Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6002,2,Mod(1,6002)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6002, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6002.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6002 = 2 \cdot 3001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6002.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: | \(47.9262112932\) |
Analytic rank: | \(1\) |
Dimension: | \(56\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 6002.1 |
$q$-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 | ||||||||
\(3\) | −1.59777 | −0.922472 | −0.461236 | − | 0.887277i | \(-0.652594\pi\) | ||||
−0.461236 | + | 0.887277i | \(0.652594\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.373803 | 0.167170 | 0.0835848 | − | 0.996501i | \(-0.473363\pi\) | ||||
0.0835848 | + | 0.996501i | \(0.473363\pi\) | |||||||
\(6\) | 1.59777 | 0.652287 | ||||||||
\(7\) | 0.398412 | 0.150586 | 0.0752928 | − | 0.997161i | \(-0.476011\pi\) | ||||
0.0752928 | + | 0.997161i | \(0.476011\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.447134 | −0.149045 | ||||||||
\(10\) | −0.373803 | −0.118207 | ||||||||
\(11\) | 3.67735 | 1.10876 | 0.554382 | − | 0.832262i | \(-0.312955\pi\) | ||||
0.554382 | + | 0.832262i | \(0.312955\pi\) | |||||||
\(12\) | −1.59777 | −0.461236 | ||||||||
\(13\) | 1.92808 | 0.534753 | 0.267377 | − | 0.963592i | \(-0.413843\pi\) | ||||
0.267377 | + | 0.963592i | \(0.413843\pi\) | |||||||
\(14\) | −0.398412 | −0.106480 | ||||||||
\(15\) | −0.597250 | −0.154209 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.55986 | −1.59100 | −0.795499 | − | 0.605954i | \(-0.792791\pi\) | ||||
−0.795499 | + | 0.605954i | \(0.792791\pi\) | |||||||
\(18\) | 0.447134 | 0.105390 | ||||||||
\(19\) | 0.0517994 | 0.0118836 | 0.00594180 | − | 0.999982i | \(-0.498109\pi\) | ||||
0.00594180 | + | 0.999982i | \(0.498109\pi\) | |||||||
\(20\) | 0.373803 | 0.0835848 | ||||||||
\(21\) | −0.636571 | −0.138911 | ||||||||
\(22\) | −3.67735 | −0.784015 | ||||||||
\(23\) | 3.45371 | 0.720148 | 0.360074 | − | 0.932924i | \(-0.382751\pi\) | ||||
0.360074 | + | 0.932924i | \(0.382751\pi\) | |||||||
\(24\) | 1.59777 | 0.326143 | ||||||||
\(25\) | −4.86027 | −0.972054 | ||||||||
\(26\) | −1.92808 | −0.378128 | ||||||||
\(27\) | 5.50772 | 1.05996 | ||||||||
\(28\) | 0.398412 | 0.0752928 | ||||||||
\(29\) | −3.77464 | −0.700934 | −0.350467 | − | 0.936575i | \(-0.613977\pi\) | ||||
−0.350467 | + | 0.936575i | \(0.613977\pi\) | |||||||
\(30\) | 0.597250 | 0.109043 | ||||||||
\(31\) | 0.705533 | 0.126717 | 0.0633587 | − | 0.997991i | \(-0.479819\pi\) | ||||
0.0633587 | + | 0.997991i | \(0.479819\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −5.87556 | −1.02280 | ||||||||
\(34\) | 6.55986 | 1.12501 | ||||||||
\(35\) | 0.148928 | 0.0251733 | ||||||||
\(36\) | −0.447134 | −0.0745223 | ||||||||
\(37\) | 10.0485 | 1.65196 | 0.825982 | − | 0.563696i | \(-0.190621\pi\) | ||||
0.825982 | + | 0.563696i | \(0.190621\pi\) | |||||||
\(38\) | −0.0517994 | −0.00840297 | ||||||||
\(39\) | −3.08063 | −0.493295 | ||||||||
\(40\) | −0.373803 | −0.0591034 | ||||||||
\(41\) | 7.53179 | 1.17627 | 0.588134 | − | 0.808764i | \(-0.299863\pi\) | ||||
0.588134 | + | 0.808764i | \(0.299863\pi\) | |||||||
\(42\) | 0.636571 | 0.0982250 | ||||||||
\(43\) | −6.24786 | −0.952790 | −0.476395 | − | 0.879231i | \(-0.658057\pi\) | ||||
−0.476395 | + | 0.879231i | \(0.658057\pi\) | |||||||
\(44\) | 3.67735 | 0.554382 | ||||||||
\(45\) | −0.167140 | −0.0249157 | ||||||||
\(46\) | −3.45371 | −0.509222 | ||||||||
\(47\) | −2.41214 | −0.351847 | −0.175924 | − | 0.984404i | \(-0.556291\pi\) | ||||
−0.175924 | + | 0.984404i | \(0.556291\pi\) | |||||||
\(48\) | −1.59777 | −0.230618 | ||||||||
\(49\) | −6.84127 | −0.977324 | ||||||||
\(50\) | 4.86027 | 0.687346 | ||||||||
\(51\) | 10.4811 | 1.46765 | ||||||||
\(52\) | 1.92808 | 0.267377 | ||||||||
\(53\) | −1.36534 | −0.187544 | −0.0937720 | − | 0.995594i | \(-0.529892\pi\) | ||||
−0.0937720 | + | 0.995594i | \(0.529892\pi\) | |||||||
\(54\) | −5.50772 | −0.749506 | ||||||||
\(55\) | 1.37460 | 0.185352 | ||||||||
\(56\) | −0.398412 | −0.0532401 | ||||||||
\(57\) | −0.0827634 | −0.0109623 | ||||||||
\(58\) | 3.77464 | 0.495635 | ||||||||
\(59\) | −1.26062 | −0.164118 | −0.0820592 | − | 0.996627i | \(-0.526150\pi\) | ||||
−0.0820592 | + | 0.996627i | \(0.526150\pi\) | |||||||
\(60\) | −0.597250 | −0.0771047 | ||||||||
\(61\) | −9.91540 | −1.26954 | −0.634768 | − | 0.772703i | \(-0.718904\pi\) | ||||
−0.634768 | + | 0.772703i | \(0.718904\pi\) | |||||||
\(62\) | −0.705533 | −0.0896028 | ||||||||
\(63\) | −0.178144 | −0.0224440 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.720722 | 0.0893945 | ||||||||
\(66\) | 5.87556 | 0.723232 | ||||||||
\(67\) | −8.33599 | −1.01840 | −0.509201 | − | 0.860647i | \(-0.670059\pi\) | ||||
−0.509201 | + | 0.860647i | \(0.670059\pi\) | |||||||
\(68\) | −6.55986 | −0.795499 | ||||||||
\(69\) | −5.51823 | −0.664317 | ||||||||
\(70\) | −0.148928 | −0.0178002 | ||||||||
\(71\) | 3.12059 | 0.370346 | 0.185173 | − | 0.982706i | \(-0.440715\pi\) | ||||
0.185173 | + | 0.982706i | \(0.440715\pi\) | |||||||
\(72\) | 0.447134 | 0.0526952 | ||||||||
\(73\) | −12.6726 | −1.48322 | −0.741610 | − | 0.670831i | \(-0.765938\pi\) | ||||
−0.741610 | + | 0.670831i | \(0.765938\pi\) | |||||||
\(74\) | −10.0485 | −1.16812 | ||||||||
\(75\) | 7.76559 | 0.896693 | ||||||||
\(76\) | 0.0517994 | 0.00594180 | ||||||||
\(77\) | 1.46510 | 0.166964 | ||||||||
\(78\) | 3.08063 | 0.348812 | ||||||||
\(79\) | 10.8981 | 1.22613 | 0.613067 | − | 0.790031i | \(-0.289935\pi\) | ||||
0.613067 | + | 0.790031i | \(0.289935\pi\) | |||||||
\(80\) | 0.373803 | 0.0417924 | ||||||||
\(81\) | −7.45867 | −0.828741 | ||||||||
\(82\) | −7.53179 | −0.831747 | ||||||||
\(83\) | −8.81151 | −0.967188 | −0.483594 | − | 0.875292i | \(-0.660669\pi\) | ||||
−0.483594 | + | 0.875292i | \(0.660669\pi\) | |||||||
\(84\) | −0.636571 | −0.0694555 | ||||||||
\(85\) | −2.45209 | −0.265967 | ||||||||
\(86\) | 6.24786 | 0.673724 | ||||||||
\(87\) | 6.03101 | 0.646592 | ||||||||
\(88\) | −3.67735 | −0.392007 | ||||||||
\(89\) | 13.7515 | 1.45765 | 0.728827 | − | 0.684698i | \(-0.240066\pi\) | ||||
0.728827 | + | 0.684698i | \(0.240066\pi\) | |||||||
\(90\) | 0.167140 | 0.0176181 | ||||||||
\(91\) | 0.768171 | 0.0805262 | ||||||||
\(92\) | 3.45371 | 0.360074 | ||||||||
\(93\) | −1.12728 | −0.116893 | ||||||||
\(94\) | 2.41214 | 0.248794 | ||||||||
\(95\) | 0.0193627 | 0.00198658 | ||||||||
\(96\) | 1.59777 | 0.163072 | ||||||||
\(97\) | 9.40196 | 0.954624 | 0.477312 | − | 0.878734i | \(-0.341611\pi\) | ||||
0.477312 | + | 0.878734i | \(0.341611\pi\) | |||||||
\(98\) | 6.84127 | 0.691072 | ||||||||
\(99\) | −1.64427 | −0.165255 | ||||||||
\(100\) | −4.86027 | −0.486027 | ||||||||
\(101\) | −7.85216 | −0.781319 | −0.390660 | − | 0.920535i | \(-0.627753\pi\) | ||||
−0.390660 | + | 0.920535i | \(0.627753\pi\) | |||||||
\(102\) | −10.4811 | −1.03779 | ||||||||
\(103\) | 4.51819 | 0.445190 | 0.222595 | − | 0.974911i | \(-0.428547\pi\) | ||||
0.222595 | + | 0.974911i | \(0.428547\pi\) | |||||||
\(104\) | −1.92808 | −0.189064 | ||||||||
\(105\) | −0.237952 | −0.0232217 | ||||||||
\(106\) | 1.36534 | 0.132614 | ||||||||
\(107\) | 0.359079 | 0.0347135 | 0.0173567 | − | 0.999849i | \(-0.494475\pi\) | ||||
0.0173567 | + | 0.999849i | \(0.494475\pi\) | |||||||
\(108\) | 5.50772 | 0.529981 | ||||||||
\(109\) | 3.90597 | 0.374124 | 0.187062 | − | 0.982348i | \(-0.440103\pi\) | ||||
0.187062 | + | 0.982348i | \(0.440103\pi\) | |||||||
\(110\) | −1.37460 | −0.131063 | ||||||||
\(111\) | −16.0552 | −1.52389 | ||||||||
\(112\) | 0.398412 | 0.0376464 | ||||||||
\(113\) | −5.24695 | −0.493591 | −0.246796 | − | 0.969068i | \(-0.579378\pi\) | ||||
−0.246796 | + | 0.969068i | \(0.579378\pi\) | |||||||
\(114\) | 0.0827634 | 0.00775151 | ||||||||
\(115\) | 1.29101 | 0.120387 | ||||||||
\(116\) | −3.77464 | −0.350467 | ||||||||
\(117\) | −0.862110 | −0.0797021 | ||||||||
\(118\) | 1.26062 | 0.116049 | ||||||||
\(119\) | −2.61353 | −0.239582 | ||||||||
\(120\) | 0.597250 | 0.0545213 | ||||||||
\(121\) | 2.52293 | 0.229358 | ||||||||
\(122\) | 9.91540 | 0.897698 | ||||||||
\(123\) | −12.0341 | −1.08507 | ||||||||
\(124\) | 0.705533 | 0.0633587 | ||||||||
\(125\) | −3.68580 | −0.329668 | ||||||||
\(126\) | 0.178144 | 0.0158703 | ||||||||
\(127\) | 10.5093 | 0.932547 | 0.466274 | − | 0.884641i | \(-0.345596\pi\) | ||||
0.466274 | + | 0.884641i | \(0.345596\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 9.98264 | 0.878922 | ||||||||
\(130\) | −0.720722 | −0.0632115 | ||||||||
\(131\) | −0.826010 | −0.0721689 | −0.0360844 | − | 0.999349i | \(-0.511489\pi\) | ||||
−0.0360844 | + | 0.999349i | \(0.511489\pi\) | |||||||
\(132\) | −5.87556 | −0.511402 | ||||||||
\(133\) | 0.0206375 | 0.00178950 | ||||||||
\(134\) | 8.33599 | 0.720119 | ||||||||
\(135\) | 2.05880 | 0.177193 | ||||||||
\(136\) | 6.55986 | 0.562503 | ||||||||
\(137\) | 1.18957 | 0.101632 | 0.0508159 | − | 0.998708i | \(-0.483818\pi\) | ||||
0.0508159 | + | 0.998708i | \(0.483818\pi\) | |||||||
\(138\) | 5.51823 | 0.469743 | ||||||||
\(139\) | 10.1836 | 0.863762 | 0.431881 | − | 0.901931i | \(-0.357850\pi\) | ||||
0.431881 | + | 0.901931i | \(0.357850\pi\) | |||||||
\(140\) | 0.148928 | 0.0125867 | ||||||||
\(141\) | 3.85405 | 0.324569 | ||||||||
\(142\) | −3.12059 | −0.261874 | ||||||||
\(143\) | 7.09023 | 0.592915 | ||||||||
\(144\) | −0.447134 | −0.0372612 | ||||||||
\(145\) | −1.41097 | −0.117175 | ||||||||
\(146\) | 12.6726 | 1.04880 | ||||||||
\(147\) | 10.9308 | 0.901554 | ||||||||
\(148\) | 10.0485 | 0.825982 | ||||||||
\(149\) | 16.4388 | 1.34672 | 0.673359 | − | 0.739315i | \(-0.264851\pi\) | ||||
0.673359 | + | 0.739315i | \(0.264851\pi\) | |||||||
\(150\) | −7.76559 | −0.634058 | ||||||||
\(151\) | −23.4575 | −1.90894 | −0.954470 | − | 0.298305i | \(-0.903579\pi\) | ||||
−0.954470 | + | 0.298305i | \(0.903579\pi\) | |||||||
\(152\) | −0.0517994 | −0.00420148 | ||||||||
\(153\) | 2.93313 | 0.237130 | ||||||||
\(154\) | −1.46510 | −0.118061 | ||||||||
\(155\) | 0.263730 | 0.0211833 | ||||||||
\(156\) | −3.08063 | −0.246648 | ||||||||
\(157\) | −9.75430 | −0.778478 | −0.389239 | − | 0.921137i | \(-0.627262\pi\) | ||||
−0.389239 | + | 0.921137i | \(0.627262\pi\) | |||||||
\(158\) | −10.8981 | −0.867008 | ||||||||
\(159\) | 2.18150 | 0.173004 | ||||||||
\(160\) | −0.373803 | −0.0295517 | ||||||||
\(161\) | 1.37600 | 0.108444 | ||||||||
\(162\) | 7.45867 | 0.586008 | ||||||||
\(163\) | 8.06388 | 0.631612 | 0.315806 | − | 0.948824i | \(-0.397725\pi\) | ||||
0.315806 | + | 0.948824i | \(0.397725\pi\) | |||||||
\(164\) | 7.53179 | 0.588134 | ||||||||
\(165\) | −2.19630 | −0.170982 | ||||||||
\(166\) | 8.81151 | 0.683906 | ||||||||
\(167\) | 23.4217 | 1.81243 | 0.906214 | − | 0.422819i | \(-0.138960\pi\) | ||||
0.906214 | + | 0.422819i | \(0.138960\pi\) | |||||||
\(168\) | 0.636571 | 0.0491125 | ||||||||
\(169\) | −9.28251 | −0.714039 | ||||||||
\(170\) | 2.45209 | 0.188067 | ||||||||
\(171\) | −0.0231613 | −0.00177119 | ||||||||
\(172\) | −6.24786 | −0.476395 | ||||||||
\(173\) | −0.914248 | −0.0695090 | −0.0347545 | − | 0.999396i | \(-0.511065\pi\) | ||||
−0.0347545 | + | 0.999396i | \(0.511065\pi\) | |||||||
\(174\) | −6.03101 | −0.457210 | ||||||||
\(175\) | −1.93639 | −0.146377 | ||||||||
\(176\) | 3.67735 | 0.277191 | ||||||||
\(177\) | 2.01418 | 0.151395 | ||||||||
\(178\) | −13.7515 | −1.03072 | ||||||||
\(179\) | −8.76427 | −0.655073 | −0.327536 | − | 0.944839i | \(-0.606218\pi\) | ||||
−0.327536 | + | 0.944839i | \(0.606218\pi\) | |||||||
\(180\) | −0.167140 | −0.0124579 | ||||||||
\(181\) | 17.0757 | 1.26922 | 0.634612 | − | 0.772831i | \(-0.281160\pi\) | ||||
0.634612 | + | 0.772831i | \(0.281160\pi\) | |||||||
\(182\) | −0.768171 | −0.0569406 | ||||||||
\(183\) | 15.8425 | 1.17111 | ||||||||
\(184\) | −3.45371 | −0.254611 | ||||||||
\(185\) | 3.75616 | 0.276158 | ||||||||
\(186\) | 1.12728 | 0.0826561 | ||||||||
\(187\) | −24.1229 | −1.76404 | ||||||||
\(188\) | −2.41214 | −0.175924 | ||||||||
\(189\) | 2.19434 | 0.159615 | ||||||||
\(190\) | −0.0193627 | −0.00140472 | ||||||||
\(191\) | −21.6593 | −1.56722 | −0.783608 | − | 0.621256i | \(-0.786623\pi\) | ||||
−0.783608 | + | 0.621256i | \(0.786623\pi\) | |||||||
\(192\) | −1.59777 | −0.115309 | ||||||||
\(193\) | −17.2120 | −1.23895 | −0.619474 | − | 0.785017i | \(-0.712654\pi\) | ||||
−0.619474 | + | 0.785017i | \(0.712654\pi\) | |||||||
\(194\) | −9.40196 | −0.675021 | ||||||||
\(195\) | −1.15155 | −0.0824640 | ||||||||
\(196\) | −6.84127 | −0.488662 | ||||||||
\(197\) | −3.88082 | −0.276497 | −0.138248 | − | 0.990398i | \(-0.544147\pi\) | ||||
−0.138248 | + | 0.990398i | \(0.544147\pi\) | |||||||
\(198\) | 1.64427 | 0.116853 | ||||||||
\(199\) | 7.81861 | 0.554247 | 0.277123 | − | 0.960834i | \(-0.410619\pi\) | ||||
0.277123 | + | 0.960834i | \(0.410619\pi\) | |||||||
\(200\) | 4.86027 | 0.343673 | ||||||||
\(201\) | 13.3190 | 0.939448 | ||||||||
\(202\) | 7.85216 | 0.552476 | ||||||||
\(203\) | −1.50386 | −0.105551 | ||||||||
\(204\) | 10.4811 | 0.733826 | ||||||||
\(205\) | 2.81540 | 0.196636 | ||||||||
\(206\) | −4.51819 | −0.314797 | ||||||||
\(207\) | −1.54427 | −0.107334 | ||||||||
\(208\) | 1.92808 | 0.133688 | ||||||||
\(209\) | 0.190485 | 0.0131761 | ||||||||
\(210\) | 0.237952 | 0.0164202 | ||||||||
\(211\) | −23.8920 | −1.64479 | −0.822396 | − | 0.568916i | \(-0.807363\pi\) | ||||
−0.822396 | + | 0.568916i | \(0.807363\pi\) | |||||||
\(212\) | −1.36534 | −0.0937720 | ||||||||
\(213\) | −4.98598 | −0.341634 | ||||||||
\(214\) | −0.359079 | −0.0245461 | ||||||||
\(215\) | −2.33547 | −0.159278 | ||||||||
\(216\) | −5.50772 | −0.374753 | ||||||||
\(217\) | 0.281093 | 0.0190818 | ||||||||
\(218\) | −3.90597 | −0.264546 | ||||||||
\(219\) | 20.2480 | 1.36823 | ||||||||
\(220\) | 1.37460 | 0.0926758 | ||||||||
\(221\) | −12.6479 | −0.850792 | ||||||||
\(222\) | 16.0552 | 1.07755 | ||||||||
\(223\) | −21.2389 | −1.42226 | −0.711131 | − | 0.703060i | \(-0.751817\pi\) | ||||
−0.711131 | + | 0.703060i | \(0.751817\pi\) | |||||||
\(224\) | −0.398412 | −0.0266200 | ||||||||
\(225\) | 2.17319 | 0.144879 | ||||||||
\(226\) | 5.24695 | 0.349022 | ||||||||
\(227\) | −2.92250 | −0.193973 | −0.0969865 | − | 0.995286i | \(-0.530920\pi\) | ||||
−0.0969865 | + | 0.995286i | \(0.530920\pi\) | |||||||
\(228\) | −0.0827634 | −0.00548114 | ||||||||
\(229\) | −15.9402 | −1.05336 | −0.526678 | − | 0.850065i | \(-0.676563\pi\) | ||||
−0.526678 | + | 0.850065i | \(0.676563\pi\) | |||||||
\(230\) | −1.29101 | −0.0851264 | ||||||||
\(231\) | −2.34090 | −0.154020 | ||||||||
\(232\) | 3.77464 | 0.247818 | ||||||||
\(233\) | −2.42535 | −0.158890 | −0.0794451 | − | 0.996839i | \(-0.525315\pi\) | ||||
−0.0794451 | + | 0.996839i | \(0.525315\pi\) | |||||||
\(234\) | 0.862110 | 0.0563579 | ||||||||
\(235\) | −0.901666 | −0.0588182 | ||||||||
\(236\) | −1.26062 | −0.0820592 | ||||||||
\(237\) | −17.4127 | −1.13108 | ||||||||
\(238\) | 2.61353 | 0.169410 | ||||||||
\(239\) | 23.7583 | 1.53680 | 0.768400 | − | 0.639970i | \(-0.221053\pi\) | ||||
0.768400 | + | 0.639970i | \(0.221053\pi\) | |||||||
\(240\) | −0.597250 | −0.0385524 | ||||||||
\(241\) | 7.40717 | 0.477137 | 0.238569 | − | 0.971126i | \(-0.423322\pi\) | ||||
0.238569 | + | 0.971126i | \(0.423322\pi\) | |||||||
\(242\) | −2.52293 | −0.162180 | ||||||||
\(243\) | −4.60594 | −0.295471 | ||||||||
\(244\) | −9.91540 | −0.634768 | ||||||||
\(245\) | −2.55728 | −0.163379 | ||||||||
\(246\) | 12.0341 | 0.767264 | ||||||||
\(247\) | 0.0998734 | 0.00635479 | ||||||||
\(248\) | −0.705533 | −0.0448014 | ||||||||
\(249\) | 14.0788 | 0.892205 | ||||||||
\(250\) | 3.68580 | 0.233110 | ||||||||
\(251\) | 2.72576 | 0.172048 | 0.0860242 | − | 0.996293i | \(-0.472584\pi\) | ||||
0.0860242 | + | 0.996293i | \(0.472584\pi\) | |||||||
\(252\) | −0.178144 | −0.0112220 | ||||||||
\(253\) | 12.7005 | 0.798474 | ||||||||
\(254\) | −10.5093 | −0.659411 | ||||||||
\(255\) | 3.91788 | 0.245347 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −12.2989 | −0.767185 | −0.383592 | − | 0.923503i | \(-0.625313\pi\) | ||||
−0.383592 | + | 0.923503i | \(0.625313\pi\) | |||||||
\(258\) | −9.98264 | −0.621492 | ||||||||
\(259\) | 4.00345 | 0.248762 | ||||||||
\(260\) | 0.720722 | 0.0446973 | ||||||||
\(261\) | 1.68777 | 0.104470 | ||||||||
\(262\) | 0.826010 | 0.0510311 | ||||||||
\(263\) | 29.1191 | 1.79556 | 0.897780 | − | 0.440444i | \(-0.145179\pi\) | ||||
0.897780 | + | 0.440444i | \(0.145179\pi\) | |||||||
\(264\) | 5.87556 | 0.361616 | ||||||||
\(265\) | −0.510368 | −0.0313517 | ||||||||
\(266\) | −0.0206375 | −0.00126537 | ||||||||
\(267\) | −21.9717 | −1.34465 | ||||||||
\(268\) | −8.33599 | −0.509201 | ||||||||
\(269\) | 30.1751 | 1.83981 | 0.919905 | − | 0.392142i | \(-0.128266\pi\) | ||||
0.919905 | + | 0.392142i | \(0.128266\pi\) | |||||||
\(270\) | −2.05880 | −0.125295 | ||||||||
\(271\) | 9.70043 | 0.589259 | 0.294629 | − | 0.955612i | \(-0.404804\pi\) | ||||
0.294629 | + | 0.955612i | \(0.404804\pi\) | |||||||
\(272\) | −6.55986 | −0.397750 | ||||||||
\(273\) | −1.22736 | −0.0742832 | ||||||||
\(274\) | −1.18957 | −0.0718646 | ||||||||
\(275\) | −17.8729 | −1.07778 | ||||||||
\(276\) | −5.51823 | −0.332158 | ||||||||
\(277\) | −10.9154 | −0.655842 | −0.327921 | − | 0.944705i | \(-0.606348\pi\) | ||||
−0.327921 | + | 0.944705i | \(0.606348\pi\) | |||||||
\(278\) | −10.1836 | −0.610772 | ||||||||
\(279\) | −0.315468 | −0.0188866 | ||||||||
\(280\) | −0.148928 | −0.00890012 | ||||||||
\(281\) | 14.3811 | 0.857903 | 0.428951 | − | 0.903328i | \(-0.358883\pi\) | ||||
0.428951 | + | 0.903328i | \(0.358883\pi\) | |||||||
\(282\) | −3.85405 | −0.229505 | ||||||||
\(283\) | −21.9537 | −1.30501 | −0.652506 | − | 0.757783i | \(-0.726282\pi\) | ||||
−0.652506 | + | 0.757783i | \(0.726282\pi\) | |||||||
\(284\) | 3.12059 | 0.185173 | ||||||||
\(285\) | −0.0309372 | −0.00183256 | ||||||||
\(286\) | −7.09023 | −0.419254 | ||||||||
\(287\) | 3.00076 | 0.177129 | ||||||||
\(288\) | 0.447134 | 0.0263476 | ||||||||
\(289\) | 26.0317 | 1.53128 | ||||||||
\(290\) | 1.41097 | 0.0828551 | ||||||||
\(291\) | −15.0222 | −0.880615 | ||||||||
\(292\) | −12.6726 | −0.741610 | ||||||||
\(293\) | −9.89021 | −0.577792 | −0.288896 | − | 0.957360i | \(-0.593288\pi\) | ||||
−0.288896 | + | 0.957360i | \(0.593288\pi\) | |||||||
\(294\) | −10.9308 | −0.637495 | ||||||||
\(295\) | −0.471222 | −0.0274356 | ||||||||
\(296\) | −10.0485 | −0.584058 | ||||||||
\(297\) | 20.2539 | 1.17525 | ||||||||
\(298\) | −16.4388 | −0.952274 | ||||||||
\(299\) | 6.65903 | 0.385102 | ||||||||
\(300\) | 7.76559 | 0.448347 | ||||||||
\(301\) | −2.48922 | −0.143476 | ||||||||
\(302\) | 23.4575 | 1.34983 | ||||||||
\(303\) | 12.5459 | 0.720746 | ||||||||
\(304\) | 0.0517994 | 0.00297090 | ||||||||
\(305\) | −3.70640 | −0.212228 | ||||||||
\(306\) | −2.93313 | −0.167676 | ||||||||
\(307\) | −6.45061 | −0.368156 | −0.184078 | − | 0.982912i | \(-0.558930\pi\) | ||||
−0.184078 | + | 0.982912i | \(0.558930\pi\) | |||||||
\(308\) | 1.46510 | 0.0834820 | ||||||||
\(309\) | −7.21902 | −0.410676 | ||||||||
\(310\) | −0.263730 | −0.0149789 | ||||||||
\(311\) | −7.46794 | −0.423468 | −0.211734 | − | 0.977327i | \(-0.567911\pi\) | ||||
−0.211734 | + | 0.977327i | \(0.567911\pi\) | |||||||
\(312\) | 3.08063 | 0.174406 | ||||||||
\(313\) | −26.0247 | −1.47100 | −0.735502 | − | 0.677522i | \(-0.763054\pi\) | ||||
−0.735502 | + | 0.677522i | \(0.763054\pi\) | |||||||
\(314\) | 9.75430 | 0.550467 | ||||||||
\(315\) | −0.0665905 | −0.00375195 | ||||||||
\(316\) | 10.8981 | 0.613067 | ||||||||
\(317\) | −23.6850 | −1.33028 | −0.665142 | − | 0.746717i | \(-0.731629\pi\) | ||||
−0.665142 | + | 0.746717i | \(0.731629\pi\) | |||||||
\(318\) | −2.18150 | −0.122332 | ||||||||
\(319\) | −13.8807 | −0.777170 | ||||||||
\(320\) | 0.373803 | 0.0208962 | ||||||||
\(321\) | −0.573725 | −0.0320222 | ||||||||
\(322\) | −1.37600 | −0.0766814 | ||||||||
\(323\) | −0.339796 | −0.0189068 | ||||||||
\(324\) | −7.45867 | −0.414371 | ||||||||
\(325\) | −9.37099 | −0.519809 | ||||||||
\(326\) | −8.06388 | −0.446617 | ||||||||
\(327\) | −6.24084 | −0.345119 | ||||||||
\(328\) | −7.53179 | −0.415873 | ||||||||
\(329\) | −0.961027 | −0.0529831 | ||||||||
\(330\) | 2.19630 | 0.120902 | ||||||||
\(331\) | 25.6303 | 1.40877 | 0.704383 | − | 0.709820i | \(-0.251224\pi\) | ||||
0.704383 | + | 0.709820i | \(0.251224\pi\) | |||||||
\(332\) | −8.81151 | −0.483594 | ||||||||
\(333\) | −4.49303 | −0.246216 | ||||||||
\(334\) | −23.4217 | −1.28158 | ||||||||
\(335\) | −3.11601 | −0.170246 | ||||||||
\(336\) | −0.636571 | −0.0347278 | ||||||||
\(337\) | −26.0207 | −1.41744 | −0.708719 | − | 0.705491i | \(-0.750726\pi\) | ||||
−0.708719 | + | 0.705491i | \(0.750726\pi\) | |||||||
\(338\) | 9.28251 | 0.504902 | ||||||||
\(339\) | 8.38341 | 0.455324 | ||||||||
\(340\) | −2.45209 | −0.132983 | ||||||||
\(341\) | 2.59449 | 0.140500 | ||||||||
\(342\) | 0.0231613 | 0.00125242 | ||||||||
\(343\) | −5.51453 | −0.297757 | ||||||||
\(344\) | 6.24786 | 0.336862 | ||||||||
\(345\) | −2.06273 | −0.111054 | ||||||||
\(346\) | 0.914248 | 0.0491503 | ||||||||
\(347\) | −25.9125 | −1.39106 | −0.695528 | − | 0.718499i | \(-0.744830\pi\) | ||||
−0.695528 | + | 0.718499i | \(0.744830\pi\) | |||||||
\(348\) | 6.03101 | 0.323296 | ||||||||
\(349\) | 27.9290 | 1.49501 | 0.747504 | − | 0.664258i | \(-0.231252\pi\) | ||||
0.747504 | + | 0.664258i | \(0.231252\pi\) | |||||||
\(350\) | 1.93639 | 0.103504 | ||||||||
\(351\) | 10.6193 | 0.566818 | ||||||||
\(352\) | −3.67735 | −0.196004 | ||||||||
\(353\) | 2.49607 | 0.132853 | 0.0664263 | − | 0.997791i | \(-0.478840\pi\) | ||||
0.0664263 | + | 0.997791i | \(0.478840\pi\) | |||||||
\(354\) | −2.01418 | −0.107052 | ||||||||
\(355\) | 1.16648 | 0.0619106 | ||||||||
\(356\) | 13.7515 | 0.728827 | ||||||||
\(357\) | 4.17581 | 0.221007 | ||||||||
\(358\) | 8.76427 | 0.463206 | ||||||||
\(359\) | −28.6233 | −1.51068 | −0.755339 | − | 0.655334i | \(-0.772528\pi\) | ||||
−0.755339 | + | 0.655334i | \(0.772528\pi\) | |||||||
\(360\) | 0.167140 | 0.00880904 | ||||||||
\(361\) | −18.9973 | −0.999859 | ||||||||
\(362\) | −17.0757 | −0.897477 | ||||||||
\(363\) | −4.03106 | −0.211576 | ||||||||
\(364\) | 0.768171 | 0.0402631 | ||||||||
\(365\) | −4.73707 | −0.247949 | ||||||||
\(366\) | −15.8425 | −0.828102 | ||||||||
\(367\) | −10.7527 | −0.561289 | −0.280644 | − | 0.959812i | \(-0.590548\pi\) | ||||
−0.280644 | + | 0.959812i | \(0.590548\pi\) | |||||||
\(368\) | 3.45371 | 0.180037 | ||||||||
\(369\) | −3.36772 | −0.175316 | ||||||||
\(370\) | −3.75616 | −0.195273 | ||||||||
\(371\) | −0.543968 | −0.0282414 | ||||||||
\(372\) | −1.12728 | −0.0584467 | ||||||||
\(373\) | 30.6816 | 1.58864 | 0.794318 | − | 0.607503i | \(-0.207829\pi\) | ||||
0.794318 | + | 0.607503i | \(0.207829\pi\) | |||||||
\(374\) | 24.1229 | 1.24737 | ||||||||
\(375\) | 5.88905 | 0.304109 | ||||||||
\(376\) | 2.41214 | 0.124397 | ||||||||
\(377\) | −7.27782 | −0.374827 | ||||||||
\(378\) | −2.19434 | −0.112865 | ||||||||
\(379\) | −13.8183 | −0.709796 | −0.354898 | − | 0.934905i | \(-0.615484\pi\) | ||||
−0.354898 | + | 0.934905i | \(0.615484\pi\) | |||||||
\(380\) | 0.0193627 | 0.000993288 0 | ||||||||
\(381\) | −16.7914 | −0.860249 | ||||||||
\(382\) | 21.6593 | 1.10819 | ||||||||
\(383\) | 0.639382 | 0.0326709 | 0.0163354 | − | 0.999867i | \(-0.494800\pi\) | ||||
0.0163354 | + | 0.999867i | \(0.494800\pi\) | |||||||
\(384\) | 1.59777 | 0.0815358 | ||||||||
\(385\) | 0.547659 | 0.0279113 | ||||||||
\(386\) | 17.2120 | 0.876069 | ||||||||
\(387\) | 2.79363 | 0.142008 | ||||||||
\(388\) | 9.40196 | 0.477312 | ||||||||
\(389\) | 32.9254 | 1.66938 | 0.834692 | − | 0.550717i | \(-0.185646\pi\) | ||||
0.834692 | + | 0.550717i | \(0.185646\pi\) | |||||||
\(390\) | 1.15155 | 0.0583108 | ||||||||
\(391\) | −22.6558 | −1.14575 | ||||||||
\(392\) | 6.84127 | 0.345536 | ||||||||
\(393\) | 1.31977 | 0.0665738 | ||||||||
\(394\) | 3.88082 | 0.195513 | ||||||||
\(395\) | 4.07375 | 0.204973 | ||||||||
\(396\) | −1.64427 | −0.0826277 | ||||||||
\(397\) | 1.29574 | 0.0650312 | 0.0325156 | − | 0.999471i | \(-0.489648\pi\) | ||||
0.0325156 | + | 0.999471i | \(0.489648\pi\) | |||||||
\(398\) | −7.81861 | −0.391912 | ||||||||
\(399\) | −0.0329740 | −0.00165076 | ||||||||
\(400\) | −4.86027 | −0.243014 | ||||||||
\(401\) | −19.7778 | −0.987654 | −0.493827 | − | 0.869560i | \(-0.664402\pi\) | ||||
−0.493827 | + | 0.869560i | \(0.664402\pi\) | |||||||
\(402\) | −13.3190 | −0.664290 | ||||||||
\(403\) | 1.36032 | 0.0677626 | ||||||||
\(404\) | −7.85216 | −0.390660 | ||||||||
\(405\) | −2.78807 | −0.138540 | ||||||||
\(406\) | 1.50386 | 0.0746355 | ||||||||
\(407\) | 36.9519 | 1.83164 | ||||||||
\(408\) | −10.4811 | −0.518893 | ||||||||
\(409\) | 22.1810 | 1.09678 | 0.548390 | − | 0.836223i | \(-0.315241\pi\) | ||||
0.548390 | + | 0.836223i | \(0.315241\pi\) | |||||||
\(410\) | −2.81540 | −0.139043 | ||||||||
\(411\) | −1.90066 | −0.0937526 | ||||||||
\(412\) | 4.51819 | 0.222595 | ||||||||
\(413\) | −0.502245 | −0.0247139 | ||||||||
\(414\) | 1.54427 | 0.0758967 | ||||||||
\(415\) | −3.29377 | −0.161685 | ||||||||
\(416\) | −1.92808 | −0.0945319 | ||||||||
\(417\) | −16.2710 | −0.796797 | ||||||||
\(418\) | −0.190485 | −0.00931691 | ||||||||
\(419\) | −20.0904 | −0.981482 | −0.490741 | − | 0.871306i | \(-0.663274\pi\) | ||||
−0.490741 | + | 0.871306i | \(0.663274\pi\) | |||||||
\(420\) | −0.237952 | −0.0116109 | ||||||||
\(421\) | −35.9570 | −1.75244 | −0.876218 | − | 0.481915i | \(-0.839941\pi\) | ||||
−0.876218 | + | 0.481915i | \(0.839941\pi\) | |||||||
\(422\) | 23.8920 | 1.16304 | ||||||||
\(423\) | 1.07855 | 0.0524409 | ||||||||
\(424\) | 1.36534 | 0.0663068 | ||||||||
\(425\) | 31.8827 | 1.54654 | ||||||||
\(426\) | 4.98598 | 0.241572 | ||||||||
\(427\) | −3.95041 | −0.191174 | ||||||||
\(428\) | 0.359079 | 0.0173567 | ||||||||
\(429\) | −11.3286 | −0.546948 | ||||||||
\(430\) | 2.33547 | 0.112626 | ||||||||
\(431\) | −13.3871 | −0.644833 | −0.322417 | − | 0.946598i | \(-0.604495\pi\) | ||||
−0.322417 | + | 0.946598i | \(0.604495\pi\) | |||||||
\(432\) | 5.50772 | 0.264990 | ||||||||
\(433\) | −5.92414 | −0.284696 | −0.142348 | − | 0.989817i | \(-0.545465\pi\) | ||||
−0.142348 | + | 0.989817i | \(0.545465\pi\) | |||||||
\(434\) | −0.281093 | −0.0134929 | ||||||||
\(435\) | 2.25441 | 0.108091 | ||||||||
\(436\) | 3.90597 | 0.187062 | ||||||||
\(437\) | 0.178900 | 0.00855794 | ||||||||
\(438\) | −20.2480 | −0.967485 | ||||||||
\(439\) | −5.36749 | −0.256176 | −0.128088 | − | 0.991763i | \(-0.540884\pi\) | ||||
−0.128088 | + | 0.991763i | \(0.540884\pi\) | |||||||
\(440\) | −1.37460 | −0.0655317 | ||||||||
\(441\) | 3.05896 | 0.145665 | ||||||||
\(442\) | 12.6479 | 0.601601 | ||||||||
\(443\) | −38.8316 | −1.84494 | −0.922472 | − | 0.386065i | \(-0.873834\pi\) | ||||
−0.922472 | + | 0.386065i | \(0.873834\pi\) | |||||||
\(444\) | −16.0552 | −0.761946 | ||||||||
\(445\) | 5.14034 | 0.243675 | ||||||||
\(446\) | 21.2389 | 1.00569 | ||||||||
\(447\) | −26.2654 | −1.24231 | ||||||||
\(448\) | 0.398412 | 0.0188232 | ||||||||
\(449\) | −2.29896 | −0.108495 | −0.0542474 | − | 0.998528i | \(-0.517276\pi\) | ||||
−0.0542474 | + | 0.998528i | \(0.517276\pi\) | |||||||
\(450\) | −2.17319 | −0.102445 | ||||||||
\(451\) | 27.6971 | 1.30420 | ||||||||
\(452\) | −5.24695 | −0.246796 | ||||||||
\(453\) | 37.4796 | 1.76095 | ||||||||
\(454\) | 2.92250 | 0.137160 | ||||||||
\(455\) | 0.287144 | 0.0134615 | ||||||||
\(456\) | 0.0827634 | 0.00387575 | ||||||||
\(457\) | 5.91510 | 0.276697 | 0.138348 | − | 0.990384i | \(-0.455821\pi\) | ||||
0.138348 | + | 0.990384i | \(0.455821\pi\) | |||||||
\(458\) | 15.9402 | 0.744835 | ||||||||
\(459\) | −36.1299 | −1.68640 | ||||||||
\(460\) | 1.29101 | 0.0601934 | ||||||||
\(461\) | −24.9692 | −1.16293 | −0.581467 | − | 0.813570i | \(-0.697521\pi\) | ||||
−0.581467 | + | 0.813570i | \(0.697521\pi\) | |||||||
\(462\) | 2.34090 | 0.108908 | ||||||||
\(463\) | −4.35799 | −0.202533 | −0.101266 | − | 0.994859i | \(-0.532289\pi\) | ||||
−0.101266 | + | 0.994859i | \(0.532289\pi\) | |||||||
\(464\) | −3.77464 | −0.175233 | ||||||||
\(465\) | −0.421380 | −0.0195410 | ||||||||
\(466\) | 2.42535 | 0.112352 | ||||||||
\(467\) | −40.4929 | −1.87379 | −0.936893 | − | 0.349616i | \(-0.886312\pi\) | ||||
−0.936893 | + | 0.349616i | \(0.886312\pi\) | |||||||
\(468\) | −0.862110 | −0.0398511 | ||||||||
\(469\) | −3.32116 | −0.153357 | ||||||||
\(470\) | 0.901666 | 0.0415907 | ||||||||
\(471\) | 15.5851 | 0.718124 | ||||||||
\(472\) | 1.26062 | 0.0580246 | ||||||||
\(473\) | −22.9756 | −1.05642 | ||||||||
\(474\) | 17.4127 | 0.799791 | ||||||||
\(475\) | −0.251759 | −0.0115515 | ||||||||
\(476\) | −2.61353 | −0.119791 | ||||||||
\(477\) | 0.610490 | 0.0279524 | ||||||||
\(478\) | −23.7583 | −1.08668 | ||||||||
\(479\) | 6.16146 | 0.281524 | 0.140762 | − | 0.990043i | \(-0.455045\pi\) | ||||
0.140762 | + | 0.990043i | \(0.455045\pi\) | |||||||
\(480\) | 0.597250 | 0.0272606 | ||||||||
\(481\) | 19.3743 | 0.883394 | ||||||||
\(482\) | −7.40717 | −0.337387 | ||||||||
\(483\) | −2.19853 | −0.100037 | ||||||||
\(484\) | 2.52293 | 0.114679 | ||||||||
\(485\) | 3.51448 | 0.159584 | ||||||||
\(486\) | 4.60594 | 0.208930 | ||||||||
\(487\) | −7.85545 | −0.355964 | −0.177982 | − | 0.984034i | \(-0.556957\pi\) | ||||
−0.177982 | + | 0.984034i | \(0.556957\pi\) | |||||||
\(488\) | 9.91540 | 0.448849 | ||||||||
\(489\) | −12.8842 | −0.582644 | ||||||||
\(490\) | 2.55728 | 0.115526 | ||||||||
\(491\) | −23.6342 | −1.06660 | −0.533299 | − | 0.845927i | \(-0.679048\pi\) | ||||
−0.533299 | + | 0.845927i | \(0.679048\pi\) | |||||||
\(492\) | −12.0341 | −0.542537 | ||||||||
\(493\) | 24.7611 | 1.11518 | ||||||||
\(494\) | −0.0998734 | −0.00449352 | ||||||||
\(495\) | −0.614632 | −0.0276257 | ||||||||
\(496\) | 0.705533 | 0.0316794 | ||||||||
\(497\) | 1.24328 | 0.0557688 | ||||||||
\(498\) | −14.0788 | −0.630884 | ||||||||
\(499\) | −8.48110 | −0.379666 | −0.189833 | − | 0.981816i | \(-0.560795\pi\) | ||||
−0.189833 | + | 0.981816i | \(0.560795\pi\) | |||||||
\(500\) | −3.68580 | −0.164834 | ||||||||
\(501\) | −37.4225 | −1.67191 | ||||||||
\(502\) | −2.72576 | −0.121657 | ||||||||
\(503\) | −14.6700 | −0.654101 | −0.327051 | − | 0.945007i | \(-0.606055\pi\) | ||||
−0.327051 | + | 0.945007i | \(0.606055\pi\) | |||||||
\(504\) | 0.178144 | 0.00793514 | ||||||||
\(505\) | −2.93516 | −0.130613 | ||||||||
\(506\) | −12.7005 | −0.564606 | ||||||||
\(507\) | 14.8313 | 0.658681 | ||||||||
\(508\) | 10.5093 | 0.466274 | ||||||||
\(509\) | −6.68312 | −0.296224 | −0.148112 | − | 0.988971i | \(-0.547320\pi\) | ||||
−0.148112 | + | 0.988971i | \(0.547320\pi\) | |||||||
\(510\) | −3.91788 | −0.173486 | ||||||||
\(511\) | −5.04893 | −0.223352 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0.285297 | 0.0125962 | ||||||||
\(514\) | 12.2989 | 0.542481 | ||||||||
\(515\) | 1.68891 | 0.0744223 | ||||||||
\(516\) | 9.98264 | 0.439461 | ||||||||
\(517\) | −8.87030 | −0.390115 | ||||||||
\(518\) | −4.00345 | −0.175901 | ||||||||
\(519\) | 1.46076 | 0.0641201 | ||||||||
\(520\) | −0.720722 | −0.0316057 | ||||||||
\(521\) | 9.19072 | 0.402653 | 0.201326 | − | 0.979524i | \(-0.435475\pi\) | ||||
0.201326 | + | 0.979524i | \(0.435475\pi\) | |||||||
\(522\) | −1.68777 | −0.0738717 | ||||||||
\(523\) | 30.0993 | 1.31615 | 0.658076 | − | 0.752952i | \(-0.271371\pi\) | ||||
0.658076 | + | 0.752952i | \(0.271371\pi\) | |||||||
\(524\) | −0.826010 | −0.0360844 | ||||||||
\(525\) | 3.09391 | 0.135029 | ||||||||
\(526\) | −29.1191 | −1.26965 | ||||||||
\(527\) | −4.62819 | −0.201607 | ||||||||
\(528\) | −5.87556 | −0.255701 | ||||||||
\(529\) | −11.0719 | −0.481387 | ||||||||
\(530\) | 0.510368 | 0.0221690 | ||||||||
\(531\) | 0.563665 | 0.0244610 | ||||||||
\(532\) | 0.0206375 | 0.000894749 0 | ||||||||
\(533\) | 14.5219 | 0.629013 | ||||||||
\(534\) | 21.9717 | 0.950808 | ||||||||
\(535\) | 0.134225 | 0.00580304 | ||||||||
\(536\) | 8.33599 | 0.360060 | ||||||||
\(537\) | 14.0033 | 0.604286 | ||||||||
\(538\) | −30.1751 | −1.30094 | ||||||||
\(539\) | −25.1578 | −1.08362 | ||||||||
\(540\) | 2.05880 | 0.0885967 | ||||||||
\(541\) | −28.5534 | −1.22761 | −0.613803 | − | 0.789459i | \(-0.710361\pi\) | ||||
−0.613803 | + | 0.789459i | \(0.710361\pi\) | |||||||
\(542\) | −9.70043 | −0.416669 | ||||||||
\(543\) | −27.2830 | −1.17082 | ||||||||
\(544\) | 6.55986 | 0.281251 | ||||||||
\(545\) | 1.46006 | 0.0625422 | ||||||||
\(546\) | 1.22736 | 0.0525261 | ||||||||
\(547\) | −15.6193 | −0.667832 | −0.333916 | − | 0.942603i | \(-0.608370\pi\) | ||||
−0.333916 | + | 0.942603i | \(0.608370\pi\) | |||||||
\(548\) | 1.18957 | 0.0508159 | ||||||||
\(549\) | 4.43351 | 0.189218 | ||||||||
\(550\) | 17.8729 | 0.762105 | ||||||||
\(551\) | −0.195524 | −0.00832961 | ||||||||
\(552\) | 5.51823 | 0.234871 | ||||||||
\(553\) | 4.34195 | 0.184638 | ||||||||
\(554\) | 10.9154 | 0.463751 | ||||||||
\(555\) | −6.00148 | −0.254749 | ||||||||
\(556\) | 10.1836 | 0.431881 | ||||||||
\(557\) | 9.53629 | 0.404066 | 0.202033 | − | 0.979379i | \(-0.435245\pi\) | ||||
0.202033 | + | 0.979379i | \(0.435245\pi\) | |||||||
\(558\) | 0.315468 | 0.0133548 | ||||||||
\(559\) | −12.0464 | −0.509508 | ||||||||
\(560\) | 0.148928 | 0.00629334 | ||||||||
\(561\) | 38.5428 | 1.62728 | ||||||||
\(562\) | −14.3811 | −0.606629 | ||||||||
\(563\) | 0.185083 | 0.00780032 | 0.00390016 | − | 0.999992i | \(-0.498759\pi\) | ||||
0.00390016 | + | 0.999992i | \(0.498759\pi\) | |||||||
\(564\) | 3.85405 | 0.162285 | ||||||||
\(565\) | −1.96132 | −0.0825135 | ||||||||
\(566\) | 21.9537 | 0.922783 | ||||||||
\(567\) | −2.97162 | −0.124796 | ||||||||
\(568\) | −3.12059 | −0.130937 | ||||||||
\(569\) | 35.0989 | 1.47142 | 0.735711 | − | 0.677295i | \(-0.236848\pi\) | ||||
0.735711 | + | 0.677295i | \(0.236848\pi\) | |||||||
\(570\) | 0.0309372 | 0.00129582 | ||||||||
\(571\) | −45.7097 | −1.91289 | −0.956446 | − | 0.291910i | \(-0.905709\pi\) | ||||
−0.956446 | + | 0.291910i | \(0.905709\pi\) | |||||||
\(572\) | 7.09023 | 0.296458 | ||||||||
\(573\) | 34.6066 | 1.44571 | ||||||||
\(574\) | −3.00076 | −0.125249 | ||||||||
\(575\) | −16.7860 | −0.700023 | ||||||||
\(576\) | −0.447134 | −0.0186306 | ||||||||
\(577\) | −6.40613 | −0.266691 | −0.133345 | − | 0.991070i | \(-0.542572\pi\) | ||||
−0.133345 | + | 0.991070i | \(0.542572\pi\) | |||||||
\(578\) | −26.0317 | −1.08278 | ||||||||
\(579\) | 27.5008 | 1.14290 | ||||||||
\(580\) | −1.41097 | −0.0585874 | ||||||||
\(581\) | −3.51061 | −0.145645 | ||||||||
\(582\) | 15.0222 | 0.622689 | ||||||||
\(583\) | −5.02084 | −0.207942 | ||||||||
\(584\) | 12.6726 | 0.524398 | ||||||||
\(585\) | −0.322259 | −0.0133238 | ||||||||
\(586\) | 9.89021 | 0.408561 | ||||||||
\(587\) | −39.9071 | −1.64714 | −0.823571 | − | 0.567214i | \(-0.808021\pi\) | ||||
−0.823571 | + | 0.567214i | \(0.808021\pi\) | |||||||
\(588\) | 10.9308 | 0.450777 | ||||||||
\(589\) | 0.0365462 | 0.00150586 | ||||||||
\(590\) | 0.471222 | 0.0193999 | ||||||||
\(591\) | 6.20065 | 0.255061 | ||||||||
\(592\) | 10.0485 | 0.412991 | ||||||||
\(593\) | 3.25624 | 0.133718 | 0.0668590 | − | 0.997762i | \(-0.478702\pi\) | ||||
0.0668590 | + | 0.997762i | \(0.478702\pi\) | |||||||
\(594\) | −20.2539 | −0.831026 | ||||||||
\(595\) | −0.976943 | −0.0400508 | ||||||||
\(596\) | 16.4388 | 0.673359 | ||||||||
\(597\) | −12.4923 | −0.511277 | ||||||||
\(598\) | −6.65903 | −0.272308 | ||||||||
\(599\) | 6.07518 | 0.248225 | 0.124113 | − | 0.992268i | \(-0.460392\pi\) | ||||
0.124113 | + | 0.992268i | \(0.460392\pi\) | |||||||
\(600\) | −7.76559 | −0.317029 | ||||||||
\(601\) | 9.63572 | 0.393049 | 0.196525 | − | 0.980499i | \(-0.437034\pi\) | ||||
0.196525 | + | 0.980499i | \(0.437034\pi\) | |||||||
\(602\) | 2.48922 | 0.101453 | ||||||||
\(603\) | 3.72730 | 0.151787 | ||||||||
\(604\) | −23.4575 | −0.954470 | ||||||||
\(605\) | 0.943079 | 0.0383416 | ||||||||
\(606\) | −12.5459 | −0.509644 | ||||||||
\(607\) | −21.1397 | −0.858034 | −0.429017 | − | 0.903297i | \(-0.641140\pi\) | ||||
−0.429017 | + | 0.903297i | \(0.641140\pi\) | |||||||
\(608\) | −0.0517994 | −0.00210074 | ||||||||
\(609\) | 2.40283 | 0.0973675 | ||||||||
\(610\) | 3.70640 | 0.150068 | ||||||||
\(611\) | −4.65081 | −0.188151 | ||||||||
\(612\) | 2.93313 | 0.118565 | ||||||||
\(613\) | 33.5186 | 1.35381 | 0.676903 | − | 0.736072i | \(-0.263322\pi\) | ||||
0.676903 | + | 0.736072i | \(0.263322\pi\) | |||||||
\(614\) | 6.45061 | 0.260325 | ||||||||
\(615\) | −4.49836 | −0.181392 | ||||||||
\(616\) | −1.46510 | −0.0590307 | ||||||||
\(617\) | −18.8008 | −0.756893 | −0.378446 | − | 0.925623i | \(-0.623542\pi\) | ||||
−0.378446 | + | 0.925623i | \(0.623542\pi\) | |||||||
\(618\) | 7.21902 | 0.290391 | ||||||||
\(619\) | −39.8438 | −1.60146 | −0.800728 | − | 0.599028i | \(-0.795554\pi\) | ||||
−0.800728 | + | 0.599028i | \(0.795554\pi\) | |||||||
\(620\) | 0.263730 | 0.0105917 | ||||||||
\(621\) | 19.0221 | 0.763329 | ||||||||
\(622\) | 7.46794 | 0.299437 | ||||||||
\(623\) | 5.47875 | 0.219502 | ||||||||
\(624\) | −3.08063 | −0.123324 | ||||||||
\(625\) | 22.9236 | 0.916944 | ||||||||
\(626\) | 26.0247 | 1.04016 | ||||||||
\(627\) | −0.304350 | −0.0121546 | ||||||||
\(628\) | −9.75430 | −0.389239 | ||||||||
\(629\) | −65.9168 | −2.62827 | ||||||||
\(630\) | 0.0665905 | 0.00265303 | ||||||||
\(631\) | −28.0231 | −1.11558 | −0.557792 | − | 0.829981i | \(-0.688351\pi\) | ||||
−0.557792 | + | 0.829981i | \(0.688351\pi\) | |||||||
\(632\) | −10.8981 | −0.433504 | ||||||||
\(633\) | 38.1739 | 1.51727 | ||||||||
\(634\) | 23.6850 | 0.940652 | ||||||||
\(635\) | 3.92840 | 0.155894 | ||||||||
\(636\) | 2.18150 | 0.0865020 | ||||||||
\(637\) | −13.1905 | −0.522627 | ||||||||
\(638\) | 13.8807 | 0.549542 | ||||||||
\(639\) | −1.39532 | −0.0551980 | ||||||||
\(640\) | −0.373803 | −0.0147759 | ||||||||
\(641\) | −15.7649 | −0.622676 | −0.311338 | − | 0.950299i | \(-0.600777\pi\) | ||||
−0.311338 | + | 0.950299i | \(0.600777\pi\) | |||||||
\(642\) | 0.573725 | 0.0226431 | ||||||||
\(643\) | −43.0963 | −1.69955 | −0.849776 | − | 0.527143i | \(-0.823263\pi\) | ||||
−0.849776 | + | 0.527143i | \(0.823263\pi\) | |||||||
\(644\) | 1.37600 | 0.0542220 | ||||||||
\(645\) | 3.73154 | 0.146929 | ||||||||
\(646\) | 0.339796 | 0.0133691 | ||||||||
\(647\) | −14.0227 | −0.551288 | −0.275644 | − | 0.961260i | \(-0.588891\pi\) | ||||
−0.275644 | + | 0.961260i | \(0.588891\pi\) | |||||||
\(648\) | 7.45867 | 0.293004 | ||||||||
\(649\) | −4.63574 | −0.181969 | ||||||||
\(650\) | 9.37099 | 0.367561 | ||||||||
\(651\) | −0.449122 | −0.0176025 | ||||||||
\(652\) | 8.06388 | 0.315806 | ||||||||
\(653\) | −10.0906 | −0.394875 | −0.197437 | − | 0.980316i | \(-0.563262\pi\) | ||||
−0.197437 | + | 0.980316i | \(0.563262\pi\) | |||||||
\(654\) | 6.24084 | 0.244036 | ||||||||
\(655\) | −0.308765 | −0.0120644 | ||||||||
\(656\) | 7.53179 | 0.294067 | ||||||||
\(657\) | 5.66637 | 0.221066 | ||||||||
\(658\) | 0.961027 | 0.0374647 | ||||||||
\(659\) | −28.3266 | −1.10345 | −0.551724 | − | 0.834027i | \(-0.686030\pi\) | ||||
−0.551724 | + | 0.834027i | \(0.686030\pi\) | |||||||
\(660\) | −2.19630 | −0.0854909 | ||||||||
\(661\) | −44.1576 | −1.71753 | −0.858767 | − | 0.512367i | \(-0.828769\pi\) | ||||
−0.858767 | + | 0.512367i | \(0.828769\pi\) | |||||||
\(662\) | −25.6303 | −0.996148 | ||||||||
\(663\) | 20.2085 | 0.784832 | ||||||||
\(664\) | 8.81151 | 0.341953 | ||||||||
\(665\) | 0.00771435 | 0.000299150 0 | ||||||||
\(666\) | 4.49303 | 0.174101 | ||||||||
\(667\) | −13.0365 | −0.504776 | ||||||||
\(668\) | 23.4217 | 0.906214 | ||||||||
\(669\) | 33.9349 | 1.31200 | ||||||||
\(670\) | 3.11601 | 0.120382 | ||||||||
\(671\) | −36.4624 | −1.40762 | ||||||||
\(672\) | 0.636571 | 0.0245562 | ||||||||
\(673\) | −35.1435 | −1.35468 | −0.677342 | − | 0.735668i | \(-0.736868\pi\) | ||||
−0.677342 | + | 0.735668i | \(0.736868\pi\) | |||||||
\(674\) | 26.0207 | 1.00228 | ||||||||
\(675\) | −26.7690 | −1.03034 | ||||||||
\(676\) | −9.28251 | −0.357019 | ||||||||
\(677\) | 37.4090 | 1.43774 | 0.718872 | − | 0.695143i | \(-0.244659\pi\) | ||||
0.718872 | + | 0.695143i | \(0.244659\pi\) | |||||||
\(678\) | −8.38341 | −0.321963 | ||||||||
\(679\) | 3.74585 | 0.143753 | ||||||||
\(680\) | 2.45209 | 0.0940334 | ||||||||
\(681\) | 4.66948 | 0.178935 | ||||||||
\(682\) | −2.59449 | −0.0993483 | ||||||||
\(683\) | −7.28168 | −0.278626 | −0.139313 | − | 0.990248i | \(-0.544489\pi\) | ||||
−0.139313 | + | 0.990248i | \(0.544489\pi\) | |||||||
\(684\) | −0.0231613 | −0.000885593 0 | ||||||||
\(685\) | 0.444665 | 0.0169898 | ||||||||
\(686\) | 5.51453 | 0.210546 | ||||||||
\(687\) | 25.4687 | 0.971691 | ||||||||
\(688\) | −6.24786 | −0.238197 | ||||||||
\(689\) | −2.63249 | −0.100290 | ||||||||
\(690\) | 2.06273 | 0.0785267 | ||||||||
\(691\) | 21.9578 | 0.835315 | 0.417658 | − | 0.908604i | \(-0.362851\pi\) | ||||
0.417658 | + | 0.908604i | \(0.362851\pi\) | |||||||
\(692\) | −0.914248 | −0.0347545 | ||||||||
\(693\) | −0.655097 | −0.0248851 | ||||||||
\(694\) | 25.9125 | 0.983625 | ||||||||
\(695\) | 3.80666 | 0.144395 | ||||||||
\(696\) | −6.03101 | −0.228605 | ||||||||
\(697\) | −49.4074 | −1.87144 | ||||||||
\(698\) | −27.9290 | −1.05713 | ||||||||
\(699\) | 3.87516 | 0.146572 | ||||||||
\(700\) | −1.93639 | −0.0731887 | ||||||||
\(701\) | 48.8467 | 1.84492 | 0.922458 | − | 0.386098i | \(-0.126177\pi\) | ||||
0.922458 | + | 0.386098i | \(0.126177\pi\) | |||||||
\(702\) | −10.6193 | −0.400801 | ||||||||
\(703\) | 0.520507 | 0.0196313 | ||||||||
\(704\) | 3.67735 | 0.138595 | ||||||||
\(705\) | 1.44065 | 0.0542581 | ||||||||
\(706\) | −2.49607 | −0.0939410 | ||||||||
\(707\) | −3.12840 | −0.117655 | ||||||||
\(708\) | 2.01418 | 0.0756974 | ||||||||
\(709\) | 31.1783 | 1.17093 | 0.585463 | − | 0.810699i | \(-0.300913\pi\) | ||||
0.585463 | + | 0.810699i | \(0.300913\pi\) | |||||||
\(710\) | −1.16648 | −0.0437774 | ||||||||
\(711\) | −4.87292 | −0.182749 | ||||||||
\(712\) | −13.7515 | −0.515358 | ||||||||
\(713\) | 2.43671 | 0.0912553 | ||||||||
\(714\) | −4.17581 | −0.156276 | ||||||||
\(715\) | 2.65035 | 0.0991174 | ||||||||
\(716\) | −8.76427 | −0.327536 | ||||||||
\(717\) | −37.9604 | −1.41766 | ||||||||
\(718\) | 28.6233 | 1.06821 | ||||||||
\(719\) | −1.84751 | −0.0689005 | −0.0344503 | − | 0.999406i | \(-0.510968\pi\) | ||||
−0.0344503 | + | 0.999406i | \(0.510968\pi\) | |||||||
\(720\) | −0.167140 | −0.00622893 | ||||||||
\(721\) | 1.80010 | 0.0670392 | ||||||||
\(722\) | 18.9973 | 0.707007 | ||||||||
\(723\) | −11.8349 | −0.440146 | ||||||||
\(724\) | 17.0757 | 0.634612 | ||||||||
\(725\) | 18.3458 | 0.681346 | ||||||||
\(726\) | 4.03106 | 0.149607 | ||||||||
\(727\) | −12.7001 | −0.471019 | −0.235510 | − | 0.971872i | \(-0.575676\pi\) | ||||
−0.235510 | + | 0.971872i | \(0.575676\pi\) | |||||||
\(728\) | −0.768171 | −0.0284703 | ||||||||
\(729\) | 29.7352 | 1.10131 | ||||||||
\(730\) | 4.73707 | 0.175327 | ||||||||
\(731\) | 40.9851 | 1.51589 | ||||||||
\(732\) | 15.8425 | 0.585556 | ||||||||
\(733\) | −40.9636 | −1.51303 | −0.756513 | − | 0.653979i | \(-0.773099\pi\) | ||||
−0.756513 | + | 0.653979i | \(0.773099\pi\) | |||||||
\(734\) | 10.7527 | 0.396891 | ||||||||
\(735\) | 4.08595 | 0.150713 | ||||||||
\(736\) | −3.45371 | −0.127305 | ||||||||
\(737\) | −30.6544 | −1.12917 | ||||||||
\(738\) | 3.36772 | 0.123967 | ||||||||
\(739\) | −41.7795 | −1.53688 | −0.768442 | − | 0.639919i | \(-0.778968\pi\) | ||||
−0.768442 | + | 0.639919i | \(0.778968\pi\) | |||||||
\(740\) | 3.75616 | 0.138079 | ||||||||
\(741\) | −0.159575 | −0.00586212 | ||||||||
\(742\) | 0.543968 | 0.0199697 | ||||||||
\(743\) | 4.55608 | 0.167146 | 0.0835731 | − | 0.996502i | \(-0.473367\pi\) | ||||
0.0835731 | + | 0.996502i | \(0.473367\pi\) | |||||||
\(744\) | 1.12728 | 0.0413280 | ||||||||
\(745\) | 6.14487 | 0.225130 | ||||||||
\(746\) | −30.6816 | −1.12333 | ||||||||
\(747\) | 3.93992 | 0.144154 | ||||||||
\(748\) | −24.1229 | −0.882021 | ||||||||
\(749\) | 0.143061 | 0.00522735 | ||||||||
\(750\) | −5.88905 | −0.215038 | ||||||||
\(751\) | −40.0084 | −1.45993 | −0.729963 | − | 0.683487i | \(-0.760463\pi\) | ||||
−0.729963 | + | 0.683487i | \(0.760463\pi\) | |||||||
\(752\) | −2.41214 | −0.0879618 | ||||||||
\(753\) | −4.35513 | −0.158710 | ||||||||
\(754\) | 7.27782 | 0.265042 | ||||||||
\(755\) | −8.76846 | −0.319117 | ||||||||
\(756\) | 2.19434 | 0.0798075 | ||||||||
\(757\) | −28.2055 | −1.02515 | −0.512573 | − | 0.858644i | \(-0.671308\pi\) | ||||
−0.512573 | + | 0.858644i | \(0.671308\pi\) | |||||||
\(758\) | 13.8183 | 0.501901 | ||||||||
\(759\) | −20.2925 | −0.736570 | ||||||||
\(760\) | −0.0193627 | −0.000702361 0 | ||||||||
\(761\) | 19.8495 | 0.719545 | 0.359772 | − | 0.933040i | \(-0.382854\pi\) | ||||
0.359772 | + | 0.933040i | \(0.382854\pi\) | |||||||
\(762\) | 16.7914 | 0.608288 | ||||||||
\(763\) | 1.55619 | 0.0563377 | ||||||||
\(764\) | −21.6593 | −0.783608 | ||||||||
\(765\) | 1.09641 | 0.0396409 | ||||||||
\(766\) | −0.639382 | −0.0231018 | ||||||||
\(767\) | −2.43057 | −0.0877629 | ||||||||
\(768\) | −1.59777 | −0.0576545 | ||||||||
\(769\) | 45.9680 | 1.65765 | 0.828825 | − | 0.559508i | \(-0.189010\pi\) | ||||
0.828825 | + | 0.559508i | \(0.189010\pi\) | |||||||
\(770\) | −0.547659 | −0.0197363 | ||||||||
\(771\) | 19.6508 | 0.707707 | ||||||||
\(772\) | −17.2120 | −0.619474 | ||||||||
\(773\) | 42.8945 | 1.54281 | 0.771404 | − | 0.636346i | \(-0.219555\pi\) | ||||
0.771404 | + | 0.636346i | \(0.219555\pi\) | |||||||
\(774\) | −2.79363 | −0.100415 | ||||||||
\(775\) | −3.42908 | −0.123176 | ||||||||
\(776\) | −9.40196 | −0.337511 | ||||||||
\(777\) | −6.39659 | −0.229476 | ||||||||
\(778\) | −32.9254 | −1.18043 | ||||||||
\(779\) | 0.390142 | 0.0139783 | ||||||||
\(780\) | −1.15155 | −0.0412320 | ||||||||
\(781\) | 11.4755 | 0.410626 | ||||||||
\(782\) | 22.6558 | 0.810171 | ||||||||
\(783\) | −20.7897 | −0.742963 | ||||||||
\(784\) | −6.84127 | −0.244331 | ||||||||
\(785\) | −3.64618 | −0.130138 | ||||||||
\(786\) | −1.31977 | −0.0470748 | ||||||||
\(787\) | −32.3714 | −1.15392 | −0.576958 | − | 0.816774i | \(-0.695760\pi\) | ||||
−0.576958 | + | 0.816774i | \(0.695760\pi\) | |||||||
\(788\) | −3.88082 | −0.138248 | ||||||||
\(789\) | −46.5256 | −1.65635 | ||||||||
\(790\) | −4.07375 | −0.144937 | ||||||||
\(791\) | −2.09045 | −0.0743277 | ||||||||
\(792\) | 1.64427 | 0.0584266 | ||||||||
\(793\) | −19.1177 | −0.678889 | ||||||||
\(794\) | −1.29574 | −0.0459840 | ||||||||
\(795\) | 0.815450 | 0.0289210 | ||||||||
\(796\) | 7.81861 | 0.277123 | ||||||||
\(797\) | −6.44983 | −0.228465 | −0.114232 | − | 0.993454i | \(-0.536441\pi\) | ||||
−0.114232 | + | 0.993454i | \(0.536441\pi\) | |||||||
\(798\) | 0.0329740 | 0.00116727 | ||||||||
\(799\) | 15.8233 | 0.559788 | ||||||||
\(800\) | 4.86027 | 0.171837 | ||||||||
\(801\) | −6.14875 | −0.217255 | ||||||||
\(802\) | 19.7778 | 0.698377 | ||||||||
\(803\) | −46.6018 | −1.64454 | ||||||||
\(804\) | 13.3190 | 0.469724 | ||||||||
\(805\) | 0.514352 | 0.0181285 | ||||||||
\(806\) | −1.36032 | −0.0479154 | ||||||||
\(807\) | −48.2129 | −1.69717 | ||||||||
\(808\) | 7.85216 | 0.276238 | ||||||||
\(809\) | −20.7450 | −0.729355 | −0.364677 | − | 0.931134i | \(-0.618821\pi\) | ||||
−0.364677 | + | 0.931134i | \(0.618821\pi\) | |||||||
\(810\) | 2.78807 | 0.0979628 | ||||||||
\(811\) | 3.44480 | 0.120963 | 0.0604817 | − | 0.998169i | \(-0.480736\pi\) | ||||
0.0604817 | + | 0.998169i | \(0.480736\pi\) | |||||||
\(812\) | −1.50386 | −0.0527753 | ||||||||
\(813\) | −15.4990 | −0.543575 | ||||||||
\(814\) | −36.9519 | −1.29516 | ||||||||
\(815\) | 3.01430 | 0.105586 | ||||||||
\(816\) | 10.4811 | 0.366913 | ||||||||
\(817\) | −0.323635 | −0.0113226 | ||||||||
\(818\) | −22.1810 | −0.775541 | ||||||||
\(819\) | −0.343475 | −0.0120020 | ||||||||
\(820\) | 2.81540 | 0.0983181 | ||||||||
\(821\) | 25.3199 | 0.883671 | 0.441836 | − | 0.897096i | \(-0.354327\pi\) | ||||
0.441836 | + | 0.897096i | \(0.354327\pi\) | |||||||
\(822\) | 1.90066 | 0.0662931 | ||||||||
\(823\) | 24.5968 | 0.857391 | 0.428695 | − | 0.903449i | \(-0.358973\pi\) | ||||
0.428695 | + | 0.903449i | \(0.358973\pi\) | |||||||
\(824\) | −4.51819 | −0.157398 | ||||||||
\(825\) | 28.5568 | 0.994221 | ||||||||
\(826\) | 0.502245 | 0.0174754 | ||||||||
\(827\) | −19.2282 | −0.668630 | −0.334315 | − | 0.942461i | \(-0.608505\pi\) | ||||
−0.334315 | + | 0.942461i | \(0.608505\pi\) | |||||||
\(828\) | −1.54427 | −0.0536671 | ||||||||
\(829\) | −12.2055 | −0.423914 | −0.211957 | − | 0.977279i | \(-0.567984\pi\) | ||||
−0.211957 | + | 0.977279i | \(0.567984\pi\) | |||||||
\(830\) | 3.29377 | 0.114328 | ||||||||
\(831\) | 17.4403 | 0.604996 | ||||||||
\(832\) | 1.92808 | 0.0668442 | ||||||||
\(833\) | 44.8777 | 1.55492 | ||||||||
\(834\) | 16.2710 | 0.563420 | ||||||||
\(835\) | 8.75511 | 0.302983 | ||||||||
\(836\) | 0.190485 | 0.00658805 | ||||||||
\(837\) | 3.88588 | 0.134316 | ||||||||
\(838\) | 20.0904 | 0.694012 | ||||||||
\(839\) | 44.7209 | 1.54394 | 0.771968 | − | 0.635661i | \(-0.219273\pi\) | ||||
0.771968 | + | 0.635661i | \(0.219273\pi\) | |||||||
\(840\) | 0.237952 | 0.00821012 | ||||||||
\(841\) | −14.7521 | −0.508692 | ||||||||
\(842\) | 35.9570 | 1.23916 | ||||||||
\(843\) | −22.9776 | −0.791391 | ||||||||
\(844\) | −23.8920 | −0.822396 | ||||||||
\(845\) | −3.46983 | −0.119366 | ||||||||
\(846\) | −1.07855 | −0.0370813 | ||||||||
\(847\) | 1.00517 | 0.0345379 | ||||||||
\(848\) | −1.36534 | −0.0468860 | ||||||||
\(849\) | 35.0769 | 1.20384 | ||||||||
\(850\) | −31.8827 | −1.09357 | ||||||||
\(851\) | 34.7046 | 1.18966 | ||||||||
\(852\) | −4.98598 | −0.170817 | ||||||||
\(853\) | −31.2113 | −1.06865 | −0.534327 | − | 0.845278i | \(-0.679435\pi\) | ||||
−0.534327 | + | 0.845278i | \(0.679435\pi\) | |||||||
\(854\) | 3.95041 | 0.135180 | ||||||||
\(855\) | −0.00865774 | −0.000296088 0 | ||||||||
\(856\) | −0.359079 | −0.0122731 | ||||||||
\(857\) | 29.0720 | 0.993079 | 0.496539 | − | 0.868014i | \(-0.334604\pi\) | ||||
0.496539 | + | 0.868014i | \(0.334604\pi\) | |||||||
\(858\) | 11.3286 | 0.386751 | ||||||||
\(859\) | 26.5897 | 0.907227 | 0.453614 | − | 0.891198i | \(-0.350135\pi\) | ||||
0.453614 | + | 0.891198i | \(0.350135\pi\) | |||||||
\(860\) | −2.33547 | −0.0796388 | ||||||||
\(861\) | −4.79452 | −0.163397 | ||||||||
\(862\) | 13.3871 | 0.455966 | ||||||||
\(863\) | 26.2425 | 0.893307 | 0.446653 | − | 0.894707i | \(-0.352616\pi\) | ||||
0.446653 | + | 0.894707i | \(0.352616\pi\) | |||||||
\(864\) | −5.50772 | −0.187377 | ||||||||
\(865\) | −0.341748 | −0.0116198 | ||||||||
\(866\) | 5.92414 | 0.201311 | ||||||||
\(867\) | −41.5927 | −1.41256 | ||||||||
\(868\) | 0.281093 | 0.00954091 | ||||||||
\(869\) | 40.0763 | 1.35949 | ||||||||
\(870\) | −2.25441 | −0.0764316 | ||||||||
\(871\) | −16.0725 | −0.544594 | ||||||||
\(872\) | −3.90597 | −0.132273 | ||||||||
\(873\) | −4.20393 | −0.142282 | ||||||||
\(874\) | −0.178900 | −0.00605138 | ||||||||
\(875\) | −1.46847 | −0.0496432 | ||||||||
\(876\) | 20.2480 | 0.684115 | ||||||||
\(877\) | 2.05062 | 0.0692445 | 0.0346223 | − | 0.999400i | \(-0.488977\pi\) | ||||
0.0346223 | + | 0.999400i | \(0.488977\pi\) | |||||||
\(878\) | 5.36749 | 0.181144 | ||||||||
\(879\) | 15.8023 | 0.532997 | ||||||||
\(880\) | 1.37460 | 0.0463379 | ||||||||
\(881\) | 20.4402 | 0.688649 | 0.344325 | − | 0.938851i | \(-0.388108\pi\) | ||||
0.344325 | + | 0.938851i | \(0.388108\pi\) | |||||||
\(882\) | −3.05896 | −0.103001 | ||||||||
\(883\) | −12.7597 | −0.429398 | −0.214699 | − | 0.976680i | \(-0.568877\pi\) | ||||
−0.214699 | + | 0.976680i | \(0.568877\pi\) | |||||||
\(884\) | −12.6479 | −0.425396 | ||||||||
\(885\) | 0.752905 | 0.0253086 | ||||||||
\(886\) | 38.8316 | 1.30457 | ||||||||
\(887\) | −17.9443 | −0.602512 | −0.301256 | − | 0.953543i | \(-0.597406\pi\) | ||||
−0.301256 | + | 0.953543i | \(0.597406\pi\) | |||||||
\(888\) | 16.0552 | 0.538777 | ||||||||
\(889\) | 4.18702 | 0.140428 | ||||||||
\(890\) | −5.14034 | −0.172305 | ||||||||
\(891\) | −27.4282 | −0.918878 | ||||||||
\(892\) | −21.2389 | −0.711131 | ||||||||
\(893\) | −0.124947 | −0.00418121 | ||||||||
\(894\) | 26.2654 | 0.878446 | ||||||||
\(895\) | −3.27611 | −0.109508 | ||||||||
\(896\) | −0.398412 | −0.0133100 | ||||||||
\(897\) | −10.6396 | −0.355246 | ||||||||
\(898\) | 2.29896 | 0.0767174 | ||||||||
\(899\) | −2.66314 | −0.0888206 | ||||||||
\(900\) | 2.17319 | 0.0724397 | ||||||||
\(901\) | 8.95644 | 0.298382 | ||||||||
\(902\) | −27.6971 | −0.922211 | ||||||||
\(903\) | 3.97720 | 0.132353 | ||||||||
\(904\) | 5.24695 | 0.174511 | ||||||||
\(905\) | 6.38293 | 0.212176 | ||||||||
\(906\) | −37.4796 | −1.24518 | ||||||||
\(907\) | 53.9235 | 1.79050 | 0.895250 | − | 0.445564i | \(-0.146997\pi\) | ||||
0.895250 | + | 0.445564i | \(0.146997\pi\) | |||||||
\(908\) | −2.92250 | −0.0969865 | ||||||||
\(909\) | 3.51097 | 0.116451 | ||||||||
\(910\) | −0.287144 | −0.00951874 | ||||||||
\(911\) | −18.5141 | −0.613399 | −0.306699 | − | 0.951806i | \(-0.599225\pi\) | ||||
−0.306699 | + | 0.951806i | \(0.599225\pi\) | |||||||
\(912\) | −0.0827634 | −0.00274057 | ||||||||
\(913\) | −32.4030 | −1.07238 | ||||||||
\(914\) | −5.91510 | −0.195654 | ||||||||
\(915\) | 5.92198 | 0.195774 | ||||||||
\(916\) | −15.9402 | −0.526678 | ||||||||
\(917\) | −0.329093 | −0.0108676 | ||||||||
\(918\) | 36.1299 | 1.19246 | ||||||||
\(919\) | 42.4600 | 1.40063 | 0.700313 | − | 0.713836i | \(-0.253044\pi\) | ||||
0.700313 | + | 0.713836i | \(0.253044\pi\) | |||||||
\(920\) | −1.29101 | −0.0425632 | ||||||||
\(921\) | 10.3066 | 0.339613 | ||||||||
\(922\) | 24.9692 | 0.822318 | ||||||||
\(923\) | 6.01675 | 0.198044 | ||||||||
\(924\) | −2.34090 | −0.0770098 | ||||||||
\(925\) | −48.8385 | −1.60580 | ||||||||
\(926\) | 4.35799 | 0.143212 | ||||||||
\(927\) | −2.02023 | −0.0663532 | ||||||||
\(928\) | 3.77464 | 0.123909 | ||||||||
\(929\) | −52.0968 | −1.70924 | −0.854620 | − | 0.519254i | \(-0.826210\pi\) | ||||
−0.854620 | + | 0.519254i | \(0.826210\pi\) | |||||||
\(930\) | 0.421380 | 0.0138176 | ||||||||
\(931\) | −0.354373 | −0.0116141 | ||||||||
\(932\) | −2.42535 | −0.0794451 | ||||||||
\(933\) | 11.9320 | 0.390637 | ||||||||
\(934\) | 40.4929 | 1.32497 | ||||||||
\(935\) | −9.01721 | −0.294894 | ||||||||
\(936\) | 0.862110 | 0.0281789 | ||||||||
\(937\) | −7.27137 | −0.237545 | −0.118773 | − | 0.992921i | \(-0.537896\pi\) | ||||
−0.118773 | + | 0.992921i | \(0.537896\pi\) | |||||||
\(938\) | 3.32116 | 0.108440 | ||||||||
\(939\) | 41.5815 | 1.35696 | ||||||||
\(940\) | −0.901666 | −0.0294091 | ||||||||
\(941\) | 35.3320 | 1.15179 | 0.575895 | − | 0.817524i | \(-0.304654\pi\) | ||||
0.575895 | + | 0.817524i | \(0.304654\pi\) | |||||||
\(942\) | −15.5851 | −0.507790 | ||||||||
\(943\) | 26.0126 | 0.847087 | ||||||||
\(944\) | −1.26062 | −0.0410296 | ||||||||
\(945\) | 0.820252 | 0.0266828 | ||||||||
\(946\) | 22.9756 | 0.747001 | ||||||||
\(947\) | 3.37705 | 0.109739 | 0.0548696 | − | 0.998494i | \(-0.482526\pi\) | ||||
0.0548696 | + | 0.998494i | \(0.482526\pi\) | |||||||
\(948\) | −17.4127 | −0.565538 | ||||||||
\(949\) | −24.4339 | −0.793157 | ||||||||
\(950\) | 0.251759 | 0.00816814 | ||||||||
\(951\) | 37.8432 | 1.22715 | ||||||||
\(952\) | 2.61353 | 0.0847049 | ||||||||
\(953\) | 43.6879 | 1.41519 | 0.707595 | − | 0.706618i | \(-0.249780\pi\) | ||||
0.707595 | + | 0.706618i | \(0.249780\pi\) | |||||||
\(954\) | −0.610490 | −0.0197653 | ||||||||
\(955\) | −8.09632 | −0.261991 | ||||||||
\(956\) | 23.7583 | 0.768400 | ||||||||
\(957\) | 22.1782 | 0.716918 | ||||||||
\(958\) | −6.16146 | −0.199068 | ||||||||
\(959\) | 0.473939 | 0.0153043 | ||||||||
\(960\) | −0.597250 | −0.0192762 | ||||||||
\(961\) | −30.5022 | −0.983943 | ||||||||
\(962\) | −19.3743 | −0.624654 | ||||||||
\(963\) | −0.160556 | −0.00517386 | ||||||||
\(964\) | 7.40717 | 0.238569 | ||||||||
\(965\) | −6.43390 | −0.207115 | ||||||||
\(966\) | 2.19853 | 0.0707365 | ||||||||
\(967\) | 14.6782 | 0.472020 | 0.236010 | − | 0.971751i | \(-0.424160\pi\) | ||||
0.236010 | + | 0.971751i | \(0.424160\pi\) | |||||||
\(968\) | −2.52293 | −0.0810901 | ||||||||
\(969\) | 0.542916 | 0.0174410 | ||||||||
\(970\) | −3.51448 | −0.112843 | ||||||||
\(971\) | 31.9087 | 1.02400 | 0.512000 | − | 0.858985i | \(-0.328905\pi\) | ||||
0.512000 | + | 0.858985i | \(0.328905\pi\) | |||||||
\(972\) | −4.60594 | −0.147736 | ||||||||
\(973\) | 4.05727 | 0.130070 | ||||||||
\(974\) | 7.85545 | 0.251705 | ||||||||
\(975\) | 14.9727 | 0.479510 | ||||||||
\(976\) | −9.91540 | −0.317384 | ||||||||
\(977\) | 11.7237 | 0.375075 | 0.187538 | − | 0.982257i | \(-0.439949\pi\) | ||||
0.187538 | + | 0.982257i | \(0.439949\pi\) | |||||||
\(978\) | 12.8842 | 0.411992 | ||||||||
\(979\) | 50.5690 | 1.61619 | ||||||||
\(980\) | −2.55728 | −0.0816895 | ||||||||
\(981\) | −1.74649 | −0.0557612 | ||||||||
\(982\) | 23.6342 | 0.754199 | ||||||||
\(983\) | −55.6677 | −1.77552 | −0.887762 | − | 0.460303i | \(-0.847741\pi\) | ||||
−0.887762 | + | 0.460303i | \(0.847741\pi\) | |||||||
\(984\) | 12.0341 | 0.383632 | ||||||||
\(985\) | −1.45066 | −0.0462219 | ||||||||
\(986\) | −24.7611 | −0.788555 | ||||||||
\(987\) | 1.53550 | 0.0488755 | ||||||||
\(988\) | 0.0998734 | 0.00317740 | ||||||||
\(989\) | −21.5783 | −0.686150 | ||||||||
\(990\) | 0.614632 | 0.0195343 | ||||||||
\(991\) | 5.98304 | 0.190058 | 0.0950288 | − | 0.995475i | \(-0.469706\pi\) | ||||
0.0950288 | + | 0.995475i | \(0.469706\pi\) | |||||||
\(992\) | −0.705533 | −0.0224007 | ||||||||
\(993\) | −40.9512 | −1.29955 | ||||||||
\(994\) | −1.24328 | −0.0394345 | ||||||||
\(995\) | 2.92262 | 0.0926532 | ||||||||
\(996\) | 14.0788 | 0.446102 | ||||||||
\(997\) | 17.5408 | 0.555523 | 0.277762 | − | 0.960650i | \(-0.410407\pi\) | ||||
0.277762 | + | 0.960650i | \(0.410407\pi\) | |||||||
\(998\) | 8.48110 | 0.268465 | ||||||||
\(999\) | 55.3444 | 1.75102 |
(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 | 6002.2.a.b.1.19 | ✓ | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6002.2.a.b.1.19 | ✓ | 56 | 1.1 | even | 1 | trivial |