||||||
\(611\) | −4.87224 | −0.197110 | ||||||||
\(612\) | −3.28093 | −0.132624 | ||||||||
\(613\) | 4.84273 | 0.195596 | 0.0977980 | − | 0.995206i | \(-0.468820\pi\) | ||||
0.0977980 | + | 0.995206i | \(0.468820\pi\) | |||||||
\(614\) | 30.5600 | 1.23330 | ||||||||
\(615\) | −11.3511 | −0.457721 | ||||||||
\(616\) | 4.53584 | 0.182754 | ||||||||
\(617\) | −5.70514 | −0.229680 | −0.114840 | − | 0.993384i | \(-0.536636\pi\) | ||||
−0.114840 | + | 0.993384i | \(0.536636\pi\) | |||||||
\(618\) | −5.52932 | −0.222422 | ||||||||
\(619\) | 41.3552 | 1.66220 | 0.831102 | − | 0.556119i | \(-0.187710\pi\) | ||||
0.831102 | + | 0.556119i | \(0.187710\pi\) | |||||||
\(620\) | −5.55239 | −0.222989 | ||||||||
\(621\) | 19.0877 | 0.765964 | ||||||||
\(622\) | −15.7508 | −0.631551 | ||||||||
\(623\) | −64.6609 | −2.59058 | ||||||||
\(624\) | −6.15572 | −0.246426 | ||||||||
\(625\) | −2.51691 | −0.100676 | ||||||||
\(626\) | 27.8952 | 1.11491 | ||||||||
\(627\) | −0.0327187 | −0.00130666 | ||||||||
\(628\) | 10.4405 | 0.416621 | ||||||||
\(629\) | −6.80154 | −0.271195 | ||||||||
\(630\) | 8.37645 | 0.333726 | ||||||||
\(631\) | 23.4081 | 0.931861 | 0.465930 | − | 0.884821i | \(-0.345720\pi\) | ||||
0.465930 | + | 0.884821i | \(0.345720\pi\) | |||||||
\(632\) | −3.75592 | −0.149403 | ||||||||
\(633\) | 5.98811 | 0.238006 | ||||||||
\(634\) | −16.8081 | −0.667537 | ||||||||
\(635\) | −20.5659 | −0.816134 | ||||||||
\(636\) | 14.1927 | 0.562779 | ||||||||
\(637\) | 63.3898 | 2.51159 | ||||||||
\(638\) | 3.84555 | 0.152247 | ||||||||
\(639\) | 10.7558 | 0.425495 | ||||||||
\(640\) | 1.46276 | 0.0578208 | ||||||||
\(641\) | 35.8595 | 1.41636 | 0.708182 | − | 0.706030i | \(-0.249516\pi\) | ||||
0.708182 | + | 0.706030i | \(0.249516\pi\) | |||||||
\(642\) | 0.902206 | 0.0356072 | ||||||||
\(643\) | −18.6741 | −0.736434 | −0.368217 | − | 0.929740i | \(-0.620032\pi\) | ||||
−0.368217 | + | 0.929740i | \(0.620032\pi\) | |||||||
\(644\) | −15.4094 | −0.607215 | ||||||||
\(645\) | −6.60690 | −0.260146 | ||||||||
\(646\) | −0.0645062 | −0.00253796 | ||||||||
\(647\) | 39.1856 | 1.54054 | 0.770272 | − | 0.637715i | \(-0.220120\pi\) | ||||
0.770272 | + | 0.637715i | \(0.220120\pi\) | |||||||
\(648\) | −3.61865 | −0.142154 | ||||||||
\(649\) | 7.61960 | 0.299095 | ||||||||
\(650\) | −13.3577 | −0.523931 | ||||||||
\(651\) | −22.6949 | −0.889483 | ||||||||
\(652\) | 18.9201 | 0.740969 | ||||||||
\(653\) | −19.3221 | −0.756132 | −0.378066 | − | 0.925779i | \(-0.623411\pi\) | ||||
−0.378066 | + | 0.925779i | \(0.623411\pi\) | |||||||
\(654\) | 24.3963 | 0.953970 | ||||||||
\(655\) | −8.72470 | −0.340902 | ||||||||
\(656\) | 5.88709 | 0.229852 | ||||||||
\(657\) | 7.85970 | 0.306636 | ||||||||
\(658\) | 4.73230 | 0.184484 | ||||||||
\(659\) | −1.52151 | −0.0592697 | −0.0296348 | − | 0.999561i | \(-0.509434\pi\) | ||||
−0.0296348 | + | 0.999561i | \(0.509434\pi\) | |||||||
\(660\) | 1.92814 | 0.0750526 | ||||||||
\(661\) | −29.3132 | −1.14015 | −0.570075 | − | 0.821592i | \(-0.693086\pi\) | ||||
−0.570075 | + | 0.821592i | \(0.693086\pi\) | |||||||
\(662\) | −5.46500 | −0.212403 | ||||||||
\(663\) | −15.9973 | −0.621285 | ||||||||
\(664\) | −13.1972 | −0.512149 | ||||||||
\(665\) | 0.164689 | 0.00638637 | ||||||||
\(666\) | 3.30420 | 0.128035 | ||||||||
\(667\) | −13.0643 | −0.505851 | ||||||||
\(668\) | 1.16959 | 0.0452526 | ||||||||
\(669\) | 28.7024 | 1.10970 | ||||||||
\(670\) | −20.3352 | −0.785619 | ||||||||
\(671\) | −4.98477 | −0.192435 | ||||||||
\(672\) | 5.97891 | 0.230641 | ||||||||
\(673\) | 15.0588 | 0.580472 | 0.290236 | − | 0.956955i | \(-0.406266\pi\) | ||||
0.290236 | + | 0.956955i | \(0.406266\pi\) | |||||||
\(674\) | −9.06460 | −0.349155 | ||||||||
\(675\) | −16.0710 | −0.618573 | ||||||||
\(676\) | 8.80872 | 0.338797 | ||||||||
\(677\) | −35.3887 | −1.36010 | −0.680048 | − | 0.733167i | \(-0.738041\pi\) | ||||
−0.680048 | + | 0.733167i | \(0.738041\pi\) | |||||||
\(678\) | 4.93037 | 0.189350 | ||||||||
\(679\) | 77.6877 | 2.98138 | ||||||||
\(680\) | 3.80139 | 0.145777 | ||||||||
\(681\) | 5.68245 | 0.217752 | ||||||||
\(682\) | 3.79582 | 0.145350 | ||||||||
\(683\) | 14.3648 | 0.549652 | 0.274826 | − | 0.961494i | \(-0.411380\pi\) | ||||
0.274826 | + | 0.961494i | \(0.411380\pi\) | |||||||
\(684\) | 0.0313372 | 0.00119821 | ||||||||
\(685\) | −19.3813 | −0.740522 | ||||||||
\(686\) | −29.8181 | −1.13846 | ||||||||
\(687\) | −25.4162 | −0.969689 | ||||||||
\(688\) | 3.42657 | 0.130637 | ||||||||
\(689\) | −50.2826 | −1.91561 | ||||||||
\(690\) | −6.55035 | −0.249368 | ||||||||
\(691\) | −42.9587 | −1.63423 | −0.817113 | − | 0.576478i | \(-0.804427\pi\) | ||||
−0.817113 | + | 0.576478i | \(0.804427\pi\) | |||||||
\(692\) | 1.58761 | 0.0603517 | ||||||||
\(693\) | −5.72646 | −0.217530 | ||||||||
\(694\) | −20.4406 | −0.775915 | ||||||||
\(695\) | 13.3900 | 0.507912 | ||||||||
\(696\) | 5.06900 | 0.192140 | ||||||||
\(697\) | 15.2992 | 0.579499 | ||||||||
\(698\) | −21.3694 | −0.808844 | ||||||||
\(699\) | 14.8943 | 0.563355 | ||||||||
\(700\) | 12.9740 | 0.490371 | ||||||||
\(701\) | −12.2510 | −0.462716 | −0.231358 | − | 0.972869i | \(-0.574317\pi\) | ||||
−0.231358 | + | 0.972869i | \(0.574317\pi\) | |||||||
\(702\) | 26.2387 | 0.990315 | ||||||||
\(703\) | 0.0649638 | 0.00245016 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | 2.01164 | 0.0757629 | ||||||||
\(706\) | 14.5443 | 0.547383 | ||||||||
\(707\) | 14.1039 | 0.530432 | ||||||||
\(708\) | 10.0437 | 0.377467 | ||||||||
\(709\) | 29.5882 | 1.11121 | 0.555605 | − | 0.831446i | \(-0.312487\pi\) | ||||
0.555605 | + | 0.831446i | \(0.312487\pi\) | |||||||
\(710\) | −12.4621 | −0.467694 | ||||||||
\(711\) | 4.74181 | 0.177832 | ||||||||
\(712\) | 14.2555 | 0.534249 | ||||||||
\(713\) | −12.8954 | −0.482935 | ||||||||
\(714\) | 15.5378 | 0.581489 | ||||||||
\(715\) | −6.83107 | −0.255468 | ||||||||
\(716\) | 2.59384 | 0.0969363 | ||||||||
\(717\) | 4.24820 | 0.158652 | ||||||||
\(718\) | −5.04096 | −0.188127 | ||||||||
\(719\) | −14.0402 | −0.523612 | −0.261806 | − | 0.965120i | \(-0.584318\pi\) | ||||
−0.261806 | + | 0.965120i | \(0.584318\pi\) | |||||||
\(720\) | −1.84672 | −0.0688233 | ||||||||
\(721\) | −19.0268 | −0.708596 | ||||||||
\(722\) | −18.9994 | −0.707084 | ||||||||
\(723\) | −10.3994 | −0.386759 | ||||||||
\(724\) | 10.5987 | 0.393899 | ||||||||
\(725\) | 10.9995 | 0.408512 | ||||||||
\(726\) | −1.31815 | −0.0489210 | ||||||||
\(727\) | −25.3104 | −0.938711 | −0.469355 | − | 0.883009i | \(-0.655514\pi\) | ||||
−0.469355 | + | 0.883009i | \(0.655514\pi\) | |||||||
\(728\) | −21.1823 | −0.785069 | ||||||||
\(729\) | 26.7869 | 0.992106 | ||||||||
\(730\) | −9.10651 | −0.337047 | ||||||||
\(731\) | 8.90489 | 0.329359 | ||||||||
\(732\) | −6.57066 | −0.242859 | ||||||||
\(733\) | −17.0730 | −0.630607 | −0.315304 | − | 0.948991i | \(-0.602106\pi\) | ||||
−0.315304 | + | 0.948991i | \(0.602106\pi\) | |||||||
\(734\) | 0.931053 | 0.0343658 | ||||||||
\(735\) | −26.1723 | −0.965380 | ||||||||
\(736\) | 3.39725 | 0.125224 | ||||||||
\(737\) | 13.9019 | 0.512085 | ||||||||
\(738\) | −7.43239 | −0.273590 | ||||||||
\(739\) | −23.0350 | −0.847357 | −0.423679 | − | 0.905813i | \(-0.639261\pi\) | ||||
−0.423679 | + | 0.905813i | \(0.639261\pi\) | |||||||
\(740\) | −3.82836 | −0.140733 | ||||||||
\(741\) | 0.152796 | 0.00561310 | ||||||||
\(742\) | 48.8383 | 1.79291 | ||||||||
\(743\) | 17.8764 | 0.655820 | 0.327910 | − | 0.944709i | \(-0.393656\pi\) | ||||
0.327910 | + | 0.944709i | \(0.393656\pi\) | |||||||
\(744\) | 5.00345 | 0.183435 | ||||||||
\(745\) | 18.2864 | 0.669962 | ||||||||
\(746\) | 9.53258 | 0.349013 | ||||||||
\(747\) | 16.6613 | 0.609605 | ||||||||
\(748\) | −2.59877 | −0.0950206 | ||||||||
\(749\) | 3.10456 | 0.113438 | ||||||||
\(750\) | 15.1558 | 0.553411 | ||||||||
\(751\) | 44.7023 | 1.63121 | 0.815605 | − | 0.578609i | \(-0.196404\pi\) | ||||
0.815605 | + | 0.578609i | \(0.196404\pi\) | |||||||
\(752\) | −1.04331 | −0.0380456 | ||||||||
\(753\) | 10.9841 | 0.400283 | ||||||||
\(754\) | −17.9586 | −0.654015 | ||||||||
\(755\) | −16.9110 | −0.615455 | ||||||||
\(756\) | −25.4850 | −0.926882 | ||||||||
\(757\) | 27.1075 | 0.985239 | 0.492619 | − | 0.870245i | \(-0.336040\pi\) | ||||
0.492619 | + | 0.870245i | \(0.336040\pi\) | |||||||
\(758\) | −25.5474 | −0.927924 | ||||||||
\(759\) | 4.47807 | 0.162544 | ||||||||
\(760\) | −0.0363084 | −0.00131704 | ||||||||
\(761\) | −4.64957 | −0.168547 | −0.0842734 | − | 0.996443i | \(-0.526857\pi\) | ||||
−0.0842734 | + | 0.996443i | \(0.526857\pi\) | |||||||
\(762\) | 18.5327 | 0.671368 | ||||||||
\(763\) | 83.9495 | 3.03918 | ||||||||
\(764\) | −15.8379 | −0.572997 | ||||||||
\(765\) | −4.79922 | −0.173516 | ||||||||
\(766\) | 4.42112 | 0.159742 | ||||||||
\(767\) | −35.5834 | −1.28484 | ||||||||
\(768\) | −1.31815 | −0.0475645 | ||||||||
\(769\) | −30.3365 | −1.09396 | −0.546981 | − | 0.837145i | \(-0.684223\pi\) | ||||
−0.546981 | + | 0.837145i | \(0.684223\pi\) | |||||||
\(770\) | 6.63486 | 0.239104 | ||||||||
\(771\) | −9.59015 | −0.345381 | ||||||||
\(772\) | 27.5855 | 0.992826 | ||||||||
\(773\) | 11.2227 | 0.403651 | 0.201825 | − | 0.979422i | \(-0.435313\pi\) | ||||
0.201825 | + | 0.979422i | \(0.435313\pi\) | |||||||
\(774\) | −4.32601 | −0.155495 | ||||||||
\(775\) | 10.8573 | 0.390006 | ||||||||
\(776\) | −17.1275 | −0.614842 | ||||||||
\(777\) | −15.6481 | −0.561371 | ||||||||
\(778\) | 26.6493 | 0.955423 | ||||||||
\(779\) | −0.146128 | −0.00523558 | ||||||||
\(780\) | −9.00435 | −0.322408 | ||||||||
\(781\) | 8.51955 | 0.304854 | ||||||||
\(782\) | 8.82868 | 0.315713 | ||||||||
\(783\) | −21.6066 | −0.772155 | ||||||||
\(784\) | 13.5739 | 0.484782 | ||||||||
\(785\) | 15.2720 | 0.545079 | ||||||||
\(786\) | 7.86213 | 0.280433 | ||||||||
\(787\) | 29.4930 | 1.05131 | 0.525657 | − | 0.850697i | \(-0.323820\pi\) | ||||
0.525657 | + | 0.850697i | \(0.323820\pi\) | |||||||
\(788\) | 1.00000 | 0.0356235 | ||||||||
\(789\) | 27.3783 | 0.974695 | ||||||||
\(790\) | −5.49402 | −0.195469 | ||||||||
\(791\) | 16.9658 | 0.603233 | ||||||||
\(792\) | 1.26249 | 0.0448606 | ||||||||
\(793\) | 23.2788 | 0.826654 | ||||||||
\(794\) | 33.9654 | 1.20539 | ||||||||
\(795\) | 20.7606 | 0.736303 | ||||||||
\(796\) | −9.49262 | −0.336457 | ||||||||
\(797\) | 52.7756 | 1.86941 | 0.934703 | − | 0.355429i | \(-0.115665\pi\) | ||||
0.934703 | + | 0.355429i | \(0.115665\pi\) | |||||||
\(798\) | −0.148407 | −0.00525355 | ||||||||
\(799\) | −2.71133 | −0.0959200 | ||||||||
\(800\) | −2.86033 | −0.101128 | ||||||||
\(801\) | −17.9975 | −0.635909 | ||||||||
\(802\) | 19.9873 | 0.705776 | ||||||||
\(803\) | 6.22555 | 0.219695 | ||||||||
\(804\) | 18.3248 | 0.646266 | ||||||||
\(805\) | −22.5403 | −0.794440 | ||||||||
\(806\) | −17.7264 | −0.624387 | ||||||||
\(807\) | −28.8240 | −1.01465 | ||||||||
\(808\) | −3.10944 | −0.109390 | ||||||||
\(809\) | −7.72464 | −0.271584 | −0.135792 | − | 0.990737i | \(-0.543358\pi\) | ||||
−0.135792 | + | 0.990737i | \(0.543358\pi\) | |||||||
\(810\) | −5.29323 | −0.185985 | ||||||||
\(811\) | −33.7411 | −1.18481 | −0.592404 | − | 0.805641i | \(-0.701821\pi\) | ||||
−0.592404 | + | 0.805641i | \(0.701821\pi\) | |||||||
\(812\) | 17.4428 | 0.612123 | ||||||||
\(813\) | 16.9525 | 0.594548 | ||||||||
\(814\) | 2.61721 | 0.0917332 | ||||||||
\(815\) | 27.6756 | 0.969435 | ||||||||
\(816\) | −3.42557 | −0.119919 | ||||||||
\(817\) | −0.0850536 | −0.00297565 | ||||||||
\(818\) | −13.2776 | −0.464239 | ||||||||
\(819\) | 26.7424 | 0.934457 | ||||||||
\(820\) | 8.61141 | 0.300724 | ||||||||
\(821\) | 4.30254 | 0.150160 | 0.0750798 | − | 0.997178i | \(-0.476079\pi\) | ||||
0.0750798 | + | 0.997178i | \(0.476079\pi\) | |||||||
\(822\) | 17.4652 | 0.609168 | ||||||||
\(823\) | 18.1369 | 0.632214 | 0.316107 | − | 0.948724i | \(-0.397624\pi\) | ||||
0.316107 | + | 0.948724i | \(0.397624\pi\) | |||||||
\(824\) | 4.19477 | 0.146132 | ||||||||
\(825\) | −3.77033 | −0.131266 | ||||||||
\(826\) | 34.5613 | 1.20254 | ||||||||
\(827\) | 24.1572 | 0.840028 | 0.420014 | − | 0.907518i | \(-0.362025\pi\) | ||||
0.420014 | + | 0.907518i | \(0.362025\pi\) | |||||||
\(828\) | −4.28899 | −0.149053 | ||||||||
\(829\) | −27.8647 | −0.967781 | −0.483890 | − | 0.875129i | \(-0.660777\pi\) | ||||
−0.483890 | + | 0.875129i | \(0.660777\pi\) | |||||||
\(830\) | −19.3043 | −0.670063 | ||||||||
\(831\) | 10.5342 | 0.365427 | ||||||||
\(832\) | 4.66998 | 0.161902 | ||||||||
\(833\) | 35.2755 | 1.22222 | ||||||||
\(834\) | −12.0662 | −0.417819 | ||||||||
\(835\) | 1.71083 | 0.0592056 | ||||||||
\(836\) | 0.0248218 | 0.000858479 0 | ||||||||
\(837\) | −21.3272 | −0.737175 | ||||||||
\(838\) | 12.0765 | 0.417177 | ||||||||
\(839\) | −3.57511 | −0.123427 | −0.0617133 | − | 0.998094i | \(-0.519656\pi\) | ||||
−0.0617133 | + | 0.998094i | \(0.519656\pi\) | |||||||
\(840\) | 8.74572 | 0.301756 | ||||||||
\(841\) | −14.2117 | −0.490060 | ||||||||
\(842\) | 5.00005 | 0.172313 | ||||||||
\(843\) | 21.5438 | 0.742006 | ||||||||
\(844\) | −4.54282 | −0.156370 | ||||||||
\(845\) | 12.8851 | 0.443260 | ||||||||
\(846\) | 1.31717 | 0.0452852 | ||||||||
\(847\) | −4.53584 | −0.155853 | ||||||||
\(848\) | −10.7672 | −0.369747 | ||||||||
\(849\) | −8.22427 | −0.282256 | ||||||||
\(850\) | −7.43334 | −0.254962 | ||||||||
\(851\) | −8.89132 | −0.304790 | ||||||||
\(852\) | 11.2300 | 0.384734 | ||||||||
\(853\) | 2.95659 | 0.101232 | 0.0506159 | − | 0.998718i | \(-0.483882\pi\) | ||||
0.0506159 | + | 0.998718i | \(0.483882\pi\) | |||||||
\(854\) | −22.6102 | −0.773704 | ||||||||
\(855\) | 0.0458389 | 0.00156766 | ||||||||
\(856\) | −0.684451 | −0.0233940 | ||||||||
\(857\) | 12.6615 | 0.432509 | 0.216254 | − | 0.976337i | \(-0.430616\pi\) | ||||
0.216254 | + | 0.976337i | \(0.430616\pi\) | |||||||
\(858\) | 6.15572 | 0.210153 | ||||||||
\(859\) | 14.0078 | 0.477940 | 0.238970 | − | 0.971027i | \(-0.423190\pi\) | ||||
0.238970 | + | 0.971027i | \(0.423190\pi\) | |||||||
\(860\) | 5.01226 | 0.170917 | ||||||||
\(861\) | 35.1984 | 1.19956 | ||||||||
\(862\) | 21.5480 | 0.733926 | ||||||||
\(863\) | 12.8050 | 0.435888 | 0.217944 | − | 0.975961i | \(-0.430065\pi\) | ||||
0.217944 | + | 0.975961i | \(0.430065\pi\) | |||||||
\(864\) | 5.61859 | 0.191148 | ||||||||
\(865\) | 2.32229 | 0.0789603 | ||||||||
\(866\) | 28.9405 | 0.983440 | ||||||||
\(867\) | 13.5062 | 0.458695 | ||||||||
\(868\) | 17.2173 | 0.584392 | ||||||||
\(869\) | 3.75592 | 0.127411 | ||||||||
\(870\) | 7.41474 | 0.251383 | ||||||||
\(871\) | −64.9218 | −2.19979 | ||||||||
\(872\) | −18.5080 | −0.626761 | ||||||||
\(873\) | 21.6233 | 0.731838 | ||||||||
\(874\) | −0.0843257 | −0.00285236 | ||||||||
\(875\) | 52.1522 | 1.76307 | ||||||||
\(876\) | 8.20619 | 0.277262 | ||||||||
\(877\) | −33.5833 | −1.13403 | −0.567014 | − | 0.823708i | \(-0.691902\pi\) | ||||
−0.567014 | + | 0.823708i | \(0.691902\pi\) | |||||||
\(878\) | 5.31799 | 0.179474 | ||||||||
\(879\) | −26.1492 | −0.881991 | ||||||||
\(880\) | −1.46276 | −0.0493097 | ||||||||
\(881\) | 19.2099 | 0.647199 | 0.323599 | − | 0.946194i | \(-0.395107\pi\) | ||||
0.323599 | + | 0.946194i | \(0.395107\pi\) | |||||||
\(882\) | −17.1369 | −0.577029 | ||||||||
\(883\) | 54.6291 | 1.83841 | 0.919207 | − | 0.393774i | \(-0.128831\pi\) | ||||
0.919207 | + | 0.393774i | \(0.128831\pi\) | |||||||
\(884\) | 12.1362 | 0.408186 | ||||||||
\(885\) | 14.6916 | 0.493853 | ||||||||
\(886\) | −4.59279 | −0.154298 | ||||||||
\(887\) | 42.3730 | 1.42275 | 0.711374 | − | 0.702814i | \(-0.248073\pi\) | ||||
0.711374 | + | 0.702814i | \(0.248073\pi\) | |||||||
\(888\) | 3.44987 | 0.115770 | ||||||||
\(889\) | 63.7724 | 2.13886 | ||||||||
\(890\) | 20.8525 | 0.698976 | ||||||||
\(891\) | 3.61865 | 0.121229 | ||||||||
\(892\) | −21.7748 | −0.729074 | ||||||||
\(893\) | 0.0258968 | 0.000866604 0 | ||||||||
\(894\) | −16.4785 | −0.551124 | ||||||||
\(895\) | 3.79417 | 0.126825 | ||||||||
\(896\) | −4.53584 | −0.151532 | ||||||||
\(897\) | −20.9125 | −0.698248 | ||||||||
\(898\) | −31.4568 | −1.04973 | ||||||||
\(899\) | 14.5970 | 0.486838 | ||||||||
\(900\) | 3.61113 | 0.120371 | ||||||||
\(901\) | −27.9815 | −0.932200 | ||||||||
\(902\) | −5.88709 | −0.196019 | ||||||||
\(903\) | 20.4872 | 0.681770 | ||||||||
\(904\) | −3.74038 | −0.124403 | ||||||||
\(905\) | 15.5034 | 0.515352 | ||||||||
\(906\) | 15.2391 | 0.506286 | ||||||||
\(907\) | 7.93844 | 0.263592 | 0.131796 | − | 0.991277i | \(-0.457926\pi\) | ||||
0.131796 | + | 0.991277i | \(0.457926\pi\) | |||||||
\(908\) | −4.31094 | −0.143064 | ||||||||
\(909\) | 3.92563 | 0.130205 | ||||||||
\(910\) | −30.9847 | −1.02713 | ||||||||
\(911\) | −8.36949 | −0.277294 | −0.138647 | − | 0.990342i | \(-0.544275\pi\) | ||||
−0.138647 | + | 0.990342i | \(0.544275\pi\) | |||||||
\(912\) | 0.0327187 | 0.00108343 | ||||||||
\(913\) | 13.1972 | 0.436762 | ||||||||
\(914\) | −42.5459 | −1.40729 | ||||||||
\(915\) | −9.61132 | −0.317740 | ||||||||
\(916\) | 19.2818 | 0.637088 | ||||||||
\(917\) | 27.0542 | 0.893409 | ||||||||
\(918\) | 14.6014 | 0.481919 | ||||||||
\(919\) | 32.5862 | 1.07492 | 0.537459 | − | 0.843290i | \(-0.319384\pi\) | ||||
0.537459 | + | 0.843290i | \(0.319384\pi\) | |||||||
\(920\) | 4.96937 | 0.163835 | ||||||||
\(921\) | −40.2826 | −1.32736 | ||||||||
\(922\) | −33.8876 | −1.11603 | ||||||||
\(923\) | −39.7862 | −1.30958 | ||||||||
\(924\) | −5.97891 | −0.196692 | ||||||||
\(925\) | 7.48608 | 0.246141 | ||||||||
\(926\) | −17.2341 | −0.566348 | ||||||||
\(927\) | −5.29585 | −0.173939 | ||||||||
\(928\) | −3.84555 | −0.126236 | ||||||||
\(929\) | −14.7296 | −0.483262 | −0.241631 | − | 0.970368i | \(-0.577682\pi\) | ||||
−0.241631 | + | 0.970368i | \(0.577682\pi\) | |||||||
\(930\) | 7.31886 | 0.239995 | ||||||||
\(931\) | −0.336928 | −0.0110424 | ||||||||
\(932\) | −11.2994 | −0.370126 | ||||||||
\(933\) | 20.7619 | 0.679714 | ||||||||
\(934\) | −26.4443 | −0.865285 | ||||||||
\(935\) | −3.80139 | −0.124319 | ||||||||
\(936\) | −5.89580 | −0.192710 | ||||||||
\(937\) | 33.2345 | 1.08572 | 0.542861 | − | 0.839822i | \(-0.317341\pi\) | ||||
0.542861 | + | 0.839822i | \(0.317341\pi\) | |||||||
\(938\) | 63.0571 | 2.05889 | ||||||||
\(939\) | −36.7699 | −1.19994 | ||||||||
\(940\) | −1.52612 | −0.0497764 | ||||||||
\(941\) | 49.7545 | 1.62195 | 0.810975 | − | 0.585081i | \(-0.198937\pi\) | ||||
0.810975 | + | 0.585081i | \(0.198937\pi\) | |||||||
\(942\) | −13.7621 | −0.448393 | ||||||||
\(943\) | 19.9999 | 0.651286 | ||||||||
\(944\) | −7.61960 | −0.247997 | ||||||||
\(945\) | −37.2786 | −1.21267 | ||||||||
\(946\) | −3.42657 | −0.111408 | ||||||||
\(947\) | −15.4538 | −0.502180 | −0.251090 | − | 0.967964i | \(-0.580789\pi\) | ||||
−0.251090 | + | 0.967964i | \(0.580789\pi\) | |||||||
\(948\) | 4.95086 | 0.160796 | ||||||||
\(949\) | −29.0732 | −0.943756 | ||||||||
\(950\) | 0.0709984 | 0.00230349 | ||||||||
\(951\) | 22.1556 | 0.718445 | ||||||||
\(952\) | −11.7876 | −0.382040 | ||||||||
\(953\) | −58.8609 | −1.90669 | −0.953346 | − | 0.301879i | \(-0.902386\pi\) | ||||
−0.953346 | + | 0.301879i | \(0.902386\pi\) | |||||||
\(954\) | 13.5935 | 0.440105 | ||||||||
\(955\) | −23.1672 | −0.749671 | ||||||||
\(956\) | −3.22286 | −0.104235 | ||||||||
\(957\) | −5.06900 | −0.163857 | ||||||||
\(958\) | −18.2359 | −0.589176 | ||||||||
\(959\) | 60.0990 | 1.94070 | ||||||||
\(960\) | −1.92814 | −0.0622303 | ||||||||
\(961\) | −16.5917 | −0.535217 | ||||||||
\(962\) | −12.2223 | −0.394064 | ||||||||
\(963\) | 0.864112 | 0.0278456 | ||||||||
\(964\) | 7.88943 | 0.254101 | ||||||||
\(965\) | 40.3511 | 1.29895 | ||||||||
\(966\) | 20.3118 | 0.653523 | ||||||||
\(967\) | 30.4623 | 0.979600 | 0.489800 | − | 0.871835i | \(-0.337070\pi\) | ||||
0.489800 | + | 0.871835i | \(0.337070\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | 0.0850286 | 0.00273151 | ||||||||
\(970\) | −25.0535 | −0.804419 | ||||||||
\(971\) | 4.88016 | 0.156612 | 0.0783058 | − | 0.996929i | \(-0.475049\pi\) | ||||
0.0783058 | + | 0.996929i | \(0.475049\pi\) | |||||||
\(972\) | −12.0858 | −0.387654 | ||||||||
\(973\) | −41.5208 | −1.33109 | ||||||||
\(974\) | 39.2794 | 1.25859 | ||||||||
\(975\) | 17.6074 | 0.563887 | ||||||||
\(976\) | 4.98477 | 0.159559 | ||||||||
\(977\) | 11.7518 | 0.375972 | 0.187986 | − | 0.982172i | \(-0.439804\pi\) | ||||
0.187986 | + | 0.982172i | \(0.439804\pi\) | |||||||
\(978\) | −24.9395 | −0.797476 | ||||||||
\(979\) | −14.2555 | −0.455609 | ||||||||
\(980\) | 19.8554 | 0.634257 | ||||||||
\(981\) | 23.3662 | 0.746025 | ||||||||
\(982\) | 28.5260 | 0.910301 | ||||||||
\(983\) | −16.3167 | −0.520422 | −0.260211 | − | 0.965552i | \(-0.583792\pi\) | ||||
−0.260211 | + | 0.965552i | \(0.583792\pi\) | |||||||
\(984\) | −7.76005 | −0.247381 | ||||||||
\(985\) | 1.46276 | 0.0466075 | ||||||||
\(986\) | −9.99372 | −0.318265 | ||||||||
\(987\) | −6.23786 | −0.198553 | ||||||||
\(988\) | −0.115917 | −0.00368782 | ||||||||
\(989\) | 11.6409 | 0.370160 | ||||||||
\(990\) | 1.84672 | 0.0586927 | ||||||||
\(991\) | 46.3234 | 1.47151 | 0.735755 | − | 0.677248i | \(-0.236827\pi\) | ||||
0.735755 | + | 0.677248i | \(0.236827\pi\) | |||||||
\(992\) | −3.79582 | −0.120518 | ||||||||
\(993\) | 7.20368 | 0.228602 | ||||||||
\(994\) | 38.6434 | 1.22569 | ||||||||
\(995\) | −13.8855 | −0.440198 | ||||||||
\(996\) | 17.3958 | 0.551207 | ||||||||
\(997\) | −27.4837 | −0.870419 | −0.435210 | − | 0.900329i | \(-0.643326\pi\) | ||||
−0.435210 | + | 0.900329i | \(0.643326\pi\) | |||||||
\(998\) | 33.4415 | 1.05857 | ||||||||
\(999\) | −14.7050 | −0.465246 |
(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 | 4334.2.a.d.1.8 | ✓ | 17 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4334.2.a.d.1.8 | ✓ | 17 | 1.1 | even | 1 | trivial |